def compute_HRP_weights(covariances, res_order):
weights = pd.Series(1, index=res_order)
clustered_alphas = [res_order]
while len(clustered_alphas) > 0:
clustered_alphas = [
cluster[start:end] for cluster in clustered_alphas
for start, end in ((0, len(cluster) // 2), (len(cluster) // 2,
len(cluster)))
if len(cluster) > 1
]
for subcluster in range(0, len(clustered_alphas), 2):
left_cluster = clustered_alphas[subcluster]
right_cluster = clustered_alphas[subcluster + 1]
left_subcovar = covariances[left_cluster, :][:, left_cluster]
inv_diag = 1 / cupy.diag(left_subcovar)
parity_w = inv_diag * (1 / cupy.sum(inv_diag))
left_cluster_var = cupy.dot(parity_w,
cupy.dot(left_subcovar, parity_w))
right_subcovar = covariances[right_cluster, :][:, right_cluster]
inv_diag = 1 / cupy.diag(right_subcovar)
parity_w = inv_diag * (1 / cupy.sum(inv_diag))
right_cluster_var = cupy.dot(parity_w,
cupy.dot(right_subcovar, parity_w))
alloc_factor = 1 - left_cluster_var / \
(left_cluster_var + right_cluster_var)
weights[left_cluster] *= alloc_factor.item()
weights[right_cluster] *= 1 - alloc_factor.item()
return weights
def _mutate(self):
weight_mask = cp.random.normal(
size=(self.weights.shape), dtype='single') * .05 * cp.tile(
cp.triu(cp.ones(shape=(self.total, self.total), dtype='bool_'),
1), (self.pop_size, 1, 1)) * (cp.random.uniform(
size=(self.weights.shape), dtype='single') <
.2) * (self.weights != 0)
new_weights_mask = cp.random.normal(
size=(self.weights.shape), dtype='single') * .05 * cp.tile(
cp.triu(cp.ones(shape=(self.total, self.total), dtype='bool_'),
1), (self.pop_size, 1, 1)) * (cp.random.uniform(
size=(self.weights.shape),
dtype='single') < .05) * (self.weights == 0)
self.weights += weight_mask + new_weights_mask
self.weights *= (cp.random.uniform(size=self.weights.shape,
dtype='single') < 1)
self.weights[:, :self.inputs, :self.inputs] = 0
self.weights[:, -self.outputs:, -self.outputs:] = cp.tile(
cp.diag(
cp.diag(
cp.ones(shape=(self.outputs, self.outputs),
dtype='bool_'))), (self.pop_size, 1, 1))
self.biases += cp.random.normal(
size=self.biases.shape, dtype='single') * .05 * (cp.random.normal(
size=self.biases.shape, dtype='single') < .2)
def Vpi(self, X, Y, a, b, OT_plan):
"""Return the second order matrix of the displacements: sum_ij { (OT_plan)_ij (X_i-Y_j)(X_i-Y_j)^T }."""
A = X.T.dot(OT_plan).dot(Y)
if self.use_gpu:
return X.T.dot(cp.diag(a)).dot(X) + Y.T.dot(cp.diag(b)).dot(Y) - A - A.T
else:
return X.T.dot(np.diag(a)).dot(X) + Y.T.dot(np.diag(b)).dot(Y) - A - A.T
def initialize(self, a, b, X, Y, Omega, k):
"""Initialize Omega with the projection onto the subspace spanned by top-k eigenvectors of V_pi*, where pi* (=OT_plan) is the (classical) optimal transport plan."""
