def compute_displace(self, amp, r, buffer):
r = self.map_coordinates(r)
ex = cp.exp(self._iqx * r.x() + self._iqxz * r.z(),
dtype=cp.complex64)
ey = cp.exp(self._iqy * r.y() + self._iqyz * r.z(),
dtype=cp.complex64)
cp.outer(amp * ey, ex, buffer)
def wint(n, t):
N = len(t)
s = cp.linspace(1e-40, 1, n)
# Inverse vandermonde matrix
tmp1 = cp.arange(n)
tmp2 = cp.arange(1, n + 2)
iv = cp.linalg.inv(cp.exp(cp.outer(tmp1, cp.log(s))))
u = cp.diff(
cp.exp(cp.outer(tmp2, cp.log(s))) *
cp.tile(1.0 / tmp2[..., cp.newaxis],
[1, n])) # integration over short intervals
W1 = cp.matmul(iv, u[1:n + 1, :]) # x*pn(x) term
W2 = cp.matmul(iv, u[0:n, :]) # const*pn(x) term
# Compensate for overlapping short intervals
tmp1 = cp.arange(1, n)
tmp2 = (n - 1) * cp.ones((N - 2 * (n - 1) - 1))
tmp3 = cp.arange(n - 1, 0, -1)
p = 1 / cp.concatenate((tmp1, tmp2, tmp3))
w = cp.zeros(N)
for j in range(N - n + 1):
# Change coordinates, and constant and linear parts
W = ((t[j + n - 1] - t[j])**2) * W1 + (t[j + n - 1] - t[j]) * t[j] * W2
for k in range(n - 1):
w[j:j + n] = w[j:j + n] + p[j + k] * W[:, k]
wn = w
wn[-40:] = (w[-40]) / (N - 40) * cp.arange(N - 40, N)
return wn
def train(self, x):
self.n = self.n + 1
# update norms
self.norm_max[x > self.norm_max] = x[x > self.norm_max]
self.norm_min[x < self.norm_min] = x[x < self.norm_min]
# 0-1 normalize
x = (x - self.norm_min) / (self.norm_max - self.norm_min +
0.0000000000000001)
if self.params.corruption_level > 0.0:
tilde_x = self.get_corrupted_input(x, self.params.corruption_level)
else:
tilde_x = x
y = self.get_hidden_values(tilde_x)
z = self.get_reconstructed_input(y)
L_h2 = x - z
L_h1 = cupy.dot(L_h2, self.W) * y * (1 - y)
L_vbias = L_h2
L_hbias = L_h1
L_W = cupy.outer(tilde_x.T, L_h1) + cupy.outer(L_h2.T, y)
self.W += self.params.lr * L_W
self.hbias += self.params.lr * cupy.mean(L_hbias, axis=0)
self.vbias += self.params.lr * cupy.mean(L_vbias, axis=0)
return cupy.sqrt(cupy.mean(
L_h2**2)) #the RMSE reconstruction error during training
def build_cbow_model(self):
#Iterate over epochs
for k in range(self.epochs):
print("We are at epoch : ", k + 1)
#For each training example
for i in range(len(self.X_train)):
#Forward propagation of the CBOW network-----
#Take average
x = np.zeros((self.vocab_size, 1))
for word in self.X_train[i]:
x += self.one_hot(self.words_to_int[word])
x /= len(self.X_train[i])
h = np.dot(self.w_hidden.T, x)
'''
h = np.zeros((self.dim, 1))
for word in self.X_train[i]:
h += np.dot(self.w_hidden.T, self.one_hot(self.words_to_int[word]))
h/=len(self.X_train[i])
print ("Forward propagation done...", i, k)
'''
print("-----------")
print("Forward propagation done CBOW...: ", i, "Epoch: ",
k + 1)
#h = np.dot(self.w_hidden.T , onehot(X_train[i])
u = np.dot(self.w_output.T, h)
pred = self.softmax(u)
#Backward propagation------
#err_sum = np.zeros((self.vocab_size,1))
err = pred - self.one_hot(self.words_to_int[self.Y_train[i]])
print("Calculated error..", i, k + 1)
#Calculate dL/dW
dw_hidden = np.outer(x, np.dot(self.w_output, err))
#Calculate dL/dW'
dw_output = np.outer(h, err)
#Gradient descent
self.w_hidden += -self.lr * dw_hidden
self.w_output += -self.lr * dw_output
print("Gradient descent done..", i, k + 1)
#Update model after each epoch
print("Saving model...")
