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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.


linalg_tensorinv(A, ind = 3L)



(Tensor): tensor to invert.


(int): index at which to compute the inverse of torch_tensordot(). Default: 3.


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


Consider using linalg_tensorsolve() if possible for multiplying a tensor on the left by the tensor inverse as linalg_tensorsolve(A, B) == torch_tensordot(linalg_tensorinv(A), B))

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


if (torch_is_installed()) {
A <- torch_eye(4 * 6)$reshape(c(4, 6, 8, 3))
Ainv <- linalg_tensorinv(A, ind = 3)
B <- torch_randn(4, 6)
torch_allclose(torch_tensordot(Ainv, B), linalg_tensorsolve(A, B))

A <- torch_randn(4, 4)
Atensorinv <- linalg_tensorinv(A, 2)
Ainv <- linalg_inv(A)
torch_allclose(Atensorinv, Ainv)
#> [1] TRUE