def compute_analysis_cuda2(self,
xb,
y,
R,
P,
H,
HT=None,
hph=None,
calcP=True):
if HT is None:
HT = culinalg.transpose(H)
HP = culinalg.dot(H, P)
if hph is None:
hph = culinalg.dot(HP, HT)
Rhph = misc.add(R, hph)
inv = culinalg.inv(Rhph)
W = culinalg.dot(HP, inv, transa='T')
Hxb = culinalg.dot(H, xb)
yHxb = misc.subtract(y, Hxb)
WyHxb = culinalg.dot(W, yHxb)
xhat = misc.add(xb, WyHxb)
#xhat = xb + culinalg.dot(W, (y - culinalg.dot(H, xb)))
if calcP:
I = culinalg.eye(P.shape[0])
WH = culinalg.dot(W, H)
IWH = I - WH
Phat = culinalg.dot(IWH, P)
else:
Phat = misc.zeros((1, ), dtype=P.dtype)
return xhat, Phat
def impl_test_binaryop_2d(self, dtype):
if issubclass(dtype, numbers.Integral):
a_sca = np.array(np.random.randint(1, 10), dtype=dtype)
b_sca = np.array(np.random.randint(1, 10), dtype=dtype)
a_vec = np.random.randint(1, 10, 3).astype(dtype)
b_vec = np.random.randint(1, 10, 3).astype(dtype)
a_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
b_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
else:
a_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
b_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
a_vec = np.random.normal(scale=5.0, size=(3, )).astype(dtype)
b_vec = np.random.normal(scale=5.0, size=(3, )).astype(dtype)
a_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
b_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
a_sca_gpu = gpuarray.to_gpu(a_sca)
b_sca_gpu = gpuarray.to_gpu(b_sca)
a_vec_gpu = gpuarray.to_gpu(a_vec)
b_vec_gpu = gpuarray.to_gpu(b_vec)
a_mat_gpu = gpuarray.to_gpu(a_mat)
b_mat_gpu = gpuarray.to_gpu(b_mat)
# addition
assert np.allclose(misc.add(a_sca_gpu, b_sca_gpu).get(), a_sca + b_sca)
assert np.allclose(misc.add(a_vec_gpu, b_vec_gpu).get(), a_vec + b_vec)
assert np.allclose(misc.add(a_mat_gpu, b_mat_gpu).get(), a_mat + b_mat)
# subtract
assert np.allclose(
misc.subtract(a_sca_gpu, b_sca_gpu).get(), a_sca - b_sca)
assert np.allclose(
misc.subtract(a_vec_gpu, b_vec_gpu).get(), a_vec - b_vec)
assert np.allclose(
misc.subtract(a_mat_gpu, b_mat_gpu).get(), a_mat - b_mat)
# multiplication
assert np.allclose(
misc.multiply(a_sca_gpu, b_sca_gpu).get(), a_sca * b_sca)
assert np.allclose(
misc.multiply(a_vec_gpu, b_vec_gpu).get(), a_vec * b_vec)
assert np.allclose(
misc.multiply(a_mat_gpu, b_mat_gpu).get(), a_mat * b_mat)
# division
assert np.allclose(
misc.divide(a_sca_gpu, b_sca_gpu).get(), a_sca / b_sca)
assert np.allclose(
misc.divide(a_vec_gpu, b_vec_gpu).get(), a_vec / b_vec)
assert np.allclose(
misc.divide(a_mat_gpu, b_mat_gpu).get(), a_mat / b_mat)
def thunk():
alpha = gpuarray.to_gpu(np.squeeze(np.asarray(inputs[0]))[:, None])
x_t = gpuarray.to_gpu(np.asarray(inputs[1])[0, :, :])
x_f = gpuarray.to_gpu(np.asarray(inputs[2])[0, :, :])
Xt = cumath.exp(misc.add(linalg.dot(x_t, A), b))
Xf = cumath.exp(misc.add(linalg.dot(x_f, A), b))
Xtn = misc.sum(Xt, axis=1, keepdims=True)
Xfn = misc.sum(Xf, axis=1, keepdims=True)
Xt = misc.divide(Xt, Xtn)
Xf = misc.divide(Xf, Xfn)
w = misc.multiply(Xt, alpha) + misc.multiply(Xf, 1 - alpha)
dq = Xt - Xf
qdw = dq / w
t1 = misc.sum(x * qdw, axis=1)
f = 2 * depth + self.base.n
t2 = f * misc.sum(dq, axis=1) / misc.sum(w, axis=1)
t3 = misc.sum(x, axis=1) * misc.sum(qdw, axis=1)
dalpha = t1 - t2 + t3
del dq, t1, f, t2, t3
iw = 1 / w
S1 = misc.multiply(
depth[:, None] * (self.base.n - 1) / self.base.n, iw)
S2 = (self.base.n + depth[:, None]) / cumath.log(
misc.sum(w, axis=1, keepdims=True))
