def get_rnn_lin_layer_bias_params(
handle, rnn_desc, layer, x_desc, w_desc, w, lin_layer_id):
bias_desc = Descriptor(cudnn.createFilterDescriptor(),
cudnn.destroyFilterDescriptor)
ptr = numpy.array(0, dtype=numpy.intp)
cudnn.getRNNLinLayerBiasParams(
handle, rnn_desc.value, layer, x_desc.value, w_desc.value, w.data.ptr,
lin_layer_id, bias_desc.value, ptr.ctypes.data)
offset = (ptr - w.data.ptr) // 4
_, _, _, dim = cudnn.getFilterNdDescriptor(bias_desc.value, 3)
size = internal.prod(dim)
bias = w[offset: offset + size]
return bias
def _potrf_batched(a):
"""Batched Cholesky decomposition.
Decompose a given array of two-dimensional square matrices into
``L * L.T``, where ``L`` is a lower-triangular matrix and ``.T``
is a conjugate transpose operator.
Args:
a (cupy.ndarray): The input array of matrices
with dimension ``(..., N, N)``
Returns:
cupy.ndarray: The lower-triangular matrix.
"""
if not check_availability('potrfBatched'):
raise RuntimeError('potrfBatched is not available')
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
if dtype == 'f':
potrfBatched = cusolver.spotrfBatched
elif dtype == 'd':
potrfBatched = cusolver.dpotrfBatched
elif dtype == 'F':
potrfBatched = cusolver.cpotrfBatched
else: # dtype == 'D':
potrfBatched = cusolver.zpotrfBatched
x = a.astype(dtype, order='C', copy=True)
xp = cupy.core._mat_ptrs(x)
n = x.shape[-1]
ldx = x.strides[-2] // x.dtype.itemsize
handle = device.get_cusolver_handle()
batch_size = internal.prod(x.shape[:-2])
dev_info = cupy.empty(batch_size, dtype=numpy.int32)
potrfBatched(
handle, cublas.CUBLAS_FILL_MODE_UPPER, n, xp.data.ptr, ldx,
dev_info.data.ptr, batch_size)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrfBatched, dev_info)
return cupy.tril(x)
def tensorsolve(a, b, axes=None):
"""Solves tensor equations denoted by ``ax = b``.
Suppose that ``b`` is equivalent to ``cupy.tensordot(a, x)``.
This function computes tensor ``x`` from ``a`` and ``b``.
Args:
a (cupy.ndarray): The tensor with ``len(shape) >= 1``
b (cupy.ndarray): The tensor with ``len(shape) >= 1``
axes (tuple of ints): Axes in ``a`` to reorder to the right
before inversion.
Returns:
cupy.ndarray:
The tensor with shape ``Q`` such that ``b.shape + Q == a.shape``.
.. warning::
This function calls one or more cuSOLVER routine(s) which may yield
invalid results if input conditions are not met.
To detect these invalid results, you can set the `linalg`
configuration to a value that is not `ignore` in
:func:`cupyx.errstate` or :func:`cupyx.seterr`.
.. seealso:: :func:`numpy.linalg.tensorsolve`
"""
if axes is not None:
allaxes = list(range(a.ndim))
for k in axes:
allaxes.remove(k)
allaxes.insert(a.ndim, k)
a = a.transpose(allaxes)
oldshape = a.shape[-(a.ndim - b.ndim):]
prod = internal.prod(oldshape)
a = a.reshape(-1, prod)
b = b.ravel()
result = solve(a, b)
return result.reshape(oldshape)
def tensorinv(a, ind=2):
"""Computes the inverse of a tensor.
This function computes tensor ``a_inv`` from tensor ``a`` such that
``tensordot(a_inv, a, ind) == I``, where ``I`` denotes the identity tensor.
Args:
a (cupy.ndarray):
The tensor such that
``prod(a.shape[:ind]) == prod(a.shape[ind:])``.
ind (int):
The positive number used in ``axes`` option of ``tensordot``.
Returns:
cupy.ndarray:
The inverse of a tensor whose shape is equivalent to
``a.shape[ind:] + a.shape[:ind]``.
