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magreete.py
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import numpy as onp
import torch as np
import scipy as sp
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import matplotlib.colors as clr
import colorsys
import hickle as hkl
import sys
import os
import utils
from Transmission2D import Transmission2D_vector, Transmission2D_scalar
from Transmission3D import Transmission3D_vector, Transmission3D_scalar
import lattices
import argparse
def main(ndim, # Required arguments
refractive_n = 1.65 + 0.025j, phi = 0.1, regularize = True, N_raw = 16384, beam_waist = 0.2, L = 1, size_subsample = 1.0, source = "beam", scalar = False, # Physical parameters
lattice=None, cold_atoms=False, kresonant_ = None, annulus = 0, composite = False, kick = 0.0, shift = 0.0, input_files_args = None, # Special cases
k0range_args = None, thetarange_args = None, polarization_angle_degrees = 0, switch_angle_scans = False, rotate_u = [0,0], # Range of values to use
compute_transmission = False, plot_transmission = False, single_scattering_transmission = False, scattered_fields=False, transmission_radius = 2.0,
compute_DOS=False, compute_cavityDOS = False, compute_interDOS=False, compute_SDOS=False, compute_LDOS=False, dos_sizes_args = None, dospoints=1, spacing_factor = 1.0, idos_radius = 1.0, N_fibo = 1000,
compute_eigenmodes = False, number_eigenmodes = 1, plot_eigenmodes = False, sorting_type = 'IPR', adapt_z = True, slice_coordinate = 0,
intensity_fields = False, amplitude_fields = False, phase_fields = False, just_compute_averages = False,# Computations to perform
write_eigenvalues=False, write_ldos= False, gridsize=(301,301), window_width=1.2, angular_width = 0.0, plot_theta_index = 0, batch_size = 101*101, adapt_scale = False, output_directory="" # Parameters for outputs
):
'''
Simple front-end for MAGreeTe
'''
# Keep cut_radius as the internal here
cut_radius = 0.5 * size_subsample
beam_waist *= size_subsample
transmission_radius *= size_subsample
polarization_angle_radians = polarization_angle_degrees * onp.pi / 180.0
# The full option does not conserve energy but is interesting to have for pedagogy?
self_interaction_type = "Rayleigh" # Rayleigh or full
if onp.imag(refractive_n) < 0:
print("Imaginary parts of indices should be positive!")
sys.exit()
# Name the output directory in a human-readable way containing the three physical parameters: raw number of particles, volume fraction and refractive index
output_directory_suffix = "phi_"+str(phi)+"/"
if cold_atoms:
output_directory_suffix += "cold_atoms"
else:
output_directory_suffix += "refractive_n_"+str(refractive_n)
if kick != 0.0:
output_directory_suffix +="_kicked_"+str(kick)
if regularize:
output_directory_suffix += "_reg"
if scalar:
output_directory_suffix += "_scalar"
# Angles to use for transmission and fields
if thetarange_args == None:
Ntheta = 360
thetas = onp.arange(Ntheta)/Ntheta*2*np.pi
else:
if len(thetarange_args)==1:
Ntheta = 1
thetas = onp.array(thetarange_args)*np.pi / 180.0
elif len(thetarange_args)==2:
thetas = onp.arange(thetarange_args[0],thetarange_args[1]+1,1) * np.pi / 180.0
Ntheta = len(thetas)
else:
thetas = onp.arange(thetarange_args[0],thetarange_args[1]+thetarange_args[2],thetarange_args[2]) * np.pi / 180.0
Ntheta = len(thetas)
# Sizes to use for DOS
if dos_sizes_args == None:
Ndos_sizes = 1
dos_sizes = onp.array([1.0])
else:
if len(dos_sizes_args)==1:
Ndos_sizes = 1
dos_sizes = onp.array(dos_sizes_args)
elif len(dos_sizes_args)==2:
dos_sizes = onp.linspace(dos_sizes_args[0],dos_sizes_args[1],num=10)
Ndos_sizes = len(dos_sizes)
else:
dos_sizes = onp.arange(dos_sizes_args[0],dos_sizes_args[1]+dos_sizes_args[2],dos_sizes_args[2])
Ndos_sizes = len(dos_sizes)
# Keep a copy of the thetas used to plot if thetas get overwritten when loading files
thetas_plot = thetas
# Figure out how many angles around the central one to use for the definition of transmission
n_thetas_trans = int(onp.floor(angular_width * 0.5 * len(thetas)))
# Beam waist
w = beam_waist * L
# Check number of configurations to go over
if input_files_args != None:
number_copies = len(input_files_args)
file_index_list = onp.arange(number_copies)
elif lattice != None:
file_index_list = [0]
else:
print("Please provide a valid input either as an input file or as a lattice option")
sys.exit()
# Loop over copies
for file_index in file_index_list:
print("____________________________________________________\nCopy #"+str(file_index)+"\n____________________________________________________")
# First define full file name to check if modified point pattern already exists
if lattice == None:
raw_file_name = input_files_args[file_index]
print_type = "custom ("+raw_file_name+")"
# Load here to get N_raw
points = utils.loadpoints(raw_file_name, ndim)
points = np.tensor(points,dtype=np.double)
shape_before = points.shape
N_raw = shape_before[0]
# Override filename so that output files are well-behaved
file_name = raw_file_name.split("/")[-1]
else:
file_name = lattice
print_type = lattice
# Create output directory
output_directory = os.path.abspath(output_directory)
output_directory = os.path.join(output_directory, "N"+str(N_raw), output_directory_suffix)
utils.trymakedir(output_directory)
# Add suffixes
if annulus > 0:
file_name += '_annulus_'+str(annulus)
if composite:
file_name += '_composite'
if source != "beam":
source_suffix = "_"+source
else:
source_suffix = ""
# XXX May need to make this more flexible if more complete scans
if ndim == 3 and not scalar:
if polarization_angle_degrees != 0.0:
# Human-readable rotation for polarization
source_suffix += "_pangle_"+str(1.0*polarization_angle_degrees)
if rotate_u != [0,0]:
source_suffix += "_urot_"+str(rotate_u[0])+"_"+str(rotate_u[1])
if switch_angle_scans:
source_suffix += "_switchangles"
# Check if points file already exists in the right place
output_directory = os.path.join(output_directory,file_name+source_suffix)