for key, value in self.words_to_int.items():
self.model[key] = self.w_hidden[value].reshape(
1, self.w_hidden.shape[1])
#Store model after every epoch
print("Model to npy file...")
np.save('./utils/cbow_new_' + str(k), self.model)
def build_skipgram_model(self):
#Iterate over epochs
print("No. of training samples are: ", len(self.X_train))
for k in range(self.epochs):
print("We are at epoch : ", k)
print()
print("No. of training samples: ", len(self.X_train))
#For each training example
for i in range(len(self.X_train)):
#Forward propagation of the SkipGram network-----
#Here X_train[i] is a Vx1 vector.
#print "self.X_train[i] is ", self.X_train[i]
#print "self.words_to_int[i] is ", self.words_to_int[self.X_train[i]]
h = np.dot(self.w_hidden.T,
self.one_hot(self.words_to_int[self.X_train[i]]))
output = np.dot(self.w_output.T, h)
pred = self.softmax(output)
print("---------------")
print("Forward propagation done SKIPGRAM...",
str(i) + "/" + str(len(self.X_train)), " Epoch: ",
str(k + 1) + "/" + str(self.epochs))
#Backward propagation------
err_sum = np.zeros((self.vocab_size, 1))
for word in self.Y_train[i]:
err_sum += (pred - self.one_hot(self.words_to_int[word]))
#err_sum/= self.vocab_size
print("Calculated error..", i, k + 1)
#Calculate dL/dW
dw_hidden = np.outer(
self.one_hot(self.words_to_int[self.X_train[i]]),
np.dot(self.w_output, err_sum))
#Calculate dL/dW'
dw_output = np.outer(h, err_sum)
#Gradient descent
self.w_hidden += -self.lr * dw_hidden
self.w_output += -self.lr * dw_output
print("Gradient descent done..", i, k + 1)
#Update model after each epoch
print("Saving model...")
for key, value in self.int_to_words.items():
self.model[value] = self.w_hidden[key].reshape(
1, self.w_hidden.shape[1])
#Store model after every epoch
#if (k!k%2==0):
print("Model to npy file...")
np.save('./utils/skipgram_' + str(k), self.model)
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 dftUpsample(imageCorr, upsampleFactor, xyShift):
"""
This performs a matrix multiply DFT around a small neighboring region of the inital
correlation peak. By using the matrix multiply DFT to do the Fourier upsampling, the
efficiency is greatly improved. This is adapted from the subfuction dftups found in
the dftregistration function on the Matlab File Exchange.
https://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation
The matrix multiplication DFT is from:
Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup, "Efficient subpixel
image registration algorithms," Opt. Lett. 33, 156-158 (2008).
http://www.sciencedirect.com/science/article/pii/S0045790612000778
Args:
imageCorr (complex valued ndarray):
Correlation image between two images in Fourier space.
upsampleFactor (int):
Scalar integer of how much to upsample.
xyShift (list of 2 floats):
Coordinates in the UPSAMPLED GRID around which to upsample.
These must be single-pixel IN THE UPSAMPLED GRID
Returns:
(ndarray):
Upsampled image from region around correlation peak.
