Fix missing import in finiterectlat-scatter.py

Stupid typo with possibly serious consequences...

.drone.yml

@@ -0,0 +1,83 @@
+---
+kind: pipeline
+type: docker
+name: buildqpms-alpine-preinstlibs
+
+workspace:
+  path: /home/qpmsbuild/qpms
+
+# don't run in master until the python/lapacke linking problem is resolved
+trigger:
+  branch:
+    exclude: 
+      - master
+
+steps:
+- name: chown
+  image: qpms/buildenv/alpine/pkgdnumlib
+  pull: never
+  commands:
+    - chown -R qpmsbuild.qpmsbuild .
+- name: submodules
+  image: qpms/buildenv/alpine/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+    - git submodule init
+    - git submodule update
+- name: build
+  image: qpms/buildenv/alpine/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+  - cmake -DCMAKE_INSTALL_PREFIX=$HOME/.local .
+  - make install
+  - export LIBRARY_PATH=$HOME/.local/lib
+  - python3 setup.py install --user
+  - cd examples/rectangular/modes
+  - pip3 install --user matplotlib #needed to run the example
+  - export LD_LIBRARY_PATH=$HOME/.local/lib
+  - ./01a_realfreq_svd.sh
+
+---
+kind: pipeline
+type: docker
+name: buildqpms-debian-preinstlibs
+
+workspace:
+  path: /home/qpmsbuild/qpms
+
+steps:
+- name: chown
+  image: qpms/buildenv/debian/pkgdnumlib
+  pull: never
+  commands:
+    - chown -R qpmsbuild.qpmsbuild .
+- name: submodules
+  image: qpms/buildenv/debian/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+    - git submodule init
+    - git submodule update
+- name: build
+  image: qpms/buildenv/debian/pkgdnumlib
+  pull: never
+  user: qpmsbuild
+  commands:
+  - cmake -DCMAKE_INSTALL_PREFIX=/home/qpmsbuild/.local .
+  - make install
+  - export LIBRARY_PATH=$HOME/.local/lib
+  - python3 setup.py install --user
+  - pip3 install --user matplotlib #needed to run the examples
+  - export LD_LIBRARY_PATH=$HOME/.local/lib
+  - cd examples/rectangular/modes
+  - ./01a_realfreq_svd.sh
+  - cd -
+  - cd examples/hexagonal/modes
+  #- ./01a_realfreq_svd.sh 
+  #- ./01_compute_modes.sh 
+  #- ./02b_compute_disp_0M.sh 
+  #- ./02_compute_disp.sh 
+  #- ./02x_compute_disp.sh
+

.gitignore

@@ -5,4 +5,29 @@
 *.pdf
 *.o
 docs/*
+
 qpms/qpms_c.c
+qpms/cy*.c
+CMakeCache.txt
+CMakeFiles/*
+faddeeva/*
+qpms/CMakeFiles/*
+qpms/libqpms.so
+qpms/cmake_install.cmake
+qpms_version.c
+qpms.egg_info/*
+dist/*
+build/*
+Makefile
+CTestTestfile.cmake
+
+amos/CMakeFiles/*
+amos/Makefile
+amos/amos_mangling.h
+cmake_install.cmake
+cython_debug/*
+qpms.egg-info/*
+tests/CmakeFiles/*
+tests/cmake_install.cmake
+tests/CMakeFiles/*
+

.gitmodules

@@ -0,0 +1,4 @@
+[submodule "camos"]
+	path = camos
+	url = https://codeberg.org/QPMS/zbessel.git
+	branch = purec

CLIUTILS.md

@@ -0,0 +1,43 @@
+Overview of QPMS command line utilities
+=======================================
+
+The utilities are located in the `misc` directory. Run the
+utility with `-h` argument to get more info.
+
+
+Rectangular and square 2D lattices
+----------------------------------
+
+These scripts deal with simple 2D rectangular lattices,
+finite or infinite, one scatterer per unit cell. 
+\f$ D_{2h} \f$ or \f$ D_{4h} \f$ symmetric adapted bases
+are used where applicable.
+
+### Finite lattices
+
+ * `finiterectlat-modes.py`:  Search for resonances using Beyn's algorithm.
+ * `finiterectlat-scatter.py`:  Plane wave scattering.
+ * `finiterectlat-constant-driving.py`: Rectangular array response to
+   a driving where a subset of particles are excited by basis VSWFs with the
+   same phase.
+
+### Infinite lattices
+
+ * `rectlat_simple_modes.py`: Search for lattice modes using Beyn's algorithm.
+ * `infiniterectlat-k0realfreqsvd.py`: 
+    Evaluate the lattice mode problem singular values at the Γ point for a real frequency interval.
+    Useful as a starting point in lattice mode search before using Beyn's algorithm.
+ * `infiniterectlat-scatter.py`: Plane wave scattering.
+
+
+General 2D lattices
+-------------------
+
+### Infinite lattices
+
+These can contain several scatterers per unit cell. Symmetry adapted bases currently not implemented.
+
+ * `lat2d_modes.py`: Search for lattice modes using Beyn's algorithm.
+ * `lat2d_realfreqsvd.py`: 
+    Evaluate the lattice mode problem singular values at the Γ point for a real frequency interval.
+    Useful as a starting point in lattice mode search before using Beyn's algorithm.

CMakeLists.txt

@@ -1,11 +1,16 @@
 cmake_minimum_required(VERSION 3.0.2)
+
+option(QPMS_USE_FORTRAN_AMOS "Use the original AMOS Fortran libraries instead of the C ones" OFF)
+
+if (QPMS_USE_FORTRAN_AMOS)
 include(CMakeAddFortranSubdirectory)
+endif (QPMS_USE_FORTRAN_AMOS)
 include(version.cmake)
 include(GNUInstallDirs)
 
 project (QPMS)
 
-set(CMAKE_BUILD_TYPE Debug)
+list(APPEND CMAKE_MODULE_PATH "${CMAKE_CURRENT_SOURCE_DIR}/cmake/")
 
 macro(use_c99)
   if (CMAKE_VERSION VERSION_LESS "3.1")
@@ -24,10 +29,23 @@ set(CMAKE_POSITION_INDEPENDENT_CODE ON)
 
 set (QPMS_VERSION_MAJOR 0)
 #set (QPMS_VERSION_MINOR 3)
-cmake_add_fortran_subdirectory (amos
-	PROJECT amos
-	LIBRARIES amos
-	NO_EXTERNAL_INSTALL)
+
+if (QPMS_USE_FORTRAN_AMOS)
+	cmake_add_fortran_subdirectory (amos
+		PROJECT amos
+		LIBRARIES amos
+		NO_EXTERNAL_INSTALL)
+	set(QPMS_AMOSLIB amos)
+else (QPMS_USE_FORTRAN_AMOS)
+	set(CAMOS_BUILD_STATIC ON)
+	add_subdirectory (camos)
+	set(QPMS_AMOSLIB camos)
+endif (QPMS_USE_FORTRAN_AMOS)
+
+
+set(FADDEEVA_BUILD_STATIC ON)
+add_subdirectory(faddeeva)
+
 add_subdirectory (qpms)
 
 

COPYING.md

@@ -0,0 +1,675 @@
+### GNU GENERAL PUBLIC LICENSE
+
+Version 3, 29 June 2007
+
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+<https://fsf.org/>
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+
+You may not impose any further restrictions on the exercise of the
+rights granted or affirmed under this License. For example, you may
+not impose a license fee, royalty, or other charge for exercise of
+rights granted under this License, and you may not initiate litigation
+(including a cross-claim or counterclaim in a lawsuit) alleging that
+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+#### 11. Patents.
+
+A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based. The
+work thus licensed is called the contributor's "contributor version".
+
+A contributor's "essential patent claims" are all patent claims owned
+or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
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+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version. For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
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+
+Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
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+propagate the contents of its contributor version.
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+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement). To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
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+If you convey a covered work, knowingly relying on a patent license,
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+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients. "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+A patent license is "discriminatory" if it does not include within the
+scope of its coverage, prohibits the exercise of, or is conditioned on
+the non-exercise of one or more of the rights that are specifically
+granted under this License. You may not convey a covered work if you
+are a party to an arrangement with a third party that is in the
+business of distributing software, under which you make payment to the
+third party based on the extent of your activity of conveying the
+work, and under which the third party grants, to any of the parties
+who would receive the covered work from you, a discriminatory patent
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+connection with specific products or compilations that contain the
+covered work, unless you entered into that arrangement, or that patent
+license was granted, prior to 28 March 2007.
+
+Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+#### 12. No Surrender of Others' Freedom.
+
+If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License. If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under
+this License and any other pertinent obligations, then as a
+consequence you may not convey it at all. For example, if you agree to
+terms that obligate you to collect a royalty for further conveying
+from those to whom you convey the Program, the only way you could
+satisfy both those terms and this License would be to refrain entirely
+from conveying the Program.
+
+#### 13. Use with the GNU Affero General Public License.
+
+Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
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+but the special requirements of the GNU Affero General Public License,
+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+#### 14. Revised Versions of this License.
+
+The Free Software Foundation may publish revised and/or new versions
+of the GNU General Public License from time to time. Such new versions
+will be similar in spirit to the present version, but may differ in
+detail to address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies that a certain numbered version of the GNU General Public
+License "or any later version" applies to it, you have the option of
+following the terms and conditions either of that numbered version or
+of any later version published by the Free Software Foundation. If the
+Program does not specify a version number of the GNU General Public
+License, you may choose any version ever published by the Free
+Software Foundation.
+
+If the Program specifies that a proxy can decide which future versions
+of the GNU General Public License can be used, that proxy's public
+statement of acceptance of a version permanently authorizes you to
+choose that version for the Program.
+
+Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+#### 15. Disclaimer of Warranty.
+
+THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT
+WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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+PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE
+DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR
+CORRECTION.
+
+#### 16. Limitation of Liability.
+
+IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR
+CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES
+ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT
+NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR
+LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM
+TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER
+PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
+
+#### 17. Interpretation of Sections 15 and 16.
+
+If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+END OF TERMS AND CONDITIONS
+
+### How to Apply These Terms to Your New Programs
+
+If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these
+terms.
+
+To do so, attach the following notices to the program. It is safest to
+attach them to the start of each source file to most effectively state
+the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+        <one line to give the program's name and a brief idea of what it does.>
+        Copyright (C) <year>  <name of author>
+
+        This program is free software: you can redistribute it and/or modify
+        it under the terms of the GNU General Public License as published by
+        the Free Software Foundation, either version 3 of the License, or
+        (at your option) any later version.
+
+        This program is distributed in the hope that it will be useful,
+        but WITHOUT ANY WARRANTY; without even the implied warranty of
+        MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+        GNU General Public License for more details.
+
+        You should have received a copy of the GNU General Public License
+        along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper
+mail.
+
+If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+        <program>  Copyright (C) <year>  <name of author>
+        This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+        This is free software, and you are welcome to redistribute it
+        under certain conditions; type `show c' for details.
+
+The hypothetical commands \`show w' and \`show c' should show the
+appropriate parts of the General Public License. Of course, your
+program's commands might be different; for a GUI interface, you would
+use an "about box".
+
+You should also get your employer (if you work as a programmer) or
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. For more information on this, and how to apply and follow
+the GNU GPL, see <https://www.gnu.org/licenses/>.
+
+The GNU General Public License does not permit incorporating your
+program into proprietary programs. If your program is a subroutine
+library, you may consider it more useful to permit linking proprietary
+applications with the library. If this is what you want to do, use the
+GNU Lesser General Public License instead of this License. But first,
+please read <https://www.gnu.org/licenses/why-not-lgpl.html>.

Doxyfile

@@ -51,7 +51,7 @@ PROJECT_BRIEF          = "Electromagnetic multiple scattering library and toolki
 # and the maximum width should not exceed 200 pixels. Doxygen will copy the logo
 # to the output directory.
 
-PROJECT_LOGO           =
+PROJECT_LOGO           = farfield.png
 
 # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path
 # into which the generated documentation will be written. If a relative path is
@@ -753,7 +753,7 @@ WARN_LOGFILE           =
 # spaces.
 # Note: If this tag is empty the current directory is searched.
 
-INPUT                  = qpms notes finite_systems.md README.md README.Triton.md finite_systems.md lattices.md TODO.md
+INPUT                  = qpms notes misc finite_systems.md MIRRORS.md CLIUTILS.md README.md README.Triton.md finite_systems.md lattices.md TODO.md
 
 # This tag can be used to specify the character encoding of the source files
 # that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses
@@ -773,7 +773,7 @@ INPUT_ENCODING         = UTF-8
 # *.md, *.mm, *.dox, *.py, *.f90, *.f, *.for, *.tcl, *.vhd, *.vhdl, *.ucf,
 # *.qsf, *.as and *.js.
 
-FILE_PATTERNS          =
+FILE_PATTERNS          = 
 
 # The RECURSIVE tag can be used to specify whether or not subdirectories should
 # be searched for input files as well.
@@ -1462,7 +1462,7 @@ MATHJAX_FORMAT         = HTML-CSS
 # The default value is: http://cdn.mathjax.org/mathjax/latest.
 # This tag requires that the tag USE_MATHJAX is set to YES.
 
-MATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest
+MATHJAX_RELPATH        = https://uslugi.necada.org/js/mathjax
 
 # The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax
 # extension names that should be enabled during MathJax rendering. For example

MIRRORS.md

@@ -0,0 +1,14 @@
+QPMS source code mirrors
+========================
+
+QPMS source code is available at several locations; in all of the following,
+upstream `master` branch is kept up-to-date. Various development branches
+are not necessarily pushed everywhere (and they should be considered
+unstable in the sense that rebases and forced pushes are possible).
+
+mirror                                          | note                    | provider                                          | backend
+----------------------------------------------- | ----------------------- | ------------------------------------------------- | ------
+<https://repo.or.cz/qpms.git>                   | primary public upstream | [repo.or.cz](https://repo.or.cz/)                 | girocco
+<https://codeberg.org/QPMS/qpms>                |                         | [Codeberg](https://codeberg.org)                  | gitea
+<https://git.piraattipuolue.fi/QPMS/qpms.git>   |                         | [Pirate Party Finland](https://piraattipuolue.fi) | gitea
+<https://version.aalto.fi/gitlab/qpms/qpms.git> |                         | [Aalto University](https://aalto.fi)              | gitlab 

README.md

@@ -1,10 +1,14 @@
+[![Build Status](https://drone.perkele.eu/api/badges/QPMS/qpms/status.svg)](https://drone.perkele.eu/QPMS/qpms)
+
 QPMS README
 ===========
 
-QPMS is a toolkit for frequency-domain simulations of photonic systems
+[QPMS][homepage] (standing for QPMS Photonic Multiple Scattering) 
+is a toolkit for frequency-domain simulations of photonic systems
 consisting of compact objects (particles) inside a homogeneous medium. Scattering
 properties of the individual particles are described by their T-matrices
-(which can be obtained e.g. with the `scuff-tmatrix` tool from 
+(which can be obtained using one of the built-in generators or
+ e.g. with the `scuff-tmatrix` tool from 
 the [SCUFF-EM] suite).
 
 QPMS handles the multiple scattering of electromagnetic radiation between 
@@ -12,26 +16,39 @@ the particles. The system can consist either of a finite number of particles
 or an infinite number of periodically arranged lattices (with finite number
 of particles in a single unit cell).
 
+
 Features
 ========
 
+
 Finite systems
 --------------
- * Computing multipole excitations *and fields (TODO)* scattered from nanoparticle
+ * Computing multipole excitations and fields scattered from nanoparticle
    clusters illuminated by plane, spherical or *cylindrical (TODO)* waves.
- * Finding eigenmodes.
- * *Calculating cross sections (TODO).*
+ * Finding eigenmodes (optical resonances).
+ * Calculating cross sections.
  * Reducing numerical complexity of the computations by exploiting
    symmetries of the cluster (decomposition to irreducible representations).
 
+
 Infinite systems (lattices)
 ---------------------------
- * 2D-periodic systems supported. (TODO 1D and 3D.)
- * *Calculation of transmission and reflection properties (TODO).*
+ * 2D-periodic systems with arbitrary unit cell geometry supported. (TODO 1D and 3D.)
+ * Computing multipole excitations and fields scattered from nanoparticle
  * Finding eigenmodes and calculating dispersion relations.
- * *Calculation of far-field radiation patterns of an excited array (TODO).*
- * Reducing numerical complexity of the computations by exploiting
-   symmetries of the lattice (decomposition to irreducible representations).
+ * Calculation of the scattered fields.
+ * *Calculation of total transmission and reflection properties (TODO).*
+ * *Reducing numerical complexity of the computations by exploiting
+   symmetries of the lattice (decomposition to irreducible representations) (in development).* 
+
+
+Getting the code
+================
+
+The codebase is available at the main upstream public repository
+<https://repo.or.cz/qpms.git> or any of the [maintained mirrors][MIRRORS].
+Just clone the repository with `git` and proceed to the installation instructions
+below.
 
 
 Installation
@@ -47,7 +64,16 @@ you can [get the source and compile it yourself][GSL].
 
 You also need a fresh enough version of [cmake][].
 
