Throws a runtime_error if the matrix is not invertible.
Details
Letting K be R or C, for a matrix A K^n n, its inverse matrix A^-1 K^n n (if it exists) is defined as
where I_n is the n-dimensional identity matrix.
The inverse matrix exists if and only if A is invertible. In this case,
the inverse is unique.
Supports input of float, double, cfloat and cdouble dtypes.
Also supports batches of matrices, and if A is a batch of matrices
then the output has the same batch dimensions.
Consider using linalg_solve() if possible for multiplying a matrix on the left by
the inverse, as linalg_solve(A, B) == A$inv() %*% B
It is always prefered to use linalg_solve() when possible, as it is faster and more
numerically stable than computing the inverse explicitly.
See also
linalg_pinv() computes the pseudoinverse (Moore-Penrose inverse) of matrices
of any shape.
linalg_solve() computes A$inv() %*% B with a
numerically stable algorithm.
Other linalg:
linalg_cholesky(),
linalg_cholesky_ex(),
linalg_det(),
linalg_eig(),
linalg_eigh(),
linalg_eigvals(),
linalg_eigvalsh(),
linalg_householder_product(),
linalg_inv_ex(),
linalg_lstsq(),
linalg_matrix_norm(),
linalg_matrix_power(),
linalg_matrix_rank(),
linalg_multi_dot(),
linalg_norm(),
linalg_pinv(),
linalg_qr(),
linalg_slogdet(),
linalg_solve(),
linalg_solve_triangular(),
linalg_svd(),
linalg_svdvals(),
linalg_tensorinv(),
linalg_tensorsolve(),
linalg_vector_norm()
Examples
if (torch_is_installed()) {
A <- torch_randn(4, 4)
linalg_inv(A)
}
#> torch_tensor
#> 3.8402 6.7315 -9.2205 -21.2161
#> 0.2035 1.3422 -1.5934 -3.8556
#> -0.0105 -0.3134 -0.0132 -0.5598
#> 2.0899 0.6437 0.3838 -2.6318
#> [ CPUFloatType{4,4} ]