"""
imageSize = imageCorr.shape
pixelRadius = 1.5
numRow = np.ceil(pixelRadius * upsampleFactor)
numCol = numRow
colKern = cp.exp(
(-1j * 2 * cp.pi / (imageSize[1] * upsampleFactor))
* cp.outer(
(cp.fft.ifftshift((cp.arange(imageSize[1]))) - cp.floor(imageSize[1] / 2)),
(cp.arange(numCol) - xyShift[1]),
)
)
rowKern = cp.exp(
(-1j * 2 * cp.pi / (imageSize[0] * upsampleFactor))
* cp.outer(
(cp.arange(numRow) - xyShift[0]),
(cp.fft.ifftshift(cp.arange(imageSize[0])) - cp.floor(imageSize[0] / 2)),
)
)
imageUpsample = cp.real(rowKern @ imageCorr @ colKern)
return imageUpsample
def policy_backward(eph, epdlogp):
""" backward pass. (eph is array of intermediate hidden states) """
dW2 = np.dot(eph.T, epdlogp).ravel()
dh = np.outer(epdlogp, model['W2'])
dh[eph <= 0] = 0 # backpro prelu
dW1 = np.dot(dh.T, epx)
return {'W1': dW1, 'W2': dW2}
def update(self,x):
self.N += 1
self.c += x
c_rt = x - self.c/self.N
self.c_r += c_rt
self.c_rs += c_rt**2
self.C += cupy.outer(c_rt,c_rt)
def corrDist(self):
c_rs_sqrt = cupy.sqrt(self.c_rs)
C_rs_sqrt = cupy.outer(c_rs_sqrt,c_rs_sqrt)
C_rs_sqrt[C_rs_sqrt==0] = 1e-100 #this protects against dive by zero erros (occurs when a feature is a constant)
D = 1-self.C/C_rs_sqrt #the correlation distance matrix
D[D<0] = 0 #small negatives may appear due to the incremental fashion in which we update the mean. Therefore, we 'fix' them
return D
def ret_energy(Edge, Person):
if GPU:
return cp.sum(Edge * tri_array * (1.0 - cp.outer(Person, Person)) /
2.0)
else:
return np.sum(Edge * tri_array * (1.0 - np.outer(Person, Person)) /
2.0)
def _derivativenorm(self):
"""Compute the derivative of the norm
Returns
-------
derivative : numpy array, shape (m_parameters,)
"""
w2 = cp.reshape(self.w,(self.n_features,self.d,self.D,self.D))
derivative = cp.zeros((self.n_features,self.d,self.D,self.D))
tmp=cp.zeros((self.n_features,self.D))
tmp2=cp.zeros((self.n_features,self.D))
tmp[0,:]=cp.sum(cp.square(w2[0,:,0,:]),0)
for i in range(1,self.n_features-1):
tmp[i,:]=cp.dot(tmp[i-1,:],cp.sum(cp.square(w2[i,:,:,:]),0))
tmp[self.n_features-1,:]=cp.inner(tmp[self.n_features-2,:],
cp.sum(cp.square(w2[self.n_features-1,:,:,0]),0))
tmp2[self.n_features-1,:]=cp.sum(cp.square(w2[self.n_features-1,:,:,0]),0)
for i in range(self.n_features-2,-1,-1):
tmp2[i,:]=cp.dot(cp.sum(cp.square(w2[i,:,:,:]),0),tmp2[i+1,:])
tmp2[0,:]=cp.inner(cp.sum(cp.square(w2[0,:,0,:]),0),tmp2[1,:])
