Fix finiterectlat-modes.py obvious errors.

Former-commit-id: a538ed6c3c84cebffccd41272994027039e46b57

.drone.yml

@@ -1,83 +0,0 @@
----
-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

@@ -5,29 +5,4 @@
 *.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

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

CLIUTILS.md

@@ -1,43 +0,0 @@
-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

@@ -1,17 +1,10 @@
 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)
 
-list(APPEND CMAKE_MODULE_PATH "${CMAKE_CURRENT_SOURCE_DIR}/cmake/")
-
 macro(use_c99)
   if (CMAKE_VERSION VERSION_LESS "3.1")
     if (CMAKE_C_COMPILER_ID STREQUAL "GNU")
@@ -29,23 +22,10 @@ set(CMAKE_POSITION_INDEPENDENT_CODE ON)
 
 set (QPMS_VERSION_MAJOR 0)
 #set (QPMS_VERSION_MINOR 3)
-
+cmake_add_fortran_subdirectory (amos
-if (QPMS_USE_FORTRAN_AMOS)
+	PROJECT amos
-	cmake_add_fortran_subdirectory (amos
+	LIBRARIES amos
-		PROJECT amos
+	NO_EXTERNAL_INSTALL)
-		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

@@ -1,675 +0,0 @@
-### GNU GENERAL PUBLIC LICENSE
-
-Version 3, 29 June 2007
-
-Copyright (C) 2007 Free Software Foundation, Inc.
-<https://fsf.org/>
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-#### 12. No Surrender of Others' Freedom.
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-copy of the Program in return for a fee.
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-END OF TERMS AND CONDITIONS
-
-### How to Apply These Terms to Your New Programs
-
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-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
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-the exclusion of warranty; and each file should have at least the
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-        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.
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-        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           = farfield.png
+PROJECT_LOGO           =
 
 # 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 misc finite_systems.md MIRRORS.md CLIUTILS.md README.md README.Triton.md finite_systems.md lattices.md TODO.md
+INPUT                  = qpms notes finite_systems.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
@@ -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        = https://uslugi.necada.org/js/mathjax
+MATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest
 
 # 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

@@ -1,14 +0,0 @@
-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

@@ -1,14 +1,10 @@
-[![Build Status](https://drone.perkele.eu/api/badges/QPMS/qpms/status.svg)](https://drone.perkele.eu/QPMS/qpms)
-
 QPMS README
 ===========
 
-[QPMS][homepage] (standing for QPMS Photonic Multiple Scattering) 
+QPMS is a toolkit for frequency-domain simulations of photonic systems
-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 using one of the built-in generators or
+(which can be obtained e.g. with the `scuff-tmatrix` tool from 
- e.g. with the `scuff-tmatrix` tool from 
 the [SCUFF-EM] suite).
 
 QPMS handles the multiple scattering of electromagnetic radiation between 
@@ -16,39 +12,26 @@ 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 scattered from nanoparticle
+ * Computing multipole excitations *and fields (TODO)* scattered from nanoparticle
    clusters illuminated by plane, spherical or *cylindrical (TODO)* waves.
- * Finding eigenmodes (optical resonances).
+ * Finding eigenmodes.
- * Calculating cross sections.
+ * *Calculating cross sections (TODO).*
  * Reducing numerical complexity of the computations by exploiting
    symmetries of the cluster (decomposition to irreducible representations).
 
-
 Infinite systems (lattices)
 ---------------------------
- * 2D-periodic systems with arbitrary unit cell geometry supported. (TODO 1D and 3D.)
+ * 2D-periodic systems supported. (TODO 1D and 3D.)
- * Computing multipole excitations and fields scattered from nanoparticle
+ * *Calculation of transmission and reflection properties (TODO).*
  * Finding eigenmodes and calculating dispersion relations.
- * Calculation of the scattered fields.
+ * *Calculation of far-field radiation patterns of an excited array (TODO).*
- * *Calculation of total transmission and reflection properties (TODO).*
+ * Reducing numerical complexity of the computations by exploiting
- * *Reducing numerical complexity of the computations by exploiting
+   symmetries of the lattice (decomposition to irreducible representations).
-   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
@@ -64,16 +47,7 @@ you can [get the source and compile it yourself][GSL].
 
 You also need a fresh enough version of [cmake][].
 
