scipy.linalg.pinv#
- scipy.linalg.pinv(a, atol=None, rtol=None, return_rank=False, check_finite=True, cond=None, rcond=None)[source]#
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate a generalized inverse of a matrix using its singular-value decomposition
U @ S @ V
in the economy mode and picking up only the columns/rows that are associated with significant singular values.If
s
is the maximum singular value ofa
, then the significance cut-off value is determined byatol + rtol * s
. Any singular value below this value is assumed insignificant.- Parameters
- a(M, N) array_like
Matrix to be pseudo-inverted.
- atolfloat, optional
Absolute threshold term, default value is 0.
New in version 1.7.0.
- rtolfloat, optional
Relative threshold term, default value is
max(M, N) * eps
whereeps
is the machine precision value of the datatype ofa
.New in version 1.7.0.
- return_rankbool, optional
If True, return the effective rank of the matrix.
- check_finitebool, optional
Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.
- cond, rcondfloat, optional
In older versions, these values were meant to be used as
atol
withrtol=0
. If both were givenrcond
overwrotecond
and hence the code was not correct. Thus using these are strongly discouraged and the tolerances above are recommended instead. In fact, if provided, atol, rtol takes precedence over these keywords.Changed in version 1.7.0: Deprecated in favor of
rtol
andatol
parameters above and will be removed in future versions of SciPy.Changed in version 1.3.0: Previously the default cutoff value was just
eps*f
wheref
was1e3
for single precision and1e6
for double precision.
- Returns
- B(N, M) ndarray
The pseudo-inverse of matrix a.
- rankint
The effective rank of the matrix. Returned if return_rank is True.
- Raises
- LinAlgError
If SVD computation does not converge.
Examples
>>> from scipy import linalg >>> rng = np.random.default_rng() >>> a = rng.standard_normal((9, 6)) >>> B = linalg.pinv(a) >>> np.allclose(a, a @ B @ a) True >>> np.allclose(B, B @ a @ B) True