if self.verbose:
print('Initializing')
n = X.shape[0]
m = Y.shape[0]
# Compute the cost matrix
if self.use_gpu:
ones = cp.ones((n,m))
C = cp.diag(cp.diag(X.dot(X.T))).dot(ones) + ones.dot(cp.diag(cp.diag(Y.dot(Y.T)))) - 2*X.dot(Y.T)
else:
ones = np.ones((n,m))
C = np.diag(np.diag(X.dot(X.T))).dot(ones) + ones.dot(np.diag(np.diag(Y.dot(Y.T)))) - 2*X.dot(Y.T)
# Compute the OT plan
_, OT_plan = self.OT(a, b, C)
V = self.Vpi(X, Y, a, b, OT_plan)
# Eigendecompose V
d = V.shape[0]
if self.use_gpu:
_, eigenvectors = cp.linalg.eigh(V)
eigenvectors = eigenvectors[:,-k:]
else:
_, eigenvectors = sp.linalg.eigh(V, eigvals=(d-k,d-1))
# Return the projection
Omega = eigenvectors.dot(eigenvectors.T)
return Omega
def evol(s, B, U, chi, d):
for i_bond in [0, 1]:
ia = np.mod(i_bond - 1, 2)
ib = np.mod(i_bond, 2)
ic = np.mod(i_bond + 1, 2)
chia = B[ib].shape[1]
chic = B[ic].shape[2]
# Construct theta matrix and time evolution #
theta = cp.tensordot(B[ib], B[ic], axes=(2, 1)) # i a j b
theta = cp.tensordot(U, theta, axes=([2, 3], [0, 2])) # ip jp a b
theta = cp.tensordot(cp.diag(s[ia]), theta, axes=([1, 2])) # a ip jp b
theta = cp.reshape(cp.transpose(theta, (1, 0, 2, 3)),
(d * chia, d * chic)) # ip a jp b
# Schmidt decomposition #
X, Y, Z = cp.linalg.svd(theta, full_matrices=0)
chi2 = np.min([cp.sum(Y > 10.**(-10)).get(), chi])
piv = cp.zeros(len(Y), cp.bool)
piv[(cp.argsort(Y)[::-1])[:chi2]] = True
Y = Y[piv]
invsq = cp.sqrt(sum(Y**2))
X = X[:, piv]
Z = Z[piv, :]
# Obtain the new values for B and s #
s[ib] = Y / invsq
X = cp.reshape(X, (d, chia, chi2))
X = cp.transpose(cp.tensordot(cp.diag(s[ia]**(-1)), X, axes=(1, 1)),
(1, 0, 2))
B[ib] = cp.tensordot(X, cp.diag(s[ib]), axes=(2, 0))
B[ic] = cp.transpose(cp.reshape(Z, (chi2, d, chic)), (1, 0, 2))
return s, B
def xx(x):
RL = [1.0, ]
iRL = [1.0, ]
S = cp.matmul(x.T, x).reshape(32, 32, 32, 32)
D = cp.zeros((34, 34), dtype = cp.float32)
#print("before",S[:][0][0][0])
#print("before",D)
conv3check(conv_blocks, conv_threads, (S, S, D))
#print("after",S[:][0][0][0])
#print("after",D)
T = cp.zeros((32, 32, 32, 32), dtype = cp.float32)
if not fix:
T += S
for i in range(1, d - 1):
#cupy.diag only take diagonal array output length 1024
#cupy.sqrt Elementwise square root
L = cp.sqrt(cp.diag(S.reshape(1024, 1024)).reshape(32, 32))
iL = 1.0 / L
RL.append(L)
iRL.append(iL)
trans(trans_blocks, trans_threads, (S, T, L, L, iL, iL))
conv3(conv_blocks, conv_threads, (S, S))
conv3(conv_blocks, conv_threads, (T, T))
L = cp.sqrt(cp.diag(S.reshape(1024, 1024)).reshape(32, 32))
iL = 1.0 / L
RL.append(L)
iRL.append(iL)
trans(trans_blocks, trans_threads, (S, T, L, L, iL, iL))
