torch.linalg.pinv¶
-
torch.linalg.
pinv
(A, rcond=1e-15, hermitian=False, *, out=None) → Tensor¶ Computes the pseudoinverse (Moore-Penrose inverse) of a matrix.
The pseudoinverse may be defined algebraically but it is more computationally convenient to understand it through the SVD
Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if
A
is a batch of matrices then the output has the same batch dimensions.If
hermitian
= True,A
is assumed to be Hermitian if complex or symmetric if real, but this is not checked internally. Instead, just the lower triangular part of the matrix is used in the computations.The singular values (or the norm of the eigenvalues when
hermitian
= True) that are below the specifiedrcond
threshold are treated as zero and discarded in the computation.Note
This function uses
torch.linalg.svd()
ifhermitian
= False andtorch.linalg.eigh()
ifhermitian
= True. For CUDA inputs, this function synchronizes that device with the CPU.Note
Consider using
torch.linalg.lstsq()
if possible for multiplying a matrix on the left by the pseudoinverse, as:torch.linalg.lstsq(A, B).solution == A.pinv() @ B
It is always prefered to use
lstsq()
when possible, as it is faster and more numerically stable than computing the pseudoinverse explicitly.Warning
This function uses internally
torch.linalg.svd()
(ortorch.linalg.eigh()
whenhermitian
= True), so its derivative has the same problems as those of these functions. See the warnings intorch.linalg.svd()
andtorch.linalg.eigh()
for more details.See also
torch.linalg.inv()
computes the inverse of a square matrix.torch.linalg.lstsq()
computesA
.pinv() @B
with a numerically stable algorithm.- Parameters
A (Tensor) – tensor of shape (*, m, n) where * is zero or more batch dimensions.
rcond (float or Tensor, optional) – the tolerance value to determine when is a singular value zero If it is a
torch.Tensor
, its shape must be broadcastable to that of the singular values ofA
as returned bytorch.svd()
. Default: 1e-15.hermitian (bool, optional) – indicates whether
A
is Hermitian if complex or symmetric if real. Default: False.
- Keyword Arguments
out (Tensor, optional) – output tensor. Ignored if None. Default: None.
Examples:
>>> A = torch.randn(3, 5) >>> A tensor([[ 0.5495, 0.0979, -1.4092, -0.1128, 0.4132], [-1.1143, -0.3662, 0.3042, 1.6374, -0.9294], [-0.3269, -0.5745, -0.0382, -0.5922, -0.6759]]) >>> torch.linalg.pinv(A) tensor([[ 0.0600, -0.1933, -0.2090], [-0.0903, -0.0817, -0.4752], [-0.7124, -0.1631, -0.2272], [ 0.1356, 0.3933, -0.5023], [-0.0308, -0.1725, -0.5216]]) >>> A = torch.randn(2, 6, 3) >>> Apinv = torch.linalg.pinv(A) >>> torch.dist(Apinv @ A, torch.eye(3)) tensor(8.5633e-07) >>> A = torch.randn(3, 3, dtype=torch.complex64) >>> A = A + A.T.conj() # creates a Hermitian matrix >>> Apinv = torch.linalg.pinv(A, hermitian=True) >>> torch.dist(Apinv @ A, torch.eye(3)) tensor(1.0830e-06)