misc/lat2d_realfreqsvd.py

   1 #!/usr/bin/env python3
   2
   3 import math
   4 from qpms.argproc import ArgParser, sfloat, annotate_pdf_metadata
   5
   6 ap = ArgParser(['background', 'lattice2d', 'multi_particle',  'omega_seq'])
   7
   8 ap.add_argument("-k", nargs=2, type=sfloat, required=True, help='k vector', metavar=('K_X', 'K_Y'))
   9 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)")
  10
  11 ap.add_argument("-g", "--little-group", type=str, default="trivial_g", help="Little group for subspace irrep classification", action="store")
  12
  13 ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
  14 ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
  15 ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
  16 ap.add_argument("-s", "--singular_values", type=int, default=10, help="Number of singular values to plot")
  17
  18 a=ap.parse_args()
  19
  20 import logging
  21 logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
  22
  23
  24 #Important! The particles are supposed to be of D2h/D4h symmetry
  25 # thegroup = 'D4h' if px == py and not a.D2 else 'D2h'
  26
  27 a1 = ap.direct_basis[0]
  28 a2 = ap.direct_basis[1]
  29
  30 particlestr = "svdinterval" # TODO particle string specifier or some hash, do this in argproc.py
  31 defaultprefix = "%s_basis%gnm_%gnm__%gnm_%gnm_f(%g..%g..%g)eV_k%g_%g" % (
  32     particlestr, a1[0]*1e9, a1[1]*1e9, a2[0]*1e9, a2[1]*1e9, *(a.eV_seq), ap.k[0], ap.k[1])
  33 logging.info("Default file prefix: %s" % defaultprefix)
  34
  35
  36 import numpy as np
  37 import qpms
  38 import warnings
  39 from qpms.cybspec import BaseSpec
  40 from qpms.cytmatrices import CTMatrix, TMatrixGenerator
  41 from qpms.qpms_c import Particle, pgsl_ignore_error, empty_lattice_modes_xy
  42 from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
  43 from qpms.cycommon import DebugFlags, dbgmsg_enable
  44 from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
  45 from qpms.symmetries import point_group_info
  46 eh = eV/hbar
  47
  48 # not used; TODO:
  49 irrep_labels = {"B2''":"$B_2''$",
  50                 "B2'":"$B_2'$",
  51                 "A1''":"$A_1''$",
  52                 "A1'":"$A_1'$",
  53                 "A2''":"$A_2''$",
  54                 "B1''":"$B_1''$",
  55                 "A2'":"$A_2'$",
  56                 "B1'":"$B_1'$",
  57                 "E'":"$E'$",
  58                 "E''":"$E''$",}
  59
  60 dbgmsg_enable(DebugFlags.INTEGRATION)
  61
  62
  63
  64 omegas = ap.omegas
  65
  66 logging.info("%d frequencies from %g to %g eV" % (len(omegas), omegas[0]/eh, omegas[-1]/eh))
  67
  68 particles = ap.get_particles()
  69
  70 ss, ssw = ScatteringSystem.create(particles, ap.background_emg, omegas[0], latticebasis=ap.direct_basis)
  71 k = np.array([ap.k[0], ap.k[1], 0])
  72 # Auxillary finite scattering system for irrep decomposition, quite a hack
  73 ss1, ssw1 = ScatteringSystem.create(particles, ap.background_emg, omegas[0],sym=FinitePointGroup(point_group_info[ap.little_group]))
  74
  75 wavenumbers = np.empty(omegas.shape)
  76 SVs = [None] * ss1.nirreps
  77 for iri in range(ss1.nirreps):
  78     SVs[iri] = np.empty(omegas.shape+(ss1.saecv_sizes[iri],))
  79 for i, omega in enumerate(omegas):
  80     ssw = ss(omega)
  81     wavenumbers[i] = ssw.wavenumber.real
  82     if ssw.wavenumber.imag:
  83         warnings.warn("Non-zero imaginary wavenumber encountered")
  84     with pgsl_ignore_error(15): # avoid gsl crashing on underflow; maybe not needed
  85         ImTW = ssw.modeproblem_matrix_full(k)
  86     for iri in range(ss1.nirreps):
  87         ImTW_packed = ss1.pack_matrix(ImTW, iri)
  88         SVs[iri][i] = np.linalg.svd(ImTW_packed, compute_uv = False)
  89
  90 outfile = defaultprefix + ".npz" if a.output is None else a.output
  91 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
  92        )
  93 logging.info("Saved to %s" % outfile)
  94
  95
  96 if a.plot or (a.plot_out is not None):
  97     import matplotlib
  98     matplotlib.use('pdf')
  99     from matplotlib import pyplot as plt
 100     from matplotlib.backends.backend_pdf import PdfPages
 101
 102     fig = plt.figure()
 103     ax = fig.add_subplot(111)
 104     cc = plt.rcParams['axes.prop_cycle']()
 105     for iri in range(ss1.nirreps):
 106         cargs = next(cc)
 107         nlines = min(a.singular_values, ss1.saecv_sizes[iri])
 108         for i in range(nlines):
 109             ax.plot(omegas/eh, SVs[iri][:,-1-i],
 110                 label= None if i else irrep_labels.get(ss1.irrep_names[iri], ss1.irrep_names[iri]),
 111                 **cargs)
 112     ax.set_ylim([0,1.1])
 113     if hasattr(ap, "background_epsmu"):
 114         xlim = ax.get_xlim()
 115         omegas_empty = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, k, omegas[-1])
 116         for om in omegas_empty:
 117             if om/eh > xlim[0] and om/eh < xlim[1]:
 118                 ax.axvline(om/eh, ls=':')
 119     ax.set_xlabel('$\hbar \omega / \mathrm{eV}$')
 120     ax.set_ylabel('Singular values')
 121     ax.legend()
 122
 123     plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
 124     with PdfPages(plotfile) as pdf:
 125         pdf.savefig(fig)
 126         annotate_pdf_metadata(pdf, scriptname='lat2d_realfreqsvd.py')
 127
 128 exit(0)
 129