-QPMS uses a C version of the Amos library for calculating Bessel function
+After GSL is installed, you can install qpms to your local python library using
-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} .
@@ -92,21 +66,13 @@ 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
 =============
 
-[QPMS documentation][homepage] is a work in progress. Most of the newer code
+Documentation of QPMS is a work in progress. Most of the newer code
-is documented using [doxygen][] comments. Documentation generated for the
+is documented using [doxygen][] comments. To build the documentation, just run
-upstream version is hosted on the QPMS homepage <https://qpms.necada.org>.
-
-To build the documentation yourself, 
-just run
 `doxygen`
-in the QPMS source root directory; the documentation will then be found in 
+in the root directory; the documentation will then be found in 
 `docs/html/index.html`.
 
 Of course, the prerequisite of this is having doxygen installed.
@@ -118,77 +84,14 @@ 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

@@ -1,12 +1,11 @@
-TODO list before 1.0 release
+TODO list before public release
-============================
+===============================
 
 - Tests!
 - Docs!
-- Cross section calculations. (Done in some Python scripts.)
+- Cross section calculations.
-- Field calculations. (Partly done, needs more testing.)
+- Field calculations.
-  * Also test periodic vs. nonperiodic consistence (big finite lattice + absorbing medium vs. infinite lattice + absorbing medium).
+- Complex frequencies, n's, k's.
-- 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
@@ -25,12 +24,11 @@ TODO list before 1.0 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
@@ -41,16 +39,3 @@ 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

@@ -1,30 +0,0 @@
-#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

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

ci/00_make_dockerfiles.sh

@@ -1,7 +0,0 @@
-#!/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

@@ -1,5 +0,0 @@
-#!/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

@@ -1,5 +0,0 @@
-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

@@ -1,6 +0,0 @@
-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

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

ci/Dockerfile_parts/01_numlibs.built

@@ -1,16 +0,0 @@
-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

@@ -1,4 +0,0 @@
-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

@@ -1,12 +0,0 @@
-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

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

cmake/GetGitRevisionDescription.cmake

@@ -1,284 +0,0 @@
-# - 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

@@ -1,43 +0,0 @@
-#
-# 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

@@ -1,23 +0,0 @@
-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

@@ -1,36 +0,0 @@
-#!/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

@@ -1,38 +0,0 @@
-#!/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

@@ -1,18 +0,0 @@
-#!/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

@@ -1,16 +0,0 @@
-#!/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

@@ -1,22 +0,0 @@
-#!/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

@@ -1,24 +0,0 @@
-#!/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

@@ -1,24 +0,0 @@
-#!/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

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

examples/rectangular/modes/00_params.sh

@@ -1,37 +0,0 @@
-#!/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

@@ -1,18 +0,0 @@
-#!/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

@@ -1,17 +0,0 @@
-#!/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

@@ -1,15 +0,0 @@
-#!/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

@@ -1,22 +0,0 @@
-#!/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

@@ -1,24 +0,0 @@
-#!/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

@@ -1,21 +0,0 @@
-#!/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

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

examples/rectangular/scattering/01_scattering_infinite.sh

@@ -1,19 +0,0 @@
-#!/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

@@ -1,19 +0,0 @@
-#!/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

@@ -1,19 +0,0 @@
-#!/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

@@ -1,25 +0,0 @@
-#!/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

@@ -1,25 +0,0 @@
-#!/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

@@ -1,25 +0,0 @@
-#!/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

@@ -1,21 +0,0 @@
-#!/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

@@ -1,19 +0,0 @@
-#!/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

@@ -1,13 +0,0 @@
-#!/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

@@ -1,11 +0,0 @@
-#!/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

@@ -1,300 +0,0 @@
-{
- "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

@@ -1,19 +0,0 @@
-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

@@ -1,3 +0,0 @@
-/* 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

@@ -1,68 +0,0 @@
-/* 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

@@ -1,62 +0,0 @@
-/* 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

@@ -1,8 +1,6 @@
 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

@@ -0,0 +1,118 @@
+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

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+#!/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

@@ -0,0 +1,79 @@
+#!/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

@@ -0,0 +1,81 @@
+#!/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

@@ -0,0 +1,547 @@
+#!/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

@@ -0,0 +1,403 @@
+#!/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

@@ -0,0 +1,239 @@
+#!/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

@@ -1,719 +0,0 @@
-{
- "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

@@ -1,362 +0,0 @@
-#!/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

@@ -1,10 +1,10 @@
 #!/usr/bin/env python3
 
 import math
-from qpms.argproc import ArgParser, annotate_pdf_metadata
+from qpms.argproc import ArgParser
 
