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from __future__ import division
import math
import numpy as np
import meep as mp
from . import map_data
from . import MPBArray
class MPBData(object):
TWOPI = 6.2831853071795864769252867665590057683943388
def __init__(self,
lattice=None,
kpoint=None,
rectify=False,
x=0,
y=0,
z=0,
periods=0,
resolution=0,
phase_angle=0,
pick_nearest=False,
ve=None,
verbose=False):
self.lattice = lattice
self.kpoint = kpoint
self.rectify = rectify
if periods:
self.multiply_size = [periods, periods, periods]
else:
self.multiply_size = [
x if x else 1,
y if y else 1,
z if z else 1
]
self.resolution = resolution
self.phase_angle = phase_angle
self.pick_nearest = pick_nearest
self.ve = ve
if self.ve:
self.have_ve = True
self.rectify = True
else:
self.have_ve = False
self.ve = mp.Vector3(1, 0, 0)
self.verbose = verbose
self.scaleby = complex(1, 0)
self.phase = complex(math.cos(self.TWOPI * self.phase_angle / 360.0),
math.sin(self.TWOPI * self.phase_angle / 360.0))
self.scaleby *= self.phase
def handle_dataset(self, in_arr):
out_dims = [1, 1, 1]
rank = len(in_arr.shape)
num_ones = 3 - rank
in_dims = [x for x in in_arr.shape] + [1] * num_ones
if np.iscomplexobj(in_arr):
in_arr_re = np.real(in_arr)
in_arr_im = np.imag(in_arr)
else:
in_arr_re = in_arr
in_arr_im = None
if self.verbose:
fmt = "Input data is rank {}, size {}x{}x{}."
print(fmt.format(rank, in_dims[0], in_dims[1], in_dims[2]))
if self.resolution > 0:
out_dims[0] = math.floor(self.Rout.c1.norm() * self.resolution + 0.5)
out_dims[1] = math.floor(self.Rout.c2.norm() * self.resolution + 0.5)
out_dims[2] = math.floor(self.Rout.c3.norm() * self.resolution + 0.5)
else:
for i in range(3):
out_dims[i] = in_dims[i] * self.multiply_size[i]
for i in range(rank, 3):
out_dims[i] = 1
N = 1
for i in range(3):
out_dims[i] = int(max(out_dims[i], 1))
N *= out_dims[i]
if self.verbose:
print("Output data {}x{}x{}".format(out_dims[0], out_dims[1], out_dims[2]))
out_arr_re = np.zeros(int(N))
if isinstance(in_arr_im, np.ndarray):
out_arr_im = np.zeros(int(N))
else:
out_arr_im = np.array([])
flat_in_arr_re = in_arr_re.ravel()
flat_in_arr_im = in_arr_im.ravel() if isinstance(in_arr_im, np.ndarray) else np.array([])
if self.kpoint:
kvector = [self.kpoint.x, self.kpoint.y, self.kpoint.z]
else:
kvector = []
map_data(flat_in_arr_re, flat_in_arr_im, np.array(in_dims, dtype=np.intc),
out_arr_re, out_arr_im, np.array(out_dims, dtype=np.intc), self.coord_map,
kvector, self.pick_nearest, self.verbose, False)
if np.iscomplexobj(in_arr):
# multiply * scaleby for complex data
complex_out = np.vectorize(complex)(out_arr_re, out_arr_im)
complex_out *= self.scaleby
return np.reshape(complex_out, out_dims[:rank])
return np.reshape(out_arr_re, out_dims[:rank])
def handle_cvector_dataset(self, in_arr, multiply_bloch_phase):
in_x_re = np.real(in_arr[:, :, :, 0]).ravel()
in_x_im = np.imag(in_arr[:, :, :, 0]).ravel()
in_y_re = np.real(in_arr[:, :, :, 1]).ravel()
in_y_im = np.imag(in_arr[:, :, :, 1]).ravel()
in_z_re = np.real(in_arr[:, :, :, 2]).ravel()
in_z_im = np.imag(in_arr[:, :, :, 2]).ravel()
d_in = [[in_x_re, in_x_im], [in_y_re, in_y_im], [in_z_re, in_z_im]]
in_dims = [in_arr.shape[0], in_arr.shape[1], 1]
rank = 2
if self.verbose:
print("Found complex vector dataset...")
if self.verbose:
fmt = "Input data is rank {}, size {}x{}x{}."
print(fmt.format(rank, in_dims[0], in_dims[1], in_dims[2]))
# rotate vector field according to cart_map
if self.verbose:
fmt1 = "Rotating vectors by matrix [ {:.10g}, {:.10g}, {:.10g}"
fmt2 = " {:.10g}, {:.10g}, {:.10g}"
fmt3 = " {:.10g}, {:.10g}, {:.10g} ]"
print(fmt1.format(self.cart_map.c1.x, self.cart_map.c2.x, self.cart_map.c3.x))
print(fmt2.format(self.cart_map.c1.y, self.cart_map.c2.y, self.cart_map.c3.y))
print(fmt3.format(self.cart_map.c1.z, self.cart_map.c2.z, self.cart_map.c3.z))
N = in_dims[0] * in_dims[1]
for ri in range(2):
for i in range(N):
v = mp.Vector3(d_in[0][ri][i], d_in[1][ri][i], d_in[2][ri][i])
v = self.cart_map * v
d_in[0][ri][i] = v.x
d_in[1][ri][i] = v.y
d_in[2][ri][i] = v.z
out_dims = [1, 1, 1]
if self.resolution > 0:
out_dims[0] = self.Rout.c1.norm() * self.resolution + 0.5
out_dims[1] = self.Rout.c2.norm() * self.resolution + 0.5
out_dims[2] = self.Rout.c3.norm() * self.resolution + 0.5
else:
for i in range(3):
out_dims[i] = in_dims[i] * self.multiply_size[i]
out_dims[2] = 1
N = 1
for i in range(3):
out_dims[i] = int(max(out_dims[i], 1))
N *= out_dims[i]
if self.verbose:
fmt = "Output data {}x{}x{}."
