Rectangular lattice SVD cut at gamma point, real frequency

(cherry picked from commit 3fd87de397b5a2228e377e525dabd3e64a641d62 [formerly 57a498625671d8fefccd688fde848ce484f0a6ef])


Former-commit-id: e1b8cab071a5ba2b4f0328aba6930981ba1b3293

misc/infiniterectlat-k0realfreqsvd.py

@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+
+import math
+from qpms.argproc import ArgParser
+
+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")
+
+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 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_n%g_f(%g..%g..%g)eV_L%d_SVGamma" % (
+    particlestr, px*1e9, py*1e9, str(a.material), a.refractive_index, *(a.eV_seq), a.lMax)
+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, 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.cyunitcell import unitcell
+#from qpms.symmetries import point_group_info # TODO
+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'":"$B_1'$"}
+
+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], tmgen=ap.tmgen, bspec=bspec)
+par = [pp]
+
+u = unitcell(a1, a2, par, refractive_index=a.refractive_index)
+eta = (np.pi / u.Area)**.5
+
+wavenumbers = np.empty(omegas.shape)
+SVs = np.empty(omegas.shape+(nelem,))
+beta = np.array([0.,0.])
+for i, omega in enumerate(omegas):
+    wavenumbers[i] = ap.background_epsmu.k(omega).real # Currently, ScatteringSystem does not "remember" frequency nor wavenumber
+    with pgsl_ignore_error(15): # avoid gsl crashing on underflow; maybe not needed
+        ImTW = u.evaluate_ImTW(eta, omega, beta)
+    SVs[i] = np.linalg.svd(ImTW, compute_uv = False)
+
+outfile = defaultprefix + ".npz" if a.output is None else a.output
+np.savez(outfile, meta=vars(a), omegas=omegas, wavenumbers=wavenumbers, SVs=SVs, unitcell_area=u.Area
+       )
+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
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    for i in range(a.singular_values):
+        ax.plot(omegas/eh, SVs[:,-1-i])
+    ax.set_xlabel('$\hbar \omega / \mathrm{eV}$')
+    ax.set_ylabel('Singular values')
+    
+    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
+    fig.savefig(plotfile)
+
+exit(0)
+

qpms/argproc.py

@@ -26,6 +26,7 @@ class ArgParser:
             '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'),
+            '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')),
             '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),
             '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'),
@@ -45,6 +46,7 @@ class ArgParser:
             'single_particle': ("Single particle definition (shape [currently spherical or cylindrical]) and materials, incl. background)", ('background',), ('single_material', 'single_radius', 'single_height', 'single_lMax_extend'), ('_eval_single_tmgen',)),
             'single_lMax': ("Single particle lMax definition", (), ('single_lMax',), ()),
             'single_omega': ("Single angular frequency", (), ('single_frequency_eV',), ('_eval_single_omega',)),
+            'omega_seq': ("Equidistant real frequency range", (), ('seq_frequency_eV',), ('_eval_omega_seq',)),
             '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',), ()),
@@ -119,6 +121,13 @@ class ArgParser:
         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)
+        self.omegas *= eV/hbar
+
     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)