if fix:
T -= S
return RL, iRL
def xx(x):
RL = [
1.0,
]
iRL = [
1.0,
]
S = cp.matmul(x.T, x).reshape(32, 32, 32, 32)
conv3(conv_blocks, conv_threads, (S, S))
T = cp.zeros((32, 32, 32, 32), dtype=cp.float32)
if not fix:
T += S
for i in range(1, d - 1):
L = cp.sqrt(cp.diag(S.reshape(1024, 1024)).reshape(32, 32))
iL = 1.0 / L
RL.append(L)
iRL.append(iL)
trans(trans_blocks, trans_threads, (S, T, L, L, iL, iL))
conv3(conv_blocks, conv_threads, (S, S))
conv3(conv_blocks, conv_threads, (T, T))
L = cp.sqrt(cp.diag(S.reshape(1024, 1024)).reshape(32, 32))
iL = 1.0 / L
RL.append(L)
iRL.append(iL)
trans(trans_blocks, trans_threads, (S, T, L, L, iL, iL))
if fix:
T -= S
return RL, iRL
def test_dgmm_out(self, dtype):
self._setup(dtype)
if self.side == 'L':
ref = cupy.diag(self.x) @ self.a
elif self.side == 'R':
ref = self.a @ cupy.diag(self.x)
c = cupy.empty(self.shape, order=self.orderc, dtype=dtype)
cublas.dgmm(self.side, self.a, self.x, out=c)
cupy.testing.assert_allclose(c, ref, rtol=self.tol, atol=self.tol)
def test_gdmm_incx_minus_one(self, dtype):
if self.orderc != 'F':
raise unittest.SkipTest()
self._setup(dtype)
if self.side == 'L':
ref = cupy.diag(self.x[::-1]) @ self.a
elif self.side == 'R':
ref = self.a @ cupy.diag(self.x[::-1])
c = cublas.dgmm(self.side, self.a, self.x, incx=-1)
cupy.testing.assert_allclose(c, ref, rtol=self.tol, atol=self.tol)
def test_dgmm_inplace(self, dtype):
if self.orderc != 'F':
pytest.skip()
self._setup(dtype)
if self.side == 'L':
ref = cupy.diag(self.x) @ self.a
elif self.side == 'R':
ref = self.a @ cupy.diag(self.x)
cublas.dgmm(self.side, self.a, self.x, out=self.a)
cupy.testing.assert_allclose(self.a, ref, rtol=self.tol, atol=self.tol)
def test_dgmm(self, dtype):
if self.orderc != 'F':
raise unittest.SkipTest()
self._setup(dtype)
if self.side == 'L':
ref = cupy.diag(self.x) @ self.a
elif self.side == 'R':
ref = self.a @ cupy.diag(self.x)
c = cublas.dgmm(self.side, self.a, self.x)
cupy.testing.assert_allclose(c, ref, rtol=self.tol, atol=self.tol)
def Mahalanobis(self, X, Y, Omega):
"""Return the matrix of Mahalanobis costs."""
n = X.shape[0]
m = Y.shape[0]
if self.use_gpu:
ones = cp.ones((n,m))
return cp.diag(cp.diag(X.dot(Omega).dot(X.T))).dot(ones) + ones.dot(cp.diag(cp.diag(Y.dot(Omega).dot(Y.T)))) - 2*X.dot(Omega).dot(Y.T)
else:
ones = np.ones((n,m))
return np.diag(np.diag(X.dot(Omega).dot(X.T))).dot(ones) + ones.dot(np.diag(np.diag(Y.dot(Omega).dot(Y.T)))) - 2*X.dot(Omega).dot(Y.T)
def magnetization(s, B, d):
sz = cp.diag([Sz(conf, 0) for conf in range(0, d)])
# sz=cp.array([[0,1],[1,0]])
mag = cp.array(0., dtype=np.float32)
for i_bond in range(2):