-After GSL is installed, you can install qpms to your local python library using
+QPMS uses a C version of the Amos library for calculating Bessel function
+from a submodule. Before proceeding with running `cmake`, the submodules
+need to be downloaded first (in the QPMS source root directory):
+
+```{.sh}
+  git submodule init
+  git submodule update
+```
+
+After GSL is installed and submodules updated, you can install qpms to your local python library using
 
 ```{.sh}
   cmake -DCMAKE_INSTALL_PREFIX=${YOUR_PREFIX} .
@@ -66,13 +92,21 @@ Special care might need to be taken when installing QPMS in cluster environments
 Specific installation instructions for Aalto University's Triton cluster
 can be found in a [separate document][TRITON-README].
 
+Instructions for installation on Android-based devices are
+in [another document][INSTALL-ANDROID].
+
+
 Documentation
 =============
 
-Documentation of QPMS is a work in progress. Most of the newer code
-is documented using [doxygen][] comments. To build the documentation, just run
+[QPMS documentation][homepage] is a work in progress. Most of the newer code
+is documented using [doxygen][] comments. Documentation generated for the
+upstream version is hosted on the QPMS homepage <https://qpms.necada.org>.
+
+To build the documentation yourself, 
+just run
 `doxygen`
-in the root directory; the documentation will then be found in 
+in the QPMS source root directory; the documentation will then be found in 
 `docs/html/index.html`.
 
 Of course, the prerequisite of this is having doxygen installed.
@@ -84,14 +118,77 @@ under root.
 Tutorials
 ---------
 
-  * [Infinite system (lattice) tutorial][tutorial-infinite]
   * [Finite system tutorial][tutorial-finite]
 
+See also the examples directory in the source repository.
+
+
+Command line utilities
+----------------------
+
+  * [Overview of the Python command line utilities][cliutils]
+
+
+Acknowledgments
+================
+
+This software has been developed in the [Quantum Dynamics research group][QD],
+Aalto University, Finland. If you use the code in your work, please cite 
+**M. Nečada and P. Törmä, Multiple-scattering T-matrix simulations for nanophotonics: symmetries and periodic lattices, [arXiv: 2006.12968][lepaper] (2020)**
+in your publications, presentations, and similar. 
+
+Please also have a look at other publications by the group 
+(google scholar Päivi Törmä), they may be useful for your work as well. 
+
+
+Bug reports
+===========
+
+If you believe that some parts of QPMS behave incorrectly, please mail
+a bug report to [marek@necada.org][authormail]. To ensure that your message is not
+considered spam, please start the subject line with `QPMS`.
+
+If you were able to fix a bug yourself, please include the patch as well,
+see below.
+
+
+Contributions
+=============
+
+Contributions to QPMS are welcome, be it bug fixes, improvements to the
+documentation, code quality, or new features.
+
+You can send patches prepared using the 
+[`git format-patch`](https://git-scm.com/docs/git-format-patch) tool
+to [marek@necada.org][authormail].
+
+If you plan to contribute with major changes to the codebase, it is 
+recommended to discuss that first (see the contact information below).
+
+
+Contact & discussion
+====================
+
+You can contact the main author e.g. via [e-mail][authormail]
+or [Telegram](https://t.me/necadam).
+
+You are also warmly welcome to the [QPMS user chat][telegramchat]
+in Telegram!
+
+
+[homepage]: https://qpms.necada.org
 [SCUFF-EM]: https://homerreid.github.io/scuff-em-documentation/
 [OpenBLAS]: https://www.openblas.net/
 [GSL]: https://www.gnu.org/software/gsl/
 [cmake]: https://cmake.org
 [TRITON-README]: README.Triton.md
+[INSTALL-ANDROID]: notes/INSTALL_ANDROID.md
 [tutorial-finite]: finite_systems.md
 [tutorial-infinite]: lattices.md
 [doxygen]: http://doxygen.nl/
+[QD]: https://www.aalto.fi/en/department-of-applied-physics/quantum-dynamics-qd
+[lepaper]: https://arxiv.org/abs/2006.12968
+[telegramchat]: https://t.me/QPMScattering
+[authormail]: mailto:marek@necada.org
+[cliutils]: CLIUTILS.md
+[MIRRORS]: MIRRORS.md

TODO.md

@@ -1,11 +1,12 @@
-TODO list before public release
-===============================
+TODO list before 1.0 release
+============================
 
 - Tests!
 - Docs!
-- Cross section calculations.
-- Field calculations.
-- Complex frequencies, n's, k's.
+- Cross section calculations. (Done in some Python scripts.)
+- Field calculations. (Partly done, needs more testing.)
+  * Also test periodic vs. nonperiodic consistence (big finite lattice + absorbing medium vs. infinite lattice + absorbing medium).
+- Complex frequencies, n's, k's. (Mostly done.)
 - Transforming point (meta)generators.
 - Check whether moble's quaternions and my 
   quaternions give the same results in tmatrices.py
@@ -24,11 +25,12 @@ TODO list before public release
   * As a description of a T-matrix / particle metadata.
 - Nice CLI for all general enough utilities.
 - Remove legacy code.
-- Split qpms_c.pyx.
+- Split `qpms_c.pyx`.
 - Reduce compiler warnings.
+- Serialisation (saving, loading) of `ScatteringSystem` and other structures.
 - Python exceptions instead of hard crashes in the C library where possible.
 - Scatsystem init sometimes fail due to rounding errors and hardcoded absolute tolerance 
-  in the qpms_tmatrix_isclose() call.
+  in the `qpms_tmatrix_isclose()` call.
 - Prefix all identifiers. Maybe think about a different prefix than qpms?
 - Consistent indentation and style overall.
 - Rewrite the parallelized translation matrix, mode problem matrix generators
@@ -39,3 +41,16 @@ Nice but less important features
 
 - Static, thread-safe caches of constant coefficients + API without the current "calculators".
 
+
+Optimisations
+-------------
+
+- Leaving out the irrelevant elements if a "rectangular" block of the translations matrix is needed.
+- Ewald sums with "non-parallel" shifts (are about 20 times slower than the purely parallel ones).
+- Reusing intermediate results (profiling needed)
+  * Bessel, Legendre functions (see also branch `finite_lattice_speedup`)
+  * Lattice points (sorting and scaling)
+  * Γ/Δ functions (for periodic lattices)
+- More parallelisation.
+- Possibly pre-calculation of the (precise) coefficients in Bessel and Legendre functions (using gmp)
+- Asymptotic approximations of the Bessel functions for far fields.

amos/camos.h

@@ -0,0 +1,30 @@
+#ifndef CAMOS_H_
+#define CAMOS_H_
+#include "amos.h"
+
+// TODO what about all the INTEGER_t and DOUBLE_PRECISION_t?
+
+static inline int camos_zbesh(double zr, double zi, double fnu, int kode, int m,
+          int n, double *cyr, double *cyi, int *nz) {
+	int ierr;
+	amos_zbesh(&zr, &zi, &fnu, &kode, &m, &n, cyr, cyi, nz, &ierr);
+	return ierr;
+}
+
+static inline int camos_zbesj(double zr, double zi, double fnu, int kode, int n, double *cyr,
+          double *cyi, int *nz) {
+	int ierr;
+	double cwrkr[n], cwrki[n];
+	amos_zbesj(&zr, &zi, &fnu, &kode, &n, cyr, cyi, nz, &ierr);
+	return ierr;
+}
+
+static inline int camos_zbesy(double zr, double zi, double fnu, int kode, int n, double *cyr,
+          double *cyi, int *nz, double *cwrkr, double *cwrki) {
+	int ierr;
+	amos_zbesy(&zr, &zi, &fnu, &kode, &n, cyr, cyi, nz, cwrkr, cwrki, &ierr);
+	return ierr;
+}
+
+
+#endif // CAMOS_H_

camos

@@ -0,0 +1 @@
+Subproject commit 19e7ae82e7e0b436bd273557a87d288f8f338221

ci/00_make_dockerfiles.sh

@@ -0,0 +1,7 @@
+#!/bin/sh
+DP=Dockerfile_parts
+# "Build environment" Dockerfiles
+cat >Dockerfile.benv.debian.bnl ${DP}/00_common.debian ${DP}/01_numlibs.built
+cat >Dockerfile.benv.debian.pnl ${DP}/00_common.debian ${DP}/01_numlibs.debian.pkgd
+cat >Dockerfile.benv.alpine.bnl ${DP}/00_common.alpine ${DP}/01_numlibs.built
+cat >Dockerfile.benv.alpine.pnl ${DP}/00_common.alpine ${DP}/01_numlibs.alpine.pkgd

ci/01_make_buildenv_images.sh

@@ -0,0 +1,5 @@
+#!/bin/sh
+docker build -t qpms/buildenv/debian/builtnumlib -f Dockerfile.benv.debian.bnl .
+docker build -t qpms/buildenv/debian/pkgdnumlib -f Dockerfile.benv.debian.pnl .
+docker build -t qpms/buildenv/alpine/builtnumlib -f Dockerfile.benv.alpine.bnl .
+docker build -t qpms/buildenv/alpine/pkgdnumlib -f Dockerfile.benv.alpine.pnl .

ci/Dockerfile_parts/00_common.alpine

@@ -0,0 +1,5 @@
+FROM alpine:latest AS commondeps
+RUN apk update \
+ && apk add cmake python3-dev py3-pip gcc g++ wget git make libc-dev bc \
+ && adduser -D qpmsbuild
+

ci/Dockerfile_parts/00_common.debian

@@ -0,0 +1,6 @@
+FROM debian:stable AS commondeps
+RUN apt-get update \
+ && apt-get -y install --no-install-recommends build-essential cmake python3 python3-pip git wget python3-dev bc \
+ && apt-get clean \
+ && useradd -m qpmsbuild
+

ci/Dockerfile_parts/01_numlibs.alpine.pkgd

@@ -0,0 +1,3 @@
+FROM commondeps AS numlibs
+# openblas-dev adds gfortran :(
+RUN apk add openblas-dev gsl-dev

ci/Dockerfile_parts/01_numlibs.built

@@ -0,0 +1,16 @@
+FROM commondeps AS buildopenblas
+USER qpmsbuild
+RUN cd && git clone --depth 1 https://github.com/xianyi/OpenBLAS.git \
+ && cd OpenBLAS && make \
+ && make install PREFIX=$HOME/.local/ \
+ && make clean \
+ && cd .. && rm -rf OpenBLAS
+
+FROM buildopenblas AS numlibs
+USER qpmsbuild
+RUN cd && wget https://ftp.gnu.org/gnu/gsl/gsl-latest.tar.gz \
+ && tar xf gsl-latest.tar.gz \
+ && cd $( tar tf gsl-latest.tar.gz | head -n 1 ) \
+ && ./configure --prefix=$HOME/.local \
+ && make && make install && make clean \
+ && cd .. && rm -rf $OLDPWD gsl-latest.tar.gz

ci/Dockerfile_parts/01_numlibs.debian.pkgd

@@ -0,0 +1,4 @@
+FROM commondeps AS numlibs
+RUN apt-get -y install --no-install-recommends libopenblas-dev libgsl-dev liblapacke-dev \
+ && apt-get clean
+

ci/Dockerfile_parts/02_buildqpms

@@ -0,0 +1,12 @@
+FROM numlibs AS buildqpms
+USER qpmsbuild
+ENV LD_LIBRARY_PATH /home/qpmsbuild/.local/lib
+ENV LIBRARY_PATH /home/qpmsbuild/.local/lib
+ENV C_INCLUDE_PATH /home/qpmsbuild/.local/include
+RUN cd && git clone --depth 1 https://repo.or.cz/qpms.git \
+ && cd qpms && git submodule init && git submodule update 
+RUN cd ~/qpms && cmake -DCMAKE_INSTALL_PREFIX=$HOME/.local . \
+ && make \
+ && make install
+RUN cd ~/qpms && python3 setup.py install --user
+

ci/drone.yml

@@ -0,0 +1 @@
+../.drone.yml

cmake/GetGitRevisionDescription.cmake

@@ -0,0 +1,284 @@
+# - Returns a version string from Git
+#
+# These functions force a re-configure on each git commit so that you can
+# trust the values of the variables in your build system.
+#
+#  get_git_head_revision(<refspecvar> <hashvar> [ALLOW_LOOKING_ABOVE_CMAKE_SOURCE_DIR])
+#
+# Returns the refspec and sha hash of the current head revision
+#
+#  git_describe(<var> [<additional arguments to git describe> ...])
+#
+# Returns the results of git describe on the source tree, and adjusting
+# the output so that it tests false if an error occurs.
+#
+#  git_describe_working_tree(<var> [<additional arguments to git describe> ...])
+#
+# Returns the results of git describe on the working tree (--dirty option),
+# and adjusting the output so that it tests false if an error occurs.
+#
+#  git_get_exact_tag(<var> [<additional arguments to git describe> ...])
+#
+# Returns the results of git describe --exact-match on the source tree,
+# and adjusting the output so that it tests false if there was no exact
+# matching tag.
+#
+#  git_local_changes(<var>)
+#
+# Returns either "CLEAN" or "DIRTY" with respect to uncommitted changes.
+# Uses the return code of "git diff-index --quiet HEAD --".
+# Does not regard untracked files.
+#
+# Requires CMake 2.6 or newer (uses the 'function' command)
+#
+# Original Author:
+# 2009-2020 Ryan Pavlik <ryan.pavlik@gmail.com> <abiryan@ryand.net>
+# http://academic.cleardefinition.com
+#
+# Copyright 2009-2013, Iowa State University.
+# Copyright 2013-2020, Ryan Pavlik
+# Copyright 2013-2020, Contributors
+# SPDX-License-Identifier: BSL-1.0
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+if(__get_git_revision_description)
+    return()
+endif()
+set(__get_git_revision_description YES)
+
+# We must run the following at "include" time, not at function call time,
+# to find the path to this module rather than the path to a calling list file
+get_filename_component(_gitdescmoddir ${CMAKE_CURRENT_LIST_FILE} PATH)
+
+# Function _git_find_closest_git_dir finds the next closest .git directory
+# that is part of any directory in the path defined by _start_dir.
+# The result is returned in the parent scope variable whose name is passed
+# as variable _git_dir_var. If no .git directory can be found, the
+# function returns an empty string via _git_dir_var.
+#
+# Example: Given a path C:/bla/foo/bar and assuming C:/bla/.git exists and
+# neither foo nor bar contain a file/directory .git. This wil return
+# C:/bla/.git
+#
+function(_git_find_closest_git_dir _start_dir _git_dir_var)
+    set(cur_dir "${_start_dir}")
+    set(git_dir "${_start_dir}/.git")
+    while(NOT EXISTS "${git_dir}")
+        # .git dir not found, search parent directories
+        set(git_previous_parent "${cur_dir}")
+        get_filename_component(cur_dir "${cur_dir}" DIRECTORY)
+        if(cur_dir STREQUAL git_previous_parent)
+            # We have reached the root directory, we are not in git
+            set(${_git_dir_var}
+                ""
+                PARENT_SCOPE)
+            return()
+        endif()
+        set(git_dir "${cur_dir}/.git")
+    endwhile()
+    set(${_git_dir_var}
+        "${git_dir}"
+        PARENT_SCOPE)
+endfunction()
+
+function(get_git_head_revision _refspecvar _hashvar)
+    _git_find_closest_git_dir("${CMAKE_CURRENT_SOURCE_DIR}" GIT_DIR)
+
+    if("${ARGN}" STREQUAL "ALLOW_LOOKING_ABOVE_CMAKE_SOURCE_DIR")
+        set(ALLOW_LOOKING_ABOVE_CMAKE_SOURCE_DIR TRUE)
+    else()
+        set(ALLOW_LOOKING_ABOVE_CMAKE_SOURCE_DIR FALSE)
+    endif()
+    if(NOT "${GIT_DIR}" STREQUAL "")
+        file(RELATIVE_PATH _relative_to_source_dir "${CMAKE_SOURCE_DIR}"
+             "${GIT_DIR}")
+        if("${_relative_to_source_dir}" MATCHES "[.][.]" AND NOT ALLOW_LOOKING_ABOVE_CMAKE_SOURCE_DIR)
+            # We've gone above the CMake root dir.
+            set(GIT_DIR "")
+        endif()
+    endif()
+    if("${GIT_DIR}" STREQUAL "")
+        set(${_refspecvar}
+            "GITDIR-NOTFOUND"
+            PARENT_SCOPE)
+        set(${_hashvar}
+            "GITDIR-NOTFOUND"
+            PARENT_SCOPE)
+        return()
+    endif()
+
+    # Check if the current source dir is a git submodule or a worktree.
+    # In both cases .git is a file instead of a directory.
+    #
+    if(NOT IS_DIRECTORY ${GIT_DIR})
+        # The following git command will return a non empty string that
+        # points to the super project working tree if the current
+        # source dir is inside a git submodule.
+        # Otherwise the command will return an empty string.
+        #
+        execute_process(
+            COMMAND "${GIT_EXECUTABLE}" rev-parse
+                    --show-superproject-working-tree
+            WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
+            OUTPUT_VARIABLE out
+            ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE)
+        if(NOT "${out}" STREQUAL "")
+            # If out is empty, GIT_DIR/CMAKE_CURRENT_SOURCE_DIR is in a submodule
+            file(READ ${GIT_DIR} submodule)
+            string(REGEX REPLACE "gitdir: (.*)$" "\\1" GIT_DIR_RELATIVE
+                                 ${submodule})
+            string(STRIP ${GIT_DIR_RELATIVE} GIT_DIR_RELATIVE)
+            get_filename_component(SUBMODULE_DIR ${GIT_DIR} PATH)
+            get_filename_component(GIT_DIR ${SUBMODULE_DIR}/${GIT_DIR_RELATIVE}
+                                   ABSOLUTE)
+            set(HEAD_SOURCE_FILE "${GIT_DIR}/HEAD")
+        else()
+            # GIT_DIR/CMAKE_CURRENT_SOURCE_DIR is in a worktree
+            file(READ ${GIT_DIR} worktree_ref)
+            # The .git directory contains a path to the worktree information directory
+            # inside the parent git repo of the worktree.
+            #
+            string(REGEX REPLACE "gitdir: (.*)$" "\\1" git_worktree_dir
+                                 ${worktree_ref})
+            string(STRIP ${git_worktree_dir} git_worktree_dir)
+            _git_find_closest_git_dir("${git_worktree_dir}" GIT_DIR)
+            set(HEAD_SOURCE_FILE "${git_worktree_dir}/HEAD")
+        endif()
+    else()
+        set(HEAD_SOURCE_FILE "${GIT_DIR}/HEAD")
+    endif()
+    set(GIT_DATA "${CMAKE_CURRENT_BINARY_DIR}/CMakeFiles/git-data")
+    if(NOT EXISTS "${GIT_DATA}")
+        file(MAKE_DIRECTORY "${GIT_DATA}")
+    endif()
+
+    if(NOT EXISTS "${HEAD_SOURCE_FILE}")
+        return()
+    endif()
+    set(HEAD_FILE "${GIT_DATA}/HEAD")
+    configure_file("${HEAD_SOURCE_FILE}" "${HEAD_FILE}" COPYONLY)
+
+    configure_file("${_gitdescmoddir}/GetGitRevisionDescription.cmake.in"
+                   "${GIT_DATA}/grabRef.cmake" @ONLY)
+    include("${GIT_DATA}/grabRef.cmake")
+
+    set(${_refspecvar}
+        "${HEAD_REF}"
+        PARENT_SCOPE)
+    set(${_hashvar}
+        "${HEAD_HASH}"
+        PARENT_SCOPE)
+endfunction()
+
+function(git_describe _var)
+    if(NOT GIT_FOUND)
+        find_package(Git QUIET)
+    endif()
+    get_git_head_revision(refspec hash)
+    if(NOT GIT_FOUND)
+        set(${_var}
+            "GIT-NOTFOUND"
+            PARENT_SCOPE)
+        return()
+    endif()
+    if(NOT hash)
+        set(${_var}
+            "HEAD-HASH-NOTFOUND"
+            PARENT_SCOPE)
+        return()
+    endif()
+
+    # TODO sanitize
+    #if((${ARGN}" MATCHES "&&") OR
+    #	(ARGN MATCHES "||") OR
+    #	(ARGN MATCHES "\\;"))
+    #	message("Please report the following error to the project!")
+    #	message(FATAL_ERROR "Looks like someone's doing something nefarious with git_describe! Passed arguments ${ARGN}")
+    #endif()
+
+    #message(STATUS "Arguments to execute_process: ${ARGN}")
+
+    execute_process(
+        COMMAND "${GIT_EXECUTABLE}" describe --tags --always ${hash} ${ARGN}
+        WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
+        RESULT_VARIABLE res
+        OUTPUT_VARIABLE out
+        ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE)
+    if(NOT res EQUAL 0)
+        set(out "${out}-${res}-NOTFOUND")
+    endif()
+
+    set(${_var}
+        "${out}"
+        PARENT_SCOPE)
+endfunction()
+
+function(git_describe_working_tree _var)
+    if(NOT GIT_FOUND)
+        find_package(Git QUIET)
+    endif()
+    if(NOT GIT_FOUND)
+        set(${_var}
+            "GIT-NOTFOUND"
+            PARENT_SCOPE)
+        return()
+    endif()
+
+    execute_process(
+        COMMAND "${GIT_EXECUTABLE}" describe --dirty ${ARGN}
+        WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
+        RESULT_VARIABLE res
+        OUTPUT_VARIABLE out
+        ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE)
+    if(NOT res EQUAL 0)
+        set(out "${out}-${res}-NOTFOUND")
+    endif()
+
+    set(${_var}
+        "${out}"
+        PARENT_SCOPE)
+endfunction()
+
+function(git_get_exact_tag _var)
+    git_describe(out --exact-match ${ARGN})
+    set(${_var}
+        "${out}"
+        PARENT_SCOPE)
+endfunction()
+
+function(git_local_changes _var)
+    if(NOT GIT_FOUND)
+        find_package(Git QUIET)
+    endif()
+    get_git_head_revision(refspec hash)
+    if(NOT GIT_FOUND)
+        set(${_var}
+            "GIT-NOTFOUND"
+            PARENT_SCOPE)
+        return()
+    endif()
+    if(NOT hash)
+        set(${_var}
+            "HEAD-HASH-NOTFOUND"
+            PARENT_SCOPE)
+        return()
+    endif()
+
+    execute_process(
+        COMMAND "${GIT_EXECUTABLE}" diff-index --quiet HEAD --
+        WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
+        RESULT_VARIABLE res
+        OUTPUT_VARIABLE out
+        ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE)
+    if(res EQUAL 0)
+        set(${_var}
+            "CLEAN"
+            PARENT_SCOPE)
+    else()
+        set(${_var}
+            "DIRTY"
+            PARENT_SCOPE)
+    endif()
+endfunction()

cmake/GetGitRevisionDescription.cmake.in

@@ -0,0 +1,43 @@
+#
+# Internal file for GetGitRevisionDescription.cmake
+#
+# Requires CMake 2.6 or newer (uses the 'function' command)
+#
+# Original Author:
+# 2009-2010 Ryan Pavlik <rpavlik@iastate.edu> <abiryan@ryand.net>
+# http://academic.cleardefinition.com
+# Iowa State University HCI Graduate Program/VRAC
+#
+# Copyright 2009-2012, Iowa State University
+# Copyright 2011-2015, Contributors
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+# SPDX-License-Identifier: BSL-1.0
+
+set(HEAD_HASH)
+
+file(READ "@HEAD_FILE@" HEAD_CONTENTS LIMIT 1024)
+
+string(STRIP "${HEAD_CONTENTS}" HEAD_CONTENTS)
+if(HEAD_CONTENTS MATCHES "ref")
+	# named branch
+	string(REPLACE "ref: " "" HEAD_REF "${HEAD_CONTENTS}")
+	if(EXISTS "@GIT_DIR@/${HEAD_REF}")
+		configure_file("@GIT_DIR@/${HEAD_REF}" "@GIT_DATA@/head-ref" COPYONLY)
+	else()
+		configure_file("@GIT_DIR@/packed-refs" "@GIT_DATA@/packed-refs" COPYONLY)
+		file(READ "@GIT_DATA@/packed-refs" PACKED_REFS)
+		if(${PACKED_REFS} MATCHES "([0-9a-z]*) ${HEAD_REF}")
+			set(HEAD_HASH "${CMAKE_MATCH_1}")
+		endif()
+	endif()
+else()
+	# detached HEAD
+	configure_file("@GIT_DIR@/HEAD" "@GIT_DATA@/head-ref" COPYONLY)
+endif()
+
+if(NOT HEAD_HASH)
+	file(READ "@GIT_DATA@/head-ref" HEAD_HASH LIMIT 1024)
+	string(STRIP "${HEAD_HASH}" HEAD_HASH)
+endif()

cmake/LICENSE_1_0.txt

@@ -0,0 +1,23 @@
+Boost Software License - Version 1.0 - August 17th, 2003
+
+Permission is hereby granted, free of charge, to any person or organization
+obtaining a copy of the software and accompanying documentation covered by
+this license (the "Software") to use, reproduce, display, distribute,
+execute, and transmit the Software, and to prepare derivative works of the
+Software, and to permit third-parties to whom the Software is furnished to
+do so, all subject to the following:
+
+The copyright notices in the Software and this entire statement, including
+the above license grant, this restriction and the following disclaimer,
+must be included in all copies of the Software, in whole or in part, and
+all derivative works of the Software, unless such copies or derivative
+works are solely in the form of machine-executable object code generated by
+a source language processor.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+DEALINGS IN THE SOFTWARE.

examples/api/custom_tmatrix/custom_tmatrices_simple.py

@@ -0,0 +1,36 @@
+#!/usr/bin/env python3
+from qpms import TMatrixGenerator, BaseSpec, eV, hbar
+import numpy as np
+import sys
+
+errors = 0
+
+def tmg_diagonal_fun(tmatrix, omega):
+    '''
+    Example of a python function used as a custom T-matrix generator
+
+    It receives a CTMatrix argument with pre-filled BaseSpec
+    (in tmatrix.spec) and angular frequency.
+
+    It has to fill in the T-matrix elements tmatrix[...] 
+    (a numpy array of shape (len(tmatrix.spec),len(tmatrix.spec)))
+    and return zero (on success) or other integral value on error.
+
+    Note that this in justa an example of using the API,
+    not supposed to be anything physical.
+    '''
+    l = tmatrix.spec.l()
+    tmatrix[...] = np.diag(1./l**2)
+    return 0
+
+# Wrap the function as an actual TMatrixGenerator
+tmg_diagonal = TMatrixGenerator(tmg_diagonal_fun)
+
+bspec = BaseSpec(lMax=2)
+
+tmatrix = tmg_diagonal(bspec, (2.0+.01j) * eV/hbar)
+
+errors += np.sum(tmatrix[...] != np.diag(1./bspec.l()**2))
+
+sys.exit(errors)
+

examples/hexagonal/modes/00_params.sh

@@ -0,0 +1,38 @@
+#!/bin/bash
+echo 'scale=20;pi=3.14159265358979323846;' > bc_env
+export BC_ENV_ARGS="bc_env"
+
+# We put those into bc, which does not understant exponential notation
+SEPARATION_nm=576
+
+# Particle positions within unit cell
+export P1X_nm=0
+export P1Y_nm=$(bc <<< ${SEPARATION_nm}/2)
+export P2X_nm=0
+export P2Y_nm=-$P1Y_nm
+
+# Lattice vectors
+export A1X_nm=$(bc <<< ${SEPARATION_nm}'*sqrt(3)')
+export A1Y_nm=0
+export A2X_nm=$(bc <<< ${SEPARATION_nm}'*sqrt(3)/2')
+export A2Y_nm=$(bc <<< ${SEPARATION_nm}'*3/2')
+
+# Reciprocal lattice vectors
+export B1X_nmi=$(bc <<< '2*pi/sqrt(3)/'${SEPARATION_nm})
+export B1Y_nmi=$(bc <<< '-2*pi/3/'${SEPARATION_nm})
+export B2X_nmi=0
+export B2Y_nmi=$(bc <<< '4*pi/3/'${SEPARATION_nm})
+
+# a K-point coordinates
+export KPOINTX_nmi=$(bc <<< '4*pi/3/sqrt(3)'/${SEPARATION_nm})
+export KPOINTY_nmi=0.0 #$(bc <<< '4*pi/3/sqrt(3)'/${SEPARATION_nm})
+
+# a M-point coordinates
+export MPOINTX_nmi=0.0 
+export MPOINTY_nmi=$(bc <<< '2*pi/3'/${SEPARATION_nm})
+
+
+export RADIUS_nm=50
+export HEIGHT_nm=50
+export METAL=Au
+export BG_REFINDEX=1.52

examples/hexagonal/modes/01_compute_modes.sh

@@ -0,0 +1,18 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s${KPOINTX_nmi}e9 s${KPOINTY_nmi}e9 \
+	-d -3 \
+	-t 0.01 \
+	-c 250 \
+	-P

examples/hexagonal/modes/01a_realfreq_svd.sh

@@ -0,0 +1,16 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+${MISCDIR}/lat2d_realfreqsvd.py \
+       	-B $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s${KPOINTX_nmi}e9 s${KPOINTY_nmi}e9 \
+	-F 1.3 0.001 1.5 \
+	-P

examples/hexagonal/modes/02_compute_disp.sh

@@ -0,0 +1,22 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for bbb in 1 -2 -3 -4 ; do
+  for coeff in $(seq 0.80 0.01 1.50 | sed -e s/,/./g) ; do
+    ${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s$(bc <<< ${KPOINTX_nmi}*${coeff})e9 s$(bc <<< ${KPOINTY_nmi}*${coeff})e9 \
+	-d $bbb \
+	-t 1e13 \
+	-T 0.2 \
+	-c 250 
+  done
+done

examples/hexagonal/modes/02b_compute_disp_0M.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for bbb in 1 -2 -3 -4 ; do
+  for coeff in $(seq 0.00 0.01 1.00 | sed -e s/,/./g) ; do
+    ${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s$(bc <<< ${MPOINTX_nmi}*${coeff})e9 s$(bc <<< ${MPOINTY_nmi}*${coeff})e9 \
+	-d $bbb \
+	-t 1e12 \
+	-T 0.3 \
+	-c 250 \
+	-P
+  done
+done
+

examples/hexagonal/modes/02x_compute_disp.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for bbb in 1 2 ; do
+  for coeff in $(seq 0.80 0.01 2.00 | sed -e s/,/./g) ; do
+    ${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s$(bc <<< ${KPOINTX_nmi}*${coeff})e9 s$(bc <<< ${KPOINTY_nmi}*${coeff})e9 \
+	-d -$bbb \
+	-t 1e12 \
+	-T 0.2 \
+	-c 250 \
+	-P
+  done
+done
+

examples/hexagonal/modes/bc_env

@@ -0,0 +1 @@
+scale=20;pi=3.14159265358979323846;

examples/rectangular/modes/00_params.sh

@@ -0,0 +1,37 @@
+#!/bin/bash
+
+# Common parameters for a rectangular array
+# N.B. We put those into bc, which does not understant exponential notation
+
+export PX_nm=375
+export PY_nm=375
+export RADIUS_nm=30
+export HEIGHT_nm=30
+export METAL=Ag
+export BG_REFINDEX=1.52
+
+
+# Setup bc
+
+echo 'scale=20;pi=3.14159265358979323846;' > bc_env
+export BC_ENV_ARGS="bc_env"
+
+
+# We have only one particle per unit cell here
+export P1X_nm=0
+export P1Y_nm=0
+
+
+# Lattice vectors (for the general scripts)
+export A1X_nm=${PX_nm}
+export A1Y_nm=0
+export A2X_nm=0
+export A2Y_nm=${PY_nm}
+
+# Reciprocal lattice vectors
+export B1X_nmi=$(bc <<< '1/'${PX_nm})
+export B1Y_nmi=0
+export B2X_nmi=0
+export B2Y_nmi=$(bc <<< '1/'${PY_nm})
+
+

examples/rectangular/modes/01_compute_modes.sh

@@ -0,0 +1,18 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s${KPOINTX_nmi}e9 s${KPOINTY_nmi}e9 \
+	-d -3 \
+	-t 0.01 \
+	-c 250 \
+	-P

examples/rectangular/modes/01a_realfreq_svd.sh

@@ -0,0 +1,17 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+# try several lMaxes
+
+${MISCDIR}/lat2d_realfreqsvd.py \
+       	-B $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-L 2 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k 0 0 \
+	-F 2.001 0.001 2.250  \
+	-P

examples/rectangular/modes/01b_realfreq_svd_sym.sh

@@ -0,0 +1,15 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+
+for LMAX in 1 2 3 ; do  # try several cutoffs
+  ${MISCDIR}/infiniterectlat-k0realfreqsvd.py \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L $LMAX -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-F 2.001 0.001 2.250  \
+	-P
+done

examples/rectangular/modes/02_compute_disp.sh

@@ -0,0 +1,22 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for bbb in 1 -2 -3 -4 ; do
+  for coeff in $(seq 0.80 0.01 1.50 | sed -e s/,/./g) ; do
+    ${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s$(bc <<< ${KPOINTX_nmi}*${coeff})e9 s$(bc <<< ${KPOINTY_nmi}*${coeff})e9 \
+	-d $bbb \
+	-t 1e13 \
+	-T 0.2 \
+	-c 250 
+  done
+done

examples/rectangular/modes/02b_compute_disp_0M.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for bbb in 1 -2 -3 -4 ; do
+  for coeff in $(seq 0.00 0.01 1.00 | sed -e s/,/./g) ; do
+    ${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-p s${P2X_nm}e-9 s${P2Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s$(bc <<< ${MPOINTX_nmi}*${coeff})e9 s$(bc <<< ${MPOINTY_nmi}*${coeff})e9 \
+	-d $bbb \
+	-t 1e12 \
+	-T 0.3 \
+	-c 250 \
+	-P
+  done
+done
+

examples/rectangular/modes/02x_compute_disp.sh

@@ -0,0 +1,21 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for bbb in 1 -2 2 -3 ; do
+  for coeff in $(seq -0.200 0.010 0.200 | sed -e s/,/./g) ; do
+    ${MISCDIR}/lat2d_modes.py \
+       	-n $BG_REFINDEX \
+	-b s${A1X_nm}e-9 s${A1Y_nm}e-9 \
+	-b s${A2X_nm}e-9 s${A2Y_nm}e-9 \
+	-p s${P1X_nm}e-9 s${P1Y_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	-k s$(bc <<< ${B1X_nmi}*${coeff})e9 s$(bc <<< ${B1Y_nmi}*${coeff})e9 \
+	-d $bbb \
+	-T 0.2 \
+	-c 250 
+  done
+done
+

examples/rectangular/scattering/00_params.sh

@@ -0,0 +1 @@
+../modes/00_params.sh

examples/rectangular/scattering/01_scattering_infinite.sh

@@ -0,0 +1,19 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in 0 1; do
+  ${MISCDIR}/infiniterectlat-scatter.py \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.015:0.015|201" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-f "s2.110:2.230|100" \
+	-P
+done
+

examples/rectangular/scattering/02_scattering_finite_single.sh

@@ -0,0 +1,19 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in 1; do
+  ${MISCDIR}/finiterectlat-scatter.py \
+	--size 5 5\
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 2 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.05:0.05|101" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-f 2.15
+done
+

examples/rectangular/scattering/02b_scattering_infinite_single.sh

@@ -0,0 +1,19 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in 0 1; do
+  ${MISCDIR}/infiniterectlat-scatter.py \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 2 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.05:0.05|101" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-P \
+	-f 2.15
+done
+

examples/rectangular/scattering/02c_scattering_finite_single_huge.sh

@@ -0,0 +1,25 @@
+#!/bin/bash
+##SBATCH --mem=50000
+##SBATCH -c 12
+##SBATCH -t 14:00:00
+##SBATCH -p batch
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in 0 1; do
+  ${MISCDIR}/finiterectlat-scatter.py \
+	--size 140 100 \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 2 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.05:0.05|101" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-o 140x100.npz -O 140x100.pdf \
+	-P \
+	-f 2.15
+done
+

examples/rectangular/scattering/02d_scattering_finite_single_big.sh

@@ -0,0 +1,25 @@
+#!/bin/bash
+##SBATCH --mem=30000
+##SBATCH -c 12
+##SBATCH -t 14:00:00
+##SBATCH -p batch
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in  1; do
+  ${MISCDIR}/finiterectlat-scatter.py \
+	--size 100 100 \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 2 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.05:0.05|101" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-o 100x100.npz -O 100x100.pdf \
+	-P \
+	-f 2.15
+done
+

examples/rectangular/scattering/02e_scattering_finite_single_huge.sh

@@ -0,0 +1,25 @@
+#!/bin/bash
+##SBATCH --mem=50000
+##SBATCH -c 12
+##SBATCH -t 14:00:00
+##SBATCH -p batch
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in 0 1; do
+  ${MISCDIR}/finiterectlat-scatter.py \
+	--size 140 140 \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 2 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.05:0.05|101" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-o 140x140.npz -O 140x140.pdf \
+	-P \
+	-f 2.15
+done
+

examples/rectangular/scattering/03_scattering_finite.sh

@@ -0,0 +1,21 @@
+#!/bin/bash
+SCRIPTDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
+MISCDIR=../../../misc
+
+source ${SCRIPTDIR}/00_params.sh
+
+for PSI in 1; do
+  ${MISCDIR}/finiterectlat-scatter.py \
+	--size 20 20 \
+       	-B $BG_REFINDEX \
+	-p ${PX_nm}e-9 ${PY_nm}e-9 \
+	-L 3 -m $METAL -r ${RADIUS_nm}e-9 -H ${HEIGHT_nm}e-9 \
+	--theta "s-0.005:0.005|101" \
+	--phi 0 \
+        --psi $PSI \
+	--chi 0	\
+	-P \
+	-f "s2.150:2.180|100" \
+	
+done
+

examples/size_vs_lMax/AuSphere/parallel_generate.sh

@@ -0,0 +1,19 @@
+#!/bin/bash
+#SBATCH --mem=200
+#SBATCH -t 30:00
+#SBATCH -c 4
+#SBATCH -p short-ivb
+#SBATCH --array=0-250
+
+cat $0
+
+contour_points=410
+
+#radii_nm=(`seq 80 1 150`)
+radii_nm=(`seq 50 1 300`)
+radius_nm=${radii_nm[$SLURM_ARRAY_TASK_ID]}
+
+for lMax in $(seq 1 5); do
+  srun rectlat_simple_modes.py -p 580e-9 -m '4+0.7j' -r ${radius_nm}e-9 -k 0 0 --kpi -n 1.52 -L lMax -t 1e11 -b -2 -f 0.1 -i 1. -T .3 -N ${contour_points} 
+done
+

examples/size_vs_lMax/AuSphere/serial.sh

@@ -0,0 +1,13 @@
+#!/bin/bash
+
+kx=0.0
+contour_points=410
+
+radii_nm=(`seq 50 1 300`)
+radius_nm=${radii_nm[$SLURM_ARRAY_TASK_ID]}
+
+for lMax in $(seq 1 5) ; do
+  for radius_nm in $(seq 50 1 300) ; do
+    rectlat_simple_modes.py -p 580e-9 -m 'Au' -r ${radius_nm}e-9 -k $kx 0 --kpi -n 1.52 -L $lMax -t 1e11 -b -2 -f 0.1 -i 1. -T .3 -N ${contour_points} --lMax-extend 10
+  done 
+done

examples/size_vs_lMax/AuSphere/serial1.sh

@@ -0,0 +1,11 @@
+#!/bin/bash
+
+kx=0.0
+contour_points=410
+
+radii_nm=(`seq 50 1 300`)
+radius_nm=${radii_nm[$SLURM_ARRAY_TASK_ID]}
+
+  for radius_nm in $(seq 50 1 300) ; do
+    rectlat_simple_modes.py -p 580e-9 -m 'Au' -r ${radius_nm}e-9 -k $kx 0 --kpi -n 1.52 -L 1 -t 1e11 -b -2 -f 0.1 -i 1. -T .3 -N ${contour_points} 
+  done 

examples/size_vs_lMax/_mode_r_dep.ipynb

@@ -0,0 +1,300 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import re\n",
+    "import numpy as np\n",
+    "import matplotlib\n",
+    "from matplotlib import pyplot as plt\n",
+    "from scipy.constants import hbar, e as eV, c\n",
+    "eh = eV/hbar\n",
+    "import glob\n",
+    "def ri(z): return (z.real, z.imag)\n",
+    "#m = re.compile(r\"([^_]+)_r([0-9.]+)nm_\")\n",
+    "#removek = re.compile(r\"(k\\([^)]+\\)um-1_)\")\n",
+    "remover = re.compile(r\"r[0-9.]+nm_\")\n",
+    "\n",
+    "\n",
+    "markerdict = {\n",
+    "    4: \"3\",\n",
+    "    -4: \"4\",\n",
+    "    3: \"^\",\n",
+    "    -3: \"v\",\n",
+    "    -2: 'x',\n",
+    "    2: '+',\n",
+    "    1: 's',\n",
+    "    -1: 'd',\n",
+    "}\n",
+    "\n",
+    "prop_cycle = plt.rcParams['axes.prop_cycle']\n",
+    "colors = prop_cycle.by_key()['color']\n",
+    "colordict = {i: colors[(i+1)] for i in range(-4,8)}\n",
+    "\n",
+    "def markerfun(b):\n",
+    "    if b in markerdict.keys():\n",
+    "        return markerdict[b]\n",
+    "    else: return 'X'\n",
+    "\n",
+    "def colorfun(b):\n",
+    "    if (b+1) in colordict.keys():\n",
+    "        return colordict[b+1]\n",
+    "    else: return colordict[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "allfiles=glob.glob('*sph*k(0_0)*.npz')\n",
+    "allgraphs=dict()\n",
+    "for f in allfiles:\n",
+    "    base = remover.sub('', f)\n",
+    "    if base in allgraphs.keys():\n",
+    "        allgraphs[base] += 1\n",
+    "    else:\n",
+    "        allgraphs[base] = 1\n",
+    "for k in sorted(allgraphs.keys()):\n",
+    "    print(k, allgraphs[k])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "FileNotFoundError",
+     "evalue": "[Errno 2] No such file or directory: 'projectors_D4h_lMax1.npz'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-3-0c266089be08>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mlMaxes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mlMax\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mlMax\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mlMax\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlMaxes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0mproj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'projectors_D4h_lMax%d.npz'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mlMax\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     \u001b[0mirlabels\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mproj\u001b[0m \u001b[0;34m=\u001b[0m  \u001b[0;34m{\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mproj\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mf\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mirlabels\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/.local/lib/python3.7/site-packages/numpy-1.17.3-py3.7-linux-x86_64.egg/numpy/lib/npyio.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(file, mmap_mode, allow_pickle, fix_imports, encoding)\u001b[0m\n\u001b[1;32m    426\u001b[0m         \u001b[0mown_fid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    427\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 428\u001b[0;31m         \u001b[0mfid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mos_fspath\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfile\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"rb\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    429\u001b[0m         \u001b[0mown_fid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    430\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: 'projectors_D4h_lMax1.npz'"
+     ]
+    }
+   ],
+   "source": [
+    "projectors = dict()\n",
+    "projectors_list = dict()\n",
+    "lMaxes = [lMax for lMax in range(1,6)]\n",
+    "for lMax in lMaxes:\n",
+    "    proj = np.load('projectors_D4h_lMax%d.npz' % lMax)\n",
+    "    irlabels = sorted(proj.keys())\n",
+    "    proj =  {f: proj[f] for f in irlabels}\n",
+    "    proj_list = [proj[irlabels[i]] for i in range(len(proj))]\n",
+    "    projectors[lMax] = proj\n",
+    "    projectors_list[lMax] = proj_list\n",
+    "globpattern = '*sph_r*_p580nmx580nm_mAu_n1.52_b?2_k(0_0)um-1_L?_cn???.npz'\n",
+    "filenames=glob.glob(globpattern)\n",
+    "plotfilename = 'collected_' + globpattern.replace('*', 'XXX').replace('?', 'X').replace('npz','pdf')\n",
+    "print(filenames[:4], plotfilename)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#projectors\n",
+    "#glob.glob('cyl_r100nm*L3*3100.npz')\n",
+    "#glob.glob('sph_r100*m5*.npz')\n",
+    "#dat['meta'][()],list(dat.keys())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "inpure result detected [1.         0.99999999 1.         0.97991334 0.99999996 0.9999989\n",
+      " 0.99999983 0.99999966 0.99999322 0.99999721 0.99999653] [3.28735741e-04 2.66532534e-05 2.47011478e-05 1.45012420e-01\n",
+      " 2.44785416e-04 7.05405359e-04 1.60203586e-03 1.71245137e-03\n",
+      " 1.03244480e-02 9.18732728e-03 1.18651583e-02]\n",
+      "inpure result detected [1.         1.         0.99999998 0.99999999 0.99999996 0.96608887\n",
+      " 0.99999852 0.99999397 0.99998951 0.99999912 0.99982435] [2.66223026e-04 2.12357147e-05 3.54211968e-05 1.06651057e-04\n",
+      " 2.79595790e-04 2.41939163e-01 2.17645058e-03 3.41541473e-03\n",
+      " 1.14507609e-02 1.49639498e-02 2.33483138e-02]\n",
+      "inpure result detected [1.         1.         0.92521572 1.         0.99999627 0.99990293\n",
+      " 0.99946049] [1.59712906e-05 3.60193407e-05 2.48341492e-01 1.21848930e-03\n",
+      " 3.81805601e-03 2.42649228e-02 2.99534246e-02]\n",
+      "inpure result detected [1.         1.         0.99999998 0.99999961 0.93267685 0.99999964\n",
+      " 0.99999822 0.99921774 0.99995547 0.99997301] [5.22490396e-04 3.01556792e-05 4.88795563e-05 6.29703960e-04\n",
+      " 2.34414238e-01 3.72766210e-03 4.72444059e-03 7.62106094e-02\n",
+      " 6.32796684e-02 5.63231562e-02]\n"
+     ]
+    }
+   ],
+   "source": [
+    "plotdata = {}\n",
+    "for file in filenames:\n",
+    "    dat = np.load(file, allow_pickle=True)\n",
+    "    kx = dat['meta'][()]['k'][0]\n",
+    "    radius = dat['meta'][()]['radius']\n",
+    "    b = dat['meta'][()]['band_index']\n",
+    "    eigvals = dat['eigval']\n",
+    "    lMax = dat['meta'][()]['lMax']\n",
+    "    residuals = dat['residuals']\n",
+    "    ef =dat['empty_freqs']\n",
+    "    eigvecs = dat['eigvec']\n",
+    "    irweights = []\n",
+    "    #for proj in projectors_list[lMax]:\n",
+    "    #    try:\n",
+    "    #        irweights.append(np.linalg.norm(np.tensordot(proj, eigvecs, axes=(-1, -1)), axis=0,ord=2) if len(proj) != 0 else np.zeros((len(eigvecs),)))\n",
+    "    #    except ValueError as err:\n",
+    "    #        print(proj, len(proj))\n",
+    "    #        raise err\n",
+    "    irweights = np.array(irweights)\n",
+    "    #print(irweights)\n",
+    "    irweights = np.array([np.linalg.norm(np.tensordot(proj, eigvecs, axes=(-1, -1)), axis=0,ord=2) if len(proj) != 0 else np.zeros((len(eigvecs),)) for proj in projectors_list[lMax]]).T\n",
+    "    irclass = np.argmax(irweights, axis=-1)\n",
+    "    purities = np.amax(irweights, axis=-1)\n",
+    "    if (np.any(purities < 0.98)):\n",
+    "        print(\"inpure result detected\", purities, residuals)\n",
+    "    #print(purities)\n",
+    "    \n",
+    "    #for i in range(len(residuals)): \n",
+    "    #    if residuals[i] < 0.01:\n",
+    "    #        vec = eigvecs[i]\n",
+    "    #        for irlabel, proj in projectors.items():\n",
+    "    #            print(irlabel, np.linalg.norm(np.dot(proj, vec))) #maybe some conj() here?\n",
+    "    #        print('--->', irlabels[irclass[i]])\n",
+    "\n",
+    "    \n",
+    "    plotdata[(lMax,radius)] = (eigvals, residuals, b, ef, irclass,)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig = plt.figure(figsize=(15,6))\n",
+    "axesR = {}\n",
+    "axesI = {}\n",
+    "for i, lMax in enumerate(lMaxes):\n",
+    "    axesR[lMax] = fig.add_subplot(2,len(lMaxes),i+1)\n",
+    "    axesR[lMax].set_xlim([50,300])\n",
+    "    axesR[lMax].set_ylim([1.25, ef[1]/eh])\n",
+    "    axesI[lMax] = fig.add_subplot(2,len(lMaxes),len(lMaxes)+i+1)\n",
+    "    axesI[lMax].set_xlim([50,300])\n",
+    "    axesI[lMax].set_ylim([-60, 30])\n",
+    "    axesR[lMax].set_title('$l_\\max = %d $' % lMax)    \n",
+    "    axesR[lMax].tick_params(labelbottom=False) \n",
+    "    if i == len(lMaxes)//2:\n",
+    "        axesI[lMax].set_xlabel(\"Particle base radius / nm\")\n",
+    "    if i == 0:\n",
+    "        axesR[lMax].set_ylabel('$\\hbar \\Re \\omega / \\mathrm{eV}$')\n",
+    "        axesI[lMax].set_ylabel('$\\hbar \\Im \\omega / \\mathrm{meV}$')\n",
+    "    else:\n",
+    "        axesR[lMax].tick_params(labelleft=False) \n",
+    "        axesI[lMax].tick_params(labelleft=False) \n",
+    "\n",
+    "res_thr = 0.005\n",
+    "\n",
+    "ir_labeled=set()\n",
+    "if True:\n",
+    "  for (lMax, radius), (eigvals, residuals, b, ef, irclass) in plotdata.items():\n",
+    "    for i, (e, res, iri) in enumerate(zip(eigvals, residuals, irclass)):\n",
+    "        #if i == 0:\n",
+    "        if res < res_thr:# and e.real < 2.14e15:\n",
+    "            if iri in ir_labeled: \n",
+    "                label=None\n",
+    "            else:\n",
+    "                ir_labeled.add(iri)\n",
+    "                label=irlabels[iri]\n",
+    "            axesR[lMax].plot(radius*1e9, e.real/eh, \n",
+    "                             marker='.',\n",
+    "                             #marker=markerfun(b),\n",
+    "                    ms=4, #c=colorfun(b)\n",
+    "                    c=matplotlib.cm.hsv(iri/9),\n",
+    "                    #c = colorfun(iri),\n",
+    "                    label=label,\n",
+    "                   )\n",
+    "            axesI[lMax].plot(radius*1e9, e.imag/eh*1000, \n",
+    "                    #marker='x', \n",
+    "                    #c=colorfun(b), \n",
+    "                    c=matplotlib.cm.hsv(iri/9),#colorfun(iri),\n",
+    "                    marker='.', #markerfun(b),\n",
+    "                             ms=4,\n",
+    "                    #label=label\n",
+    "                   )\n",
+    "fig.legend(title=\"Irrep\", loc=\"center right\")\n",
+    "#fig.suptitle('$l_\\mathrm{max}=%d$, residual threshold = %g' % (lMax, res_thr) )\n",
+    "fig.savefig(plotfilename)\n",
+    "fig.savefig(plotfilename.replace('pdf', 'png'))\n",
+    "print(plotfilename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.        , 1.40635433, 1.98888536, 2.81270865, 3.14470387,\n",
+       "       3.97777072, 4.21906298, 4.44728287])"
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ef / eh"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

faddeeva/CMakeLists.txt

@@ -0,0 +1,19 @@
+cmake_minimum_required(VERSION 3.0)
+include(GNUInstallDirs)
+
+project(Faddeeva VERSION 1.0 LANGUAGES C)
+
+option(FADDEEVA_BUILD_STATIC "Build Faddeeva as static library" OFF)
+
+if (FADDEEVA_BUILD_STATIC)
+	add_library(Faddeeva STATIC Faddeeva.h Faddeeva.c Faddeeva.cc)
+else (FADDEEVA_BUILD_STATIC)
+	add_library(Faddeeva SHARED Faddeeva.c)
+	set_target_properties(Faddeeva PROPERTIES PUBLIC_HEADER "Faddeeva.h")
+	install(TARGETS Faddeeva
+		LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
+		PUBLIC_HEADER DESTINATION ${CMAKE_INSTALL_INCLUDEDIR})
+endif (FADDEEVA_BUILD_STATIC)
+target_include_directories(Faddeeva PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
+	
+

faddeeva/Faddeeva.c

@@ -0,0 +1,3 @@
+/* The Faddeeva.cc file contains macros to let it compile as C code
+   (assuming C99 complex-number support), so just #include it. */
+#include "Faddeeva.cc"

faddeeva/Faddeeva.h

@@ -0,0 +1,68 @@
+/* Copyright (c) 2012 Massachusetts Institute of Technology
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ * 
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+ * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+ * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+ * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 
+ */
+
+/* Available at: http://ab-initio.mit.edu/Faddeeva
+
+   Header file for Faddeeva.c; see Faddeeva.cc for more information. */
+
+#ifndef FADDEEVA_H
+#define FADDEEVA_H 1
+
+// Require C99 complex-number support
+#include <complex.h>
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif /* __cplusplus */
+
+// compute w(z) = exp(-z^2) erfc(-iz) [ Faddeeva / scaled complex error func ]
+extern double complex Faddeeva_w(double complex z,double relerr);
+extern double Faddeeva_w_im(double x); // special-case code for Im[w(x)] of real x
+
+// Various functions that we can compute with the help of w(z)
+
+// compute erfcx(z) = exp(z^2) erfc(z)
+extern double complex Faddeeva_erfcx(double complex z, double relerr);
+extern double Faddeeva_erfcx_re(double x); // special case for real x
+
+// compute erf(z), the error function of complex arguments
+extern double complex Faddeeva_erf(double complex z, double relerr);
+extern double Faddeeva_erf_re(double x); // special case for real x
+
+// compute erfi(z) = -i erf(iz), the imaginary error function
+extern double complex Faddeeva_erfi(double complex z, double relerr);
+extern double Faddeeva_erfi_re(double x); // special case for real x
+
+// compute erfc(z) = 1 - erf(z), the complementary error function
+extern double complex Faddeeva_erfc(double complex z, double relerr);
+extern double Faddeeva_erfc_re(double x); // special case for real x
+
+// compute Dawson(z) = sqrt(pi)/2  *  exp(-z^2) * erfi(z)
+extern double complex Faddeeva_Dawson(double complex z, double relerr);
+extern double Faddeeva_Dawson_re(double x); // special case for real x
+
+#ifdef __cplusplus
+}
+#endif /* __cplusplus */
+
+#endif // FADDEEVA_H

faddeeva/Faddeeva.hh

@@ -0,0 +1,62 @@
+/* Copyright (c) 2012 Massachusetts Institute of Technology
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ * 
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+ * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+ * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+ * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 
+ */
+
+/* Available at: http://ab-initio.mit.edu/Faddeeva
+
+   Header file for Faddeeva.cc; see that file for more information. */
+
+#ifndef FADDEEVA_HH
+#define FADDEEVA_HH 1
+
+#include <complex>
+
+namespace Faddeeva {
+
+// compute w(z) = exp(-z^2) erfc(-iz) [ Faddeeva / scaled complex error func ]
+extern std::complex<double> w(std::complex<double> z,double relerr=0);
+extern double w_im(double x); // special-case code for Im[w(x)] of real x
+
+// Various functions that we can compute with the help of w(z)
+
+// compute erfcx(z) = exp(z^2) erfc(z)
+extern std::complex<double> erfcx(std::complex<double> z, double relerr=0);
+extern double erfcx(double x); // special case for real x
+
+// compute erf(z), the error function of complex arguments
+extern std::complex<double> erf(std::complex<double> z, double relerr=0);
+extern double erf(double x); // special case for real x
+
+// compute erfi(z) = -i erf(iz), the imaginary error function
+extern std::complex<double> erfi(std::complex<double> z, double relerr=0);
+extern double erfi(double x); // special case for real x
+
+// compute erfc(z) = 1 - erf(z), the complementary error function
+extern std::complex<double> erfc(std::complex<double> z, double relerr=0);
+extern double erfc(double x); // special case for real x
+
+// compute Dawson(z) = sqrt(pi)/2  *  exp(-z^2) * erfi(z)
+extern std::complex<double> Dawson(std::complex<double> z, double relerr=0);
+extern double Dawson(double x); // special case for real x
+
+} // namespace Faddeeva
+
+#endif // FADDEEVA_HH

finite_systems.md

@@ -1,6 +1,8 @@
 Using QPMS library for simulating finite systems
 ================================================
 
+*** This tutorial is partly obsolete, the interpolators are no longer the first choice of getting the T-matrices. ***
+
 The main C API for finite systems is defined in [scatsystem.h][], and the
 most relevant parts are wrapped into python modules. The central data structure
 defining the system of scatterers is [qpms_scatsys_t][],

lattices.md

@@ -1,118 +0,0 @@
-Using QPMS library for finding modes of 2D-periodic systems
-===========================================================
-
-Calculating modes of infinite 2D arrays is now done 
-in several steps (assuming the T-matrices have already
-been obtained using `scuff-tmatrix` or can be obtained
-from Lorenz-Mie solution (spherical particles)):
-
- 1. Sampling the *k*, *ω* space.
- 2. Pre-calculating the
-    Ewald-summed translation operators.
- 3. For each *k*, *ω* pair, build the LHS operator
-    for the scattering problem (TODO reference), optionally decomposed
-    into suitable irreducible representation subspaces.
- 4. Evaluating the singular values and finding their minima.
-
-The steps above may (and will) change as more user-friendly interface
-will be developed.
-
-
-Preparation: compile the `ew_gen_kin` utility
----------------------------------------------
-
-This will change, but at this point, the lattice-summed
-translation operators are computed using the `ew_gen_kin`
-utility located in the `qpms/apps` directory. It has to be built
-manually like this:
-
-```bash
-  cd qpms/apps
-  c99 -o ew_gen_kin -Wall -I ../.. -I ../../amos/ -O2 -ggdb -DQPMS_VECTORS_NICE_TRANSFORMATIONS -DLATTICESUMS32 2dlattice_ewald.c ../translations.c ../ewald.c ../ewaldsf.c ../gaunt.c ../lattices2d.c ../latticegens.c ../bessel.c -lgsl -lm -lblas ../../amos/libamos.a -lgfortran ../error.c
-``` 
-
-Step 1: Sampling the *k*, *ω* space
---------------------------------------
-
-`ew_gen_kin` expects a list of (*k_x*, *k_y*)
-pairs on standard input (separated by whitespaces),
-the rest is specified via command line arguments.
-
-So if we want to examine the line between the Г point and the point
-\f$ k = (0, 10^5\,\mathrm{m}^{-1}) \f$, we can generate an input
-running
-```bash
-  for ky in $(seq 0 1e3 1e5); do
-    echo 0 $ky >> klist
-  done
-```
-
-It also make sense to pre-generate the list of *ω* values,
-e.g. 
-```bash
-  seq 6.900 0.002 7.3 | sed -e 's/,/./g' > omegalist
-```
-
-
-Step 2: Pre-calculating the translation operators
--------------------------------------------------
-
-`ew_gen_kin` currently uses command-line arguments in
-an atrocious way with a hard-coded order:
-```
-  ew_gen_kin outfile b1.x b1.y b2.x b2.y lMax scuffomega refindex npart part0.x part0.y [part1.x part1.y [...]]
