def Huniaxialanisotropy(self):
"""
Calculate uniaxial anisotropy field.
"""
mx_ = self.magnet.mx
my_ = self.magnet.my
mz_ = self.magnet.mz
Ku_ = self.magnet.Ku
thetaK_ = self.magnet.thetaK * degree
phiK_ = self.magnet.phiK * degree
Kux_ = Ku_ * np.sin(thetaK_) * np.cos(phiK_)
Kuy_ = Ku_ * np.sin(thetaK_) * np.sin(phiK_)
Kuz_ = Ku_ * np.cos(thetaK_)
Hux_ = 2 * Kux_ / (self.magnet.Ms + 10**-10) * self.magnet.mask
Huy_ = 2 * Kuy_ / (self.magnet.Ms + 10**-10) * self.magnet.mask
Huz_ = 2 * Kuz_ / (self.magnet.Ms + 10**-10) * self.magnet.mask
Hu_ = Hux_ * mx_ + Huy_ * my_ + Huz_ * mz_
self.hux = Hu_ * np.sin(thetaK_) * np.cos(phiK_)
self.huy = Hu_ * np.sin(thetaK_) * np.sin(phiK_)
self.huz = Hu_ * np.cos(thetaK_)
def HaversineLocal(busMatrix, lineMatrix, haversine=True):
MatrizOnibus = cp.copy(busMatrix)
MatrizLinhas = cp.copy(lineMatrix)
MatrizLinhas = cp.dsplit(MatrizLinhas, 2)
MatrizOnibus = cp.dsplit(MatrizOnibus, 2)
infVector = cp.squeeze(cp.sum(cp.isnan(MatrizLinhas[0]), axis=1), axis=-1)
MatrizLinhas[0] = cp.expand_dims(MatrizLinhas[0], axis=-1)
MatrizLinhas[1] = cp.expand_dims(MatrizLinhas[1], axis=-1)
MatrizOnibus[0] = cp.expand_dims(MatrizOnibus[0], axis=-1)
MatrizOnibus[1] = cp.expand_dims(MatrizOnibus[1], axis=-1)
MatrizOnibus[0] *= cp.pi / 180
MatrizOnibus[1] *= cp.pi / 180
MatrizLinhas[1] = cp.transpose(MatrizLinhas[1], [2, 3, 0, 1]) * cp.pi / 180
MatrizLinhas[0] = cp.transpose(MatrizLinhas[0], [2, 3, 0, 1]) * cp.pi / 180
# Haversine or euclidian, based on <haversine>
if haversine:
results = 1000*2*6371.0088*cp.arcsin(
cp.sqrt(
(cp.sin((MatrizOnibus[0] - MatrizLinhas[0])*0.5)**2 + \
cp.cos(MatrizOnibus[0])* cp.cos(MatrizLinhas[0]) * cp.sin((MatrizOnibus[1] - MatrizLinhas[1])*0.5)**2)
))
else:
results = cp.sqrt((MatrizOnibus[0] - MatrizLinhas[0])**2 +
(MatrizOnibus[1] - MatrizLinhas[1])**2)
return results, infVector
def geodistance_cp(lng1, lat1, lng2, lat2):
lng1, lat1, lng2, lat2 = map(cp.radians, [lng1, lat1, lng2, lat2])
dlon = lng2 - lng1
dlat = lat2 - lat1
a = cp.sin(dlat / 2)**2 + cp.cos(lat1) * cp.cos(lat2) * cp.sin(dlon / 2)**2
dis = 2 * cp.arcsin(cp.sqrt(a)) * 6371 * 1000
return dis
def take_filter(N, filter):
os = 4
d = 0.5
Ne = os * N
t = cp.arange(0, Ne / 2 + 1) / Ne
if (filter == 'ramp'):
wfa = Ne * 0.5 * wint(12, t) # .*(t/(2*d)<=1)%compute the weigths
elif (filter == 'shepp-logan'):
wfa = Ne * 0.5 * wint(12, t) * cp.sinc(t / (2 * d)) * (t / d <= 2)
elif (filter == 'cosine'):
wfa = Ne * 0.5 * wint(12, t) * cp.cos(cp.pi * t /
(2 * d)) * (t / d <= 1)
elif (filter == 'cosine2'):
wfa = Ne * 0.5 * wint(12, t) * (cp.cos(cp.pi * t /
(2 * d)))**2 * (t / d <= 1)
elif (filter == 'hamming'):
wfa = Ne * 0.5 * wint(
12, t) * (.54 + .46 * cp.cos(cp.pi * t / d)) * (t / d <= 1)