sB = cp.tensordot(cp.diag(s[np.mod(i_bond - 1, 2)]),
B[i_bond],
axes=(1, 1))
C = cp.tensordot(sB, cp.conj(sB), axes=([0, 2], [0, 2]))
mag += cp.real(cp.tensordot(C, sz, axes=([0, 1], [0, 1])).get())
return mag * 0.5
def test_dgmm_x_matrix(self, dtype):
if self.orderc != 'F':
pytest.skip()
self._setup(dtype, xdim=2)
if self.side == 'L':
ref = cupy.diag(cupy.diag(self.x)) @ self.a
incx = self.shape[0] + 1
elif self.side == 'R':
ref = self.a @ cupy.diag(cupy.diag(self.x))
incx = self.shape[1] + 1
c = cublas.dgmm(self.side, self.a, self.x, incx=incx)
cupy.testing.assert_allclose(c, ref, rtol=self.tol, atol=self.tol)
def test_dgmm_incx_minus_one(self, dtype):
if self.orderc != 'F':
pytest.skip()
if cupy.cuda.runtime.is_hip:
if self._check_dgmm_incx_minus_one_hip_skip_condition():
pytest.xfail('HIP dgmm may have a bug')
self._setup(dtype)
if self.side == 'L':
ref = cupy.diag(self.x[::-1]) @ self.a
elif self.side == 'R':
ref = self.a @ cupy.diag(self.x[::-1])
c = cublas.dgmm(self.side, self.a, self.x, incx=-1)
cupy.testing.assert_allclose(c, ref, rtol=self.tol, atol=self.tol)
def itkrm(data,K,S,maxitr,startD=np.array([1])):
M, N = data.shape
if startD.all()==1:
D_init = np.random.randn(M, K)
else:
D_init = startD
#Algorithm
GPU_D_old = cp.asarray(D_init)
GPU_Y = cp.asarray(data)
GPU_M = int(cp.asarray(M))
GPU_N = int(cp.asarray(N))
GPU_S = int(cp.asarray(S))
GPU_maxitr = int(cp.asarray(maxitr))
GPU_I_D = cp.zeros((S,N),dtype=cp.int32)
for i in range(GPU_maxitr):
start_time = N_timer.cont_timer(0,0)
N_timer.Timer(i,maxitr)
for n in range(GPU_N):
GPU_I_D[:,n] = max_atoms(GPU_D_old,GPU_Y[:,n],GPU_S)
GPU_D_new = cp.zeros((M,K))
GPU_DtD = GPU_D_old.T @ GPU_D_old
for n in range(GPU_N):
GPU_DtY = GPU_D_old[:,GPU_I_D[:,n]].T @ GPU_Y[:,n]
GPU_matproj = cp.repeat((GPU_D_old[:,GPU_I_D[:,n]] @ cp.linalg.inv(GPU_DtD[GPU_I_D[:,n,None], GPU_I_D[:,n]]) @ GPU_DtY)[:,None],GPU_S,axis=1)
GPU_vecproj = GPU_D_old[:,GPU_I_D[:,n]] @ cp.diag(cp.diag( GPU_DtD[GPU_I_D[:,n,None], GPU_I_D[:,n]] )**-1*( GPU_DtY ))
GPU_signer = cp.sign( GPU_DtY )
GPU_D_new[:,GPU_I_D[:,n]] = GPU_D_new[:,GPU_I_D[:,n]] + (cp.repeat(GPU_Y[:,n,None], S, axis=1) - GPU_matproj + GPU_vecproj)*GPU_signer
GPU_scale = cp.sum(GPU_D_new*GPU_D_new, axis=0)
GPU_iszero = cp.where(GPU_scale < 0.00001)[0]
# GPU_D_new[:,GPU_iszero] = np.random.randn(GPU_M, len(GPU_iszero)) # generate random with GPU
GPU_D_new[:,GPU_iszero] = cp.asarray(np.random.randn(M, len(GPU_iszero))) # generate random with CPU
#end hugget
GPU_D_new = normalize_mat_col(GPU_D_new)
GPU_D_old = 1*GPU_D_new
return cp.asnumpy(GPU_D_old)
def triageTemplates2(params, iW, C2C, W, U, dWU, mu, nsp, ndrop):