for j in range(self.d):
derivative[0,j,0,:]=cp.multiply(tmp2[1,:],2*(w2[0,j,0,:]))
derivative[self.n_features-1,j,:,0]=\
cp.multiply(tmp[self.n_features-2,:],2*(w2[self.n_features-1,j,:,0]))
for i in range(1,self.n_features-1):
temp3=cp.outer(tmp[i-1,:],tmp2[i+1,:])
for j in range(self.d):
derivative[i,j,:,:]=cp.multiply(temp3,2*(w2[i,j,:,:]))
return derivative.reshape(self.m_parameters)
def backward(self):
W, t, output = self.get_ctx('W', 't', 'output')
if output.grad is not None:
grad_W = xp.outer(output.grad, t.data)
grad_t = xp.dot(output.grad, W.data)
W.accumulate_grad(grad_W)
t.accumulate_grad(grad_t)
def _findCarrier_cupy(self, band0, band1, mask):
band0 = cp.asarray(band0)
band1 = cp.asarray(band1)
mask = cp.asarray(mask)
band = band0 * band1
ixf = abs(cp.fft.fftshift(cp.fft.fft2(cp.fft.fftshift(band))))
pyc0, pxc0 = self._findPeak_cupy(
(ixf - gaussian_filter_cupy(ixf, 20)) * mask)
ixfz, Kx, Ky = self._zoomf_cupy(band, self.N,
cp.asarray(self._kx)[pyc0, pxc0],
cp.asarray(self._ky)[pyc0, pxc0], 100,
self._dk * self.N)
pyc, pxc = self._findPeak_cupy(abs(ixfz))
kx = Kx[pxc]
ky = Ky[pyc]
otf_exclude_min_radius = 0.5
otf_exclude_max_radius = 1.5
kr = cp.sqrt(cp.asarray(self._kx)**2 + cp.asarray(self._ky)**2)
m = (kr < 2)
otf = cp.fft.fftshift(self._tfm_cupy(kr, m) + (1 - m))
otf_mask = (kr > otf_exclude_min_radius) & (kr <
otf_exclude_max_radius)
otf_mask_for_band_common_freq = cp.fft.fftshift(
otf_mask
& cupyx.scipy.ndimage.shift(otf_mask, (pyc0 -
(self.N // 2 + 1), pxc0 -
(self.N // 2 + 1)),
order=0))
band0_common = cp.fft.ifft2(
cp.fft.fft2(band0) / otf * otf_mask_for_band_common_freq)
xx = cp.arange(-self.N / 2 * self._dx,
self.N / 2 * self._dx,
self._dx,
dtype=np.single)
phase_shift_to_xpeak = cp.exp(-1j * kx * xx * 2 * pi * self.NA /
self.wavelength)
phase_shift_to_ypeak = cp.exp(-1j * ky * xx * 2 * pi * self.NA /
self.wavelength)
band1_common = cp.fft.ifft2(
cp.fft.fft2(band1) /
otf * otf_mask_for_band_common_freq) * cp.outer(
phase_shift_to_ypeak, phase_shift_to_xpeak)
scaling = 1 / cp.sum(band0_common * cp.conj(band0_common))
cross_corr_result = cp.sum(band0_common * band1_common) * scaling
ampl = cp.abs(cross_corr_result) * 2
phase = cp.angle(cross_corr_result)
return kx.get(), ky.get(), phase.get(), ampl.get()
def gkern(kernlen=21, nsig=3):
"""Returns a 2D Gaussian kernel array."""