saved_points_file = os.path.join(output_directory, "points.hkl")
if os.path.exists(saved_points_file):
# If file was already generated, overwrite points data here to have consistent content
print("\nFound hkl file, loading points from MAGreeTe dir structure")
points = np.from_numpy(hkl.load(saved_points_file),dtype=np.float64)
else:
# No previous analysis: need to load external point pattern
# A custom file was provided
if lattice == None:
# Points were already loaded from external file
if np.amax(points)>0.5:
points -= np.mean(points)
points /= points.amax()
points /= 2.0
# Adjust point pattern by removing overlap, cutting, kicking
points = np.unique(points, dim=0)
shape_after = points.shape
if shape_before[0] != shape_after[0]:
print("There were {} points overlapping with others! Removing.".format(shape_before[0]-shape_after[0]))
# Add random kicks
if kick != 0.0:
points = lattices.add_displacement(points, dr=kick)
if shift != 0.0:
points += shift * lattices.uniform_unit_ball_picking(1,ndim)
# A generative recipe was selected
else:
points = make_lattice(lattice, N_raw, kick, ndim)
if lattice == 'poisson':
file_name += str(ndim)+'d'
if lattice == 'quasicrystal' and ndim == 3:
file_name += '_icosahedral'
if shift != 0.0:
points += shift * lattices.uniform_unit_ball_picking(1,ndim)
# Cut configuration if needed
if annulus > 0:
points = lattices.exclude_circle(points,annulus)
if composite:
comp = lattices.square(128)
comp = lattices.cut_circle(comp,annulus)
points = np.vstack([points,comp])
# Save point patterns after generation if random, cut, kicks
hkl.dump(points.numpy(), saved_points_file)
# Now, cut points according to sss
points = lattices.cut_circle(points,cut_radius)
if size_subsample < 1.0:
sss_subdir = "size_subsampling_"+str(size_subsample)
output_directory = os.path.join(output_directory, sss_subdir)
utils.trymakedir(output_directory)
file_name = os.path.join(output_directory, file_name)
# After all this, write down the actual N and make the system the right size
N = points.shape[0]
if N == 0:
print("0 points remain after cutting")
sys.exit()
points *= L
assert ndim == points.shape[1]
print("\n\nLoaded a "+print_type+" system of N = "+str(N_raw)+" points in d = "+str(ndim))
print("N = "+str(N)+" points remain after cutting to a disk and rescaling to L = "+str(L)+"\n\n")
hkl.dump(points.numpy(),"triangular.hkl")
# Define wave-vector list here to avoid defining it again when averaging
if ndim == 2:
# Volume and radius of (circular cross-section) scatterers
volume = L**2 * phi/N_raw
radius = onp.sqrt(volume/onp.pi )
if k0range_args == None:
# Set the max to be the last one where the assumptions are still somewhat ok, 2pi / radius
k_max = 0.25 * L /radius
k0range = onp.arange(1.0, k_max, 0.5)*2*onp.pi/L
else:
if len(k0range_args)==1:
k0range = onp.array([k0range_args[0]])* 2*onp.pi/L
elif len(k0range_args)==2:
k0range = onp.arange(k0range_args[0],k0range_args[1]+1,1)* 2*onp.pi/L
else:
k0range = onp.arange(k0range_args[0],k0range_args[1]+k0range_args[2],k0range_args[2])* 2*onp.pi/L
# Consistency check: plot set of scatterers
utils.plot_2d_points(points,file_name)
# Polarizability list
if cold_atoms:
if kresonant_ == None:
kresonant_ = 0.1 * L / radius
kresonant = 2 * onp.pi * kresonant_
static_deltaeps = refractive_n**2 - 1
# as omega -> 0, Lorentz -> omegap**2 / omega0 ** 2
# Therefore kplasma = kresonant * sqrt(static_deltaeps)
kplasma = kresonant * onp.sqrt(onp.real(static_deltaeps))
damping = onp.imag(static_deltaeps) * kplasma # Just an ansatz
alpharange = utils.alpha_Lorentz(k0range, volume, kresonant, kplasma, damping)
self_interaction = True
print("Effective indices:"+str(onp.sqrt(alpharange/volume + 1)))
else:
alpharange = onp.ones(len(k0range)) * utils.alpha_small_dielectric_object(refractive_n,volume)
self_interaction = True
elif ndim ==3:
# Volume and radius of (spherical) scatterers
volume = L**3 * phi/N_raw
radius = onp.cbrt(volume * 3.0 / (4.0 * onp.pi))
if k0range_args == None:
# Set the max to be the last one where the assumptions are still somewhat ok, 2pi / radius
k_max = 0.25 * L /radius
k0range = onp.arange(1.0, k_max, 0.5)*2*onp.pi/L
else:
if len(k0range_args)==1:
k0range = onp.array([k0range_args[0]])* 2*onp.pi/L
elif len(k0range_args)==2:
k0range = onp.arange(k0range_args[0],k0range_args[1]+1,1)* 2*onp.pi/L
else:
k0range = onp.arange(k0range_args[0],k0range_args[1]+k0range_args[2],k0range_args[2])* 2*onp.pi/L
# Consistency check: plot set of scatterers
utils.plot_3d_points(points,file_name)
# Polarizability list
if cold_atoms:
if kresonant_ == None:
kresonant_ = 0.1 * L / radius
kresonant = 2 * onp.pi * kresonant_
static_deltaeps = refractive_n**2 - 1
# as omega -> 0, Lorentz -> omegap**2 / omega0 ** 2
# Therefore kplasma = kresonant * sqrt(static_deltaeps)
kplasma = kresonant * onp.sqrt(onp.real(static_deltaeps))
damping = onp.imag(static_deltaeps) * kplasma # Just an ansatz
alpharange = utils.alpha_Lorentz(k0range, volume, kresonant, kplasma, damping)
self_interaction = True
print("Effective indices:"+str(onp.sqrt(alpharange/volume + 1)))
else:
alpharange = onp.ones(len(k0range)) * utils.alpha_small_dielectric_object(refractive_n,volume)
self_interaction = True
# Generate the corresponding list of optical thicknesses, and plot them
utils.plot_optical_thickness(k0range, L, alpharange, ndim, phi, volume, file_name)
# Also plot the values of ka to check whether hypotheses are consistent
utils.plot_k_times_radius(k0range, radius, L, file_name)
# Finally, plot dressed polarizability of a single scatterer to pinpoint resonances
utils.plot_dressed_polarizability(k0range, L, alpharange, ndim, radius, volume, self_interaction, file_name, self_interaction_type=self_interaction_type, scalar = scalar)
# If the code is run solely to put together data already obtained for several copies, skip this
if just_compute_averages:
break