# This function checks if some templates should be dropped
# either because they are very similar to another template,
# or because they are not catching any spikes, (low mean firing rate).
# Takes as inputs almost all the information that determines templates, and
# outputs the same variables back after removing some clusters.
# this is the firing rate threshold
m0 = params.minFR * params.NT / params.fs
idrop = nsp < m0 # drop any templates with firing rate below this
# remove those templates everywhere
W = W[:, ~idrop, :]
U = U[:, ~idrop, :]
dWU = dWU[:, :, ~idrop]
mu = mu[~idrop]
nsp = nsp[~idrop]
# keep track of how many templates have been removed this way
ndrop[0] = .9 * ndrop[0] + .1 * idrop.sum()
# compute pairwise correlations between templates
cc = getMeWtW2(W, U, None)
cc = cc - cp.diag(cp.diag(cc)) # exclude the diagonal
sd = sqrt(10) # this is hard-coded here
# compute a score for the separation of the means
r0 = 4 * sd / cp.abs(mu[:, np.newaxis] - mu[np.newaxis, :])
# determine which template has more spikes (that one survives)
rdir = (nsp[:, np.newaxis] - nsp[np.newaxis, :]) < 0
# for each pair of template, score their similarity by their template correlation,
# and amplitude separation
ipair = (cc > 0.9) & (r0 > 1) & rdir
# for each template, find its most similar other template
amax = cp.max(ipair, axis=1)
# if this score is 1, then all the criteria have bene met for dropping this template
idrop = amax > 0
# remove these templates everywhere like before
W = W[:, ~idrop, :]
U = U[:, ~idrop, :]
dWU = dWU[:, :, ~idrop]
mu = mu[~idrop]
nsp = nsp[~idrop]
# keep track of how many templates have been removed this way
ndrop[1] = .9 * ndrop[1] + .1 * idrop.sum()
return W, U, dWU, mu, nsp, ndrop
def svdecon(X, nPC0=None):
"""
Input:
X : m x n matrix
Output:
X = U*S*V'
Description:
Does equivalent to svd(X,'econ') but faster
Vipin Vijayan (2014)
"""
m, n = X.shape
nPC = nPC0 or min(m, n)
if m <= n:
C = cp.dot(X, X.T)
D, U = cp.linalg.eigh(C, 'U')
ix = cp.argsort(np.abs(D))[::-1]
d = D[ix]
U = U[:, ix]
d = d[:nPC]
U = U[:, :nPC]
V = cp.dot(X.T, U)
s = cp.sqrt(d)
V = V / s.T
S = cp.diag(s)
else:
C = cp.dot(X.T, X)
D, V = cp.linalg.eigh(C)
ix = cp.argsort(cp.abs(D))[::-1]
d = D[ix]
V = V[:, ix]
# convert evecs from X'*X to X*X'. the evals are the same.
U = cp.dot(X, V)
s = cp.sqrt(d)
U = U / s.T
S = cp.diag(s)
return U, S, V
def diagflat(v, k=0):
"""Creates a diagonal array from the flattened input.
Args:
v (array-like): Array or array-like object.
k (int): Index of diagonals. See :func:`cupy.diag` for detail.
Returns:
cupy.ndarray: A 2-D diagonal array with the diagonal copied from ``v``.
"""
if isinstance(v, cupy.ndarray):
return cupy.diag(v.ravel(), k)
else:
return cupy.diag(numpy.ndarray(v).ravel(), k)
def decompose(
self,
lhs: List[int],
rhs: List[int],
mergeV: bool = True,
cutoff: float = 1e-12,
maxdim: int = 2147483648
) -> Tuple["Tensor", "Tensor", xp.array, int]:
lhs_size = reduce(lambda x, y: x * y,
[self._indices[i].size for i in lhs])
rhs_size = reduce(lambda x, y: x * y,
[self._indices[i].size for i in rhs])
self.transpose(lhs + rhs)
u, s, v = xp.linalg.svd(self._data.reshape([lhs_size, rhs_size]),
full_matrices=False,
compute_uv=True)
s_norm = xp.linalg.norm(s)
s_cutoff = (1 - cutoff) * s_norm * s_norm
s_squared_cumsum = xp.cumsum(xp.power(s, 2))