elif (filter == 'hann'):
wfa = Ne * 0.5 * wint(
12, t) * (1 + np.cos(cp.pi * t / d)) / 2.0 * (t / d <= 1)
elif (filter == 'parzen'):
wfa = Ne * 0.5 * wint(12, t) * pow(1 - t / d, 3) * (t / d <= 1)
wfa = wfa * (wfa >= 0)
wfamid = cp.array([2 * wfa[0]])
tmp = wfa
wfa = cp.concatenate((cp.flipud(tmp[1:]), wfamid))
wfa = cp.concatenate((wfa, tmp[1:]))
wfa = wfa[:-1].astype('float32')
return wfa
def ripple(x, y, z, t):
f = cp.sin(x + t / 5) + cp.sin(y + t / 5)
r = cp.abs(z - f) < 0.2
f = cp.cos(x + t / 5) + cp.cos(y + t / 5)
g = cp.abs(z - f) < 0.2
b = g * 0
return r * 10, g * 10, b
def _cubic_smooth_coeff(signal, lamb):
rho, omega = _coeff_smooth(lamb)
cs = 1 - 2 * rho * cos(omega) + rho * rho
K = len(signal)
yp = zeros((K, ), signal.dtype.char)
k = arange(K)
yp[0] = (_hc(0, cs, rho, omega) * signal[0] +
add(_hc(k + 1, cs, rho, omega) * signal))
yp[1] = (_hc(0, cs, rho, omega) * signal[0] +
_hc(1, cs, rho, omega) * signal[1] +
add(_hc(k + 2, cs, rho, omega) * signal))
for n in range(2, K):
yp[n] = (cs * signal[n] + 2 * rho * cos(omega) * yp[n - 1] -
rho * rho * yp[n - 2])
y = zeros((K, ), signal.dtype.char)
y[K - 1] = add(
(_hs(k, cs, rho, omega) + _hs(k + 1, cs, rho, omega)) * signal[::-1])
y[K - 2] = add((_hs(k - 1, cs, rho, omega) + _hs(k + 2, cs, rho, omega)) *
signal[::-1])
for n in range(K - 3, -1, -1):
y[n] = (cs * yp[n] + 2 * rho * cos(omega) * y[n + 1] -
rho * rho * y[n + 2])
return y
def CheckIfEscaped(photon_state, tau_atm, escaped_mu):
######################################################################################
# This checks if a photon has escaped, calculates the momentum that photon takes with it
# then removes that photon from the list.
#
# photon_state -- A CuPy array consisting of [x,y,z,phi,theta,lambda] for each photon.
# tau_atm -- The depth of the atmosphere.
######################################################################################
# Looks for all the photons above the atmosphere.
escaped_photons = cp.where(photon_state[:, 2] >= tau_atm)[0]
momentum_transfer = 0
if len(escaped_photons) > 0:
# Find the angles the particles escaped at
escaped_mu += cp.cos(photon_state[escaped_photons, 4]).tolist()
# Calculates the momentum transferred, this is the difference between the initial z momentum and the final z momentum
momentum_transfer = float(
cp.sum(h * (-cp.cos(photon_state[escaped_photons, 4])) /
photon_state[escaped_photons, 5]))
# Remove the escaped photons
photon_state = RemovePhotons(photon_state, escaped_photons)
return photon_state, momentum_transfer, escaped_mu
def latlong2osgbgrid_cupy(lat, long, input_degrees=True):
'''
Converts latitude and longitude (ellipsoidal) coordinates into northing and easting (grid) coordinates, using a Transverse Mercator projection.