F = misc.multiply(misc.subtract((x * iw) - S1, S2), alpha)
del w, iw, S1, S2
cast = gpuarray.zeros((x_t.shape[1], Xt.shape[1]),
dtype=theano.config.floatX)
dLq_t = gpuarray.zeros(x_t.shape, dtype=theano.config.floatX)
dLq_f = gpuarray.zeros(x_f.shape, dtype=theano.config.floatX)
for i in range(Xt.shape[0]):
S1 = misc.multiply(Xt[None, i, :], A)
S2 = misc.sum(S1, axis=1, keepdims=True)
S2 = misc.multiply(S2, misc.add(Xt[None, i, :], cast))
dLq_t[i, :] = misc.sum(misc.multiply(F[None, i, :], S1 - S2),
axis=1)
S1 = misc.multiply(Xf[None, i, :], A)
S2 = misc.sum(S1, axis=1, keepdims=True)
S2 = misc.multiply(S2, misc.add(Xf[None, i, :], cast))
dLq_f[i, :] = misc.sum(misc.multiply(F[None, i, :], S1 - S2),
axis=1)
outputs[0][0] = dalpha.get()
outputs[1][0] = dLq_t.get()
outputs[2][0] = dLq_f.get()
for v in node.outputs:
compute_map[v][0] = True
def impl_test_binaryop_2d(self, dtype):
if issubclass(dtype, numbers.Integral):
a_sca = np.array(np.random.randint(1, 10), dtype=dtype)
b_sca = np.array(np.random.randint(1, 10), dtype=dtype)
a_vec = np.random.randint(1, 10, 3).astype(dtype)
b_vec = np.random.randint(1, 10, 3).astype(dtype)
a_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
b_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
else:
a_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
b_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
a_vec = np.random.normal(scale=5.0, size=(3,)).astype(dtype)
b_vec = np.random.normal(scale=5.0, size=(3,)).astype(dtype)
a_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
b_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
a_sca_gpu = gpuarray.to_gpu(a_sca)
b_sca_gpu = gpuarray.to_gpu(b_sca)
a_vec_gpu = gpuarray.to_gpu(a_vec)
b_vec_gpu = gpuarray.to_gpu(b_vec)
a_mat_gpu = gpuarray.to_gpu(a_mat)
b_mat_gpu = gpuarray.to_gpu(b_mat)
# addition
assert np.allclose(misc.add(a_sca_gpu, b_sca_gpu).get(), a_sca+b_sca)
assert np.allclose(misc.add(a_vec_gpu, b_vec_gpu).get(), a_vec+b_vec)
assert np.allclose(misc.add(a_mat_gpu, b_mat_gpu).get(), a_mat+b_mat)
# subtract
assert np.allclose(misc.subtract(a_sca_gpu, b_sca_gpu).get(), a_sca-b_sca)
assert np.allclose(misc.subtract(a_vec_gpu, b_vec_gpu).get(), a_vec-b_vec)
assert np.allclose(misc.subtract(a_mat_gpu, b_mat_gpu).get(), a_mat-b_mat)
# multiplication
assert np.allclose(misc.multiply(a_sca_gpu, b_sca_gpu).get(), a_sca*b_sca)
assert np.allclose(misc.multiply(a_vec_gpu, b_vec_gpu).get(), a_vec*b_vec)
assert np.allclose(misc.multiply(a_mat_gpu, b_mat_gpu).get(), a_mat*b_mat)
# division
assert np.allclose(misc.divide(a_sca_gpu, b_sca_gpu).get(), a_sca/b_sca)
assert np.allclose(misc.divide(a_vec_gpu, b_vec_gpu).get(), a_vec/b_vec)
assert np.allclose(misc.divide(a_mat_gpu, b_mat_gpu).get(), a_mat/b_mat)
def thunk():
alpha = gpuarray.to_gpu(np.squeeze(np.asarray(inputs[0]))[:, None])
x_t = gpuarray.to_gpu(np.asarray(inputs[1])[0, :, :])
x_f = gpuarray.to_gpu(np.asarray(inputs[2])[0, :, :])
Xt = cumath.exp(misc.add(linalg.dot(x_t, A), b))
Xf = cumath.exp(misc.add(linalg.dot(x_f, A), b))
Xtn = misc.sum(Xt, axis=1, keepdims=True)
Xfn = misc.sum(Xf, axis=1, keepdims=True)
Xt = misc.divide(Xt, Xtn)
Xf = misc.divide(Xf, Xfn)
w = misc.multiply(Xt, alpha) + misc.multiply(Xf, 1 - alpha)
wp = cumath.log(w)
wpn = misc.sum(wp, axis=1, keepdims=True) / self.n
wp = misc.subtract(wp, wpn)
t1 = misc.sum(x * wp, axis=1)
t2 = (self.n + depth) * cumath.log(misc.sum(w, axis=1))
t3 = depth * wpn
outputs[0][0] = misc.sum(t1 - t2 + t3).get()