# dim = 0
# for i in range(s.size):
# dim += 1
# if s_squared_cumsum[i] >= s_cutoff or (dim + 1) > maxdim:
# break
dim = int(xp.searchsorted(s_squared_cumsum[:maxdim], s_cutoff)) + 1
dim = min(dim, s.size, maxdim)
u = u[:, :dim]
s = xp.clip(s[:dim] * s_norm / xp.sqrt(s_squared_cumsum[dim - 1]),
a_min=1e-32,
a_max=None)
v = v[:dim, :]
if mergeV:
v = xp.diag(s) @ v
else:
u = u @ xp.diag(s)
a = Index(dim)
lhs_indices = self._indices[:len(lhs)] + [a]
rhs_indices = [a] + self._indices[len(lhs):]
lhs_tensor = Tensor(lhs_indices,
u.reshape([idx.size for idx in lhs_indices]))
rhs_tensor = Tensor(rhs_indices,
v.reshape([idx.size for idx in rhs_indices]))
return lhs_tensor, rhs_tensor, s, dim
def getRandomHermitianMatrix(M):
ret = xp.diag(0j + randn(M))
for y in range(0, M - 1):
for x in range(y + 1, M):
ret[y, x] = randn_c()
ret[x, y] = xp.conj(ret[y, x])
return ret
def setUp(self):
self.dtype = numpy.dtype(self.dtype)
if self.dtype.char in 'fF':
self.r_dtype = numpy.float32
else:
self.r_dtype = numpy.float64
n = self.n
nrhs = 1 if self.nrhs is None else self.nrhs
# Diagonally dominant matrix is used as it is stable
alpha = 2.0 / n
a = self._make_matrix((n, n), alpha, -alpha / 2)
diag = cupy.diag(cupy.ones((n, ), dtype=self.r_dtype))
a[diag > 0] = 0
a += diag
x = self._make_matrix((n, nrhs), 0.2, 0.9)
b = cupy.matmul(a, x)
b_shape = [n]
if self.nrhs is not None:
b_shape.append(nrhs)
self.a = a
self.b = b.reshape(b_shape)
self.x_ref = x.reshape(b_shape)
if self.r_dtype == numpy.float32:
self.tol = self._tol['f']
elif self.r_dtype == numpy.float64:
self.tol = self._tol['d']
def lanczos(op: LinearOp,
x: Tensor,
krylov_size: int,
num_restarts: int,
smallest: bool = True) -> Tuple[float, Tensor]:
v_next = x._data.copy()
beta = xp.zeros(krylov_size + 1)
alpha = xp.zeros(krylov_size)
for _ in range(num_restarts):
beta[0] = 0.0
v_prev = xp.zeros(x._data.shape)
v_next /= xp.linalg.norm(v_next)
V = xp.zeros([x.size, krylov_size])
for i in range(0, krylov_size):
w = op(v_next)
alpha[i] = xp.dot(w.reshape(x.size), v_next.reshape(x.size))
w -= (alpha[i] * v_next + beta[i] * v_prev)
beta[i + 1] = xp.linalg.norm(w)
v_prev = v_next.copy()
v_next = w / beta[i + 1]
V[:, i] = v_prev.reshape(x.size)
tridiag = xp.diag(alpha)
for i in range(0, krylov_size - 1):
tridiag[i + 1, i] = beta[i + 1]
d, v = xp.linalg.eigh(tridiag, UPLO="L")
if smallest:
ev = d[0]
v_next = (V @ v[:, 0]).reshape(x._data.shape)
else:
ev = d[-1]
v_next = (V @ v[:, -1]).reshape(x._data.shape)
x._data = v_next
return ev, x
def _make_matrix(self, dtype):
if not cusparse.check_availability('csrilu02'):
pytest.skip('csrilu02 is not available')
a = testing.shaped_random(
(self.n, self.n), cupy, dtype=dtype, scale=0.9) + 0.1
a = a + cupy.diag(cupy.ones((self.n, ), dtype=dtype.char.lower()))
return a
def admittanceMatrixD(self):
all_el_nodes_coords = self.pts[:(self.ne * self.n_per_el)].reshape(
(self.ne, self.n_per_el, 2))
lengths = cp.linalg.norm((all_el_nodes_coords[:, 0] -
all_el_nodes_coords[:, (self.n_per_el - 1)]),
axis=1)
admittanceMatrixD = cp.diag(lengths / self.z)
return admittanceMatrixD
def _eigsh_solve_ritz(alpha, beta, beta_k, k, which):
t = cupy.diag(alpha)
t = t + cupy.diag(beta[:-1], k=1)
t = t + cupy.diag(beta[:-1], k=-1)
if beta_k is not None:
t[k, :k] = beta_k
t[:k, k] = beta_k
w, s = cupy.linalg.eigh(t)