### ###############
### Solver choice: 2d or 3d, vector or scalar
### ###############
if ndim==2:
if scalar:
solver = Transmission2D_scalar(points, source = source)
else:
solver = Transmission2D_vector(points, source = source)
elif ndim == 3:
if scalar:
solver = Transmission3D_scalar(points, source = source)
else:
solver = Transmission3D_vector(points, source = source)
else:
raise NotImplementedError
### ###############
### Transmission plot computations
### ###############
if compute_transmission or plot_transmission or single_scattering_transmission:
# Define the list of measurement points for transmission plots
if ndim ==2:
# Use regularly spaced angles on the circle
Ntheta_meas = 360
thetas_measurement = onp.arange(Ntheta_meas)/Ntheta_meas*2*np.pi
measurement_points = transmission_radius*L*onp.vstack([onp.cos(thetas_measurement),onp.sin(thetas_measurement)]).T
measurement_points = np.from_numpy(measurement_points)
else:
# Use Fibonacci sphere as samples on the sphere
measurement_points = transmission_radius*L*utils.fibonacci_sphere(N_fibo)
measurement_points = np.from_numpy(measurement_points)
# Also define the unit vectors describing the source orientation and its polarization from here
u, p = utils.vector_3d_u_and_p(thetas, rotate_u = rotate_u, polarization_angle_radians = polarization_angle_radians, switch_angle_scans = switch_angle_scans)
if not scalar:
utils.plot_3d_points(p,file_name+"_polarization")
utils.plot_3d_points(u,file_name+"_incomingorientation")
# A fresh computation is required
if compute_transmission:
Eall = []
E0all = []
Eall_scat = []
for k0, alpha in zip(k0range,alpharange):
# Compute source value AT scatterers and measurement points
if ndim == 2:
# In 2d: no ambiguity to make thetas into k vectors and polarizations even if vector wave
E0_scat = solver.generate_source(points, k0, thetas, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, thetas, beam_waist, print_statement='Source at measurement points')
else:
if scalar:
# In 3d scalar, no need to specify polarization vector
E0_scat = solver.generate_source(points, k0, u, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, u, beam_waist, print_statement='Source at measurement points')
else:
# In 3d vector, need to specify polarization vector
E0_scat = solver.generate_source(points, k0, u, p, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, u, p, beam_waist, print_statement='Source at measurement points')
Ej = solver.solve(k0, alpha, radius, E0_scat, self_interaction=self_interaction, self_interaction_type=self_interaction_type)
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
params = [alpha, k0]
hkl.dump([onp.array(Ej), onp.array(params),onp.array(points), onp.array(thetas)],file_name+'_Ek_k0_'+str(k0_)+'_'+str(file_index)+'.hkl')
Ek = solver.propagate(measurement_points, Ej, k0, alpha, E0_meas, regularize = regularize, radius=radius)
if scattered_fields:
Ek_scat = Ek - E0_meas
Eall_scat.append(Ek_scat.numpy())
E0all.append(E0_meas.numpy())
Eall.append(Ek.numpy())
# A computation has already been performed
elif plot_transmission:
Eall = []
E0all = []
Eall_scat = []
for k0, alpha in zip(k0range,alpharange):
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
Ej, params, _, thetas = hkl.load(file_name+'_Ek_k0_'+str(k0_)+'_'+str(file_index)+'.hkl')
Ej = np.from_numpy(Ej)
thetas = onp.float64(thetas)
alpha, k0 = params
k0 = onp.float64(k0)
alpha = onp.complex128(alpha)
# Compute source value AT scatterers and measurement points
if ndim == 2:
# In 2d: no ambiguity to make thetas into k vectors and polarizations even if vector wave
E0_scat = solver.generate_source(points, k0, thetas, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, thetas, beam_waist, print_statement='Source at measurement points')
else:
# In 3d, need to specify polarization vector
E0_scat = solver.generate_source(points, k0, u, p, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, u, p, beam_waist, print_statement='Source at measurement points')
Ek = solver.propagate(measurement_points, Ej, k0, alpha, E0_meas, regularize = regularize, radius = radius)
if scattered_fields:
Ek_scat = Ek - E0_meas
Eall_scat.append(Ek_scat.numpy())
E0all.append(E0_meas.numpy())
Eall.append(Ek.numpy())
if compute_transmission or plot_transmission:
# Save final transmission data for plotting purposes and/or averaging purposes
hkl.dump([onp.array(Eall), onp.array(k0range), onp.array(thetas)],file_name+'_transmission_'+str(file_index)+'.hkl')
# If required: plot results
if plot_transmission:
# Compute intensities at measurement points
Eall = onp.array(Eall)
total = onp.absolute(Eall)**2
if not scalar:
total = onp.sum(total, axis=2)
# Produce plots
if ndim == 2:
utils.plot_transmission_angularbeam(k0range, L, thetas, total, file_name, n_thetas_trans = n_thetas_trans, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index), adapt_scale = adapt_scale)
else:
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total, measurement_points, file_name, angular_width = angular_width, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index), adapt_scale = adapt_scale)
# Produce transmission normalized by total intensity of the INCIDENT FIELD on the sphere
I0all = onp.absolute(E0all)**2
if not scalar:
I0all = onp.sum(I0all, axis = 2)
if ndim ==2:
utils.plot_transmission_angularbeam(k0range, L, thetas, total, file_name, n_thetas_trans = n_thetas_trans, normalization = I0all, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_incnorm')
utils.plot_transmission_angularbeam(k0range, L, thetas, total, file_name, n_thetas_trans = n_thetas_trans, normalization = total, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_norm')
else:
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total, measurement_points, file_name, angular_width = angular_width, normalization = I0all, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_incnorm')