for v in node.outputs:
compute_map[v][0] = True
def __radd__(self, other): return cumisc.add(other, self) def __rsub__(self, other): return cumisc.subtract(other, self)
def __add__(self, other): return cumisc.add(self, other) def __sub__(self, other): return cumisc.subtract(self, other)
def add(a, b):
''' Calculates matrix addition "a+b".'''
a_gpu = gpuarray.to_gpu(a)
b_gpu = gpuarray.to_gpu(b)
return misc.add(a, b)
def _impl_test_binaryop_2d(self, dtype):
if issubclass(dtype, numbers.Integral):
a_sca = np.array(np.random.randint(1, 10), dtype=dtype)
b_sca = np.array(np.random.randint(1, 10), dtype=dtype)
a_vec = np.random.randint(1, 10, 3).astype(dtype)
b_vec = np.random.randint(1, 10, 3).astype(dtype)
a_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
b_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
b_mat_f = np.random.randint(1, 10, 6).reshape(
(3, 2)).astype(dtype, order='F')
else:
a_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
b_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
a_vec = np.random.normal(scale=5.0, size=(3, )).astype(dtype)
b_vec = np.random.normal(scale=5.0, size=(3, )).astype(dtype)
a_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
b_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
b_mat_f = np.random.normal(scale=5.0,
size=(3, 2)).astype(dtype, order='F')
a_sca_gpu = gpuarray.to_gpu(a_sca)
b_sca_gpu = gpuarray.to_gpu(b_sca)
a_vec_gpu = gpuarray.to_gpu(a_vec)
b_vec_gpu = gpuarray.to_gpu(b_vec)
a_mat_gpu = gpuarray.to_gpu(a_mat)
b_mat_gpu = gpuarray.to_gpu(b_mat)
b_mat_f_gpu = gpuarray.to_gpu(b_mat_f)
# addition
assert_allclose(misc.add(a_sca_gpu, b_sca_gpu).get(),
a_sca + b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.add(a_vec_gpu, b_vec_gpu).get(),
a_vec + b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.add(a_mat_gpu, b_mat_gpu).get(),
a_mat + b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# subtract
assert_allclose(misc.subtract(a_sca_gpu, b_sca_gpu).get(),
a_sca - b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.subtract(a_vec_gpu, b_vec_gpu).get(),
a_vec - b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.subtract(a_mat_gpu, b_mat_gpu).get(),
a_mat - b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# multiplication
assert_allclose(misc.multiply(a_sca_gpu, b_sca_gpu).get(),
a_sca * b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.multiply(a_vec_gpu, b_vec_gpu).get(),
a_vec * b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.multiply(a_mat_gpu, b_mat_gpu).get(),
a_mat * b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# division
if issubclass(dtype, numbers.Integral):
assert_allclose(misc.divide(a_sca_gpu, b_sca_gpu).get(),
a_sca // b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_vec_gpu, b_vec_gpu).get(),
a_vec // b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_mat_gpu, b_mat_gpu).get(),
a_mat // b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
else:
assert_allclose(misc.divide(a_sca_gpu, b_sca_gpu).get(),
a_sca / b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_vec_gpu, b_vec_gpu).get(),
a_vec / b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_mat_gpu, b_mat_gpu).get(),
a_mat / b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# mismatched order
assert_raises(ValueError, misc.add, a_mat_gpu, b_mat_f_gpu)
def almLasso_mat_fun(self):
'''
This function represents the Augumented Lagrangian Multipliers method for Lasso problem.