-```
-where `outfile` specifies the path to the output, `b1` and `b2` are the
-direct lattice vectors, `lMax` is the multipole degree cutoff,
-`scuffomega` is the frequency in the units used by `scuff-tmatrix`
-(TODO specify), `refindex` is the refractive index of the background
-medium, `npart` number of particles in the unit cell, and `partN` are 
-the positions of these particles inside the unit cell.
-
-Assuming we have the `ew_gen_kin` binary in our `${PATH}`, we can
-now run e.g.
-```bash
-  for omega in $(cat omegalist); do
-    ew_gen_kin $omega 621e-9 0 0 571e-9 3 w_$omega 1.52 1 0 0 < klist
-  done
-```
-This pre-calculates the translation operators for a simple (one particle per unit cell)
-621 nm × 571 nm rectangular lattice inside a medium with refractive index 1.52, 
-up to the octupole (`lMax` = 3) order, yielding one file per frequency. 
-This can take some time and
-it makes sense to run a parallelised `for`-loop instead; this is a stupid but working
-way to do it in bash:
-```bash
-  N=4   # number of parallel processes
-  for omega in $(cat omegalist); do
-    ((i=i%N)); ((i++==0)) && wait
-    ew_gen_kin $omega 621e-9 0 0 571e-9 3 w_$omega 1.52 1 0 0 < klist
-    echo $omega   # optional, to follow progress
-  done
-```
-
-When this is done, we convert all the text output files into 
-numpy's binary format in order to speed up loading in the following steps.
-This is done using the processWfiles_sortnames.py script located in the 
-`misc` directory. Its usage pattern is
-```
-  processWfiles_sortnames.py npart dest src1 [src2 ...]
-```
-where `npart` is the number of particles in the unit cell, `dest`
-is the destination path for the converted data (this will be 
-a directory), and the remaining arguments are paths to the
-files generated by `ew_gen_kin`. In the case above, one could use
-```
-  processWfiles_sortnames.py 1 all w_*
-```
-which would create a directory named `all` containing several
-.npy files.
-
-
-Steps 3, 4
-----------
-
-TODO. For the time being, see e.g. the `SaraRect/dispersions.ipynb` jupyter notebook
-from the `qpms_ipynotebooks` repository
-for the remaining steps.
-

misc/201903_finiterectlat_AaroBEC.py

@@ -1,67 +0,0 @@
-#!/usr/bin/env python
-# coding: utf-8
-from qpms import Particle, CTMatrix, BaseSpec, FinitePointGroup, ScatteringSystem, TMatrixInterpolator, eV, hbar, c, MaterialInterpolator, scatsystem_set_nthreads
-from qpms.symmetries import point_group_info
-import numpy as np
-import os
-import sys
-from pathlib import Path
-
-if 'SLURM_CPUS_PER_TASK' in os.environ:
-    scatsystem_set_nthreads(int(os.environ['SLURM_CPUS_PER_TASK']))
-nm = 1e-9
-
-rewrite_output = '--rewrite-output' in sys.argv
-
-sym = FinitePointGroup(point_group_info['D2h'])
-bspec = BaseSpec(lMax = 2)
-tmfile = '/m/phys/project/qd/Marek/tmatrix-experiments/Cylinder/AaroBEC/cylinder_50nm_lMax4_longer.TMatrix'
-#outputdatadir = '/home/necadam1/wrkdir/AaroBECfinite_new'
-outputdatadir = '/u/46/necadam1/unix/project/AaroBECfinite_new'
-os.makedirs(outputdatadir, exist_ok = True)
-interp = TMatrixInterpolator(tmfile, bspec, symmetrise = sym, atol = 1e-8)
-# There is only one t-matrix in the system for each frequency. We initialize the matrix with the lowest frequency data.
-# Later, we can replace it using the tmatrix[...] = interp(freq) and s.update_tmatrices NOT YET; TODO
-
-omega = float(sys.argv[3]) * eV/hbar
-sv_threshold = float(sys.argv[4])
-
-# Now place the particles and set background index.
-px = 571*nm; py = 621*nm
-n = 1.52
-Nx = int(sys.argv[1])
-Ny = int(sys.argv[2])
-
-orig_x = (np.arange(Nx/2) + (0 if (Nx % 2) else .5)) * px
-orig_y = (np.arange(Ny/2) + (0 if (Ny % 2) else .5)) * py
-
-orig_xy = np.stack(np.meshgrid(orig_x, orig_y), axis = -1)
-
-tmatrix = interp(omega)
-#print(tmatrix.m)
-
-particles = [Particle(orig_xy[i], tmatrix) for i in np.ndindex(orig_xy.shape[:-1])]
-
-ss = ScatteringSystem(particles, sym)
-
-k = n * omega / c
-
-for iri in range(ss.nirreps):
-    destpath = os.path.join(outputdatadir, 'Nx%d_Ny%d_%geV_ir%d.npz'%(Nx, Ny, omega/eV*hbar, iri,))
-    touchpath = os.path.join(outputdatadir, 'Nx%d_Ny%d_%geV_ir%d.done'%(Nx, Ny, omega/eV*hbar, iri,))
-    if (os.path.isfile(destpath) or os.path.isfile(touchpath)) and not rewrite_output:
-      print(destpath, 'already exists, skipping')
-      continue
-    mm_iri = ss.modeproblem_matrix_packed(k, iri)
-    #print(mm_iri)
-    U, S, Vh = np.linalg.svd(mm_iri)
-    del U
-    print(iri, ss.irrep_names[iri], S[-1])
-    starti = max(0,len(S) - np.searchsorted(S[::-1], sv_threshold, side='left')-1)
-    np.savez(destpath,
-        S=S[starti:], omega=omega, Vh = Vh[starti:], iri=iri, Nx = Nx, Ny= Ny )
-    del S
-    del Vh
-    Path(touchpath).touch()
-    # Don't forget to conjugate Vh before transforming it to the full vector!
-

misc/201903_finiterectlat_AaroBEC_Mie.py

@@ -1,79 +0,0 @@
-#!/usr/bin/env python3
-# coding: utf-8
-from qpms import Particle, CTMatrix, BaseSpec, FinitePointGroup, ScatteringSystem, TMatrixInterpolator, eV, hbar, c, MaterialInterpolator, scatsystem_set_nthreads
-from qpms.symmetries import point_group_info
-from pathlib import Path
-import numpy as np
-import os
-import sys
-nm = 1e-9
-
-
-if 'SLURM_CPUS_PER_TASK' in os.environ:
-        scatsystem_set_nthreads(int(os.environ['SLURM_CPUS_PER_TASK']))
-
-
-rewrite_output = '--rewrite-output' in sys.argv
-
-cyr_part_height = 50*nm
-cyr_part_radius = 50*nm
-cyr_part_volume = cyr_part_height * np.pi * cyr_part_radius**2
-eqv_sph_radius = (3/4/np.pi*cyr_part_volume)**(1/3)
-
-sym = FinitePointGroup(point_group_info['D2h'])
-bspec = BaseSpec(lMax = 2)
-#tmfile = '/m/phys/project/qd/Marek/tmatrix-experiments/Cylinder/AaroBEC/cylinder_50nm_lMax4_cleaned.TMatrix'
-materialfile = '/home/necadam1/wrkdir/repo/refractiveindex.info-database/database/data/main/Au/Johnson.yml'
-
-#outputdatadir = '/home/necadam1/wrkdir/AaroBECfinite_new'
-#outputdatadir = '/u/46/necadam1/unix/project/AaroBECfinite_sph'
-outputdatadir = '/home/necadam1/wrkdir/AaroBECfinite_sph'
-os.makedirs(outputdatadir, exist_ok = True)
-mi = MaterialInterpolator(materialfile)
-#interp = TMatrixInterpolator(tmfile, bspec, symmetrise = sym, atol = 1e-8)
-# There is only one t-matrix in the system for each frequency. We initialize the matrix with the lowest frequency data.
-# Later, we can replace it using the tmatrix[...] = interp(freq) and s.update_tmatrices NOT YET; TODO
-
-omega = float(sys.argv[3]) * eV/hbar
-sv_threshold = float(sys.argv[4])
-
-# Now place the particles and set background index.
-px = 571*nm; py = 621*nm
-n = 1.52
-Nx = int(sys.argv[1])
-Ny = int(sys.argv[2])
-
-orig_x = (np.arange(Nx/2) + (0 if (Nx % 2) else .5)) * px
-orig_y = (np.arange(Ny/2) + (0 if (Ny % 2) else .5)) * py
-
-orig_xy = np.stack(np.meshgrid(orig_x, orig_y), axis = -1)
-
-#tmatrix = interp(omega)
-tmatrix = CTMatrix.spherical_perm(bspec, eqv_sph_radius, omega, mi(omega), n**2)
-particles = [Particle(orig_xy[i], tmatrix) for i in np.ndindex(orig_xy.shape[:-1])]
-
-
-ss = ScatteringSystem(particles, sym)
-
-
-k = n * omega / c
-
-
-for iri in range(ss.nirreps):
-    destpath = os.path.join(outputdatadir, 'Nx%d_Ny%d_%geV_ir%d.npz'%(Nx, Ny, omega/eV*hbar, iri))
-    touchpath = os.path.join(outputdatadir, 'Nx%d_Ny%d_%geV_ir%d.done'%(Nx, Ny, omega/eV*hbar, iri))
-    if (os.path.isfile(destpath) or os.path.isfile(touchpath)) and not rewrite_output:
-      print(destpath, 'already exists, skipping')
-      continue
-    mm_iri = ss.modeproblem_matrix_packed(k, iri)
-    U, S, Vh = np.linalg.svd(mm_iri)
-    del U
-    print(iri, ss.irrep_names[iri], S[-1])
-    starti = max(0,len(S) - np.searchsorted(S[::-1], sv_threshold, side='left')-1)
-    np.savez(destpath,
-        S=S[starti:], omega=omega, Vh = Vh[starti:], iri=iri, Nx = Nx, Ny= Ny )
-    del S
-    del Vh
-    Path(touchpath).touch()
-    # Don't forget to conjugate Vh before transforming it to the full vector!
-

misc/201903_finiterectlat_AaroBEC_fatMie.py

@@ -1,81 +0,0 @@
-#!/usr/bin/env python3
-# coding: utf-8
-from qpms import Particle, CTMatrix, BaseSpec, FinitePointGroup, ScatteringSystem, TMatrixInterpolator, eV, hbar, c, MaterialInterpolator, scatsystem_set_nthreads
-from qpms.symmetries import point_group_info
-import numpy as np
-import os
-import sys
-from pathlib import Path
-
-if 'SLURM_CPUS_PER_TASK' in os.environ:
-    scatsystem_set_nthreads(int(os.environ['SLURM_CPUS_PER_TASK']))
-
-nm = 1e-9
-
-rewrite_output = '--rewrite-output' in sys.argv
-
-radiusfactor = float(sys.argv[5])
-
-cyr_part_height = 50*nm
-cyr_part_radius = 50*nm
-cyr_part_volume = cyr_part_height * np.pi * cyr_part_radius**2
-eqv_sph_radius = (3/4/np.pi*cyr_part_volume)**(1/3) * radiusfactor
-
-sym = FinitePointGroup(point_group_info['D2h'])
-bspec = BaseSpec(lMax = 2)
-#tmfile = '/m/phys/project/qd/Marek/tmatrix-experiments/Cylinder/AaroBEC/cylinder_50nm_lMax4_cleaned.TMatrix'
-materialfile = '/home/necadam1/wrkdir/repo/refractiveindex.info-database/database/data/main/Au/Johnson.yml'
-
-#outputdatadir = '/home/necadam1/wrkdir/AaroBECfinite_new'
-#outputdatadir = '/u/46/necadam1/unix/project/AaroBECfinite_sph'
-outputdatadir = '/home/necadam1/wrkdir/AaroBECfinite_fatsph'
-os.makedirs(outputdatadir, exist_ok = True)
-mi = MaterialInterpolator(materialfile)
-#interp = TMatrixInterpolator(tmfile, bspec, symmetrise = sym, atol = 1e-8)
-# There is only one t-matrix in the system for each frequency. We initialize the matrix with the lowest frequency data.
-# Later, we can replace it using the tmatrix[...] = interp(freq) and s.update_tmatrices NOT YET; TODO
-
-omega = float(sys.argv[3]) * eV/hbar
-sv_threshold = float(sys.argv[4])
-
-
-# Now place the particles and set background index.
-px = 571*nm; py = 621*nm
-n = 1.52
-Nx = int(sys.argv[1])
-Ny = int(sys.argv[2])
-
-orig_x = (np.arange(Nx/2) + (0 if (Nx % 2) else .5)) * px
-orig_y = (np.arange(Ny/2) + (0 if (Ny % 2) else .5)) * py
-
-orig_xy = np.stack(np.meshgrid(orig_x, orig_y), axis = -1)
-
-#tmatrix = interp(omega)
-tmatrix = CTMatrix.spherical_perm(bspec, eqv_sph_radius, omega, mi(omega), n**2)
-particles = [Particle(orig_xy[i], tmatrix) for i in np.ndindex(orig_xy.shape[:-1])]
-
-
-ss = ScatteringSystem(particles, sym)
-
-
-k = n * omega / c
-
-
-for iri in range(ss.nirreps):
-    destpath = os.path.join(outputdatadir, 'Nx%d_Ny%d_%geV_ir%d_r%gnm.npz'%(Nx, Ny, omega/eV*hbar, iri, eqv_sph_radius/nm))
-    touchpath = os.path.join(outputdatadir, 'Nx%d_Ny%d_%geV_ir%d_r%gnm.done'%(Nx, Ny, omega/eV*hbar, iri, eqv_sph_radius/nm))
-    if (os.path.isfile(destpath) or os.path.isfile(touchpath)) and not rewrite_output:
-      print(destpath, 'already exists, skipping')
-      continue
-    mm_iri = ss.modeproblem_matrix_packed(k, iri)
-    U, S, Vh = np.linalg.svd(mm_iri)
-    del U
-    print(iri, ss.irrep_names[iri], S[-1])
-    starti = max(0,len(S) - np.searchsorted(S[::-1], sv_threshold, side='left')-1)
-    np.savez(destpath,
-        S=S[starti:], omega=omega, Vh = Vh[starti:], iri=iri, Nx = Nx, Ny= Ny )
-    del S
-    del Vh
-    Path(touchpath).touch()
-    # Don't forget to conjugate Vh before transforming it to the full vector!
-

misc/dispersion-SVD.py

@@ -1,547 +0,0 @@
-#!/usr/bin/env python3
-
-
-import argparse, re, random, string
-import subprocess
-from scipy.constants import hbar, e as eV, pi, c
-
-def make_action_sharedlist(opname, listname):
-    class opAction(argparse.Action):
-        def __call__(self, parser, args, values, option_string=None):
-            if (not hasattr(args, listname)) or getattr(args, listname) is None:
-                setattr(args, listname, list())
-            getattr(args,listname).append((opname, values))
-    return opAction
-
-parser = argparse.ArgumentParser()
-#TODO? použít type=argparse.FileType('r') ?
-parser.add_argument('--TMatrix', action='store', required=True, help='Path to TMatrix file')
-parser.add_argument('--griddir', action='store', required=True, help='Path to the directory with precalculated translation operators')
-#sizepar = parser.add_mutually_exclusive_group(required=True)
-parser.add_argument('--hexside', action='store', type=float, required=True, help='Lattice hexagon size length')
-parser.add_argument('--output', action='store', help='Path to output PDF')
-parser.add_argument('--store_SVD', action='store_true', help='If specified without --SVD_output, it will save the data in a file named as the PDF output, but with .npz extension instead')
-#parser.add_argument('--SVD_output', action='store', help='Path to output singular value decomposition result')
-parser.add_argument('--nSV', action='store', metavar='N', type=int, default=1, help='Store and draw N minimun singular values')
-parser.add_argument('--scp_to', action='store', metavar='N', type=str, help='SCP the output files to a given destination')
-parser.add_argument('--background_permittivity', action='store', type=float, default=1., help='Background medium relative permittivity (default 1)')
-parser.add_argument('--sparse', action='store', type=int, help='Skip frequencies for preview')
-parser.add_argument('--eVmax', action='store', type=float, help='Skip frequencies above this value')
-parser.add_argument('--eVmin', action='store', type=float, help='Skip frequencies below this value')
-parser.add_argument('--kdensity', action='store', type=int, default=66, help='Number of k-points per x-axis segment')
-parser.add_argument('--lMax', action='store', type=int, help='Override lMax from the TMatrix file')
-#TODO some more sophisticated x axis definitions
-parser.add_argument('--gaussian', action='store', type=float, metavar='σ', help='Use a gaussian envelope for weighting the interaction matrix contributions (depending on the distance), measured in unit cell lengths (?) FIxME).')
-popgrp=parser.add_argument_group(title='Operations')
-popgrp.add_argument('--tr', dest='ops', action=make_action_sharedlist('tr', 'ops'), default=list()) # the default value for dest can be set once
-popgrp.add_argument('--tr0', dest='ops', action=make_action_sharedlist('tr0', 'ops'))
-popgrp.add_argument('--tr1', dest='ops', action=make_action_sharedlist('tr1', 'ops'))
-popgrp.add_argument('--sym', dest='ops', action=make_action_sharedlist('sym', 'ops'))
-popgrp.add_argument('--sym0', dest='ops', action=make_action_sharedlist('sym0', 'ops'))
-popgrp.add_argument('--sym1', dest='ops', action=make_action_sharedlist('sym1', 'ops'))
-#popgrp.add_argument('--mult', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult', 'ops'))
-#popgrp.add_argument('--mult0', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult0', 'ops'))
-#popgrp.add_argument('--mult1', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult1', 'ops'))
-popgrp.add_argument('--multl', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl', 'ops'))
-popgrp.add_argument('--multl0', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl0', 'ops'))
-popgrp.add_argument('--multl1', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl1', 'ops'))
-parser.add_argument('--frequency_multiplier', action='store', type=float, default=1., help='Multiplies the frequencies in the TMatrix file by a given factor.')
-# TODO enable more flexible per-sublattice specification
-pargs=parser.parse_args()
-print(pargs)
-
-
-translations_dir = pargs.griddir 
-TMatrix_file = pargs.TMatrix
-pdfout = pargs.output if pargs.output else (''.join(random.choice(string.ascii_uppercase + string.digits) for _ in range(10)) + '.pdf')
-print(pdfout)
-if(pargs.store_SVD):
-    if re.search('.pdf$', pdfout):
-        svdout = re.sub('.pdf$', r'.npz', pdfout)
-    else:
-        svdout = pdfout + '.npz'
-else:
-     svdout = None
-
-
-hexside = pargs.hexside #375e-9
-epsilon_b = pargs.background_permittivity #2.3104
-gaussianSigma = pargs.gaussian if pargs.gaussian else None # hexside * 222 / 7
-interpfreqfactor = pargs.frequency_multiplier
-scp_dest = pargs.scp_to if pargs.scp_to else None
-kdensity = pargs.kdensity
-minfreq = pargs.eVmin*eV/hbar if pargs.eVmin else None
-maxfreq = pargs.eVmax*eV/hbar if pargs.eVmax else None
-skipfreq = pargs.sparse if pargs.sparse else None
-svn = pargs.nSV
-
-# TODO multiplier operation definitions and parsing
-#factor13inc = 10
-#factor13scat=10
-
-ops = list()
-opre = re.compile('(tr|sym|copy|multl|mult)(\d*)')
-for oparg in pargs.ops:
-    opm = opre.match(oparg[0])
-    if opm:
-        ops.append(((opm.group(2),) if opm.group(2) else (0,1), opm.group(1), oparg[1]))
-    else:
-        raise # should not happen
-print(ops)
-
-#ops = (
-#    # co, typ operace (symetrizace / transformace / kopie), specifikace (operace nebo zdroj), 
-#    # co: 0, 1, (0,1), (0,), (1,), #NI: 'all'
-#    # typ operace: sym, tr, copy
-#    # specifikace:
-#    # sym, tr: 'σ_z', 'σ_y', 'C2'; sym: 'C3', 
-#    # copy: 0, 1 (zdroj)
-#    ((0,1), 'sym', 'σ_z'),
-#    #((0,1), 'sym', 'σ_x'),
-#    #((0,1), 'sym', 'σ_y'),
-#    ((0,1), 'sym', 'C3'),
-#    ((1), 'tr', 'C2'),
-#
-#)
-
-# -----------------finished basic CLI parsing (except for op arguments) ------------------
-import time
-begtime=time.time()
-
-from matplotlib.path import Path
-import matplotlib.patches as patches
-import matplotlib.pyplot as plt
-import qpms
-import numpy as np
-import os, sys, warnings, math
-from matplotlib import pyplot as plt
-from matplotlib.backends.backend_pdf import PdfPages
-from scipy import interpolate
-nx = None
-s3 = math.sqrt(3)
-
-
-
-pdf = PdfPages(pdfout)
-
-# In[3]:
-
-# specifikace T-matice zde
-cdn = c/ math.sqrt(epsilon_b)
-TMatrices_orig, freqs_orig, freqs_weirdunits_orig, lMaxTM = qpms.loadScuffTMatrices(TMatrix_file)
-if pargs.lMax:
-    lMax = pargs.lMax if pargs.lMax else lMaxTM    
-my, ny = qpms.get_mn_y(lMax)
-nelem = len(my)
-if pargs.lMax: #force commandline specified lMax
-    TMatrices_orig = TMatrices_orig[...,0:nelem,:,0:nelem]
-
-ž = np.arange(2*nelem)
-tž = ž // nelem
-mž = my[ž%nelem]
-nž = ny[ž%nelem]
-TEž = ž[(mž+nž+tž) % 2 == 0]
-TMž = ž[(mž+nž+tž) % 2 == 1]
-
-č = np.arange(2*2*nelem)
-žč = č % (2* nelem)
-tč = tž[žč]
-mč = mž[žč]
-nč = nž[žč]
-TEč = č[(mč+nč+tč) % 2 == 0]
-TMč = č[(mč+nč+tč) % 2 == 1]
-
-TMatrices = np.array(np.broadcast_to(TMatrices_orig[:,nx,:,:,:,:],(len(freqs_orig),2,2,nelem,2,nelem)) )
-
-#TMatrices[:,:,:,:,:,ny==3] *= factor13inc
-#TMatrices[:,:,:,ny==3,:,:] *= factor13scat
-xfl = qpms.xflip_tyty(lMax)
-yfl = qpms.yflip_tyty(lMax)
-zfl = qpms.zflip_tyty(lMax)
-c2rot = qpms.apply_matrix_left(qpms.yflip_yy(3),qpms.xflip_yy(3),-1)
-
-reCN = re.compile('(\d*)C(\d+)')
-#TODO C nekonečno
-
-for op in ops:
-    if op[0] == 'all':
-        targets = (0,1)
-    elif isinstance(op[0],int):
-        targets = (op[0],)
-    else:
-        targets = op[0]
-        
-    if op[1] == 'sym':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'C2': # special case of the latter
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1))/2                
-        elif mCN:
-            rotN = int(mCN.group(2))
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                for i in range(rotN):
-                    rotangle = 2*np.pi*i / rotN
-                    rot =  qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle]))
-                    rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle]))
-                    TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-                TMatrices[:,t] = np.sum(TMatrix_contribs, axis=0) / rotN
-        else:
-            raise
-    elif op[1] == 'tr':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'C2':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1)       
-        elif mCN:
-            rotN = int(mCN.group(2))
-            power = int(mCN.group(1)) if mCN.group(1) else 1
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                rotangle = 2*np.pi*power/rotN
-                rot = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,rotangle]))
-                rotinv = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,-rotangle]))
-                TMatrices[:,t] = qpms.apply_matrix_left(rot, qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-        else:
-            raise
-    elif op[1] == 'copy':
-        raise # not implemented
-    elif op[1] == 'mult':
-        raise # not implemented
-    elif op[1] == 'multl':
-        incy = np.full((nelem,), False, dtype=bool)
-        for incl in op[2][0].split(','):
-            l = int(incl)
-            incy += (l == ny)
-        scaty = np.full((nelem,), False, dtype=bool)
-        for scatl in op[2][1].split(','):
-            l = int(scatl)
-            scaty += (l == ny)
-        for t in targets:
-            TMatrices[np.ix_(np.arange(TMatrices.shape[0]),np.array([t]),np.array([0,1]),scaty,np.array([0,1]),incy)] *= float(op[2][2])
-    else:
-        raise #unknown operation; should not happen
-
-TMatrices_interp = interpolate.interp1d(freqs_orig*interpfreqfactor, TMatrices, axis=0, kind='linear',fill_value="extrapolate")
-
-
-
-# In[4]:
-
-om = np.linspace(np.min(freqs_orig), np.max(freqs_orig),100)
-TMatrix0ip = np.reshape(TMatrices_interp(om)[:,0], (len(om), 2*nelem*2*nelem))
-f, axa = plt.subplots(2, 2, figsize=(15,15))
-
-#print(TMatrices.shape)
-#plt.plot(om, TMatrices[:,0,0,0,0].imag,'r',om, TMatrices[:,0,0,0,0].real,'r--',om, TMatrices[:,0,2,0,2].imag,'b',om, TMatrices[:,0,2,0,2].real,'b--'))
-        
-ax = axa[0,0]
-ax2 = ax.twiny()
-ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar])
-ax.plot(
-         om, TMatrix0ip[:,:].imag,'-',om, TMatrix0ip[:,:].real,'--',
-)
-ax = axa[0,1]
-ax2 = ax.twiny()
-ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar])
-ax.plot(
-         om, abs(TMatrix0ip[:,:]),'-'
-)
-ax.set_yscale('log')
-
-ax = axa[1,1]
-ax2 = ax.twiny()
-ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar])
-ax.plot(
-         om, np.unwrap(np.angle(TMatrix0ip[:,:]),axis=0),'-'
-)
-
-ax = axa[1,0]
-ax.text(0.5,0.5,str(pargs).replace(',',',\n'),horizontalalignment='center',verticalalignment='center',transform=ax.transAxes)
-pdf.savefig(f)
-
-
-# In[ ]:
-
-#kdensity = 66 #defined from cl arguments
-bz_0 = np.array((0,0,0.,))
-bz_K1 = np.array((1.,0,0))*4*np.pi/3/hexside/s3
-bz_K2 = np.array((1./2.,s3/2,0))*4*np.pi/3/hexside/s3
-bz_M = np.array((3./4, s3/4,0))*4*np.pi/3/hexside/s3
-k0Mlist = bz_0 + (bz_M-bz_0) * np.linspace(0,1,kdensity)[:,nx]
-kMK1list = bz_M + (bz_K1-bz_M) * np.linspace(0,1,kdensity)[:,nx]
-kK10list = bz_K1 + (bz_0-bz_K1) * np.linspace(0,1,kdensity)[:,nx]
-k0K2list = bz_0 + (bz_K2-bz_0) * np.linspace(0,1,kdensity)[:,nx]
-kK2Mlist = bz_K2 + (bz_M-bz_K2) * np.linspace(0,1,kdensity)[:,nx]
-B1 = 2* bz_K1 - bz_K2
-B2 = 2* bz_K2 - bz_K1
-klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0)
-kxmaplist = np.concatenate((np.array([0]),np.cumsum(np.linalg.norm(np.diff(klist, axis=0), axis=-1))))
-
-
-# In[ ]:
-
-n2id = np.identity(2*nelem)
-n2id.shape = (2,nelem,2,nelem)
-extlistlist = list()
-leftmatrixlistlist = list()
-minsvTElistlist=list()
-minsvTMlistlist=list()
-if svdout:
-    svUfullTElistlist = list()
-    svVfullTElistlist = list()
-    svSfullTElistlist = list()
-    svUfullTMlistlist = list()
-    svVfullTMlistlist = list()
-    svSfullTMlistlist = list()
-
-nan = float('nan')
-omegalist = list()
-filecount = 0
-for trfile in os.scandir(translations_dir):
-    filecount += 1
-    if (skipfreq and filecount % skipfreq):
-        continue
-    try:
-        npz = np.load(trfile.path, mmap_mode='r')
-        k_0 = npz['precalc_params'][()]['k_hexside'] / hexside
-        omega = k_0 * c / math.sqrt(epsilon_b)
-        if((minfreq and omega < minfreq) or (maxfreq and omega > maxfreq)):
-            continue
-    except:
-        print ("Unexpected error, trying to continue with another file:", sys.exc_info()[0])
-        continue   
-    try:
-        tdic = qpms.hexlattice_precalc_AB_loadunwrap(trfile.path, return_points=True)
-    except:
-        print ("Unexpected error, trying to continue with another file:", sys.exc_info()[0])
-        continue
-    k_0 = tdic['k_hexside'] / hexside
-    omega = k_0 * c / math.sqrt(epsilon_b)
-    omegalist.append(omega)
-    print(filecount, omega/eV*hbar)
-    sys.stdout.flush()
-    a_self = tdic['a_self'][:,:nelem,:nelem]
-    b_self = tdic['b_self'][:,:nelem,:nelem]
-    a_u2d = tdic['a_u2d'][:,:nelem,:nelem]
-    b_u2d = tdic['b_u2d'][:,:nelem,:nelem]
-    a_d2u = tdic['a_d2u'][:,:nelem,:nelem]
-    b_d2u = tdic['b_d2u'][:,:nelem,:nelem]
-    unitcell_translations = tdic['self_tr']*hexside*s3
-    u2d_translations = tdic['u2d_tr']*hexside*s3
-    d2u_translations = tdic['d2u_tr']*hexside*s3
-    if gaussianSigma:
-        unitcell_envelope = np.exp(-np.sum(tdic['self_tr']**2,axis=-1)/(2*gaussianSigma**2))
-        u2d_envelope = np.exp(-np.sum(tdic['u2d_tr']**2,axis=-1)/(2*gaussianSigma**2))
-        d2u_envelope = np.exp(-np.sum(tdic['d2u_tr']**2,axis=-1)/(2*gaussianSigma**2))
-    
-    
-    TMatrices_om = TMatrices_interp(omega)
-    if svdout:
-        svUfullTElist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
-        svVfullTElist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
-        svSfullTElist = np.full((klist.shape[0], 2*nelem), np.nan, dtype=complex)
-        svUfullTMlist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
-        svVfullTMlist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
-        svSfullTMlist = np.full((klist.shape[0], 2*nelem), np.nan, dtype=complex)
-
-     
-    minsvTElist = np.full((klist.shape[0], svn),np.nan)
-    minsvTMlist = np.full((klist.shape[0], svn),np.nan)
-    leftmatrixlist = np.full((klist.shape[0],2,2,nelem,2,2,nelem),np.nan,dtype=complex)
-    isNaNlist = np.zeros((klist.shape[0]), dtype=bool)
-    
-    # sem nějaká rozumná smyčka
-    for ki in range(klist.shape[0]):
-        k = klist[ki]
-        if (k_0*k_0 - k[0]*k[0] - k[1]*k[1] < 0):
-            isNaNlist[ki] = True
-            continue
-
-        phases_self = np.exp(1j*np.tensordot(k,unitcell_translations,axes=(0,-1)))
-        phases_u2d = np.exp(1j*np.tensordot(k,u2d_translations,axes=(0,-1)))
-        phases_d2u = np.exp(1j*np.tensordot(k,d2u_translations,axes=(0,-1)))
-        if gaussianSigma:
-            phases_self *= unitcell_envelope
-            phases_u2d *= u2d_envelope
-            phases_d2u *= d2u_envelope
-        leftmatrix = np.zeros((2,2,nelem, 2,2,nelem), dtype=complex)
-
-        leftmatrix[0,0,:,0,0,:] = np.tensordot(a_self,phases_self, axes=(0,-1)) # u2u, E2E
-        leftmatrix[1,0,:,1,0,:] = leftmatrix[0,0,:,0,0,:] # d2d, E2E
-        leftmatrix[0,1,:,0,1,:] = leftmatrix[0,0,:,0,0,:] # u2u, M2M
-        leftmatrix[1,1,:,1,1,:] = leftmatrix[0,0,:,0,0,:] # d2d, M2M
-        leftmatrix[0,0,:,0,1,:] = np.tensordot(b_self,phases_self, axes=(0,-1)) # u2u, M2E
-        leftmatrix[0,1,:,0,0,:] = leftmatrix[0,0,:,0,1,:] # u2u, E2M
-        leftmatrix[1,1,:,1,0,:] = leftmatrix[0,0,:,0,1,:] # d2d, E2M
-        leftmatrix[1,0,:,1,1,:] = leftmatrix[0,0,:,0,1,:] # d2d, M2E
-        leftmatrix[0,0,:,1,0,:] = np.tensordot(a_d2u, phases_d2u,axes=(0,-1)) #d2u,E2E
-        leftmatrix[0,1,:,1,1,:] = leftmatrix[0,0,:,1,0,:] #d2u, M2M
-        leftmatrix[1,0,:,0,0,:] = np.tensordot(a_u2d, phases_u2d,axes=(0,-1)) #u2d,E2E
-        leftmatrix[1,1,:,0,1,:] = leftmatrix[1,0,:,0,0,:] #u2d, M2M
-        leftmatrix[0,0,:,1,1,:] = np.tensordot(b_d2u, phases_d2u,axes=(0,-1)) #d2u,M2E
-        leftmatrix[0,1,:,1,0,:] = leftmatrix[0,0,:,1,1,:] #d2u, E2M
-        leftmatrix[1,0,:,0,1,:] = np.tensordot(b_u2d, phases_u2d,axes=(0,-1)) #u2d,M2E
-        leftmatrix[1,1,:,0,0,:] = leftmatrix[1,0,:,0,1,:] #u2d, E2M
-        #leftmatrix is now the translation matrix T
-        for j in range(2):
-            leftmatrix[j] = -np.tensordot(TMatrices_om[j], leftmatrix[j], axes=([-2,-1],[0,1]))
-            # at this point, jth row of leftmatrix is that of -MT
-            leftmatrix[j,:,:,j,:,:] += n2id
-        #now we are done, 1-MT
-
-        leftmatrixlist[ki] = leftmatrix
-
-
-    nnlist = np.logical_not(isNaNlist)
-    leftmatrixlist_s = np.reshape(leftmatrixlist,(klist.shape[0], 2*2*nelem,2*2*nelem))[nnlist]
-    leftmatrixlist_TE = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TEč,TEč)]
-    leftmatrixlist_TM = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TMč,TMč)]
-    #svarr = np.linalg.svd(leftmatrixlist_TE, compute_uv=False)
-    #argsortlist = np.argsort(svarr, axis=-1)[...,:svn]
-    #minsvTElist[nnlist] = svarr[...,argsortlist]
-    #minsvTElist[nnlist] = np.amin(np.linalg.svd(leftmatrixlist_TE, compute_uv=False), axis=-1)
-    if svdout:
-        svUfullTElist[nnlist], svSfullTElist[nnlist], svVfullTElist[nnlist] = np.linalg.svd(leftmatrixlist_TE, compute_uv=True)
-        svUfullTMlist[nnlist], svSfullTMlist[nnlist], svVfullTMlist[nnlist] = np.linalg.svd(leftmatrixlist_TM, compute_uv=True)
-        svUfullTElistlist.append(svUfullTElist)
-        svVfullTElistlist.append(svVfullTElist)
-        svSfullTElistlist.append(svSfullTElist)
-        svUfullTMlistlist.append(svUfullTMlist)
-        svVfullTMlistlist.append(svVfullTMlist)
-        svSfullTMlistlist.append(svSfullTMlist)
-    minsvTElist[nnlist] = np.linalg.svd(leftmatrixlist_TE, compute_uv=False)[...,-svn:]
-    #svarr = np.linalg.svd(leftmatrixlist_TM, compute_uv=False)
-    #argsortlist = np.argsort(svarr, axis=-1)[...,:svn]
-    #minsvTMlist[nnlist] = svarr[...,argsortlist]
-    #minsvTMlist[nnlist] = np.amin(np.linalg.svd(leftmatrixlist_TM, compute_uv=False), axis=-1)
-    minsvTMlist[nnlist] = np.linalg.svd(leftmatrixlist_TM, compute_uv=False)[...,-svn:]
-    minsvTMlistlist.append(minsvTMlist)
-    minsvTElistlist.append(minsvTElist) 
-
-minsvTElistarr = np.array(minsvTElistlist)
-minsvTMlistarr = np.array(minsvTMlistlist)
-del minsvTElistlist, minsvTMlistlist
-if svdout:
-    svUfullTElistarr = np.array(svUfullTElistlist)
-    svVfullTElistarr = np.array(svVfullTElistlist)
-    svSfullTElistarr = np.array(svSfullTElistlist)
-    del svUfullTElistlist, svVfullTElistlist, svSfullTElistlist
-    svUfullTMlistarr = np.array(svUfullTMlistlist)
-    svVfullTMlistarr = np.array(svVfullTMlistlist)
-    svSfullTMlistarr = np.array(svSfullTMlistlist)
-    del svUfullTMlistlist, svVfullTMlistlist, svSfullTMlistlist
-omegalist = np.array(omegalist)
-# order to make the scatter plots "nice"
-omegaorder = np.argsort(omegalist)
-omegalist = omegalist[omegaorder]
-minsvTElistarr = minsvTElistarr[omegaorder]
-minsvTMlistarr = minsvTMlistarr[omegaorder]
-if svdout:
-    svUfullTElistarr = svUfullTElistarr[omegaorder]
-    svVfullTElistarr = svVfullTElistarr[omegaorder]
-    svSfullTElistarr = svSfullTElistarr[omegaorder]
-    svUfullTMlistarr = svUfullTMlistarr[omegaorder]
-    svVfullTMlistarr = svVfullTMlistarr[omegaorder]
-    svSfullTMlistarr = svSfullTMlistarr[omegaorder]
-    np.savez(svdout, omega = omegalist, klist = klist, bzpoints = np.array([bz_0, bz_K1, bz_K2, bz_M, B1, B2]), 
-                     uTE = svUfullTElistarr,
-                     vTE = svVfullTElistarr,
-                     sTE = svSfullTElistarr,
-                     uTM = svUfullTMlistarr,
-                     vTM = svVfullTMlistarr,
-                     sTM = svSfullTMlistarr,
-    )
-                     
-
-omlist = np.broadcast_to(omegalist[:,nx], minsvTElistarr[...,0].shape)
-kxmlarr = np.broadcast_to(kxmaplist[nx,:], minsvTElistarr[...,0].shape)
-klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0)
-
-
-# In[ ]:
-for minN in reversed(range(svn)):
-    f, ax = plt.subplots(1, figsize=(20,15))
-    sc = ax.scatter(kxmlarr, omlist/eV*hbar, c = np.sqrt(minsvTMlistarr[...,minN]), s =40, lw=0)
-    ax.plot(kxmaplist, np.linalg.norm(klist,axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist+B1, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist+B2, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist-B2, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist-B1, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist+B2-B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-B2+B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-B2-B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist+B2+B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B2, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B2-B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B1-B2, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B1-2*B2, axis=-1)*cdn/eV*hbar, '-',
-    #        kxmaplist, np.linalg.norm(klist+2*B2-B1, axis=-1)*cdn, '-',
-    #        kxmaplist, np.linalg.norm(klist+2*B1-B2, axis=-1)*cdn, '-',
-           )
-    ax.set_xlim([np.min(kxmlarr),np.max(kxmlarr)])
-    #ax.set_ylim([2.15,2.30])
-    ax.set_ylim([np.min(omlist/eV*hbar),np.max(omlist/eV*hbar)])
-    ax.set_xticks([0, kxmaplist[len(k0Mlist)-1], kxmaplist[len(k0Mlist)+len(kMK1list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)+len(kK2Mlist)-1]])
-    ax.set_xticklabels(['Γ', 'M', 'K', 'Γ', 'K\'','M'])
-    f.colorbar(sc)
-    
-    pdf.savefig(f)
-    
-    
-    # In[ ]:
-    
-    f, ax = plt.subplots(1, figsize=(20,15))
-    sc = ax.scatter(kxmlarr, omlist/eV*hbar, c = np.sqrt(minsvTElistarr[...,minN]), s =40, lw=0)
-    ax.plot(kxmaplist, np.linalg.norm(klist,axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist+B1, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist+B2, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist-B2, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist-B1, axis=-1)*cdn/eV*hbar, '-',
-           kxmaplist, np.linalg.norm(klist+B2-B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-B2+B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-B2-B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist+B2+B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B2, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B2-B1, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B1-B2, axis=-1)*cdn/eV*hbar, '-',
-            kxmaplist, np.linalg.norm(klist-2*B1-2*B2, axis=-1)*cdn/eV*hbar, '-',
-    #        kxmaplist, np.linalg.norm(klist+2*B2-B1, axis=-1)*cdn, '-',
-    #        kxmaplist, np.linalg.norm(klist+2*B1-B2, axis=-1)*cdn, '-',
-           )
-    ax.set_xlim([np.min(kxmlarr),np.max(kxmlarr)])
-    #ax.set_ylim([2.15,2.30])
-    ax.set_ylim([np.min(omlist/eV*hbar),np.max(omlist/eV*hbar)])
-    ax.set_xticks([0, kxmaplist[len(k0Mlist)-1], kxmaplist[len(k0Mlist)+len(kMK1list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)+len(kK2Mlist)-1]])
-    ax.set_xticklabels(['Γ', 'M', 'K', 'Γ', 'K\'','M'])
-    f.colorbar(sc)
-    
-    pdf.savefig(f)
-pdf.close()
-
-if scp_dest:
-    subprocess.run(['scp', pdfout, scp_dest])
-    if svdout:
-        subprocess.run(['scp', svdout, scp_dest])
-
-print(time.strftime("%H.%M:%S",time.gmtime(time.time()-begtime)))

misc/dispersion2D-SVD.py

@@ -1,403 +0,0 @@
-#!/usr/bin/env python3
-
-
-import argparse, re, random, string
-import subprocess
-from scipy.constants import hbar, e as eV, pi, c
-
-def make_action_sharedlist(opname, listname):
-    class opAction(argparse.Action):
-        def __call__(self, parser, args, values, option_string=None):
-            if (not hasattr(args, listname)) or getattr(args, listname) is None:
-                setattr(args, listname, list())
-            getattr(args,listname).append((opname, values))
-    return opAction
-
-parser = argparse.ArgumentParser()
-#TODO? použít type=argparse.FileType('r') ?
-parser.add_argument('--TMatrix', action='store', required=True, help='Path to TMatrix file')
-#parser.add_argument('--griddir', action='store', required=True, help='Path to the directory with precalculated translation operators')
-parser.add_argument('--output_prefix', action='store', required=True, help='Prefix to the pdf and/or npz output (will be appended frequency and hexside)')
-#sizepar = parser.add_mutually_exclusive_group(required=True)
-parser.add_argument('--hexside', action='store', type=float, required=True, help='Lattice hexagon size length')
-parser.add_argument('--output', action='store', help='Path to output PDF')
-parser.add_argument('--store_SVD', action='store_false', help='If specified without --SVD_output, it will save the data in a file named as the PDF output, but with .npz extension instead')
-parser.add_argument('--plot_TMatrix', action='store_true', help='Visualise TMatrix on the first page of the output')
-#parser.add_argument('--SVD_output', action='store', help='Path to output singular value decomposition result')
-parser.add_argument('--nSV', action='store', metavar='N', type=int, default=1, help='Store and draw N minimun singular values')
-parser.add_argument('--maxlayer', action='store', type=int, default=100, help='How far to sum the lattice points to obtain the dispersion')
-parser.add_argument('--scp_to', action='store', metavar='N', type=str, help='SCP the output files to a given destination')
-parser.add_argument('--background_permittivity', action='store', type=float, default=1., help='Background medium relative permittivity (default 1)')
-parser.add_argument('--eVfreq', action='store', required=True, type=float, help='Frequency in eV')
-parser.add_argument('--kdensity', action='store', type=int, default=33, help='Number of k-points per x-axis segment')
-parser.add_argument('--lMax', action='store', type=int, help='Override lMax from the TMatrix file')
-#TODO some more sophisticated x axis definitions
-parser.add_argument('--gaussian', action='store', type=float, metavar='σ', help='Use a gaussian envelope for weighting the interaction matrix contributions (depending on the distance), measured in unit cell lengths (?) FIxME).')
-popgrp=parser.add_argument_group(title='Operations')
-popgrp.add_argument('--tr', dest='ops', action=make_action_sharedlist('tr', 'ops'), default=list()) # the default value for dest can be set once
-popgrp.add_argument('--tr0', dest='ops', action=make_action_sharedlist('tr0', 'ops'))
-popgrp.add_argument('--tr1', dest='ops', action=make_action_sharedlist('tr1', 'ops'))
-popgrp.add_argument('--sym', dest='ops', action=make_action_sharedlist('sym', 'ops'))
-popgrp.add_argument('--sym0', dest='ops', action=make_action_sharedlist('sym0', 'ops'))
-popgrp.add_argument('--sym1', dest='ops', action=make_action_sharedlist('sym1', 'ops'))
-#popgrp.add_argument('--mult', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult', 'ops'))
-#popgrp.add_argument('--mult0', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult0', 'ops'))
-#popgrp.add_argument('--mult1', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult1', 'ops'))
-popgrp.add_argument('--multl', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl', 'ops'))
-popgrp.add_argument('--multl0', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl0', 'ops'))
-popgrp.add_argument('--multl1', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl1', 'ops'))
-parser.add_argument('--frequency_multiplier', action='store', type=float, default=1., help='Multiplies the frequencies in the TMatrix file by a given factor.')
-# TODO enable more flexible per-sublattice specification
-pargs=parser.parse_args()
-print(pargs)
-
-maxlayer=pargs.maxlayer
-hexside=pargs.hexside
-eVfreq = pargs.eVfreq
-freq = eVfreq*eV/hbar
-
-TMatrix_file = pargs.TMatrix
-pdfout = pargs.output if pargs.output else (
-	'%s_%dnm_%.4f.pdf' % (pargs.output_prefix,hexside/1e-9,eVfreq) if pargs.output_prefix else
-	(''.join(random.choice(string.ascii_uppercase + string.digits) for _ in range(10)) + '.pdf'))
-print(pdfout)
-if(pargs.store_SVD):
-    if re.search('.pdf$', pdfout):
-        svdout = re.sub('.pdf$', r'.npz', pdfout)
-    else:
-        svdout = pdfout + '.npz'
-else:
-     svdout = None
-
-
-epsilon_b = pargs.background_permittivity #2.3104
-gaussianSigma = pargs.gaussian if pargs.gaussian else None # hexside * 222 / 7
-interpfreqfactor = pargs.frequency_multiplier
-scp_dest = pargs.scp_to if pargs.scp_to else None
-kdensity = pargs.kdensity
-svn = pargs.nSV
-
-# TODO multiplier operation definitions and parsing
-#factor13inc = 10
-#factor13scat=10
-
-ops = list()
-opre = re.compile('(tr|sym|copy|multl|mult)(\d*)')
-for oparg in pargs.ops:
-    opm = opre.match(oparg[0])
-    if opm:
-        ops.append(((opm.group(2),) if opm.group(2) else (0,1), opm.group(1), oparg[1]))
-    else:
-        raise # should not happen
-print(ops)
-
-#ops = (
-#    # co, typ operace (symetrizace / transformace / kopie), specifikace (operace nebo zdroj), 
-#    # co: 0, 1, (0,1), (0,), (1,), #NI: 'all'
-#    # typ operace: sym, tr, copy
-#    # specifikace:
-#    # sym, tr: 'σ_z', 'σ_y', 'C2'; sym: 'C3', 
-#    # copy: 0, 1 (zdroj)
-#    ((0,1), 'sym', 'σ_z'),
-#    #((0,1), 'sym', 'σ_x'),
-#    #((0,1), 'sym', 'σ_y'),
-#    ((0,1), 'sym', 'C3'),
-#    ((1), 'tr', 'C2'),
-#
-#)
-
-# -----------------finished basic CLI parsing (except for op arguments) ------------------
-import time
-begtime=time.time()
-
-from matplotlib.path import Path
-import matplotlib.patches as patches
-import matplotlib.pyplot as plt
-import qpms
-import numpy as np
-import os, sys, warnings, math
-from matplotlib import pyplot as plt
-from matplotlib.backends.backend_pdf import PdfPages
-from scipy import interpolate
-nx = None
-s3 = math.sqrt(3)
-
-
-
-pdf = PdfPages(pdfout)
-
-# In[3]:
-
-# specifikace T-matice zde
-cdn = c/ math.sqrt(epsilon_b)
-TMatrices_orig, freqs_orig, freqs_weirdunits_orig, lMaxTM = qpms.loadScuffTMatrices(TMatrix_file)
-lMax = lMaxTM
-if pargs.lMax:
-    lMax = pargs.lMax if pargs.lMax else lMaxTM    
-my, ny = qpms.get_mn_y(lMax)
-nelem = len(my)
-if pargs.lMax: #force commandline specified lMax
-    TMatrices_orig = TMatrices_orig[...,0:nelem,:,0:nelem]
-
-TMatrices = np.array(np.broadcast_to(TMatrices_orig[:,nx,:,:,:,:],(len(freqs_orig),2,2,nelem,2,nelem)) )
-
-#TMatrices[:,:,:,:,:,ny==3] *= factor13inc
-#TMatrices[:,:,:,ny==3,:,:] *= factor13scat
-xfl = qpms.xflip_tyty(lMax)
-yfl = qpms.yflip_tyty(lMax)
-zfl = qpms.zflip_tyty(lMax)
-c2rot = qpms.apply_matrix_left(qpms.yflip_yy(3),qpms.xflip_yy(3),-1)
-
-reCN = re.compile('(\d*)C(\d+)')
-#TODO C nekonečno
-
-for op in ops:
-    if op[0] == 'all':
-        targets = (0,1)
-    elif isinstance(op[0],int):
-        targets = (op[0],)
-    else:
-        targets = op[0]
-        
-    if op[1] == 'sym':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'C2': # special case of the latter
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1))/2                
-        elif mCN:
-            rotN = int(mCN.group(2))
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                for i in range(rotN):
-                    rotangle = 2*np.pi*i / rotN
-                    rot =  qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle]))
-                    rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle]))
-                    TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-                TMatrices[:,t] = np.sum(TMatrix_contribs, axis=0) / rotN
-        else:
-            raise
-    elif op[1] == 'tr':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'C2':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1)       
-        elif mCN:
-            rotN = int(mCN.group(2))
-            power = int(mCN.group(1)) if mCN.group(1) else 1
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                rotangle = 2*np.pi*power/rotN
-                rot = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,rotangle]))
-                rotinv = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,-rotangle]))
-                TMatrices[:,t] = qpms.apply_matrix_left(rot, qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-        else:
-            raise
-    elif op[1] == 'copy':
-        raise # not implemented
-    elif op[1] == 'mult':
-        raise # not implemented
-    elif op[1] == 'multl':
-        incy = np.full((nelem,), False, dtype=bool)
-        for incl in op[2][0].split(','):
-            l = int(incl)
-            incy += (l == ny)
-        scaty = np.full((nelem,), False, dtype=bool)
-        for scatl in op[2][1].split(','):
-            l = int(scatl)
-            scaty += (l == ny)
-        for t in targets:
-            TMatrices[np.ix_(np.arange(TMatrices.shape[0]),np.array([t]),np.array([0,1]),scaty,np.array([0,1]),incy)] *= float(op[2][2])
-    else:
-        raise #unknown operation; should not happen
-
-TMatrices_interp = interpolate.interp1d(freqs_orig*interpfreqfactor, TMatrices, axis=0, kind='linear',fill_value="extrapolate")
-
-
-
-# In[4]:
-if(pargs.plot_TMatrix):    
-    om = np.linspace(np.min(freqs_orig), np.max(freqs_orig),100)
-    TMatrix0ip = np.reshape(TMatrices_interp(om)[:,0], (len(om), 2*nelem*2*nelem))
-    f, axa = plt.subplots(2, 2, figsize=(15,15))
-    
-    #print(TMatrices.shape)
-    #plt.plot(om, TMatrices[:,0,0,0,0].imag,'r',om, TMatrices[:,0,0,0,0].real,'r--',om, TMatrices[:,0,2,0,2].imag,'b',om, TMatrices[:,0,2,0,2].real,'b--'))
-            
-    ax = axa[0,0]
-    ax2 = ax.twiny()
-    ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar])
-    ax.plot(
-             om, TMatrix0ip[:,:].imag,'-',om, TMatrix0ip[:,:].real,'--',
-    )
-    ax = axa[0,1]
-    ax2 = ax.twiny()
-    ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar])
-    ax.plot(
-             om, abs(TMatrix0ip[:,:]),'-'
-    )
-    ax.set_yscale('log')
-    
-    ax = axa[1,1]
-    ax2 = ax.twiny()
-    ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar])
-    ax.plot(
-             om, np.unwrap(np.angle(TMatrix0ip[:,:]),axis=0),'-'
-    )
-
-    ax = axa[1,0]
-    ax.text(0.5,0.5,str(pargs).replace(',',',\n'),horizontalalignment='center',verticalalignment='center',transform=ax.transAxes)
-    pdf.savefig(f)
-
-
-# In[ ]:
-
-'''
-#kdensity = 66 #defined from cl arguments
-bz_0 = np.array((0,0,0.,))
-bz_K1 = np.array((1.,0,0))*4*np.pi/3/hexside/s3
-bz_K2 = np.array((1./2.,s3/2,0))*4*np.pi/3/hexside/s3
-bz_M = np.array((3./4, s3/4,0))*4*np.pi/3/hexside/s3
-k0Mlist = bz_0 + (bz_M-bz_0) * np.linspace(0,1,kdensity)[:,nx]
-kMK1list = bz_M + (bz_K1-bz_M) * np.linspace(0,1,kdensity)[:,nx]
-kK10list = bz_K1 + (bz_0-bz_K1) * np.linspace(0,1,kdensity)[:,nx]
-k0K2list = bz_0 + (bz_K2-bz_0) * np.linspace(0,1,kdensity)[:,nx]
-kK2Mlist = bz_K2 + (bz_M-bz_K2) * np.linspace(0,1,kdensity)[:,nx]
-B1 = 2* bz_K1 - bz_K2
-B2 = 2* bz_K2 - bz_K1
-klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0)
-kxmaplist = np.concatenate((np.array([0]),np.cumsum(np.linalg.norm(np.diff(klist, axis=0), axis=-1))))
-'''
-klist = qpms.generate_trianglepoints(kdensity, v3d=True, include_origin=True)*3*math.pi/(3*kdensity*hexside)
-TMatrices_om = TMatrices_interp(freq)
-
-svdres = qpms.hexlattice_zsym_getSVD(lMax=lMax, TMatrices_om=TMatrices_om, epsilon_b=epsilon_b, hexside=hexside, maxlayer=maxlayer,
-        omega=freq, klist=klist, gaussianSigma=gaussianSigma, onlyNmin=(0 if svdout else svn))
-if svdout:
-   ((svUfullTElist, svSfullTElist, svVfullTElist), (svUfullTMlist, svSfullTMlist, svVfullTMlist)) = svdres
-   (minsvElist, minsvTMlist) = (svSfullTElist[...,-svn:], svSfullTMlist[...,-svn:])
-else:
-    minsvTElist, minsvTMlist = svdres
-
-
-
-''' The new pretty diffracted order drawing '''
-maxlayer_reciprocal=4 
-cdn = c/ math.sqrt(epsilon_b)
-bz_0 = np.array((0,0,))
-bz_K1 = np.array((1.,0))*4*np.pi/3/hexside/s3
-bz_K2 = np.array((1./2.,s3/2))*4*np.pi/3/hexside/s3
-bz_M = np.array((3./4, s3/4))*4*np.pi/3/hexside/s3
-
-# reciprocal lattice basis
-B1 = 2* bz_K1 - bz_K2
-B2 = 2* bz_K2 - bz_K1
-
-if svdout:
-    np.savez(svdout, omega = freq, klist = klist, bzpoints = np.array([bz_0, bz_K1, bz_K2, bz_M, B1, B2]), 
-                     uTE = svUfullTElist,
-                     vTE = svVfullTElist,
-                     sTE = svSfullTElist,
-                     uTM = svUfullTMlist,
-                     vTM = svVfullTMlist,
-                     sTM = svSfullTMlist,
-    )
- 
-k2density = 100
-k0Mlist = bz_0 + (bz_M-bz_0) * np.linspace(0,1,k2density)[:,nx]
-kMK1list = bz_M + (bz_K1-bz_M) * np.linspace(0,1,k2density)[:,nx]
-kK10list = bz_K1 + (bz_0-bz_K1) * np.linspace(0,1,k2density)[:,nx]
-k0K2list = bz_0 + (bz_K2-bz_0) * np.linspace(0,1,k2density)[:,nx]
-kK2Mlist = bz_K2 + (bz_M-bz_K2) * np.linspace(0,1,k2density)[:,nx]
-k2list = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0)
-kxmaplist = np.concatenate((np.array([0]),np.cumsum(np.linalg.norm(np.diff(k2list, axis=0), axis=-1))))
-
-centers2=qpms.generate_trianglepoints(maxlayer_reciprocal, v3d = False, include_origin= True)*4*np.pi/3/hexside
-rot90 = np.array([[0,-1],[1,0]])
-centers2=np.dot(centers2,rot90)
-
-import matplotlib.pyplot as plt
-import matplotlib
-from matplotlib.path import Path
-import matplotlib.patches as patches
-cmap = matplotlib.cm.prism
-colormax = np.amax(np.linalg.norm(centers2,axis=0))
-
-
-# In[ ]:
-for minN in reversed(range(svn)):
-    f, axes = plt.subplots(1,3, figsize=(20,4.8))
-    ax = axes[0]
-    sc = ax.scatter(klist[:,0], klist[:,1], c = np.clip(np.abs(minsvTElist[:,minN]),0,1), lw=0)
-    for center in centers2:
-        circle=plt.Circle((center[0],center[1]),omega/cdn, facecolor='none', edgecolor=cmap(np.linalg.norm(center)/colormax),lw=0.5)
-        ax.add_artist(circle)
-    verts = [(math.cos(math.pi*i/3)*4*np.pi/3/hexside/s3,math.sin(math.pi*i/3)*4*np.pi/3/hexside/s3) for i in range(6 +1)]
-    codes = [Path.MOVETO,Path.LINETO,Path.LINETO,Path.LINETO,Path.LINETO,Path.LINETO,Path.CLOSEPOLY,]
-    path = Path(verts, codes)
-    patch = patches.PathPatch(path, facecolor='none', edgecolor='black',  lw=1)
-    ax.add_patch(patch)
-    ax.set_xticks([]) 
-    ax.set_yticks([]) 
-    ax.title.set_text('E in-plane ("TE")')
-    f.colorbar(sc,ax=ax)
-    
-    
-    ax = axes[1]
-    sc = ax.scatter(klist[:,0], klist[:,1], c = np.clip(np.abs(minsvTMlist[:,minN]),0,1), lw=0)
-    for center in centers2:
-        circle=plt.Circle((center[0],center[1]),omega/cdn, facecolor='none', edgecolor=cmap(np.linalg.norm(center)/colormax),lw=0.5)
-        ax.add_artist(circle)
-    verts = [(math.cos(math.pi*i/3)*4*np.pi/3/hexside/s3,math.sin(math.pi*i/3)*4*np.pi/3/hexside/s3) for i in range(6 +1)]
-    codes = [Path.MOVETO,Path.LINETO,Path.LINETO,Path.LINETO,Path.LINETO,Path.LINETO,Path.CLOSEPOLY,]
-    path = Path(verts, codes)
-    patch = patches.PathPatch(path, facecolor='none', edgecolor='black',  lw=1)
-    ax.add_patch(patch)
-    ax.set_xticks([]) 
-    ax.set_yticks([])
-    ax.title.set_text('E perpendicular ("TM")')
-    f.colorbar(sc,ax=ax)
-
-    ax = axes[2]
-    for center in centers2:
-        ax.plot(kxmaplist, np.linalg.norm(k2list-center,axis=-1)*cdn, '-', color=cmap(np.linalg.norm(center)/colormax))
-
-    #ax.set_xlim([np.min(kxmlarr),np.max(kxmlarr)])
-    #ax.set_ylim([np.min(omegalist),np.max(omegalist)])
-    xticklist = [0, kxmaplist[len(k0Mlist)-1], kxmaplist[len(k0Mlist)+len(kMK1list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)+len(kK2Mlist)-1]]
-    ax.set_xticks(xticklist)
-    for xt in xticklist:
-        ax.axvline(xt, ls='dotted', lw=0.3,c='k')
-    ax.set_xticklabels(['Γ', 'M', 'K', 'Γ', 'K\'','M'])
-    ax.axhline(omega, c='black')
-    ax.set_ylim([0,5e15])
-    ax2 = ax.twinx()
-    ax2.set_ylim([ax.get_ylim()[0]/eV*hbar,ax.get_ylim()[1]/eV*hbar])
-   
-    pdf.savefig(f)
-    
-pdf.close()
-
-if scp_dest:
-    subprocess.run(['scp', pdfout, scp_dest])
-    if svdout:
-        subprocess.run(['scp', svdout, scp_dest])
-
-print(time.strftime("%H.%M:%S",time.gmtime(time.time()-begtime)))

misc/dispersion_hex_chunks.py

@@ -1,239 +0,0 @@
-#!/usr/bin/env python3
-
-import argparse, re, random, string
-import subprocess
-from scipy.constants import hbar, e as eV, pi, c
-
-def make_action_sharedlist(opname, listname):
-    class opAction(argparse.Action):
-        def __call__(self, parser, args, values, option_string=None):
-            if (not hasattr(args, listname)) or getattr(args, listname) is None:
-                setattr(args, listname, list())
-            getattr(args,listname).append((opname, values))
-    return opAction
-
-parser = argparse.ArgumentParser()
-#TODO? použít type=argparse.FileType('r') ?
-parser.add_argument('--TMatrix', action='store', required=True, help='Path to TMatrix file')
-#parser.add_argument('--griddir', action='store', required=True, help='Path to the directory with precalculated translation operators')
-parser.add_argument('--output_prefix', action='store', required=True, help='Prefix to the npz output (will be appended frequency, hexside and chunkno)')
-#sizepar = parser.add_mutually_exclusive_group(required=True)
-parser.add_argument('--hexside', action='store', type=float, required=True, help='Lattice hexagon size length')