Inputs:
lat: latitude coordinate (north)
long: longitude coordinate (east)
input_degrees: if True (default), interprets the coordinates as degrees; otherwise, interprets coordinates as radians
Output:
(northing, easting)
'''
if input_degrees:
lat = lat * cp.pi / 180
long = long * cp.pi / 180
a = 6377563.396
b = 6356256.909
e2 = (a**2 - b**2) / a**2
N0 = -100000 # northing of true origin
E0 = 400000 # easting of true origin
F0 = .9996012717 # scale factor on central meridian
phi0 = 49 * cp.pi / 180 # latitude of true origin
lambda0 = -2 * cp.pi / 180 # longitude of true origin and central meridian
sinlat = cp.sin(lat)
coslat = cp.cos(lat)
tanlat = cp.tan(lat)
latdiff = lat - phi0
longdiff = long - lambda0
n = (a - b) / (a + b)
nu = a * F0 * (1 - e2 * sinlat**2)**-.5
rho = a * F0 * (1 - e2) * (1 - e2 * sinlat**2)**-1.5
eta2 = nu / rho - 1
M = b * F0 * (
(1 + n + 5 / 4 * (n**2 + n**3)) * latdiff -
(3 *
(n + n**2) + 21 / 8 * n**3) * cp.sin(latdiff) * cp.cos(lat + phi0) +
15 / 8 * (n**2 + n**3) * cp.sin(2 * (latdiff)) * cp.cos(2 *
(lat + phi0)) -
35 / 24 * n**3 * cp.sin(3 * (latdiff)) * cp.cos(3 * (lat + phi0)))
I = M + N0
II = nu / 2 * sinlat * coslat
III = nu / 24 * sinlat * coslat**3 * (5 - tanlat**2 + 9 * eta2)
IIIA = nu / 720 * sinlat * coslat**5 * (61 - 58 * tanlat**2 + tanlat**4)
IV = nu * coslat
V = nu / 6 * coslat**3 * (nu / rho - cp.tan(lat)**2)
VI = nu / 120 * coslat**5 * (5 - 18 * tanlat**2 + tanlat**4 + 14 * eta2 -
58 * tanlat**2 * eta2)
northing = I + II * longdiff**2 + III * longdiff**4 + IIIA * longdiff**6
easting = E0 + IV * longdiff + V * longdiff**3 + VI * longdiff**5
return (northing, easting)
def rotate(x, theta, reverse=False):
"""Rotate coordinates with respect to the angle theta
"""
R = cp.array([[cp.cos(theta), -cp.sin(theta)],
[cp.sin(theta), cp.cos(theta)]])
if (reverse):
R = R.swapaxes(0, 1)
xr = cp.zeros(x.shape, dtype='float32')
xr[:, 0] = R[1, 0] * x[:, 1] + R[1, 1] * x[:, 0]
xr[:, 1] = R[0, 0] * x[:, 1] + R[0, 1] * x[:, 0]
return xr
def create_fwd(P):
# convolution function
fZ = cp.fft.fftshift(fzeta_loop_weights(
P.Ntheta, P.Nrho, 2*P.beta, P.g-cp.log(P.am), 0, 4))
# (lp2C1,lp2C2), transformed log-polar to Cartesian coordinates
tmp1 = cp.outer(cp.exp(cp.array(P.rhosp)), cp.cos(cp.array(P.thsp))).flatten()
tmp2 = cp.outer(cp.exp(cp.array(P.rhosp)), cp.sin(cp.array(P.thsp))).flatten()
lp2C1 = [None]*P.Nspan
lp2C2 = [None]*P.Nspan
for k in range(P.Nspan):
lp2C1[k] = ((tmp1-(1-P.aR))*cp.cos(k*P.beta+P.beta/2) -
tmp2*cp.sin(k*P.beta+P.beta/2))/P.aR
lp2C2[k] = ((tmp1-(1-P.aR))*cp.sin(k*P.beta+P.beta/2) +
tmp2*cp.cos(k*P.beta+P.beta/2))/P.aR
lp2C2[k] *= (-1) # adjust for Tomopy
cids = cp.where((lp2C1[k]**2+lp2C2[k]**2) <= 1)[0]
lp2C1[k] = lp2C1[k][cids]
lp2C2[k] = lp2C2[k][cids]
# pids, index in polar grids after splitting by spans
pids = [None]*P.Nspan
[s0, th0] = cp.meshgrid(P.s, P.proj)
th0 = th0.flatten()