 
-ap = ArgParser(['rectlattice2d_finite', 'background_analytical', 'single_particle', 'single_lMax', ])
+ap = ArgParser(['rectlattice2d_finite', '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')
@@ -19,9 +19,8 @@ ap.add_argument("-f", "--centre", type=complex, required=True, help='Contour cen
 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")
+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()
 
@@ -31,15 +30,11 @@ 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" % (
+defaultprefix = "%s_p%gnmx%gnm_%dx%d_m%s_n%g_L%d_c(%s±%g±%gj)eV_cn%d" % (
-    particlestr, px*1e9, py*1e9, Nx, Ny, str(a.material), str(a.background), a.lMax,
+    particlestr, px*1e9, py*1e9, Nx, Ny, str(a.material), a.refractive_index, a.lMax,
-    str(a.centre), a.ar, a.ai, a.N,
+    str(a.centre), a.ai, a.ar, a.N)
-    thegroup,
-    )
 logging.info("Default file prefix: %s" % defaultprefix)
 
 def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
@@ -74,9 +69,9 @@ 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])
+sym = FinitePointGroup(point_group_info['D2h'])
 logging.info("Creating scattering system object")
-ss, ssw = ScatteringSystem.create(particles, medium, a.centre * eh, sym=sym)
+ss, ssw = ScatteringSystem.create(particles, medium, sym, a.centre * eh)
 
 if a.irrep == 'none':
     iri = None # no irrep decomposition
@@ -100,7 +95,7 @@ results['inside_contour'] = inside_ellipse((results['eigval'].real, results['eig
 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)
+np.savez(outfile, meta=vars(a), **results)
 logging.info("Saved to %s" % outfile)
 
 exit(0)
@@ -110,7 +105,7 @@ 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='$\sigma_\mathrm{ext}$')
@@ -121,9 +116,7 @@ if a.plot or (a.plot_out is not None):
     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:
+    fig.savefig(plotfile)
-        pdf.savefig(fig)
-        annotate_pdf_metadata(pdf, scriptname='finiterectlat-modes.py')
 
 exit(0)
 

misc/finiterectlat-scatter.py

@@ -1,12 +1,14 @@
 #!/usr/bin/env python3
 
-from qpms.argproc import ArgParser, annotate_pdf_metadata
 import math
-pi = math.pi
+from qpms.argproc import ArgParser
 
 
-ap = ArgParser(['rectlattice2d_finite', 'single_particle', 'single_lMax', 'omega_seq_real_ng', 'planewave'])
+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.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")
@@ -17,9 +19,18 @@ 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
@@ -31,209 +42,94 @@ 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)
-particles= [Particle(orig_xy[i], ap.tmgen, bspec=bspec) for i in np.ndindex(orig_xy.shape[:-1])]
+Tmatrix = ap.tmgen(bspec, ap.omega)
+particles= [Particle(orig_xy[i], Tmatrix) for i in np.ndindex(orig_xy.shape[:-1])]
 
 sym = FinitePointGroup(point_group_info['D2h'])
-ss, ssw = ScatteringSystem.create(particles, ap.background_emg, ap.allomegas[0], sym=sym)
+ss = ScatteringSystem(particles, sym)
 
+wavenumber = ap.background_epsmu.k(omega).real # Currently, ScatteringSystem does not "remember" frequency nor wavenumber
 
-## Plane wave data
+sinalpha_list = np.linspace(a.kx_lim[0],a.kx_lim[1],a.N)
-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) 
 
-dir_cart_list = sph2cart(dir_sph_list)
+# Plane wave data
-E_cart_list = sph_loccart2cart(E_sph, dir_sph_list)
+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
 
-nfreq = len(ap.allomegas)
+σ_ext_list_ir = np.empty((a.N, ss.nirreps), dtype=float)
-ndir = a.theta.shape[0]
+σ_scat_list_ir = np.empty((a.N, ss.nirreps), dtype=float)
-
-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 i, omega in enumerate(ap.allomegas):
+for iri in range(ss.nirreps):
-    logging.info("Processing frequency %g eV" % (omega / eV,))
+    logging.info("processing irrep %d/%d" % (iri, ss.nirreps))
-    if i != 0:
+    LU = None # to trigger garbage collection before the next call
-        ssw = ss(omega)
+    translation_matrix = None
-    if ssw.wavenumber.imag != 0:
+    LU = ss.scatter_solver(wavenumber,iri)
-        warnings.warn("The background medium wavenumber has non-zero imaginary part. Don't expect emaningful results for cross sections.")
+    logging.info("LU solver created")
-    wavenumber = ssw.wavenumber.real
+    translation_matrix = ss.translation_matrix_packed(wavenumber, iri, BesselType.REGULAR) + np.eye(ss.saecv_sizes[iri]) 
-    wavenumbers[i] = wavenumber
+    logging.info("auxillary translation matrix created")
 