-parser.add_argument('--plot_TMatrix', action='store_true', help='Visualise TMatrix on the first page of the output')
-#parser.add_argument('--SVD_output', action='store', help='Path to output singular value decomposition result')
-parser.add_argument('--maxlayer', action='store', type=int, default=100, help='How far to sum the lattice points to obtain the dispersion')
-parser.add_argument('--scp_to', action='store', metavar='N', type=str, help='SCP the output files to a given destination')
-parser.add_argument('--background_permittivity', action='store', type=float, default=1., help='Background medium relative permittivity (default 1)')
-parser.add_argument('--eVfreq', action='store', required=True, type=float, help='Frequency in eV')
-parser.add_argument('--kdensity', action='store', type=int, default=33, help='Number of k-points per x-axis segment')
-parser.add_argument('--chunklen', action='store', type=int, default=1000, help='Number of k-points per output file (default 1000)')
-parser.add_argument('--lMax', action='store', type=int, help='Override lMax from the TMatrix file')
-#TODO some more sophisticated x axis definitions
-parser.add_argument('--gaussian', action='store', type=float, metavar='σ', help='Use a gaussian envelope for weighting the interaction matrix contributions (depending on the distance), measured in unit cell lengths (?) FIxME).')
-parser.add_argument('--verbose', '-v', action='count', help='Be verbose (about computation times, mostly)')
-popgrp=parser.add_argument_group(title='Operations')
-popgrp.add_argument('--tr', dest='ops', action=make_action_sharedlist('tr', 'ops'), default=list()) # the default value for dest can be set once
-popgrp.add_argument('--tr0', dest='ops', action=make_action_sharedlist('tr0', 'ops'))
-popgrp.add_argument('--tr1', dest='ops', action=make_action_sharedlist('tr1', 'ops'))
-popgrp.add_argument('--sym', dest='ops', action=make_action_sharedlist('sym', 'ops'))
-popgrp.add_argument('--sym0', dest='ops', action=make_action_sharedlist('sym0', 'ops'))
-popgrp.add_argument('--sym1', dest='ops', action=make_action_sharedlist('sym1', 'ops'))
-#popgrp.add_argument('--mult', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult', 'ops'))
-#popgrp.add_argument('--mult0', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult0', 'ops'))
-#popgrp.add_argument('--mult1', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult1', 'ops'))
-popgrp.add_argument('--multl', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl', 'ops'))
-popgrp.add_argument('--multl0', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl0', 'ops'))
-popgrp.add_argument('--multl1', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl1', 'ops'))
-parser.add_argument('--frequency_multiplier', action='store', type=float, default=1., help='Multiplies the frequencies in the TMatrix file by a given factor.')
-# TODO enable more flexible per-sublattice specification
-pargs=parser.parse_args()
-print(pargs)
-
-maxlayer=pargs.maxlayer
-hexside=pargs.hexside
-eVfreq = pargs.eVfreq
-freq = eVfreq*eV/hbar
-verbose=pargs.verbose
-
-TMatrix_file = pargs.TMatrix
-
-epsilon_b = pargs.background_permittivity #2.3104
-gaussianSigma = pargs.gaussian if pargs.gaussian else None # hexside * 222 / 7
-interpfreqfactor = pargs.frequency_multiplier
-scp_dest = pargs.scp_to if pargs.scp_to else None
-kdensity = pargs.kdensity
-chunklen = pargs.chunklen
-
-ops = list()
-opre = re.compile('(tr|sym|copy|multl|mult)(\d*)')
-for oparg in pargs.ops:
-    opm = opre.match(oparg[0])
-    if opm:
-        ops.append(((opm.group(2),) if opm.group(2) else (0,1), opm.group(1), oparg[1]))
-    else:
-        raise # should not happen
-print(ops)
-
-
-# -----------------finished basic CLI parsing (except for op arguments) ------------------
-from qpms.timetrack import _time_b, _time_e
-btime=_time_b(verbose)
-
-import qpms
-import numpy as np
-import os, sys, warnings, math
-from scipy import interpolate
-nx = None
-s3 = math.sqrt(3)
-
-
-# specifikace T-matice zde
-cdn = c/ math.sqrt(epsilon_b)
-TMatrices_orig, freqs_orig, freqs_weirdunits_orig, lMaxTM = qpms.loadScuffTMatrices(TMatrix_file)
-lMax = lMaxTM
-if pargs.lMax:
-    lMax = pargs.lMax if pargs.lMax else lMaxTM    
-my, ny = qpms.get_mn_y(lMax)
-nelem = len(my)
-if pargs.lMax: #force commandline specified lMax
-    TMatrices_orig = TMatrices_orig[...,0:nelem,:,0:nelem]
-
-TMatrices = np.array(np.broadcast_to(TMatrices_orig[:,nx,:,:,:,:],(len(freqs_orig),2,2,nelem,2,nelem)) )
-
-#TMatrices[:,:,:,:,:,ny==3] *= factor13inc
-#TMatrices[:,:,:,ny==3,:,:] *= factor13scat
-xfl = qpms.xflip_tyty(lMax)
-yfl = qpms.yflip_tyty(lMax)
-zfl = qpms.zflip_tyty(lMax)
-c2rot = qpms.apply_matrix_left(qpms.yflip_yy(3),qpms.xflip_yy(3),-1)
-
-reCN = re.compile('(\d*)C(\d+)')
-#TODO C nekonečno
-
-for op in ops:
-    if op[0] == 'all':
-        targets = (0,1)
-    elif isinstance(op[0],int):
-        targets = (op[0],)
-    else:
-        targets = op[0]
-        
-    if op[1] == 'sym':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'C2': # special case of the latter
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1))/2                
-        elif mCN:
-            rotN = int(mCN.group(2))
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                for i in range(rotN):
-                    rotangle = 2*np.pi*i / rotN
-                    rot =  qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle]))
-                    rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle]))
-                    TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-                TMatrices[:,t] = np.sum(TMatrix_contribs, axis=0) / rotN
-        else:
-            raise
-    elif op[1] == 'tr':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'C2':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1)       
-        elif mCN:
-            rotN = int(mCN.group(2))
-            power = int(mCN.group(1)) if mCN.group(1) else 1
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                rotangle = 2*np.pi*power/rotN
-                rot = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,rotangle]))
-                rotinv = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,-rotangle]))
-                TMatrices[:,t] = qpms.apply_matrix_left(rot, qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-        else:
-            raise
-    elif op[1] == 'copy':
-        raise # not implemented
-    elif op[1] == 'mult':
-        raise # not implemented
-    elif op[1] == 'multl':
-        incy = np.full((nelem,), False, dtype=bool)
-        for incl in op[2][0].split(','):
-            l = int(incl)
-            incy += (l == ny)
-        scaty = np.full((nelem,), False, dtype=bool)
-        for scatl in op[2][1].split(','):
-            l = int(scatl)
-            scaty += (l == ny)
-        for t in targets:
-            TMatrices[np.ix_(np.arange(TMatrices.shape[0]),np.array([t]),np.array([0,1]),scaty,np.array([0,1]),incy)] *= float(op[2][2])
-    else:
-        raise #unknown operation; should not happen
-
-TMatrices_interp = interpolate.interp1d(freqs_orig*interpfreqfactor, TMatrices, axis=0, kind='linear',fill_value="extrapolate")
-
-klist_full = qpms.generate_trianglepoints(kdensity, v3d=True, include_origin=True)*3*math.pi/(3*kdensity*hexside)
-TMatrices_om = TMatrices_interp(freq)
-
-chunkn = math.ceil(klist_full.shape[0] / chunklen)
-
-if verbose:
-    print('Evaluating %d k-points in %d chunks' % (klist_full.shape[0], chunkn), file = sys.stderr)
-    sys.stderr.flush()
-
-metadata = np.array({
-		'lMax' : lMax,
-                'maxlayer' : maxlayer,
-                'gaussianSigma' : gaussianSigma,
-                'epsilon_b' : epsilon_b,
-		'hexside' : hexside,
-                'chunkn' : chunkn,
-                'TMatrix_file' : TMatrix_file,
-                'ops' : ops,
-                })
-
-for chunki in range(chunkn):
-    svdout = '%s_%dnm_%.4f_c%03d.npz' % (pargs.output_prefix, hexside/1e-9, eVfreq, chunki)
-
-    klist = klist_full[chunki * chunklen : (chunki + 1) * chunklen]
-
-    svdres = qpms.hexlattice_zsym_getSVD(lMax=lMax, TMatrices_om=TMatrices_om, epsilon_b=epsilon_b, hexside=hexside, maxlayer=maxlayer,
-            omega=freq, klist=klist, gaussianSigma=gaussianSigma, onlyNmin=False, verbose=verbose)
-
-    #((svUfullTElist, svSfullTElist, svVfullTElist), (svUfullTMlist, svSfullTMlist, svVfullTMlist)) = svdres
-
-    np.savez(svdout, omega = freq, klist = klist,
-            metadata=metadata,
-                     uTE = svdres[0][0],
-                     vTE = svdres[0][2],
-                     sTE = svdres[0][1],
-                     uTM = svdres[1][0],
-                     vTM = svdres[1][2],
-                     sTM = svdres[1][1],
-
-    )
-    svdres=None
-
-    if scp_dest:
-        if svdout:
-            subprocess.run(['scp', svdout, scp_dest])
-
-_time_e(btime, verbose)
-#print(time.strftime("%H.%M:%S",time.gmtime(time.time()-begtime)))

misc/eval_TMatrices_generator_vs_scuffNotFixed_vs_scuffFixed2-spheres.ipynb

@@ -0,0 +1,719 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import qpms\n",
+    "import warnings\n",
+    "from qpms.cybspec import BaseSpec\n",
+    "from qpms.cytmatrices import CTMatrix, TMatrixGenerator, TMatrixInterpolator\n",
+    "from qpms.qpms_c import Particle, pgsl_ignore_error\n",
+    "from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude\n",
+    "from qpms.cycommon import DebugFlags, dbgmsg_enable\n",
+    "from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar\n",
+    "import scipy.constants as sci\n",
+    "eh = eV/hbar"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#TODO\n",
+    "period = 520e-9\n",
+    "a1 = np.array([0,period])                                 \n",
+    "a2 = np.array([period,0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Particle positions\n",
+    "orig_x = [0]\n",
+    "orig_y = [0]\n",
+    "orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "period = 0.52\n",
+    "refractive_index = 1.52 # for background medium\n",
+    "height = 50e-9 # Particle height\n",
+    "radius = 50e-9 # Particle radius\n",
+    "medium = EpsMu(refractive_index**2) # non-lossy background medium with constant refr. index #OK\n",
+    "# global symmetry group of the system\n",
+    "#sym = FinitePointGroup(point_group_info['D4h'])\n",
+    "omega = 1.58*eh\n",
+    "metal = lorentz_drude['Ag']\n",
+    "kx_lim = np.array([-0.2, 0.2], dtype=float)\n",
+    "N=501"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(7.59633723939313, 8.305328715069821, 7.94387469344152, 8.001475225494097)"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "omega_scuff_min=1.5*eh/3e14\n",
+    "omega_scuff_max=1.64*eh/3e14\n",
+    "omega_scuff=omega/3e14\n",
+    "omega_scuff_slr=(2*np.pi*sci.c/(1.52*0.52e-6))/3e14\n",
+    "omega_scuff_min, omega_scuff_max, omega_scuff_slr, omega_scuff"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bspec = BaseSpec(lMax = 1)\n",
+    "\n",
+    "tmfile_scuffOld = '/home/javier/tmatrices/sphereAg_50nm_oldScuff.TMatrix'\n",
+    "tmfile_scuffNew = '/home/javier/tmatrices/sphere50nm_newScuff.TMatrix'\n",
+    "interp_old = TMatrixInterpolator(tmfile_scuffOld, bspec, atol=1e-8)  \n",
+    "interp_new = TMatrixInterpolator(tmfile_scuffNew, bspec, atol=1e-8)  \n",
+    "tmscuff_not_fixed = interp_old(omega)\n",
+    "tmscuff_bugfixed = interp_new(omega)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tmgen = TMatrixGenerator.sphere(medium, metal, radius)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tmgen_omega=tmgen(bspec,omega)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[-0.07824951+0.25215549j,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ],\n",
+       "       [ 0.        +0.j        , -0.07824951+0.25215549j,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ],\n",
+       "       [ 0.        +0.j        ,  0.        +0.j        , -0.07824951+0.25215549j,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ],\n",
+       "       [ 0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        , -0.00083788-0.01420874j,  0.        +0.j        ,  0.        +0.j        ],\n",
+       "       [ 0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        , -0.00083788-0.01420874j,  0.        +0.j        ],\n",
+       "       [ 0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        ,  0.        +0.j        , -0.00083788-0.01420874j]])"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tmgen_omega.as_ndarray() # T-Matrix from generator"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[-4.70886671e-03+1.79440815e-02j,  1.60098226e-13+4.20092462e-13j,  2.26455777e-07+3.98932962e-07j, -2.13258227e-14-6.01930824e-14j,  7.66251504e-08-1.32539814e-08j,\n",
+       "        -7.76488937e-14+1.08532726e-13j],\n",
+       "       [-4.41531068e-13+9.81757019e-14j, -4.70582367e-03+1.79389513e-02j, -1.60702588e-13-4.19762769e-13j,  6.32372612e-08+4.71302619e-08j, -2.36039655e-14+1.00983241e-13j,\n",
+       "         7.76590838e-08-1.38092126e-08j],\n",
+       "       [-4.58579591e-07-7.49053314e-09j,  4.41175187e-13-9.87457125e-14j, -4.70886672e-03+1.79440815e-02j,  2.13790755e-14+1.31812722e-13j,  6.25535562e-08+4.61875295e-08j,\n",
+       "         4.59276044e-14-4.47400043e-14j],\n",
+       "       [ 4.93366461e-14-4.29235249e-14j, -6.94450011e-09-1.60278760e-08j, -7.79609985e-14+1.07845028e-13j, -3.03166095e-05-2.01474828e-03j, -2.39253108e-13-1.34944425e-13j,\n",
+       "         1.16328171e-08+6.36863105e-09j],\n",
+       "       [ 8.21008790e-09-1.53591010e-08j, -2.36580203e-14+1.00878213e-13j, -5.41800099e-09-1.65573897e-08j,  2.26431323e-13-1.55248143e-13j, -3.03231670e-05-2.01493037e-03j,\n",
+       "         2.38800352e-13+1.35401679e-13j],\n",
+       "       [ 2.18731933e-14+1.31428484e-13j,  7.13657440e-09-1.65412452e-08j, -2.48667583e-14-6.12974376e-14j, -1.11447700e-08+7.19733229e-09j, -2.26916383e-13+1.54810715e-13j,\n",
+       "        -3.03166170e-05-2.01474828e-03j]])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tmscuff_not_fixed.as_ndarray() # T-Matrix of not fixed version of Scuff-EM"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[-9.43033280e-02+3.59361755e-01j,  3.20658236e-12+8.41416904e-12j,  5.13892659e-06+8.57797510e-06j, -4.28949536e-13-1.20456867e-12j,  1.41239218e-06-2.46862181e-07j,\n",
+       "        -1.55480479e-12+2.17400571e-12j],\n",
+       "       [-8.84386127e-12+1.96169624e-12j, -9.42395846e-02+3.59248336e-01j, -3.22166474e-12-8.40342496e-12j,  1.16868119e-06+8.68484583e-07j, -4.72874254e-13+2.02296639e-12j,\n",
+       "         1.43308826e-06-2.58864855e-07j],\n",
+       "       [-9.99885677e-06+6.63229466e-08j,  8.83605486e-12-1.97841571e-12j, -9.43033282e-02+3.59361755e-01j,  4.27888728e-13+2.63976219e-12j,  1.15544356e-06+8.48824647e-07j,\n",
+       "         9.21093604e-13-8.94225073e-13j],\n",
+       "       [ 9.85267406e-13-8.59818272e-13j, -1.43866720e-06+2.57952214e-07j, -1.56233879e-12+2.15974773e-12j, -6.07143255e-04-4.03488631e-02j, -4.79139425e-12-2.70322093e-12j,\n",
+       "         1.52945653e-07+8.36194839e-08j],\n",
+       "       [-1.15196465e-06-8.46913318e-07j, -4.73514628e-13+2.02574744e-12j, -1.40806670e-06+2.47097086e-07j,  4.53481568e-12-3.10854698e-12j, -6.07256494e-04-4.03513114e-02j,\n",
+       "         4.78231690e-12+2.71099900e-12j],\n",
+       "       [ 4.39050064e-13+2.63269196e-12j, -1.17350730e-06-8.70822943e-07j, -4.95069921e-13-1.22744130e-12j, -1.44529174e-07+9.78280211e-08j, -4.54412580e-12+3.10101417e-12j,\n",
+       "        -6.07143303e-04-4.03488631e-02j]])"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tmscuff_bugfixed.as_ndarray() # T-Matrix of FIXED version of Scuff-EM"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(matrix([[-9.43033280e-02+3.59361755e-01j,  3.20658236e-12+8.41416904e-12j],\n",
+       "         [-8.84386127e-12+1.96169624e-12j, -9.42395846e-02+3.59248336e-01j]]),\n",
+       " matrix([[-9.43033280e-02-3.59361755e-01j, -8.84386127e-12-1.96169624e-12j],\n",
+       "         [ 3.20658236e-12-8.41416904e-12j, -9.42395846e-02-3.59248336e-01j]]))"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#I play around with the different operations so everything is correct\n",
+    "tmscuffnew = tmscuff_bugfixed.as_ndarray()\n",
+    "tmscuffnew_mat = np.asmatrix(tmscuffnew)\n",
+    "tmscuffnew_dag = tmscuffnew_mat.getH()\n",
+    "tmscuffnew_mat[0:2,0:2], tmscuffnew_dag[0:2,0:2]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(matrix([[1, 0],\n",
+       "         [9, 4]]), matrix([[4, 9],\n",
+       "         [0, 1]]))"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A = np.matrix([[0,1],[2,3]])\n",
+    "B = np.matrix([[3,2],[1,0]])\n",
+    "AB = np.dot(A,B)\n",
+    "BA = np.dot(B,A)\n",
+    "AB,BA"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sum1new = np.dot(tmscuffnew_dag,tmscuffnew) #is this the right order? Regarding the above, yes it is.\n",
+    "sum2new = 0.5*tmscuffnew.__add__(tmscuffnew_dag) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "powermatrix_scuffnew = sum1new.__add__(sum2new) #powermatrix for bugfixed scuff"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Power matrix for NOT bugfixed scuff\n",
+    "tmscuffold = tmscuff_not_fixed.as_ndarray()\n",
+    "tmscuffold_mat = np.asmatrix(tmscuffold)\n",
+    "tmscuffold_dag = tmscuffold_mat.getH()\n",
+    "sum1old = np.dot(tmscuffold_dag,tmscuffold) #is this the right order? Regarding the above, yes it is.\n",
+    "sum2old = 0.5*tmscuffold.__add__(tmscuffold_dag)\n",
+    "\n",
+    "powermatrix_scuffold = sum1old.__add__(sum2old) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Power matrix for T matrix generator\n",
+    "tmscuffgen = tmgen_omega.as_ndarray()\n",
+    "tmscuffgen_mat = np.asmatrix(tmscuffgen)\n",
+    "tmscuffgen_dag = tmscuffgen_mat.getH()\n",
+    "sum1gen = np.dot(tmscuffgen_dag,tmscuffgen) #is this the right order? Regarding the above, yes it is.\n",
+    "sum2gen = 0.5*tmscuffgen.__add__(tmscuffgen_dag)\n",
+    "\n",
+    "powermatrix_scuffgen = sum1gen.__add__(sum2gen) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-0.008544129580638216+0j),\n",
+       " (-0.008544129580638216+0j),\n",
+       " (-0.008544129580638216+0j),\n",
+       " (-0.0006352854997266949+0j),\n",
+       " (-0.0006352854997266949+0j),\n",
+       " (-0.0006352854997266949+0j))"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#Power matrix of generator is diagonal and all its eigenvalues are negative:\n",
+    "powermatrix_scuffgen[0,0], powermatrix_scuffgen[1,1], powermatrix_scuffgen[2,2], powermatrix_scuffgen[3,3], powermatrix_scuffgen[4,4], powermatrix_scuffgen[5,5]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0.04373066071852283+0j),\n",
+       " (0.04370088172427582+0j),\n",
+       " (0.043730660553373296+0j),\n",
+       " (0.001021256123757952+0j),\n",
+       " (0.0010213406041430792+0j),\n",
+       " (0.0010212560750220145+0j))"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "powermatrix_scuffnew[0,0], powermatrix_scuffnew[1,1], powermatrix_scuffnew[2,2], powermatrix_scuffnew[3,3], powermatrix_scuffnew[4,4], powermatrix_scuffnew[5,5]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-0.004364703222422517+0j),\n",
+       " (-0.004361872918812184+0j),\n",
+       " (-0.004364703232328262+0j),\n",
+       " (-2.6256479824067564e-05+0j),\n",
+       " (-2.6262303053141142e-05+0j),\n",
+       " (-2.6256487319428013e-05+0j))"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "powermatrix_scuffold[0,0], powermatrix_scuffold[1,1], powermatrix_scuffold[2,2], powermatrix_scuffold[3,3], powermatrix_scuffold[4,4], powermatrix_scuffold[5,5]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-10.019160178833705-0j),\n",
+       " (-10.018834234211564-0j),\n",
+       " (-10.019160118257586-0j),\n",
+       " (-38.895393845668316-0j),\n",
+       " (-38.88998623145963-0j),\n",
+       " (-38.89538088616882-0j))"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#So! There is a fixed factor between the N/M elements of Scuff new and old:\n",
+    "powermatrix_scuffnew[0,0]/powermatrix_scuffold[0,0], powermatrix_scuffnew[1,1]/powermatrix_scuffold[1,1], powermatrix_scuffnew[2,2]/powermatrix_scuffold[2,2], powermatrix_scuffnew[3,3]/powermatrix_scuffold[3,3], powermatrix_scuffnew[4,4]/powermatrix_scuffold[4,4], powermatrix_scuffnew[5,5]/powermatrix_scuffold[5,5]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-5.118211317583541-0j),\n",
+       " (-5.11472600126595-0j),\n",
+       " (-5.118211298254535-0j),\n",
+       " (-1.6075545942687262-0j),\n",
+       " (-1.6076875744566317-0j),\n",
+       " (-1.60755451755371-0j))"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#And there is a fixed factor for new / generated as well! (hence also for old / generated)\n",
+    "powermatrix_scuffnew[0,0]/powermatrix_scuffgen[0,0], powermatrix_scuffnew[1,1]/powermatrix_scuffgen[1,1], powermatrix_scuffnew[2,2]/powermatrix_scuffgen[2,2], powermatrix_scuffnew[3,3]/powermatrix_scuffgen[3,3], powermatrix_scuffnew[4,4]/powermatrix_scuffgen[4,4], powermatrix_scuffnew[5,5]/powermatrix_scuffgen[5,5]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-1.60755451755371-0j), (-2.557363000632975+0j))"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "powermatrix_scuffnew[5,5]/powermatrix_scuffgen[5,5], powermatrix_scuffnew[1,1]/powermatrix_scuffgen[1,1]/2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((1.599227713011597e-16-0j),\n",
+       " (8.902299490051238e-14+0j),\n",
+       " (1.504486797691096e-21-0j))"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#Let's also calculate the determinants\n",
+    "detnew = powermatrix_scuffnew[0,0]*powermatrix_scuffnew[1,1]*powermatrix_scuffnew[2,2]*powermatrix_scuffnew[3,3]*powermatrix_scuffnew[4,4]*powermatrix_scuffnew[5,5]\n",
+    "detold = powermatrix_scuffold[0,0]*powermatrix_scuffold[1,1]*powermatrix_scuffold[2,2]*powermatrix_scuffold[3,3]*powermatrix_scuffold[4,4]*powermatrix_scuffold[5,5]\n",
+    "detgen = powermatrix_scuffgen[0,0]*powermatrix_scuffgen[1,1]*powermatrix_scuffgen[2,2]*powermatrix_scuffgen[3,3]*powermatrix_scuffgen[4,4]*powermatrix_scuffgen[5,5]\n",
+    "detgen, detnew, detold"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((1.5992277130116025e-16+0j),\n",
+       " (8.902299447416401e-14+2.6128569373609595e-39j),\n",
+       " (1.504486701753944e-21-2.892571608172536e-45j))"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.linalg.det(powermatrix_scuffgen), np.linalg.det(powermatrix_scuffnew), np.linalg.det(powermatrix_scuffold)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#We try to normalize the power matrix elements for each case with the corresponding determinants."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-53426597795433.88+0j),\n",
+       " (-53426597795433.88+0j),\n",
+       " (-53426597795433.88+0j),\n",
+       " (-3972451793812.1055+0j),\n",
+       " (-3972451793812.1055+0j),\n",
+       " (-3972451793812.1055+0j))"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#T-matrix generator: \n",
+    "powermatrix_scuffgen[0,0]/detgen, powermatrix_scuffgen[1,1]/detgen, powermatrix_scuffgen[2,2]/detgen, powermatrix_scuffgen[3,3]/detgen, powermatrix_scuffgen[4,4]/detgen, powermatrix_scuffgen[5,5]/detgen  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-2.901124309712079e+18+0j),\n",
+       " (-2.899243067806416e+18+0j),\n",
+       " (-2.901124316296214e+18+0j),\n",
+       " (-1.7452117136795634e+16+0j),\n",
+       " (-1.7455987711853198e+16+0j),\n",
+       " (-1.7452122118800434e+16+0j))"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#Not bugfixed Scuff-EM: \n",
+    "powermatrix_scuffold[0,0]/detold, powermatrix_scuffold[1,1]/detold, powermatrix_scuffold[2,2]/detold, powermatrix_scuffold[3,3]/detold, powermatrix_scuffold[4,4]/detold, powermatrix_scuffold[5,5]/detold  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((491228819782.9563+0j),\n",
+       " (490894310768.96173+0j),\n",
+       " (491228817927.8229+0j),\n",
+       " (11471823936.043226+0j),\n",
+       " (11472772908.667904+0j),\n",
+       " (11471823388.58987+0j))"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#New Scuff-EM: \n",
+    "powermatrix_scuffnew[0,0]/detnew, powermatrix_scuffnew[1,1]/detnew, powermatrix_scuffnew[2,2]/detnew, powermatrix_scuffnew[3,3]/detnew, powermatrix_scuffnew[4,4]/detnew, powermatrix_scuffnew[5,5]/detnew  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#It might make more sense to renormalize the electric and magnetic parts of the power matrices separately:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((13698.226641508763-0j),\n",
+       " (13698.226641508763-0j),\n",
+       " (13698.226641508763-0j),\n",
+       " (2477776.413504498-0j),\n",
+       " (2477776.413504498-0j),\n",
+       " (2477776.413504498-0j))"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#T-matrix generator:\n",
+    "detgen_el = powermatrix_scuffgen[0,0]*powermatrix_scuffgen[1,1]*powermatrix_scuffgen[2,2]\n",
+    "detgen_mag = powermatrix_scuffgen[3,3]*powermatrix_scuffgen[4,4]*powermatrix_scuffgen[5,5]\n",
+    "powermatrix_scuffgen[0,0]/detgen_el, powermatrix_scuffgen[1,1]/detgen_el, powermatrix_scuffgen[2,2]/detgen_el, powermatrix_scuffgen[3,3]/detgen_mag, powermatrix_scuffgen[4,4]/detgen_mag, powermatrix_scuffgen[5,5]/detgen_mag  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((52525.751093170744-0j),\n",
+       " (52491.69062780147-0j),\n",
+       " (52525.75121237855-0j),\n",
+       " (1450208903.6280527-0j),\n",
+       " (1450530534.6580672-0j),\n",
+       " (1450209317.614944-0j))"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#NOT bugfixed Scuff-EM:\n",
+    "detold_el = powermatrix_scuffold[0,0]*powermatrix_scuffold[1,1]*powermatrix_scuffold[2,2]\n",
+    "detold_mag = powermatrix_scuffold[3,3]*powermatrix_scuffold[4,4]*powermatrix_scuffold[5,5]\n",
+    "powermatrix_scuffold[0,0]/detold_el, powermatrix_scuffold[1,1]/detold_el, powermatrix_scuffold[2,2]/detold_el, powermatrix_scuffold[3,3]/detold_mag, powermatrix_scuffold[4,4]/detold_mag, powermatrix_scuffold[5,5]/detold_mag  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((523.2675016470721+0j),\n",
+       " (522.9111754524715+0j),\n",
+       " (523.2674996709441+0j),\n",
+       " (958726.5381294343+0j),\n",
+       " (958805.8459399715+0j),\n",
+       " (958726.4923775065+0j))"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#Bugfixed Scuff-EM:\n",
+    "detnew_el = powermatrix_scuffnew[0,0]*powermatrix_scuffnew[1,1]*powermatrix_scuffnew[2,2]\n",
+    "detnew_mag = powermatrix_scuffnew[3,3]*powermatrix_scuffnew[4,4]*powermatrix_scuffnew[5,5]\n",
+    "powermatrix_scuffnew[0,0]/detnew_el, powermatrix_scuffnew[1,1]/detnew_el, powermatrix_scuffnew[2,2]/detnew_el, powermatrix_scuffnew[3,3]/detnew_mag, powermatrix_scuffnew[4,4]/detnew_mag, powermatrix_scuffnew[5,5]/detnew_mag  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

misc/finiterectlat-constant-driving.py

@@ -0,0 +1,362 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser, make_dict_action, sslice, annotate_pdf_metadata
+figscale=3
+
+ap = ArgParser(['rectlattice2d_finite', 'single_particle', 'single_lMax', 'single_omega'])
+ap.add_argument("-k", '--wavevector', nargs=2, type=float, required=True, help='"Bloch" vector, modulating phase of the driving', metavar=('KX', 'KY'), default=(0., 0.))
+# ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+ap.add_argument("-g", "--save-gradually", action='store_true', help="saves the partial result after computing each irrep")
+ap.add_argument("-S", "--symmetry-adapted", default=None, help="Use a symmetry-adapted basis of a given point group instead of individual spherical harmonics")
+ap.add_argument("-d", "--ccd-distance", type=float, default=math.nan, help='Far-field "CCD" distance from the sample')
+ap.add_argument("-D", "--ccd-size", type=float, default=math.nan, help='Far-field "CCD" width and heighth')
+ap.add_argument("-R", "--ccd-resolution", type=int, default=101, help='Far-field "CCD" resolution')
+ap.add_argument("--xslice", default={None:None}, nargs=2, 
+        action=make_dict_action(argtype=sslice, postaction='append', first_is_key=True), 
+        )
+ap.add_argument("--yslice", default={None:None}, nargs=2, 
+        action=make_dict_action(argtype=sslice, postaction='append', first_is_key=True), 
+        )
+
+
+#ap.add_argument("--irrep", type=str, default="none", help="Irrep subspace (irrep index from 0 to 7, irrep label, or 'none' for no irrep decomposition")
+
+
+a=ap.parse_args()
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+Nx, Ny = a.size
+px, py = a.period
+
+particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
+if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
+defaultprefix = "cd_%s_p%gnmx%gnm_%dx%d_m%s_n%s_k_%g_%g_f%geV_L%d_micro-%s" % (
+    particlestr, px*1e9, py*1e9, Nx, Ny, str(a.material), str(a.background), a.wavevector[0], a.wavevector[1], a.eV, a.lMax, "SO3" if a.symmetry_adapted is None else a.symmetry_adapted)
+logging.info("Default file prefix: %s" % defaultprefix)
+
+import numpy as np
+import qpms
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix, TMatrixGenerator
+from qpms.qpms_c import Particle, qpms_library_version
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.cycommon import DebugFlags, dbgmsg_enable
+from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
+from qpms.symmetries import point_group_info
+eh = eV/hbar
+
+# Check slice ranges and generate all corresponding combinations
+slicepairs = []
+slicelabels = set(a.xslice.keys())  | set(a.yslice.keys())
+for label in slicelabels:
+    rowslices = a.xslice.get(label, None)
+    colslices = a.yslice.get(label, None)
+    # TODO check validity of the slices.
+    if rowslices is None:
+        rowslices = [slice(None, None, None)]
+    if colslices is None:
+        colslices = [slice(None, None, None)]
+    for rs in rowslices:
+        for cs in colslices:
+            slicepairs.append((rs, cs))
+
+def realdipfieldlabels(yp):
+    if yp == 0: return 'x'
+    if yp == 1: return 'y'
+    if yp == 2: return 'z'
+    raise ValueError
+def realdipfields(vecgrid, yp):
+    if yp == 1:
+        return vecgrid[...,0] + vecgrid[...,2]
+    if yp == 0:
+        return -1j*(vecgrid[...,0] - vecgrid[...,2])
+    if yp == 2:
+        return vecgrid[...,1]
+    raise ValueError
+
+def float_nicestr(x, tol=1e-5):
+    x = float(x)
+    if .5**2 - abs(x) < tol:
+        return(("-" if x < 0 else '+') + "2^{-2}")
+    else: 
+        return "%+.3g" % x
+
+def cplx_nicestr(x, tol=1e-5):
+    x = complex(x)
+    if x == 0:
+        return '0'
+    ret = ""
+    if x.real:
+        ret = ret + float_nicestr(x.real, tol)
+    if x.imag:
+        ret = ret + float_nicestr(x.imag, tol) + 'i'
+    if x.real and x.imag:
+        return '(' + ret + ')'
+    else:
+        return ret
+
+def cleanarray(a, atol=1e-10, copy=True):
+    a = np.array(a, copy=copy)
+    sieve = abs(a.real) < atol
+    a[sieve] = 1j * a[sieve].imag
+    sieve = abs(a.imag) < atol
+    a[sieve] = a[sieve].real
+    return a
+
+def nicerot(a, atol=1e-10, copy=True): #gives array a "nice" phase
+    a = np.array(a, copy=copy)
+    i = np.argmax(abs(a))
+    a = a / a[i] * abs(a[i])
+    return a
+
+dbgmsg_enable(DebugFlags.INTEGRATION)
+
+#Particle positions
+orig_x = (np.arange(Nx/2) + (0 if (Nx % 2) else .5)) * px
+orig_y = (np.arange(Ny/2) + (0 if (Ny % 2) else .5)) * py
+
+orig_xy = np.stack(np.meshgrid(orig_x, orig_y), axis = -1)
+
+
+omega = ap.omega
+
+bspec = BaseSpec(lMax = a.lMax)
+medium = EpsMuGenerator(ap.background_epsmu)
+particles= [Particle(orig_xy[i], ap.tmgen, bspec) for i in np.ndindex(orig_xy.shape[:-1])]
+
+sym = FinitePointGroup(point_group_info['D2h'])
+ss, ssw = ScatteringSystem.create(particles=particles, medium=medium, omega=omega, sym=sym)
+
+wavenumber = ap.background_epsmu.k(omega) # Currently, ScatteringSystem does not "remember" frequency nor wavenumber
+
+# Mapping between ss particles and grid positions
+positions = ss.positions
+xpositions = np.unique(positions[:,0])
+assert(len(xpositions) == Nx)
+ypositions = np.unique(positions[:,1])
+assert(len(ypositions == Ny))
+# particle positions as integer indices
+posmap = np.empty((positions.shape[0],2), dtype=int)
+invposmap = np.empty((Nx, Ny), dtype=int)
+for i, pos in enumerate(positions):
+    posmap[i,0] = np.searchsorted(xpositions, positions[i,0])
+    posmap[i,1] = np.searchsorted(ypositions, positions[i,1])
+    invposmap[posmap[i,0], posmap[i, 1]] = i
+
+def fullvec2grid(fullvec, swapxy=False):
+    arr = np.empty((Nx,Ny,nelem), dtype=complex)
+    for pi, offset in enumerate(ss.fullvec_poffsets):
+        ix, iy = posmap[pi]
+        arr[ix, iy] = fullvec[offset:offset+nelem]
+    return np.swapaxes(arr, 0, 1) if swapxy else arr
+
+
+outfile_tmp = defaultprefix + ".tmp" if a.output is None else a.output + ".tmp"
+
+nelem = len(bspec)
+phases = np.exp(1j*np.dot(ss.positions[:,:2], np.array(a.wavevector)))
+driving_full = np.zeros((nelem, ss.fecv_size),dtype=complex)
+if a.symmetry_adapted is not None:
+    ss1, ssw1 = ScatteringSystem.create(particles=[Particle((0,0,0), ap.tmgen, bspec)], medium=medium, omega=omega, 
+                    sym=FinitePointGroup(point_group_info[a.symmetry_adapted]))
+    fvcs1 = np.empty((nelem, nelem), dtype=complex)
+    y = 0
+    iris1 = []
+    for iri1 in range(ss1.nirreps):
+        for j in range(ss1.saecv_sizes[iri1]):
+            pvc1 = np.zeros((ss1.saecv_sizes[iri1],), dtype=complex)
+            pvc1[j] = 1
+            fvcs1[y] = ss1.unpack_vector(pvc1, iri1)
+            fvcs1[y] = cleanarray(nicerot(fvcs1[y], copy=False), copy=False)
+            driving_full[y] = (phases[:, None] * fvcs1[y][None,:]).flatten()
+            y += 1
+            iris1.append(iri1)
+    iris1 = np.array(iris1)
+else:
+    for y in range(nelem):
+        driving_full[y,y::nelem] = phases
+
+
+# Apply the driving on the specified slices only
+nsp = len(slicepairs)
+driving_full_sliced = np.zeros((nsp,) + driving_full.shape, dtype=complex)
+p1range = np.arange(nelem)
+for spi in range(nsp):
+    xs, ys = slicepairs[spi]
+    driven_pi = invposmap[xs, ys].flatten()
+    driven_y = ((driven_pi * nelem)[:,None] + p1range[None,:]).flatten()
+    driving_full_sliced[spi][:, driven_y] = driving_full[:, driven_y]
+
+scattered_full = np.zeros((nsp, nelem, ss.fecv_size),dtype=complex)
+scattered_ir = [None for iri in range(ss.nirreps)]
+
+ir_contained = np.ones((nsp, nelem, ss.nirreps), dtype=bool)
+
+for iri in range(ss.nirreps):
+    logging.info("processing irrep %d/%d" % (iri, ss.nirreps))
+    LU = None # to trigger garbage collection before the next call
+    translation_matrix = None
+    LU = ssw.scatter_solver(iri)
+    logging.info("LU solver created")
+    #translation_matrix = ss.translation_matrix_packed(wavenumber, iri, BesselType.REGULAR) + np.eye(ss.saecv_sizes[iri]) 
+    #logging.info("auxillary translation matrix created")
+
+    scattered_ir[iri] = np.zeros((nsp, nelem, ss.saecv_sizes[iri]), dtype=complex)
+    scattered_ir_unpacked = np.zeros((nsp, nelem, ss.fecv_size), dtype=complex)
+
+    for spi in range(nsp):
+        for y in range(nelem):
+            ã = driving_full_sliced[spi,y]
+            ãi = cleanarray(ss.pack_vector(ã, iri), copy=False)
+            if np.all(ãi == 0):
+                ir_contained[spi, y, iri] = False
+                continue
+            Tã  = ssw.apply_Tmatrices_full(ã)
+            Tãi = ss.pack_vector(Tã, iri)
+            fi = LU(Tãi)
+            scattered_ir[iri][spi, y] = fi
+            scattered_ir_unpacked[spi, y] = ss.unpack_vector(fi, iri)
+            scattered_full[spi, y] += scattered_ir_unpacked[spi, y]
+    if a.save_gradually:
+        iriout = outfile_tmp + ".%d" % iri
+        np.savez(iriout, iri=iri, meta={**vars(a), 'qpms_version' : qpms.__version__()}, 
+		 omega=omega, wavenumber=wavenumber, nelem=nelem, wavevector=np.array(a.wavevector), phases=phases, 
+                 positions = ss.positions[:,:2],
+                 scattered_ir_packed = scattered_ir[iri], 
+                 scattered_ir_full = scattered_ir_unpacked, 
+                 )
+        logging.info("partial results saved to %s"%iriout)
+
+t, l, m = bspec.tlm()
+
+if not math.isnan(a.ccd_distance):
+    logging.info("Computing the far fields")
+    if math.isnan(a.ccd_size):
+        a.ccd_size = (50 * a.ccd_distance / (max(Nx*px, Ny*py) *ssw.wavenumber.real))
+    ccd_size = a.ccd_size
+    ccd_x = np.linspace(-ccd_size/2, ccd_size/2, a.ccd_resolution)
+    ccd_y = np.linspace(-ccd_size/2, ccd_size/2, a.ccd_resolution)
+    ccd_grid = np.meshgrid(ccd_x, ccd_y, (a.ccd_distance,), indexing='ij')
+    ccd_points = np.swapaxes(np.stack(ccd_grid, axis=-1).squeeze(axis=-2), 0,1) # First axis is y, second is x, because of imshow...
+    ccd_fields = np.empty((nsp, nelem,) + ccd_points.shape, dtype=complex)
+    for spi in range(nsp):
+        for y in range(nelem):
+            ccd_fields[spi, y] = ssw.scattered_E(scattered_full[spi, y], ccd_points, btyp=BesselType.HANKEL_PLUS)
+    logging.info("Far fields done")
+
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, 
+		 omega=omega, wavenumber=wavenumber, nelem=nelem, wavevector=np.array(a.wavevector), phases=phases, 
+                 positions = ss.positions[:,:2],
+                 scattered_ir_packed = np.array(scattered_ir, dtype=np.object),
+                 scattered_full = scattered_full,
+                 ir_contained = ir_contained,
+                 t=t, l=l, m=m,
+                 iris1 = iris1 if (a.symmetry_adapted is not None) else None,
+                 irnames1 = ss1.irrep_names if (a.symmetry_adapted is not None) else None,
+                 fvcs1 = fvcs1 if (a.symmetry_adapted is not None) else None,
+                 #ccd_size = ccd_size if not math.isnan(a.ccd_distance) else None,
+                 ccd_points = ccd_points if not math.isnan(a.ccd_distance) else None,
+                 ccd_fields = ccd_fields if not math.isnan(a.ccd_distance) else None,
+       )
+logging.info("Saved to %s" % outfile)
+
+
+if a.plot or (a.plot_out is not None): 
+
+
+    import matplotlib
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt, cm
+    from matplotlib.backends.backend_pdf import PdfPages
+    t, l, m = bspec.tlm()
+    phasecm = cm.twilight
+    pmcm = cm.bwr
+    abscm = cm.plasma 
+    
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    pp = PdfPages(plotfile)
+
+    for spi in range(nsp):
+        fig, axes = plt.subplots(nelem, 12 if math.isnan(a.ccd_distance) else 16, figsize=(figscale*(12 if math.isnan(a.ccd_distance) else 16), figscale*nelem))
+        for yp in range(0,3): # TODO xy-dipoles instead?
+            axes[0,4*yp+0].set_title("abs / (E,1,%s)" % realdipfieldlabels(yp))
+            axes[0,4*yp+1].set_title("arg / (E,1,%s)" % realdipfieldlabels(yp))
+            axes[0,4*yp+2].set_title("Fabs / (E,1,%s)" % realdipfieldlabels(yp))
+            axes[0,4*yp+3].set_title("Farg / (E,1,%s)" % realdipfieldlabels(yp))
+        if not math.isnan(a.ccd_distance):
+            #axes[0,12].set_title("$E_{xy}$ @ $z = %g; \phi$" % a.ccd_distance)
+            #axes[0,13].set_title("$E_{xy}$ @ $z = %g; \phi + \pi/2$" % a.ccd_distance)
+            axes[0,12].set_title("$|E_{x}|^2$ @ $z = %g\,\mathrm{m}$" % a.ccd_distance)
+            axes[0,13].set_title("$|E_{y}|^2$ @ $z = %g\,\mathrm{m}$" % a.ccd_distance)
+            axes[0,14].set_title("$|E_x + E_y|^2$ @ $z = %g\,\mathrm{m}$" % a.ccd_distance)
+            axes[0,15].set_title("$|E_{z}|^2$ @ $z = %g\,\mathrm{m}$" % a.ccd_distance)
+            for gg in range(12,16):
+                axes[-1,gg].set_xlabel("$x/\mathrm{m}$")
+            
+
+        for y in range(nelem):
+            fulvec = scattered_full[spi,y]
+            if a.symmetry_adapted is not None:
+                driving_nonzero_y = [j for j in range(nelem) if abs(fvcs1[y,j]) > 1e-5]
+                driving_descr = ss1.irrep_names[iris1[y]]+'\n'+', '.join(('$'+cplx_nicestr(fvcs1[y,j])+'$' +
+    "(%s,%d,%+d)" % (("E" if t[j] == 2 else "M"), l[j], m[j]) for j in
+    driving_nonzero_y)) # TODO shorten the complex number precision
+            else:
+                driving_descr = "%s,%d,%+d"%('E' if t[y]==2 else 'M', l[y], m[y],)
+            axes[y,0].set_ylabel(driving_descr)
+            axes[y,-1].yaxis.set_label_position("right")
+            axes[y,-1].set_ylabel("$y/\mathrm{m}$\n"+driving_descr)
+            vecgrid = fullvec2grid(fulvec, swapxy=True)
+            vecgrid_ff = np.fft.fftshift(np.fft.fft2(vecgrid, axes=(0,1)),axes=(0,1))
+            lemax = np.amax(abs(vecgrid))
+            for yp in range(0,3):
+                if(np.amax(abs(realdipfields(vecgrid,yp))) > lemax*1e-5):
+                    axes[y,yp*4].imshow(abs(realdipfields(vecgrid,yp)), vmin=0, interpolation='none')
+                    axes[y,yp*4].text(0.5, 0.5, '%g' % np.amax(abs(realdipfields(vecgrid,yp))), horizontalalignment='center', verticalalignment='center', transform=axes[y,yp*4].transAxes)
+                    axes[y,yp*4+1].imshow(np.angle(realdipfields(vecgrid,yp)), vmin=-np.pi, vmax=np.pi, cmap=phasecm, interpolation='none')
+                    axes[y,yp*4+2].imshow(abs(realdipfields(vecgrid_ff,yp)), vmin=0, interpolation='none')
+                    axes[y,yp*4+3].imshow(np.angle(realdipfields(vecgrid_ff,yp)), vmin=-np.pi, vmax=np.pi, cmap=phasecm, interpolation='none')
+                else:
+                    for c in range(0,4):
+                        axes[y,yp*4+c].tick_params(bottom=False, left=False, labelbottom=False, labelleft=False)
+            if not math.isnan(a.ccd_distance):
+                fxye=(-ccd_size/2, ccd_size/2, -ccd_size/2, ccd_size/2)
+                e2vmax = np.amax(np.linalg.norm(ccd_fields[spi,y], axis=-1)**2)
+                xint = abs(ccd_fields[spi,y,...,0])**2
+                yint = abs(ccd_fields[spi,y,...,1])**2
+                xyint = abs(ccd_fields[spi,y,...,0] + ccd_fields[spi,y,...,1])**2
+                zint = abs(ccd_fields[spi,y,...,2])**2
+                xintmax = np.amax(xint)
+                yintmax = np.amax(yint)
+                zintmax = np.amax(zint)
+                xyintmax = np.amax(xyint)
+                axes[y, 12].imshow(xint, origin="lower", extent=fxye, cmap=abscm, interpolation='none')
+                axes[y, 13].imshow(yint, origin="lower", extent=fxye, cmap=abscm, interpolation='none')
+                axes[y, 14].imshow(xyint, origin="lower", extent=fxye, cmap=abscm, interpolation='none')
+                axes[y, 15].imshow(zint, origin='lower', extent=fxye, cmap=abscm, interpolation='none')
+                axes[y, 12].text(0.5, 0.5, '%g\n%g' % (xintmax,xintmax/e2vmax), 
+                        horizontalalignment='center', verticalalignment='center', transform=axes[y,12].transAxes)
+                axes[y, 13].text(0.5, 0.5, '%g\n%g' % (yintmax,yintmax/e2vmax), 
+                        horizontalalignment='center', verticalalignment='center', transform=axes[y,13].transAxes)
+                axes[y, 14].text(0.5, 0.5, '%g\n%g' % (xyintmax,xyintmax/e2vmax), 
+                        horizontalalignment='center', verticalalignment='center', transform=axes[y,14].transAxes)
+                axes[y, 15].text(0.5, 0.5, '%g\n%g' % (zintmax,zintmax/e2vmax), 
+                        horizontalalignment='center', verticalalignment='center', transform=axes[y,15].transAxes)
+                for gg in range(12,16):
+                    axes[y,gg].yaxis.tick_right()
+                for gg in range(12,15):
+                    axes[y,gg].yaxis.set_major_formatter(plt.NullFormatter())
+        fig.text(0, 0, str(slicepairs[spi]), horizontalalignment='left', verticalalignment='bottom')
+        pp.savefig()
+    annotate_pdf_metadata(pp, scriptname="finiterectlat-constant-driving.py")
+    pp.close()
+
+exit(0)
+

misc/finiterectlat-modes.py

@@ -0,0 +1,129 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser, annotate_pdf_metadata
+
+
+ap = ArgParser(['rectlattice2d_finite', 'background_analytical', 'single_particle', 'single_lMax', ])
+
+ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
+ap.add_argument("-c", "--min-candidates", type=int, default=1, help='always try at least this many eigenvalue candidates, even if their SVs in the rank tests are lower than rank_tolerance')
+ap.add_argument("-T", "--residual-tolerance", type=float, default=0.)
+
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+#ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+#ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+#ap.add_argument("-g", "--save-gradually", action='store_true', help="saves the partial result after computing each irrep")
+
+ap.add_argument("-f", "--centre", type=complex, required=True, help='Contour centre in eV')
+ap.add_argument("--ai", type=float, default=0.05, help="Contour imaginary half-axis in eV")
+ap.add_argument("--ar", type=float, default=0.05, help="Contour real half-axis in eV")
+ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
+ap.add_argument("--D2", action='store_true', help="Use D2h symmetry even if the array has square symmetry")
+
+ap.add_argument("--irrep", type=str, default="none", help="Irrep subspace (irrep index from 0 to 7 (9 for D4h), irrep label, or 'none' for no irrep decomposition")
+
+a=ap.parse_args()
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+Nx, Ny = a.size
+px, py = a.period
+
+thegroup = 'D4h' if px == py and Nx == Ny and not a.D2 else 'D2h'
+
+particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
+if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
+defaultprefix = "%s_p%gnmx%gnm_%dx%d_m%s_B%s_L%d_c(%s±%g±%gj)eV_cn%d_%s" % (
+    particlestr, px*1e9, py*1e9, Nx, Ny, str(a.material), str(a.background), a.lMax,
+    str(a.centre), a.ar, a.ai, a.N,
+    thegroup,
+    )
+logging.info("Default file prefix: %s" % defaultprefix)
+
+def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
+    x = point_xy[0] - centre_xy[0]
+    y = point_xy[1] - centre_xy[1]
+    ax = halfaxes_xy[0]
+    ay = halfaxes_xy[1]
+    return ((x/ax)**2 + (y/ay)**2) <= 1
+
+
+import numpy as np
+import qpms
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix, TMatrixGenerator
+from qpms.qpms_c import Particle
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.cycommon import DebugFlags, dbgmsg_enable
+from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
+from qpms.symmetries import point_group_info
+eh = eV/hbar
+
+dbgmsg_enable(DebugFlags.INTEGRATION)
+
+#Particle positions
+orig_x = (np.arange(Nx/2) + (0 if (Nx % 2) else .5)) * px
+orig_y = (np.arange(Ny/2) + (0 if (Ny % 2) else .5)) * py
+
+orig_xy = np.stack(np.meshgrid(orig_x, orig_y), axis = -1)
+
+
+bspec = BaseSpec(lMax = a.lMax)
+medium = EpsMuGenerator(ap.background_epsmu)
+particles= [Particle(orig_xy[i], ap.tmgen, bspec) for i in np.ndindex(orig_xy.shape[:-1])]
+
+sym = FinitePointGroup(point_group_info[thegroup])
+logging.info("Creating scattering system object")
+ss, ssw = ScatteringSystem.create(particles, medium, a.centre * eh, sym=sym)
+
+if a.irrep == 'none':
+    iri = None # no irrep decomposition
+    irname = 'full'
+    logging.info("Not performing irrep decomposition and working with the full space of dimension %d." % ss.fecv_size)
+else:
+    try:
+        iri = int(a.irrep)
+    except ValueError:
+        iri = ss.irrep_names.index(a.irrep)
+    irname = ss.irrep_names[iri]
+    logging.info("Using irrep subspace %s (iri = %d) of dimension %d." % (irname, iri, ss.saecv_sizes[iri]))
+
+outfile_tmp = defaultprefix + ".tmp" if a.output is None else a.output + ".tmp"
+
+logging.info("Starting Beyn's algorithm")
+results = ss.find_modes(iri=iri, omega_centre = a.centre*eh, omega_rr=a.ar*eh, omega_ri=a.ai*eh, contour_points=a.N,
+        rank_tol=a.rank_tolerance, rank_min_sel=a.min_candidates, res_tol=a.residual_tolerance)
+results['inside_contour'] = inside_ellipse((results['eigval'].real, results['eigval'].imag),
+        (a.centre.real*eh, a.centre.imag*eh), (a.ar*eh, a.ai*eh))
+results['refractive_index_internal'] = [medium(om).n for om in results['eigval']]
+
+outfile = defaultprefix + (('_ir%s_%s.npz' % (str(iri), irname)) if iri is not None else '.npz') if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, **results)
+logging.info("Saved to %s" % outfile)
+
+exit(0)
+
+# TODO plots.
+if a.plot or (a.plot_out is not None):
+    import matplotlib
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt
+    from matplotlib.backends.backend_pdf import PdfPages
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    ax.plot(sinalpha_list, σ_ext*1e12,label='$\sigma_\mathrm{ext}$')
+    ax.plot(sinalpha_list, σ_scat*1e12, label='$\sigma_\mathrm{scat}$')
+    ax.plot(sinalpha_list, σ_abs*1e12, label='$\sigma_\mathrm{abs}$')
+    ax.legend()
+    ax.set_xlabel('$\sin\\alpha$')
+    ax.set_ylabel('$\sigma/\mathrm{\mu m^2}$')
+        
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    with PdfPages(plotfile) as pdf:
+        pdf.savefig(fig)
+        annotate_pdf_metadata(pdf, scriptname='finiterectlat-modes.py')
+
+exit(0)
+

misc/finiterectlat-scatter.py

@@ -1,14 +1,12 @@
 #!/usr/bin/env python3
 
+from qpms.argproc import ArgParser, annotate_pdf_metadata
 import math
-from qpms.argproc import ArgParser
+pi = math.pi
 
 
-ap = ArgParser(['rectlattice2d_finite', 'single_particle', 'single_lMax', 'single_omega'])
-ap.add_argument("-k", '--kx-lim', nargs=2, type=float, required=True, help='k vector', metavar=('KX_MIN', 'KX_MAX'))
-# ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
+ap = ArgParser(['rectlattice2d_finite', 'single_particle', 'single_lMax', 'omega_seq_real_ng', 'planewave'])
 ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
-ap.add_argument("-N", type=int, default="151", help="Number of angles")
 ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
 ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
 ap.add_argument("-g", "--save-gradually", action='store_true', help="saves the partial result after computing each irrep")
@@ -19,18 +17,9 @@ a=ap.parse_args()
 import logging
 logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
 
-Nx, Ny = a.size
-px, py = a.period
-
-particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
-if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
-defaultprefix = "%s_p%gnmx%gnm_%dx%d_m%s_n%g_angles(%g_%g)_Ey_f%geV_L%d_cn%d" % (
-    particlestr, px*1e9, py*1e9, Nx, Ny, str(a.material), a.refractive_index, a.kx_lim[0], a.kx_lim[1], a.eV, a.lMax, a.N)
-logging.info("Default file prefix: %s" % defaultprefix)
-
-
 import numpy as np
 import qpms
+from qpms.qpms_p import cart2sph, sph2cart, sph_loccart2cart, sph_loccart_basis
 from qpms.cybspec import BaseSpec
 from qpms.cytmatrices import CTMatrix, TMatrixGenerator
 from qpms.qpms_c import Particle
@@ -42,94 +31,209 @@ eh = eV/hbar
 
 dbgmsg_enable(DebugFlags.INTEGRATION)
 
+Nx, Ny = a.size
+px, py = a.period
+
+particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
+if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
+defaultprefix = "%s_p%gnmx%gnm_%dx%d_m%s_bg%s_φ%gπ_θ(%g_%g)π_ψ%gπ_χ%gπ_f%s_L%d" % (
+    particlestr, px*1e9, py*1e9, Nx, Ny, str(a.material), str(a.background), a.phi/pi, np.amin(a.theta)/pi, np.amax(a.theta)/pi, a.psi/pi, a.chi/pi, ap.omega_descr, a.lMax, )
+logging.info("Default file prefix: %s" % defaultprefix)
+
+
 #Particle positions
 orig_x = (np.arange(Nx/2) + (0 if (Nx % 2) else .5)) * px
 orig_y = (np.arange(Ny/2) + (0 if (Ny % 2) else .5)) * py
 
 orig_xy = np.stack(np.meshgrid(orig_x, orig_y), axis = -1)
 
-
-omega = ap.omega
-
 bspec = BaseSpec(lMax = a.lMax)
-Tmatrix = ap.tmgen(bspec, ap.omega)
-particles= [Particle(orig_xy[i], Tmatrix) for i in np.ndindex(orig_xy.shape[:-1])]
+particles= [Particle(orig_xy[i], ap.tmgen, bspec=bspec) for i in np.ndindex(orig_xy.shape[:-1])]
 
 sym = FinitePointGroup(point_group_info['D2h'])
-ss = ScatteringSystem(particles, sym)
+ss, ssw = ScatteringSystem.create(particles, ap.background_emg, ap.allomegas[0], sym=sym)
 
-wavenumber = ap.background_epsmu.k(omega).real # Currently, ScatteringSystem does not "remember" frequency nor wavenumber
 
-sinalpha_list = np.linspace(a.kx_lim[0],a.kx_lim[1],a.N)
+## Plane wave data
+a.theta = np.atleast_1d(np.array(a.theta))
+dir_sph_list = np.stack((np.broadcast_to(1, a.theta.shape), a.theta, np.broadcast_to(a.phi, a.theta.shape)), axis=-1)
+sψ, cψ = math.sin(a.psi), math.cos(a.psi)
