def pinv(a, rcond=1e-15):
"""Compute the Moore-Penrose pseudoinverse of a matrix.
It computes a pseudoinverse of a matrix ``a``, which is a generalization
of the inverse matrix with Singular Value Decomposition (SVD).
Note that it automatically removes small singular values for stability.
Args:
a (cupy.ndarray): The matrix with dimension ``(M, N)``
rcond (float): Cutoff parameter for small singular values.
For stability it computes the largest singular value denoted by
``s``, and sets all singular values smaller than ``s`` to zero.
Returns:
cupy.ndarray: The pseudoinverse of ``a`` with dimension ``(N, M)``.
.. 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.pinv`
"""
u, s, vt = decomposition.svd(a, full_matrices=False)
cutoff = rcond * s.max()
s1 = 1 / s
s1[s <= cutoff] = 0
return core.dot(vt.T, s1[:, None] * u.T)
def pinv(a, rcond=1e-15):
"""Compute the Moore-Penrose pseudoinverse of a matrix.
It computes a pseudoinverse of a matrix ``a``, which is a generalization
of the inverse matrix with Singular Value Decomposition (SVD).
Note that it automatically removes small singular values for stability.
Args:
a (cupy.ndarray): The matrix with dimension ``(M, N)``
rcond (float): Cutoff parameter for small singular values.
For stability it computes the largest singular value denoted by
``s``, and sets all singular values smaller than ``s`` to zero.
Returns:
cupy.ndarray: The pseudoinverse of ``a`` with dimension ``(N, M)``.
.. seealso:: :func:`numpy.linalg.pinv`
"""
u, s, vt = decomposition.svd(a, full_matrices=False)
cutoff = rcond * s.max()
s1 = 1 / s
s1[s <= cutoff] = 0
return core.dot(vt.T, s1[:, None] * u.T)
def matrix_rank(M, tol=None):
"""Return matrix rank of array using SVD method
Args:
M (cupy.ndarray): Input array. Its `ndim` must be less than or equal to
2.
tol (None or float): Threshold of singular value of `M`.
When `tol` is `None`, and `eps` is the epsilon value for datatype
of `M`, then `tol` is set to `S.max() * max(M.shape) * eps`,
where `S` is the singular value of `M`.
It obeys :func:`numpy.linalg.matrix_rank`.
Returns:
cupy.ndarray: Rank of `M`.
.. seealso:: :func:`numpy.linalg.matrix_rank`
"""
if M.ndim < 2:
return (M != 0).any().astype(int)
S = decomposition.svd(M, compute_uv=False)
if tol is None:
tol = (S.max(axis=-1, keepdims=True) * max(M.shape[-2:]) *
numpy.finfo(S.dtype).eps)
return (S > tol).sum(axis=-1, dtype=numpy.intp)
def _multi_svd_norm(x, row_axis, col_axis, op):
y = cupy.moveaxis(x, (row_axis, col_axis), (-2, -1))
result = op(decomposition.svd(y, compute_uv=False), axis=-1)
return result