-    k_sph_list = np.array(dir_sph_list, copy=True)
+    for j in range(a.N):
-    k_sph_list[:,0] = wavenumber
+        # 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_cart_arr[i] = sph2cart(k_sph_list)
+        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)
 
-    for iri in range(ss.nirreps):
+σ_abs_list_ir = σ_ext_list_ir - σ_scat_list_ir
-        logging.info("processing irrep %d/%d" % (iri, ss.nirreps))
+σ_abs= np.sum(σ_abs_list_ir, axis=-1)
-        LU = None # to trigger garbage collection before the next call
+σ_scat= np.sum(σ_scat_list_ir, axis=-1)
-        translation_matrix = None
+σ_ext= np.sum(σ_ext_list_ir, axis=-1)
-        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), 'qpms_version' : qpms.__version__()}, 
+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,
-        k_sph=k_sph_list, k_cart = k_cart_arr, E_cart=E_cart_list, E_sph=np.array(E_sph),
+ 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
-        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
-    with PdfPages(plotfile) as pdf:
+    fig.savefig(plotfile)
-        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

@@ -0,0 +1,376 @@
+#!/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

@@ -0,0 +1,340 @@
+#!/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

@@ -0,0 +1,35 @@
+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

@@ -1,128 +0,0 @@
-#!/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

@@ -1,219 +0,0 @@
-#!/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

@@ -1,166 +0,0 @@
-#!/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

@@ -1,129 +0,0 @@
-#!/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

@@ -0,0 +1,11 @@
+#!/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

@@ -0,0 +1,10 @@
+#!/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

@@ -0,0 +1,13 @@
+#!/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

@@ -1,167 +0,0 @@
-#!/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

@@ -0,0 +1,31 @@
+'''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

@@ -0,0 +1,85 @@
+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

@@ -0,0 +1,11 @@
+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

@@ -1,461 +0,0 @@
-#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
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-\tocdepth 3
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-\paragraph_indentation default
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-\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

@@ -1,107 +0,0 @@
-# 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

@@ -1,266 +0,0 @@
-#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_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
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-\output_sync 0
-\bibtex_command default
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-\use_package amsmath 1
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-\use_package mhchem 1
-\use_package stackrel 1
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-\use_package undertilde 1
-\cite_engine basic
-\cite_engine_type default
-\use_bibtopic false
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-\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/Scattering and Shit.lyx

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

notes/ewald_1D_and_2D_in_3D.lyx

@@ -1,677 +0,0 @@
-#LyX 2.4 created this file. For more info see https://www.lyx.org/
-\lyxformat 584
-\begin_document
-\begin_header
-\save_transient_properties true
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-
-\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}}
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-
-
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-\begin_inset FormulaMacro
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-
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-\newcommand{\vshD}{\vect{A'}}
-\end_inset
-
-
-\begin_inset FormulaMacro
-\newcommand{\wfkc}{\vect y}
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-
-
-\begin_inset FormulaMacro
-\newcommand{\wfkcout}{\vect u}
-\end_inset
-
-
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-\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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-\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

@@ -1,305 +0,0 @@
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-
-\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

@@ -1,386 +0,0 @@
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-\newcommand{\vect}[1]{\mathbf{#1}}
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-
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-
-\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

qpms/CMakeLists.txt

@@ -7,35 +7,25 @@ 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 trivialgroup.c version.c
+	lll.c beyn.c scatsys_translation_booster.c
 	)
 use_c99()
 
 set(LIBS ${LIBS} ${GSL_LIBRARIES} ${GSLCBLAS_LIBRARIES})
 