s0 = s0.flatten()
for k in range(0, P.Nspan):
pids[k] = cp.where((th0 >= k*P.beta-P.beta/2) &
(th0 < k*P.beta+P.beta/2))[0]
# (p2lp1,p2lp2), transformed polar to log-polar coordinates
p2lp1 = [None]*P.Nspan
p2lp2 = [None]*P.Nspan
for k in range(P.Nspan):
th00 = th0[pids[k]]-k*P.beta
s00 = s0[pids[k]]
p2lp1[k] = th00
p2lp2[k] = np.log(s00*P.aR+(1-P.aR)*np.cos(th00))
# adapt for gpu interp
for k in range(0, P.Nspan):
lp2C1[k] = (lp2C1[k]+1)/2*(P.N-1)
lp2C2[k] = (lp2C2[k]+1)/2*(P.N-1)
p2lp1[k] = (p2lp1[k]-P.thsp[0])/(P.thsp[-1]-P.thsp[0])*(P.Ntheta-1)
p2lp2[k] = (p2lp2[k]-P.rhosp[0])/(P.rhosp[-1]-P.rhosp[0])*(P.Nrho-1)
const = cp.sqrt(P.N*P.osangles/P.Nproj)*cp.pi/4 / \
P.aR/cp.sqrt(2) # adjust constant
fZgpu = fZ[:, :P.Ntheta//2+1]*const
if(P.interp_type == 'cubic'):
fZgpu = fZgpu/(P.B3com[:, :P.Ntheta//2+1])
Pfwd0 = Pfwd(fZgpu, lp2C1, lp2C2, p2lp1, p2lp2, cids, pids)
# array representation
parsi, parsf = savePfwdpars(Pfwd0)
return Pfwd0, parsi, parsf
def nonlin_evo(psiP2, psiP1, psi0, psiM1, psiM2, c0, c2, c4, V, p, dt, spin_f):
# Calculate densities:
n = abs(psiP2) ** 2 + abs(psiP1) ** 2 + abs(psi0) ** 2 + abs(psiM1) ** 2 + abs(psiM2) ** 2
A00 = 1 / cp.sqrt(5) * (psi0 ** 2 - 2 * psiP1 * psiM1 + 2 * psiP2 * psiM2)
fz = 2 * (abs(psiP2) ** 2 - abs(psiM2) ** 2) + abs(psiP1) ** 2 - abs(psiM1) ** 2
# Evolve spin-singlet term -c4*(n^2-|alpha|^2)
S = cp.sqrt(n ** 2 - abs(A00) ** 2)
S = cp.nan_to_num(S)
cosT = cp.cos(c4 * S * dt)
sinT = cp.sin(c4 * S * dt) / S
sinT[S == 0] = 0 # Corrects division by 0
Wfn = [psiP2 * cosT + 1j * (n * psiP2 - A00 * cp.conj(psiM2)) * sinT,
psiP1 * cosT + 1j * (n * psiP1 + A00 * cp.conj(psiM1)) * sinT,
psi0 * cosT + 1j * (n * psi0 - A00 * cp.conj(psi0)) * sinT,
psiM1 * cosT + 1j * (n * psiM1 + A00 * cp.conj(psiP1)) * sinT,
psiM2 * cosT + 1j * (n * psiM2 - A00 * cp.conj(psiP2)) * sinT]
# Calculate spin vectors
fp = cp.sqrt(6) * (Wfn[1] * cp.conj(Wfn[2]) + Wfn[2] * cp.conj(Wfn[3])) + 2 * (Wfn[3] * cp.conj(Wfn[4]) +
Wfn[0] * cp.conj(Wfn[1]))
F = cp.sqrt(fz ** 2 + abs(fp) ** 2)
# Calculate cos, sin and Qfactor terms:
C1, S1 = cp.cos(c2 * F * dt), cp.sin(c2 * F * dt)
C2, S2 = cp.cos(2 * c2 * F * dt), cp.sin(2 * c2 * F * dt)
Qfactor = 1j * (-4 / 3 * S1 + 1 / 6 * S2)
Q2factor = (-5 / 4 + 4 / 3 * C1 - 1 / 12 * C2)
Q3factor = 1j * (1 / 3 * S1 - 1 / 6 * S2)
Q4factor = (1 / 4 - 1 / 3 * C1 + 1 / 12 * C2)
fzQ = cp.nan_to_num(fz / F)
fpQ = cp.nan_to_num(fp / F)
Qpsi = calc_Qpsi(fzQ, fpQ, Wfn)
Q2psi = calc_Qpsi(fzQ, fpQ, Qpsi)
Q3psi = calc_Qpsi(fzQ, fpQ, Q2psi)
Q4psi = calc_Qpsi(fzQ, fpQ, Q3psi)
# Evolve spin term c2 * F^2
for ii in range(len(Wfn)):
Wfn[ii] += Qfactor * Qpsi[ii] + Q2factor * Q2psi[ii] + Q3factor * Q3psi[ii] + Q4factor * Q4psi[ii]
# Evolve (c0+c4)*n^2 + (V + pm)*n:
for ii in range(len(Wfn)):
mF = spin_f - ii
Wfn[ii] *= cp.exp(-1j * dt * ((c0 + c4) * n + V + p * mF))
return Wfn
def apply(self, helper, qubits, targets):
