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test_matrixtools.py
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test_matrixtools.py
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import numpy as np
import scipy.linalg as spl
import scipy.sparse as sps
import pygsti.tools.matrixtools as mt
from ..util import BaseCase
class MatrixToolsTester(BaseCase):
def test_is_hermitian(self):
herm_mx = np.array([[ 1, 1+2j],
[1-2j, 3]], 'complex')
non_herm_mx = np.array([[ 1, 4+2j],
[1+2j, 3]], 'complex')
self.assertTrue(mt.is_hermitian(herm_mx))
self.assertFalse(mt.is_hermitian(non_herm_mx))
def test_is_pos_def(self):
pos_mx = np.array([[ 4, 0.2],
[0.1, 3]], 'complex')
non_pos_mx = np.array([[ 0, 1],
[1, 0]], 'complex')
self.assertTrue(mt.is_pos_def(pos_mx))
self.assertFalse(mt.is_pos_def(non_pos_mx))
def test_mx_to_string(self):
mx = np.array([[ 1, 1+2j],
[1-2j, 3]], 'complex')
s = mt.mx_to_string(mx)
ls = s.split('\n')[:-1] # trim empty last line
mx2 = np.zeros_like(mx)
for i, row in enumerate(ls):
entries = row.split()
for j in range(len(entries) // 2):
mx2[i, j] = float(entries[2*j]) + 1j*float(entries[2*j+1][:-1]) # trim 'j'
self.assertArraysAlmostEqual(mx, mx2)
def test_is_valid_density_mx(self):
density_mx = np.array([[ 0.9, 0],
[ 0, 0.1]], 'complex')
non_density_mx = np.array([[ 2.0, 1.0],
[-1.0, 0]], 'complex')
self.assertTrue(mt.is_valid_density_mx(density_mx))
self.assertFalse(mt.is_valid_density_mx(non_density_mx))
def test_nullspace(self):
a = np.array([[1, 1], [1, 1]])
#print("Nullspace = ", mt.nullspace(a))
expected = np.array(
[[ 0.70710678],
[-0.70710678]]
)
diff1 = np.linalg.norm(mt.nullspace(a) - expected)
diff2 = np.linalg.norm(mt.nullspace(a) + expected) # -1*expected is OK too (just an eigenvector)
self.assertTrue(np.isclose(diff1, 0) or np.isclose(diff2, 0))
diff1 = np.linalg.norm(mt.nullspace_qr(a) - expected)
diff2 = np.linalg.norm(mt.nullspace_qr(a) + expected) # -1*expected is OK too (just an eigenvector)
self.assertTrue(np.isclose(diff1, 0) or np.isclose(diff2, 0))
#mt.print_mx(a)
def test_matrix_log(self):
M = np.array([[-1, 0], [0, -1]], 'complex') # degenerate negative evals
logM = mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
self.assertArraysAlmostEqual(spl.expm(logM), M)
M = np.array([[-1, 1e-10], [1e-10, -1]], 'complex') # degenerate negative evals, but will generate complex evecs
logM = mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
self.assertArraysAlmostEqual(spl.expm(logM), M)
with self.assertRaises(ValueError):
M = np.array([[1, 0], [0, -1]], 'd') # a negative *unparied* eigenvalue => log may be imaginary
mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
M = np.array([[1, 0], [0, -1]], 'd') # a negative *unparied* eigenvalue => log may be imaginary
logM = mt.real_matrix_log(M, action_if_imaginary="ignore", tol=1e-6)
self.assertArraysAlmostEqual(spl.expm(logM), M)
def test_matrix_log_warns_on_imaginary(self):
M = np.array([[1, 0], [0, -1]], 'd')
self.assertWarns(Warning, mt.real_matrix_log, M, action_if_imaginary="warn", tol=1e-6)
def test_matrix_log_raises_on_imaginary(self):
M = np.array([[1, 0], [0, -1]], 'd')
with self.assertRaises(ValueError):
mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