-
 target_link_libraries (qpms
-	${GSL_LIBRARIES}
+	gsl
-	${LAPACK_LIBRARIES}
+	lapack
-	${BLAS_LIBRARIES}
+	blas
-	${QPMS_AMOSLIB}
+	amos
-	Faddeeva
 	)
 target_include_directories (qpms PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
 

qpms/__init__.py

@@ -1,3 +1,5 @@
+from pkg_resources import get_distribution
+__version__ = get_distribution('qpms').version
 
 import os as __os
 from sys import platform as __platform
@@ -5,7 +7,7 @@ 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, qpms_library_version
+    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, ScatteringSystemCachingMode
 except ImportError as ex:
     if __platform == "linux" or __platform == "linux2":
         if 'LD_LIBRARY_PATH' not in __os.environ.keys():
@@ -22,12 +24,7 @@ from .cymaterials import MaterialInterpolator, EpsMu, LorentzDrudeModel, lorentz
 from .cycommon import dbgmsg_enable, dbgmsg_disable, dbgmsg_active, BesselType, VSWFType
 from .cywaves import vswf_single
 
-def __version__():
+from .qpms_p import * # maybe don't import automatically in the future (adds around 0.5 s delay)
-    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

@@ -1,17 +1,9 @@
 '''
-Common snippets for argument processing in command line scripts.
+Common snippets for argument processing in command line scripts; legacy scripts use scripts_common.py instead.
 '''
 
 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):
@@ -21,40 +13,6 @@ 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):
@@ -62,299 +20,51 @@ 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'),
-            'multiple_frequency_eV_optional': lambda ap: ap.add_argument("-f", "--eV", type=float, nargs='*', help='radiation angular frequency in eV (additional)'),
+            '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),
-            '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=sfloat, required=True, help='k vector', metavar=('KX_MIN', 'KX_MAX')),
+            'single_kvec2': lambda ap: ap.add_argument("-k", '--kx-lim', nargs=2, type=float, 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_real_refractive_index': lambda ap: ap.add_argument("-n", "--refractive-index", type=float, default=1., help='background medium strictly real refractive index'),
+            'bg_refractive_index': lambda ap: ap.add_argument("-n", "--refractive-index", type=float, default=1.52, help='background medium 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", nargs='+', action=AppendTupleAction, help="basis vector in xy-cartesian coordinates (two required)", required=True, type=sfloat, dest='basis_vectors', metavar=('X', 'Y')),
+            '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')),
-            '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, "virtual" features provided) 
+    feature_sets_available = { # name : (description, dependencies, atoms not in other dependencies, methods called after parsing) 
-            'const_real_background': ("Background medium with constant real refractive index", (), ('bg_real_refractive_index',), ('_eval_const_background_epsmu',), ('background', 'background_analytical')),
+            'background': ("Background medium definition (currently only constant epsilon supported)", (), ('bg_refractive_index',), ('_eval_background_epsmu',)),
-            'background' : ("Most general background medium specification currently supported", ('background_analytical',), (), (), ()),
+            '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',)),
-            'background_analytical' : ("Background medium model holomorphic for 'reasonably large' complex frequency areas", (), ('bg_analytical',), ('_eval_analytical_background_epsmugen',), ('background',)),
+            'single_lMax': ("Single particle lMax definition", (), ('single_lMax',), ()),
-            '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_omega': ("Single angular frequency", (), ('single_frequency_eV',), ('_eval_single_omega',)),
-            'multi_particle': ("One or more particle definition (shape [curently spherical or cylindrical]), materials, and positions)", ('background',), ('multi_particle',), ('_process_multi_particle',), ()),
+            'lattice2d': ("Specification of a generic 2d lattice (spanned by the x,y axes)", (), ('lattice2d_basis',), ('_eval_lattice2d',)),
-            'single_lMax': ("Single particle lMax definition", (), ('single_lMax',), (), ()),
+            'rectlattice2d': ("Specification of a rectangular 2d lattice; conflicts with lattice2d", (), ('rectlattice2d_periods',), ('_eval_rectlattice2d',)),
-            'single_omega': ("Single angular frequency", (), ('single_frequency_eV',), ('_eval_single_omega',), ()),
+            'rectlattice2d_finite': ("Specification of a rectangular 2d lattice; conflicts with lattice2d", ('rectlattice2d',), ('rectlattice2d_counts',), ()),
-            '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=[]):
-        prefix_chars = '+-' if 'multi_particle' in features else '-'
+        self.ap = argparse.ArgumentParser()
-        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, provides_virtual = ArgParser.feature_sets_available[feat]
+            _, deps, atoms, atparse = 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?
@@ -362,26 +72,16 @@ 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'''
-        return self.ap.add_argument(*args, **kwargs)
+        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:
-                try:
+                getattr(self, method)()
-                    getattr(self, method)()
-                except ArgumentProcessingError:
-                    err = sys.exc_info()[1]
-                    self.ap.error(str(err))
         return self.args
     
     def __getattr__(self, name):
@@ -390,67 +90,42 @@ class ArgParser:
 