n_qubits = helper["n_qubits"]
i = helper["indices"]
theta = self.theta
for target in slicing(targets, n_qubits):
newq = cupy.zeros_like(qubits)
newq[(i & (1 << target)) == 0] = (
cupy.cos(theta / 2) * qubits[(i & (1 << target)) == 0] +
-cupy.sin(theta / 2) * qubits[(i & (1 << target)) != 0])
newq[(i & (1 << target)) != 0] = (
cupy.sin(theta / 2) * qubits[(i & (1 << target)) == 0] +
cupy.cos(theta / 2) * qubits[(i & (1 << target)) != 0])
qubits = newq
return qubits
def random_in_unit_sphere_list(size: int) -> Vec3List:
u = random_float_list(size)
v = random_float_list(size)
theta = u * 2 * cp.pi
phi = cp.arccos(2 * v - 1)
r = cp.cbrt(random_float_list(size))
sinTheta = cp.sin(theta)
cosTheta = cp.cos(theta)
sinPhi = cp.sin(phi)
cosPhi = cp.cos(phi)
x = r * sinPhi * cosTheta
y = r * sinPhi * sinTheta
z = r * cosPhi
return Vec3List(cp.transpose(cp.array([x, y, z])))
def rotshift3D_spline(v, phi=0, 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
rot_origin = 0.5*np.array(v.shape)
rot_rad = -phi*np.pi/180.0
rot_matrix = np.array([[np.cos(rot_rad), np.sin(rot_rad), 0],
[-np.sin(rot_rad),np.cos(rot_rad), 0],
[0 , 0 , 1]])
offset = -(rot_origin-rot_origin.dot(rot_matrix)).dot(np.linalg.inv(rot_matrix))
offset = offset - shifts
transformed_v = ndimage.interpolation.affine_transform(v,rot_matrix,offset=offset,mode=mode)
return transformed_v
def random_in_unit_sphere():
u = random_float()
v = random_float()
theta = u * 2 * cp.pi
phi = cp.arccos(2 * v - 1)
r = cp.cbrt(random_float())
sinTheta = cp.sin(theta)
cosTheta = cp.cos(theta)
sinPhi = cp.sin(phi)
cosPhi = cp.cos(phi)
x = r * sinPhi * cosTheta
y = r * sinPhi * sinTheta
z = r * cosPhi
return Vec3(x, y, z)
def run_cupy(lat2, lon2):
import cupy as cp
# Allocate temporary arrays
size = len(lat2)
a = cp.empty(size, dtype='float64')
dlat = cp.empty(size, dtype='float64')
dlon = cp.empty(size, dtype='float64')
# Transfer inputs to the GPU
lat2 = cp.array(lat2)
lon2 = cp.array(lon2)
# Begin computation
lat1 = 0.70984286
lon1 = 1.23892197
MILES_CONST = 3959.0
cp.subtract(lat2, lat1, out=dlat)
cp.subtract(lon2, lon1, out=dlon)
# dlat = sin(dlat / 2.0) ** 2.0
cp.divide(dlat, 2.0, out=dlat)
cp.sin(dlat, out=dlat)
cp.multiply(dlat, dlat, out=dlat)
# a = cos(lat1) * cos(lat2)
lat1_cos = math.cos(lat1)
cp.cos(lat2, out=a)
cp.multiply(a, lat1_cos, out=a)
# a = a + sin(dlon / 2.0) ** 2.0
cp.divide(dlon, 2.0, out=dlon)
cp.sin(dlon, out=dlon)
cp.multiply(dlon, dlon, out=dlon)
cp.multiply(a, dlon, out=a)
cp.add(dlat, a, out=a)
c = a
cp.sqrt(a, out=a)
cp.arcsin(a, out=a)
cp.multiply(a, 2.0, out=c)
mi = c
cp.multiply(c, MILES_CONST, out=mi)
# Transfer outputs back to CPU
a = cp.asnumpy(a)
return a
def spherical_cosmask(n,mask_radius, edge_width, origin=None):
"""mask = spherical_cosmask(n, mask_radius, edge_width, origin)
"""
if type(n) is int:
n = np.array([n])
sz = np.array([1, 1, 1])
sz[0:np.size(n)] = n[:]
