torch.inverse

torch.inverse(input, *, out=None) → Tensor

Takes the inverse of the square matrix input. input can be batches of 2D square tensors, in which case this function would return a tensor composed of individual inverses.

Supports real and complex input.

Note

Irrespective of the original strides, the returned tensors will be transposed, i.e. with strides like input.contiguous().transpose(-2, -1).stride()

Parameters

input (Tensor) – the input tensor of size $(*, n, n)$ where * is zero or more batch dimensions

Keyword Arguments

out (Tensor, optional) – the output tensor.

Examples:

>>> x = torch.rand(4, 4)
>>> y = torch.inverse(x)
>>> z = torch.mm(x, y)
>>> z
tensor([[ 1.0000, -0.0000, -0.0000,  0.0000],
        [ 0.0000,  1.0000,  0.0000,  0.0000],
        [ 0.0000,  0.0000,  1.0000,  0.0000],
        [ 0.0000, -0.0000, -0.0000,  1.0000]])
>>> torch.max(torch.abs(z - torch.eye(4))) # Max non-zero
tensor(1.1921e-07)

>>> # Batched inverse example
>>> x = torch.randn(2, 3, 4, 4)
>>> y = torch.inverse(x)
>>> z = torch.matmul(x, y)
>>> torch.max(torch.abs(z - torch.eye(4).expand_as(x))) # Max non-zero
tensor(1.9073e-06)

>>> x = torch.rand(4, 4, dtype=torch.cdouble)
>>> y = torch.inverse(x)
>>> z = torch.mm(x, y)
>>> z
tensor([[ 1.0000e+00+0.0000e+00j, -1.3878e-16+3.4694e-16j,
        5.5511e-17-1.1102e-16j,  0.0000e+00-1.6653e-16j],
        [ 5.5511e-16-1.6653e-16j,  1.0000e+00+6.9389e-17j,
        2.2204e-16-1.1102e-16j, -2.2204e-16+1.1102e-16j],
        [ 3.8858e-16-1.2490e-16j,  2.7756e-17+3.4694e-17j,
        1.0000e+00+0.0000e+00j, -4.4409e-16+5.5511e-17j],
        [ 4.4409e-16+5.5511e-16j, -3.8858e-16+1.8041e-16j,
        2.2204e-16+0.0000e+00j,  1.0000e+00-3.4694e-16j]],
    dtype=torch.complex128)
>>> torch.max(torch.abs(z - torch.eye(4, dtype=torch.cdouble))) # Max non-zero
tensor(7.5107e-16, dtype=torch.float64)