pinv(a, atol=None, rtol=None, return_rank=False, check_finite=True, cond=None, rcond=None)
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 of a
, then the significance cut-off value is determined by atol + rtol * s
. Any singular value below this value is assumed insignificant.
Matrix to be pseudo-inverted.
Absolute threshold term, default value is 0.
Relative threshold term, default value is max(M, N) * eps
where eps
is the machine precision value of the datatype of a
.
If True, return the effective rank of the matrix.
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.
In older versions, these values were meant to be used as atol
with rtol=0
. If both were given rcond
overwrote cond
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.
Deprecated in favor of rtol
and atol
parameters above and will be removed in future versions of SciPy.
Previously the default cutoff value was just eps*f
where f
was 1e3
for single precision and 1e6
for double precision.
If SVD computation does not converge.
The pseudo-inverse of matrix a.
The effective rank of the matrix. Returned if :None:None:`return_rank` is True.
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
>>> 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) TrueSee :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._basic.pinv2
scipy.linalg._basic.pinv
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them