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total, measurement_points, file_name, angular_width = angular_width, normalization = total, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_norm')
if scattered_fields:
# Compute scattered intensities at measurement points
Eall_scat = onp.array(Eall_scat)
total_scat = onp.absolute(Eall_scat)**2
if not scalar:
total_scat = onp.sum(total_scat, axis=2)
# Produce plots
if ndim == 2:
utils.plot_transmission_angularbeam(k0range, L, thetas, total_scat, file_name, n_thetas_trans = n_thetas_trans, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat')
utils.plot_transmission_angularbeam(k0range, L, thetas, total_scat, file_name, n_thetas_trans = n_thetas_trans, adapt_scale = adapt_scale, normalization = total_scat, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat_norm')
else:
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total_scat, measurement_points, file_name, angular_width = angular_width, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat', adapt_scale = adapt_scale)
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total_scat, measurement_points, file_name, angular_width = angular_width, normalization = total, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat_norm')
# Single-scattering transmission
if single_scattering_transmission:
Eall_ss = []
Eall_scat_ss = []
for k0, alpha in zip(k0range,alpharange):
# Compute source value AT scatterers and measurement points
if ndim == 2:
# In 2d: no ambiguity to make thetas into k vectors and polarizations even if vector wave
E0_scat = solver.generate_source(points, k0, thetas, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, thetas, beam_waist, print_statement='Source at measurement points')
else:
if scalar:
# In 3d scalar, no need to specify polarization vector
E0_scat = solver.generate_source(points, k0, u, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, u, beam_waist, print_statement='Source at measurement points')
else:
# In 3d vector, need to specify polarization vector
E0_scat = solver.generate_source(points, k0, u, p, beam_waist, print_statement='Source at scatterers')
E0_meas = solver.generate_source(measurement_points, k0, u, p, beam_waist, print_statement='Source at measurement points')
Ek_ss = solver.propagate_ss(measurement_points, k0, alpha, E0_meas, E0_scat, regularize = regularize, radius = radius)
if scattered_fields:
Ek_scat_ss = Ek_ss - E0_meas
Eall_scat_ss.append(Ek_scat_ss.numpy())
Eall_ss.append(Ek_ss.numpy())
# Compute intensities at measurement points
Eall_ss = onp.array(Eall_ss)
total_ss = onp.absolute(Eall_ss)**2
if not scalar:
total_ss = onp.sum(total_ss, axis=2)
# Produce plots
if ndim == 2:
utils.plot_transmission_angularbeam(k0range, L, thetas, total_ss, file_name, n_thetas_trans = n_thetas_trans, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_ss')
theta_plot = onp.round(180 * thetas[plot_theta_index]/onp.pi)
utils.plot_singlebeam_angular_frequency_plot(k0range, L, thetas, total_ss, file_name, plot_theta_index = plot_theta_index, appended_string='_'+str(file_index)+'_angle_'+str(theta_plot)+'_ss')
else:
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total_ss, measurement_points, file_name, angular_width = angular_width, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_ss', adapt_scale = adapt_scale)
if plot_transmission:
# Also compute the intensity associated to the multiple-scattering contribution of the field, if the full field was computed
Eall_multiple = Eall - Eall_ss
total_multiple = onp.absolute(Eall_multiple)**2
if not scalar:
total_multiple = onp.sum(total_multiple, axis=2)
# Produce plots
if ndim == 2:
utils.plot_transmission_angularbeam(k0range, L, thetas, total_multiple, file_name, n_thetas_trans = n_thetas_trans, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_multiple')
utils.plot_singlebeam_angular_frequency_plot(k0range, L, thetas, total_multiple, file_name, plot_theta_index = plot_theta_index, appended_string='_'+str(file_index)+'_angle_'+str(theta_plot)+'_multiple')
else:
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total_multiple, measurement_points, file_name, angular_width = angular_width, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_multiple', adapt_scale = adapt_scale)
if scattered_fields:
# Compute scattered intensities at measurement points
Eall_scat_ss = onp.array(Eall_scat_ss)
total_scat_ss = onp.absolute(Eall_scat_ss)**2
if not scalar:
total_scat_ss = onp.sum(total_scat_ss, axis=2)
# Produce plots
if ndim == 2:
utils.plot_transmission_angularbeam(k0range, L, thetas, total_scat_ss, file_name, n_thetas_trans = n_thetas_trans, adapt_scale = adapt_scale, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat_ss')
utils.plot_transmission_angularbeam(k0range, L, thetas, total_scat_ss, file_name, n_thetas_trans = n_thetas_trans, adapt_scale = adapt_scale, normalization=total_scat_ss, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat_ss_norm')
utils.plot_singlebeam_angular_frequency_plot(k0range, L, thetas, total_scat_ss, file_name, plot_theta_index = plot_theta_index, appended_string='_'+str(file_index)+'_angle_'+str(theta_plot)+'_scat_ss')
utils.plot_singlebeam_angular_frequency_plot(k0range, L, thetas, total_scat_ss, file_name, plot_theta_index = plot_theta_index, normalization = total_scat_ss, appended_string='_'+str(file_index)+'_angle_'+str(theta_plot)+'_scat_ss_norm')
else:
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total_scat_ss, measurement_points, file_name, angular_width = angular_width, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat_ss', adapt_scale = adapt_scale)
utils.plot_transmission_angularbeam_3d(k0range, L, thetas, u, total_scat_ss, measurement_points, file_name, angular_width = angular_width, normalization=total_scat_ss, appended_string='_trad'+str(transmission_radius)+'_angwidth'+str(angular_width)+'_'+str(file_index)+'_scat_ss_norm', adapt_scale = adapt_scale)