szl = -np.floor(sz/2)
szh = szl + sz
x,y,z = np.meshgrid( np.arange(szl[0],szh[0]),
np.arange(szl[1],szh[1]),
np.arange(szl[2],szh[2]), indexing='ij', sparse=True)
r = np.sqrt(x*x + y*y + z*z)
m = np.zeros(sz.tolist())
# edgezone = np.where( (x*x + y*y + z*z >= mask_radius) & (x*x + y*y + z*z <= np.square(mask_radius + edge_width)))
edgezone = np.all( [ (x*x + y*y + z*z >= mask_radius), (x*x + y*y + z*z <= np.square(mask_radius + edge_width))], axis=0)
m[edgezone] = 0.5 + 0.5*np.cos( 2*np.pi*(r[edgezone] - mask_radius) / (2*edge_width))
m[ np.all( [ (x*x + y*y + z*z <= mask_radius*mask_radius) ], axis=0 ) ] = 1
# m[ np.where(x*x + y*y + z*z <= mask_radius*mask_radius)] = 1
return m
def _log_polar_mapping(output_coords, k_angle, k_radius, center):
"""Inverse mapping function to convert from Cartesian to polar coordinates
Parameters
----------
output_coords : ndarray
`(M, 2)` array of `(col, row)` coordinates in the output image
k_angle : float
Scaling factor that relates the intended number of rows in the output
image to angle: ``k_angle = nrows / (2 * np.pi)``
k_radius : float
Scaling factor that relates the radius of the circle bounding the
area to be transformed to the intended number of columns in the output
image: ``k_radius = width / math.log(radius)``
center : tuple (row, col)
Coordinates that represent the center of the circle that bounds the
area to be transformed in an input image.
Returns
-------
coords : ndarray
`(M, 2)` array of `(col, row)` coordinates in the input image that
correspond to the `output_coords` given as input.
"""
angle = output_coords[:, 1] / k_angle
rr = ((cp.exp(output_coords[:, 0] / k_radius)) * cp.sin(angle)) + center[0]
cc = ((cp.exp(output_coords[:, 0] / k_radius)) * cp.cos(angle)) + center[1]
coords = cp.column_stack((cc, rr))
return coords
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 cos(a, cuda=False):
if cuda:
res = cp.cos(a)
cp.cuda.Stream.null.synchronize()
return res
else:
return np.cos(a)
def fzeta_loop_weights(Ntheta, Nrho, betas, rhos, a, osthlarge):
krho = cp.arange(-Nrho/2, Nrho/2, dtype='float32')
Nthetalarge = osthlarge*Ntheta
thsplarge = cp.arange(-Nthetalarge/2, Nthetalarge/2,
dtype='float32') / Nthetalarge*betas
fZ = cp.zeros([Nrho, Nthetalarge], dtype='complex64')
h = cp.ones(Nthetalarge, dtype='float32')
# correcting = 1+[-3 4 -1]/24correcting(1) = 2*(correcting(1)-0.5)
# correcting = 1+array([-23681,55688,-66109,57024,-31523,9976,-1375])/120960.0correcting[0] = 2*(correcting[0]-0.5)
correcting = 1+cp.array([-216254335, 679543284, -1412947389, 2415881496, -3103579086,
2939942400, -2023224114, 984515304, -321455811, 63253516, -5675265])/958003200.0
correcting[0] = 2*(correcting[0]-0.5)
h[0] = h[0]*(correcting[0])
for j in range(1, len(correcting)):
h[j] = h[j]*correcting[j]
h[-1-j+1] = h[-1-j+1]*(correcting[j])
for j in range(len(krho)):
fcosa = pow(cp.cos(thsplarge), (-2*cp.pi*1j*krho[j]/rhos-1-a))