The lagrangian form of the Lasso can be expressed as following:
MIN{ 1/2||Y-XBHETA||_2^2 + lambda||THETA||_1} s.t B-T=0
When applied to this problem, the ADMM updates take the form
BHETA^t+1 = (XtX + rhoI)^-1(Xty + rho^t - mu^t)
THETA^t+1 = Shrinkage_lambda/rho(BHETA(t+1) + mu(t)/rho)
mu(t+1) = mu(t) + rho(BHETA(t+1) - BHETA(t+1))
The algorithm involves a 'ridge regression' update for BHETA, a soft-thresholding (shrinkage) step for THETA and
then a simple linear update for mu
NB: Actually, this ADMM version contains several variations such as the using of two penalty parameters instead
of just one of them (mu1, mu2)
'''
print('\tADMM processing...')
alpha1 = alpha2 = 0
if (len(self.reg_params) == 1):
alpha1 = self.reg_params[0]
alpha2 = self.reg_params[0]
elif (len(self.reg_params) == 2):
alpha1 = self.reg_params[0]
alpha2 = self.reg_params[1]
#thresholds parameters for stopping criteria
if (len(self.thr) == 1):
thr1 = self.thr[0]
thr2 = self.thr[0]
elif (len(self.thr) == 2):
thr1 = self.thr[0]
thr2 = self.thr[1]
# entry condition
err1 = 10 * thr1
err2 = 10 * thr2
start_time = time.time()
# setting penalty parameters for the ALM
mu1p = alpha1 * 1 / self.computeLambda()
print("\t\t-Compute Lambda- Time = %s seconds" %
(time.time() - start_time))
mu2p = alpha2 * 1
mu1 = mu1p
mu2 = mu2p
i = 1
start_time = time.time()
if self.GPU == True:
# defining penalty parameters e constraint to minimize, lambda and C matrix respectively
THETA = misc.zeros((self.num_columns, self.num_columns),
dtype='float64')
lambda2 = misc.zeros((self.num_columns, self.num_columns),
dtype='float64')
gpu_data = gpuarray.to_gpu(self.data)
P_GPU = linalg.dot(gpu_data, gpu_data, transa='T')
OP1 = P_GPU
linalg.scale(np.float32(mu1), OP1)
OP2 = linalg.eye(self.num_columns)
linalg.scale(mu2, OP2)
if self.affine == True:
print('\t\tGPU affine...')
OP3 = misc.ones((self.num_columns, self.num_columns),
dtype='float64')
linalg.scale(mu2, OP3)
lambda3 = misc.zeros((1, self.num_columns), dtype='float64')
# TODO: Because of some problem with linalg.inv version of scikit-cuda we fix it using np.linalg.inv of numpy
A = np.linalg.inv(
misc.add(misc.add(OP1.get(), OP2.get()), OP3.get()))
A_GPU = gpuarray.to_gpu(A)
while ((err1 > thr1 or err2 > thr1) and i < self.max_iter):
_lambda2 = gpuarray.to_gpu(lambda2)
_lambda3 = gpuarray.to_gpu(lambda3)
linalg.scale(1 / mu2, _lambda2)
term_OP2 = gpuarray.to_gpu(_lambda2.get())
OP2 = gpuarray.to_gpu(misc.subtract(THETA, term_OP2))
linalg.scale(mu2, OP2)
OP4 = gpuarray.to_gpu(
np.matlib.repmat(_lambda3.get(), self.num_columns, 1))
# updating Z
BHETA = linalg.dot(
A_GPU, misc.add(misc.add(misc.add(OP1, OP2), OP3),
OP4))
# deallocating unnecessary GPU variables
OP2.gpudata.free()
OP4.gpudata.free()
_lambda2.gpudata.free()
_lambda3.gpudata.free()
# updating C
THETA = misc.add(BHETA, term_OP2)
THETA = self.shrinkL1Lq(THETA.get(), 1 / mu2)
THETA = THETA.astype('float64')
# updating Lagrange multipliers
term_lambda2 = misc.subtract(BHETA, gpuarray.to_gpu(THETA))
linalg.scale(mu2, term_lambda2)
term_lambda2 = gpuarray.to_gpu(term_lambda2.get())
lambda2 = misc.add(lambda2, term_lambda2) # on GPU
term_lambda3 = misc.subtract(
misc.ones((1, self.num_columns), dtype='float64'),
