def estimate_rank(A, eps):
"""
Estimate matrix rank to a specified relative precision using randomized
methods.
The matrix `A` can be given as either a :class:`numpy.ndarray` or a
:class:`scipy.sparse.linalg.LinearOperator`, with different algorithms used
for each case. If `A` is of type :class:`numpy.ndarray`, then the output
rank is typically about 8 higher than the actual numerical rank.
.. This function automatically detects the form of the input parameters and
passes them to the appropriate backend. For details,
see :func:`backend.idd_estrank`, :func:`backend.idd_findrank`,
:func:`backend.idz_estrank`, and :func:`backend.idz_findrank`.
Parameters
----------
A : :class:`numpy.ndarray` or :class:`scipy.sparse.linalg.LinearOperator`
Matrix whose rank is to be estimated, given as either a
:class:`numpy.ndarray` or a :class:`scipy.sparse.linalg.LinearOperator`
with the `rmatvec` method (to apply the matrix adjoint).
eps : float
Relative error for numerical rank definition.
Returns
-------
int
Estimated matrix rank.
"""
from scipy.sparse.linalg import LinearOperator
real = _is_real(A)
if isinstance(A, np.ndarray):
if real:
rank = backend.idd_estrank(eps, A)
else:
rank = backend.idz_estrank(eps, A)
if rank == 0:
# special return value for nearly full rank
rank = min(A.shape)
return rank
elif isinstance(A, LinearOperator):
m, n = A.shape
matveca = A.rmatvec
if real:
return backend.idd_findrank(eps, m, n, matveca)
else:
return backend.idz_findrank(eps, m, n, matveca)
else:
raise _TYPE_ERROR
def estimate_rank(A, eps):
"""
Estimate matrix rank to a specified relative precision using randomized
methods.
The matrix `A` can be given as either a :class:`numpy.ndarray` or a
:class:`scipy.sparse.linalg.LinearOperator`, with different algorithms used
for each case. If `A` is of type :class:`numpy.ndarray`, then the output
rank is typically about 8 higher than the actual numerical rank.
.. This function automatically detects the form of the input parameters and
passes them to the appropriate backend. For details,
see :func:`backend.idd_estrank`, :func:`backend.idd_findrank`,
:func:`backend.idz_estrank`, and :func:`backend.idz_findrank`.
Parameters
----------
A : :class:`numpy.ndarray` or :class:`scipy.sparse.linalg.LinearOperator`
Matrix whose rank is to be estimated, given as either a
:class:`numpy.ndarray` or a :class:`scipy.sparse.linalg.LinearOperator`
with the `rmatvec` method (to apply the matrix adjoint).
eps : float
Relative error for numerical rank definition.
Returns
-------
int
Estimated matrix rank.
"""
from scipy.sparse.linalg import LinearOperator
real = _is_real(A)
if isinstance(A, np.ndarray):
if real:
rank = backend.idd_estrank(eps, A)
else:
rank = backend.idz_estrank(eps, A)
if rank == 0:
# special return value for nearly full rank
rank = min(A.shape)
return rank
elif isinstance(A, LinearOperator):
m, n = A.shape
matveca = A.rmatvec
if real:
return backend.idd_findrank(eps, m, n, matveca)
else:
return backend.idz_findrank(eps, m, n, matveca)
else:
raise _TYPE_ERROR
