toqito.matrix_props.is_block_positive

Checks if the matrix is block positive.

Module Contents

toqito.matrix_props.is_block_positive.is_block_positive(mat, k=1, dim=None, effort=2, rtol=1e-05)[source]

Check if matrix is block positive [@Johnston_2012_Norms].

Examples

The swap operator is always block positive, since it is the Choi matrix of the transpose map.

```python exec=”1” source=”above” from toqito.perms.swap_operator import swap_operator from toqito.matrix_props.is_block_positive import is_block_positive

mat = swap_operator(3)

print(is_block_positive(mat=mat)) ```

However, it’s not 2 - block positive.

```python exec=”1” source=”above” from toqito.perms.swap_operator import swap_operator from toqito.matrix_props.is_block_positive import is_block_positive

mat = swap_operator(3)

print(is_block_positive(mat=mat, k=2)) ```

Raises:

  • RuntimeError – Unable to determine k-block positivity. Please consider increasing the relative tolerance or the

  • effort level. –

Parameters:

  • mat (numpy.ndarray) – A bipartite Hermitian operator.

  • k (int) – A positive integer indicating that the function should determine whether or not the input operator is k-block

  • positive

  • i.e.

  • with (whether or not it remains nonnegative under left and right multiplication by vectors)

  • k

  • dim (int | list[int] | None) – The dimension of the two sub-systems. By default it’s assumed to be equal.

  • effort (int) – An integer value indicating the amount of computation you want to devote to determine block positivity

  • up. (before giving)

  • rtol (float) – The relative tolerance parameter (default 1e-05).

Returns:

Return True if matrix is k-block positive definite, False if not, or raise a runtime error if we are unable to determine whether or not the operator is block positive.

Return type:

bool | RuntimeError