aesara.tensor.nlinalg.pinv

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aesara.tensor.nlinalg.pinv#

aesara.tensor.nlinalg.pinv(x, hermitian=False)[source]#

Computes the pseudo-inverse of a matrix $A$ .

The pseudo-inverse of a matrix $A$ , denoted $A^+$ , is defined as: “the matrix that ‘solves’ [the least-squares problem] $Ax = b$ ,” i.e., if $\bar{x}$ is said solution, then $A^+$ is that matrix such that $\bar{x} = A^+b$ .

Note that $Ax=AA^+b$ , so $AA^+$ is close to the identity matrix. This method is not faster than matrix_inverse. Its strength comes from that it works for non-square matrices. If you have a square matrix though, matrix_inverse can be both more exact and faster to compute. Also this op does not get optimized into a solve op.