misc.sum(BHETA, axis=0))
linalg.scale(mu2, term_lambda3)
term_lambda3 = gpuarray.to_gpu(term_lambda3.get())
lambda3 = misc.add(lambda3, term_lambda3) # on GPU
# deallocating unnecessary GPU variables
term_OP2.gpudata.free()
term_lambda2.gpudata.free()
term_lambda3.gpudata.free()
err1 = self.errorCoef(BHETA.get(), THETA)
err2 = self.errorCoef(np.sum(BHETA.get(), axis=0),
np.ones([1, self.num_columns]))
# deallocating unnecessary GPU variables
BHETA.gpudata.free()
THETA = gpuarray.to_gpu((THETA))
# reporting errors
if (self.verbose and (i % self.step == 0)):
print(
'\t\tIteration = %d, ||Z - C|| = %2.5e, ||1 - C^T 1|| = %2.5e'
% (i, err1, err2))
i += 1
THETA = THETA.get()
Err = [err1, err2]
if (self.verbose):
print(
'\t\tTerminating ADMM at iteration %5.0f, \n ||Z - C|| = %2.5e, ||1 - C^T 1|| = %2.5e. \n'
% (i, err1, err2))
else:
print '\t\tGPU not affine'
# TODO: Because of some problem with linalg.inv version of scikit-cuda we fix it using np.linalg.inv of numpy
A = np.linalg.inv(misc.add(OP1.get(), OP2.get()))
A_GPU = gpuarray.to_gpu(A)
while (err1 > thr1 and i < self.max_iter):
_lambda2 = gpuarray.to_gpu(lambda2)
term_OP2 = THETA
linalg.scale(mu2, term_OP2)
term_OP2 = misc.subtract(term_OP2, _lambda2)
OP2 = gpuarray.to_gpu(term_OP2.get())
BHETA = linalg.dot(A_GPU, misc.add(OP1, OP2))
linalg.scale(1 / mu2, _lambda2)
term_THETA = gpuarray.to_gpu(_lambda2.get())
THETA = misc.add(BHETA, term_THETA)
THETA = self.shrinkL1Lq(THETA.get(), 1 / mu2)
THETA = THETA.astype('float32')
# updating Lagrange multipliers
term_lambda2 = misc.subtract(BHETA, gpuarray.to_gpu(THETA))
linalg.scale(mu2, term_lambda2)
term_lambda2 = gpuarray.to_gpu(term_lambda2.get())
lambda2 = misc.add(lambda2, term_lambda2) # on GPU
err1 = self.errorCoef(BHETA.get(), THETA)
THETA = gpuarray.to_gpu((THETA))
# reporting errors
if (self.verbose and (i % self.step == 0)):
print('\t\tIteration %5.0f, ||Z - C|| = %2.5e' %
(i, err1))
i += 1
THETA = THETA.get()
Err = [err1, err2]
if (self.verbose):
print(
'\t\tTerminating ADMM at iteration %5.0f, \n ||Z - C|| = %2.5e'
% (i, err1))
else: #CPU version
# defining penalty parameters e constraint to minimize, lambda and C matrix respectively
THETA = np.zeros([self.num_columns, self.num_columns])
lambda2 = np.zeros([self.num_columns, self.num_columns])
P = self.data.T.dot(self.data)
OP1 = np.multiply(P, mu1)
if self.affine == True:
# INITIALIZATION
lambda3 = np.zeros(self.num_columns).T
A = np.linalg.inv(
np.multiply(mu1, P) +
np.multiply(mu2, np.eye(self.num_columns, dtype=int)) +
np.multiply(mu2,
np.ones([self.num_columns, self.num_columns])))
OP3 = np.multiply(
mu2, np.ones([self.num_columns, self.num_columns]))
while ((err1 > thr1 or err2 > thr1) and i < self.max_iter):
# updating Bheta
OP2 = np.multiply(THETA - np.divide(lambda2, mu2), mu2)
OP4 = np.matlib.repmat(lambda3, self.num_columns, 1)
BHETA = A.dot(OP1 + OP2 + OP3 + OP4)
# updating C
THETA = BHETA + np.divide(lambda2, mu2)
THETA = self.shrinkL1Lq(THETA, 1 / mu2)
# updating Lagrange multipliers
lambda2 = lambda2 + np.multiply(mu2, BHETA - THETA)
lambda3 = lambda3 + np.multiply(
mu2,
np.ones([1, self.num_columns]) - np.sum(BHETA, axis=0))
err1 = self.errorCoef(BHETA, THETA)
err2 = self.errorCoef(np.sum(BHETA, axis=0),
