Pinverse — torch_pinverse • torch

Pinverse

Usage

torch_pinverse(self, rcond = 1e-15)

Arguments

self: (Tensor) The input tensor of size $(*, m, n)$ where $*$ is zero or more batch dimensions
rcond: (float) A floating point value to determine the cutoff for small singular values. Default: 1e-15

Note

This method is implemented using the Singular Value Decomposition.

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 `~torch.svd` for more details.

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

Examples

if (torch_is_installed()) {

input = torch_randn(c(3, 5))
input
torch_pinverse(input)
# Batched pinverse example
a = torch_randn(c(2,6,3))
b = torch_pinverse(a)
torch_matmul(b, a)
}
#> torch_tensor
#> (1,.,.) = 
#>   1.0000e+00  1.2784e-07  8.0884e-08
#>   4.4212e-08  1.0000e+00  1.4450e-08
#>   9.3164e-08 -1.1478e-07  1.0000e+00
#> 
#> (2,.,.) = 
#>   1.0000e+00 -5.2335e-08  1.0375e-07
#>  -2.2728e-08  1.0000e+00  2.8106e-08
#>   1.5014e-07 -1.5240e-08  1.0000e+00
#> [ CPUFloatType{2,3,3} ]