def unit_vectors(direction, return_numpy=True):
"""
Calculate the unit vectors (UnitX, UnitY) from a given direction angle.
Args:
direction: 3D NumPy array - direction angles in degrees
return_numpy: Necessary if using `use_gpu`. Specifies if a CuPy or Numpy
array will be returned.
Returns:
UnitX, UnitY: 3D NumPy array, 3D NumPy array
x- and y-vector component in arrays
"""
direction_gpu = cupy.array(direction)
direction_gpu_rad = cupy.deg2rad(direction_gpu)
UnitX = -cupy.sin(0.5 * cupy.pi) * cupy.cos(direction_gpu_rad)
UnitY = cupy.sin(0.5 * cupy.pi) * cupy.sin(direction_gpu_rad)
del direction_gpu_rad
UnitX[cupy.isclose(direction_gpu, -1)] = 0
UnitY[cupy.isclose(direction_gpu, -1)] = 0
del direction_gpu
if return_numpy:
return UnitX.get(), UnitY.get()
return UnitX, UnitY
def createWedge(self, subunit_num=0):
###Initialize the location of the protofilament to remove
theta0=np.arctan2(self.com[0], self.com[1])+\
np.deg2rad(subunit_num*self.twist_per_subunit)
z0=(self.com[2]+self.rise_per_subunit*subunit_num)/self.pixel_size
###Define the length along the protofilament in terms of subunits
zsubunits=(self.zline.copy()-z0)*self.pixel_size/self.dimer_repeat_dist
###Define the angle of the center of the protofilament along the length of the segment
theta=np.deg2rad((-self.helical_twist)*zsubunits)+theta0
###Initialize the wedge mask
wedge=np.zeros(self.vol_dim.tolist())
###Define the size of the wedgemask
fudge=np.deg2rad(360.0/(self.num_pfs*2))
###Generate the wedge mask
for i in range(len(theta)):
temp1=np.remainder(theta[i]-fudge+2*np.pi,2*np.pi)-2*np.pi
temp2=np.remainder(theta[i]+fudge+2*np.pi,2*np.pi)-2*np.pi
angles=[temp1, temp2]
if max(angles)-min(angles)>2*fudge+.2:
above=max(angles)
below=min(angles)
inds=np.logical_or(self.radmatrix>above,self.radmatrix<below)
else:
above=min(angles)
below=max(angles)
inds=np.logical_and(self.radmatrix>above,self.radmatrix<below)
wedge[i,:,:][inds]=1
return wedge
def rotshift3D_spline(self, v, eulers, shifts=np.array([0,0,0]), mode='wrap'):
# With a nod to:
# http://stackoverflow.com/questions/20161175/how-can-i-use-scipy-ndimage-interpolation-affine-transform-to-rotate-an-image-ab
print shifts
print eulers
rot_origin = 0.5*np.array(v.shape)
rot_rad = -np.deg2rad(eulers)
phi = np.array([[np.cos(rot_rad[0]), np.sin(rot_rad[0]), 0],
[-np.sin(rot_rad[0]),np.cos(rot_rad[0]), 0],
[0 , 0 , 1]])
theta=np.array([[np.cos(rot_rad[1]), 0,-np.sin(rot_rad[1])],[0,1,0],\
[np.sin(rot_rad[1]), 0, np.cos(rot_rad[1])]])
psi=np.array([[np.cos(rot_rad[2]), np.sin(rot_rad[2]), 0],\
[-np.sin(rot_rad[2]),np.cos(rot_rad[2]), 0],\
[0,0,1]])
rot_matrix=np.dot(np.dot(phi,theta),psi)
offset = -(rot_origin-rot_origin.dot(rot_matrix)).dot(np.linalg.inv(rot_matrix))
offset = offset - shifts
transformed_v = affine_transform(v,rot_matrix,offset=offset,mode=mode)
return transformed_v
def receive_power(self, tx_ant):
# 「EEM-RTM理論説明書」3.1伝達公式参照
# http://www.e-em.co.jp/doc/rtm_theory.pdf
distance = self.get_distance_by_points(tx_ant) / 100 # Unit[m]
theta = self.calc_theta_tx(tx_ant)
phi = self.calc_phi_tx(distance[1]*100, tx_ant)
R = self.R_horizontal(phi, const.epsilon_r)
def E(reflection_coefficient, distance):
E = cp.sqrt(self.directivity(theta)) * \
cp.sqrt(self.directivity(theta)) * \
reflection_coefficient * \
(tx_ant.lambda_0 / (4 * cp.pi * distance)) * \
cp.exp((-1j * tx_ant.k) * distance)
return E
Pr = (E(const.reflection_coefficient, distance[0]) + E(R, distance[1])) * \
cp.exp(1j * cp.deg2rad(tx_ant.phase_offset)) * \
cp.sqrt(tx_ant.power)
return Pr
def rotate(input,
angle,
axes=(1, 0),
reshape=True,
output=None,
order=None,
mode='constant',
cval=0.0,
prefilter=True):
"""Rotate an array.