fZ[j, :] = cp.fft.fftshift(cp.fft.fft(cp.fft.fftshift(h*fcosa)))
fZ = fZ[:, Nthetalarge//2-Ntheta//2:Nthetalarge//2+Ntheta//2]
fZ = fZ*(thsplarge[1]-thsplarge[0])
# put imag to 0 for the border
fZ[0] = 0
fZ[:, 0] = 0
return fZ
def signal_func(ts):
# Calculate adjusted center frequencies, according to chirp
chirp_phase = 2 * xp.pi * (
(f_start - self.fch1) * ts + 0.5 * drift_rate * ts**2)
if not self.ascending:
chirp_phase = -chirp_phase
return level * xp.cos(chirp_phase + phase)
def jackson(
num_moments,
precision=32,
):
"""
This function generates the Jackson kernel for a given number of
Chebyscev moments
Parameters
----------
num_moments: (uint)
number of Chebyshev moments
Return
------
jackson_kernel: cupy array(shape=(num_moments,), dtype=tf_float)
Note
----
See .. _The Kernel Polynomial Method:
https://arxiv.org/pdf/cond-mat/0504627.pdf for more details
"""
cp_float = cp.float64
if precision == 32:
cp_float = cp.float32
kernel_moments = cp.arange(num_moments, dtype=cp_float)
norm = cp.pi / (num_moments + 1)
phase_vec = norm * kernel_moments
kernel = (num_moments - kernel_moments + 1) * cp.cos(phase_vec)
kernel = kernel + cp.sin(phase_vec) / cp.tan(norm)
kernel = kernel / (num_moments + 1)
return kernel
def updateGeometry(self):
# GPU variables
self._psi = cp.zeros(self.shape, dtype=cp.complex64)
self._phi = cp.zeros(self.shape, dtype=cp.uint8)
self._theta = cp.zeros(self.shape, dtype=cp.float32)
self._rho = cp.zeros(self.shape, dtype=cp.float32)
alpha = cp.cos(cp.radians(self.phis, dtype=cp.float32))
x = alpha*(cp.arange(self.width, dtype=cp.float32) -
cp.float64(self.xs))
y = cp.arange(self.height, dtype=cp.float32) - cp.float32(self.ys)
qx = self.qprp * x
qy = self.qprp * y
self._iqx = (1j * qx).astype(cp.complex64)
self._iqy = (1j * qy).astype(cp.complex64)
self._iqxz = (1j * self.qpar * x * x).astype(cp.complex64)
self._iqyz = (1j * self.qpar * y * y).astype(cp.complex64)
self.outeratan2f(y, x, self._theta)
self.outerhypot(qy, qx, self._rho)
# CPU variables
self.phi = self._phi.get()
self.iqx = self._iqx.get()
self.iqy = self._iqy.get()
self.theta = self._theta.get().astype(cp.float64)
self.qr = self._rho.get().astype(cp.float64)
self.sigUpdateGeometry.emit()
def test_elementwise_trinary(self):
desc_a = cutensor.create_tensor_descriptor(self.a, ct.OP_SQRT)
desc_b = cutensor.create_tensor_descriptor(self.b, ct.OP_TANH)
desc_c = cutensor.create_tensor_descriptor(self.c, ct.OP_COS)
d = cutensor.elementwise_trinary(self.alpha,
self.a,
desc_a,
self.mode_a,
self.beta,
self.b,
desc_b,
self.mode_b,
self.gamma,
self.c,
desc_c,
self.mode_c,
op_AB=ct.OP_ADD,
op_ABC=ct.OP_MUL)
testing.assert_allclose((self.alpha * cupy.sqrt(self.a_transposed) +
self.beta * cupy.tanh(self.b_transposed)) *
self.gamma * cupy.cos(self.c),
d,
rtol=1e-6,
atol=1e-6)
def setRandomMagnetization(self):
"""
Set initial magnetization to a random state.