+sχ, cχ = math.sin(a.chi), math.cos(a.chi)
+E_sph = (0., cψ*cχ + 1j*sψ*sχ, sψ*cχ + 1j*cψ*sχ) 
 
-# Plane wave data
-E_cart_list = np.empty((a.N,3), dtype=complex)
-E_cart_list[:,:] = np.array((0,1,0))[None,:]
-k_cart_list = np.empty((a.N,3), dtype=float)
-k_cart_list[:,0] = sinalpha_list
-k_cart_list[:,1] = 0
-k_cart_list[:,2] = np.sqrt(1-sinalpha_list**2)
-k_cart_list *= wavenumber
+dir_cart_list = sph2cart(dir_sph_list)
+E_cart_list = sph_loccart2cart(E_sph, dir_sph_list)
 
-σ_ext_list_ir = np.empty((a.N, ss.nirreps), dtype=float)
-σ_scat_list_ir = np.empty((a.N, ss.nirreps), dtype=float)
+nfreq = len(ap.allomegas)
+ndir = a.theta.shape[0]
+
+k_cart_arr = np.empty((nfreq, ndir, 3), dtype=float)
+wavenumbers = np.empty((nfreq,), dtype=float)
+
+σ_ext_arr_ir = np.empty((nfreq, ndir, ss.nirreps), dtype=float)
+σ_scat_arr_ir = np.empty((nfreq, ndir, ss.nirreps), dtype=float)
 
 outfile_tmp = defaultprefix + ".tmp" if a.output is None else a.output + ".tmp"
 
-for iri in range(ss.nirreps):
-    logging.info("processing irrep %d/%d" % (iri, ss.nirreps))
-    LU = None # to trigger garbage collection before the next call
-    translation_matrix = None
-    LU = ss.scatter_solver(wavenumber,iri)
-    logging.info("LU solver created")
-    translation_matrix = ss.translation_matrix_packed(wavenumber, iri, BesselType.REGULAR) + np.eye(ss.saecv_sizes[iri]) 
-    logging.info("auxillary translation matrix created")
+for i, omega in enumerate(ap.allomegas):
+    logging.info("Processing frequency %g eV" % (omega / eV,))
+    if i != 0:
+        ssw = ss(omega)
+    if ssw.wavenumber.imag != 0:
+        warnings.warn("The background medium wavenumber has non-zero imaginary part. Don't expect emaningful results for cross sections.")
+    wavenumber = ssw.wavenumber.real
+    wavenumbers[i] = wavenumber
 
-    for j in range(a.N):
-        # the following two could be calculated only once, but probably not a big deal
-        ã = ss.planewave_full(k_cart=k_cart_list[j], E_cart=E_cart_list[j])
-        Tã = ss.apply_Tmatrices_full(ã)
+    k_sph_list = np.array(dir_sph_list, copy=True)
+    k_sph_list[:,0] = wavenumber
 
-        Tãi = ss.pack_vector(Tã, iri)
-        ãi = ss.pack_vector(ã, iri)
-        fi = LU(Tãi)
-        σ_ext_list_ir[j, iri] = -np.vdot(ãi, fi).real/wavenumber**2
-        σ_scat_list_ir[j, iri] = np.vdot(fi,np.dot(translation_matrix, fi)).real/wavenumber**2
-    if a.save_gradually:
-        iriout = outfile_tmp + ".%d" % iri
-        np.savez(iriout, iri=iri, meta=vars(a), sinalpha=sinalpha_list, k_cart = k_cart_list, E_cart=E_cart_list,
-		 omega=omega, wavenumber=wavenumber, σ_ext_list_ir=σ_ext_list_ir[:,iri], σ_scat_list_ir=σ_scat_list_ir[:,iri])
-        logging.info("partial results saved to %s"%iriout)
+    k_cart_arr[i] = sph2cart(k_sph_list)
 
-σ_abs_list_ir = σ_ext_list_ir - σ_scat_list_ir
-σ_abs= np.sum(σ_abs_list_ir, axis=-1)
-σ_scat= np.sum(σ_scat_list_ir, axis=-1)
-σ_ext= np.sum(σ_ext_list_ir, axis=-1)
+    for iri in range(ss.nirreps):
+        logging.info("processing irrep %d/%d" % (iri, ss.nirreps))
+        LU = None # to trigger garbage collection before the next call
+        translation_matrix = None
+        LU = ssw.scatter_solver(iri)
+        logging.info("LU solver created")
+        translation_matrix = ssw.translation_matrix_packed(iri, BesselType.REGULAR) + np.eye(ss.saecv_sizes[iri]) 
+        logging.info("auxillary translation matrix created")
+
+        for j in range(ndir):
+            k_cart = k_cart_arr[i,j]
+            # the following two could be calculated only once, but probably not a big deal
+            ã = ss.planewave_full(k_cart=k_cart_arr[i,j], E_cart=E_cart_list[j])
+            Tã = ssw.apply_Tmatrices_full(ã)
+
+            Tãi = ss.pack_vector(Tã, iri)
+            ãi = ss.pack_vector(ã, iri)
+            fi = LU(Tãi)
+            σ_ext_arr_ir[i, j, iri] = -np.vdot(ãi, fi).real/wavenumber**2
+            σ_scat_arr_ir[i, j, iri] = np.vdot(fi,np.dot(translation_matrix, fi)).real/wavenumber**2
+        if a.save_gradually:
+            iriout = outfile_tmp + ".%d.%d" % (i, iri)
+            np.savez(iriout, omegai=i, iri=iri, meta={**vars(a), 'qpms_version' : qpms.__version__()}, omega=omega, k_sph=k_sph_list, k_cart = k_cart_arr, E_cart=E_cart_list, E_sph=np.array(E_sph),
+                     wavenumber=wavenumber, σ_ext_list_ir=σ_ext_arr_ir[i,:,iri], σ_scat_list_ir=σ_scat_list_ir[i,:,iri])
+            logging.info("partial results saved to %s"%iriout)
+
+σ_abs_arr_ir = σ_ext_arr_ir - σ_scat_arr_ir
+σ_abs_arr = np.sum(σ_abs_arr_ir, axis=-1)
+σ_scat_arr = np.sum(σ_scat_arr_ir, axis=-1)
+σ_ext_arr = np.sum(σ_ext_arr_ir, axis=-1)
 
 
 outfile = defaultprefix + ".npz" if a.output is None else a.output
-np.savez(outfile, meta=vars(a), sinalpha=sinalpha_list, k_cart = k_cart_list, E_cart=E_cart_list, σ_ext=σ_ext,σ_abs=σ_abs,σ_scat=σ_scat,
- σ_ext_ir=σ_ext_list_ir,σ_abs_ir=σ_abs_list_ir,σ_scat_ir=σ_scat_list_ir, omega=omega, wavenumber=wavenumber
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, 
+        k_sph=k_sph_list, k_cart = k_cart_arr, E_cart=E_cart_list, E_sph=np.array(E_sph),
+        σ_ext=σ_ext_arr,σ_abs=σ_abs_arr,σ_scat=σ_scat_arr,
+        σ_ext_ir=σ_ext_arr_ir,σ_abs_ir=σ_abs_arr_ir,σ_scat_ir=σ_scat_arr_ir, omega=ap.allomegas, wavenumbers=wavenumbers
        )
 logging.info("Saved to %s" % outfile)
 
-
 if a.plot or (a.plot_out is not None):
     import matplotlib
+    from matplotlib.backends.backend_pdf import PdfPages
     matplotlib.use('pdf')
     from matplotlib import pyplot as plt
+    from scipy.interpolate import griddata
 
-    fig = plt.figure()
-    ax = fig.add_subplot(111)
-    ax.plot(sinalpha_list, σ_ext*1e12,label='$\sigma_\mathrm{ext}$')
-    ax.plot(sinalpha_list, σ_scat*1e12, label='$\sigma_\mathrm{scat}$')
-    ax.plot(sinalpha_list, σ_abs*1e12, label='$\sigma_\mathrm{abs}$')
-    ax.legend()
-    ax.set_xlabel('$\sin\\alpha$')
-    ax.set_ylabel('$\sigma/\mathrm{\mu m^2}$')
-    
     plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
-    fig.savefig(plotfile)
+    with PdfPages(plotfile) as pdf:
+        ipm = 'nearest'
+        sintheta = np.sin(a.theta)
+        if False: #len(ap.omega_ranges) != 0:
+            # angle plot ---------------------------------
+            fig = plt.figure(figsize=(210/25.4, 297/25.4))
+            vmax = max(np.amax(σ_ext_arr), np.amax(σ_scat_arr), np.amax(σ_abs_arr))
+            vmin = min(np.amin(σ_ext_arr), np.amin(σ_scat_arr), np.amin(σ_abs_arr))
+
+            ax = fig.add_subplot(311)
+            ax.pcolormesh(a.theta, ap.allomegas/eh, σ_ext_arr, vmin=vmin, vmax=vmax)
+            ax.set_xlabel('$\\theta$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{ext}$')
+
+            ax = fig.add_subplot(312)
+            ax.pcolormesh(a.theta, ap.allomegas/eh, σ_scat_arr, vmin=vmin, vmax=vmax)
+            ax.set_xlabel('$\\theta$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{scat}$')
+
+            ax = fig.add_subplot(313)
+            im = ax.pcolormesh(a.theta, ap.allomegas/eh, σ_abs_arr, vmin=vmin, vmax=vmax)
+            ax.set_xlabel('$\\theta$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{abs}$')
+
+
+            fig.subplots_adjust(right=0.8)
+            fig.colorbar(im, cax = fig.add_axes([0.85, 0.15, 0.05, 0.7]))
+
+            pdf.savefig(fig)
+            plt.close(fig)
+
+        if len(ap.omega_ranges) != 0:
+            # "k-space" plot -----------------------------
+            domega = np.amin(np.diff(ap.allomegas))
+            dsintheta = np.amin(abs(np.diff(sintheta)))
+            dk = dsintheta * wavenumbers[0]
+
+            # target image grid
+            grid_y, grid_x = np.mgrid[ap.allomegas[0] : ap.allomegas[-1] : domega, np.amin(sintheta) * wavenumbers[-1] : np.amax(sintheta) * wavenumbers[-1] : dk]
+            imextent = (np.amin(sintheta) * wavenumbers[-1] / 1e6, np.amax(sintheta) * wavenumbers[-1] / 1e6, ap.allomegas[0] / eh, ap.allomegas[-1] / eh)
+
+            # source coordinates for griddata
+            ktheta = sintheta[None, :] * wavenumbers[:, None]
+            omegapoints = np.broadcast_to(ap.allomegas[:, None], ktheta.shape)
+            points = np.stack( (ktheta.flatten(), omegapoints.flatten()), axis = -1)
+
+            fig = plt.figure(figsize=(210/25.4, 297/25.4))
+            vmax = np.amax(σ_ext_arr)
+
+            ax = fig.add_subplot(311)
+            grid_z = griddata(points, σ_ext_arr.flatten(), (grid_x, grid_y), method = ipm)
+            ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
+            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{ext}$')
+
+            ax = fig.add_subplot(312)
+            grid_z = griddata(points, σ_scat_arr.flatten(), (grid_x, grid_y), method = ipm)
+            ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
+            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{scat}$')
+
+            ax = fig.add_subplot(313)
+            grid_z = griddata(points, σ_abs_arr.flatten(), (grid_x, grid_y), method = ipm)
+            im = ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
+            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{abs}$')
+
+            fig.subplots_adjust(right=0.8)
+            fig.colorbar(im, cax = fig.add_axes([0.85, 0.15, 0.05, 0.7]))
+
+            pdf.savefig(fig)
+            plt.close(fig)
+
+        for omega in ap.omega_singles:
+            i = np.searchsorted(ap.allomegas, omega)
+
+            fig = plt.figure()
+            fig.suptitle("%g eV" % (omega / eh))
+            ax = fig.add_subplot(111)
+            sintheta = np.sin(a.theta)
+            ax.plot(sintheta, σ_ext_arr[i]*1e12,label='$\sigma_\mathrm{ext}$')
+            ax.plot(sintheta, σ_scat_arr[i]*1e12, label='$\sigma_\mathrm{scat}$')
+            ax.plot(sintheta, σ_abs_arr[i]*1e12, label='$\sigma_\mathrm{abs}$')
+            ax.legend()
+            ax.set_xlabel('$\sin\\theta$')
+            ax.set_ylabel('$\sigma/\mathrm{\mu m^2}$')
+
+            pdf.savefig(fig)
+            plt.close(fig)
+        annotate_pdf_metadata(pdf, scriptname="finiterectlat-scatter.py")
+
 
 exit(0)
 

misc/finitesqlatzsym-scatter.py

@@ -1,376 +0,0 @@
-#!/usr/bin/env python3
-
-import argparse, re, random, string, sys
-import subprocess
-import warnings
-from scipy.constants import hbar, e as eV, pi, c
-
-unitcell_size = 1 # rectangular lattice
-unitcell_indices = tuple(range(unitcell_size))
-
-def make_action_sharedlist(opname, listname):
-    class opAction(argparse.Action):
-        def __call__(self, parser, args, values, option_string=None):
-            if (not hasattr(args, listname)) or getattr(args, listname) is None:
-                setattr(args, listname, list())
-            getattr(args,listname).append((opname, values))
-    return opAction
-
-parser = argparse.ArgumentParser()
-#TODO? použít type=argparse.FileType('r') ?
-parser.add_argument('--TMatrix', action='store', required=True, help='Path to TMatrix file')
-#parser.add_argument('--griddir', action='store', required=True, help='Path to the directory with precalculated translation operators')
-parser.add_argument('--output_prefix', '-p', '-o', action='store', required=True, help='Prefix to the npz output (will be appended frequency, hexside and chunkno)')
-parser.add_argument('--nosuffix', action='store_true', help='Do not add dimension metadata to the output filenames')
-#sizepar = parser.add_mutually_exclusive_group(required=True)
-#parser.add_argument('--hexside', action='store', type=float, required=True, help='Lattice hexagon size length')
-parser.add_argument('--dx', action='store', type=float, required=True, help='x-direction lattice constant')
-parser.add_argument('--dy', action='store', type=float, required=True, help='y-direction lattice constant')
-
-parser.add_argument('--Nx', '--nx', action='store', type=int, required=True, help='Lattice points in the x-direction')
-parser.add_argument('--Ny', '--ny', action='store', type=int, required=True, help='Lattice points in the y-direction')
-
-# In these default settings, the area is 2x2 times larger than first BZ
-parser.add_argument('--kxmin', action='store', type=float, default=-1., help='TODO')
-parser.add_argument('--kxmax', action='store', type=float, default=1., help='TODO')
-parser.add_argument('--kymin', action='store', type=float, default=-1., help='TODO')
-parser.add_argument('--kymax', action='store', type=float, default=1., help='TODO')
-
-#parser.add_argument('--kdensity', action='store', type=int, default=33, help='Number of k-points per x-axis segment')
-parser.add_argument('--kxdensity', action='store', type=int, default=51, help='k-space resolution in the x-direction')
-parser.add_argument('--kydensity', action='store', type=int, default=51, help='k-space resolution in the y-direction')
-
-partgrp = parser.add_mutually_exclusive_group()
-partgrp.add_argument('--only_TE', action='store_true', help='Calculate only the projection on the E⟂z modes')
-partgrp.add_argument('--only_TM', action='store_true', help='Calculate only the projection on the E∥z modes')
-partgrp.add_argument('--serial', action='store_true', help='Calculate the TE and TM parts separately to save memory')
-
-parser.add_argument('--nocentre', action='store_true', help='Place the coordinate origin to the left bottom corner rather that to the centre of the array')
-
-parser.add_argument('--plot_TMatrix', action='store_true', help='Visualise TMatrix on the first page of the output')
-#parser.add_argument('--SVD_output', action='store', help='Path to output singular value decomposition result')
-parser.add_argument('--maxlayer', action='store', type=int, default=100, help='How far to sum the lattice points to obtain the dispersion')
-parser.add_argument('--scp_to', action='store', metavar='N', type=str, help='SCP the output files to a given destination')
-parser.add_argument('--background_permittivity', action='store', type=float, default=1., help='Background medium relative permittivity (default 1)')
-parser.add_argument('--eVfreq', action='store', required=True, type=float, help='Frequency in eV')
-
-parser.add_argument('--chunklen', action='store', type=int, default=3000, help='Number of k-points per output file (default 3000)')
-parser.add_argument('--lMax', action='store', type=int, help='Override lMax from the TMatrix file')
-#TODO some more sophisticated x axis definitions
-#parser.add_argument('--gaussian', action='store', type=float, metavar='σ', help='Use a gaussian envelope for weighting the interaction matrix contributions (depending on the distance), measured in unit cell lengths (?) FIxME).')
-parser.add_argument('--verbose', '-v', action='count', help='Be verbose (about computation times, mostly)')
-popgrp=parser.add_argument_group(title='Operations')
-popgrp.add_argument('--tr', dest='ops', action=make_action_sharedlist('tr', 'ops'), default=list()) # the default value for dest can be set once
-for i in unitcell_indices:
-    popgrp.add_argument('--tr%d'%i, dest='ops', action=make_action_sharedlist('tr%d'%i, 'ops'))
-popgrp.add_argument('--sym', dest='ops', action=make_action_sharedlist('sym', 'ops'))
-for i in unitcell_indices:
-    popgrp.add_argument('--sym%d'%i, dest='ops', action=make_action_sharedlist('sym%d'%i, 'ops'))
-#popgrp.add_argument('--mult', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult', 'ops'))
-#popgrp.add_argument('--mult0', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult0', 'ops'))
-#popgrp.add_argument('--mult1', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult1', 'ops'))
-popgrp.add_argument('--multl', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl', 'ops'))
-for i in unitcell_indices:
-    popgrp.add_argument('--multl%d'%i, dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl%d'%i, 'ops'))
-#popgrp.add_argument('--multl1', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl1', 'ops'))
-parser.add_argument('--frequency_multiplier', action='store', type=float, default=1., help='Multiplies the frequencies in the TMatrix file by a given factor.')
-# TODO enable more flexible per-sublattice specification
-pargs=parser.parse_args()
-if pargs.verbose:
-    print(pargs, file = sys.stderr)
-
-maxlayer=pargs.maxlayer
-eVfreq = pargs.eVfreq
-freq = eVfreq*eV/hbar
-verbose=pargs.verbose
-dy = pargs.dy
-dx = pargs.dx
-Ny = pargs.Ny
-Nx = pargs.Nx
-
-TMatrix_file = pargs.TMatrix
-
-epsilon_b = pargs.background_permittivity #2.3104
-#gaussianSigma = pargs.gaussian if pargs.gaussian else None # hexside * 222 / 7
-interpfreqfactor = pargs.frequency_multiplier
-scp_dest = pargs.scp_to if pargs.scp_to else None
-kxdensity = pargs.kxdensity
-kydensity = pargs.kydensity
-chunklen = pargs.chunklen
-
-ops = list()
-opre = re.compile('(tr|sym|copy|multl|mult)(\d*)')
-for oparg in pargs.ops:
-    opm = opre.match(oparg[0])
-    if opm:
-        ops.append(((opm.group(2),) if opm.group(2) else unitcell_indices, opm.group(1), oparg[1]))
-    else:
-        raise # should not happen
-if(verbose):
-    print(ops, file = sys.stderr)
-
-
-# -----------------finished basic CLI parsing (except for op arguments) ------------------
-from qpms.timetrack import _time_b, _time_e
-btime=_time_b(verbose)
-
-import qpms
-import numpy as np
-import os, warnings, math
-from scipy import interpolate
-nx = None
-s3 = math.sqrt(3)
-
-
-# specifikace T-matice zde
-refind = math.sqrt(epsilon_b)
-cdn = c / refind
-k_0 = freq * refind / c # = freq / cdn
-TMatrices_orig, freqs_orig, freqs_weirdunits_orig, lMaxTM = qpms.loadScuffTMatrices(TMatrix_file)
-lMax = lMaxTM
-if pargs.lMax:
-    lMax = pargs.lMax if pargs.lMax else lMaxTM    
-my, ny = qpms.get_mn_y(lMax)
-nelem = len(my)
-if pargs.lMax: #force commandline specified lMax
-    TMatrices_orig = TMatrices_orig[...,0:nelem,:,0:nelem]
-TMatrices = np.array(np.broadcast_to(TMatrices_orig[:,nx,:,:,:,:],(len(freqs_orig),unitcell_size,2,nelem,2,nelem)) )
-xfl = qpms.xflip_tyty(lMax)
-yfl = qpms.yflip_tyty(lMax)
-zfl = qpms.zflip_tyty(lMax)
-c2rot = qpms.apply_matrix_left(qpms.yflip_yy(3),qpms.xflip_yy(3),-1)
-
-reCN = re.compile('(\d*)C(\d+)')
-#TODO C nekonečno
-
-for op in ops:
-    if op[0] == 'all':
-        #targets = (0,1)
-        targets = unitcell_indices
-    elif isinstance(op[0],int):
-        targets = (op[0],)
-    else:
-        targets = op[0]
-        
-    if op[1] == 'sym':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'C2': # special case of the latter
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1))/2                
-        elif mCN:
-            rotN = int(mCN.group(2))
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                for i in range(rotN):
-                    rotangle = 2*np.pi*i / rotN
-                    rot =  qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle]))
-                    rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle]))
-                    TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-                TMatrices[:,t] = np.sum(TMatrix_contribs, axis=0) / rotN
-        else:
-            raise
-    elif op[1] == 'tr':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'C2':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1)       
-        elif mCN:
-            rotN = int(mCN.group(2))
-            power = int(mCN.group(1)) if mCN.group(1) else 1
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                rotangle = 2*np.pi*power/rotN
-                rot = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,rotangle]))
-                rotinv = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,-rotangle]))
-                TMatrices[:,t] = qpms.apply_matrix_left(rot, qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-        else:
-            raise
-    elif op[1] == 'copy':
-        raise # not implemented
-    elif op[1] == 'mult':
-        raise # not implemented
-    elif op[1] == 'multl':
-        incy = np.full((nelem,), False, dtype=bool)
-        for incl in op[2][0].split(','):
-            l = int(incl)
-            incy += (l == ny)
-        scaty = np.full((nelem,), False, dtype=bool)
-        for scatl in op[2][1].split(','):
-            l = int(scatl)
-            scaty += (l == ny)
-        for t in targets:
-            TMatrices[np.ix_(np.arange(TMatrices.shape[0]),np.array([t]),np.array([0,1]),scaty,np.array([0,1]),incy)] *= float(op[2][2])
-    else:
-        raise #unknown operation; should not happen
-
-TMatrices_interp = interpolate.interp1d(freqs_orig*interpfreqfactor, TMatrices, axis=0, kind='linear',fill_value="extrapolate")
-
-
-xpositions = np.arange(Nx) * dx
-ypositions = np.arange(Ny) * dy
-if not pargs.nocentre:
-    xpositions -= Nx * dx / 2
-    ypositions -= Ny * dy / 2
-xpositions, ypositions = np.meshgrid(xpositions, ypositions, indexing='ij', copy=False)
-positions=np.stack((xpositions.ravel(),ypositions.ravel()), axis=-1)
-positions=positions[np.random.permutation(len(positions))]
-N = positions.shape[0]
-
-kx = np.linspace(pargs.kxmin, pargs.kxmax, num=pargs.kxdensity, endpoint=True) * 2*np.pi / dx
-ky = np.linspace(pargs.kymin, pargs.kymax, num=pargs.kydensity, endpoint=True) * 2*np.pi / dy
-kx, ky = np.meshgrid(kx, ky, indexing='ij', copy=False)
-kz = np.sqrt(k_0**2 - (kx ** 2 + ky ** 2))
-
-klist_full = np.stack((kx,ky,kz), axis=-1).reshape((-1,3))
-TMatrices_om = TMatrices_interp(freq)
-
-chunkn = math.ceil(klist_full.size / 3 / chunklen)
-
-if verbose:
-    print('Evaluating %d k-points' % klist_full.size + ('in %d chunks'%chunkn) if chunkn>1 else '' , file = sys.stderr)
-    sys.stderr.flush()
-
-try:
-    version = qpms.__version__
-except NameError:
-    version = None
-
-metadata = np.array({
-                'script': os.path.basename(__file__),
-                'version': version,
-                'type' : 'Plane wave scattering on a finite rectangular lattice',
-		'lMax' : lMax,
-                'dx' : dx,
-                'dy' : dy,
-                'Nx' : Nx,
-                'Ny' : Ny,
-                #'maxlayer' : maxlayer,
-                #'gaussianSigma' : gaussianSigma,
-                'epsilon_b' : epsilon_b,
-		#'hexside' : hexside,
-                'chunkn' : chunkn,
-                'chunki' : 0,
-                'TMatrix_file' : TMatrix_file,
-                'ops' : ops,
-                'centred' : not pargs.nocentre
-                })
-
-
-scat = qpms.Scattering_2D_zsym(positions, TMatrices_om, k_0, verbose=verbose)
-
-if pargs.only_TE:
-    actions = (0,)
-elif pargs.only_TM:
-    actions = (1,)
-elif pargs.serial:
-    actions = (0,1)
-else:
-    actions = (None,)
-
-xu = np.array((1,0,0))
-yu = np.array((0,1,0))
-zu = np.array((0,0,1))
-TEč, TMč = qpms.symz_indexarrays(lMax)
-
-klist_full_2D = klist_full[...,:2]
-klist_full_dir = klist_full/np.linalg.norm(klist_full, axis=-1, keepdims=True)
-for action in actions:
-    if action is None:
-        scat.prepare(verbose=verbose)
-        actionstring = ''
-    else:
-        scat.prepare_partial(action, verbose=verbose)
-        actionstring = '.TM' if action else '.TE'
-    for chunki in range(chunkn):
-        sbtime = _time_b(verbose, step='Solving the scattering problem, chunk %d'%chunki+actionstring)
-        if pargs.nosuffix:
-            outfile = pargs.output_prefix + actionstring + (
-                    ('.%03d' % chunki) if chunkn > 1 else '')
-        else:
-            outfile = '%s_%dx%d_%.0fnmx%.0fnm_%.4f%s%s.npz' % (
-                    pargs.output_prefix, Nx, Ny, dx/1e-9, dy/1e-9,
-                    eVfreq, actionstring,
-                    (".%03d" % chunki) if chunkn > 1 else '')
-
-        klist = klist_full[chunki * chunklen : (chunki + 1) * chunklen]
-        klist2d = klist_full_2D[chunki * chunklen : (chunki + 1) * chunklen]
-        klistdir = klist_full_dir[chunki * chunklen : (chunki + 1) * chunklen]
-        
-        '''
-        The following loop is a fuckup that has its roots in the fact that
-        the function qpms.get_π̃τ̃_y1 in qpms_p.py is not vectorized
-        (and consequently, neither is plane_pq_y.)
-
-        And Scattering_2D_zsym.scatter_partial is not vectorized, either.
-        '''
-        if action == 0 or action is None:
-            xresult = np.full((klist.shape[0], N, nelem), np.nan, dtype=complex)
-            yresult = np.full((klist.shape[0], N, nelem), np.nan, dtype=complex)
-        if action == 1 or action is None:
-            zresult = np.full((klist.shape[0], N, nelem), np.nan, dtype=complex)
-        for i in range(klist.shape[0]):
-            if math.isnan(klist[i,2]):
-                if(verbose):
-                    print("%d. momentum %s invalid (k_0=%f), skipping" % (i, str(klist[i]),k_0))
-                continue
-            kdir = klistdir[i]
-            phases = np.exp(-1j*np.sum(klist2d[i] * positions, axis=-1))
-            if action == 0 or action is None:
-                pq = np.array(qpms.plane_pq_y(lMax, kdir, xu)).ravel()[TEč] * phases[:, nx] 
-                xresult[i] = scat.scatter_partial(0, pq)
-                pq = np.array(qpms.plane_pq_y(lMax, kdir, yu)).ravel()[TEč] * phases[:, nx] 
-                yresult[i] = scat.scatter_partial(0, pq)
-            if action == 1 or action is None:
-                pq = np.array(qpms.plane_pq_y(lMax, kdir, zu)).ravel()[TMč] * phases[:, nx] 
-                zresult[i] = scat.scatter_partial(1, pq)
-        _time_e(sbtime, verbose, step='Solving the scattering problem, chunk %d'%chunki+actionstring)
-
-        metadata[()]['chunki'] = chunki
-        if action is None:
-            np.savez(outfile, omega = freq, klist = klist,
-                metadata=metadata,
-                positions=positions,
-                ab_x=xresult,
-                ab_y=yresult,
-                ab_z=zresult
-                )
-        elif action == 0:
-            np.savez(outfile, omega = freq, klist = klist,
-                metadata=metadata,
-                positions=positions,
-                ab_x=xresult,
-                ab_y=yresult,
-                )
-        elif action == 1:
-            np.savez(outfile, omega = freq, klist = klist,
-                metadata=metadata,
-                positions=positions,
-                ab_z=zresult
-                )
-        else:
-            raise
-
-        if scp_dest:
-            if outfile:
-                subprocess.run(['scp', outfile, scp_dest])
-    scat.forget_matrices() # free memory in case --serial was used
-
-_time_e(btime, verbose)

misc/generaldisp.py

@@ -1,340 +0,0 @@
-#!/usr/bin/env python3
-'''
-Bulk SVD mode computation for compact scatterer 2D lattices
-'''
-
-__TODOs__ = '''
-BIG TODO: Use more efficient way to calculate the interaction sums: perhaps some customized Ewald-type summation?
-
-Small TODOs:
-    - Implement a more user-friendly way to define the lattice base vectors and positions of the particles.
-      cf. https://stackoverflow.com/questions/2371436/evaluating-a-mathematical-expression-in-a-string/2371789
-    - low priority: allow to perform some more custom operations on T-Matrix, using some kind of parsing from the previous point
-    - Autodetect symmetries
-
-'''
-import argparse, re, random, string
-import subprocess
-from scipy.constants import hbar, e as eV, pi, c
-import warnings
-
-def make_action_sharedlist(opname, listname):
-    class opAction(argparse.Action):
-        def __call__(self, parser, args, values, option_string=None):
-            if (not hasattr(args, listname)) or getattr(args, listname) is None:
-                setattr(args, listname, list())
-            getattr(args,listname).append((opname, values))
-    return opAction
-
-parser = argparse.ArgumentParser()
-#TODO? použít type=argparse.FileType('r') ?
-#TODO create some user-friendlier way to define lattice vectors, cf. https://stackoverflow.com/questions/2371436/evaluating-a-mathematical-expression-in-a-string/2371789
-parser.add_argument('--lattice_base', nargs=4, action='store', type=float, required=True, help='Lattice basis vectors x1, y1, x2, y2')
-parser.add_argument('--particle', '-p', nargs='+', action=make_action_sharedlist('particle', 'particlespec'), help='Particle label, coordinates x,y, and (optionally) path to the T-Matrix.')
-parser.add_argument('--TMatrix', '-t', nargs='+', action=make_action_sharedlist('TMatrix_path', 'particlespec'), help='Path to TMatrix file')
-#parser.add_argument('--griddir', action='store', required=True, help='Path to the directory with precalculated translation operators')
-parser.add_argument('--output_prefix', action='store', required=True, help='Prefix to the npz output (will be appended frequency, hexside and chunkno)')
-#sizepar = parser.add_mutually_exclusive_group(required=True)
-#DEL parser.add_argument('--hexside', action='store', type=float, required=True, help='Lattice hexagon size length')
-parser.add_argument('--plot_TMatrix', action='store_true', help='Visualise TMatrix on the first page of the output')
-#parser.add_argument('--SVD_output', action='store', help='Path to output singular value decomposition result')
-parser.add_argument('--maxlayer', action='store', type=int, default=100, help='How far to sum the lattice points to obtain the dispersion')
-parser.add_argument('--scp_to', action='store', metavar='N', type=str, help='SCP the output files to a given destination')
-parser.add_argument('--background_permittivity', action='store', type=float, default=1., help='Background medium relative permittivity (default 1)')
-parser.add_argument('--eVfreq', action='store', required=True, type=float, help='Frequency in eV')
-parser.add_argument('--kdensity', '--k_density', action='store', type=int, default=33, help='Number of k-points per x-axis segment FIXME DESCRIPTION')
-parser.add_argument('--bz_coverage', action='store', type=float, default=1., help='Brillouin zone coverage in relative length (default 1 for whole 1. BZ)')
-parser.add_argument('--bz_edge_width', action='store', type=float, default=0., help='Width of the more densely covered belt along the 1. BZ edge in relative lengths')
-parser.add_argument('--bz_edge_factor', action='store', type=float, default=8., help='Relative density of the belt along the 1. BZ edge w.r.t. k_density (default==8)')
-parser.add_argument('--bz_edge_twoside', action='store_true', help='Compute also the parts of the densely covered edge belt outside the 1. BZ')
-parser.add_argument('--bz_corner_width', action='store', type=float, default=0., help='Size of the more densely covered subcell along the 1. BZ corners in relative lengths')
-parser.add_argument('--bz_corner_factor', action='store', type=float, default=16., help='Relative density of the subcell along the 1. BZ corner w.r.t. k_density (default==16)')
-parser.add_argument('--bz_corner_twoside', action='store_true', help='Compute also the parts of the densely covered subcell outside the 1. BZ')
-
-parser.add_argument('--chunklen', action='store', type=int, default=1000, help='Number of k-points per output file (default 1000)')
-parser.add_argument('--lMax', action=make_action_sharedlist('lMax', 'particlespec'), nargs=+, help='Override lMax from the TMatrix file')
-#TODO some more sophisticated x axis definitions
-parser.add_argument('--gaussian', action='store', type=float, metavar='σ', help='Use a gaussian envelope for weighting the interaction matrix contributions (depending on the distance), measured in unit cell lengths (?) FIxME).')
-parser.add_argument('--verbose', '-v', action='count', help='Be verbose (about computation times, mostly)')
-popgrp=parser.add_argument_group(title='Operations')
-popgrp.add_argument('--tr', dest='ops', nargs='+', action=make_action_sharedlist('tr', 'ops'), default=list()) # the default value for dest can be set once
-popgrp.add_argument('--sym', dest='ops', nargs='+', action=make_action_sharedlist('sym', 'ops'))
-#popgrp.add_argument('--mult', dest='ops', nargs=3, metavar=('INCSPEC', 'SCATSPEC', 'MULTIPLIER'), action=make_action_sharedlist('mult', 'ops'))
-#popgrp.add_argument('--multl', dest='ops', nargs=3, metavar=('INCL[,INCL,...]', 'SCATL[,SCATL,...]', 'MULTIPLIER'), action=make_action_sharedlist('multl', 'ops'))
-parser.add_argument('--frequency_multiplier', action='store', type=float, default=1., help='Multiplies the frequencies in the TMatrix file by a given factor.')
-pargs=parser.parse_args()
-print(pargs)
-
-exit(0) ###
-
-maxlayer=pargs.maxlayer
-#DEL hexside=pargs.hexside
-eVfreq = pargs.eVfreq
-freq = eVfreq*eV/hbar
-verbose=pargs.verbose
-
-#DEL TMatrix_file = pargs.TMatrix
-
-epsilon_b = pargs.background_permittivity #2.3104
-gaussianSigma = pargs.gaussian if pargs.gaussian else None # hexside * 222 / 7
-interpfreqfactor = pargs.frequency_multiplier
-scp_dest = pargs.scp_to if pargs.scp_to else None
-kdensity = pargs.kdensity
-chunklen = pargs.chunklen
-
-#### Nanoparticle position and T-matrix path parsing ####
-TMatrix_paths = dict()
-lMax_overrides = dict()
-default_TMatrix_path = None
-default_lMax_override = None
-if not any((arg_type == 'particle') in (arg_type, arg_content) for in pargs.particlespec):
-    # no particles positions given: suppose only one per unit cell, in the cell origin
-    positions = {None: (0.0)}
-else:
-    positions = dict()
-for arg_type, arg_content in pargs.particlespec:
-    if arg_type == 'particle' # --particle option
-        if  3 <= len(arg_content) <= 4:
-            try:
-                positions[arg_content[0]] = (float(arg_content[1]), float(arg_content[2]))
-            except ValueError as e:
-                e.args += ("second and third argument of --particle must be valid floats, given: ", arg_content)
-                raise
-            if len(arg_content == 4):
-                if arg_content[0] in TMatrix_paths:
-                    warnings.warn('T-matrix path for particle \'%s\' already specified.' 
-                    'Overriding with the last value.' % arg_content[0], SyntaxWarning)
-                TMatrix_paths[arg_content[0]] = arg_content[3]
-
-        else:
-            raise ValueError("--particle expects 3 or 4 arguments, %d given: " % len(arg_content), arg_content)
-    elif arg_type == 'TMatrix_path': # --TMatrix option
-        if len(arg_content) == 1: # --TMatrix default_path
-            if default_TMatrix_path is not None:
-                warnings.warn('Default T-matrix path already specified. Overriding with the last value.', SyntaxWarning)
-            default_TMatrix_path = arg_content[0]
-        elif len(arg_content) > 1: # --TMatrix label [label2 [...]] path
-            for label in arg_content[:-1]:
-                if label in TMatrix_paths.keys():
-                    warnings.warn('T-matrix path for particle \'%s\' already specified.' 
-                    'Overriding with the last value.' % label, SyntaxWarning)
-                TMatrix_paths[label] = arg_content[-1]
-    elif arg_type == 'lMax': # --lMax option
-        if len(arg_content) == 1: # --lMax default_lmax_override
-            if default_lMax_override is not None:
-                warnings.warn('Default lMax override value already specified. Overriding the last value.', SyntaxWarning)
-            default_lMax_override = int(arg_content[-1])
-        else:
-            for label in arg_content[:-1]:
-                if label in lMax_overrides.keys:
-                    warnings.warn('lMax override for particle \'%s\' already specified.'
-                        'overriding with the last value.' % label, SyntaxWarning)
-                lMax_overrides[label] = int(arg_content[-1])
-    else: assert False, 'unknown option type'
-# Check the info from positions and TMatrix_paths and lMax_overrides
-if not set(TMatrix_paths.keys()) <= set(positions.keys()):
-    raise ValueError("T-Matrix path(s) for particle(s) labeled %s was given, but not their positions" 
-            % str(set(TMatrix_paths.keys()) - set(positions.keys())))
-if not set(lMax_overrides.keys()) <= set(positions.keys()):
-    raise ValueError("lMax override(s) for particle(s) labeled %s was given, but not their positions"
-            %str(set(lMax_overrides.keys()) - set(positions.keys())))
-if (set(TMatrix_paths.keys()) != set(positions.keys())) and default_TMatrix_path is None:
-    raise ValueError("Position(s) of particles(s) labeled %s was given without their T-matrix"
-        " and no default T-matrix was specified" 
-        % str(set(positions.keys()) - set(TMatrix_paths_keys())))
-for path in TMatrix_paths.values():
-    if not os.path.exists(path):
-        raise ValueError("Cannot access T-matrix file %s. Does it exist?" % path)
-
-# Assign (pre-parse) the T-matrix operations to individual particles
-ops = dict()
-for label in positions.keys(): ops[label] = list()
-for optype, arg_content in pargs.ops:
-    # if, no label given, apply to all, otherwise on the specifield particles
-    for label in (positions.keys() if len(arg_content) == 1 else arg_content[:-1]): 
-        try:
-            ops[label].append((optype, arg_content[-1]))
-        except KeyError as e:
-            e.args += 'Specified operation on undefined particle labeled \'%s\'' % label
-            raise
-
-print(sys.stderr, "ops: ", ops) #DEBUG
-
-#### Collect all the info about the particles / their T-matrices into one list ####
-# Enumerate and assign all the _different_ T-matrices (without any intelligent group-theory checking, though)
-TMatrix_specs = dict((spec, number) 
-        for (number, spec) in enumerate(set(
-                (lMax_overrides[label] if label in lMax_overrides.keys() else None, 
-                 TMatrix_paths[label], 
-                 tuple(ops[label])) 
-            for label in positions.keys()
-        )))
-# particles_specs contains (label, (xpos, ypos), tmspec_index per element)
-particles_specs = [(label, positions(label), 
-    TMatrix_specs[(lMax_overrides[label] if label in lMax_overrides.keys() else None, 
-                   TMatrix_paths[label], 
-                   tuple(ops[label]))]
-    ) for label in positions.keys()]
-
-# -----------------finished basic CLI parsing (except for op arguments) ------------------
-from qpms.timetrack import _time_b, _time_e
-btime=_time_b(verbose)
-
-import qpms
-import numpy as np
-import os, sys, warnings, math
-from scipy import interpolate
-nx = None
-s3 = math.sqrt(3)
-
-
-# specifikace T-matice zde
-cdn = c/ math.sqrt(epsilon_b)
-TMatrices_orig, freqs_orig, freqs_weirdunits_orig, lMaxTM = qpms.loadScuffTMatrices(TMatrix_file)
-lMax = lMaxTM
-if pargs.lMax:
-    lMax = pargs.lMax if pargs.lMax else lMaxTM    
-my, ny = qpms.get_mn_y(lMax)
-nelem = len(my)
-if pargs.lMax: #force commandline specified lMax
-    TMatrices_orig = TMatrices_orig[...,0:nelem,:,0:nelem]
-
-TMatrices = np.array(np.broadcast_to(TMatrices_orig[:,nx,:,:,:,:],(len(freqs_orig),2,2,nelem,2,nelem)) )
-
-#TMatrices[:,:,:,:,:,ny==3] *= factor13inc
-#TMatrices[:,:,:,ny==3,:,:] *= factor13scat
-xfl = qpms.xflip_tyty(lMax)
-yfl = qpms.yflip_tyty(lMax)
-zfl = qpms.zflip_tyty(lMax)
-c2rot = qpms.apply_matrix_left(qpms.yflip_yy(3),qpms.xflip_yy(3),-1)
-
-reCN = re.compile('(\d*)C(\d+)')
-#TODO C nekonečno
-
-for op in ops:
-    if op[0] == 'all':
-        targets = (0,1)
-    elif isinstance(op[0],int):
-        targets = (op[0],)
-    else:
-        targets = op[0]
-        
-    if op[1] == 'sym':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2
-        elif op[2] == 'C2': # special case of the latter
-            for t in targets:
-                TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1))/2                
-        elif mCN:
-            rotN = int(mCN.group(2))
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                for i in range(rotN):
-                    rotangle = 2*np.pi*i / rotN
-                    rot =  qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle]))
-                    rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle]))
-                    TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-                TMatrices[:,t] = np.sum(TMatrix_contribs, axis=0) / rotN
-        else:
-            raise ValueError('\'%d\' is not an implemented symmetry operation' % op[2])
-    elif op[1] == 'tr':
-        mCN = reCN.match(op[2]) # Fuck van Rossum for not having assignments inside expressions
-        if op[2] == 'σ_z':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_y':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'σ_x':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1))
-        elif op[2] == 'C2':
-            for t in targets:
-                TMatrices[:,t] = qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1)       
-        elif mCN:
-            rotN = int(mCN.group(2))
-            power = int(mCN.group(1)) if mCN.group(1) else 1
-            TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_)
-            for t in targets:
-                rotangle = 2*np.pi*power/rotN
-                rot = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,rotangle]))
-                rotinv = qpms.WignerD_yy_fromvector(lMax, np.array([0,0,-rotangle]))
-                TMatrices[:,t] = qpms.apply_matrix_left(rot, qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1)
-        else:
-            raise ValueError('\'%d\' is not an implemented T-matrix transformation operation' % op[2])
-    elif op[1] == 'copy':
-        raise # not implemented
-    elif op[1] == 'mult':
-        raise # not implemented
-    elif op[1] == 'multl':
-        incy = np.full((nelem,), False, dtype=bool)
-        for incl in op[2][0].split(','):
-            l = int(incl)
-            incy += (l == ny)
-        scaty = np.full((nelem,), False, dtype=bool)
-        for scatl in op[2][1].split(','):
-            l = int(scatl)
-            scaty += (l == ny)
-        for t in targets:
-            TMatrices[np.ix_(np.arange(TMatrices.shape[0]),np.array([t]),np.array([0,1]),scaty,np.array([0,1]),incy)] *= float(op[2][2])
-    else:
-        raise #unknown operation; should not happen
-
-TMatrices_interp = interpolate.interp1d(freqs_orig*interpfreqfactor, TMatrices, axis=0, kind='linear',fill_value="extrapolate")
-
-klist_full = qpms.generate_trianglepoints(kdensity, v3d=True, include_origin=True)*3*math.pi/(3*kdensity*hexside)
-TMatrices_om = TMatrices_interp(freq)
-
-chunkn = math.ceil(klist_full.shape[0] / chunklen)
-
-if verbose:
-    print('Evaluating %d k-points in %d chunks' % (klist_full.shape[0], chunkn), file = sys.stderr)
-    sys.stderr.flush()
-
-metadata = np.array({
-		'lMax' : lMax,
-                'maxlayer' : maxlayer,
-                'gaussianSigma' : gaussianSigma,
-                'epsilon_b' : epsilon_b,
-		'hexside' : hexside,
-                'chunkn' : chunkn,
-                'TMatrix_file' : TMatrix_file,
-                'ops' : ops,
-                })
-
-for chunki in range(chunkn):
-    svdout = '%s_%dnm_%.4f_c%03d.npz' % (pargs.output_prefix, hexside/1e-9, eVfreq, chunki)
-
-    klist = klist_full[chunki * chunklen : (chunki + 1) * chunklen]
-
-    svdres = qpms.hexlattice_zsym_getSVD(lMax=lMax, TMatrices_om=TMatrices_om, epsilon_b=epsilon_b, hexside=hexside, maxlayer=maxlayer,
-            omega=freq, klist=klist, gaussianSigma=gaussianSigma, onlyNmin=False, verbose=verbose)
-
-    #((svUfullTElist, svSfullTElist, svVfullTElist), (svUfullTMlist, svSfullTMlist, svVfullTMlist)) = svdres
-
-    np.savez(svdout, omega = freq, klist = klist,
-            metadata=metadata,
-                     uTE = svdres[0][0],
-                     vTE = svdres[0][2],
-                     sTE = svdres[0][1],
-                     uTM = svdres[1][0],
-                     vTM = svdres[1][2],
-                     sTM = svdres[1][1],
-
-    )
-    svdres=None
-
-    if scp_dest:
-        if svdout:
-            subprocess.run(['scp', svdout, scp_dest])
-
-_time_e(btime, verbose)
-#print(time.strftime("%H.%M:%S",time.gmtime(time.time()-begtime)))

misc/iht-saving.py

@@ -1,35 +0,0 @@
-import qpms
-import numpy as np
-from numpy import newaxis as nx
-import math
-import cmath
-import os
-from scipy.constants import c, e as eV, hbar
-s3 = math.sqrt(3)
-
-import argparse
-
-parser = argparse.ArgumentParser()
-parser.add_argument("omega")
-#parser.add_argument("maxlayer")
-args = parser.parse_args()
-omega_eV = float(args.omega)
-
-print(omega_eV)
-
-epsilon_b = 2.3104
-hexside = 375e-9
-lMax = 3
-maxlayer = 222
-my, ny = qpms.get_mn_y(lMax)
-nelem = len(my)
-
-omega = omega_eV * eV / hbar
-
-k_0 = omega * math.sqrt(epsilon_b) / c
-
-output_prefix = '/tmp/diracpoints-newdata2/%d/' % maxlayer
-
-os.makedirs(output_prefix, exist_ok=True)
-qpms.hexlattice_precalc_AB_save(file=output_prefix+str(omega_eV), lMax=lMax, k_hexside=k_0*hexside,
-        maxlayer=maxlayer, savepointinfo=True)

misc/infiniterectlat-k0realfreqsvd.py

@@ -0,0 +1,128 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser, annotate_pdf_metadata
+
+ap = ArgParser(['rectlattice2d', 'single_particle', 'single_lMax', 'omega_seq'])
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+ap.add_argument("-s", "--singular_values", type=int, default=10, help="Number of singular values to plot")
+ap.add_argument("--D2", action='store_true', help="Use D2h symmetry even if the x and y periods are equal")
+
+a=ap.parse_args()
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+px, py = a.period
+
+#Important! The particles are supposed to be of D2h/D4h symmetry
+thegroup = 'D4h' if px == py and not a.D2 else 'D2h'
+
+particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
+if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
+defaultprefix = "%s_p%gnmx%gnm_m%s_bg%s_f(%g..%g..%g)eV_L%d_SVGamma" % (
+    particlestr, px*1e9, py*1e9, str(a.material), str(a.background), *(a.eV_seq), a.lMax)
+logging.info("Default file prefix: %s" % defaultprefix)
+
+
+import numpy as np
+import qpms
+import warnings
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix, TMatrixGenerator
+from qpms.qpms_c import Particle, pgsl_ignore_error
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.cycommon import DebugFlags, dbgmsg_enable
+from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
+from qpms.symmetries import point_group_info 
+eh = eV/hbar
+
+# not used; TODO:
+irrep_labels = {"B2''":"$B_2''$",
+                "B2'":"$B_2'$",
+                "A1''":"$A_1''$",
+                "A1'":"$A_1'$",
+                "A2''":"$A_2''$",
+                "B1''":"$B_1''$",
+                "A2'":"$A_2'$", 
+                "B1'":"$B_1'$",
+                "E'":"$E'$",
+                "E''":"$E''$",}
+
+dbgmsg_enable(DebugFlags.INTEGRATION)
+
+a1 = ap.direct_basis[0]
+a2 = ap.direct_basis[1]
+
+#Particle positions
+orig_x = [0]
+orig_y = [0]
+orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)
+
+omegas = ap.omegas
+
+logging.info("%d frequencies from %g to %g eV" % (len(omegas), omegas[0]/eh, omegas[-1]/eh))
+
+bspec = BaseSpec(lMax = a.lMax)
+nelem = len(bspec)
+# The parameters here should probably be changed (needs a better qpms_c.Particle implementation)
+pp = Particle(orig_xy[0][0], ap.tmgen, bspec=bspec)
+
+ss, ssw = ScatteringSystem.create([pp], ap.background_emg, omegas[0], latticebasis=ap.direct_basis)
+k = np.array([0.,0.,0])
+# Auxillary finite scattering system for irrep decomposition, quite a hack
+ss1, ssw1 = ScatteringSystem.create([pp], ap.background_emg, omegas[0],sym=FinitePointGroup(point_group_info[thegroup]))
+
+wavenumbers = np.empty(omegas.shape)
+SVs = [None] * ss1.nirreps
+for iri in range(ss1.nirreps):
+    SVs[iri] = np.empty(omegas.shape+(ss1.saecv_sizes[iri],))
+for i, omega in enumerate(omegas):
+    ssw = ss(omega)
+    wavenumbers[i] = ssw.wavenumber.real
+    if ssw.wavenumber.imag: 
+        warnings.warn("Non-zero imaginary wavenumber encountered")
+    with pgsl_ignore_error(15): # avoid gsl crashing on underflow; maybe not needed
+        ImTW = ssw.modeproblem_matrix_full(k)
+    for iri in range(ss1.nirreps):
+        if ss1.saecv_sizes[iri] == 0:
+            continue
+        ImTW_packed = ss1.pack_matrix(ImTW, iri)
+        SVs[iri][i] = np.linalg.svd(ImTW_packed, compute_uv = False)
+
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, omegas=omegas, wavenumbers=wavenumbers, SVs=np.concatenate(SVs, axis=-1), irrep_names=ss1.irrep_names, irrep_sizes=ss1.saecv_sizes, unitcell_area=ss.unitcell_volume
+       )
+logging.info("Saved to %s" % outfile)
+
+
+if a.plot or (a.plot_out is not None):
+    import matplotlib
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt
+    from matplotlib.backends.backend_pdf import PdfPages
+    
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    cc = plt.rcParams['axes.prop_cycle']()
+    for iri in range(ss1.nirreps):
+        cargs = next(cc)
+        nlines = min(a.singular_values, ss1.saecv_sizes[iri])
+        for i in range(nlines):
+            ax.plot(omegas/eh, SVs[iri][:,-1-i],
+                label= None if i else irrep_labels[ss1.irrep_names[iri]], 
+                **cargs)
+    ax.set_ylim([0,1.1])
+    ax.set_xlabel('$\hbar \omega / \mathrm{eV}$')
+    ax.set_ylabel('Singular values')
+    ax.legend()
+
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    with PdfPages(plotfile) as pdf:
+        pdf.savefig(fig)
+        annotate_pdf_metadata(pdf, scriptname='infiniterectlat-k0realfreqsvd.py')
+
+exit(0)
+

misc/infiniterectlat-scatter.py

@@ -0,0 +1,219 @@
+#!/usr/bin/env python3
+
+import math
+pi = math.pi
+from qpms.argproc import ArgParser, annotate_pdf_metadata
+
+ap = ArgParser(['rectlattice2d', 'single_particle', 'single_lMax', 'omega_seq_real_ng', 'planewave'])
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+#ap.add_argument("-g", "--save-gradually", action='store_true', help="saves the partial result after computing each irrep")
+
+
+a=ap.parse_args()
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+import numpy as np
+import qpms
+from qpms.qpms_p import cart2sph, sph2cart, sph_loccart2cart, sph_loccart_basis
+import warnings
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix, TMatrixGenerator
+from qpms.qpms_c import Particle, pgsl_ignore_error
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.cycommon import DebugFlags, dbgmsg_enable
+from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
+eh = eV/hbar
+
+dbgmsg_enable(DebugFlags.INTEGRATION)
+
+px, py = a.period
+
+particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
+if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
+defaultprefix = "%s_p%gnmx%gnm_m%s_bg%s_φ%g_θ(%g_%g)π_ψ%gπ_χ%gπ_f%s_L%d" % (
+    particlestr, px*1e9, py*1e9, str(a.material), str(a.background), a.phi/pi, np.amin(a.theta)/pi, np.amax(a.theta)/pi, a.psi/pi, a.chi/pi, ap.omega_descr, a.lMax)
+logging.info("Default file prefix: %s" % defaultprefix)
+
+
+a1 = ap.direct_basis[0]
+a2 = ap.direct_basis[1]
+
+#Particle positions
+orig_x = [0]
+orig_y = [0]
+orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)
+
+bspec = BaseSpec(lMax = a.lMax)
+# The parameters here should probably be changed (needs a better qpms_c.Particle implementation)
+pp = Particle(orig_xy[0][0], ap.tmgen, bspec=bspec)
+par = [pp]
+
+
+ss, ssw = ScatteringSystem.create(par, ap.background_emg, ap.allomegas[0], latticebasis = ap.direct_basis)
+
+
+## Plane wave data
+a.theta = np.array(a.theta)
+dir_sph_list = np.stack((np.broadcast_to(1, a.theta.shape), a.theta, np.broadcast_to(a.phi, a.theta.shape)), axis=-1)
+sψ, cψ = math.sin(a.psi), math.cos(a.psi)
+sχ, cχ = math.sin(a.chi), math.cos(a.chi)
+E_sph = (0., cψ*cχ + 1j*sψ*sχ, sψ*cχ + 1j*cψ*sχ)
+
+dir_cart_list = sph2cart(dir_sph_list)
+E_cart_list = sph_loccart2cart(E_sph, dir_sph_list)
+
+nfreq = len(ap.allomegas)
+ndir = len(dir_sph_list)
+
+k_cart_arr = np.empty((nfreq, ndir, 3), dtype=float)
+wavenumbers = np.empty((nfreq,), dtype=float)
+
+σ_ext_arr = np.empty((nfreq,ndir), dtype=float)
+σ_scat_arr = np.empty((nfreq,ndir), dtype=float)
+
+with pgsl_ignore_error(15): # avoid gsl crashing on underflow
+    for i, omega in enumerate(ap.allomegas):
+        if i != 0:
+            ssw = ss(omega)
+        if ssw.wavenumber.imag != 0:
+            warnings.warn("The background medium wavenumber has non-zero imaginary part. Don't expect meaningful results for cross sections.")
+        wavenumber = ssw.wavenumber.real
+        wavenumbers[i] = wavenumber
+
+        k_sph_list = np.array(dir_sph_list, copy=True)
+        k_sph_list[:,0] = wavenumber
+
+        k_cart_arr[i] = sph2cart(k_sph_list)
+
+
+        for j in range(ndir):
+            k_cart = k_cart_arr[i,j]
+            blochvector = (k_cart[0], k_cart[1], 0)
+            # the following two could be calculated only once, but probably not a big deal
