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op {
graph_op_name: "MatrixLogarithm"
visibility: HIDDEN
in_arg {
name: "input"
description: <<END
Shape is `[..., M, M]`.
END
}
out_arg {
name: "output"
description: <<END
Shape is `[..., M, M]`.
@compatibility(scipy)
Equivalent to scipy.linalg.logm
@end_compatibility
END
}
summary: "Computes the matrix logarithm of one or more square matrices:"
description: <<END
log(exp(A)) = A
This op is only defined for complex matrices. If A is positive-definite and
real, then casting to a complex matrix, taking the logarithm and casting back
to a real matrix will give the correct result.
This function computes the matrix logarithm using the Schur-Parlett algorithm.
Details of the algorithm can be found in Section 11.6.2 of:
Nicholas J. Higham, Functions of Matrices: Theory and Computation, SIAM 2008.
ISBN 978-0-898716-46-7.
The input is a tensor of shape `[..., M, M]` whose inner-most 2 dimensions
form square matrices. The output is a tensor of the same shape as the input
containing the exponential for all input submatrices `[..., :, :]`.
END
}
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