torch.linalg.tensorinv(A, ind=2, *, out=None)Tensor

Computes the multiplicative inverse of torch.tensordot().

If m is the product of the first ind dimensions of A and n is the product of the rest of the dimensions, this function expects m and n to be equal. If this is the case, it computes a tensor X such that tensordot(A, X, ind) is the identity matrix in dimension m. X will have the shape of A but with the first ind dimensions pushed back to the end

X.shape == A.shape[ind:] + A.shape[:ind]

Supports input of float, double, cfloat and cdouble dtypes.


When A is a 2-dimensional tensor and ind= 1, this function computes the (multiplicative) inverse of A (see torch.linalg.inv()).


Consider using torch.linalg.tensorsolve() if possible for multiplying a tensor on the left by the tensor inverse, as:

tensorsolve(A, B) == torch.tensordot(tensorinv(A), B)

It is always prefered to use tensorsolve() when possible, as it is faster and more numerically stable than computing the pseudoinverse explicitly.

See also

torch.linalg.tensorsolve() computes torch.tensordot(tensorinv(A), B).

  • A (Tensor) – tensor to invert. Its shape must satisfy prod(A.shape[:ind]) == prod(A.shape[ind:]).

  • ind (int) – index at which to compute the inverse of torch.tensordot(). Default: 2.

Keyword Arguments

out (Tensor, optional) – output tensor. Ignored if None. Default: None.


RuntimeError – if the reshaped A is not invertible or the product of the first ind dimensions is not equal to the product of the rest.


>>> A = torch.eye(4 * 6).reshape((4, 6, 8, 3))
>>> Ainv = torch.linalg.tensorinv(A, ind=2)
>>> Ainv.shape
torch.Size([8, 3, 4, 6])
>>> B = torch.randn(4, 6)
>>> torch.allclose(torch.tensordot(Ainv, B), torch.linalg.tensorsolve(A, B))

>>> A = torch.randn(4, 4)
>>> Atensorinv = torch.linalg.tensorinv(A, ind=1)
>>> Ainv = torch.linalg.inverse(A)
>>> torch.allclose(Atensorinv, Ainv)


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