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

torch.inverse() is deprecated. Please use torch.linalg.inv() instead.

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)