The array is rotated in the plane defined by the two axes given by the
``axes`` parameter using spline interpolation of the requested order.
Args:
input (cupy.ndarray): The input array.
angle (float): The rotation angle in degrees.
axes (tuple of 2 ints): The two axes that define the plane of rotation.
Default is the first two axes.
reshape (bool): If ``reshape`` is True, the output shape is adapted so
that the input array is contained completely in the output. Default
is True.
output (cupy.ndarray or ~cupy.dtype): The array in which to place the
output, or the dtype of the returned array.
order (int): The order of the spline interpolation. If it is not given,
order 1 is used. It is different from :mod:`scipy.ndimage` and can
change in the future. Currently it supports only order 0 and 1.
mode (str): Points outside the boundaries of the input are filled
according to the given mode (``'constant'``, ``'nearest'``,
``'mirror'`` or ``'opencv'``). Default is ``'constant'``.
cval (scalar): Value used for points outside the boundaries of
the input if ``mode='constant'`` or ``mode='opencv'``. Default is
0.0
prefilter (bool): It is not used yet. It just exists for compatibility
with :mod:`scipy.ndimage`.
Returns:
cupy.ndarray or None:
The rotated input.
.. seealso:: :func:`scipy.ndimage.rotate`
"""
_check_parameter('rotate', order, mode)
if mode == 'opencv':
mode = '_opencv_edge'
axes = list(axes)
if axes[0] < 0:
axes[0] += input.ndim
if axes[1] < 0:
axes[1] += input.ndim
if axes[0] > axes[1]:
axes = axes[1], axes[0]
if axes[0] < 0 or input.ndim <= axes[1]:
raise IndexError
rad = cupy.deg2rad(angle)
sin = math.sin(rad)
cos = math.cos(rad)
matrix = cupy.identity(input.ndim)
matrix[axes[0], axes[0]] = cos
matrix[axes[0], axes[1]] = sin
matrix[axes[1], axes[0]] = -sin
matrix[axes[1], axes[1]] = cos
iy = input.shape[axes[0]]
ix = input.shape[axes[1]]
if reshape:
mtrx = cupy.array([[cos, sin], [-sin, cos]])
minc = [0, 0]
maxc = [0, 0]
coor = cupy.dot(mtrx, cupy.array([0, ix]))
minc, maxc = _minmax(coor, minc, maxc)
coor = cupy.dot(mtrx, cupy.array([iy, 0]))
minc, maxc = _minmax(coor, minc, maxc)
coor = cupy.dot(mtrx, cupy.array([iy, ix]))
minc, maxc = _minmax(coor, minc, maxc)
oy = int(maxc[0] - minc[0] + 0.5)
ox = int(maxc[1] - minc[1] + 0.5)
else:
oy = input.shape[axes[0]]
ox = input.shape[axes[1]]
offset = cupy.zeros(input.ndim)
offset[axes[0]] = oy / 2.0 - 0.5
offset[axes[1]] = ox / 2.0 - 0.5
offset = cupy.dot(matrix, offset)
tmp = cupy.zeros(input.ndim)
tmp[axes[0]] = iy / 2.0 - 0.5
tmp[axes[1]] = ix / 2.0 - 0.5
offset = tmp - offset
output_shape = list(input.shape)
output_shape[axes[0]] = oy
output_shape[axes[1]] = ox
return affine_transform(input, matrix, offset, output_shape, output, order,
mode, cval, prefilter)
def backProjectGPU2(vol_img, vol_bp, vol_phi, vol_the, recPosVol=[0,0,0], vol_offsetProjections=[0,0,0]):
from pytom_numpy import vol2npy
import cupy as cp
from cupy import cos, sin
import voltools
projections = vol2npy(vol_img)
proj_angles = vol2npy(vol_the)[0,0,:]
dims = (vol_bp.sizeX(), vol_bp.sizeY(), vol_bp.sizeZ())
# TODO add offsets
# preparation
reconstruction = cp.zeros(dims, dtype=cp.float32)