+            LU = ssw.scatter_solver(k=blochvector)
+            ã = ss.planewave_full(k_cart=k_cart, E_cart=E_cart_list[j])
+            Tã = ssw.apply_Tmatrices_full(ã)
+            f = LU(Tã)
+
+            σ_ext_arr[i,j] = -np.vdot(ã, f).real/wavenumber**2
+            translation_matrix = ssw.translation_matrix_full(blochvector=blochvector) + np.eye(ss.fecv_size)
+            σ_scat_arr[i,j] = np.vdot(f,np.dot(translation_matrix, f)).real/wavenumber**2
+
+σ_abs_arr = σ_ext_arr - σ_scat_arr
+
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, dir_sph=dir_sph_list, k_cart = k_cart_arr, omega = ap.allomegas, E_cart = E_cart_list, wavenumbers= wavenumbers, σ_ext=σ_ext_arr,σ_abs=σ_abs_arr,σ_scat=σ_scat_arr, unitcell_area=ss.unitcell_volume
+       )
+logging.info("Saved to %s" % outfile)
+
+
+if a.plot or (a.plot_out is not None):
+    import matplotlib
+    from matplotlib.backends.backend_pdf import PdfPages
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt
+    from scipy.interpolate import griddata
+
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    with PdfPages(plotfile) as pdf:
+        ipm = 'nearest'
+        sintheta = np.sin(a.theta)
+        if False: #len(ap.omega_ranges) != 0:
+            # angle plot ---------------------------------
+            fig = plt.figure(figsize=(210/25.4, 297/25.4))
+            vmax = max(np.amax(σ_ext_arr), np.amax(σ_scat_arr), np.amax(σ_abs_arr))
+            vmin = min(np.amin(σ_ext_arr), np.amin(σ_scat_arr), np.amin(σ_abs_arr))
+
+            ax = fig.add_subplot(311)
+            ax.pcolormesh(a.theta, ap.allomegas/eh, σ_ext_arr, vmin=vmin, vmax=vmax)
+            ax.set_xlabel('$\\theta$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{ext}$')
+
+            ax = fig.add_subplot(312)
+            ax.pcolormesh(a.theta, ap.allomegas/eh, σ_scat_arr, vmin=vmin, vmax=vmax)
+            ax.set_xlabel('$\\theta$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{scat}$')
+
+            ax = fig.add_subplot(313)
+            im = ax.pcolormesh(a.theta, ap.allomegas/eh, σ_abs_arr, vmin=vmin, vmax=vmax)
+            ax.set_xlabel('$\\theta$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{abs}$')
+            
+            
+            fig.subplots_adjust(right=0.8)
+            fig.colorbar(im, cax = fig.add_axes([0.85, 0.15, 0.05, 0.7]))
+
+            pdf.savefig(fig)
+            plt.close(fig)
+
+        if len(ap.omega_ranges) != 0:
+            # "k-space" plot -----------------------------
+            domega = np.amin(np.diff(ap.allomegas))
+            dsintheta = np.amin(abs(np.diff(sintheta)))
+            dk = dsintheta * wavenumbers[0]
+
+            # target image grid
+            grid_y, grid_x = np.mgrid[ap.allomegas[0] : ap.allomegas[-1] : domega, np.amin(sintheta) * wavenumbers[-1] : np.amax(sintheta) * wavenumbers[-1] : dk]
+            imextent = (np.amin(sintheta) * wavenumbers[-1] / 1e6, np.amax(sintheta) * wavenumbers[-1] / 1e6, ap.allomegas[0] / eh, ap.allomegas[-1] / eh)
+            
+            # source coordinates for griddata
+            ktheta = sintheta[None, :] * wavenumbers[:, None]
+            omegapoints = np.broadcast_to(ap.allomegas[:, None], ktheta.shape)
+            points = np.stack( (ktheta.flatten(), omegapoints.flatten()), axis = -1)
+
+            fig = plt.figure(figsize=(210/25.4, 297/25.4))
+            vmax = np.amax(σ_ext_arr)
+
+            ax = fig.add_subplot(311)
+            grid_z = griddata(points, σ_ext_arr.flatten(), (grid_x, grid_y), method = ipm)
+            ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
+            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{ext}$')
+
+            ax = fig.add_subplot(312)
+            grid_z = griddata(points, σ_scat_arr.flatten(), (grid_x, grid_y), method = ipm)
+            ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
+            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{scat}$')
+
+            ax = fig.add_subplot(313)
+            grid_z = griddata(points, σ_abs_arr.flatten(), (grid_x, grid_y), method = ipm)
+            im = ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
+            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
+            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
+            ax.set_title('$\\sigma_\\mathrm{abs}$')
+
+            fig.subplots_adjust(right=0.8)
+            fig.colorbar(im, cax = fig.add_axes([0.85, 0.15, 0.05, 0.7]))
+
+            pdf.savefig(fig)
+            plt.close(fig)
+
+        for omega in ap.omega_singles:
+            i = np.searchsorted(ap.allomegas, omega)
+
+            fig = plt.figure()
+            fig.suptitle("%g eV" % (omega / eh))
+            ax = fig.add_subplot(111)
+            sintheta = np.sin(a.theta)
+            ax.plot(sintheta, σ_ext_arr[i]*1e12,label='$\sigma_\mathrm{ext}$')
+            ax.plot(sintheta, σ_scat_arr[i]*1e12, label='$\sigma_\mathrm{scat}$')
+            ax.plot(sintheta, σ_abs_arr[i]*1e12, label='$\sigma_\mathrm{abs}$')
+            ax.legend()
+            ax.set_xlabel('$\sin\\theta$')
+            ax.set_ylabel('$\sigma/\mathrm{\mu m^2}$')
+            
+            pdf.savefig(fig)
+            plt.close(fig)
+        annotate_pdf_metadata(pdf)
+exit(0)
+

misc/lat2d_modes.py

@@ -0,0 +1,166 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser, sfloat, annotate_pdf_metadata
+
+ap = ArgParser(['const_real_background', 'lattice2d', 'multi_particle']) # TODO general analytical background
+    
+ap.add_argument("-k", nargs=2, type=sfloat, required=True, help='k vector', metavar=('K_X', 'K_Y'))
+ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
+ap.add_argument("--rank-tol", type=float, required=False)
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
+ap.add_argument("-c", "--min-candidates", type=int, default=1, help='always try at least this many eigenvalue candidates, even if their SVs in the rank tests are lower than rank_tolerance')
+ap.add_argument("-T", "--residual-tolerance", type=float, default=2.)
+ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
+
+
+#TODO alternative specification of the contour by center and half-axes
+dospec = ap.add_argument_group("Eigenvalue search area by diffracted order specification", "Specification of eigenvalue search area by diffracted order number (requires constant real refractive index for background): the integration contour 'touches' the empty lattice band specified by -b, and its axis lying on the real axis reaches '-f'-way to the next diffractive order")
+dospec.add_argument("-d", "--band-index", type=int, help="Argument's absolute value determines the empty lattice band order (counted from 1), -/+ determines whether the eigenvalues are searched below/above that empty lattice band.", required=True)
+dospec.add_argument("-f", "--interval-factor", type=float, default=0.1, help="Relative length of the integration ellipse axis w.r.t. the interval between two empty lattice bands; this should be be less than 1.") #TODO check
+dospec.add_argument("-i", "--imaginary-aspect-ratio", type=float, default=1., help="Aspect ratio of the integration ellipse (Im/Re); this should not exceed 1/interval_factor.")
+
+ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+
+a = ap.parse_args()
+
+a1 = ap.direct_basis[0]
+a2 = ap.direct_basis[1]
+
+particlestr = "modes" # TODO particle string specifier or some hash, do this in argproc.py
+defaultprefix = "%s_basis%gnm_%gnm__%gnm_%gnm_n%g_b%+d_k(%g_%g)um-1_cn%d" % (
+            particlestr, a1[0]*1e9, a1[1]*1e9, a2[0]*1e9, a2[1]*1e9, a.refractive_index, a.band_index, a.k[0]*1e-6, a.k[1]*1e-6, a.N)
+
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+import numpy as np
+import qpms
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix
+from qpms.qpms_c import Particle, ScatteringSystem, empty_lattice_modes_xy
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.constants import eV, hbar
+eh = eV/hbar
+
+def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
+    x = point_xy[0] - centre_xy[0]
+    y = point_xy[1] - centre_xy[1]
+    ax = halfaxes_xy[0]
+    ay = halfaxes_xy[1]
+    return ((x/ax)**2 + (y/ay)**2) <= 1
+
+beta = np.array(a.k)
+
+if True: # TODO alternative specification of the contour by center and half-axes
+    empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, np.array([0,0]), 1)
+    empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, beta, (1+abs(a.band_index)) * empty_freqs[1])
+
+    # make the frequencies in the list unique
+    empty_freqs = list(empty_freqs)
+    i = 0
+    while i < len(empty_freqs) - 1:
+        if math.isclose(empty_freqs[i], empty_freqs[i+1], rel_tol=1e-13):
+            del empty_freqs[i+1]
+        else:
+            i += 1
+
+    logging.info("Empty freqs: %s", str(empty_freqs))
+    logging.info("Empty freqs (eV): %s", str([ff / eh for ff in empty_freqs]))
+    if a.band_index > 0:
+        top = empty_freqs[a.band_index]
+        bottom = empty_freqs[a.band_index - 1]
+        lebeta_om = bottom
+    else: # a.band_index < 0
+        top = empty_freqs[abs(a.band_index) - 1]
+        bottom = empty_freqs[abs(a.band_index) - 2] if abs(a.band_index) > 1 else 0.
+        lebeta_om = top
+    #print(top,bottom,lebeta_om)
+    freqradius = .5 * (top - bottom) * a.interval_factor
+
+    centfreq = bottom + freqradius if a.band_index > 0 else top - freqradius
+    if freqradius == 0:
+            raise ValueError("Integration contour radius is set to zero. Are you trying to look below the lowest empty lattice band at the gamma point?")
+
+    freqradius *= (1-1e-13) # to not totally touch the singularities
+
+logging.info("Direct lattice basis: %s" % str(ap.direct_basis))
+logging.info("Reciprocal lattice basis: %s" % str(ap.reciprocal_basis2pi))
+
+ss, ssw = ScatteringSystem.create(ap.get_particles(), ap.background_emg, centfreq, latticebasis=ap.direct_basis)
+
+logging.info("Finding eigenvalues around %s (= %s eV)" % (str(centfreq), str(centfreq/eh)))
+logging.info("Real half-axis %s (= %s eV)" % (str(freqradius), str(freqradius/eh)))
+logging.info("Imaginary half-axis %s (= %s eV)" % (str(freqradius*a.imaginary_aspect_ratio), str(freqradius*a.imaginary_aspect_ratio/eh)))
+
+with qpms.pgsl_ignore_error(15):
+    res = ss.find_modes(centfreq, freqradius, freqradius * a.imaginary_aspect_ratio,
+            blochvector = a.k, contour_points = a.N, rank_tol = a.rank_tolerance,
+            res_tol = a.residual_tolerance, rank_min_sel = a.min_candidates)
+
+logging.info("Eigenfrequencies found: %s" % str(res['eigval']))
+logging.info("Eigenfrequencies found (eV): %s" % str(res['eigval'] / eh))
+
+res['inside_contour'] = inside_ellipse((res['eigval'].real, res['eigval'].imag),
+         (centfreq.real, centfreq.imag), (freqradius, freqradius * a.imaginary_aspect_ratio))
+
+#res['refractive_index_internal'] = [emg(om).n for om in res['eigval']]
+
+#del res['omega']  If contour points are not needed...
+#del res['ImTW'] # not if dbg=false anyway
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, empty_freqs=np.array(empty_freqs), 
+        ss_positions=ss.positions, ss_fullvec_poffsets=ss.fullvec_poffsets, 
+        ss_fullvec_psizes=ss.fullvec_psizes,
+        ss_bspecs_flat = np.concatenate(ss.bspecs),
+        ss_lattice_basis=ss.lattice_basis, ss_reciprocal_basis = ss.reciprocal_basis,
+        **res)
+logging.info("Saved to %s" % outfile)
+
+
+if a.plot or (a.plot_out is not None):
+    if len(res['eigval']) == 0:
+        logging.info("No eigenvalues found; nothing to plot")
+        exit(1)
+    imcut = np.linspace(0, -freqradius)
+    recut1 = np.sqrt(lebeta_om**2+imcut**2) # incomplete Gamma-related cut
+    recut2 = np.sqrt((lebeta_om/2)**2-imcut**2) + lebeta_om/2 # odd-power-lilgamma-related cut
+
+    import matplotlib
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt
+    from matplotlib.backends.backend_pdf import PdfPages
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111,)
+    #ax.plot(res['omega'].real/eh, res['omega'].imag/eh*1e3, ':') #res['omega'] not implemented in ScatteringSystem
+    ax.add_artist(matplotlib.patches.Ellipse((centfreq.real/eh, centfreq.imag/eh*1e3),
+        2*freqradius/eh, 2*freqradius*a.imaginary_aspect_ratio/eh*1e3, fill=False,
+        ls=':'))
+    ax.scatter(x=res['eigval'].real/eh, y=res['eigval'].imag/eh*1e3 , c = res['inside_contour']
+                      )
+    ax.plot(recut1/eh, imcut/eh*1e3)
+    ax.plot(recut2/eh, imcut/eh*1e3)
+    for i,om in enumerate(res['eigval']):
+            ax.annotate(str(i), (om.real/eh, om.imag/eh*1e3))
+    xmin = np.amin(res['eigval'].real)/eh
+    xmax = np.amax(res['eigval'].real)/eh
+    xspan = xmax-xmin
+    ymin = np.amin(res['eigval'].imag)/eh*1e3
+    ymax = np.amax(res['eigval'].imag)/eh*1e3
+    yspan = ymax-ymin
+    ax.set_xlim([xmin-.1*xspan, xmax+.1*xspan])
+    ax.set_ylim([ymin-.1*yspan, ymax+.1*yspan])
+    ax.set_xlabel('$\hbar \Re \omega / \mathrm{eV}$')
+    ax.set_ylabel('$\hbar \Im \omega / \mathrm{meV}$')
+
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    with PdfPages(plotfile) as pdf:
+        pdf.savefig(fig)
+        annotate_pdf_metadata(pdf, scriptname='lat2d_modes.py')
+
+exit(0)
+

misc/lat2d_realfreqsvd.py

@@ -0,0 +1,129 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser, sfloat, annotate_pdf_metadata
+
+ap = ArgParser(['background', 'lattice2d', 'multi_particle',  'omega_seq'])
+
+ap.add_argument("-k", nargs=2, type=sfloat, required=True, help='k vector', metavar=('K_X', 'K_Y'))
+ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
+
+ap.add_argument("-g", "--little-group", type=str, default="trivial_g", help="Little group for subspace irrep classification", action="store")
+
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+ap.add_argument("-s", "--singular_values", type=int, default=10, help="Number of singular values to plot")
+
+a=ap.parse_args()
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+
+#Important! The particles are supposed to be of D2h/D4h symmetry
+# thegroup = 'D4h' if px == py and not a.D2 else 'D2h'
+
+a1 = ap.direct_basis[0]
+a2 = ap.direct_basis[1]
+
+particlestr = "svdinterval" # TODO particle string specifier or some hash, do this in argproc.py
+defaultprefix = "%s_basis%gnm_%gnm__%gnm_%gnm_f(%g..%g..%g)eV_k%g_%g" % (
+    particlestr, a1[0]*1e9, a1[1]*1e9, a2[0]*1e9, a2[1]*1e9, *(a.eV_seq), ap.k[0], ap.k[1])
+logging.info("Default file prefix: %s" % defaultprefix)
+
+
+import numpy as np
+import qpms
+import warnings
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix, TMatrixGenerator
+from qpms.qpms_c import Particle, pgsl_ignore_error, empty_lattice_modes_xy
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.cycommon import DebugFlags, dbgmsg_enable
+from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
+from qpms.symmetries import point_group_info 
+eh = eV/hbar
+
+# not used; TODO:
+irrep_labels = {"B2''":"$B_2''$",
+                "B2'":"$B_2'$",
+                "A1''":"$A_1''$",
+                "A1'":"$A_1'$",
+                "A2''":"$A_2''$",
+                "B1''":"$B_1''$",
+                "A2'":"$A_2'$", 
+                "B1'":"$B_1'$",
+                "E'":"$E'$",
+                "E''":"$E''$",}
+
+dbgmsg_enable(DebugFlags.INTEGRATION)
+
+
+
+omegas = ap.omegas
+
+logging.info("%d frequencies from %g to %g eV" % (len(omegas), omegas[0]/eh, omegas[-1]/eh))
+
+particles = ap.get_particles()
+
+ss, ssw = ScatteringSystem.create(particles, ap.background_emg, omegas[0], latticebasis=ap.direct_basis)
+k = np.array([ap.k[0], ap.k[1], 0])
+# Auxillary finite scattering system for irrep decomposition, quite a hack
+ss1, ssw1 = ScatteringSystem.create(particles, ap.background_emg, omegas[0],sym=FinitePointGroup(point_group_info[ap.little_group]))
+
+wavenumbers = np.empty(omegas.shape)
+SVs = [None] * ss1.nirreps
+for iri in range(ss1.nirreps):
+    SVs[iri] = np.empty(omegas.shape+(ss1.saecv_sizes[iri],))
+for i, omega in enumerate(omegas):
+    ssw = ss(omega)
+    wavenumbers[i] = ssw.wavenumber.real
+    if ssw.wavenumber.imag: 
+        warnings.warn("Non-zero imaginary wavenumber encountered")
+    with pgsl_ignore_error(15): # avoid gsl crashing on underflow; maybe not needed
+        ImTW = ssw.modeproblem_matrix_full(k)
+    for iri in range(ss1.nirreps):
+        ImTW_packed = ss1.pack_matrix(ImTW, iri)
+        SVs[iri][i] = np.linalg.svd(ImTW_packed, compute_uv = False)
+
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, omegas=omegas, wavenumbers=wavenumbers, SVs=np.concatenate(SVs, axis=-1), irrep_names=ss1.irrep_names, irrep_sizes=ss1.saecv_sizes, unitcell_area=ss.unitcell_volume
+       )
+logging.info("Saved to %s" % outfile)
+
+
+if a.plot or (a.plot_out is not None):
+    import matplotlib
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt
+    from matplotlib.backends.backend_pdf import PdfPages
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    cc = plt.rcParams['axes.prop_cycle']()
+    for iri in range(ss1.nirreps):
+        cargs = next(cc)
+        nlines = min(a.singular_values, ss1.saecv_sizes[iri])
+        for i in range(nlines):
+            ax.plot(omegas/eh, SVs[iri][:,-1-i],
+                label= None if i else irrep_labels.get(ss1.irrep_names[iri], ss1.irrep_names[iri]), 
+                **cargs)
+    ax.set_ylim([0,1.1])
+    if hasattr(ap, "background_epsmu"):
+        xlim = ax.get_xlim()
+        omegas_empty = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, k, omegas[-1])
+        for om in omegas_empty:
+            if om/eh > xlim[0] and om/eh < xlim[1]:
+                ax.axvline(om/eh, ls=':')
+    ax.set_xlabel('$\hbar \omega / \mathrm{eV}$')
+    ax.set_ylabel('Singular values')
+    ax.legend()
+
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    with PdfPages(plotfile) as pdf:
+        pdf.savefig(fig)
+        annotate_pdf_metadata(pdf, scriptname='lat2d_realfreqsvd.py')
+
+exit(0)
+

misc/processWfiles.py

@@ -1,11 +0,0 @@
-#!/usr/bin/env python3
-
-import sys
-from qpms import processWfiles_sameKs
-
-npart = int(sys.argv[1])
-dest = sys.argv[2]
-srcs = sys.argv[3:]
-
-processWfiles_sameKs(srcs, dest, f='d', nparticles=npart)
-

misc/processWfiles2part.py

@@ -1,10 +0,0 @@
-#!/usr/bin/env python3
-
-import sys
-from qpms import processWfiles_sameKs
-
-dest = sys.argv[1]
-srcs = sys.argv[2:]
-
-processWfiles_sameKs(srcs, dest, f='d')
-

misc/processWfiles_sortnames.py

@@ -1,13 +0,0 @@
-#!/usr/bin/env python3
-
-import sys
-from qpms import processWfiles_sameKs
-
-npart = int(sys.argv[1])
-dest = sys.argv[2]
-srcs = sys.argv[3:]
-
-srcs_sorted = sorted(srcs, key=float)
-
-processWfiles_sameKs(srcs_sorted, dest, f='d', nparticles=npart)
-

misc/rectlat_simple_modes.py

@@ -0,0 +1,167 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser, annotate_pdf_metadata
+
+ap = ArgParser(['rectlattice2d', 'const_real_background', 'single_particle', 'single_lMax']) # const_real_background needed for calculation of the diffracted orders
+ap.add_argument("-k", nargs=2, type=float, required=True, help='k vector', metavar=('K_X', 'K_Y'))
+ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
+ap.add_argument("--rank-tol", type=float, required=False)
+ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
+ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
+ap.add_argument("-c", "--min-candidates", type=int, default=1, help='always try at least this many eigenvalue candidates, even if their SVs in the rank tests are lower than rank_tolerance')
+ap.add_argument("-T", "--residual-tolerance", type=float, default=2.)
+ap.add_argument("-b", "--band-index", type=int, required=True, help="Argument's absolute value determines the empty lattice band order (counted from 1), -/+ determines whether the eigenvalues are searched below/above that empty lattice band.")
+ap.add_argument("-f", "--interval-factor", type=float, default=0.1)
+ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
+ap.add_argument("-i", "--imaginary-aspect-ratio",  type=float, default=1, help="Aspect ratio of the integration contour (Im/Re)")
+ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
+ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
+
+a=ap.parse_args()
+
+px, py = a.period
+
+if a.kpi:
+    a.k[0] *= math.pi/px
+    a.k[1] *= math.pi/py
+
+particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
+if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
+defaultprefix = "%s_p%gnmx%gnm_m%s_n%g_b%+d_k(%g_%g)um-1_L%d_cn%d" % (
+    particlestr, px*1e9, py*1e9, str(a.material), a.refractive_index, a.band_index, a.k[0]*1e-6, a.k[1]*1e-6, a.lMax, a.N)
+
+import logging
+logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
+
+import numpy as np
+import qpms
+from qpms.cybspec import BaseSpec
+from qpms.cytmatrices import CTMatrix
+from qpms.qpms_c import Particle, ScatteringSystem, empty_lattice_modes_xy
+from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
+from qpms.constants import eV, hbar
+eh = eV/hbar
+
+def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
+    x = point_xy[0] - centre_xy[0]
+    y = point_xy[1] - centre_xy[1]
+    ax = halfaxes_xy[0]
+    ay = halfaxes_xy[1]
+    return ((x/ax)**2 + (y/ay)**2) <= 1
+
+a1 = ap.direct_basis[0]
+a2 = ap.direct_basis[1]
+
+#Particle positions
+orig_x = [0]                                 
+orig_y = [0]            
+orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)
+
+if a.material in lorentz_drude:
+	emg = EpsMuGenerator(lorentz_drude[a.material])
+else: # constant refractive index
+        emg = EpsMuGenerator(EpsMu(a.material**2))
+
+beta = np.array(a.k)
+
+empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, np.array([0,0]), 1)
+empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, beta, (1+abs(a.band_index)) * empty_freqs[1])
+
+# make the frequencies in the list unique
+empty_freqs = list(empty_freqs)
+i = 0
+while i < len(empty_freqs) - 1:
+    if math.isclose(empty_freqs[i], empty_freqs[i+1], rel_tol=1e-13):
+        del empty_freqs[i+1]
+    else:
+        i += 1
+
+logging.info("Empty freqs: %s", str(empty_freqs))
+if a.band_index > 0:
+    top = empty_freqs[a.band_index]
+    bottom = empty_freqs[a.band_index - 1]
+    lebeta_om = bottom
+else: # a.band_index < 0
+    top = empty_freqs[abs(a.band_index) - 1]
+    bottom = empty_freqs[abs(a.band_index) - 2] if abs(a.band_index) > 1 else 0.
+    lebeta_om = top
+#print(top,bottom,lebeta_om)
+freqradius = .5 * (top - bottom) * a.interval_factor
+
+centfreq = bottom + freqradius if a.band_index > 0 else top - freqradius
+
+bspec = BaseSpec(lMax = a.lMax)
+pp = Particle(orig_xy[0][0], t = ap.tmgen, bspec=bspec)
+
+ss, ssw = ScatteringSystem.create([pp], ap.background_emg, centfreq, latticebasis = ap.direct_basis)
+
+if freqradius == 0:
+    raise ValueError("Integration contour radius is set to zero. Are you trying to look below the lowest empty lattice band at the gamma point?")
+
+freqradius *= (1-1e-13) # to not totally touch the singularities
+
+with qpms.pgsl_ignore_error(15):
+    res = ss.find_modes(centfreq, freqradius, freqradius * a.imaginary_aspect_ratio,
+            blochvector = a.k, contour_points = a.N, rank_tol = a.rank_tolerance,
+            res_tol = a.residual_tolerance, rank_min_sel = a.min_candidates)
+
+logging.info("Eigenfrequencies found: %s" % str(res['eigval']))
+
+res['inside_contour'] = inside_ellipse((res['eigval'].real, res['eigval'].imag),
+         (centfreq.real, centfreq.imag), (freqradius, freqradius * a.imaginary_aspect_ratio))
+
+res['refractive_index_internal'] = [emg(om).n for om in res['eigval']]
+
+#del res['omega']  If contour points are not needed...
+#del res['ImTW'] # not if dbg=false anyway
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta={**vars(a), 'qpms_version' : qpms.__version__()}, empty_freqs=np.array(empty_freqs), 
+        ss_positions=ss.positions, ss_fullvec_poffsets=ss.fullvec_poffsets, 
+        ss_fullvec_psizes=ss.fullvec_psizes,
+        ss_bspecs_flat = np.concatenate(ss.bspecs),
+        ss_lattice_basis=ss.lattice_basis, ss_reciprocal_basis = ss.reciprocal_basis,
+        **res)
+logging.info("Saved to %s" % outfile)
+
+
+if a.plot or (a.plot_out is not None):
+    imcut = np.linspace(0, -freqradius)
+    recut1 = np.sqrt(lebeta_om**2+imcut**2) # incomplete Gamma-related cut
+    recut2 = np.sqrt((lebeta_om/2)**2-imcut**2) + lebeta_om/2 # odd-power-lilgamma-related cut
+
+    import matplotlib
+    matplotlib.use('pdf')
+    from matplotlib import pyplot as plt
+    from matplotlib.backends.backend_pdf import PdfPages
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111,)
+    #ax.plot(res['omega'].real/eh, res['omega'].imag/eh*1e3, ':') #res['omega'] not implemented in ScatteringSystem
+    ax.add_artist(matplotlib.patches.Ellipse((centfreq.real/eh, centfreq.imag/eh*1e3),
+        2*freqradius/eh, 2*freqradius*a.imaginary_aspect_ratio/eh*1e3, fill=False,
+        ls=':'))
+    ax.scatter(x=res['eigval'].real/eh, y=res['eigval'].imag/eh*1e3 , c = res['inside_contour']
+                      )
+    ax.plot(recut1/eh, imcut/eh*1e3)
+    ax.plot(recut2/eh, imcut/eh*1e3)
+    for i,om in enumerate(res['eigval']):
+            ax.annotate(str(i), (om.real/eh, om.imag/eh*1e3))
+    xmin = np.amin(res['eigval'].real)/eh
+    xmax = np.amax(res['eigval'].real)/eh
+    xspan = xmax-xmin
+    ymin = np.amin(res['eigval'].imag)/eh*1e3
+    ymax = np.amax(res['eigval'].imag)/eh*1e3
+    yspan = ymax-ymin
+    ax.set_xlim([xmin-.1*xspan, xmax+.1*xspan])
+    ax.set_ylim([ymin-.1*yspan, ymax+.1*yspan])
+    ax.set_xlabel('$\hbar \Re \omega / \mathrm{eV}$')
+    ax.set_ylabel('$\hbar \Im \omega / \mathrm{meV}$')
+
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    with PdfPages(plotfile) as pdf:
+        pdf.savefig(fig)
+        annotate_pdf_metadata(pdf, scriptname="rectlat_simple_modes.py")
+
+exit(0)
+

misc/riinfo2c.py

@@ -1,31 +0,0 @@
-'''INCOMPLETE! This will read read the refractiveindex.info yaml files
-and transforms the database into a C source.'''
-
-import re
-import os
-try:
-    from yaml import CLoader as Loader, CDumper as Dumper
-except ImportError:
-    from yaml import Loader, Dumper
-
-# Right now, we can process only the 'tabulated nk' data
-searchfor = '- type: tabulated nk'
-searchfor = re.compile(searchfor)
-
-ridatadir = "/u/46/necadam1/unix/repo/refractiveindex.info-database/database/data"
-
-nktables = dict()
-
-def find_files_by_pattern (pattern, dir):
-  r = re.compile(pattern)
-  for parent, dnames, fnames in os.walk(ridatadir):
-    for fname in fnames:
-        filename = os.path.join(parent, fname)
-        if os.path.isfile(filename):
-            with open(filename) as f:
-                text = f.read()
-                if r.search(text):
-                    yield (
-
-
-

misc/subroutines-mstm

@@ -1,85 +0,0 @@
-ricbessel # ricatti-bessel psi
-richankes # ricatti-hankel xi
-cricbessel
-crichankel # (same with complex argument)
-cspherebessel # spherical Bessel jn(z), yn(z)
-vcfunc # vector coupling coefficients C(m,n|k,l|m+k,w), w = |n-l|,...n+l
-normalizedlegendre # normalized asssociated legendre functions
-rotcoef # Generalized spherical functions
-taufunc # vector spherical harmonics, normalized
-pifunc # vector spherical harmonics, ?
-planewavecoef # regular vswf expansion coefficients for a plane wave
-gaussianbeamcoef # regular vsfw expansion for a gaussian beam
-sphereplanewavecoef # plane wave expansion coefficients at sphere origins
-axialtrancoefrecurrence # axial translation ceifficients
-axialtrancoefinit
-tranordertest # test to determine convergence of regular vswf addition theorem
-atcadd
-atcdim
-moffset
-gentrancoef # calculates the vwh translation coefficients for a general translation from one origin to another
-cartosphere # cartesian to spherical coorsinates
-eulerrotation # euler rotation of a point specified in cartesian coords
-ephicoef
-planewavetruncationorder # test to determine max order of vswf expansion of a plane wave at distance r
-vwhcalc # calculates the cartesian components of the vswf at position rpos
-vwhaxialcalc # svwf calculation for an axial translation
-twobytwoinverse # inverse of a 2x2 matrix
-transfer
-
-mpisetup
-
-module spheredata (lots of declarations!, read all the shit)
-(...)
-
-module miecoefdata
-miecoefcalc # calculation of the max order of sphere expansions and storage of mie coefficients
-readtmatrix # reads and stores a PARTICLE T matrix 
-lrmodetran # transformation between lr and te tm basis
-mieoa # optically aptive lorenz/mie coefficients
-getmiedataall # retrieve the array of mie data
-getmiedataone # retrieve mie data for a single sphere
-onemiecoeffmult # multiplies coefficients for sphere i by appropriate lm coefficient
-multmiecoeffmult # generalized mie coefficient mult
-dotproduct # vectorproduct for each rhs element of coefficient array
-
-module translation
-hostconfiguration # calculates lists for identifying host and interior sphere
-rottranmtrxsetup # sets up the stored translation matrices and sets other constants
-rottranmtrxclear # clear the stored translation matrices
-sphereinteraction # the general sphere interaction driver
-external_to_external_expansion # outgoing translation operator: a(i) = H(i-j) a(j)
-external_to_internal_expansion #
-m1_to_the_n # sign flipped for odd degrees
-rottranfarfield # far field formula for outgoing vswf translation
-farfieldtranslationerror # correction ter for hybrid bcgm solution
-rottran # the vectorized rotation translation-rotation operation !!!!	
-spheregaussianbeamcoef # GB coefficients for sphere-centered expansion, obtained via translation
-rotvec # rotation of expansion coefficients amn by euler angles
-
-module scatprops
-tranorders # determinaniot of maximum orders for target-based expansions
-amncommonorigin # translation of sphere-based expansions to common target origin
-lrsphereqeff # general efficiency factor calculation
-qefficiencyfactors # calling routine for efficiency calculation
-scatteringmatrix # scattering amplitude sa and matrix sm calculation
-s11expansion
-fosmcalc # azimuth-averaged scattering matrix
-formexpansion # determine the generalized sf expansion for the azimuth-averaged scatt. matrix
-ranorientscatmatrix
-ranorientscatmatrixcalc
-
-module nearfield
-packcoefficient
-unpackcoefficient
-nearfieldspherepart # the field at point xg generated by the spheres
-nearfieldincidentpart # the incident field at point xg using a regular vswh expansion
-nearfieldincidentcoef # reshaped array of incident field coefficients
-nearfieldpointcalc # !
-nearfieldgridcalc 
-
-module solver
-tmatrixsoln # calculation of T-mat. via solution of interaction eqs for a generalized plane wave expansion
-fixedorsoln # solution of interaction exuations for a fixed orientation
-cbicgff # hybrid bcgm, using far field translation
-cbicg # bcgm iteration solver

misc/test_vswf.gnuplot

@@ -1,11 +0,0 @@
-f = 'out'
-fc = 'outcs'
-do for [t=3:137] {
-y = ((t-3) % 45)/3
-typ = (t-3) % 3
-n = floor(sqrt(y+1))
-m = y - (n*(n+1)-1)
-print 'n = ', n, ', m = ', m, ', typ ', typ
-plot f using 1:t w linespoints, fc using 1:t w linespoints
-pause -1
-}

notes/GF_vs_SWF.lyx

@@ -0,0 +1,461 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 584
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\use_default_options true
+\maintain_unincluded_children false
+\language finnish
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Periodic Green's functions vs.
+ VSWF lattice sums
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\ud}{\mathrm{d}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\abs}[1]{\left|#1\right|}
+\end_inset
+
+ 
+\begin_inset FormulaMacro
+\newcommand{\vect}[1]{\mathbf{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\uvec}[1]{\hat{\mathbf{#1}}}
+\end_inset
+
+
+\lang english
+
+\begin_inset FormulaMacro
+\newcommand{\ush}[2]{Y_{#1}^{#2}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ushD}[2]{Y'_{#1}^{#2}}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\vsh}{\vect A}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\vshD}{\vect{A'}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkc}{\vect y}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkcout}{\vect u}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkcreg}{\vect v}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wckcreg}{a}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wckcout}{f}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Some definitions and useful relations
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\mathcal{H}_{l}^{m}\left(\vect d\right)\equiv h_{l}^{+}\left(\left|\vect d\right|\right)\ush lm\left(\uvec d\right)
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\mathcal{J}_{l}^{m}\left(\vect d\right)\equiv j_{l}\left(\left|\vect d\right|\right)\ush lm\left(\uvec d\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dual spherical harmonics and waves
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\int\ush lm\ushD{l'}{m'}\,\ud\Omega=\delta_{l,l'}\delta_{m,m'}
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\mathcal{J}'_{l}^{m}\left(\vect d\right)\equiv j_{l}\left(\left|\vect d\right|\right)\ushD lm\left(\uvec d\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Expansion of plane wave (CHECKME whether this is really convention-independent,
+ but it seems so)
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+e^{i\kappa\vect r\cdot\uvec r'}=4\pi\sum_{l,m}i^{n}\mathcal{J}'_{l}^{m}\left(\kappa\vect r\right)\ush lm\left(\uvec r'\right)=4\pi\sum_{l,m}i^{n}\mathcal{J}{}_{l}^{m}\left(\kappa\vect r\right)\ushD lm\left(\uvec r'\right)
+\]
+
+\end_inset
+
+This one should also be convention independent (similarly for 
+\begin_inset Formula $\mathcal{H}_{l}^{m}$
+\end_inset
+
+):
+\begin_inset Formula 
+\[
+\mathcal{J}_{l}^{m}\left(-\vect r\right)=\left(-1\right)^{l}\mathcal{J}_{l}^{m}\left(\vect r\right).
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Helmholtz equation and Green's functions (in 3D)
+\end_layout
+
+\begin_layout Standard
+Note that the notation does not follow Linton's (where the wavenumbers are
+ often implicit)
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\left(\nabla^{2}+\kappa^{2}\right)G^{(\kappa)}\left(\vect x,\vect x_{0}\right)=\delta\left(\vect x-\vect x_{0}\right)
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\begin{align*}
+G_{0}^{(\kappa)}\left(\vect x,\vect x_{0}\right) & =G_{0}^{(\kappa)}\left(\vect x-\vect x_{0}\right)=-\frac{\cos\left(\kappa\left|\vect x-\vect x_{0}\right|\right)}{4\pi\left|\vect x-\vect x_{0}\right|}\\
+G_{\pm}^{(\kappa)}\left(\vect x,\vect x_{0}\right) & =G_{\pm}^{(\kappa)}\left(\vect x-\vect x_{0}\right)=-\frac{e^{\pm i\kappa\left|\vect x-\vect x_{0}\right|}}{4\pi\left|\vect x-\vect x_{0}\right|}=-\frac{i\kappa}{4\pi}h_{0}^{\pm}\left(\kappa\left|\vect x-\vect x_{0}\right|\right)=-\frac{i\kappa}{\sqrt{4\pi}}\mathcal{H}_{0}^{0}\left(\kappa\left|\vect x-\vect x_{0}\right|\right)
+\end{align*}
+
+\end_inset
+
+
+\begin_inset Marginal
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula $G_{\pm}^{(\kappa)}\left(\vect x,\vect x_{0}\right)=-\frac{i\kappa}{\ush 00}\mathcal{H}_{0}^{0}\left(\kappa\left|\vect x-\vect x_{0}\right|\right)$
+\end_inset
+
+ in case wacky conventions.
+\end_layout
+
+\end_inset
+
+Lattice GF [Linton (2.3)]:
+\begin_inset Formula 
+\begin{equation}
+G_{\Lambda}^{(\kappa)}\left(\vect s,\vect k\right)\equiv\sum_{\vect R\in\Lambda}G_{+}^{\kappa}\left(\vect s-\vect R\right)e^{i\vect k\cdot\vect R}\label{eq:Lattice GF}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+GF expansion and lattice sum definition
+\end_layout
+
+\begin_layout Standard
+Let's define 
+\begin_inset Formula 
+\[
+\sigma_{l}^{m}\left(\vect s,\vect k\right)=\sum_{\vect R\in\Lambda}\mathcal{H}_{l}^{m}\left(\kappa\left(\vect s+\vect R\right)\right)e^{i\vect k\cdot\vect R},
+\]
+
+\end_inset
+
+and also its dual version
+\begin_inset Formula 
+\[
+\sigma'_{l}^{m}\left(\vect s,\vect k\right)=\sum_{\vect R\in\Lambda}\mathcal{H}'_{l}^{m}\left(\kappa\left(\vect s+\vect R\right)\right)e^{i\vect k\cdot\vect R}.
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Inspired by [Linton (4.1)]; assuming that 
+\begin_inset Formula $\vect s\notin\Lambda$
+\end_inset
+
+, let's expand the lattice Green's function around 
+\begin_inset Formula $\vect s$
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(\kappa)}\left(\vect s+\vect r,\vect k\right)=-i\kappa\sum_{l,m}\tau_{l}^{m}\left(\vect s,\vect k\right)\mathcal{J}_{l}^{m}\left(\kappa\vect r\right)
+\]
+
+\end_inset
+
+and multiply with a dual SH + integrate
+\begin_inset Formula 
+\begin{align}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(\kappa)}\left(\vect s+\vect r,\vect k\right)\ushD{l'}{m'}\left(\uvec r\right) & =-i\kappa\sum_{l,m}\tau_{l}^{m}\left(\vect s,\vect k\right)j_{l}\left(\kappa\left|\vect r\right|\right)\delta_{ll'}\delta_{mm'}\nonumber \\
+ & =-i\kappa\tau_{l'}^{m'}\left(\vect s,\vect k\right)j_{l'}\left(\kappa\left|\vect r\right|\right)\label{eq:tau extraction}
+\end{align}
+
+\end_inset
+
+The expansion coefficients 
+\begin_inset Formula $\tau_{l}^{m}\left(\vect s,\vect k\right)$
+\end_inset
+
+ is then typically extracted by taking the limit 
+\begin_inset Formula $\left|\vect r\right|\to0$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The relation between 
+\begin_inset Formula $\sigma_{l}^{m}\left(\vect s,\vect k\right)$
+\end_inset
+
+ and 
+\begin_inset Formula $\tau_{l}^{m}\left(\vect s,\vect k\right)$
+\end_inset
+
+ can be obtained e.g.
+ from the addition theorem for scalar spherical wavefunctions [Linton (C.3)],
+ 
+\begin_inset Formula 
+\[
+\mathcal{H}_{l}^{m}\left(\vect a+\vect b\right)=\sum_{l'm'}S_{ll'}^{mm'}\left(\vect b\right)\mathcal{J}_{l'}^{m'}\left(\vect a\right),\quad\left|\vect a\right|<\left|\vect b\right|
+\]
+
+\end_inset
+
+where for the zeroth degree and order one has [Linton (C.3)]
+\begin_inset Formula 
+\[
+S_{0l'}^{0m'}\left(\vect b\right)=\sqrt{4\pi}\mathcal{H}'_{l'}^{m'}\left(-\vect b\right)
+\]
+
+\end_inset
+
+
+\begin_inset Marginal
+status open
+
+\begin_layout Plain Layout
+In a totally convention-independent version probably looks like 
+\begin_inset Formula $S_{0l'}^{0m'}\left(\vect b\right)=\ush 00\mathcal{H}'_{l'}^{m'}\left(-\vect b\right)$
+\end_inset
+
+, but the 
+\begin_inset Formula $Y_{0}^{0}$
+\end_inset
+
+ will cancel with the expression for GF anyways, so no harm to the final
+ result.
+\end_layout
+
+\end_inset
+
+From the lattice GF definition 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Lattice GF"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+
+\begin_inset Formula 
+\begin{align*}
+G_{\Lambda}^{(\kappa)}\left(\vect s+\vect r,\vect k\right) & \equiv\frac{-i\kappa}{\sqrt{4\pi}}\sum_{\vect R\in\Lambda}\mathcal{H}_{0}^{0}\left(\kappa\left(\vect s+\vect r-\vect R\right)\right)e^{i\vect k\cdot\vect R}\\
+ & =\frac{-i\kappa}{\sqrt{4\pi}}\sum_{\vect R\in\Lambda}\mathcal{H}_{0}^{0}\left(\kappa\left(\vect s+\vect r-\vect R\right)\right)e^{i\vect k\cdot\vect R}\\
+ & =\frac{-i\kappa}{\sqrt{4\pi}}\sum_{\vect R\in\Lambda}\sum_{l'm'}S_{0l'}^{0m'}\left(\kappa\left(\vect s-\vect R\right)\right)\mathcal{J}_{l'}^{m'}\left(\kappa\vect r\right)e^{i\vect k\cdot\vect R}\\
+ & =-i\kappa\sum_{\vect R\in\Lambda}\sum_{lm}\mathcal{H}'_{l}^{m}\left(-\kappa\left(\vect s-\vect R\right)\right)\mathcal{J}_{l}^{m}\left(\kappa\vect r\right)e^{i\vect k\cdot\vect R}
+\end{align*}
+
+\end_inset
+
+and mutliplying with dual SH and integrating 
+\begin_inset Formula 
+\begin{align*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(\kappa)}\left(\vect s+\vect r,\vect k\right)\ushD{l'}{m'}\left(\uvec r\right) & =-i\kappa\sum_{\vect R\in\Lambda}\sum_{lm}\mathcal{H}'_{l}^{m}\left(-\kappa\left(\vect s-\vect R\right)\right)j_{l}\left(\kappa\left|\vect r\right|\right)\delta_{ll'}\delta_{mm'}e^{i\vect k\cdot\vect R}\\
+ & =-i\kappa\sum_{\vect R\in\Lambda}\mathcal{H}'_{l'}^{m'}\left(\kappa\left(-\vect s+\vect R\right)\right)j_{l'}\left(\kappa\left|\vect r\right|\right)e^{i\vect k\cdot\vect R}\\
+ & =-i\kappa\sigma'_{l'}^{m'}\left(-\vect s,\vect k\right)j_{l'}\left(\kappa\left|\vect r\right|\right)
+\end{align*}
+
+\end_inset
+
+and comparing with 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tau extraction"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ we have
+\begin_inset Formula 
+\[
+\tau_{l}^{m}\left(\vect s,\vect k\right)=\sigma'_{l}^{m}\left(-\vect s,\vect k\right).
+\]
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+TODO maybe also define some 
+\begin_inset Formula $\tau'_{l}^{m}$
+\end_inset
+
+ as expansion coefficients of GF into dual regular SSWFs.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document

notes/INSTALL_ANDROID.md

@@ -0,0 +1,107 @@
+# Installing QPMS on Android/AOSP (-based) systems
+
+Yes, it is possible. Basically all you need is a device capable of running [Termux](https://termux.com/) with enough memory to build everything.
+
+The following instructions have been tested with Termux version 0.118.0 on
+[e/OS/ R development build on a Samsung Galaxy S10e](https://doc.e.foundation/devices/beyond0lte/install)
+([e-1.0-r-20220526188878-dev-beyond0lte](https://images.ecloud.global/dev/beyond0lte/)).
+Presumably, they should work also on stock Android as well, but who
+in their right mind would run all the spyware by Google & al.?
+
+Physical keyboard or [remote access](https://wiki.termux.com/wiki/Remote_Access) is strongly recommended. :D
+
+## Get Termux
+
+Just [install the Termux app from F-Droid or Github as per instructions](https://github.com/termux/termux-app#f-droid).
+
+Open Termux; the following steps of these instructions are basically
+just commands you need to type in Termux.
+
+## Install prerequisities from termux repositories
+
+```
+pkg install python3 cmake git clang build-essential binutils
+```
+
+## Build and install GSL
+
+```
+curl -O https://www.nic.funet.fi/pub/gnu/ftp.gnu.org/pub/gnu/gsl/gsl-latest.tar.gz
+tar xf gsl-latest.tar.gz
+cd gsl-2.7.1
+./configure --prefix=$PREFIX
+make    # add -j4 or so to make it faster on multicore systems
+make install
+cd -
+```
+
+## Build and install OpenBLAS
+
+```
+git clone https://github.com/xianyi/OpenBLAS.git
+cd OpenBLAS
+make
+make PREFIX=$PREFIX install
+cd -
+```
+
+### Workaround for "broken" setup.py script
+
+The goal is to fix `setup.py` so that it finds the correct libraries automatically, but in the meantime, you can use this workaround to get the Python part of QPMS installed:
+
+```
+ln -s $PREFIX/lib/libopenblas.so $PREFIX/LIB/liblapacke.so
+```
+
+## Build and install Numpy
+
+(Successful build requires the `MATHLIB` environmental variable set, otherwise linking will fail; see https://wiki.termux.com/wiki/Python.)
+
+```
+MATHLIB=m pip3 install numpy
+```
+
+### Install Sympy
+
+```
+pip3 install sympy
+```
+
+## Build and install QPMS
+
+```
+git clone https://repo.or.cz/qpms.git
+cd qpms
+cmake -DCMAKE_INSTALL_PREFIX=$PREFIX . # ugly, TODO make a separate build tree!
+make install
+
+python3 setup.py install
+```
+
+Hopefully, QPMS has installed successfully. At this point, you should be able
+to import and use QPMS with some exceptions. First, there is some legacy code
+in the `qpms.qpms_p` module (which is no longer imported automatically with
+bare `import qpms`). You shouldn't need this unless you are trying to run some
+historic Jupyter notebooks or other old custom scripts. It contains a scipy
+dependence, and scipy is hard to get working in Android environment (as
+it requires a Fortran compiler to build).
+
+## Install matplotlib
+
+If you try to run just `pip3 install matplotlib` in Termux, it might likely
+fail when installing the `pillow` dependency.
+First, according to [Termux wiki](https://wiki.termux.com/wiki/Python#Python_module_installation_tips_and_tricks),
+pillow depends on `libpng` and `libjpeg-turbo`, which are fortunately
+available in Termux packages.
+Second, pillow instalation requires an additional environment variable
+`LDFLAGS="-L/system/lib64"` to be set on 64-bit devices.
+
+Hence:
+```
+pkg install libpng libjpeg-turbo
+export LDFLAGS="-L/system/lib64" # on 64-bit devices
+pip3 install matplotlib
+```
+
+After this step, you should be able to run the command-line scripts
+from `misc/` directory and examples from `examples/` directory.

notes/Kambe_Delta_n.lyx

@@ -0,0 +1,266 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 584
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\use_default_options true
+\maintain_unincluded_children false
+\language finnish
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\ud}{\mathrm{d}}
+\end_inset
+
+
+\begin_inset Formula 
+\begin{equation}
+\Delta_{n}(x,z)\equiv\int_{x}^{\infty}t^{-\frac{1}{2}-n}e^{-t+\frac{z^{2}}{4t}}\ud t\label{eq:Delta definition}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Integration per partes:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\int t^{-\frac{1}{2}-n}\ud t=\frac{t^{\frac{1}{2}-n}}{\frac{1}{2}-n};
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\frac{\ud}{\ud t}e^{-t+\frac{z^{2}}{4t}}=\left(-1-\frac{z^{2}}{4t^{2}}\right)e^{-t+\frac{z^{2}}{4t}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{align*}
+\left(\frac{1}{2}-n\right)\Delta_{n} & =-x^{\frac{1}{2}-n}e^{-x+\frac{z^{2}}{4x}}+\int_{x}^{\infty}t^{\frac{1}{2}-n}e^{-t+\frac{z^{2}}{4t}}\ud t+\frac{z^{2}}{4}\int_{x}^{\infty}t^{\frac{-3}{2}-n}e^{-t+\frac{z^{2}}{4t}}\ud t\\
+ & =-x^{\frac{1}{2}-n}e^{-x+\frac{z^{2}}{4x}}+\Delta_{n-1}+\frac{z^{2}}{4}\Delta_{n+1},
+\end{align*}
+
+\end_inset
+
+
+\begin_inset Formula 
+\begin{equation}
+\Delta_{n+1}=\frac{4}{z^{2}}\left(\left(\frac{1}{2}-n\right)\Delta_{n}-\Delta_{n-1}+x^{\frac{1}{2}-n}e^{-x+\frac{z^{2}}{4x}}\right).\label{eq:Delta recurrence}
+\end{equation}
+
+\end_inset
+
+There are obviously wrong signs in Kambe II, (A 3.3).
+\end_layout
+
+\begin_layout Standard
+Eq.
+ 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Delta recurrence"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ is obviously unsuitable for numerical computation when 
+\begin_inset Formula $z$
+\end_inset
+
+approaches 0.
+ However, the definition 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Delta definition"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ suggests that the function should be analytical around 
+\begin_inset Formula $z=0$
+\end_inset
+
+.
+ If 
+\begin_inset Formula $z=0$
+\end_inset
+
+, one has (by definition of incomplete Г function)
+\begin_inset Formula 
+\begin{equation}
+\Delta_{n}(x,0)=\Gamma\left(\frac{1}{2}-n,x\right).\label{eq:Delta:z = 0}
+\end{equation}
+
+\end_inset
+
+For convenience, label 
+\begin_inset Formula $w=z^{2}/4$
+\end_inset
+
+ and 
+\begin_inset Formula 
+\[
+\Delta'_{n}\left(x,w\right)\equiv\int_{x}^{\infty}t^{-\frac{1}{2}-n}e^{-t+\frac{w}{t}}\ud t.
+\]
+
+\end_inset
+
+ Differentiating by parameter 
+\begin_inset Formula $w$
+\end_inset
+
+ (which should be fine as long as the integration contour does not go through
+ zero) gives
+\begin_inset Formula 
+\[
+\frac{\partial\Delta'_{n}\left(x,w\right)}{\partial w}=\Delta'_{n+1}\left(x,w\right),
+\]
+
+\end_inset
+
+so by recurrence
+\begin_inset Formula 
+\[
+\frac{\partial^{k}}{\partial w^{k}}\Delta'_{n}\left(x,w\right)=\Delta'_{n+k}\left(x,w\right).
+\]
+
+\end_inset
+
+Together with 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Delta:z = 0"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+, this gives an expansion around 
+\begin_inset Formula $w=0$
+\end_inset
+
+:
+\begin_inset Formula 
+\[
+\Delta_{n}'\left(x,w\right)=\sum_{k=0}^{\infty}\Gamma\left(\frac{1}{2}-n-k,x\right)\frac{w^{k}}{k!},
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\Delta_{n}\left(x,z\right)=\sum_{k=0}^{\infty}\Gamma\left(\frac{1}{2}-n-k,x\right)\frac{\left(z/2\right)^{2k}}{k!}.
+\]
+
+\end_inset
+
+The big negative first arguments in incomplete 
+\begin_inset Formula $\Gamma$
+\end_inset
+
+ functions should be good (at least I think so, CHECKME), as well as the
+ 
+\begin_inset Formula $1/k!$
+\end_inset
+
+ factor (of course).
+ I am not sure what the convergence radius is, but for 
+\begin_inset Formula $\left|z\right|<2$
+\end_inset
+
+ there seems to be absolutely no problem in using this formula.
+\end_layout
+
+\end_body
+\end_document

notes/ewald_1D_and_2D_in_3D.lyx

@@ -0,0 +1,677 @@
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+\lyxformat 584
+\begin_document
+\begin_header
+\save_transient_properties true
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+\textclass article
+\use_default_options true
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+\language finnish
+\language_package default
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+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 2cm
+\topmargin 2cm
+\rightmargin 2cm
+\bottommargin 2cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
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+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+1D and 2D in 3D Ewald sum
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\ud}{\mathrm{d}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\abs}[1]{\left|#1\right|}
+\end_inset
+
+ 
+\begin_inset FormulaMacro
+\newcommand{\vect}[1]{\mathbf{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\uvec}[1]{\hat{\mathbf{#1}}}
+\end_inset
+
+
+\lang english
+
+\begin_inset FormulaMacro
+\newcommand{\ush}[2]{Y_{#1}^{#2}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ushD}[2]{Y'_{#1}^{#2}}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\vsh}{\vect A}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\vshD}{\vect{A'}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkc}{\vect y}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkcout}{\vect u}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkcreg}{\vect v}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wckcreg}{a}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wckcout}{f}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+General formula
+\end_layout
+
+\begin_layout Standard
+We need to find the long-range part of the expansion coefficient
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{equation}
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{i}{\kappa j_{l'}\left(\kappa\left|\vect r\right|\right)}\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(\kappa)}\left(\vect s+\vect r,\vect k\right)\ushD{l'}{m'}\left(\uvec r\right).\label{eq:tau extraction formula}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+We take [Linton, (2.24)] with slightly modified notation 
+\begin_inset Formula $\left(\vect k_{\vect K}\equiv\vect K+\vect k\right)$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect r}\int_{1/\eta}^{\infty e^{i\pi/4}}e^{-\kappa^{2}\gamma^{2}t^{2}/4}e^{-\left|\vect r^{\bot}\right|^{2}/t^{2}}t^{1-d_{c}}\ud t
+\]
+
+\end_inset
+
+or, evaluated at point 
+\begin_inset Formula $\vect s+\vect r$
+\end_inset
+
+ instead
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\left(\vect s+\vect r\right)}\int_{1/\eta}^{\infty e^{i\pi/4}}e^{-\kappa^{2}\gamma^{2}t^{2}/4}e^{-\left|\vect s^{\bot}+\vect r^{\bot}\right|^{2}/t^{2}}t^{1-d_{c}}\ud t
+\]
+
+\end_inset
+
+The integral can be by substitutions taken into the form 
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\lang english
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{2\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\int_{1/\eta}^{\infty\exp\left(i\pi/4\right)}e^{-\kappa^{2}\gamma_{m}^{2}\zeta^{2}/4}e^{-\left|\vect r_{\bot}\right|^{2}/\zeta^{2}}\zeta^{1-d_{c}}\ud\zeta
+\]
+
+\end_inset
+
+Try substitution 
+\begin_inset Formula $t=\zeta^{2}$
+\end_inset
+
+: then 
+\begin_inset Formula $\ud t=2\zeta\,\ud\zeta$
+\end_inset
+
+ (
+\begin_inset Formula $\ud\zeta=\ud t/2t^{1/2}$
+\end_inset
+
+) and
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{4\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\int_{1/\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\kappa^{2}\gamma_{m}^{2}t/4}e^{-\left|\vect r_{\bot}\right|^{2}/t}t^{\frac{-d_{c}}{2}}\ud t
+\]
+
+\end_inset
+
+Try subst.
+ 
+\begin_inset Formula $\tau=k^{2}\gamma_{m}^{2}/4$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\lang english
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{4\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\left(\frac{\kappa\gamma_{m}}{2}\right)^{d_{c}}\int_{\kappa^{2}\gamma_{m}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{m}^{2}/4\tau}\tau^{\frac{-d_{c}}{2}}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\left(\vect s+\vect r\right)}\int_{\kappa^{2}\gamma_{m}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{m}^{2}/4\tau}\tau^{-\frac{d_{c}}{2}}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+[Linton, (2.25)] with slightly modified notation:
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect r\right)=-\frac{1}{\sqrt{4\pi}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect r}\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}\left|\vect r^{\bot}\right|^{2j}}{j!}\left(\frac{\kappa\gamma_{\vect{\vect k_{\vect K}}}}{2}\right)^{2j-1}\Gamma_{j\vect k_{\vect K}}
+\]
+
+\end_inset
+
+We want to express an expansion in a shifted point, so let's substitute
+ 
+\begin_inset Formula $\vect r\to\vect s+\vect r$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)=-\frac{1}{\sqrt{4\pi}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\left(\vect s+\vect r\right)}\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}\left|\vect s^{\bot}+\vect r^{\bot}\right|^{2j}}{j!}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j-1}\Gamma_{j\vect k_{\vect K}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+Let's do the integration to get 
+\begin_inset Formula $\tau_{l}^{m}\left(\vect s,\vect k\right)$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\left(\vect s+\vect r\right)}\int_{\kappa^{2}\gamma_{\vect k_{\vect K}}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect k_{\vect K}}^{2}/4\tau}\tau^{-\frac{d_{c}}{2}}\ud\tau
+\]
+
+\end_inset
+
+The 
+\begin_inset Formula $\vect r$
+\end_inset
+
+-dependent plane wave factor can be also written as
+\begin_inset Formula 
+\begin{align*}
+e^{i\vect k_{\vect K}\cdot\vect r} & =e^{i\left|\vect k_{\vect K}\right|\vect r\cdot\uvec{\vect k_{\vect K}}}=4\pi\sum_{lm}i^{l}\mathcal{J}'_{l}^{m}\left(\left|\vect k_{\vect K}\right|\vect r\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\\
+ & =4\pi\sum_{lm}i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ushD lm\left(\uvec{\vect r}\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)
+\end{align*}
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+or the other way around
+\begin_inset Formula 
+\[
+e^{i\vect k_{\vect K}\cdot\vect r}=4\pi\sum_{lm}i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ush lm\left(\uvec{\vect r}\right)\ushD lm\left(\uvec{\vect k_{\vect K}}\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+so
+\begin_inset Formula 
+\begin{multline*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\frac{1}{2\pi\mathcal{A}}\times\\
+\times\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ushD lm\left(\uvec r\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\int_{\kappa^{2}\gamma_{\vect{\vect k_{\vect K}}}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect{\vect k_{\vect K}}}^{2}/4\tau}\tau^{-\frac{d_{c}}{2}}\ud\tau
+\end{multline*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+We also have
+\begin_inset Formula 
+\begin{align*}
+e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau} & =e^{-\left(\left|\vect s_{\bot}\right|^{2}+\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\\
+ & =e^{-\left|\vect s_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\sum_{j=0}^{\infty}\frac{1}{j!}\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}}{4\tau}\right)^{j},
+\end{align*}
+
+\end_inset
+
+hence
+\begin_inset Formula 
+\begin{align*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right) & =-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ushD lm\left(\uvec r\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\times\\
+ & \quad\times\sum_{j=0}^{\infty}\frac{1}{j!}\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect{\vect k_{\vect K}}}^{2}}{4}\right)^{j}\underbrace{\int_{\kappa^{2}\gamma_{\vect K}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\tau^{-\frac{d_{c}}{2}-j}\ud\tau}_{\Delta_{j}^{\left(d_{\Lambda}\right)}}\\
+ & =-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\sum_{j=0}^{\infty}\frac{\Delta_{j}^{\left(d_{\Lambda}\right)}}{j!}\times\\
+ & \quad\times\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect k_{\vect K}}^{2}}{4}\right)^{j}\\
+ & =-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\times\\
+ & \quad\times\left(\frac{\kappa\gamma_{\vect{\vect k_{\vect K}}}}{2}\right)^{2j}\sum_{k=0}^{j}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left|\vect r_{\bot}\right|^{2(j-k)}\left(2\vect r_{\bot}\cdot\vect s_{\bot}\right)^{k}.
+\end{align*}
+
+\end_inset
+
+If we label 
+\begin_inset Formula $\left|\vect r_{\bot}\right|\left|\vect s_{\bot}\right|\cos\varphi\equiv\vect r_{\bot}\cdot\vect s_{\bot}$
+\end_inset
+
+, we have
+\begin_inset Formula 
+\begin{multline*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\times\\
+\times\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j}\sum_{k=0}^{j}\left(2\left|\vect s_{\bot}\right|\right)^{k}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left|\vect r_{\bot}\right|^{2j-k}\left(\cos\varphi\right)^{k}
+\end{multline*}
+
+\end_inset
+
+and if we label 
+\begin_inset Formula $\left|\vect r\right|\sin\vartheta\equiv\left|\vect r_{\bot}\right|$
+\end_inset
+
+
+\begin_inset Formula 
+\begin{multline*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi^{d_{c}/2}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\ush lm\left(\uvec{\vect k_{\vect K}}\right)\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j}\times\\
+\times\sum_{k=0}^{j}\left|\vect r\right|^{2j-k}\left(2\left|\vect s_{\bot}\right|\right)^{k}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{2j-k}\left(\cos\varphi\right)^{k}.
+\end{multline*}
+
+\end_inset
+
+Now let's put the RHS into 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tau extraction formula"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ and try eliminating some sum by taking the limit 
+\begin_inset Formula $\left|\vect r\right|\to0$
+\end_inset
+
+.
+ We have 
+\begin_inset Formula $j_{l}\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)\sim\left(\left|\vect k_{\vect K}\right|\left|\vect r\right|\right)^{l}/\left(2l+1\right)!!$
+\end_inset
+
+; the denominator from 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tau extraction formula"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ behaves like 
+\begin_inset Formula $j_{l'}\left(\kappa\left|\vect r\right|\right)\sim\left(\kappa\left|\vect r\right|\right)^{l'}/\left(2l'+1\right)!!.$
+\end_inset
+
+ The leading terms are hence those with 
+\begin_inset Formula $\left|\vect r\right|^{l-l'+2j-k}$
+\end_inset
+
+.
+ So 
+\begin_inset Formula 
+\begin{multline*}
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi^{d_{c}/2}\mathcal{A}\kappa^{1+l'}}\left(2l'+1\right)!!\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{lm}4\pi i^{l}\frac{\left|\vect k_{\vect K}\right|^{l}}{\left(2l+1\right)!!}\ush lm\left(\uvec{\vect k_{\vect K}}\right)\times\\
+\times\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j}\sum_{k=0}^{j}\delta_{l'-l,2j-k}\left(2\left|\vect s_{\bot}\right|\right)^{k}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{l'-l}\left(\cos\varphi\right)^{k}.
+\end{multline*}
+
+\end_inset
+
+Let's now focus on rearranging the sums; we have
+\begin_inset Formula 
+\[
+S(l')\equiv\sum_{l=0}^{\infty}\sum_{j=0}^{\infty}\sum_{k=0}^{j}\delta_{l'-l,2j-k}f(l',l,j,k)=\sum_{l=0}^{\infty}\sum_{j=0}^{\infty}\sum_{k=0}^{j}\delta_{l'-l,2j-k}f(l',l,j,2j-l'+l)
+\]
+
+\end_inset
+
+We have 
+\begin_inset Formula $0\le k\le j$
+\end_inset
+
+, hence 
+\begin_inset Formula $0\le2j-l'+l\le j$
+\end_inset
+
+, hence 
+\begin_inset Formula $-2j\le-l'+l\le-j$
+\end_inset
+
+, hence also 
+\begin_inset Formula $l'-2j\le l\le l'-j$
+\end_inset
+
+, which gives the opportunity to swap the 
+\begin_inset Formula $l,j$
+\end_inset
+
+ sums and the 
+\begin_inset Formula $l$
+\end_inset
+
+-sum becomes finite; so also consuming 
+\begin_inset Formula $\sum_{k=0}^{j}\delta_{l'-l,2j-k}$
+\end_inset
+
+ we get 
+\begin_inset Formula 
+\[
+S(l')=\sum_{j=0}^{\infty}\sum_{l=\max(0,l'-2j)}^{l'-j}f(l',l,j,2j-l'+l).
+\]
+
+\end_inset
+
+Finally, we see that the interval of valid 
+\begin_inset Formula $l$
+\end_inset
+
+ becomes empty when 
+\begin_inset Formula $l'-j<0$
+\end_inset
+
+, i.e.
+ 
+\begin_inset Formula $j>l'$
+\end_inset
+
+; so we get a finite sum
+\begin_inset Formula 
+\[
+S(l')=\sum_{j=0}^{l'}\sum_{l=\max(0,l'-2j)}^{l'-j}f(l',l,j,2j-l'+l).
+\]
+
+\end_inset
+
+Applying rearrangement,
+\begin_inset Formula 
+\begin{multline*}
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi^{d_{c}/2}\mathcal{A}\kappa}\frac{\left(2l'+1\right)!!}{\kappa^{l'}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{j=0}^{l'}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j}\times\sum_{l=\max\left(0,l'-2j\right)}^{l'-j}4\pi i^{l}\left(2\left|\vect s_{\bot}\right|\right)^{2j-l'+l}\frac{\left|\vect k_{\vect K}\right|^{l}}{\left(2l+1\right)!!}\\
+\times\sum_{m=-l}^{l}\ush lm\left(\uvec{\vect k_{\vect K}}\right)\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{l'-l}\left(\cos\varphi\right)^{2j-l'+l},
+\end{multline*}
+
+\end_inset
+
+or replacing the angles with their original definition,
+\begin_inset Formula 
+\begin{multline*}
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi^{d_{c}/2}\mathcal{A}\kappa}\frac{\left(2l'+1\right)!!}{\kappa^{l'}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\sum_{j=0}^{l'}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2j}\times\sum_{l=\max\left(0,l'-2j\right)}^{l'-j}4\pi i^{l}\left(2\left|\vect s_{\bot}\right|\right)^{2j-l'+l}\frac{\left|\vect k_{\vect K}\right|^{l}}{\left(2l+1\right)!!}\\
+\times\sum_{m=-l}^{l}\ush lm\left(\uvec K\right)\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\frac{\left|\vect r_{\bot}\right|}{\left|\vect r\right|}\right)^{l'-l}\left(\frac{\vect r_{\bot}\cdot\vect s_{\bot}}{\left|\vect r_{\bot}\right|\left|\vect s_{\bot}\right|}\right)^{2j-l'+l},
+\end{multline*}
+
+\end_inset
+
+and if we want a 
+\begin_inset Formula $\sigma_{l'}^{m'}\left(\vect s,\vect k\right)$
+\end_inset
+
+ instead, we reverse the sign of 
+\begin_inset Formula $\vect s$
+\end_inset
+
+ and replace all spherical harmonics with their dual counterparts:
+\begin_inset Formula 
+\begin{multline*}
+\sigma_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi^{d_{c}/2}\mathcal{A}\kappa}\frac{\left(2l'+1\right)!!}{\kappa^{l'}}\sum_{\vect K\in\Lambda^{*}}e^{-i\vect k_{\vect K}\cdot\vect s}\sum_{j=0}^{l'}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j}\sum_{l=\max\left(0,l'-2j\right)}^{l'-j}4\pi i^{l}\left(2\left|\vect s_{\bot}\right|\right)^{2j-l'+l}\frac{\left|\vect k_{\vect K}\right|^{l}}{\left(2l+1\right)!!}\times\\
+\times\sum_{m=-l}^{l}\ushD lm\left(\uvec{\vect k_{\vect K}}\right)\int\ud\Omega_{\vect r}\,\ush{l'}{m'}\left(\uvec r\right)\ush lm\left(\uvec r\right)\left(\frac{\left|\vect r_{\bot}\right|}{\left|\vect r\right|}\right)^{l'-l}\left(\frac{-\vect r_{\bot}\cdot\vect s_{\bot}}{\left|\vect r_{\bot}\right|\left|\vect s_{\bot}\right|}\right)^{2j-l'+l},
+\end{multline*}
+
+\end_inset
+
+and remembering that in the plane wave expansion the 
+\begin_inset Quotes eld
+\end_inset
+
+duality
+\begin_inset Quotes erd
+\end_inset
+
+ is interchangeable,
+\begin_inset Formula 
+\begin{multline*}
+\sigma_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi^{d_{c}/2}\mathcal{A}\kappa}\frac{\left(2l'+1\right)!!}{\kappa^{l'}}\sum_{\vect K\in\Lambda^{*}}e^{-i\vect k_{\vect K}\cdot\vect s}\sum_{j=0}^{l'}\frac{\left(-1\right)^{j}}{j!}\Delta_{j}^{\left(d_{\Lambda}\right)}\left(\frac{\kappa\gamma_{\vect k_{\vect K}}}{2}\right)^{2j}\sum_{l=\max\left(0,l'-2j\right)}^{l'-j}4\pi i^{l}\left(2\left|\vect s_{\bot}\right|\right)^{2j-l'+l}\frac{\left|\vect k_{\vect K}\right|^{l}}{\left(2l+1\right)!!}\times\\
+\times\sum_{m=-l}^{l}\ush lm\left(\uvec{\vect k_{\vect K}}\right)\underbrace{\int\ud\Omega_{\vect r}\,\ush{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\frac{\left|\vect r_{\bot}\right|}{\left|\vect r\right|}\right)^{l'-l}\left(\frac{-\vect r_{\bot}\cdot\vect s_{\bot}}{\left|\vect r_{\bot}\right|\left|\vect s_{\bot}\right|}\right)^{2j-l'+l}}_{\equiv A_{l',l,m',m,j}^{\left(d_{\Lambda}\right)}}.
+\end{multline*}
+
+\end_inset
+
+The angular integral is easier to evaluate when 
+\begin_inset Formula $d_{\Lambda}=2$
+\end_inset
+
+, because then 
+\begin_inset Formula $\vect r_{\bot}$
+\end_inset
+
+ is parallel (or antiparallel) to 
+\begin_inset Formula $\vect s_{\bot}$
+\end_inset
+
+, which gives 
+\begin_inset Formula 
+\[
+A_{l',l,m',m,j}^{\left(2\right)}=\left(-\frac{\vect r_{\bot}\cdot\vect s_{\bot}}{\left|\vect r_{\bot}\cdot\vect s_{\bot}\right|}\right)^{2j-l'+l}\int\ud\Omega_{\vect r}\,\ush{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\frac{\left|\vect r_{\bot}\right|}{\left|\vect r\right|}\right)^{2j}
+\]
+
+\end_inset
+
+and if we set the normal of the lattice correspond to the 
+\begin_inset Formula $z$
+\end_inset
+
+ axis, the azimuthal part of the integral will become zero unless 
+\begin_inset Formula $m'=m$
+\end_inset
+
+ for any meaningful spherical harmonics convention, and the polar part for
+ the only nonzero case has a closed-form expression, see e.g.
+ [Linton (A.15)], so one arrives at an expression similar to [Kambe II, (3.15)]
+\lang english
+
+\begin_inset Formula 
+\begin{multline}
+\sigma_{l,m}^{\left(\mathrm{L},\eta\right)}\left(\vect k,\vect s\right)=-\frac{i^{l+1}}{\kappa^{2}\mathcal{A}}\pi^{3/2}2\left(\left(l-m\right)/2\right)!\left(\left(l+m\right)/2\right)!\times\\
+\times\sum_{\vect K\in\Lambda^{*}}e^{i\vect k_{\vect K}\cdot\vect s}\ush lm\left(\vect k_{\vect K}\right)\sum_{j=0}^{l-\left|m\right|}\left(-1\right)^{j}\gamma_{\vect k_{\vect K}}^{2}{}^{2j+1}\times\\
+\times\Delta_{j}\left(\frac{\kappa^{2}\gamma_{\vect k_{\vect K}}^{2}}{4\eta^{2}},-i\kappa\gamma_{\vect k_{\vect K}}^{2}s_{\perp}\right)\times\\
+\times\sum_{\substack{s\\
+j\le s\le\min\left(2j,l-\left|m\right|\right)\\
+l-j+\left|m\right|\,\mathrm{evej}
+}
+}\frac{1}{\left(2j-s\right)!\left(s-j\right)!}\frac{\left(-\kappa s_{\perp}\right)^{2j-s}\left(\left|\vect k_{\vect K}\right|/\kappa\right)^{l-s}}{\left(\frac{1}{2}\left(l-m-s\right)\right)!\left(\frac{1}{2}\left(l+m-s\right)\right)!}\label{eq:Ewald in 3D long-range part 1D 2D-1}
+\end{multline}
+
+\end_inset
+
+where 
+\begin_inset Formula $s_{\perp}\equiv\vect s\cdot\uvec z=\vect s_{\bot}\cdot\uvec z$
+\end_inset
+
+.
+ If 
+\begin_inset Formula $d_{\Lambda}=1$
+\end_inset
+
+, the angular becomes more complicated to evaluate due to the different
+ behaviour of the 
+\begin_inset Formula $\vect r_{\bot}\cdot\vect s_{\bot}/\left|\vect r_{\bot}\right|\left|\vect s_{\bot}\right|$
+\end_inset
+
+ factor.
+ The choice of coordinates can make most of the terms dissapear: if the
+ lattice is set parallel to the 
+\begin_inset Formula $z$
+\end_inset
+
+ axis, 
+\begin_inset Formula $A_{l',l,m',m,j}^{\left(1\right)}$
+\end_inset
+
+ is zero unless 
+\begin_inset Formula $m=0$
+\end_inset
+
+, but one still has 
+\begin_inset Formula 
+\[
+A_{l',l,m',0,j}^{\left(1\right)}=\pi\delta_{m',l'-l-2j}\lambda'_{l0}\lambda_{l'm'}\int_{-1}^{1}\ud x\,P_{l'}^{m'}\left(x\right)P_{l}^{0}\left(x\right)\left(1-x^{2}\right)^{\frac{l'-l}{2}}
+\]
+
+\end_inset
+
+where 
+\begin_inset Formula $\lambda_{lm}$
+\end_inset
+
+ are constants depending on the conventions for spherical harmonics.
+ This does not seem to have such a nice closed-form expression as in the
+ 2D case, but it can be evaluated e.g.
+ using the common recurrence relations for associated Legendre polynomials.
+ Of course when 
+\begin_inset Formula $\vect s=0$
+\end_inset
+
+, one gets relatively nice closed expressions, such as those in [Linton].
+\end_layout
+
+\end_body
+\end_document

notes/ewald_1D_in_3D.lyx

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+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 2cm
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+\secnumdepth 3
+\tocdepth 3
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+\end_header
+
+\begin_body
+
+\begin_layout Title
+1D in 3D Ewald sum
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\ud}{\mathrm{d}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\abs}[1]{\left|#1\right|}
+\end_inset
+
+ 
+\begin_inset FormulaMacro
+\newcommand{\vect}[1]{\mathbf{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\uvec}[1]{\hat{\mathbf{#1}}}
+\end_inset
+
+
+\lang english
+
+\begin_inset FormulaMacro
+\newcommand{\ush}[2]{Y_{#1}^{#2}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ushD}[2]{Y'_{#1}^{#2}}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\vsh}{\vect A}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\vshD}{\vect{A'}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkc}{\vect y}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkcout}{\vect u}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wfkcreg}{\vect v}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wckcreg}{a}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\wckcout}{f}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+General formula
+\end_layout
+
+\begin_layout Standard
+We need to find the expansion coefficient
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{equation}
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{i}{\kappa j_{l'}\left(\kappa\left|\vect r\right|\right)}\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(\kappa)}\left(\vect s+\vect r,\vect k\right)\ushD{l'}{m'}\left(\uvec r\right).\label{eq:tau extraction formula}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+[Linton, (2.24)] with slightly modified notation and setting 
+\begin_inset Formula $d_{c}=2$
+\end_inset
+
+:
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect r\right)=-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect r}\int_{1/\eta}^{\infty e^{i\pi/4}}e^{-\kappa^{2}\gamma^{2}t^{2}/4}e^{-\left|\vect r^{\bot}\right|^{2}/t^{2}}t^{-1}\ud t
+\]
+
+\end_inset
+
+or, evaluated at point 
+\begin_inset Formula $\vect s+\vect r$
+\end_inset
+
+ instead
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)=-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\left(\vect s+\vect r\right)}\int_{1/\eta}^{\infty e^{i\pi/4}}e^{-\kappa^{2}\gamma^{2}t^{2}/4}e^{-\left|\vect s^{\bot}+\vect r^{\bot}\right|^{2}/t^{2}}t^{-1}\ud t
+\]
+
+\end_inset
+
+The integral can be by substitutions taken into the form 
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\lang english
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{2\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\int_{1/\eta}^{\infty\exp\left(i\pi/4\right)}e^{-\kappa^{2}\gamma_{m}^{2}\zeta^{2}/4}e^{-\left|\vect r_{\bot}\right|^{2}/\zeta^{2}}\zeta^{1-d_{c}}\ud\zeta
+\]
+
+\end_inset
+
+Try substitution 
+\begin_inset Formula $t=\zeta^{2}$
+\end_inset
+
+: then 
+\begin_inset Formula $\ud t=2\zeta\,\ud\zeta$
+\end_inset
+
+ (
+\begin_inset Formula $\ud\zeta=\ud t/2t^{1/2}$
+\end_inset
+
+) and
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{4\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\int_{1/\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\kappa^{2}\gamma_{m}^{2}t/4}e^{-\left|\vect r_{\bot}\right|^{2}/t}t^{\frac{-d_{c}}{2}}\ud t
+\]
+
+\end_inset
+
+Try subst.
+ 
+\begin_inset Formula $\tau=k^{2}\gamma_{m}^{2}/4$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\lang english
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{4\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\left(\frac{\kappa\gamma_{m}}{2}\right)^{d_{c}}\int_{\kappa^{2}\gamma_{m}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{m}^{2}/4\tau}\tau^{\frac{-d_{c}}{2}}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)=-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\left(\vect s+\vect r\right)}\int_{\kappa^{2}\gamma_{m}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{m}^{2}/4\tau}\tau^{-1}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+[Linton, (2.25)] with slightly modified notation:
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect r\right)=-\frac{1}{\sqrt{4\pi}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect r}\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}\left|\vect r^{\bot}\right|^{2j}}{j!}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2j-1}\Gamma_{j\vect K}
+\]
+
+\end_inset
+
+We want to express an expansion in a shifted point, so let's substitute
+ 
+\begin_inset Formula $\vect r\to\vect s+\vect r$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)=-\frac{1}{\sqrt{4\pi}\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\left(\vect s+\vect r\right)}\sum_{j=0}^{\infty}\frac{\left(-1\right)^{j}\left|\vect s^{\bot}+\vect r^{\bot}\right|^{2j}}{j!}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2j-1}\Gamma_{j\vect K}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+Let's do the integration to get 
+\begin_inset Formula $\tau_{l}^{m}\left(\vect s,\vect k\right)$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\left(\vect s+\vect r\right)}\int_{\kappa^{2}\gamma_{\vect K}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\tau^{-1}\ud\tau
+\]
+
+\end_inset
+
+The 
+\begin_inset Formula $\vect r$
+\end_inset
+
+-dependent plane wave factor can be also written as
+\begin_inset Formula 
+\begin{align*}
+e^{i\vect K\cdot\vect r} & =e^{i\left|\vect K\right|\vect r\cdot\uvec K}=4\pi\sum_{lm}i^{l}\mathcal{J}'_{l}^{m}\left(\left|\vect K\right|\vect r\right)\ush lm\left(\uvec K\right)\\
+ & =4\pi\sum_{lm}i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ushD lm\left(\uvec{\vect r}\right)\ush lm\left(\uvec K\right)
+\end{align*}
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+or the other way around
+\begin_inset Formula 
+\[
+e^{i\vect K\cdot\vect r}=4\pi\sum_{lm}i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ush lm\left(\uvec{\vect r}\right)\ushD lm\left(\uvec K\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+so
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ushD lm\left(\uvec r\right)\ush lm\left(\uvec K\right)\int_{\kappa^{2}\gamma_{\vect K}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\tau^{-1}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+We also have
+\begin_inset Formula 
+\begin{align*}
+e^{-\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau} & =e^{-\left(\left|\vect s_{\bot}\right|^{2}+\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\\
+ & =e^{-\left|\vect s_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\sum_{n=0}^{\infty}\frac{1}{n!}\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}}{4\tau}\right)^{n},
+\end{align*}
+
+\end_inset
+
+hence
+\begin_inset Formula 
+\begin{align*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right) & =-\frac{1}{2\pi\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ushD lm\left(\uvec r\right)\ush lm\left(\uvec K\right)\sum_{n=0}^{\infty}\frac{1}{n!}\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}}{4}\right)^{n}\underbrace{\int_{\kappa^{2}\gamma_{\vect K}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect s_{\bot}\right|^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\tau^{-1-n}\ud\tau}_{\Delta_{n+1/2}}\\
+ & =-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ush lm\left(\uvec K\right)\sum_{n=0}^{\infty}\frac{\Delta_{n+1/2}}{n!}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}}{4}\right)^{n}\\
+ & =-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ush lm\left(\uvec K\right)\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{n!}\Delta_{n+1/2}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2n}\sum_{k=0}^{n}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left|\vect r_{\bot}\right|^{2(n-k)}\left(2\vect r_{\bot}\cdot\vect s_{\bot}\right)^{k}
+\end{align*}
+
+\end_inset
+
+If we label 
+\begin_inset Formula $\left|\vect r_{\bot}\right|\left|\vect s_{\bot}\right|\cos\varphi\equiv\vect r_{\bot}\cdot\vect s_{\bot}$
+\end_inset
+
+, we have
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ush lm\left(\uvec K\right)\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{n!}\Delta_{n+1/2}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2n}\sum_{k=0}^{n}\left(2\left|\vect s_{\bot}\right|\right)^{k}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left|\vect r_{\bot}\right|^{2n-k}\left(\cos\varphi\right)^{k}
+\]
+
+\end_inset
+
+and if we label 
+\begin_inset Formula $\left|\vect r\right|\sin\vartheta\equiv\left|\vect r_{\bot}\right|$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ush lm\left(\uvec K\right)\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{n!}\Delta_{n+1/2}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2n}\sum_{k=0}^{n}\left|\vect r\right|^{2n-k}\left(2\left|\vect s_{\bot}\right|\right)^{k}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{2n-k}\left(\cos\varphi\right)^{k}
+\]
+
+\end_inset
+
+Now let's put the RHS into 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tau extraction formula"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ and try eliminating some sum by taking the limit 
+\begin_inset Formula $\left|\vect r\right|\to0$
+\end_inset
+
+.
+ We have 
+\begin_inset Formula $j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\sim\left(\left|\vect K\right|\left|\vect r\right|\right)^{l}/\left(2l+1\right)!!$
+\end_inset
+
+; the denominator from 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tau extraction formula"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ behaves like 
+\begin_inset Formula $j_{l'}\left(\kappa\left|\vect r\right|\right)\sim\left(\kappa\left|\vect r\right|\right)^{l'}/\left(2l'+1\right)!!.$
+\end_inset
+
+ The leading terms are hence those with 
+\begin_inset Formula $\left|\vect r\right|^{l-l'+2n-k}$
+\end_inset
+
+.
+ So 
+\begin_inset Formula 
+\[
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi\mathcal{A}\kappa^{1+l'}}\left(2l'+1\right)!!\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}\frac{\left|\vect K\right|^{l}}{\left(2l+1\right)!!}\ush lm\left(\uvec K\right)\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{n!}\Delta_{n+1/2}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2n}\sum_{k=0}^{n}\delta_{l'-l,2n-k}\left(2\left|\vect s_{\bot}\right|\right)^{k}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{l'-l}\left(\cos\varphi\right)^{k}.
+\]
+
+\end_inset
+
+Let's now focus on rearranging the sums; we have
+\begin_inset Formula 
+\[
+S(l')\equiv\sum_{l=0}^{\infty}\sum_{n=0}^{\infty}\sum_{k=0}^{n}\delta_{l'-l,2n-k}f(l',l,n,k)=\sum_{l=0}^{\infty}\sum_{n=0}^{\infty}\sum_{k=0}^{n}\delta_{l'-l,2n-k}f(l',l,n,2n-l'+l)
+\]
+
+\end_inset
+
+We have 
+\begin_inset Formula $0\le k\le n$
+\end_inset
+
+, hence 
+\begin_inset Formula $0\le2n-l'+l\le n$
+\end_inset
+
+, hence 
+\begin_inset Formula $-2n\le-l'+l\le-n$
+\end_inset
+
+, hence also 
+\begin_inset Formula $l'-2n\le l\le l'-n$
+\end_inset
+
+, which gives the opportunity to swap the 
+\begin_inset Formula $l,n$
+\end_inset
+
+ sums and the 
+\begin_inset Formula $l$
+\end_inset
+
+-sum becomes finite; so also consuming 
+\begin_inset Formula $\sum_{k=0}^{n}\delta_{l'-l,2n-k}$
+\end_inset
+
+ we get 
+\begin_inset Formula 
+\[
+S(l')=\sum_{n=0}^{\infty}\sum_{l=\max(0,l'-2n)}^{l'-n}f(l',l,n,2n-l'+l).
+\]
+
+\end_inset
+
+Finally, we see that the interval of valid 
+\begin_inset Formula $l$
+\end_inset
+
+ becomes empty when 
+\begin_inset Formula $l'-n<0$
+\end_inset
+
+, i.e.
+ 
+\begin_inset Formula $n>l'$
+\end_inset
+
+; so we get a finite sum
+\begin_inset Formula 
+\[
+S(l')=\sum_{n=0}^{l'}\sum_{l=\max(0,l'-2n)}^{l'-n}f(l',l,n,2n-l'+l).
+\]
+
+\end_inset
+
+Applying rearrangement,
+\begin_inset Formula 
+\[
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi\mathcal{A}\kappa^{1+l'}}\left(2l'+1\right)!!\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{n=0}^{l'}\frac{\left(-1\right)^{n}}{n!}\Delta_{n+1/2}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2n}\sum_{l=\max\left(0,l'-2n\right)}^{l'-n}4\pi i^{l}\left(2\left|\vect s_{\bot}\right|\right)^{2n-l'+l}\frac{\left|\vect K\right|^{l}}{\left(2l+1\right)!!}\sum_{m=-l}^{l}\ush lm\left(\uvec K\right)\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{l'-l}\left(\cos\varphi\right)^{2n-l'+l}.
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Z-aligned lattice
+\end_layout
+
+\begin_layout Standard
+Now we set some conventions: let the lattice lie on the 
+\begin_inset Formula $z$
+\end_inset
+
+ axis, so that 
+\begin_inset Formula $\vect s_{\bot},\vect r_{\bot}$
+\end_inset
+
+ lie in the 
+\begin_inset Formula $xy$
+\end_inset
+
+-plane.
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+(TODO check the meaning of 
+\begin_inset Formula $\vect k$
+\end_inset
+
+ and possible additional phase factor.)
+\end_layout
+
+\end_inset
+
+ If we write
+\begin_inset Formula $\vect s_{\bot}=\uvec x\left|\vect s_{\bot}\right|\cos\Phi+\uvec y\left|\vect s_{\bot}\right|\sin\Phi$
+\end_inset
+
+, 
+\begin_inset Formula $\vect r_{\bot}=\uvec x\left|\vect r_{\bot}\right|\cos\phi+\uvec y\left|\vect r_{\bot}\right|\sin\phi=\uvec x\left|\vect r\right|\sin\theta\cos\phi+\uvec y\left|\vect r\right|\sin\theta\sin\phi$
+\end_inset
+
+, we have 
+\begin_inset Formula $\varphi=\phi-\Phi$
+\end_inset
+
+, and 
+\begin_inset Formula $\vartheta=\theta$
+\end_inset
+
+.
+ Also, in this convention 
+\begin_inset Formula $\ush lm\left(\uvec K\right)=0$
+\end_inset
+
+ for 
+\begin_inset Formula $m\ne0$
+\end_inset
+
+, so
+\begin_inset Formula 
+\[
+\tau_{l'}^{m'}\left(\vect s,\vect k\right)=\frac{-i}{2\pi\mathcal{A}\kappa^{1+l'}}\left(2l'+1\right)!!\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{n=0}^{l'}\frac{\left(-1\right)^{n}}{n!}\Delta_{n+1/2}\left(\frac{\kappa\gamma_{\vect K}}{2}\right)^{2n}\sum_{l=\max\left(0,l'-2n\right)}^{l'-n}4\pi i^{l}\left(2\left|\vect s_{\bot}\right|\right)^{2n-l'+l}\frac{\left|\vect K\right|^{l}}{\left(2l+1\right)!!}\ush l0\left(\uvec K\right)\underbrace{\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD l0\left(\uvec r\right)\left(\sin\theta\right)^{l'-l}\left(\cos\varphi\right)^{2n-l'+l}}_{\equiv A_{l',l,n,m'}}.
+\]
+
+\end_inset
+
+Let's also fix the (dual) spherical harmonics for now, 
+\begin_inset Formula 
+\[
+\ushD lm\left(\uvec r\right)=\lambda'_{lm}e^{-im\phi}P_{l}^{-m}\left(\cos\theta\right);
+\]
+
+\end_inset
+
+the angular integral then becomes (we also use 
+\begin_inset Formula $e^{-im'\phi}=e^{im'\Phi}e^{-im'\varphi}$
+\end_inset
+
+)
+\begin_inset Formula 
+\begin{align*}
+A_{l',l,n,m'} & \equiv\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD l0\left(\uvec r\right)\left(\sin\theta\right)^{l'-l}\left(\cos\varphi\right)^{2n-l'+l}\\
+ & =\lambda'_{l'm'}\lambda'_{l0}e^{im'\Phi}\int_{0}^{\pi}\ud\theta\,\sin\theta P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)\left(\sin\theta\right)^{l'-l}\int_{0}^{2\pi}\ud\varphi\,e^{-im'\varphi}\left(\cos\varphi\right)^{2n-l'+l}.
+\end{align*}
+
+\end_inset
+
+The asimuthal integral evaluates to 
+\begin_inset Formula 
+\[
+\int_{0}^{2\pi}\ud\varphi\,e^{-im'\varphi}\left(\cos\varphi\right)^{2n-l'+l}=\pi\delta_{\left|m'\right|,2n-l'+l}
+\]
+
+\end_inset
+
+ (note that 
+\begin_inset Formula $2n-l'+l\ge0$
+\end_inset
+
+ as it's the former index 
+\begin_inset Formula $k$
+\end_inset
+
+).
+ That eliminates one of the two remaining (finite) sums.
+ We are left with the polar integral
+\begin_inset Formula 
+\[
+\int_{0}^{\pi}\ud\theta\,\sin\theta P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)\left(\sin\theta\right)^{l'-l}
+\]
+
+\end_inset
+
+for which I couldn't find an explicit form yet.
+\end_layout
+
+\begin_layout Section
+X-aligned lattice
+\end_layout
+
+\begin_layout Standard
+If we instead set 
+\begin_inset Formula $\vect s_{\bot}=\uvec z\left|\vect s_{\bot}\right|\cos\Theta+\uvec y\left|\vect s_{\bot}\right|\sin\Theta$
+\end_inset
+
+, 
+\begin_inset Formula $\vect r_{\bot}=\uvec z\left|\vect r_{\bot}\right|\cos\theta+\uvec y\left|\vect r_{\bot}\right|\sin\theta=\uvec z\left|\vect r\right|\cos\theta+\uvec y\left|\vect r\right|\sin\theta\sin\phi$
+\end_inset
+
+, we have 
+\begin_inset Formula $\vartheta=\Theta-\theta$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD lm\left(\uvec r\right)\left(\sin\vartheta\right)^{l'-l}\left(\cos\varphi\right)^{k}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+BTW:
+\begin_inset Formula 
+\begin{align*}
+\left|\vect r_{\bot}\right|^{2} & =\left|\vect r\right|^{2}-\left|\vect r_{\parallel}\right|^{2}=\left|\vect r\right|^{2}-\left(\vect r\cdot\uvec K\right)^{2},\\
+\vect r_{\bot}\cdot\vect s_{\bot} & =\vect r\cdot\vect s_{\bot}
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Now we set the conventions: let the lattice lie on the 
+\begin_inset Formula $z$
+\end_inset
+
+ axis, so that 
+\begin_inset Formula $\vect s_{\bot},\vect r_{\bot}$
+\end_inset
+
+ lie in the 
+\begin_inset Formula $xy$
+\end_inset
+
+-plane, (TODO check the meaning of 
+\begin_inset Formula $\vect k$
+\end_inset
+
+ and possible additional phase factor.) If we write
+\begin_inset Formula $\vect s_{\bot}=\uvec xs_{\bot}\cos\Phi+\uvec ys_{\bot}\sin\Phi$
+\end_inset
+
+, 
+\begin_inset Formula $\vect r_{\bot}=\uvec xr_{\bot}\cos\phi+\uvec yr_{\bot}\sin\phi=\uvec xr\sin\theta\cos\phi+\uvec yr\sin\theta\sin\phi$
+\end_inset
+
+, we have 
+\begin_inset Formula 
+\[
+\left|\vect s_{\bot}+\vect r_{\bot}\right|^{2}=s_{\bot}^{2}+r^{2}\left(\sin\theta\right)^{2}+2s_{\bot}r\sin\theta\cos\left(\phi-\Phi\right).
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+Also, in this convention 
+\begin_inset Formula $\ush lm\left(\uvec K\right)=0$
+\end_inset
+
+ for 
+\begin_inset Formula $m\ne0$
+\end_inset
+
+, so
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Formula 
+\begin{align*}
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right) & =-\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{lm}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ush l0\left(\uvec K\right)\times\\
+ & \quad\times\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\ushD l0\left(\uvec r\right)\sum_{n=0}^{\infty}\Delta_{n+1/2}\frac{1}{n!}\left(-\frac{\left(\left|\vect r_{\bot}\right|^{2}+2\vect r_{\bot}\cdot\vect s_{\bot}\right)\kappa^{2}\gamma_{\vect K}^{2}}{4}\right)^{n}.
+\end{align*}
+
+\end_inset
+
+Let's also fix the spherical harmonics for now, 
+\begin_inset Formula 
+\[
+\ushD lm\left(\uvec r\right)=\lambda'_{lm}e^{-im\phi}P_{l}^{-m}\left(\cos\theta\right)
+\]
+
+\end_inset
+
+Also, in this convention 
+\begin_inset Formula $\ush lm\left(\uvec K\right)=0$
+\end_inset
+
+ for 
+\begin_inset Formula $m\ne0$
+\end_inset
+
+, so
+\begin_inset Formula 
+\[
+\int\ud\Omega_{\vect r}\,G_{\Lambda}^{(1;\kappa)}\left(\vect s+\vect r\right)\ushD{l'}{m'}\left(\uvec r\right)=-\frac{1}{2\pi\mathcal{A}}\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)\frac{1}{2\pi\mathcal{A}}\sum_{\vect K\in\Lambda^{*}}e^{i\vect K\cdot\vect s}\sum_{l}4\pi i^{l}j_{l}\left(\left|\vect K\right|\left|\vect r\right|\right)\ushD l0\left(\uvec r\right)\ush l0\left(\uvec K\right)\int_{\kappa^{2}\gamma_{\vect K}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left(s_{\bot}^{2}+r_{\bot}^{2}+2s_{\bot}r_{\bot}\cos\left(\phi-\Phi\right)\right)^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\tau^{-1}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+Let's also fix the spherical harmonics for now, 
+\begin_inset Formula 
+\[
+\ushD lm\left(\uvec r\right)=\lambda'_{lm}e^{-im\phi}P_{l}^{-m}\left(\cos\theta\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+The angular integral (assuming it can be separated from the rest like this)
+ is
+\begin_inset Formula 
+\[
+I_{l'}^{m'}\equiv\int\ud\Omega_{\vect r}\,\ushD{l'}{m'}\left(\uvec r\right)e^{-\left(r_{\bot}^{2}+2s_{\bot}r_{\bot}\cos\left(\phi-\Phi\right)\right)^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+Let's further extract the azimuthal part 
+\begin_inset Formula $\left(w\equiv2r_{\bot}s_{\bot}\kappa^{2}\gamma_{\vect K}^{2}/4\tau\right)$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+e^{-im'\Phi}A_{l'}^{m'}\equiv\int_{0}^{2\pi}e^{-im'\phi}e^{-w\cos\left(\phi-\Phi\right)}\ud\phi=e^{-im'\Phi}\int_{0}^{2\pi}e^{-im'\varphi}e^{-w\cos\varphi}\ud\varphi
+\]
+
+\end_inset
+
+Using [DLMF 10.9.2], 
+\begin_inset Formula $\int_{0}^{2\pi}e^{-im'\varphi}e^{-w\cos\varphi}\ud\varphi=\int_{0}^{2\pi}\cos\left(m'\varphi\right)e^{i(iw)\cos\varphi}=2\pi i^{m'}J_{m'}\left(iw\right)$
+\end_inset
+
+ we have
+\begin_inset Formula 
+\[
+e^{-m'\Phi}A_{l'}^{m'}=2\pi i^{m'}J_{m'}\left(iw\right),
+\]
+
+\end_inset
+
+assuming that 
+\begin_inset Formula $w$
+\end_inset
+
+ is real (which does not necessarily have to be true!); numerical experiments
+ in Sage show that the result is valid also for complex 
+\begin_inset Formula $w$
+\end_inset
+
+.
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset Formula 
+\begin{align*}
+A_{l}^{m} & =\int_{0}^{2\pi}e^{-im\varphi}\sum_{n=0}^{\infty}\frac{\left(-w\cos\varphi\right)^{n}}{n!}\ud\varphi\\
+ & =\int_{0}^{2\pi}e^{-im\varphi}\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\left(e^{i\varphi}+e^{-i\varphi}\right)^{n}\ud\varphi\\
+ & =\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\int_{0}^{2\pi}e^{-im\varphi}\sum_{k=0}^{n}\binom{n}{k}e^{ik\varphi}e^{-i\left(n-k\right)\varphi}\ud\varphi\\
+ & =\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\sum_{k=0}^{n}\binom{n}{k}\int_{0}^{2\pi}e^{i\left(2k-n-m\right)\varphi}\ud\varphi\\
+ & =2\pi\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\sum_{k=0}^{n}\binom{n}{k}\delta_{2k-n-m=0}\\
+ & =2\pi\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\sum_{k=0}^{n}\binom{n}{k}\delta_{2k-n-m=0}\\
+ & =2\pi\sum_{k=0}^{\infty}\sum_{n=k}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\binom{n}{k}\delta_{2k-n-m=0}\\
+ & =2\pi\sum_{k=0}^{\infty}\frac{\left(-w\right)^{2k-m}}{2^{2k-m}\left(2k-m\right)!}\binom{2k-m}{k}\delta_{2k-m\ge k}\\
+ & =2\pi\sum_{k=0}^{\infty}\frac{\left(-w\right)^{2k-m}}{2^{2k-m}}\frac{1}{k!\left(k-m\right)!}\delta_{k-m\ge0}\\
+ & =2\pi\sum_{k=\max\left(m,0\right)}^{\infty}\left(-\frac{w}{2}\right)^{2k-m}\frac{1}{k!\left(k-m\right)!}
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset Formula 
+\begin{align*}
+A_{l}^{m} & =\int_{0}^{2\pi}e^{-im\varphi}\sum_{n=0}^{\infty}\frac{\left(-w\cos\varphi\right)^{n}}{n!}\ud\varphi\\
+ & =\int_{0}^{2\pi}e^{-im\varphi}\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\left(e^{i\varphi}+e^{-i\varphi}\right)^{n}\ud\varphi\\
+ & =\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\int_{0}^{2\pi}e^{-im\varphi}\sum_{k=0}^{n}\binom{n}{k}e^{i\left(n-k\right)\varphi}e^{-ik\varphi}\ud\varphi\\
+ & =\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\sum_{k=0}^{n}\binom{n}{k}\int_{0}^{2\pi}e^{i\left(-2k+n-m\right)\varphi}\ud\varphi\\
+ & =2\pi\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\sum_{k=0}^{n}\binom{n}{k}\delta_{-2k+n-m=0}\\
+ & =2\pi\sum_{n=0}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\sum_{k=0}^{n}\binom{n}{k}\delta_{-2k+n-m=0}\\
+ & =2\pi\sum_{k=0}^{\infty}\sum_{n=k}^{\infty}\frac{\left(-w\right)^{n}}{2^{n}n!}\binom{n}{k}\delta_{-2k+n-m=0}\\
+ & =2\pi\sum_{k=0}^{\infty}\frac{\left(-w\right)^{2k+m}}{2^{2k+m}\left(2k+m\right)!}\binom{2k+m}{k}\delta_{2k+m\ge k}\\
+ & =2\pi\sum_{k=0}^{\infty}\frac{\left(-w\right)^{2k+m}}{2^{2k+m}}\frac{1}{k!\left(k+m\right)!}\delta_{k+m\ge0}\\
+ & =2\pi\sum_{k=\max\left(-m,0\right)}^{\infty}\frac{\left(-w\right)^{2k+m}}{2^{2k+m}}\frac{1}{k!\left(k+m\right)!}
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+Althought it's not superobvious, this sum is symmetric w.r.t.
+ sign change in 
+\begin_inset Formula $m$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Plain Layout
+Let's do the polar integration next: 
+\begin_inset Formula $r_{\bot}=r\sin\theta$
+\end_inset
+
+
+\begin_inset Formula 
+\[
+B_{l'}^{m'}\equiv\int_{0}^{\pi}\sin\theta\ud\theta\,P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)e^{-\left(\sin\theta\right)^{2}r^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau}\left(-\sin\theta\,rs_{\bot}\kappa^{2}\gamma_{\vect K}^{2}/4\tau\right)^{2k-m'}
+\]
+
+\end_inset
+
+Label 
+\begin_inset Formula $u\equiv r^{2}\kappa^{2}\gamma_{\vect K}^{2}/4\tau,v\equiv rs_{\bot}\kappa^{2}\gamma_{\vect K}^{2}/4\tau$
+\end_inset
+
+; then 
+\begin_inset Formula 
+\begin{align*}
+B_{l'}^{m'} & =\int_{0}^{\pi}\sin\theta\ud\theta\,P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)e^{-u\left(\sin\theta\right)^{2}}\left(-v\sin\theta\right)^{2k-m'}\\
+ & =\int_{0}^{\pi}\sin\theta\ud\theta\,P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)\left(-v\sin\theta\right)^{2k-m'}\sum_{a=0}^{\infty}\frac{\left(-u\right)^{a}}{a!}\left(\sin\theta\right)^{2a}\\
+ & =\left(-v\right)^{2k-m'}\sum_{a=0}^{\infty}\frac{\left(-u\right)^{a}}{a!}\int_{0}^{\pi}\sin\theta\ud\theta\,P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)\left(\sin\theta\right)^{2a+2k-m'}
+\end{align*}
+
+\end_inset
+
+If we now perform the limit 
+\begin_inset Formula $r\to0$
+\end_inset
+
+ and compare the radial parts (incl.
+ those in 
+\begin_inset Formula $u,v$
+\end_inset
+
+) powers, the leading term indices will have
+\begin_inset Formula 
+\[
+l'\sim l+2a+2k-m'
+\]
+
+\end_inset
+
+so we can fix 
+\begin_inset Formula $2a+2k-m'=l'-l$
+\end_inset
+
+ and get 
+\begin_inset Formula 
+\[
+\int_{0}^{\pi}\sin\theta\ud\theta\,P_{l'}^{-m'}\left(\cos\theta\right)P_{l}^{0}\left(\cos\theta\right)\left(\sin\theta\right)^{l'-l}=\begin{cases}
+0 & l'-l+m'\text{ odd}\\
+? & l'-l+m'\text{ even}
+\end{cases}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $ $
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document

notes/ewald_23_z_nonzero.lyx

@@ -0,0 +1,305 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 584
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
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+\use_package amsmath 1
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+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
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+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+
+\lang english
+\begin_inset FormulaMacro
+\newcommand{\uoft}[1]{\mathfrak{F}#1}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\uaft}[1]{\mathfrak{\mathbb{F}}#1}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\usht}[2]{\mathbb{S}_{#1}#2}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\bsht}[2]{\mathrm{S}_{#1}#2}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\sgn}{\operatorname{sgn}}
+{\mathrm{sgn}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\pht}[2]{\mathfrak{\mathbb{H}}_{#1}#2}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\vect}[1]{\mathbf{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ud}{\mathrm{d}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\basis}[1]{\mathfrak{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\dc}[1]{Ш_{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\rec}[1]{#1^{-1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\recb}[1]{#1^{\widehat{-1}}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ints}{\mathbb{Z}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\nats}{\mathbb{N}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\reals}{\mathbb{R}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ush}[2]{Y_{#1,#2}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\hgfr}{\mathbf{F}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\hgf}{F}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ghgf}[2]{\mbox{}_{#1}F_{#2}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ghgfr}[2]{\mbox{}_{#1}\mathbf{F}_{#2}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\ph}{\mathrm{ph}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\kor}[1]{\underline{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\koru}[1]{\utilde{#1}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\swv}{\mathscr{H}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\expint}{\mathrm{E}}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+\begin_inset Formula 
+\begin{eqnarray}
+\sigma_{n}^{m(1)} & = & -\frac{i^{n+1}}{2k^{2}\mathscr{A}}\left(-1\right)^{\left(n+m\right)/2}\sqrt{\left(2n+1\right)\left(n-m\right)!\left(n+m\right)!}\times\nonumber \\
+ &  & \times\sum_{\vect K_{pq}\in\Lambda^{*}}^{'}\sum_{j=0}^{\left[\left(n-\left|m\right|/2\right)\right]}\frac{\left(-1\right)^{j}\left(\beta_{pq}/2k\right)^{n-2j}e^{im\phi_{\vect{\beta}_{pq}}}\Gamma_{j,pq}}{j!\left(\frac{1}{2}\left(n-m\right)-j\right)!\left(\frac{1}{2}\left(n+m\right)-j\right)!}\left(\frac{\gamma_{pq}}{2}\right)^{2j-1}\nonumber \\
+ & = & -\frac{i^{n+1}}{2k^{2}\mathscr{A}}\sqrt{\pi}2^{n+1}\left(\left(n-m\right)/2\right)!\left(\left(n+m\right)/2\right)!\times\nonumber \\
+ &  & \times\sum_{\vect K_{pq}\in\Lambda^{*}}^{'}Y_{n}^{m}\left(\frac{\pi}{2},\phi_{\vect{\beta}_{pq}}\right)\sum_{j=0}^{\left[\left(n-\left|m\right|/2\right)\right]}\frac{\left(-1\right)^{j}\left(\beta_{pq}/2k\right)^{n-2j}\Gamma_{j,pq}}{j!\left(\frac{1}{2}\left(n-m\right)-j\right)!\left(\frac{1}{2}\left(n+m\right)-j\right)!}\left(\frac{\gamma_{pq}}{2}\right)^{2j-1}\nonumber \\
+ & = & -\frac{i^{n+1}}{k^{2}\mathscr{A}}\sqrt{\pi}2\left(\left(n-m\right)/2\right)!\left(\left(n+m\right)/2\right)!\times\nonumber \\
+ &  & \times\sum_{\vect K_{pq}\in\Lambda^{*}}^{'}Y_{n}^{m}\left(\frac{\pi}{2},\phi_{\vect{\beta}_{pq}}\right)\sum_{j=0}^{\left[\left(n-\left|m\right|/2\right)\right]}\frac{\left(-1\right)^{j}\left(\beta_{pq}/k\right)^{n-2j}\Gamma_{j,pq}}{j!\left(\frac{1}{2}\left(n-m\right)-j\right)!\left(\frac{1}{2}\left(n+m\right)-j\right)!}\left(\gamma_{pq}\right)^{2j-1}\label{eq:2D Ewald in 3D long-range part}
+\end{eqnarray}
+
+\end_inset
+
+For 
+\begin_inset Formula $z\ne0$
+\end_inset
+
+
+\begin_inset Formula 
+\begin{align*}
+ & =-\frac{i^{n+1}}{k^{2}\mathscr{A}}\sqrt{\pi}2\left(\left(n-m\right)/2\right)!\left(\left(n+m\right)/2\right)!\\
+ & \times\sum_{\vect K_{pq}\in\Lambda^{*}}^{'}Y_{n}^{m}\left(\frac{\pi}{2},\phi_{\vect{\beta}_{pq}}\right)\sum_{j=0}^{n-\left|m\right|}\frac{\Delta_{npq}}{j!}\left(-1\right)^{j}\left(\gamma_{pq}\right)^{2j-1}\sum_{s\overset{*}{=}j}^{\min(2j,n-\left|m\right|)}\binom{j}{2j-s}\frac{\left(-\kappa z\right)^{2j-s}\left(\beta_{pq}/k\right)^{n-s}}{\left(\frac{1}{2}\left(n-m-s\right)\right)!\left(\frac{1}{2}\left(n+m-s\right)\right)!}\\
+ & =-\frac{i^{n+1}}{k^{2}\mathscr{A}}\sqrt{\pi}2\left(\left(n-m\right)/2\right)!\left(\left(n+m\right)/2\right)!\\
+ & \times\sum_{\vect K_{pq}\in\Lambda^{*}}^{'}Y_{n}^{m}\left(\frac{\pi}{2},\phi_{\vect{\beta}_{pq}}\right)\sum_{j=0}^{n-\left|m\right|}\Delta_{npq}\left(\gamma_{pq}\right)^{2j-1}\sum_{s\overset{*}{=}j}^{\min(2j,n-\left|m\right|)}\frac{\left(-1\right)^{j}}{\left(2j-s\right)!\left(s-j\right)!}\frac{\left(-\kappa z\right)^{2j-s}\left(\beta_{pq}/k\right)^{n-s}}{\left(\frac{1}{2}\left(n-m-s\right)\right)!\left(\frac{1}{2}\left(n+m-s\right)\right)!}
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+
+\lang english
+Ewald long range integral
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+Linton has (2.24):
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{2\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\int_{1/\eta}^{\infty\exp\left(i\pi/4\right)}e^{-\kappa^{2}\gamma_{m}^{2}\zeta^{2}/4}e^{-\left|\vect r_{\bot}\right|^{2}/\zeta^{2}}\zeta^{1-d_{c}}\ud\zeta
+\]
+
+\end_inset
+
+Try substitution 
+\begin_inset Formula $t=\zeta^{2}$
+\end_inset
+
+: then 
+\begin_inset Formula $\ud t=2\zeta\,\ud\zeta$
+\end_inset
+
+ (
+\begin_inset Formula $\ud\zeta=\ud t/2t^{1/2}$
+\end_inset
+
+) and
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{4\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\int_{1/\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\kappa^{2}\gamma_{m}^{2}t/4}e^{-\left|\vect r_{\bot}\right|^{2}/t}t^{\frac{-d_{c}}{2}}\ud t
+\]
+
+\end_inset
+
+Try subst.
+ 
+\begin_inset Formula $\tau=k^{2}\gamma_{m}^{2}/4$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+\begin_inset Formula 
+\[
+G_{\Lambda}^{\left(1\right)}\left(\vect r\right)=\frac{\pi^{-d_{c}/2}}{4\mathcal{A}}\sum_{\vect K_{m}\in\Lambda^{*}}e^{i\vect K_{m}\cdot\vect r}\left(\frac{\kappa\gamma_{m}}{2}\right)^{d_{c}}\int_{\kappa^{2}\gamma_{m}^{2}/4\eta^{2}}^{\infty\exp\left(i\pi/2\right)}e^{-\tau}e^{-\left|\vect r_{\bot}\right|^{2}\kappa^{2}\gamma_{m}^{2}/4\tau}\tau^{\frac{-d_{c}}{2}}\ud\tau
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document

notes/kambe_linton_dict.lyx

@@ -0,0 +1,386 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 584
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\use_default_options true
+\maintain_unincluded_children false
+\language finnish
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
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+\font_sf_scale 100 100
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+\graphics default
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+\bibtex_command default
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+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
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+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+
+\lang english
+\begin_inset FormulaMacro
+\newcommand{\vect}[1]{\mathbf{#1}}
+\end_inset
+
+
+\lang finnish
+
+\begin_inset FormulaMacro
+\newcommand{\Kambe}[1]{#1^{\mathrm{K}}}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\Linton}[1]{#1^{\mathrm{L}}}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Here and in Kambe's papers, 
+\begin_inset Formula $\kappa$
+\end_inset
+
+ is the wavenumber (
+\begin_inset Formula $k$
+\end_inset
+
+ in Linton).
+ Here 
+\begin_inset Formula $\vect K_{p}$
+\end_inset
+
+ is a point of the reciprocal lattice (
+\begin_inset Formula $\vect K_{p}=\Kambe{\vect K_{pt}}=\Linton{\vect{\beta}_{\mu}}$
+\end_inset
+
+)
+\end_layout
+
+\begin_layout Section
+\begin_inset Quotes eld
+\end_inset
+
+Gammas
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For 
+\begin_inset Formula $\kappa$
+\end_inset
+
+ positive,
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\Kambe{\Gamma_{p}}\equiv\begin{cases}
+\sqrt{\kappa^{2}-\left|\vect K_{p}\right|^{2}} & \kappa^{2}-\left|\vect K_{p}\right|^{2}>0\\
+i\sqrt{\left|\vect K_{p}\right|^{2}-\kappa^{2}} & \kappa^{2}-\left|\vect K_{p}\right|^{2}<0
+\end{cases}
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\Linton{\gamma_{\mu}}\equiv\begin{cases}
+\sqrt{\left(\frac{\vect K_{p}}{\kappa}\right)^{2}-1} & \kappa-\left|\vect K_{p}\right|\le0\\
+-i\sqrt{1-\left(\frac{\vect K_{p}}{\kappa}\right)^{2}} & \kappa-\left|\vect K_{p}\right|>0
+\end{cases}
+\]
+
+\end_inset
+
+hence 
+\begin_inset Formula 
+\[
+\Kambe{\Gamma_{p}}=-i\kappa\Linton{\gamma_{\mu}},
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\Linton{\gamma_{\mu}}=i\frac{\Kambe{\Gamma_{p}}}{\kappa}.
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+D vs sigma
+\end_layout
+
+\begin_layout Standard
+In-plane sums [Linton 2009, (4.5)], replacing 
+\begin_inset Formula $n,m\rightarrow L,M$
+\end_inset
+
+, 
+\begin_inset Formula $k\rightarrow\kappa$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+\begin_inset Formula 
+\begin{eqnarray*}
+\sigma_{L}^{M(1)} & = & -\frac{i^{L+1}}{2\kappa^{2}\mathscr{A}}\left(-1\right)^{\left(L+M\right)/2}\sqrt{\left(2L+1\right)\left(L-M\right)!\left(L+M\right)!}\times\\
+ &  & \times\sum_{\vect K_{pq}\in\Lambda^{*}}^{'}\sum_{j=0}^{\left[\left(L-\left|M\right|/2\right)\right]}\frac{\left(-1\right)^{j}\left(\beta_{pq}/2\kappa\right)^{L-2j}e^{iM\phi_{\vect{\beta}_{pq}}}\Gamma_{j,pq}}{j!\left(\frac{1}{2}\left(L-M\right)-j\right)!\left(\frac{1}{2}\left(L+M\right)-j\right)!}\left(\frac{\gamma_{pq}}{2}\right)^{2j-1}
+\end{eqnarray*}
+
+\end_inset
+
+[Kambe II, (3.17)], replacing 
+\lang finnish
+
+\begin_inset Formula $n\rightarrow j$
+\end_inset
+
+
+\lang english
+, 
+\lang finnish
+
+\begin_inset Formula $A\rightarrow\mathscr{A}$
+\end_inset
+
+, 
+\begin_inset Formula $\vect K_{pt}\to\vect K_{p}$
+\end_inset
+
+, 
+\begin_inset Formula $\Gamma\left(\frac{1}{2}-j,e^{-i\pi}\Gamma_{p}^{2}\omega/2\right)\to\Gamma_{j,p}$
+\end_inset
+
+ and performing little typographic modifications
+\lang english
+
+\begin_inset Formula 
+\begin{align*}
+D_{LM} & =-\frac{1}{\mathscr{A}\kappa}i^{\left|M\right|+1}2^{-L}\sqrt{\left(2L+1\right)\left(L+\left|M\right|\right)!\left(L-\left|M\right|\right)!}\times\\
+ & \quad\times\sum_{p}e^{i\vect K_{p}\cdot\vect c_{ijt}}e^{-iM\phi_{K_{p}}}\sum_{j=0}^{\left(L-\left|M\right|\right)/2}\frac{\left(\Gamma_{p}/\kappa\right)^{2j-1}\left(K_{p}/\kappa\right)^{L-2j}\Gamma_{j,p}}{j!\left(\frac{1}{2}\left(L-\left|M\right|\right)-j\right)!\left(\frac{1}{2}\left(L+\left|M\right|\right)-j\right)!}
+\end{align*}
+
+\end_inset
+
+Using the relations between 
+\begin_inset Formula $\Kambe{\Gamma_{p}}=-i\kappa\Linton{\gamma_{\mu}}$
