torch.pinverse

torch.pinverse(input, rcond=1e-15) → Tensor

Calculates the pseudo-inverse (also known as the Moore-Penrose inverse) of a 2D tensor. Please look at Moore-Penrose inverse for more details

Note

This method is implemented using the Singular Value Decomposition.

Note

The pseudo-inverse is not necessarily a continuous function in the elements of the matrix [1]. Therefore, derivatives are not always existent, and exist for a constant rank only [2]. However, this method is backprop-able due to the implementation by using SVD results, and could be unstable. Double-backward will also be unstable due to the usage of SVD internally. See svd() for more details.

Note

Supports real and complex inputs. Batched version for complex inputs is only supported on the CPU.

Parameters

• input (Tensor) – The input tensor of size $(*, m, n)$ where $*$ is zero or more batch dimensions.

• rcond (float, optional) – A floating point value to determine the cutoff for small singular values. Default: 1e-15.

Returns

The pseudo-inverse of input of dimensions $(*, n, m)$

Example:

>>> input = torch.randn(3, 5)
>>> input
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.pinverse(input)
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]])
>>> # Batched pinverse example
>>> a = torch.randn(2,6,3)
>>> b = torch.pinverse(a)
>>> torch.matmul(b, a)
tensor([[[ 1.0000e+00,  1.6391e-07, -1.1548e-07],
        [ 8.3121e-08,  1.0000e+00, -2.7567e-07],
        [ 3.5390e-08,  1.4901e-08,  1.0000e+00]],

        [[ 1.0000e+00, -8.9407e-08,  2.9802e-08],
        [-2.2352e-07,  1.0000e+00,  1.1921e-07],
        [ 0.0000e+00,  8.9407e-08,  1.0000e+00]]])