interval = (2*nsig+1.)/(kernlen)
x = np.linspace(-nsig-interval/2., nsig+interval/2., kernlen+1)
kern1d = cp.array(np.diff(st.norm.cdf(x)))
kernel_raw = cp.sqrt(cp.outer(kern1d, kern1d))
kernel = kernel_raw/kernel_raw.sum()
return kernel
def applyHann(self):
width = self._image.shape[0]
height = self._image.shape[1]
row = cupy.hanning(width)
col = cupy.hanning(height)
window = cupy.outer(row, col)
window = cupy.sqrt(window)
image = cupy.multiply(window, self._image)
self.setImage(image)
def make_density_matrix_cupy(wf: cupy.ndarray):
if wf.ndim == 1:
return outer(wf, cupy.conj(wf))
if wf.ndim == 2:
wf_dim, num_wf = wf.shape
try:
ret = empty(shape=(num_wf, wf_dim, wf_dim), dtype=wf.dtype)
except OutOfMemoryError:
logger.critical(
"OOM when creating density matrix for wavefunction "
f"of shape {wf.shape}"
)
raise
for wf_idx in range(num_wf):
a_wf = wf[:, wf_idx]
ret[wf_idx, :, :] = outer(a_wf, conj(a_wf))
return ret
raise NotImplementedError(wf.shape)
def test_ger(self):
if self.dtype.char in 'FD':
with pytest.raises(TypeError):
cublas.ger(self.alpha, self.x, self.y, self.a)
return
ref = self.alpha * cupy.outer(self.x, self.y) + self.a
if self.mode is not None:
self.alpha = self.mode.array(self.alpha)
cublas.ger(self.alpha, self.x, self.y, self.a)
cupy.testing.assert_allclose(self.a, ref, rtol=self.tol, atol=self.tol)
def make_test_data():
#a = cp.array([cp.sin(i/3) for i in range(100)])
#b = cp.array([cp.sin(i/3) for i in range(100)])
a = cp.array([i for i in range(100)])
b = cp.array([i / 3 for i in range(100)])
A = cp.outer(a, b)
mask = cp.random.rand(A.shape[0], A.shape[1])
mask[mask >= 0.5] = 1
mask[mask < 0.5] = 0
A_masked = cp.multiply(A, mask)
return A, A_masked, mask
def partial_trace_wf_cupy(iwf: cupy.ndarray, retain_qubits):
nqb = int(math_log2(iwf.shape[0]))
if len(retain_qubits) == nqb:
return outer(iwf, iwf.conj())
iwf = iwf.reshape([2] * nqb, order="C")
retain_qubits = sorted(retain_qubits)
for idx in range(len(retain_qubits)):
r = retain_qubits[idx]
if idx != r:
iwf = iwf.swapaxes(idx, r)
iwf = iwf.reshape((2 ** nqb,))
return partial_trace_wf_keep_first_cupy(iwf, len(retain_qubits))
def policy_backward(eph, epdlogp):
"""
backward pass. (eph is array of intermediate hidden states)
Args:
eph: episode hidden states, stacked
epdlogp: episode action gradient with advantage
"""
dW2 = xp.dot(eph.T, epdlogp).ravel() # derivs wrt W2
dh = xp.outer(epdlogp, model['W2']) # derivs wrt h post activation
dh[eph <= 0] = 0 # backprop relu
dW1 = xp.dot(dh.T, epx) # derivs wrt W1
return {'W1':dW1, 'W2':dW2}
def applyHann(self):
width = self._image.shape[1]
height = self._image.shape[0]
#print("Width,Height {:3d} {:3d} .".format(width,height))
row = cupy.hanning(width)
col = cupy.hanning(height)
window = cupy.outer(col, row)
window = cupy.sqrt(window)
image = cupy.multiply(window, self._image)
#print("array ", image)
self._image = image.astype('uint8')
self.setImage(self._image)
def sigmasLancosTwo(n):
"""
sigma Lancos coefficients for calculating inverse Fourier Transforms
"""
temp = cp.zeros(2*n-1)
for i in cp.arange(2*n-1):
k=i-(n-1)
if k==0:
temp[i] = 1
continue
else:
temp[i] = cp.sin(PI*(k/n))/(PI*(k/n))
return cp.outer(temp,temp)
def deformation(self, prm):
"""
Apply 2D Gaussian and Planar deformation.
Computation is parallelized on GPU using cupy.
