Skip to content

is_nonnegative

Checks if the matrix is nonnegative or doubly nonnegative.

is_nonnegative 

is_nonnegative(
    input_mat: ndarray, mat_type: str = "nonnegative"
) -> bool

Check if the matrix is nonnegative.

When all the entries in the matrix are larger than or equal to zero the matrix of interest is a nonnegative matrix 1.

When a matrix is nonegative and positive semidefinite 2, the matrix is doubly nonnegative.

Parameters:

  • input_mat (ndarray) –

    Matrix of interest.

  • mat_type (str, default: 'nonnegative' ) –

    Type of nonnegative matrix. "nonnegative" for a nonnegative matrix and "doubly" for a doubly nonnegative matrix.

Returns:

  • bool –

    Return True if matrix is nonnegative (or doubly nonnegative if specified), and False otherwise.

Raises:

  • TypeError –

    If something other than "doubly" or "nonnegative" is used for mat_type.

Examples:

We expect an identity matrix to be nonnegative.

import numpy as np
from toqito.matrix_props import is_nonnegative

print(is_nonnegative(np.eye(2)))
print(is_nonnegative(np.eye(2), "doubly"))
print(is_nonnegative(np.array([[1, -1], [1, 1]])))

True
True
False

References

1 Wikipedia. Nonnegative matrix. link.
2 Wikipedia. Definite matrix. link.

Source code in toqito/matrix_props/is_nonnegative.py 
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
def is_nonnegative(input_mat: np.ndarray, mat_type: str = "nonnegative") -> bool:
    r"""Check if the matrix is nonnegative.

    When all the entries in the matrix are larger than or equal to zero the matrix of interest is a
    nonnegative matrix [@wikipedianonnegative].

    When a matrix is nonegative and positive semidefinite [@wikipediadefinite], the matrix is doubly nonnegative.

    Args:
        input_mat: Matrix of interest.
        mat_type: Type of nonnegative matrix. `"nonnegative"` for a nonnegative matrix and `"doubly"` for a doubly
            nonnegative matrix.

    Returns:
        Return `True` if matrix is nonnegative (or doubly nonnegative if specified), and `False` otherwise.

    Raises:
        TypeError: If something other than `"doubly"` or `"nonnegative"` is used for `mat_type`.

    Examples:
        We expect an identity matrix to be nonnegative.

        ```python exec="1" source="above" result="text"
        import numpy as np
        from toqito.matrix_props import is_nonnegative

        print(is_nonnegative(np.eye(2)))
        print(is_nonnegative(np.eye(2), "doubly"))
        print(is_nonnegative(np.array([[1, -1], [1, 1]])))
        ```

    """
    valid_types = {"nonnegative", "doubly"}
    if mat_type not in valid_types:
        raise TypeError(f"Invalid matrix check type: {mat_type}. Must be one of: {valid_types}.")

    is_entrywise_nonnegative = bool(np.all(input_mat >= 0))

    if mat_type == "doubly":
        return is_entrywise_nonnegative and is_positive_semidefinite(input_mat)
    else:
        return is_entrywise_nonnegative