### ###############
### Intensity fields calculations
### ###############
# Compute full fields
# Pretty expensive!
some_fields = intensity_fields+amplitude_fields+phase_fields
if some_fields:
ngridx = gridsize[0]
ngridy = gridsize[1]
xyratio = ngridx/ngridy
if ndim == 2:
x,y = onp.meshgrid(onp.linspace(0,xyratio,ngridx) - xyratio/2.0,onp.linspace(0,1,ngridy) - 0.5)
measurement_points = np.from_numpy((onp.vstack([x.ravel(),y.ravel()]).T)*L*window_width)
else:
x,y,z = onp.roll(onp.meshgrid(onp.linspace(0,xyratio,ngridx) - xyratio/2.0,onp.linspace(0,1,ngridy) - 0.5, [0.0]),slice_coordinate, axis=0)
measurement_points = np.from_numpy((onp.vstack([x.ravel(),y.ravel(), z.ravel()]).T)*L*window_width)
batches = np.split(measurement_points, batch_size)
n_batches = len(batches)
extra_string=""
if n_batches > 1:
extra_string = extra_string+"es"
print("Computing the full fields at "+str(gridsize)+" points in "+str(n_batches)+" batch"+extra_string+" of "+str(onp.min([batch_size, ngridx*ngridy])))
for k0, alpha in zip(k0range,alpharange):
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
print("k0L/2pi = "+str(k0_))
# Check if file already exists or if computation is needed
file = file_name+'_Ek_k0_'+str(k0_)+'_'+str(file_index)+'.hkl'
# File is there: load data
if os.path.isfile(file):
Ej, params, _, thetas = hkl.load(file_name+'_Ek_k0_'+str(k0_)+'_'+str(file_index)+'.hkl')
Ej = np.from_numpy(Ej)
thetas = onp.float64(thetas)
alpha, k0 = params
k0 = k0.real
alpha = onp.complex128(alpha)
if ndim ==3:
if scalar:
u, _ = utils.vector_3d_u_and_p(thetas, rotate_u = rotate_u)
u = u.reshape(1,-1)
else:
u, p = utils.vector_3d_u_and_p(thetas, rotate_u = rotate_u, polarization_angle_radians = polarization_angle_radians, switch_angle_scans = switch_angle_scans)
utils.plot_3d_points(p,file_name+"_polarization")
utils.plot_3d_points(u,file_name+"_incomingorientation")
# File is not there: compute
else:
if ndim == 2:
# In 2d: no ambiguity to make thetas into k vectors and polarizations even if vector wave
E0_scat = solver.generate_source(points, k0, thetas, beam_waist, print_statement='Source at scatterers')
else:
if scalar:
# In 3d scalar, no need to specify polarization vector
u, _ = utils.vector_3d_u_and_p(thetas, rotate_u = rotate_u)
u = u.reshape(1,-1)
E0_scat = solver.generate_source(points, k0, u, beam_waist, print_statement='Source at scatterers')
else:
u, p = utils.vector_3d_u_and_p(thetas, rotate_u = rotate_u, polarization_angle_radians = polarization_angle_radians, switch_angle_scans = switch_angle_scans)
E0_scat = solver.generate_source(points, k0, u, p, beam_waist, print_statement='Source at scatterers')
utils.plot_3d_points(p,file_name+"_polarization")
utils.plot_3d_points(u,file_name+"_incomingorientation")
Ej = solver.solve(k0, alpha, radius, E0_scat, self_interaction=self_interaction, self_interaction_type=self_interaction_type)
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
params = [alpha, k0]
hkl.dump([onp.array(Ej), onp.array(params),onp.array(points), onp.array(thetas)],file_name+'_Ek_k0_'+str(k0_)+'_'+str(file_index)+'.hkl')
for angle in thetas_plot:
angle_ = onp.round(angle*180/onp.pi)
index = onp.where((thetas - angle)**2 < 1e-8)[0][0] # Assumes angles are never closer than 1e-4 rad here, avoids rounding/precision errors
print("angle = "+str(angle_)+"degrees")
Eall = []
if scattered_fields:
Eall_scat = []
for batch in range(0, n_batches):
print("Batch "+str(batch+1))
batch_points = batches[batch]
if ndim == 2:
# In 2d: no ambiguity to make thetas into k vectors and polarizations even if vector wave
E0_meas = solver.generate_source(batch_points, k0, [angle], beam_waist, print_statement='Source at scatterers')
else:
if scalar:
# In 3d scalar, no need to specify polarization vector
u_angle, _ = utils.vector_3d_u_and_p([angle], rotate_u = rotate_u)
u_angle = u_angle.reshape(1,-1)
E0_meas = solver.generate_source(batch_points, k0, u_angle.reshape(1,3), beam_waist, print_statement='Source at scatterers')
else:
u_angle, p_angle = utils.vector_3d_u_and_p([angle], rotate_u = rotate_u, polarization_angle_radians = polarization_angle_radians, switch_angle_scans = switch_angle_scans)
E0_meas = solver.generate_source(batch_points, k0, u_angle.reshape(1,3), p_angle.reshape(1,3), beam_waist, print_statement='Source at scatterers')
if scalar:
E0_meas = E0_meas.reshape(batch_points.shape[0], 1)
else:
E0_meas = E0_meas.reshape(batch_points.shape[0], ndim, 1)
E_meas = solver.propagate(batch_points, Ej[:,index].unsqueeze(-1), k0, alpha, E0_meas, regularize = regularize, radius = radius)
Eall.append(E_meas)
if scattered_fields:
Eall_scat.append(E_meas - E0_meas)
Eall = np.cat(Eall, dim=0)
if not scalar:
Eall = Eall.squeeze(-1)
# The medium is centered at (0,0)
if ndim == 2:
viewing_angle = np.arctan2(measurement_points[:,1], measurement_points[:,0]) #y,x
else:
viewing_unit_vector = measurement_points / np.linalg.norm(measurement_points, axis = -1).unsqueeze(-1)
if scalar:
Eall = Eall.reshape(ngridy, ngridx)
utils.plot_full_fields(Eall, ngridx, ngridy, k0_, angle_, intensity_fields, amplitude_fields, phase_fields, file_name, appended_string='_width_'+str(window_width)+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index), my_dpi = 300)
else:
Eall_amplitude = np.sqrt(np.sum(np.absolute(Eall)**2,axis = -1))
if ndim == 2:
Eall_longitudinal = Eall[:,0]*np.cos(viewing_angle) - Eall[:,1]*np.sin(viewing_angle)
Eall_transverse = Eall[:,0]*np.sin(viewing_angle) + Eall[:,1]*np.cos(viewing_angle)
else:
Eall_longitudinal = np.sum(Eall*viewing_unit_vector, axis=1)
Eall_transverse = Eall - Eall_longitudinal.reshape(-1,1) * viewing_unit_vector
Eall_transverse = np.sqrt(np.sum(np.absolute(Eall_transverse)**2, axis =1))
Eall_amplitude = Eall_amplitude.reshape(ngridy, ngridx)
Eall_longitudinal = Eall_longitudinal.reshape(ngridy, ngridx)
Eall_transverse = Eall_transverse.reshape(ngridy, ngridx)
slice_string = ''
if ndim == 3:
slice_ = ('z','x','y')
slice_string = '_slice_'+slice_[slice_coordinate%3]
utils.plot_full_fields(Eall_amplitude, ngridx, ngridy, k0_, angle_, intensity_fields, False, False, file_name, appended_string='_width_'+str(window_width)+slice_string+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index), my_dpi = 300)
utils.plot_full_fields(Eall_longitudinal, ngridx, ngridy, k0_, angle_, intensity_fields, amplitude_fields, phase_fields, file_name, appended_string='_width_'+str(window_width)+slice_string+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_long', my_dpi = 300)
utils.plot_full_fields(Eall_transverse, ngridx, ngridy, k0_, angle_, intensity_fields, amplitude_fields, phase_fields, file_name, appended_string='_width_'+str(window_width)+slice_string+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_trans', my_dpi = 300)
if scattered_fields:
Eall = np.cat(Eall, dim=0)
if not scalar:
Eall = Eall.squeeze(-1)
if scalar:
Eall = Eall.reshape(ngridy, ngridx)
utils.plot_full_fields(Eall, ngridx, ngridy, k0_, angle_, intensity_fields, amplitude_fields, phase_fields, file_name, appended_string='_width_'+str(window_width)+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_scat', my_dpi = 300)
else:
Eall_amplitude = np.sqrt(np.sum(np.absolute(Eall)**2,axis = -1))
if ndim == 2:
Eall_longitudinal = Eall[:,0]*np.cos(viewing_angle) - Eall[:,1]*np.sin(viewing_angle)
Eall_transverse = Eall[:,0]*np.sin(viewing_angle) + Eall[:,1]*np.cos(viewing_angle)
else:
Eall_longitudinal = np.sum(Eall*viewing_unit_vector, axis=1)
Eall_transverse = Eall - Eall_longitudinal.reshape(-1,1) * viewing_unit_vector
Eall_transverse = np.sqrt(np.sum(np.absolute(Eall_transverse)**2, axis =1))
Eall_amplitude = Eall_amplitude.reshape(ngridy, ngridx)
Eall_longitudinal = Eall_longitudinal.reshape(ngridy, ngridx)
Eall_transverse = Eall_transverse.reshape(ngridy, ngridx)
utils.plot_full_fields(Eall_amplitude, ngridx, ngridy, k0_, angle_, intensity_fields, False, False, file_name, appended_string='_width_'+str(window_width)+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_scat', my_dpi = 300)
utils.plot_full_fields(Eall_longitudinal, ngridx, ngridy, k0_, angle_, intensity_fields, amplitude_fields, phase_fields, file_name, appended_string='_width_'+str(window_width)+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_long_scat', my_dpi = 300)
utils.plot_full_fields(Eall_transverse, ngridx, ngridy, k0_, angle_, intensity_fields, amplitude_fields, phase_fields, file_name, appended_string='_width_'+str(window_width)+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_trans_scat', my_dpi = 300)
### ###############
### DOS calculations
### ###############
if compute_SDOS:
DOSall = []
k0_range = []
for k0, alpha in zip(k0range,alpharange):
dos = solver.compute_eigenvalues_and_scatterer_LDOS( k0, alpha, radius, file_name, write_eigenvalues=write_eigenvalues, self_interaction = self_interaction, self_interaction_type = self_interaction_type)
DOSall.append(dos.numpy())
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
k0_range.append(k0_)
onp.savetxt(file_name+'_temp_sdos.csv',onp.stack([k0_range,DOSall]).T)
onp.savetxt(file_name+'_sdos.csv',onp.stack([k0_range,DOSall]).T)
utils.plot_averaged_DOS(k0range, L, DOSall, file_name, 'sdos', appended_string='_'+str(file_index))
if compute_eigenmodes:
if ndim==2:
if scalar:
eigen_solver = Transmission2D_scalar(points, source = None)
else:
eigen_solver = Transmission2D_vector(points, source = None)
