matrix_rank

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

Returns the rank (i.e., number of non-zero singular values) of a matrix (or a stack of matrices).

When x is a stack of matrices, the function must compute the number of non-zero singular values for each matrix in the stack.

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 real-valued 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 real-valued 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 real-valued floating-point data type determined by Type Promotion Rules (as applied to x). Default: None.

Returns:

out (array) – an array containing the ranks. The returned array must have the default integer data type and must have shape (...) (i.e., must have a shape equal to shape(x)[:-2]).

Notes

Changed in version 2022.12: Added complex data type support.