# Copyright 2018 The Cirq Developers
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""A testing class with utilities for checking linear algebra."""
from typing import Optional
import numpy as np
from cirq import linalg
[docs]def random_unitary(dim: int) -> np.ndarray:
"""Returns a random unitary matrix distributed with Haar measure.
Args:
dim: The width and height of the matrix.
Returns:
The sampled unitary matrix.
References:
'How to generate random matrices from the classical compact groups'
http://arxiv.org/abs/math-ph/0609050
"""
z = (np.random.randn(dim, dim) +
1j * np.random.randn(dim, dim)) * np.sqrt(0.5)
q, r = np.linalg.qr(z)
d = np.diag(r)
return q * (d / abs(d))
[docs]def random_orthogonal(dim: int) -> np.ndarray:
# TODO(craiggidney): Distribute with Haar measure.
m = np.random.randn(dim, dim) * 2 - 1
q, _ = np.linalg.qr(m)
return q
[docs]def random_special_unitary(dim: int) -> np.ndarray:
r = random_unitary(dim)
r[0, :] /= np.linalg.det(r)
return r
[docs]def random_special_orthogonal(dim: int) -> np.ndarray:
m = random_orthogonal(dim)
if np.linalg.det(m) < 0:
m[0, :] *= -1
return m
[docs]def assert_allclose_up_to_global_phase(
actual: np.ndarray,
desired: np.ndarray,
*, # Forces keyword args.
rtol: float = 1e-7,
atol: float, # Require atol to be specified
equal_nan: bool = True,
err_msg: Optional[str] = '',
verbose: bool = True) -> None:
"""Checks if a ~= b * exp(i t) for some t.
Args:
actual: A numpy array.
desired: Another numpy array.
rtol: Relative error tolerance.
atol: Absolute error tolerance.
equal_nan: Whether or not NaN entries should be considered equal to
other NaN entries.
err_msg: The error message to be printed in case of failure.
verbose: If True, the conflicting values are appended to the error
message.
Raises:
AssertionError: The matrices aren't nearly equal up to global phase.
"""
actual, desired = linalg.match_global_phase(actual, desired)
np.testing.assert_allclose(
actual=actual,
desired=desired,
rtol=rtol,
atol=atol,
equal_nan=equal_nan,
err_msg=err_msg,
verbose=verbose)