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Computes the sign and the log of the absolute value of the determinant of

one or more square matrices.

The input is a tensor of shape [N, M, M] whose inner-most 2 dimensions form square matrices. The outputs are two tensors containing the signs and absolute values of the log determinants for all N input submatrices [..., :, :] such that determinant = sign*exp(log_abs_determinant). The log_abs_determinant is computed as det(P)*sum(log(diag(LU))) where LU is the LU decomposition of the input and P is the corresponding permutation matrix.

input A Tensor. Must be one of the following types: half, float32, float64, complex64, complex128. Shape is [N, M, M].
name A name for the operation (optional).

A tuple of Tensor objects (sign, log_abs_determinant).
sign A Tensor. Has the same type as input.
log_abs_determinant A Tensor. Has the same type as input.