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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 -2.9802e-08 -7.4506e-08
#>   4.4703e-08  1.0000e+00  6.7055e-08
#>  -1.1921e-07 -6.7055e-08  1.0000e+00
#> 
#> (2,.,.) = 
#>   1.0000e+00 -3.7253e-09  2.9802e-08
#>   1.9372e-07  1.0000e+00  2.3842e-07
#>   5.9605e-08 -4.4703e-08  1.0000e+00
#> [ CPUFloatType{2,3,3} ]