.. warning::
This function calls one or more cuSOLVER routine(s) which may yield
invalid results if input conditions are not met.
To detect these invalid results, you can set the `linalg`
configuration to a value that is not `ignore` in
:func:`cupyx.errstate` or :func:`cupyx.seterr`.
.. seealso:: :func:`numpy.linalg.tensorinv`
"""
_util._assert_cupy_array(a)
if ind <= 0:
raise ValueError('Invalid ind argument')
oldshape = a.shape
invshape = oldshape[ind:] + oldshape[:ind]
prod = internal.prod(oldshape[ind:])
a = a.reshape(prod, -1)
a_inv = inv(a)
return a_inv.reshape(*invshape)
def test_empty(self):
self.assertEqual(internal.prod([]), 1)
def test_two(self):
self.assertEqual(internal.prod([2, 3]), 6)
def test_one(self):
self.assertEqual(internal.prod([2]), 2)
def check_usv(self, shape, dtype):
array = testing.shaped_random(
shape, numpy, dtype=dtype, seed=self.seed)
a_cpu = numpy.asarray(array, dtype=dtype)
a_gpu = cupy.asarray(array, dtype=dtype)
result_cpu = numpy.linalg.svd(a_cpu, full_matrices=self.full_matrices)
result_gpu = cupy.linalg.svd(a_gpu, full_matrices=self.full_matrices)
# Check if the input matrix is not broken
cupy.testing.assert_allclose(a_gpu, a_cpu)
assert len(result_gpu) == 3
for i in range(3):
assert result_gpu[i].shape == result_cpu[i].shape
assert result_gpu[i].dtype == result_cpu[i].dtype
u_cpu, s_cpu, vh_cpu = result_cpu
u_gpu, s_gpu, vh_gpu = result_gpu
cupy.testing.assert_allclose(s_gpu, s_cpu, rtol=1e-5, atol=1e-4)
# reconstruct the matrix
k = s_cpu.shape[-1]
if len(shape) == 2:
if self.full_matrices:
a_gpu_usv = cupy.dot(u_gpu[:, :k] * s_gpu, vh_gpu[:k, :])
else:
a_gpu_usv = cupy.dot(u_gpu * s_gpu, vh_gpu)
else:
if self.full_matrices:
a_gpu_usv = cupy.matmul(u_gpu[..., :k] * s_gpu[..., None, :],
vh_gpu[..., :k, :])
else:
a_gpu_usv = cupy.matmul(u_gpu*s_gpu[..., None, :], vh_gpu)
cupy.testing.assert_allclose(a_gpu, a_gpu_usv, rtol=1e-4, atol=1e-4)
# assert unitary
if len(shape) == 2:
cupy.testing.assert_allclose(
cupy.matmul(u_gpu.T.conj(), u_gpu),
numpy.eye(u_gpu.shape[1]),
atol=1e-4)
cupy.testing.assert_allclose(
cupy.matmul(vh_gpu, vh_gpu.T.conj()),
numpy.eye(vh_gpu.shape[0]),
atol=1e-4)
else:
batch = prod(shape[:-2])
u_len = u_gpu.shape[-1]
vh_len = vh_gpu.shape[-2]
if batch == 0:
id_u_cpu = numpy.empty(shape[:-2] + (u_len, u_len))
id_vh_cpu = numpy.empty(shape[:-2] + (vh_len, vh_len))
else:
id_u_cpu = [numpy.eye(u_len) for _ in range(batch)]
id_u_cpu = numpy.stack(id_u_cpu, axis=0).reshape(
*(shape[:-2]), u_len, u_len)
id_vh_cpu = [numpy.eye(vh_len) for _ in range(batch)]
id_vh_cpu = numpy.stack(id_vh_cpu, axis=0).reshape(
*(shape[:-2]), vh_len, vh_len)
cupy.testing.assert_allclose(
cupy.matmul(u_gpu.swapaxes(-1, -2).conj(), u_gpu),
id_u_cpu, atol=1e-4)
cupy.testing.assert_allclose(
cupy.matmul(vh_gpu, vh_gpu.swapaxes(-1, -2).conj()),
id_vh_cpu, atol=1e-4)