theta_angles = cp.deg2rad(cp.array(proj_angles))
# theta_angles_rad = (theta_angles)
assert len(theta_angles) == projections.shape[2] #'Number of angles and projections should match'
# create coordinates and stack them
x, y, z = cp.meshgrid(cp.arange(0, dims[0]), cp.arange(0, dims[1]), cp.arange(0, dims[2]), indexing='ij')
# backproject each projection into reconstruction
for n in range(projections.shape[2]):
# get projection
src = cp.array(projections[:,:,n])
# previous
Z1 = Z2 = 0.0
Y = theta_angles[n]
x_offset = y_offset = z_offset = 0
x_proj_offset = y_proj_offset = 0
tr11 = cos(Y)*cos(Z1)*cos(Z2)-sin(Z1)*sin(Z2)
# tr21 = cos(Y)*sin(Z1)*cos(Z2)+cos(Z1)*sin(Z2)
tr31 = -sin(Y)*cos(Z2)
# tr12 = -cos(Y)*cos(Z1)*sin(Z2)-sin(Z1)*cos(Z2)
tr22 = -cos(Y)*sin(Z1)*sin(Z2)+cos(Z1)*cos(Z2)
# tr32 = sin(Y)*sin(Z2)
reconstruction_center_x = dims[0] // 2 - x_offset
reconstruction_center_y = dims[1] // 2 - y_offset
reconstruction_center_z = dims[2] // 2 - z_offset
projection_center_x = dims[0] // 2 + x_proj_offset
projection_center_y = dims[1] // 2 + y_proj_offset
# interpolation_position_x = tr11 * (x - reconstruction_center_x) + tr21 * (y - reconstruction_center_y) + tr31 * (z - reconstruction_center_z) + projection_center_x
# interpolation_position_y = tr12 * (x - reconstruction_center_x) + tr22 * (y - reconstruction_center_y) + tr32 * (z - reconstruction_center_z) + projection_center_y
interpolation_position_x = tr11 * (x - reconstruction_center_x) + tr31 * (z - reconstruction_center_z) + projection_center_x
interpolation_position_y = tr22 * (y - reconstruction_center_y) + projection_center_y
proj_position_x = interpolation_position_x.astype(int)
proj_position_y = interpolation_position_y.astype(int)
interpolation_offset_x = (interpolation_position_x - proj_position_x)
interpolation_offset_y = (interpolation_position_y - proj_position_y)
m0, m1, m2 = cp.where((proj_position_x >= 1) & (proj_position_x < dims[0]) & (proj_position_y >= 1) & (proj_position_y < dims[1]))
value_x1 = src[proj_position_x[m0, m1, m2]-1, proj_position_y[m0, m1, m2]-1] + \
(src[proj_position_x[m0, m1, m2], proj_position_y[m0, m1, m2]-1] - src[proj_position_x[m0, m1, m2]-1, proj_position_y[m0, m1, m2]-1]) * interpolation_offset_x[m0, m1, m2]
value_x2 = src[proj_position_x[m0, m1, m2]-1, proj_position_y[m0, m1, m2]] + \
(src[proj_position_x[m0, m1, m2], proj_position_y[m0, m1, m2]] - src[proj_position_x[m0, m1, m2]-1, proj_position_y[m0, m1, m2]]) * interpolation_offset_x[m0, m1, m2]
value_y = value_x1 + (value_x2 - value_x1) * interpolation_offset_y[m0, m1, m2]
reconstruction[m0, m1, m2] += value_y
del value_y
del value_x1
del value_x2
del m0, m1, m2
# import napari
# with napari.gui_qt():
# viewer = napari.Viewer()
# viewer.add_image(reconstruction.get(), name='recon', interpolation='bilinear')
# viewer.add_image(np.log10(np.abs(np.fft.fftshift(np.fft.fftn(reconstruction.get())))), name='fft', interpolation='bilinear')
rec = reconstruction.get()
return rec
for i in range(dims[0]):
for j in range(dims[1]):
for k in range(dims[2]):
vol_bp.setV(float(rec[i][j][k]), int(i), int(j), int(k))
return vol_bp
def deltaE_cmc(lab1, lab2, kL=1, kC=1):
"""Color difference from the CMC l:c standard.