     # Methods to initialise the related data structures:
 
-    def _eval_const_background_epsmu(self): # feature: const_real_background
+    def _eval_background_epsmu(self): # feature: 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
-        if isinstance(a.background, (float, complex)):
+        self.background_epsmu = EpsMu(self.args.refractive_index**2)
-            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
-        self.foreground_emg = self._add_emg(a.material)
+        if a.material in lorentz_drude.keys():
-        self.tmgen = self._add_tmg((a.background, a.material, (a.radius, a.height, a.lMax_extend)))
+            self.foreground_emg = EpsMuGenerator(lorentz_drude[a.material])
-        self.bspec = self._add_bspec(a.lMax)
+        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)
 
     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_vectors, delta=1.)
+        self.direct_basis = lll_reduce(self.args.basis_vector, delta=1.)
-        import numpy as np
+        # import numpy as np
-        self.reciprocal_basis1 = np.linalg.inv(self.direct_basis.T)
+        # self.reciprocal_basis1 = np.linalg.inv(self.direct_basis)
-        self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
+        # self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
     
     def _eval_rectlattice2d(self): # feature: rectlattice2d
         a = self.args
@@ -465,97 +140,4 @@ 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 <camos.h>
+#include <amos.h>
 #include <math.h>
 
 #ifndef M_LN2
@@ -52,11 +52,6 @@ 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);
@@ -89,8 +84,7 @@ 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;
@@ -98,32 +92,30 @@ 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 {
-try_again: ;
+    const DOUBLE_PRECISION_t zr = creal(x), zi = cimag(x), fnu = 0.5;
-    int retry_counter = 0;
+    const INTEGER_t n = lmax + 1, kode = 1 /* No exponential scaling */;
-    const double zr = creal(x), zi = cimag(x), fnu = 0.5;
+    DOUBLE_PRECISION_t cyr[n], cyi[n];
-    const int n = lmax + 1, kode = 1 /* No exponential scaling */;
+    INTEGER_t ierr, nz;
-    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';
-        ierr = camos_zbesj(zr, zi, fnu, kode, n, cyr, cyi, &nz);
+        amos_zbesj(&zr, &zi, &fnu, &kode, &n, cyr, cyi, &nz, &ierr);
         break;
       case QPMS_BESSEL_SINGULAR:
         kindchar = 'y';
         {
-          double cwrkr[lmax + 1], cwrki[lmax + 1];
+          DOUBLE_PRECISION_t cwrkr[lmax + 1], cwrki[lmax + 1];
-          ierr = camos_zbesy(zr, zi, fnu, kode, n, cyr, cyi, &nz, cwrkr, cwrki);
+          amos_zbesy(&zr, &zi, &fnu, &kode, &n, cyr, cyi, &nz, cwrkr, cwrki, &ierr);
         }
         break;
       case QPMS_HANKEL_PLUS:
       case QPMS_HANKEL_MINUS: 
         kindchar = 'h';
         {
-          const int m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2;
+          const INTEGER_t m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2;
-          ierr = camos_zbesh(zr, zi, fnu, kode, m, n, cyr, cyi, &nz);
+          amos_zbesh(&zr, &zi, &fnu, &kode, &m, &n, cyr, cyi, &nz, &ierr);
         }
         break;
       default:
@@ -134,28 +126,14 @@ try_again: ;
       for (qpms_l_t l = 0; l <= lmax; ++l)
         res[l] = prefac * (cyr[l] + I * cyi[l]);
       if (ierr == 3) 
-        if (creal(x) >= 10000) {
+        QPMS_WARN("Amos's zbes%c computation done but losses of significance "
-          QPMS_WARN_ONCE("Due to large argument, "
+            "by argument reduction produce less than half of machine accuracy.", 
-                "Amos's zbes%c computation done but losses of significance "
+            kindchar);
-                "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 {
+    else
-      if (retry_counter < 5) {
+      QPMS_PR_ERROR("Amos's zbes%c failed with ierr == %d.",
-        QPMS_WARN("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi). Retrying.\n",
+         kindchar, (int) ierr);
-           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

@@ -0,0 +1,65 @@
+#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

@@ -0,0 +1,61 @@
+#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