"""
self.thetaM0 = np.random.uniform(0, 180, size=self.mask.shape)
self.phiM0 = np.random.uniform(0, 360, size=self.mask.shape)
thetaM0_ = self.thetaM0 * degree
phiM0_ = self.phiM0 * degree
self.mx = np.zeros(shape=(self.mask.shape))
self.my = np.zeros(shape=(self.mask.shape))
self.mz = np.zeros(shape=(self.mask.shape))
self.mx = self.mask * np.sin(thetaM0_) * np.cos(phiM0_)
self.my = self.mask * np.sin(thetaM0_) * np.sin(phiM0_)
self.mz = self.mask * np.cos(thetaM0_)
def apply_kernel(moments,
kernel,
num_moments,
num_vecs,
extra_points=1,
precision=32):
"""
Parameters
----------
Apply a given kernel in a given array of moments.
Return the cosine transform of type III.
"""
num_points = extra_points + num_moments
if kernel is not None:
moments = moments * kernel
mu_ext = cp.zeros(num_points, dtype=moments.dtype)
mu_ext[0:num_moments] = moments
smooth_moments = dctIII(mu_ext, precision)
points = cp.arange(0, num_points)
ek = cp.cos(cp.pi * (points + 0.5) / num_points)
gk = cp.pi * cp.sqrt(1. - ek**2)
rho = cp.divide(smooth_moments, gk)
return ek, rho
def sphere(self, n, diameter=None):
if n is None:
dia = diameter
else:
dia = self.sphere_dia[n]
s = cp.pi * self.rad * dia / self.size
s[s == 0] = 1.e-5
return ((cp.sin(s) - s * cp.cos(s)) / s**3).ravel()
def _lossP(self, A, P):
floor = 1.0E-6
inum = cupy.array(1.0j, cupy.complex64)
loss = (self.alpha * (1 - cupy.cos(P['y'] - P['x']))).mean()
grad = self._overlapadd(
cupy.fft.irfft(self.alpha * cupy.sin(P['y'] - P['x']) / cupy.fmax(
A['x'], floor) * cupy.exp(inum * (P['x'] - 0.5 * cupy.pi))) *
self.norm)
return loss, grad
def random_in_unit_sphere() -> Vec3:
"""
This method is modified from:
https://karthikkaranth.me/blog/generating-random-points-in-a-sphere/#better-choice-of-spherical-coordinates
"""
u = random_float()
v = random_float()
theta = u * 2 * cp.pi
phi = cp.arccos(2 * v - 1)
r = cp.cbrt(random_float())
sinTheta = cp.sin(theta)
cosTheta = cp.cos(theta)
sinPhi = cp.sin(phi)
cosPhi = cp.cos(phi)
x = r * sinPhi * cosTheta
y = r * sinPhi * sinTheta
z = r * cosPhi
return Vec3(x, y, z)
def testGetstateSetstate(self):
nDims = 32 # need multiple of 8, because of sse
nClass = 4
size = 20
labels = _RGEN.random_integers(0, nClass - 1, size)
samples = np.zeros((size, nDims), dtype=_DTYPE)
centers = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
for i in range(0, size):
t = 6.28 * _RGEN.random_sample()
samples[i][0] = 2 * centers[labels[i]][0] + 0.5*_RGEN.rand() * np.cos(t)
samples[i][1] = 2 * centers[labels[i]][1] + 0.5*_RGEN.rand() * np.sin(t)
classifier = svm_dense(0, nDims, seed=_SEED, probability = True)
for y, xList in zip(labels, samples):
x = np.array(xList, dtype=_DTYPE)
classifier.add_sample(float(y), x)
classifier.train(gamma=1.0/3.0, C=100, eps=1e-1)
classifier.cross_validate(2, gamma=0.5, C=10, eps=1e-3)
s1 = classifier.__getstate__()
h1 = hashlib.md5(s1).hexdigest()
classifier2 = svm_dense(0, nDims)
classifier2.__setstate__(s1)
s2 = classifier2.__getstate__()
h2 = hashlib.md5(s2).hexdigest()
self.assertEqual(h1, h2)
with open("svm_test.bin", "wb") as f:
pickle.dump(classifier, f)
with open("svm_test.bin", "rb") as f:
classifier3 = pickle.load(f)
s3 = classifier3.__getstate__()
h3 = hashlib.md5(s3).hexdigest()
self.assertEqual(h1, h3)
os.unlink("svm_test.bin")
