pinv

pinv(x: array, /, *, rtol: float | array | None = None) → array

Returns the (Moore-Penrose) pseudo-inverse of a matrix (or a stack of matrices) x.

Parameters:

• x (array) – input array having shape (..., M, N) and whose innermost two dimensions form MxN matrices. Should have a floating-point data type.

• rtol (Optional[Union[float, array]]) – relative tolerance for small singular values. Singular values approximately less than or equal to rtol * largest_singular_value are set to zero. If a float, the value is equivalent to a zero-dimensional array having a floating-point data type determined by Type Promotion Rules (as applied to x) and must be broadcast against each matrix. If an array, must have a floating-point data type and must be compatible with shape(x)[:-2] (see Broadcasting). If None, the default value is max(M, N) * eps, where eps must be the machine epsilon associated with the floating-point data type determined by Type Promotion Rules (as applied to x). Default: None.

Returns:

out (array) – an array containing the pseudo-inverses. The returned array must have a floating-point data type determined by Type Promotion Rules and must have shape (..., N, M) (i.e., must have the same shape as x, except the innermost two dimensions must be transposed).