"""
import cupy as cp
xy_cp = cp.asarray(prm.xy)
a_cp = cp.asarray(self.a)
b_cp = cp.asarray(self.b)
c_cp = cp.asarray(self.c)
d_cp = cp.asarray(self.d)
sigma_cp = cp.asarray(self.sigma)
e_cp = cp.asarray(self.e)
f_cp = cp.asarray(self.f)
g_cp = cp.asarray(self.g)
z_cp = cp.asarray(prm.z)
func_planar = cp.ElementwiseKernel(
in_params='T x, T y, T e, T f, T g',
out_params='T z',
operation= \
'''
z = e + f*x + g*y;
''',
name='func_planar'
)
func_gauss2d = cp.ElementwiseKernel(
in_params='T x, T y, T b, T c, T d, T sigma',
out_params='T z',
operation= \
'''
z = b*expf(-(powf(x-c,2) + powf(y-d,2))/(2*powf(sigma,2)));
''',
name='func_gauss2d'
)
gauss_2d_cp = cp.zeros_like(xy_cp[:, 0])
for i in range(len(self.b)):
gauss_2d_cp += func_gauss2d(xy_cp[:, 0], xy_cp[:, 1], b_cp[i], c_cp[i], d_cp[i], sigma_cp[i])
s1_cp = a_cp + (1.5 / z_cp) * cp.outer(cp.transpose(gauss_2d_cp), z_cp)
s2_cp = func_planar(xy_cp[:, 0], xy_cp[:, 1], e_cp, f_cp, g_cp)
refl_cp = cp.asarray(self.refl)
for i in range(prm.nxy_tr):
s = s1_cp[i, :] + s2_cp[i] + z_cp
mat = cp.tile(z_cp, (len(s), 1)) - cp.tile(cp.expand_dims(s, 1), (1, len(z_cp)))
refl_cp[i, :] = cp.dot(refl_cp[i, :], cp.sinc(mat))
return np.reshape(cp.asnumpy(refl_cp), [prm.nxy_tr, prm.nz_tr])
def setUp(self):
self.assets = 10
self.samples = 5
self.numbers = 30
seq = 100
self.distance = cupy.zeros(
(self.samples, self.numbers, self.assets * (self.assets-1) // 2))
cupy.random.seed(10)
for i in range(self.samples):
for j in range(self.numbers):
cov = cupy.cov(cupy.random.rand(self.assets, seq))
dia = cupy.diag(cov)
corr = cov / cupy.sqrt(cupy.outer(dia, dia))
dist = (1.0 - corr) / 2.0
self.distance[i, j] = cupy.array(squareform(dist.get()))
def outer(x1: Array, x2: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`.
See its docstring for more information.
"""
# Note: the restriction to numeric dtypes only is different from
# np.outer.
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
raise TypeError('Only numeric dtypes are allowed in outer')
# Note: the restriction to only 1-dim arrays is different from np.outer
if x1.ndim != 1 or x2.ndim != 1:
raise ValueError('The input arrays to outer must be 1-dimensional')
return Array._new(np.outer(x1._array, x2._array))
def hann(width, height, returnCupy=False):
if cupy:
row = cupy.hanning(width)
col = cupy.hanning(height)
window = cupy.outer(row, col)
window = cupy.sqrt(window)
if returnCupy:
return window
else:
return cupy.asnumpy(window)
else:
row = numpy.hanning(width)
col = numpy.hanning(height)
window = numpy.outer(row, col)
window = numpy.sqrt(window)
return window
def train(inweights, v, variables, leak, bs, steps, testflag, s, count):
T = len(s)
N = 1024
M = 1024
x1 = cp.zeros(N * layerscales["L1"], dtype=np.float32)
gradient = dict()
softerr1 = 0
err1 = 0
skipfirst = 0
t = step