np.ones([1, self.num_columns]))
# mu1 = min(mu1 * (1 + 10 ^ -5), 10 ^ 2 * mu1p);
# mu2 = min(mu2 * (1 + 10 ^ -5), 10 ^ 2 * mu2p);
# reporting errors
if (self.verbose and (i % self.step == 0)):
print(
'\t\tIteration = %d, ||Z - C|| = %2.5e, ||1 - C^T 1|| = %2.5e'
% (i, err1, err2))
i += 1
Err = [err1, err2]
if (self.verbose):
print(
'\t\tTerminating ADMM at iteration %5.0f, \n ||Z - C|| = %2.5e, ||1 - C^T 1|| = %2.5e. \n'
% (i, err1, err2))
else:
print '\t\tCPU not affine'
A = np.linalg.inv(
OP1 +
np.multiply(mu2, np.eye(self.num_columns, dtype=int)))
while (err1 > thr1 and i < self.max_iter):
# updating Z
OP2 = np.multiply(mu2, THETA) - lambda2
BHETA = A.dot(OP1 + OP2)
# updating C
THETA = BHETA + np.divide(lambda2, mu2)
THETA = self.shrinkL1Lq(THETA, 1 / mu2)
# updating Lagrange multipliers
lambda2 = lambda2 + np.multiply(mu2, BHETA - THETA)
# computing errors
err1 = self.errorCoef(BHETA, THETA)
# reporting errors
if (self.verbose and (i % self.step == 0)):
print('\t\tIteration %5.0f, ||Z - C|| = %2.5e' %
(i, err1))
i += 1
Err = [err1, err2]
if (self.verbose):
print(
'\t\tTerminating ADMM at iteration %5.0f, \n ||Z - C|| = %2.5e'
% (i, err1))
print("\t\t-ADMM- Time = %s seconds" % (time.time() - start_time))
return THETA, Err
for step in xrange(N_TIMESTEPS):
# print step
# Implementing split-step method
# Update wavefunction and resovoir, record density
cu_fft.fft(psi_gpu, psi_gpu, plan_forward)
psi_gpu *= kineticFactorHalf_gpu
cu_fft.ifft(psi_gpu, psi_gpu, plan_inverse, scale=True)
# currentDensity_gpu = abs(psi_gpu) ** 2
# currentDensity_gpu = psi_gpu.real **2 + psi_gpu.imag ** 2
currentDensity_gpu = (psi_gpu * psi_gpu.conj()).real
# modSquared.prepared_call(grid, block, psi_gpu.gpudata,
# currentDensity_gpu.gpudata, 1024)
# n_gpu *= cumath.exp(-gammaRdt_gpu + Rdt_gpu * currentDensity_gpu)
n_gpu *= cumath.exp(misc.add(- gammaRdt_gpu,
- misc.multiply(Rdt_gpu, currentDensity_gpu)))
n_gpu += Pdt_gpu
psi_gpu *= cumath.exp(
misc.add(
misc.add(misc.multiply(expFactorPolFirst_gpu, n_gpu),
misc.multiply(expFactorPolSecond_gpu, currentDensity_gpu)),
expFactorPolThird_gpu))
# psiNonlinear.prepared_call(grid, block, expFactorPolFirst,
# expFactorPolSecond, expFactorPolThird,
# psi_gpu.gpudata, n_gpu.gpudata,
# currentDensity_gpu.gpudata, 1024)
cu_fft.fft(psi_gpu, psi_gpu, plan_forward)
# record spectrum
drv.memcpy_dtod(spectrum[step, :].gpudata, psi_gpu[N//2, :].gpudata,
for step in xrange(N_TIMESTEPS):
# print step
# Implementing split-step method
# Update wavefunction and resovoir, record density
cu_fft.fft(psi_gpu, psi_gpu, plan_forward)
psi_gpu *= kineticFactorHalf_gpu
cu_fft.ifft(psi_gpu, psi_gpu, plan_inverse, scale=True)
# currentDensity_gpu = abs(psi_gpu) ** 2
# currentDensity_gpu = psi_gpu.real **2 + psi_gpu.imag ** 2
currentDensity_gpu = (psi_gpu * psi_gpu.conj()).real
# modSquared.prepared_call(grid, block, psi_gpu.gpudata,
# currentDensity_gpu.gpudata, 1024)
# n_gpu *= cumath.exp(-gammaRdt_gpu + Rdt_gpu * currentDensity_gpu)
n_gpu *= cumath.exp(
misc.add(-gammaRdt_gpu,
-misc.multiply(Rdt_gpu, currentDensity_gpu)))
n_gpu += Pdt_gpu
psi_gpu *= cumath.exp(
misc.add(
misc.add(
misc.multiply(expFactorPolFirst_gpu, n_gpu),