print(fmt.format(out_dims[0], out_dims[1], out_dims[2]))
if self.kpoint:
kvector = [self.kpoint.x, self.kpoint.y, self.kpoint.z]
else:
kvector = []
converted = []
for dim in range(3):
out_arr_re = np.zeros(int(N))
out_arr_im = np.zeros(int(N))
map_data(d_in[dim][0].ravel(), d_in[dim][1].ravel(), np.array(in_dims, dtype=np.intc),
out_arr_re, out_arr_im, np.array(out_dims, dtype=np.intc), self.coord_map,
kvector, self.pick_nearest, self.verbose, multiply_bloch_phase)
# multiply * scaleby
complex_out = np.vectorize(complex)(out_arr_re, out_arr_im)
complex_out *= self.scaleby
converted.append(complex_out)
result = np.zeros(np.prod(out_dims) * 3, np.complex128)
result[0::3] = converted[0]
result[1::3] = converted[1]
result[2::3] = converted[2]
return np.reshape(result, (out_dims[0], out_dims[1], 3))
def init_output_lattice(self):
cart_map = mp.Matrix(
mp.Vector3(1, 0, 0),
mp.Vector3(0, 1, 0),
mp.Vector3(0, 0, 1)
)
Rin = mp.Matrix(
mp.Vector3(*self.lattice[0]),
mp.Vector3(*self.lattice[1]),
mp.Vector3(*self.lattice[2])
)
if self.verbose:
print("Read lattice vectors")
if self.kpoint:
fmt = "Read Bloch wavevector ({:.6g}, {:.6g}, {:.6g})"
print(fmt.format(self.kpoint.x, self.kpoint.y, self.kpoint.z))
fmt = "Input lattice = ({:.6g}, {:.6g}, {:.6g}), ({:.6g}, {:.6g}, {:.6g}), ({:.6g}, {:.6g}, {:.6g})"
print(fmt.format(Rin.c1.x, Rin.c1.y, Rin.c1.z,
Rin.c2.x, Rin.c2.y, Rin.c2.z,
Rin.c3.x, Rin.c3.y, Rin.c3.z))
Rout = mp.Matrix(Rin.c1, Rin.c2, Rin.c3)
if self.rectify:
# Orthogonalize the output lattice vectors. If have_ve is true,
# then the first new lattice vector should be in the direction
# of the ve unit vector; otherwise, the first new lattice vector
# is the first original lattice vector. Note that we do this in
# such a way as to preserve the volume of the unit cell, and so
# that our first vector (in the direction of ve) smoothly
# interpolates between the original lattice vectors.
if self.have_ve:
ve = self.ve.unit()
else:
ve = Rout.c1.unit()
# First, compute c1 in the direction of ve by smoothly
# interpolating the old c1/c2/c3 (formula is slightly tricky)
V = Rout.c1.cross(Rout.c2).dot(Rout.c3)
Rout.c2 = Rout.c2 - Rout.c1
Rout.c3 = Rout.c3 - Rout.c1
Rout.c1 = ve.scale(V / Rout.c2.cross(Rout.c3).dot(ve))
# Now, orthogonalize c2 and c3
Rout.c2 = Rout.c2 - ve.scale(ve.dot(Rout.c2))
Rout.c3 = Rout.c3 - ve.scale(ve.dot(Rout.c3))
Rout.c3 = Rout.c3 - Rout.c2.scale(Rout.c2.dot(Rout.c3) /
Rout.c2.dot(Rout.c2))
cart_map.c1 = Rout.c1.unit()
cart_map.c2 = Rout.c2.unit()
cart_map.c3 = Rout.c3.unit()
cart_map = cart_map.inverse()
Rout.c1 = Rout.c1.scale(self.multiply_size[0])
Rout.c2 = Rout.c2.scale(self.multiply_size[1])
Rout.c3 = Rout.c3.scale(self.multiply_size[2])
if self.verbose:
fmt = "Output lattice = ({:.6g}, {:.6g}, {:.6g}), ({:.6g}, {:.6g}, {:.6g}), ({:.6g}, {:.6g}, {:.6g})"
print(fmt.format(Rout.c1.x, Rout.c1.y, Rout.c1.z,
Rout.c2.x, Rout.c2.y, Rout.c2.z,
Rout.c3.x, Rout.c3.y, Rout.c3.z))
self.coord_map = Rin.inverse() * Rout
self.Rout = Rout
self.cart_map = cart_map
def convert(self, arr, kpoint=None):
if isinstance(arr, MPBArray):
self.lattice = arr.lattice
self.kpoint = arr.kpoint
if self.lattice is None:
err = ("Couldn't find 'lattice.' You must do one of the following:\n" +
" 1. Pass the ModeSolver lattice to the MPBData constructor\n" +
" i.e., MPBData(lattice=ms.get_lattice())\n" +
" 2. Create an MPBArray to pass to MPBData.convert()\n" +
" i.e., mpb_arr = MPBArray(arr, ms.get_lattice(), ... ); mpb_data.convert(mpb_arr))")
raise ValueError(err)
if kpoint:
self.kpoint = kpoint
self.init_output_lattice()
if len(arr.shape) == 4:
return self.handle_cvector_dataset(arr, not arr.bloch_phase)
else:
return self.handle_dataset(arr)
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