pinv_op

→TensorImplPtr

int pinv_op(const int & a)

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Python wrappers

pylucid.linalg.pinvfunction

Compute the Moore-Penrose pseudoinverse $A^+$ of a rectangular matrix.

Shape

Input a: (..., m, n).
Output: (..., n, m).

Parameters

aTensorImplPtr

Input matrix of shape (..., m, n) with leading batch dims. Need not be square or full rank. Must be at least 2-D and have a floating-point dtype.

Returns

TensorImplPtr

The pseudoinverse $A^+$ of shape (..., n, m) — the last two dimensions are swapped relative to the input.

Raises

:runtime_error

If a is null, has a non-floating-point dtype, or has fewer than two dimensions.

Notes

Internally a full reduced SVD is computed; if the caller already has the SVD on hand, forming $A^+ = V \Sigma^+ U^\top$ manually avoids the redundant factorisation.

Examples

>>> // Solve a tall least-squares system via the pseudoinverse:
>>> auto x_impl = matmul_op(pinv_op(a_impl), b_impl);