rand.random_orthonormal_basis

Generates a random orthonormal basis.

Functions

random_orthonormal_basis(dim[, is_real, seed])

Generate a real random orthonormal basis of given dimension \(d\).

Module Contents

rand.random_orthonormal_basis.random_orthonormal_basis(dim, is_real=False, seed=None)

Generate a real random orthonormal basis of given dimension \(d\).

The basis is generated from the columns of a random unitary matrix of the same dimension as the columns of a unitary matrix typically form an orthonormal basis [1].

Examples

To generate a random orthonormal basis of dimension \(4\),

from toqito.rand import random_orthonormal_basis

random_orthonormal_basis(4, is_real = True)

[array([-0.31850694, -0.20467977, -0.54500128,  0.74808631]),
 array([ 0.41596141,  0.68472588, -0.59448564, -0.06865424]),
 array([-0.80366456,  0.20015375, -0.27542388, -0.4880609 ]),
 array([-0.28222812,  0.67022022,  0.52316549,  0.44435349])]

It is also possible to add a seed for reproducibility.

from toqito.rand import random_orthonormal_basis

random_orthonormal_basis(2, is_real=True, seed=42)

[array([0.37621414, 0.92653274]), array([-0.92653274,  0.37621414])]

References

dim: int

Number of elements in the random orthonormal basis.

seed: int | None

A seed used to instantiate numpy’s random number generator.

Parameters:

  • dim (int)

  • is_real (bool)

  • seed (int | None)

Return type:

list[numpy.ndarray]