misc.multiply(expFactorPolSecond_gpu, currentDensity_gpu)),
expFactorPolThird_gpu))
# psiNonlinear.prepared_call(grid, block, expFactorPolFirst,
# expFactorPolSecond, expFactorPolThird,
# psi_gpu.gpudata, n_gpu.gpudata,
# currentDensity_gpu.gpudata, 1024)
cu_fft.fft(psi_gpu, psi_gpu, plan_forward)
# record spectrum
def _impl_test_binaryop_2d(self, dtype):
if issubclass(dtype, numbers.Integral):
a_sca = np.array(np.random.randint(1, 10), dtype=dtype)
b_sca = np.array(np.random.randint(1, 10), dtype=dtype)
a_vec = np.random.randint(1, 10, 3).astype(dtype)
b_vec = np.random.randint(1, 10, 3).astype(dtype)
a_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
b_mat = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype)
b_mat_f = np.random.randint(1, 10, 6).reshape((3, 2)).astype(dtype, order='F')
else:
a_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
b_sca = np.random.normal(scale=5.0, size=()).astype(dtype)
a_vec = np.random.normal(scale=5.0, size=(3,)).astype(dtype)
b_vec = np.random.normal(scale=5.0, size=(3,)).astype(dtype)
a_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
b_mat = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype)
b_mat_f = np.random.normal(scale=5.0, size=(3, 2)).astype(dtype, order='F')
a_sca_gpu = gpuarray.to_gpu(a_sca)
b_sca_gpu = gpuarray.to_gpu(b_sca)
a_vec_gpu = gpuarray.to_gpu(a_vec)
b_vec_gpu = gpuarray.to_gpu(b_vec)
a_mat_gpu = gpuarray.to_gpu(a_mat)
b_mat_gpu = gpuarray.to_gpu(b_mat)
b_mat_f_gpu = gpuarray.to_gpu(b_mat_f)
# addition
assert_allclose(misc.add(a_sca_gpu, b_sca_gpu).get(), a_sca+b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.add(a_vec_gpu, b_vec_gpu).get(), a_vec+b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.add(a_mat_gpu, b_mat_gpu).get(), a_mat+b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# subtract
assert_allclose(misc.subtract(a_sca_gpu, b_sca_gpu).get(), a_sca-b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.subtract(a_vec_gpu, b_vec_gpu).get(), a_vec-b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.subtract(a_mat_gpu, b_mat_gpu).get(), a_mat-b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# multiplication
assert_allclose(misc.multiply(a_sca_gpu, b_sca_gpu).get(), a_sca*b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.multiply(a_vec_gpu, b_vec_gpu).get(), a_vec*b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.multiply(a_mat_gpu, b_mat_gpu).get(), a_mat*b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# division
if issubclass(dtype, numbers.Integral):
assert_allclose(misc.divide(a_sca_gpu, b_sca_gpu).get(), a_sca//b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_vec_gpu, b_vec_gpu).get(), a_vec//b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_mat_gpu, b_mat_gpu).get(), a_mat//b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
else:
assert_allclose(misc.divide(a_sca_gpu, b_sca_gpu).get(), a_sca/b_sca,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_vec_gpu, b_vec_gpu).get(), a_vec/b_vec,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
assert_allclose(misc.divide(a_mat_gpu, b_mat_gpu).get(), a_mat/b_mat,
rtol=dtype_to_rtol[dtype],
atol=dtype_to_atol[dtype])
# mismatched order
assert_raises(ValueError, misc.add, a_mat_gpu, b_mat_f_gpu)