else:
if scalar:
eigen_solver = Transmission3D_scalar(points, source = None)
else:
eigen_solver = Transmission3D_vector(points, source = None)
# Expensive computation
ngridx = gridsize[0]
ngridy = gridsize[1]
xyratio = ngridx/ngridy
if ndim == 2:
x,y = onp.meshgrid(onp.linspace(0,xyratio,ngridx) - xyratio/2.0,onp.linspace(0,1,ngridy) - 0.5)
measurement_points = np.from_numpy((onp.vstack([x.ravel(),y.ravel()]).T)*L*window_width)
else:
x,y,z = onp.roll(onp.meshgrid(onp.linspace(0,xyratio,ngridx) - xyratio/2.0,onp.linspace(0,1,ngridy) - 0.5, [0.0]),slice_coordinate,axis=0)
measurement_points = np.from_numpy((onp.vstack([x.ravel(),y.ravel(), z.ravel()]).T)*L*window_width)
batches = np.split(measurement_points, batch_size)
n_batches = len(batches)
extra_string=""
if n_batches > 1:
extra_string = extra_string+"es"
print("Computing the eigenfields and plotting the "+str(number_eigenmodes)+" most localized at "+str(gridsize)+" points in "+str(n_batches)+" batch"+extra_string+" of "+str(onp.min([batch_size, ngridx*ngridy])))
k0_range = []
for k0, alpha in zip(k0range,alpharange):
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
k0_range.append(k0_)
_, eigenmodes,_ = eigen_solver.compute_eigenmodes_IPR( k0, alpha, radius, file_name, write_eigenvalues = True, number_eigenmodes = number_eigenmodes, self_interaction = self_interaction, self_interaction_type = self_interaction_type, sorting_type = sorting_type)
if plot_eigenmodes:
for i in range(number_eigenmodes):
Eall = []
# By default, the eigenvectors are such that their modulus is 1
eigenmodes[:,i] /= np.abs(eigenmodes[:,i]).amax()
for batch in range(0, n_batches):
print("Batch "+str(batch+1))
batch_points = batches[batch]
if scalar:
dummy_E0 = np.zeros(batch_points.shape[0],1)
else:
dummy_E0 = np.zeros(batch_points.shape[0],ndim,1)
eigenfield = eigen_solver.propagate(batch_points, eigenmodes[:,i].unsqueeze(-1), k0, alpha, dummy_E0, regularize = regularize, radius=radius)
Eall.append(eigenfield)
Eall = np.cat(Eall, dim=0)
if not scalar:
Eall = Eall.squeeze(-1)
if scalar:
Eall_amplitude = Eall.reshape(ngridy, ngridx)
else:
Eall_amplitude = np.sqrt(np.sum( np.absolute(Eall)**2, axis = -1))
Eall_amplitude = Eall_amplitude.reshape(ngridy, ngridx)
plot_IPR = np.sum(np.abs(Eall**4)) / (np.sum(np.abs(Eall**2)))**2
print(f"Effective IPR of the whole eigenfield: {plot_IPR}")
slice_string = ''
if ndim == 3:
slice_ = ('z','x','y')
slice_string = '_slice_'+slice_[slice_coordinate%3]
utils.plot_full_fields(Eall_amplitude, ngridx, ngridy, k0_, 0, True, False, False, file_name, appended_string='_width_'+str(window_width)+slice_string+'_grid_'+str(ngridx)+'x'+str(ngridy)+'_'+str(file_index)+'_eigen_'+sorting_type+str(i), my_dpi = 300)
if compute_DOS:
DOSall = []
k0_range = []
M = dospoints
measurement_points = utils.uniform_unit_ball_picking(M, ndim)
measurement_points *= L/2
if ndim == 2:
utils.plot_2d_points(measurement_points, file_name+'_measurement')
else:
utils.plot_3d_points(measurement_points, file_name+'_measurement')
for k0, alpha in zip(k0range,alpharange):
dos = solver.mean_DOS_measurements(measurement_points, k0, alpha, radius, regularize = regularize, self_interaction = self_interaction, self_interaction_type = self_interaction_type)
DOSall.append(dos.numpy())
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
k0_range.append(k0_)
onp.savetxt(file_name+'_temp_dos.csv',onp.stack([k0_range,DOSall]).T)
onp.savetxt(file_name+'_dos.csv',onp.stack([k0_range,DOSall]).T)
utils.plot_averaged_DOS(k0range, L, DOSall, file_name, 'dos', appended_string='_'+str(file_index))
if compute_interDOS:
for dos_size in dos_sizes[::-1]:
DOSall = onp.array([])
k0_range = onp.array([])
if os.path.exists(file_name+'_temp_idos_size'+str(dos_size)+'_irad'+str(idos_radius)+'_sf'+str(spacing_factor)+'.csv'):
existing = onp.loadtxt(file_name+'_temp_idos_size'+str(dos_size)+'_irad'+str(idos_radius)+'_sf'+str(spacing_factor)+'.csv')
DOSall = existing[:,1]
k0_range = existing[:,0]
M = dospoints
measurement_points = utils.uniform_unit_ball_picking(M, ndim)
measurement_points *= dos_size * L/2 * idos_radius
disk_points = lattices.cut_circle(points, rad = dos_size * 0.5)
# Find all overlaps and redraw while you have some
# Following Pierrat et al., I use 1 diameter as the spacing there
spacing = 2.0*radius
spacing *= spacing_factor
overlaps = np.nonzero(np.sum(np.cdist(measurement_points.to(np.double), disk_points.to(np.double), p=2) <= spacing, axis = -1)).squeeze()
if len(overlaps.shape) == 0:
count = 0
else:
count = overlaps.shape[0]
while count > 0:
print("Removing "+str(count)+" overlaps using an exclusion distance of "+str(spacing_factor)+" scatterer diameters...")