+\end_inset
+
+, we have (also, we replace the 
+\begin_inset Formula $\mu$
+\end_inset
+
+ index with 
+\begin_inset Formula $p$
+\end_inset
+
+)
+\begin_inset Formula 
+\begin{align*}
+D_{LM} & =-\frac{1}{\mathscr{A}\kappa}i^{\left|M\right|+1}2^{-L}\sqrt{\left(2L+1\right)\left(L+\left|M\right|\right)!\left(L-\left|M\right|\right)!}\times\\
+ & \quad\times\sum_{p}e^{i\vect K_{p}\cdot\vect c_{ijt}}e^{-iM\phi_{K_{p}}}\sum_{j=0}^{\left(L-\left|M\right|\right)/2}\frac{\left(-i\gamma_{p}\right)^{2j-1}\left(K_{p}/\kappa\right)^{L-2j}\Gamma_{j,p}}{j!\left(\frac{1}{2}\left(L-\left|M\right|\right)-j\right)!\left(\frac{1}{2}\left(L+\left|M\right|\right)-j\right)!}
+\end{align*}
+
+\end_inset
+
+and now, trying to make the exponents look the same as in Linton, 
+\begin_inset Formula $2^{-1}2^{2j-L}2^{1-2j}=2^{-L}$
+\end_inset
+
+ (OK), 
+\begin_inset Formula $K_{p}^{L-2j}=K_{p}^{L-2j}$
+\end_inset
+
+ (OK), 
+\begin_inset Formula 
+\begin{align*}
+D_{LM} & =-\frac{1}{2\kappa\mathscr{A}}i^{\left|M\right|+1}\sqrt{\left(2L+1\right)\left(L+\left|M\right|\right)!\left(L-\left|M\right|\right)!}\times\\
+ & \quad\times\sum_{p}e^{i\vect K_{p}\cdot\vect c_{ij}}e^{-iM\phi_{K_{p}}}\sum_{j=0}^{\left(L-\left|M\right|\right)/2}\frac{\left(-i\right)^{2j-1}\left(K_{p}/2\kappa\right)^{L-2j}\Gamma_{j,p}}{j!\left(\frac{1}{2}\left(L-\left|M\right|\right)-j\right)!\left(\frac{1}{2}\left(L+\left|M\right|\right)-j\right)!}\left(\frac{\gamma_{p}}{2}\right)^{2j-1}
+\end{align*}
+
+\end_inset
+
+There are now these differences left:
+\end_layout
+
+\begin_layout Itemize
+
+\lang english
+Additional 
+\begin_inset Formula $\kappa$
+\end_inset
+
+ factor in 
+\begin_inset Formula $D_{LM}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+
+\lang english
+\begin_inset Formula $i^{L+1}\left(-1\right)^{\left(L+M\right)/2}\left(-1\right)^{j}$
+\end_inset
+
+ vs.
+ 
+\begin_inset Formula $i^{\left|M\right|+1}\left(-i\right)^{2j-1}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+
+\lang english
+Opposite phase in the angular part.
+\end_layout
+
+\begin_layout Itemize
+
+\lang english
+Plane wave factor in 
+\begin_inset Formula $D_{LM}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+Let's look at the 
+\begin_inset Formula $i,-1$
+\end_inset
+
+ factors (note that 
+\begin_inset Formula $L+M$
+\end_inset
+
+ is odd): 
+\begin_inset Formula $\left(-i\right)^{2j}=\left(-1\right)^{j},$
+\end_inset
+
+ leaving 
+\begin_inset Formula $i^{L+1}\left(-1\right)^{\left(L+M\right)/2}$
+\end_inset
+
+ vs.
+ 
+\begin_inset Formula $i^{\left|M\right|+1}i$
+\end_inset
+
+.
+ So there is might be a phase difference due to different conventions, but
+ it does not depend on 
+\begin_inset Formula $j$
+\end_inset
+
+, so one should be able to transplant the 
+\begin_inset Formula $z\ne0$
+\end_inset
+
+ sum from Kambe without major problems.
+\end_layout
+
+\begin_layout Section
+Ewald parameter (integration limits)
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\Linton{\eta}=\sqrt{\frac{1}{2\Kambe{\omega}}}
+\]
+
+\end_inset
+
+(Based on comparison of some function arguments, not checked.)
+\end_layout
+
+\end_body
+\end_document

notes/old_scattering_notes.lyx

@@ -1,7 +1,9 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 474
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
 \begin_document
 \begin_header
+\save_transient_properties true
+\origin unavailable
 \textclass report
 \begin_preamble
 %\renewcommand*{\chapterheadstartvskip}{\vspace*{1cm}}
@@ -13,16 +15,18 @@
 \language_package default
 \inputencoding auto
 \fontencoding global
-\font_roman TeX Gyre Pagella
-\font_sans default
-\font_typewriter default
-\font_math auto
+\font_roman "default" "TeX Gyre Pagella"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
 \font_default_family default
 \use_non_tex_fonts true
 \font_sc false
 \font_osf true
-\font_sf_scale 100
-\font_tt_scale 100
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures false
 \graphics default
 \default_output_format pdf4
 \output_sync 0
@@ -63,6 +67,7 @@
 \suppress_date false
 \justification true
 \use_refstyle 1
+\use_minted 0
 \index Index
 \shortcut idx
 \color #008000
@@ -75,7 +80,10 @@
 \tocdepth 3
 \paragraph_separation indent
 \paragraph_indentation default
-\quotes_language swedish
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style swedish
+\dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
@@ -102,7 +110,7 @@
 \end_layout
 
 \begin_layout Title
-Electromagnetic multiple scattering, spherical waves and ****
+Electromagnetic multiple scattering, spherical waves and conventions
 \end_layout
 
 \begin_layout Author
@@ -244,7 +252,7 @@ Pi and tau
 Xu
 \begin_inset CommandInset label
 LatexCommand label
-name "sub:Xu pitau"
+name "subsec:Xu pitau"
 
 \end_inset
 
@@ -373,7 +381,7 @@ The limiting expressions are obtained simply by multiplying the expressions
  
 \begin_inset CommandInset ref
 LatexCommand ref
-reference "sub:Xu pitau"
+reference "subsec:Xu pitau"
 
 \end_inset
 
@@ -462,6 +470,7 @@ Jackson
 LatexCommand cite
 after "(9.101)"
 key "jackson_classical_1998"
+literal "true"
 
 \end_inset
 
@@ -478,6 +487,7 @@ where
 LatexCommand cite
 after "(9.119)"
 key "jackson_classical_1998"
+literal "true"
 
 \end_inset
 
@@ -499,6 +509,7 @@ Normalisation
 LatexCommand cite
 after "(9.120)"
 key "jackson_classical_1998"
+literal "true"
 
 \end_inset
 
@@ -519,6 +530,7 @@ Local sum rule
 LatexCommand cite
 after "(9.153)"
 key "jackson_classical_1998"
+literal "true"
 
 \end_inset
 
@@ -793,6 +805,7 @@ As in
 LatexCommand cite
 after "eq. (36)"
 key "xu_calculation_1996"
+literal "true"
 
 \end_inset
 
@@ -816,6 +829,7 @@ where CS is
 LatexCommand cite
 after "eq. (81)"
 key "xu_calculation_1996"
+literal "true"
 
 \end_inset
 
@@ -826,7 +840,7 @@ key "xu_calculation_1996"
 Relation between Kristensson and Taylor
 \begin_inset CommandInset label
 LatexCommand label
-name "sub:Kristensson-v-Taylor"
+name "subsec:Kristensson-v-Taylor"
 
 \end_inset
 
@@ -961,7 +975,7 @@ In this section I summarize the formulae for power
 Kristensson
 \begin_inset CommandInset label
 LatexCommand label
-name "sub:Radiated enenergy-Kristensson"
+name "subsec:Radiated enenergy-Kristensson"
 
 \end_inset
 
@@ -1022,7 +1036,7 @@ Here I derive the radiated power in Taylor's convention by applying the
  relations from subsection 
 \begin_inset CommandInset ref
 LatexCommand ref
-reference "sub:Kristensson-v-Taylor"
+reference "subsec:Kristensson-v-Taylor"
 
 \end_inset
 
@@ -1030,7 +1044,7 @@ reference "sub:Kristensson-v-Taylor"
  
 \begin_inset CommandInset ref
 LatexCommand ref
-reference "sub:Radiated enenergy-Kristensson"
+reference "subsec:Radiated enenergy-Kristensson"
 
 \end_inset
 
@@ -1110,6 +1124,7 @@ Jackson
 LatexCommand cite
 after "(9.155)"
 key "jackson_classical_1998"
+literal "true"
 
 \end_inset
 
@@ -1138,6 +1153,7 @@ TODO start from
 LatexCommand cite
 after "(A7)"
 key "pustovit_plasmon-mediated_2010"
+literal "true"
 
 \end_inset
 
@@ -1317,6 +1333,7 @@ TODO start from
 LatexCommand cite
 after "(A11)"
 key "pustovit_plasmon-mediated_2010"
+literal "true"
 
 \end_inset
 
@@ -1479,6 +1496,7 @@ Cruzan's formulation, Xu's normalisation
 LatexCommand cite
 after "(59)"
 key "xu_efficient_1998"
+literal "true"
 
 \end_inset
 
@@ -1495,6 +1513,7 @@ where
 LatexCommand cite
 after "(28,5,60,61)"
 key "xu_efficient_1998"
+literal "true"
 
 \end_inset
 

qpms/CMakeLists.txt

@@ -7,31 +7,41 @@ find_package(LAPACK REQUIRED)
 # and other not very relevant warnings
 set (CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -Wno-int-in-bool-context -Wno-comment")
 
+# version file
+include(GetGitRevisionDescription)
+get_git_head_revision(GIT_REFSPEC GIT_SHA1)
+configure_file("${CMAKE_CURRENT_SOURCE_DIR}/version.c.in" "${CMAKE_CURRENT_BINARY_DIR}/version.c" @ONLY)
+list(APPEND SOURCES "${CMAKE_CURRENT_BINARY_DIR}/version.c" version.h)
+
 #includes
 set (DIRS ${GSL_INCLUDE_DIRS} ${GSLCBLAS_INCLUDE_DIRS})
 include_directories(${DIRS})
 
+
+
 add_library (qpms SHARED translations.c tmatrices.c vecprint.c vswf.c wigner.c ewald.c
 	ewaldsf.c pointgroups.c latticegens.c
 	lattices2d.c gaunt.c error.c legendre.c symmetries.c vecprint.c
 	bessel.c own_zgemm.c parsing.c scatsystem.c materials.c drudeparam_data.c
-	lll.c beyn.c
+	lll.c beyn.c trivialgroup.c version.c
 	)
 use_c99()
 
 set(LIBS ${LIBS} ${GSL_LIBRARIES} ${GSLCBLAS_LIBRARIES})
 
+
 target_link_libraries (qpms
-	gsl
-	lapack
-	blas
-	amos
+	${GSL_LIBRARIES}
+	${LAPACK_LIBRARIES}
+	${BLAS_LIBRARIES}
+	${QPMS_AMOSLIB}
+	Faddeeva
 	)
 target_include_directories (qpms PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
 
 target_compile_options(qpms PRIVATE -Wall -Wno-return-type -Wno-unused-variable -Wno-unused-function -Wno-unused-but-set-variable -Wno-unused-label)
 target_compile_definitions(qpms PRIVATE LATTICESUMS32 QPMS_VECTORS_NICE_TRANSFORMATIONS
-	EWALD_AUTO_CUTOFF
+	EWALD_AUTO_CUTOFF QPMS_EVALUATE_PARANOID_ASSERTS
 	)
 
 install(TARGETS qpms

qpms/__init__.py

@@ -1,5 +1,3 @@
-from pkg_resources import get_distribution
-__version__ = get_distribution('qpms').version
 
 import os as __os
 from sys import platform as __platform
@@ -7,7 +5,7 @@ from sys import platform as __platform
 import warnings as __warnings
 
 try:
-    from .qpms_c import PointGroup, FinitePointGroup, FinitePointGroupElement, Particle, scatsystem_set_nthreads, ScatteringSystem, ScatteringMatrix, pitau, set_gsl_pythonic_error_handling, pgsl_ignore_error, gamma_inc, lll_reduce
+    from .qpms_c import PointGroup, FinitePointGroup, FinitePointGroupElement, Particle, scatsystem_set_nthreads, ScatteringSystem, ScatteringMatrix, pitau, set_gsl_pythonic_error_handling, pgsl_ignore_error, gamma_inc, lll_reduce, qpms_library_version
 except ImportError as ex:
     if __platform == "linux" or __platform == "linux2":
         if 'LD_LIBRARY_PATH' not in __os.environ.keys():
@@ -24,7 +22,12 @@ from .cymaterials import MaterialInterpolator, EpsMu, LorentzDrudeModel, lorentz
 from .cycommon import dbgmsg_enable, dbgmsg_disable, dbgmsg_active, BesselType, VSWFType
 from .cywaves import vswf_single
 
-from .qpms_p import * # maybe don't import automatically in the future (adds around 0.5 s delay)
+def __version__():
+    from pkg_resources import get_distribution
+    librev = qpms_library_version()
+    return get_distribution('qpms').version + (("lr:"+librev) if librev else "")
+
+#from .qpms_p import * # don't import automatically (adds around 0.5 s delay and depends on scipy)
 from .constants import *
 
 # legacy code which brutally slows down the whole package init:

qpms/argproc.py

@@ -1,9 +1,17 @@
 '''
-Common snippets for argument processing in command line scripts; legacy scripts use scripts_common.py instead.
+Common snippets for argument processing in command line scripts.
 '''
 
 import argparse
 import sys
+import warnings
+
+def flatten(S):
+    if S == []:
+        return S
+    if isinstance(S[0], list):
+        return flatten(S[0]) + flatten(S[1:])
+    return S[:1] + flatten(S[1:])
 
 def make_action_sharedlist(opname, listname):
     class opAction(argparse.Action):
@@ -13,6 +21,40 @@ def make_action_sharedlist(opname, listname):
             getattr(args, listname).append((opname, values))
     return opAction
 
+def make_dict_action(argtype=None, postaction='store', first_is_key=True):
+    class DictAction(argparse.Action):
+        #def __init__(self, option_strings, dest, nargs=None, **kwargs):
+        #    if nargs is not None:
+        #    raise ValueError("nargs not allowed")
+        #    super(DictAction, self).__init__(option_strings, dest, **kwargs)
+        def __call__(self, parser, namespace, values, option_string=None):
+            if first_is_key: # For the labeled versions
+                key = values[0]
+                vals = values[1:]
+            else: # For the default values
+                key = None
+                vals = values
+            if argtype is not None:
+                if (first_is_key and self.nargs == 2) or (not first_is_key and self.nargs == 1):
+                    vals = argtype(vals[0]) # avoid having lists in this case
+                else:
+                    vals = [argtype(val) for val in vals]
+            ledict = getattr(namespace, self.dest, {})
+            if ledict is None:
+                ledict = {}
+            if postaction=='store':
+                ledict[key] = vals
+            elif postaction=='append':
+                lelist = ledict.get(key, [])
+                lelist.append(vals)
+                ledict[key] = lelist
+            setattr(namespace, self.dest, ledict)
+    return DictAction
+
+
+class ArgumentProcessingError(Exception):
+    pass
+
 class AppendTupleAction(argparse.Action):
     ''' A variation on the 'append' builtin action from argparse, but uses tuples for the internal groupings instead of lists ''' 
     def __call__(self, parser, args, values, option_string=None):
@@ -20,51 +62,299 @@ class AppendTupleAction(argparse.Action):
             setattr(args, self.dest, list())
         getattr(args, self.dest).append(tuple(values))
 
+def float_range(string):
+    """Tries to parse a string either as one individual float value
+    or one of the following patterns:
+    
+    first:last:increment
+    first:last|steps
+    first:last
+    
+    (The last one is equivalent to first:last|50.)
+    Returns either float or numpy array.
+    """
+    try:
+        res = float(string)
+        return res
+    except ValueError:
+        import re
+        steps = None
+        match = re.match(r's?([^:]+):([^|]+)\|(.+)', string)
+        if match:
+            steps = int(match.group(3))
+        else:
+            match = re.match(r's?([^:]+):([^:]+):(.+)', string)
+            if match:
+                increment = float(match.group(3))
+            else:
+                match = re.match(r's?([^:]+):(.+)', string)
+                if match:
+                    steps = 50
+                else: 
+                    argparse.ArgumentTypeError('Invalid float/sequence format: "%s"' % string)
+        first = float(match.group(1))
+        last = float(match.group(2))
+        import numpy as np
+        if steps is not None:
+            return np.linspace(first, last, num=steps)
+        else:
+            return np.arange(first, last, increment)
+
+def int_or_None(string):
+    """Tries to parse a string either as an int or None (if it contains only whitespaces)"""
+    try:
+        return int(string)
+    except ValueError as ve:
+        if string.strip() == '':
+            return None
+        else:
+            raise ve
+
+def sslice(string):
+    """Tries to parse a string either as one individual int value
+    or one of the following patterns:
+    
+    first:last:increment
+    first:last
+
+    first, last and increment must be parseable as ints
+    or be empty (then 
+
+    In each case, 's' letter can be prepended to the whole string to avoid
+    argparse interpreting this as a new option (if the argument contains
+    '-' or '+').
+    
+    Returns either int or slice containing ints or Nones.
+    """
+    if string[0] == 's':
+        string = string[1:]
+    try:
+        res = int(string)
+        return res
+    except ValueError:
+        import re
+        match = re.match(r'([^:]*):([^:]*):(.*)', string)
+        if match:
+            step = int_or_None(match.group(3))
+        else:
+            match = re.match(r'([^:]*):(.*)', string)
+            if match:
+                step = None
+            else: 
+                argparse.ArgumentTypeError('Invalid int/slice format: "%s"' % string)
+        start = int_or_None(match.group(1))
+        stop = int_or_None(match.group(2))
+        return slice(start, stop, step)
+
+def sfloat(string):
+    '''Tries to match a float, or a float with prepended 's'
+
+    Used as a workaraound for argparse's negative number matcher, which does not recognize
+    scientific notation.
+    '''
+    try:
+        res = float(string)
+    except ValueError as exc:
+        if string[0] == 's':
+            res = float(string[1:])
+        else: raise exc
+    return res
+
+def sint(string):
+    '''Tries to match an int, or an int with prepended 's'
+
+    Used as a workaraound for argparse's negative number matcher if '+' is used as a
+    prefix 
+    '''
+    try:
+        res = int(string)
+    except ValueError as exc:
+        if string[0] == 's':
+            res = int(string[1:])
+        else: raise exc
+    return res
+
+def material_spec(string):
+    """Tries to parse a string as a material specification, i.e. a 
+    real or complex number or one of the string in built-in Lorentz-Drude models.
+
+    Tries to interpret the string as 1) float, 2) complex, 3) Lorentz-Drude key.
+    Raises argparse.ArgumentTypeError on failure.
+    """
+    from .cymaterials import lorentz_drude
+    if string in lorentz_drude.keys():
+        return string
+    else:
+        try: lemat = float(string)
+        except ValueError:
+            try: lemat = complex(string)
+            except ValueError as ve:
+                raise argparse.ArgumentTypeError("Material specification must be a supported material name %s, or a number" % (str(lorentz_drude.keys()),)) from ve
+        return lemat
+
 class ArgParser:
     ''' Common argument parsing engine for QPMS python CLI scripts. '''
+    
+    def __add_planewave_argparse_group(ap):
+        pwgrp = ap.add_argument_group('Incident wave specification', """
+        Incident wave direction is given in terms of ISO polar and azimuthal angles θ, φ, 
+        which translate into cartesian coordinates as r̂ = (x, y, z) = (sin(θ) cos(φ), sin(θ) sin(φ), cos(θ)).
+
+        Wave polarisation is given in terms of parameters ψ, χ, where ψ is the angle between a polarisation 
+        ellipse axis and meridian tangent θ̂, and tg χ determines axes ratio; 
+        the electric field in the origin is then
+
+        E⃗ = cos(χ) (cos(ψ) θ̂ + sin(ψ) φ̂) + i sin(χ) (sin(ψ) θ̂ + cos(ψ) φ̂).
+
+        All the angles are given as multiples of π/2.
+        """ # TODO EXAMPLES
+        )
+        pwgrp.add_argument("-φ", "--phi", type=float, default=0,
+            help='Incident wave asimuth in multiples of π/2.')
+        pwgrp.add_argument("-θ", "--theta", type=float_range, default=0,
+            help='Incident wave polar angle in multiples of π/2. This might be a sequence in format FIRST:LAST:INCREMENT.')
+        pwgrp.add_argument("-ψ", "--psi", type=float, default=0,
+            help='Angle between polarisation ellipse axis and meridian tangent θ̂ in multiples of π/2.')
+        pwgrp.add_argument("-χ", "--chi", type=float, default=0,
+            help='Polarisation parameter χ in multiples of π/2. 0 for linear, 0.5 for circular pol.')
+
+    def __add_manyparticle_argparse_group(ap):
+        mpgrp = ap.add_argument_group('Many particle specification', "TODO DOC")
+        mpgrp.add_argument("-p", "--position", nargs='+', action=make_dict_action(argtype=sfloat, postaction='append',
+            first_is_key=False), help="Particle positions, cartesion coordinates (default particle properties)")
+        mpgrp.add_argument("+p", "++position", nargs='+', action=make_dict_action(argtype=sfloat, postaction='append', 
+            first_is_key=True), help="Particle positions, cartesian coordinates (labeled)")
+        mpgrp.add_argument("-L", "--lMax", nargs=1, default={},
+                action=make_dict_action(argtype=int, postaction='store', first_is_key=False,),
+                help="Cutoff multipole degree (default)")
+        mpgrp.add_argument("+L", "++lMax", nargs=2, 
+                action=make_dict_action(argtype=int, postaction='store', first_is_key=True,),
+            help="Cutoff multipole degree (labeled)")
+        mpgrp.add_argument("-m", "--material", nargs=1, default={},
+                action=make_dict_action(argtype=material_spec, postaction='store', first_is_key=False,),
+                help='particle material (Au, Ag, ... for Lorentz-Drude or number for constant refractive index) (default)')
+        mpgrp.add_argument("+m", "++material", nargs=2,
+                action=make_dict_action(argtype=material_spec, postaction='store', first_is_key=True,),
+                help='particle material (Au, Ag, ... for Lorentz-Drude or number for constant refractive index) (labeled)')
+        mpgrp.add_argument("-r", "--radius", nargs=1, default={},
+                action=make_dict_action(argtype=float, postaction='store', first_is_key=False,),
+                help='particle radius (sphere or cylinder; default)')
+        mpgrp.add_argument("+r", "++radius", nargs=2,
+                action=make_dict_action(argtype=float, postaction='store', first_is_key=True,),
+                help='particle radius (sphere or cylinder; labeled)')
+        mpgrp.add_argument("-H", "--height", nargs=1, default={},
+                action=make_dict_action(argtype=float, postaction='store', first_is_key=False,),
+                help='particle radius (cylinder; default)')
+        mpgrp.add_argument("+H", "++height", nargs=2,
+                action=make_dict_action(argtype=float, postaction='store', first_is_key=True,),
+                help='particle radius (cylinder; labeled)')
+
     atomic_arguments = {
             'rectlattice2d_periods': lambda ap: ap.add_argument("-p", "--period", type=float, nargs='+', required=True, help='square/rectangular lattice periods', metavar=('px','[py]')),
             'rectlattice2d_counts': lambda ap: ap.add_argument("--size", type=int, nargs=2, required=True, help='rectangular array size (particle column, row count)', metavar=('NCOLS', 'NROWS')),
             'single_frequency_eV': lambda ap: ap.add_argument("-f", "--eV", type=float, required=True, help='radiation angular frequency in eV'),
-            'single_material': lambda ap: ap.add_argument("-m", "--material", help='particle material (Au, Ag, ... for Lorentz-Drude or number for constant refractive index)', default='Au', required=True),
+            'multiple_frequency_eV_optional': lambda ap: ap.add_argument("-f", "--eV", type=float, nargs='*', help='radiation angular frequency in eV (additional)'),
+            'seq_frequency_eV': lambda ap: ap.add_argument("-F", "--eV-seq", type=float, nargs=3, required=True, help='uniform radiation angular frequency sequence in eV', metavar=('FIRST', 'INCREMENT', 'LAST')),
+            'real_frequencies_eV_ng': lambda ap: ap.add_argument("-f", "--eV", type=float_range, nargs=1, action='append', required=True, help='Angular frequency (or angular frequency range) in eV'), # nargs='+', action='extend' would be better, but action='extend' requires python>=3.8
+            'single_material': lambda ap: ap.add_argument("-m", "--material", help='particle material (Au, Ag, ... for Lorentz-Drude or number for constant refractive index)', type=material_spec, required=True),
             'single_radius': lambda ap: ap.add_argument("-r", "--radius", type=float, required=True, help='particle radius (sphere or cylinder)'),
             'single_height': lambda ap: ap.add_argument("-H", "--height", type=float, help='cylindrical particle height; if not provided, particle is assumed to be spherical'),
-            'single_kvec2': lambda ap: ap.add_argument("-k", '--kx-lim', nargs=2, type=float, required=True, help='k vector', metavar=('KX_MIN', 'KX_MAX')),
+            'single_kvec2': lambda ap: ap.add_argument("-k", '--kx-lim', nargs=2, type=sfloat, required=True, help='k vector', metavar=('KX_MIN', 'KX_MAX')),
             'kpi': lambda ap: ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)"),
-            'bg_refractive_index': lambda ap: ap.add_argument("-n", "--refractive-index", type=float, default=1.52, help='background medium refractive index'),
+            'bg_real_refractive_index': lambda ap: ap.add_argument("-n", "--refractive-index", type=float, default=1., help='background medium strictly real refractive index'),
+            'bg_analytical': lambda ap: ap.add_argument("-B", "--background", type=material_spec, default=1., help="Background medium specification (constant real or complex refractive index, or supported material label)"),
             'single_lMax': lambda ap: ap.add_argument("-L", "--lMax", type=int, required=True, default=3, help='multipole degree cutoff'),
             'single_lMax_extend': lambda ap: ap.add_argument("--lMax-extend", type=int, required=False, default=6, help='multipole degree cutoff for T-matrix calculation (cylindrical particles only'),
             'outfile': lambda ap: ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)'), # TODO consider type=argparse.FileType('w')
             'plot_out': lambda ap: ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)"),
             'plot_do': lambda ap: ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path"),
-            'lattice2d_basis': lambda ap: ap.add_argument("-b", "--basis-vector", action=AppendTupleAction, help="basis vector in xy-cartesian coordinates (two required)", dest='basis_vectors', metavar=('X', 'Y')),
+            'lattice2d_basis': lambda ap: ap.add_argument("-b", "--basis-vector", nargs='+', action=AppendTupleAction, help="basis vector in xy-cartesian coordinates (two required)", required=True, type=sfloat, dest='basis_vectors', metavar=('X', 'Y')),
+            'planewave_pol_angles': __add_planewave_argparse_group,
+            'multi_particle': __add_manyparticle_argparse_group,
     }
 
-    feature_sets_available = { # name : (description, dependencies, atoms not in other dependencies, methods called after parsing) 
-            'background': ("Background medium definition (currently only constant epsilon supported)", (), ('bg_refractive_index',), ('_eval_background_epsmu',)),
-            'single_particle': ("Single particle definition (shape [currently spherical or cylindrical]) and materials, incl. background)", ('background',), ('single_material', 'single_radius', 'single_height', 'single_lMax_extend'), ('_eval_single_tmgen',)),
-            'single_lMax': ("Single particle lMax definition", (), ('single_lMax',), ()),
-            'single_omega': ("Single angular frequency", (), ('single_frequency_eV',), ('_eval_single_omega',)),
-            'lattice2d': ("Specification of a generic 2d lattice (spanned by the x,y axes)", (), ('lattice2d_basis',), ('_eval_lattice2d',)),
-            'rectlattice2d': ("Specification of a rectangular 2d lattice; conflicts with lattice2d", (), ('rectlattice2d_periods',), ('_eval_rectlattice2d',)),
-            'rectlattice2d_finite': ("Specification of a rectangular 2d lattice; conflicts with lattice2d", ('rectlattice2d',), ('rectlattice2d_counts',), ()),
+    feature_sets_available = { # name : (description, dependencies, atoms not in other dependencies, methods called after parsing, "virtual" features provided) 
+            'const_real_background': ("Background medium with constant real refractive index", (), ('bg_real_refractive_index',), ('_eval_const_background_epsmu',), ('background', 'background_analytical')),
+            'background' : ("Most general background medium specification currently supported", ('background_analytical',), (), (), ()),
+            'background_analytical' : ("Background medium model holomorphic for 'reasonably large' complex frequency areas", (), ('bg_analytical',), ('_eval_analytical_background_epsmugen',), ('background',)),
+            'single_particle': ("Single particle definition (shape [currently spherical or cylindrical]) and materials, incl. background)", ('background',), ('single_material', 'single_radius', 'single_height', 'single_lMax_extend'), ('_eval_single_tmgen',), ()),
+            'multi_particle': ("One or more particle definition (shape [curently spherical or cylindrical]), materials, and positions)", ('background',), ('multi_particle',), ('_process_multi_particle',), ()),
+            'single_lMax': ("Single particle lMax definition", (), ('single_lMax',), (), ()),
+            'single_omega': ("Single angular frequency", (), ('single_frequency_eV',), ('_eval_single_omega',), ()),
+            'omega_seq': ("Equidistant real frequency range with possibility of adding individual frequencies", (), ('seq_frequency_eV', 'multiple_frequency_eV_optional',), ('_eval_omega_seq',), ()),
+            'omega_seq_real_ng': ("Equidistant real frequency ranges or individual frequencies (new syntax)", (), ('real_frequencies_eV_ng',), ('_eval_omega_seq_real_ng',), ()),
+            'lattice2d': ("Specification of a generic 2d lattice (spanned by the x,y axes)", (), ('lattice2d_basis',), ('_eval_lattice2d',), ()),
+            'rectlattice2d': ("Specification of a rectangular 2d lattice; conflicts with lattice2d", (), ('rectlattice2d_periods',), ('_eval_rectlattice2d',), ()),
+            'rectlattice2d_finite': ("Specification of a rectangular 2d lattice; conflicts with lattice2d", ('rectlattice2d',), ('rectlattice2d_counts',), (), ()),
+            'planewave': ("Specification of a normalised plane wave (typically used for scattering) with a full polarisation state", (), ('planewave_pol_angles',), ("_process_planewave_angles",), ()),
     }
 
 
     def __init__(self, features=[]):
-        self.ap = argparse.ArgumentParser()
+        prefix_chars = '+-' if 'multi_particle' in features else '-'
+        self.ap = argparse.ArgumentParser(prefix_chars=prefix_chars)
         self.features_enabled = set()
         self.call_at_parse_list = []
         self.parsed = False
         for feat in features:
             self.add_feature(feat)
+        self._emg_register = {} # EpsMuGenerator dictionary to avoid recreating equivalent instances; filled by _add_emg()
+        self._tmg_register = {} # TMatrixGenerator dictionary to avoid recreating equivalent instances; filled by _add_tmg()
+        self._bspec_register = {} # Dictionary of used BaseSpecs to keep the equivalent instances unique; filled by _add_bspec()
+
+    def _add_emg(self, emgspec):
+        """Looks up whether if an EpsMuGenerator from given material_spec has been already registered, and if not, creates a new one"""
+        from .cymaterials import EpsMu, EpsMuGenerator, lorentz_drude
+        if emgspec in self._emg_register.keys():
+            return self._emg_register[emgspec]
+        else:
+            if isinstance(emgspec, (float, complex)):
+                emg = EpsMuGenerator(EpsMu(emgspec**2))
+            else:
+                emg = EpsMuGenerator(lorentz_drude[emgspec])
+            self._emg_register[emgspec] = emg
+            return emg
+
+    def _add_tmg(self, tmgspec):
+        """Looks up whether if a T-matrix from given T-matrix specification tuple has been already registered, and if not, creates a new one
+        
+        T-matrix specification shall be of the form 
+        (bg_material_spec, fg_material_spec, shape_spec) where shape_spec is
+        (radius, height, lMax_extend)
+        """
+        if tmgspec in self._tmg_register.keys():
+            return self._tmg_register[tmgspec]
+        else:
+            from .cytmatrices import TMatrixGenerator
+            bgspec, fgspec, (radius, height, lMax_extend) = tmgspec
+            bg = self._add_emg(bgspec)
+            fg = self._add_emg(fgspec)
+            if height is None:
+                tmgen = TMatrixGenerator.sphere(bg, fg, radius)
+            else:
+                tmgen = TMatrixGenerator.cylinder(bg, fg, radius, height, lMax_extend=lMax_extend)
+            self._tmg_register[tmgspec] = tmgen
+            return tmgen
+
+    def _add_bspec(self, key):
+        if key in self._bspec_register.keys():
+            return self._bspec_register[key]
+        else:
+            from .cybspec import BaseSpec
+            if isinstance(key, BaseSpec):
+                bspec = key
+            elif isinstance(key, int):
+                bspec = self._add_bspec(BaseSpec(lMax=key))
+            else: raise TypeError("Can't register this as a BaseSpec")
+            self._bspec_register[key] = bspec
+            return bspec
 
     def add_feature(self, feat):
         if feat not in self.features_enabled:
             if feat not in ArgParser.feature_sets_available:
                 raise ValueError("Unknown ArgParser feature: %s" % feat)
             #resolve dependencies
-            _, deps, atoms, atparse = ArgParser.feature_sets_available[feat]
+            _, deps, atoms, atparse, provides_virtual = ArgParser.feature_sets_available[feat]
             for dep in deps:
                 self.add_feature(dep)
             for atom in atoms: # maybe check whether that atom has already been added sometimes in the future?
@@ -72,16 +362,26 @@ class ArgParser:
             for methodname in atparse:
                 self.call_at_parse_list.append(methodname)
             self.features_enabled.add(feat)
+            for feat_virt in provides_virtual:
+                self.features_enabled.add(feat_virt)
 
     def add_argument(self, *args, **kwargs):
         '''Add a custom argument directly to the standard library ArgParser object'''
-        self.ap.add_argument(*args, **kwargs)
+        return self.ap.add_argument(*args, **kwargs)
+    
+    def add_argument_group(self, *args, **kwargs):
+        '''Add a custom argument group directly to the standard library ArgParser object'''
+        return self.ap.add_argument_group(*args, **kwargs)
 
     def parse_args(self, process_data = True,  *args, **kwargs):
         self.args = self.ap.parse_args(*args, **kwargs)
         if process_data:
             for method in self.call_at_parse_list:
-                getattr(self, method)()
+                try:
+                    getattr(self, method)()
+                except ArgumentProcessingError:
+                    err = sys.exc_info()[1]
+                    self.ap.error(str(err))
         return self.args
     
     def __getattr__(self, name):
@@ -90,42 +390,67 @@ class ArgParser:
 
     # Methods to initialise the related data structures:
 
-    def _eval_background_epsmu(self): # feature: background
+    def _eval_const_background_epsmu(self): # feature: const_real_background
+        self.args.background = self.args.refractive_index
+        self._eval_analytical_background_epsmugen()
+    
+    def _eval_analytical_background_epsmugen(self): # feature: background_analytical
+        a = self.args
         from .cymaterials import EpsMu
-        self.background_epsmu = EpsMu(self.args.refractive_index**2)
+        if isinstance(a.background, (float, complex)):
+            self.background_epsmu = EpsMu(a.background**2)
+        self.background_emg = self._add_emg(a.background)
 
     def _eval_single_tmgen(self): # feature: single_particle
         a = self.args
         from .cymaterials import EpsMuGenerator, lorentz_drude
         from .cytmatrices import TMatrixGenerator
-        if a.material in lorentz_drude.keys():
-            self.foreground_emg = EpsMuGenerator(lorentz_drude[a.material])
-        else:
-            try: lemat = float(a.material)
-            except ValueError:
-                try: lemat = complex(a.material)
-                except ValueError as ve:
-                    raise ValueError("--material must be either a label such as 'Ag', 'Au', or a number") from ve
-            a.material = lemat
-            self.foreground_emg = EpsMuGenerator(EpsMu(a.material**2))
-
-        if a.height is None:
-            self.tmgen = TMatrixGenerator.sphere(self.background_epsmu, self.foreground_emg, a.radius)
-        else:
-            self.tmgen = TMatrixGenerator.cylinder(self.background_epsmu, self.foreground_emg, a.radius, a.height, lMax_extend = a.lMax_extend)
+        self.foreground_emg = self._add_emg(a.material)
+        self.tmgen = self._add_tmg((a.background, a.material, (a.radius, a.height, a.lMax_extend)))
+        self.bspec = self._add_bspec(a.lMax)
 
     def _eval_single_omega(self): # feature: single_omega
         from .constants import eV, hbar
         self.omega = self.args.eV * eV / hbar
 
+    def _eval_omega_seq(self): # feature: omega_seq
+        import numpy as np
+        from .constants import eV, hbar
+        start, step, stop = self.args.eV_seq
+        self.omegas = np.arange(start, stop, step)
+        if self.args.eV:
+            self.omegas = np.concatenate((self.omegas, np.array(self.args.eV)))
+            self.omegas.sort()
+        self.omegas *= eV/hbar
+
+    def _eval_omega_seq_real_ng(self): # feature: omega_seq_real_ng
+        import numpy as np
+        from .constants import eV, hbar
+        eh = eV / hbar
+        self.omegas = [omega_eV * eh for  omega_eV in flatten(self.args.eV)]
+        self.omega_max = max(om if isinstance(om, float) else max(om) for om in self.omegas)
+        self.omega_min = min(om if isinstance(om, float) else min(om) for om in self.omegas)
+        self.omega_singles = [om for om in self.omegas if isinstance(om, float)]
+        self.omega_ranges = [om for om in self.omegas if not isinstance(om, float)]
+        self.omega_descr = ("%geV" % (self.omega_max / eh)) if (self.omega_max == self.omega_min) else (
+                "%g–%geV" % (self.omega_min / eh, self.omega_max / eh))
+        self.allomegas = []
+        for om in self.omegas:
+            if isinstance(om, float):
+                self.allomegas.append(om)
+            else:
+                self.allomegas.extend(om)
+        self.allomegas = np.unique(self.allomegas)
+
+
     def _eval_lattice2d(self): # feature: lattice2d
         l = len(self.args.basis_vectors)
         if l != 2: raise ValueError('Two basis vectors must be specified (have %d)' % l)
         from .qpms_c import lll_reduce
-        self.direct_basis = lll_reduce(self.args.basis_vector, delta=1.)
-        # import numpy as np
-        # self.reciprocal_basis1 = np.linalg.inv(self.direct_basis)
-        # self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
+        self.direct_basis = lll_reduce(self.args.basis_vectors, delta=1.)
+        import numpy as np
+        self.reciprocal_basis1 = np.linalg.inv(self.direct_basis.T)
+        self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
     
     def _eval_rectlattice2d(self): # feature: rectlattice2d
         a = self.args
@@ -140,4 +465,97 @@ class ArgParser:
         import numpy as np
         a.basis_vectors = [(a.period[0], 0.), (0., a.period[1])]
         self.direct_basis = np.array(a.basis_vectors)
+        self.reciprocal_basis1 = np.linalg.inv(self.direct_basis.T)
+        self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
 
+    def _process_planewave_angles(self): #feature: planewave
+        import math
+        pi2 = math.pi/2
+        a = self.args
+        a.chi = a.chi * pi2
+        a.psi = a.psi * pi2
+        a.theta = a.theta * pi2
+        a.phi = a.phi * pi2
+
+    def _process_multi_particle(self): # feature: multi_particle
+        a = self.args
+        self.tmspecs = {}
+        self.tmgens = {}
+        self.bspecs = {}
+        self.positions = {}
+        pos13, pos23, pos33 = False, False, False # used to 
+        if len(a.position.keys()) == 0:
+            warnings.warn("No particle position (-p or +p) specified, assuming single particle in the origin / single particle per unit cell!")
+            a.position[None] = [(0.,0.,0.)]
+        for poslabel in a.position.keys():
+            try:
+                lMax = a.lMax.get(poslabel, False) or a.lMax[None]
+                radius = a.radius.get(poslabel, False) or a.radius[None]
+                # Height is "inherited" only together with radius
+                height = a.height.get(poslabel, None) if poslabel in a.radius.keys() else a.height.get(None, None)
+                if hasattr(a, 'lMax_extend'):
+                    lMax_extend = a.lMax_extend.get(poslabel, False) or a.lMax_extend.get(None, False) or None
+                else:
+                    lMax_extend = None
+                material = a.material.get(poslabel, False) or a.material[None]
+            except (TypeError, KeyError) as exc:
+                if poslabel is None:
+                    raise ArgumentProcessingError("Unlabeled particles' positions (-p) specified, but some default particle properties are missing (--lMax, --radius, and --material have to be specified)") from exc
+                else:
+                    raise ArgumentProcessingError(("Incomplete specification of '%s'-labeled particles: you must"
+                        "provide at least ++lMax, ++radius, ++material arguments with the label, or the fallback arguments"
+                        "--lMax, --radius, --material.")%(str(poslabel),)) from exc
+            tmspec = (a.background, material, (radius, height, lMax_extend)) 
+            self.tmspecs[poslabel] = tmspec
+            self.tmgens[poslabel] = self._add_tmg(tmspec)
+            self.bspecs[poslabel] = self._add_bspec(lMax)
+            poslist_cured = []
+            for pos in a.position[poslabel]:
+                if len(pos) == 1:
+                    pos_cured = (0., 0., pos[0])
+                    pos13 = True
+                elif len(pos) == 2:
+                    pos_cured = (pos[0], pos[1], 0.)
+                    pos23 = True
+                elif len(pos) == 3:
+                    pos_cured = pos
+                    pos33 = True
+                else:
+                    raise argparse.ArgumentTypeError("Each -p / +p argument requires 1 to 3 cartesian coordinates")
+                poslist_cured.append(pos_cured)
+            self.positions[poslabel] = poslist_cured
+        if pos13 and pos23:
+            warnings.warn("Both 1D and 2D position specifications used. The former are interpreted as z coordinates while the latter as x, y coordinates")
+
+    def get_particles(self):
+        """Creates a list of Particle instances that can be directly used in ScatteringSystem.create().
+
+        Assumes that self._process_multi_particle() has been already called.
+        """
+        from .qpms_c import Particle
+        plist = []
+        for poslabel, poss in self.positions.items():
+            t = self.tmgens[poslabel]
+            bspec = self.bspecs[poslabel]
+            plist.extend([Particle(pos, t, bspec=bspec) for pos in poss])
+        return plist
+
+#TODO perhaps move into another module
+def annotate_pdf_metadata(pdfPages, scriptname=None, keywords=None, author=None, title=None, subject=None, **kwargs):
+    """Adds QPMS version-related metadata to a matplotlib PdfPages object
+
+    Use before closing the PDF file.
+    """
+    from .qpms_c import qpms_library_version
+    d = pdfPages.infodict()
+    d['Creator'] = "QPMS%s (lib rev. %s), https://qpms.necada.org" % (
+        "" if scriptname is None else (" "+scriptname), qpms_library_version())
+    if author is not None:
+        d['Author'] = author
+    if title is not None:
+        d['Title'] = title
+    if subject is not None:
+        d['Subject'] = subject
+    if keywords is not None:
+        d['Keywords'] = ' '.join(keywords)
+    d.update(kwargs) 

qpms/bessel.c

@@ -7,7 +7,7 @@
 #include <gsl/gsl_sf_bessel.h>
 #include <complex.h>
 #include "qpms_error.h"
-#include <amos.h>
+#include <camos.h>
 #include <math.h>
 
 #ifndef M_LN2
@@ -52,6 +52,11 @@ static inline complex double spherical_yn(qpms_l_t l, complex double z) {
 qpms_errno_t qpms_sph_bessel_realx_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, complex double *result_array) {
   int retval;
   double tmparr[lmax+1];
+  if (typ != QPMS_BESSEL_REGULAR && x == 0) {
+    for (int l = 0; l <= lmax; ++l) result_array[l] = NAN + I*NAN;
+    QPMS_WARN("Evaluating singular Bessel functions at zero!");
+    return QPMS_SUCCESS; // Really?
+  }
   switch(typ) {
     case QPMS_BESSEL_REGULAR:
       retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
@@ -84,7 +89,8 @@ qpms_errno_t qpms_sph_bessel_realx_fill(qpms_bessel_t typ, qpms_l_t lmax, double
 
 // TODO DOC
 qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex double x, complex double *res) {
-  if(!cimag(x))
+  if(!cimag(x) && 
+        creal(x) < 10000) // For large arguments (around 30000 or more), gsl_sf_bessel_jl_steed_array fails
     return qpms_sph_bessel_realx_fill(typ, lmax, creal(x), res);
   else if (isnan(creal(x)) || isnan(cimag(x))) 
     for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = NAN + I*NAN;
@@ -92,30 +98,32 @@ qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex doub
   else if (fpclassify(creal(x)) == FP_INFINITE) 
     for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = INFINITY + I * INFINITY;
   else {
-    const DOUBLE_PRECISION_t zr = creal(x), zi = cimag(x), fnu = 0.5;
-    const INTEGER_t n = lmax + 1, kode = 1 /* No exponential scaling */;
-    DOUBLE_PRECISION_t cyr[n], cyi[n];
-    INTEGER_t ierr, nz;
+try_again: ;
+    int retry_counter = 0;
+    const double zr = creal(x), zi = cimag(x), fnu = 0.5;
+    const int n = lmax + 1, kode = 1 /* No exponential scaling */;
+    double cyr[n], cyi[n];
+    int ierr, nz;
     unsigned int kindchar; // Only for error output
     const complex double prefac = csqrt(M_PI_2/x);
     switch(typ) {
       case QPMS_BESSEL_REGULAR:
         kindchar = 'j';
-        amos_zbesj(&zr, &zi, &fnu, &kode, &n, cyr, cyi, &nz, &ierr);
+        ierr = camos_zbesj(zr, zi, fnu, kode, n, cyr, cyi, &nz);
         break;
       case QPMS_BESSEL_SINGULAR:
         kindchar = 'y';
         {
-          DOUBLE_PRECISION_t cwrkr[lmax + 1], cwrki[lmax + 1];
-          amos_zbesy(&zr, &zi, &fnu, &kode, &n, cyr, cyi, &nz, cwrkr, cwrki, &ierr);
+          double cwrkr[lmax + 1], cwrki[lmax + 1];
+          ierr = camos_zbesy(zr, zi, fnu, kode, n, cyr, cyi, &nz, cwrkr, cwrki);
         }
         break;
       case QPMS_HANKEL_PLUS:
       case QPMS_HANKEL_MINUS: 
         kindchar = 'h';
         {
-          const INTEGER_t m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2;
-          amos_zbesh(&zr, &zi, &fnu, &kode, &m, &n, cyr, cyi, &nz, &ierr);
+          const int m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2;
+          ierr = camos_zbesh(zr, zi, fnu, kode, m, n, cyr, cyi, &nz);
         }
         break;
       default:
@@ -126,14 +134,28 @@ qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex doub
       for (qpms_l_t l = 0; l <= lmax; ++l)
         res[l] = prefac * (cyr[l] + I * cyi[l]);
       if (ierr == 3) 
-        QPMS_WARN("Amos's zbes%c computation done but losses of significance "
-            "by argument reduction produce less than half of machine accuracy.", 
-            kindchar);
+        if (creal(x) >= 10000) {
+          QPMS_WARN_ONCE("Due to large argument, "
+                "Amos's zbes%c computation done but losses of significance "
+                "by argument reduction produce less than half of machine accuracy. "
+                "This warning is shown only once.", 
+                kindchar);
+        } else {
+          QPMS_WARN("Amos's zbes%c computation done but losses of significance "
+                "by argument reduction produce less than half of machine accuracy.", 
+                kindchar);
+        }
       return QPMS_SUCCESS; //TODO maybe something else if ierr == 3
     }
-    else
-      QPMS_PR_ERROR("Amos's zbes%c failed with ierr == %d.",
-         kindchar, (int) ierr);
+    else {
+      if (retry_counter < 5) {
+        QPMS_WARN("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi). Retrying.\n",
+           kindchar, (int) ierr, lmax, creal(x), cimag(x));
+        ++retry_counter;
+        goto try_again;
+      } else QPMS_PR_ERROR("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi).",
+           kindchar, (int) ierr, lmax, creal(x), cimag(x));
+    }
   }
   return QPMS_SUCCESS;
 }

qpms/bessels.c

@@ -1,65 +0,0 @@
-#include "bessels.h"
-#include <stdlib.h>
-#include <math.h>
-#include <stdio.h>
-#include <string.h>
-
-static const double ln2 = 0.693147180559945309417;
-
-
-// general; gives an array of size xxx with TODODESC
-complex double * hankelcoefftable_init(size_t maxn) {
-	complex double *hct = malloc((maxn+1)*(maxn+2)/2 * sizeof(complex double));
-	for(size_t n = 0; n <= maxn; ++n) {
-		complex double *hcs = hankelcoeffs_get(hct,n);
-		for (size_t k = 0; k <= n; ++k) {
-			double lcoeff = lgamma(n+k+1) - lgamma(n-k+1) - lgamma(k+1) - k*ln2;
-			// for some reason, casting k-n to double does not work,so
-			// cpow (I, k-n-1) cannot be used...
-			complex double ifactor;
-			switch ((n+1-k) % 4) {
-				case 0:
-					ifactor = 1;
-					break;
-				case 1:
-					ifactor = -I;
-					break;
-				case 2:
-					ifactor = -1;
-					break;
-				case 3:
-					ifactor = I;
-					break;
-        default:
-          abort();
-			}
-			// the result should be integer, so round to remove inaccuracies
-			hcs[k] = round(exp(lcoeff)) * ifactor;
-		}
-	}
-	return hct;
-}
-
-void hankelparts_fill(complex double *lrt, complex double *srt, size_t maxn,
-								size_t lrk_cutoff, complex double const * const hct,
-								unsigned kappa, double c, double x) {
-	if (lrt) memset(lrt, 0, (maxn+1)*sizeof(complex double));
-	memset(srt, 0, (maxn+1)*sizeof(complex double));
-	double regularisator = pow(1. - exp(-c * x), (double) kappa);
-	double antiregularisator = 1. - regularisator;
-	double xfrac = 1.; // x ** (-1-k)
-	for (size_t k = 0; k <= maxn; ++k) {
-	xfrac /= x;
-	  for(size_t n = k; n <= maxn; ++n)  // TODO Kahan sums here
-	  	srt[n] += ((k<lrk_cutoff) ? antiregularisator : 1) 
-		  				* xfrac * hankelcoeffs_get(hct,n)[k];
-	  if (lrt && k < lrk_cutoff) for (size_t n = k; n <= maxn; ++n)
-	  	lrt[n] += regularisator * xfrac * hankelcoeffs_get(hct,n)[k];
-	}
-
-	complex double expix = cexp(I * x);
-	for(size_t n = 0; n <= maxn; ++n)
-					srt[n] *= expix;
-	if (lrt) for(size_t n = 0; n <= maxn; ++n)
-					srt[n] *= expix;
-}

qpms/bessels.h

@@ -1,61 +0,0 @@
-#ifndef BESSELS_H
-#define BESSELS_H
-/* Short- and long-range parts of spherical Hankel functions
- * and (cylindrical) Hankel transforms of the long-range parts.
- * Currently, the implementation lies in bessels.c and 
- * lrhankel_recspace_dirty.c. The latter contains the implementation
- * of the Hankel transforms, but currenty only for a pretty limited
- * set of parameters. The general implementation is a BIG TODO here.
- */
-
-#include <stddef.h>
-#include <complex.h>
-
-complex double *hankelcoefftable_init(size_t maxn);
-
-
-// For navigating in the coefficients, maybe not for public use
-static inline complex double *
-trindex_cd(complex double const * const arr, size_t n){
-  return (complex double *)(arr + n*(n+1)/2);
-}
-
-// general, gives the offset such that result[ql] is 
-// the coefficient corresponding to the e**(I * x) * x**(-ql-1)
-// term of the n-th Hankel function; no boundary checks!
-static inline complex double *
-hankelcoeffs_get(complex double const * const hankelcoefftable, size_t n){
-  return trindex_cd(hankelcoefftable, n);
-}
-
-/* Compute the untransformed long- (optional) and short-range parts of spherical Hankel functions */
-// general; target_longrange and target_shortrange are of size (maxn+1)
-// if target_longrange is NULL, only the short-range part is calculated
-void hankelparts_fill(complex double *target_longrange, /* Not needed for the actual calculations
-							   (only for testing and error estimates)
-							   as summed in the reciprocal space:
-							   pass NULL to omit */
-		complex double *target_shortrange,
-		size_t maxn, size_t longrange_order_cutoff, /* terms e**(I x)/x**(k+1), 
-							       k>= longrange_order_cutoff go 
-							       completely to short-range part */
-		complex double const * const hankelcoefftable,
-		unsigned kappa, double c, /* regularisation "slope", dimensionless */ 
-		double x); // dimensionless x = k0 * r
-
-
-
-/* Hankel transforms of the long-range parts of the spherical Hankel functions */
-// this declaration is general; however, the implementation 
-// is so far only for kappa == 5, maxp <= 5, longrange_order_cutoff <= 1
-void lrhankel_recpart_fill(complex  double *target_longrange_kspace /*Must be of size maxn*(maxn+1)/2*/,
-	       size_t maxp /* Max. order of the Hankel transform */,
-	       size_t longrange_order_cutoff /* terms e**(I x)/x**(k+1), k>= longrange_order_cutoff go
-					        completely to the shortrange part
-					        index with hankelcoeffs_get(target,p)l[delta_m] */, 
-	       complex double const * const hankelcoefftable,
-	       unsigned kappa, 
-	       // These are dimensionFUL (inverse lengths):
-	       double cv, double k0, double k);
-
-#endif //BESSELS_H