def kron(a, b):
"""Returns the kronecker product of two arrays.
Args:
a (~cupy.ndarray): The first argument.
b (~cupy.ndarray): The second argument.
Returns:
~cupy.ndarray: Output array.
.. seealso:: :func:`numpy.kron`
"""
a_ndim = a.ndim
b_ndim = b.ndim
if a_ndim == 0 or b_ndim == 0:
return cupy.multiply(a, b)
ndim = b_ndim
a_shape = a.shape
b_shape = b.shape
if a_ndim != b_ndim:
if b_ndim > a_ndim:
a_shape = (1,) * (b_ndim - a_ndim) + a_shape
else:
b_shape = (1,) * (a_ndim - b_ndim) + b_shape
ndim = a_ndim
axis = ndim - 1
out = core.tensordot_core(a, b, None, a.size, b.size, 1, a_shape + b_shape)
for _ in six.moves.range(ndim):
out = core.concatenate_method(out, axis=axis)
return out
def concatenate(tup, axis=0):
"""Joins arrays along an axis.
Args:
tup (sequence of arrays): Arrays to be joined. All of these should have
same dimensionalities except the specified axis.
axis (int): The axis to join arrays along.
Returns:
cupy.ndarray: Joined array.
.. seealso:: :func:`numpy.concatenate`
"""
return core.concatenate_method(tup, axis)
def concatenate(tup, axis=0):
"""Joins arrays along an axis.
Args:
tup (sequence of arrays): Arrays to be joined. All of these should have
same dimensionalities except the specified axis.
axis (int): The axis to join arrays along.
Returns:
cupy.ndarray: Joined array.
.. seealso:: :func:`numpy.concatenate`
"""
return core.concatenate_method(tup, axis)
def concatenate(tup, axis=0):
"""Joins arrays along an axis.
Args:
tup (sequence of arrays): Arrays to be joined. All of these should have
same dimensionalities except the specified axis.
axis (int or None): The axis to join arrays along.
If axis is None, arrays are flattened before use.
Default is 0.
Returns:
cupy.ndarray: Joined array.
.. seealso:: :func:`numpy.concatenate`
"""
if axis is None:
tup = [m.ravel() for m in tup]
axis = 0
return core.concatenate_method(tup, axis)
def cov(a, y=None, rowvar=True, bias=False, ddof=None):
"""Returns the covariance matrix of an array.
This function currently does not support ``fweights`` and ``aweights``
options.
Args:
a (cupy.ndarray): Array to compute covariance matrix.
y (cupy.ndarray): An additional set of variables and observations.
rowvar (bool): If ``True``, then each row represents a variable, with
observations in the columns. Otherwise, the relationship is
transposed.
bias (bool): If ``False``, normalization is by ``(N - 1)``, where N is
the number of observations given (unbiased estimate). If ``True``,
then normalization is by ``N``.
ddof (int): If not ``None`` the default value implied by bias is
overridden. Note that ``ddof=1`` will return the unbiased estimate
and ``ddof=0`` will return the simple average.
Returns:
cupy.ndarray: The covariance matrix of the input array.
.. seealso:: :func:`numpy.cov`
"""
if ddof is not None and ddof != int(ddof):
raise ValueError('ddof must be integer')
if a.ndim > 2:
raise ValueError('Input must be <= 2-d')
if y is None:
dtype = numpy.promote_types(a.dtype, numpy.float64)
else:
if y.ndim > 2:
raise ValueError('y must be <= 2-d')
dtype = functools.reduce(numpy.promote_types,
(a.dtype, y.dtype, numpy.float64))
X = cupy.array(a, ndmin=2, dtype=dtype)
if not rowvar and X.shape[0] != 1:
X = X.T
if X.shape[0] == 0:
return cupy.array([]).reshape(0, 0)
if y is not None:
y = cupy.array(y, copy=False, ndmin=2, dtype=dtype)
if not rowvar and y.shape[0] != 1:
y = y.T
X = core.concatenate_method((X, y), axis=0)
if ddof is None:
ddof = 0 if bias else 1
fact = X.shape[1] - ddof
if fact <= 0:
warnings.warn('Degrees of freedom <= 0 for slice',
RuntimeWarning,
stacklevel=2)
fact = 0.0
X -= X.mean(axis=1)[:, None]
out = X.dot(X.T.conj()) * (1 / cupy.float64(fact))
return out.squeeze()