measurement_points[overlaps] = dos_size * L/2 * idos_radius * utils.uniform_unit_ball_picking(count, ndim).squeeze()
overlaps = np.nonzero(np.sum(np.cdist(measurement_points.to(np.double), disk_points.to(np.double), p=2) <= spacing, axis = -1)).squeeze()
if len(overlaps.shape) == 0:
count = 0
else:
count = overlaps.shape[0]
if ndim == 2:
utils.plot_2d_points(measurement_points, file_name+'_measurement')
if scalar:
dos_solver = Transmission2D_scalar(disk_points, source = None)
else:
dos_solver = Transmission2D_vector(disk_points, source = source)
else:
utils.plot_3d_points(measurement_points, file_name+'_measurement')
if scalar:
dos_solver = Transmission3D_scalar(disk_points, source = source)
else:
dos_solver = Transmission3D_vector(disk_points, source = source)
for k0, alpha in zip(k0range,alpharange):
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
if k0_ not in k0_range:
k0_range = onp.append(k0_range,k0_)
dos = dos_solver.mean_DOS_measurements(measurement_points, k0, alpha, radius, regularize = regularize, self_interaction = self_interaction, self_interaction_type = self_interaction_type)
DOSall = onp.append(DOSall,dos.numpy())
idx = onp.argsort(k0_range)
k0_range = k0_range[idx]
DOSall = DOSall[idx]
onp.savetxt(file_name+'_temp_idos_size'+str(dos_size)+'_irad'+str(idos_radius)+'_sf'+str(spacing_factor)+'.csv',onp.stack([k0_range,DOSall]).T)
onp.savetxt(file_name+'_idos_size'+str(dos_size)+'_irad'+str(idos_radius)+'_sf'+str(spacing_factor)+'.csv',onp.stack([k0_range,DOSall]).T)
utils.plot_averaged_DOS(k0range, L, DOSall, file_name, 'idos', appended_string='_'+str(file_index)+'_size'+str(dos_size)+'_irad'+str(idos_radius)+'_sf'+str(spacing_factor))
if compute_cavityDOS:
for dos_size in dos_sizes[::-1]:
DOSall = onp.array([])
k0_range = onp.array([])
if os.path.exists(file_name+'_temp_cdos_size'+str(dos_size)+'.csv'):
existing = onp.loadtxt(file_name+'_temp_cdos_size'+str(dos_size)+'.csv')
DOSall = existing[:,1]
k0_range = existing[:,0]
measurement_points = np.zeros(ndim).reshape(1, ndim)
disk_points = lattices.cut_circle(points, rad = dos_size * 0.5)
# Find all overlaps and remove from system
# Following Pierrat et al., I use 1 diameter as the spacing there
spacing = 2.0*radius
spacing *= spacing_factor
disk_points = lattices.exclude_circle(disk_points, spacing)
if ndim == 2:
utils.plot_2d_points(disk_points, file_name+'_measurement')
if scalar:
dos_solver = Transmission2D_scalar(disk_points, source = None)
else:
dos_solver = Transmission2D_vector(disk_points, source = None)
else:
if scalar:
dos_solver = Transmission3D_scalar(disk_points, source = None)
else:
dos_solver = Transmission3D_vector(disk_points, source = None)
for k0, alpha in zip(k0range,alpharange):
k0_ = onp.round(onp.real(k0*L/(2*onp.pi)),1)
if k0_ not in k0_range:
k0_range = onp.append(k0_range,k0_)
dos = dos_solver.mean_DOS_measurements(measurement_points, k0, alpha, radius, regularize = regularize, self_interaction = self_interaction, self_interaction_type = self_interaction_type)
DOSall = onp.append(DOSall,dos.numpy())
idx = onp.argsort(k0_range)
k0_range = k0_range[idx]
DOSall = DOSall[idx]
onp.savetxt(file_name+'_temp_cdos_size'+str(dos_size)+'.csv',onp.stack([k0_range,DOSall]).T)
onp.savetxt(file_name+'_cdos_size'+str(dos_size)+'.csv',onp.stack([k0_range,DOSall]).T)
utils.plot_averaged_DOS(k0range, L, DOSall, file_name, 'cdos', appended_string='_'+str(file_index)+'_size'+str(dos_size))
if compute_LDOS:
ngridx = gridsize[0]
ngridy = gridsize[1]
xyratio = ngridx/ngridy
if ndim == 2:
x,y = onp.meshgrid(onp.linspace(0,xyratio,ngridx) - xyratio/2.0,onp.linspace(0,1,ngridy) - 0.5)
measurement_points = np.from_numpy((onp.vstack([x.ravel(),y.ravel()]).T)*L*window_width)
else:
x,y,z = onp.roll(onp.meshgrid(onp.linspace(0,xyratio,ngridx) - xyratio/2.0,onp.linspace(0,1,ngridy) - 0.5, [0.0]),slice_coordinate, axis=0)
measurement_points = np.from_numpy((onp.vstack([x.ravel(),y.ravel(), z.ravel()]).T)*L*window_width)