This color difference was developed by the Colour Measurement Committee
(CMC) of the Society of Dyers and Colourists (United Kingdom). It is
intended for use in the textile industry.
The scale factors `kL`, `kC` set the weight given to differences in
lightness and chroma relative to differences in hue. The usual values are
``kL=2``, ``kC=1`` for "acceptability" and ``kL=1``, ``kC=1`` for
"imperceptibility". Colors with ``dE > 1`` are "different" for the given
scale factors.
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
Returns
-------
dE : array_like
distance between colors `lab1` and `lab2`
Notes
-----
deltaE_cmc the defines the scales for the lightness, hue, and chroma
in terms of the first color. Consequently
``deltaE_cmc(lab1, lab2) != deltaE_cmc(lab2, lab1)``
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE94.html
.. [3] F. J. J. Clarke, R. McDonald, and B. Rigg, "Modification to the
JPC79 colour-difference formula," J. Soc. Dyers Colour. 100, 128-132
(1984).
"""
L1, C1, h1 = cp.rollaxis(lab2lch(lab1), -1)[:3]
L2, C2, h2 = cp.rollaxis(lab2lch(lab2), -1)[:3]
dC = C1 - C2
dL = L1 - L2
dH2 = get_dH2(lab1, lab2)
T = cp.where(cp.logical_and(cp.rad2deg(h1) >= 164, cp.rad2deg(h1) <= 345),
0.56 + 0.2 * cp.abs(np.cos(h1 + cp.deg2rad(168))),
0.36 + 0.4 * cp.abs(np.cos(h1 + cp.deg2rad(35)))
)
c1_4 = C1 ** 4
F = cp.sqrt(c1_4 / (c1_4 + 1900))
SL = cp.where(L1 < 16, 0.511, 0.040975 * L1 / (1. + 0.01765 * L1))
SC = 0.638 + 0.0638 * C1 / (1. + 0.0131 * C1)
SH = SC * (F * T + 1 - F)
dE2 = (dL / (kL * SL)) ** 2
dE2 += (dC / (kC * SC)) ** 2
dE2 += dH2 / (SH ** 2)
return cp.sqrt(cp.maximum(dE2, 0, out=dE2), out=dE2)
Params.cur_dir = 'M3DLF_' + sample + '/Input'
Params.out_dir = 'M3DLF_' + sample + '/Output'
class viewpoint:
pos_x = 0
pos_y = 0
lon = 0
lat = 0
diag = 0
fov = 0
viewpoint.pos_x = 0
viewpoint.pos_y = 0
viewpoint.lon = cp.deg2rad(0)
viewpoint.lat = cp.deg2rad(0)
viewpoint.diag = 860
viewpoint.fov = pi / 3
viewpoint.fov = round(viewpoint.fov * 10000)
viewpoint.fov = viewpoint.fov / 10000
LFDisp_forward = cp.zeros(3 * Params.LFU_W * Params.HEIGHT * Params.WIDTH)
LFDisp_backward = cp.zeros(3 * Params.LFU_W * Params.HEIGHT * Params.WIDTH)
x = cp.arange(Params.HEIGHT)
y = cp.arange(Params.WIDTH)
TY, TX = cp.meshgrid(x, y)