tm1 = (T - 1 - t - skipfirst)
for k in range(skipfirst):
step1 = s[t - step]
x1 = (1.0 - leak) * x1 + leak * (inweights["U1"][:, step1] + cp.roll(x1, 1))
x1 = x1 / cp.linalg.norm(x1)
t += 1
for b1 in range(tm1):
step1 = s[t - step]
x1 = (1.0 - leak) * x1 + leak * (inweights["U1"][:, step1] + cp.roll(x1, 1))
x1 = x1 / cp.linalg.norm(x1)
wx = cp.dot(variables["W1"], x1)
wx = wx - cp.max(wx)
p = cp.exp(wx)
p1 = p / cp.sum(p)
pred1 = cp.argmax(p1)
target = s[t+1]
target_prob1 = p1[target]
softerr1 += 1 - target_prob1
err1 = err1 + (pred1 != target)
if testflag == 0:
gradient["W1"] = cp.outer(v[:, target] - p1, x1)
SGD.update_state(gradient)
delta = SGD.get_delta()
SGD.update_with_L1_regularization(variables, delta, L1)
t += 1
softerrors = dict()
prederrors = dict()
softerrors["lay1"] = softerr1 / (tm1)
prederrors["lay1"] = err1 * 100.0 / (tm1)
return prederrors, softerrors, variables
def extract(noisyimg_gpu, imgweights_gpu, A_gpu):
#- Set up the equation to solve (B&S eq 4)
W_gpu = cpx.scipy.sparse.spdiags(data=imgweights_gpu.ravel(),
diags=[
0,
],
m=npix,
n=npix)
iCov_gpu = A_gpu.T.dot(W_gpu.dot(A_gpu))
y_gpu = A_gpu.T.dot(W_gpu.dot(noisyimg_gpu.ravel()))
##- Solve f (B&S eq 4)
f_gpu = cp.linalg.solve(iCov_gpu.todense(),
y_gpu) #requires array, not sparse object
#- Eigen-decompose iCov to assist in upcoming steps
u_gpu, v_gpu = cp.linalg.eigh(iCov_gpu.todense())
#- Calculate C^-1 = QQ (B&S eq 10)
d_gpu = cpx.scipy.sparse.spdiags(cp.sqrt(u_gpu), 0, len(u_gpu), len(u_gpu))
Q_gpu = v_gpu.dot(d_gpu.dot(v_gpu.T))
#- normalization vector (B&S eq 11)
norm_vector_gpu = cp.sum(Q_gpu, axis=1)
#- Resolution matrix (B&S eq 12)
R_gpu = cp.outer(norm_vector_gpu**(-1), cp.ones(
norm_vector_gpu.size)) * Q_gpu
#- Decorrelated covariance matrix (B&S eq 13-15)
udiags_gpu = cpx.scipy.sparse.spdiags(1 / u_gpu, 0, len(u_gpu), len(u_gpu))
Cov_gpu = v_gpu.dot(udiags_gpu.dot(v_gpu.T))
Cx_gpu = R_gpu.dot(Cov_gpu.dot(R_gpu.T))
#- Decorrelated flux (B&S eq 16)
fx_gpu = R_gpu.dot(f_gpu.ravel()).reshape(f_gpu.shape)
#- Variance on f (B&S eq 13)
varfx_gpu = cp.diagonal(Cx_gpu)
return fx_gpu, varfx_gpu, R_gpu
def update(self, z):
# Transform sigmas into measurement space
for i in range(self.num_sp):
self.sp_h[i] = self.H(self.sp_f[i])
# Mean and covariance of the state in the measurement space
Hx_bar, PHx = unscented_transform(self.sp_h, self.weights, self.R)
# Cross variance of Fx and Hx -- used to calculate K
cross_var = np.zeros((self.Nx, self.Nz))
for i in range(self.num_sp):
cross_var += self.weights[i] * np.outer(self.sp_f[i] - self.x_hat,
self.sp_h[i] - Hx_bar)
# Calculate K and measurement residual
K = np.dot(cross_var, inv(PHx))
residual = self.difference(np.array(z), Hx_bar)
# Update predicted to new values for state and variance
self.x_hat += np.dot(K, residual)
self.P -= np.dot(K, np.dot(PHx, K.T))