# Pick-up k ritz-values and ritz-vectors
if which == 'LA':
idx = cupy.argsort(w)
elif which == 'LM':
idx = cupy.argsort(cupy.absolute(w))
wk = w[idx[-k:]]
sk = s[:, idx[-k:]]
return wk, sk
def _slogdet_one(a):
util._assert_rank2(a)
util._assert_nd_squareness(a)
dtype = a.dtype
handle = device.get_cusolver_handle()
m = len(a)
ipiv = cupy.empty(m, 'i')
info = cupy.empty((), 'i')
# Need to make a copy because getrf works inplace
a_copy = a.copy(order='F')
if dtype == 'f':
getrf_bufferSize = cusolver.sgetrf_bufferSize
getrf = cusolver.sgetrf
#<-- MODIFIED
elif dtype == 'd':
getrf_bufferSize = cusolver.dgetrf_bufferSize
getrf = cusolver.dgetrf
elif dtype == 'F':
getrf_bufferSize = cusolver.cgetrf_bufferSize
getrf = cusolver.cgetrf
else:
getrf_bufferSize = cusolver.zgetrf_bufferSize
getrf = cusolver.zgetrf
#<-- MODIFIED
buffersize = getrf_bufferSize(handle, m, m, a_copy.data.ptr, m)
workspace = cupy.empty(buffersize, dtype=dtype)
getrf(handle, m, m, a_copy.data.ptr, m, workspace.data.ptr, ipiv.data.ptr,
info.data.ptr)
if info[()] == 0:
diag = cupy.diag(a_copy)
# ipiv is 1-origin
non_zero = (cupy.count_nonzero(ipiv != cupy.arange(1, m + 1)) +
cupy.count_nonzero(diag < 0))
# Note: sign == -1 ** (non_zero % 2)
sign = (non_zero % 2) * -2 + 1
logdet = cupy.log(abs(diag)).sum()
else:
sign = cupy.array(0.0, dtype=dtype)
#ORIGINAL
# logdet = cupy.array(float('-inf'), dtype)
#<-- MODIFIED
if dtype in ['f', 'd']:
logdet = cupy.array(float('-inf'), dtype)
elif dtype == 'F':
logdet = cupy.array(float('-inf'), cupy.float32)
else:
logdet = cupy.array(float('-inf'), cupy.float64)
#<-- MODIFIED
return sign, logdet
def _initialize_nets(self):
self.weights = cp.random.normal(
size=(self.pop_size, self.total, self.total),
dtype='single') * cp.tile(
cp.triu(cp.ones(shape=(self.total, self.total), dtype='bool_'),
1), (self.pop_size, 1, 1)) * (cp.random.uniform(
size=(self.pop_size, self.total, self.total),
dtype='single') < .5)
self.weights[:, :, self.inputs:] *= cp.sqrt(4 / cp.minimum(
cp.arange(self.inputs, self.total), self.inputs + self.hidden))
self.weights[:, :self.inputs, :self.inputs] = 0
self.weights[:, -self.outputs:, -self.outputs:] = cp.tile(
cp.diag(
cp.diag(
cp.ones(shape=(self.outputs, self.outputs),
dtype='bool_'))), (self.pop_size, 1, 1))
self.biases = cp.random.normal(
size=(self.pop_size, 1, self.hidden + self.outputs),
dtype='single') * .5
def __estimate_one_step(self, threshold: int):
"""
Estimate the solution having a given threshold value and keeping only the singular values above these threshold.
Values smaller than numerical zero are always discarded.
:param threshold: Value specifying the smallest singular value (sorted in descending order) to keep. All singular
values smaller than given are discarded.
:type threshold: int
"""
self.current = cp.matmul(self.__V.T[:, :threshold],
cp.matmul(cp.diag(cp.divide(1, self.__D[:threshold])),
cp.matmul(self.__U[:, :threshold].T, self.q_estimator)))
def test_csrilu02(self, dtype):
dtype = numpy.dtype(dtype)
a_ref = self._make_matrix(dtype)
a = sparse.csr_matrix(a_ref)
cusparse.csrilu02(a, level_info=self.level_info)
a = a.todense()
al = cupy.tril(a, k=-1)
al = al + cupy.diag(cupy.ones((self.n, ), dtype=dtype.char.lower()))
au = cupy.triu(a)
a = al @ au
tol = self._tol[dtype.char.lower()]
cupy.testing.assert_allclose(a, a_ref, atol=tol, rtol=tol)