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
This method is implemented using the Singular Value Decomposition.
The pseudo-inverse is not necessarily a continuous function in the elements of the matrix . Therefore, derivatives are not always existent, and exist for a constant rank only . 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.
The pseudo-inverse of
>>> 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]]])