def test_matrix_log_raises_on_invalid_action(self):
M = np.array([[1, 0], [0, -1]], 'd')
with self.assertRaises(AssertionError):
mt.real_matrix_log(M, action_if_imaginary="foobar", tol=1e-6)
def test_matrix_log_raise_on_no_real_log(self):
a = np.array([[1, 1], [1, 1]])
with self.assertRaises(AssertionError):
mt.real_matrix_log(a)
def test_minweight_match(self):
a = np.array([1, 2, 3, 4], 'd')
b = np.array([3.1, 2.1, 4.1, 1.1], 'd')
expectedPairs = [(0, 3), (1, 1), (2, 0), (3, 2)] # (i,j) indices into a & b
wts = mt.minweight_match(a, b, metricfn=None, return_pairs=False,
pass_indices_to_metricfn=False)
wts, pairs = mt.minweight_match(a, b, metricfn=None, return_pairs=True,
pass_indices_to_metricfn=False)
self.assertEqual(set(pairs), set(expectedPairs))
def fn(x, y): return abs(x - y)
wts, pairs = mt.minweight_match(a, b, metricfn=fn, return_pairs=True,
pass_indices_to_metricfn=False)
self.assertEqual(set(pairs), set(expectedPairs))
def fn(i, j): return abs(a[i] - b[j])
wts, pairs = mt.minweight_match(a, b, metricfn=fn, return_pairs=True,
pass_indices_to_metricfn=True)
self.assertEqual(set(pairs), set(expectedPairs))
def test_fancy_assignment(self):
a = np.zeros((4, 4, 4), 'd')
twoByTwo = np.ones((2, 2), 'd')
#NOTEs from commit message motivating why we need this:
# a = np.zeros((3,3,3))
# a[:,1:2,1:3].shape == (3,1,2) # good!
# a[0,:,1:3].shape == (3,2) #good!
# a[0,:,[1,2]].shape == (2,3) # ?? (broacasting ':' makes this like a[0,[1,2]])
# a[:,[1,2],[1,2]].shape == (3,2) # ?? not (3,2,2) b/c lists broadcast
# a[:,[1],[1,2]].shape == (3,2) # ?? not (3,1,2) b/c lists broadcast
# a[:,[1,2],[0,1,2]].shape == ERROR b/c [1,2] can't broadcast to [0,1,2]!
#simple integer indices
mt._fas(a, (0, 0, 0), 4.5) # a[0,0,0] = 4.5
self.assertAlmostEqual(a[0, 0, 0], 4.5)
mt._fas(a, (0, 0, 0), 4.5, add=True) # a[0,0,0] += 4.5
self.assertAlmostEqual(a[0, 0, 0], 9.0)
#still simple: mix of slices and integers
mt._fas(a, (slice(0, 2), slice(0, 2), 0), twoByTwo) # a[0:2,0:2,0] = twoByTwo
self.assertArraysAlmostEqual(a[0:2, 0:2, 0], twoByTwo)
#complex case: some/all indices are integer arrays
mt._fas(a, ([0, 1], [0, 1], 0), twoByTwo[:, :]) # a[0:2,0:2,0] = twoByTwo - but a[[0,1],[0,1],0] wouldn't do this!
self.assertArraysAlmostEqual(a[0:2, 0:2, 0], twoByTwo)
mt._fas(a, ([0, 1], [0, 1], 0), twoByTwo[:, :], add=True) # a[0:2,0:2,0] = twoByTwo - but a[[0,1],[0,1],0] wouldn't do this!
self.assertArraysAlmostEqual(a[0:2, 0:2, 0], 2 * twoByTwo)
# Fancy indexing (without assignment)
self.assertEqual(mt._findx(a, (0, 0, 0)).shape, ()) # (1,1,1))
self.assertEqual(mt._findx(a, (slice(0, 2), slice(0, 2), slice(0, 2))).shape, (2, 2, 2))
self.assertEqual(mt._findx(a, (slice(0, 2), slice(0, 2), 0)).shape, (2, 2))
self.assertEqual(mt._findx(a, ([0, 1], [0, 1], 0)).shape, (2, 2))
self.assertEqual(mt._findx(a, ([], [0, 1], 0)).shape, (0, 2))
def test_safe_ops(self):
mx = np.array([[1+1j, 0],
[2+2j, 3+3j]], 'complex')
smx = sps.csr_matrix(mx)
smx_lil = sps.lil_matrix(mx) # currently unsupported
r = mt.safe_real(mx, inplace=False)
self.assertArraysAlmostEqual(r, np.real(mx))
i = mt.safe_imag(mx, inplace=False)
self.assertArraysAlmostEqual(i, np.imag(mx))
r = mt.safe_real(smx, inplace=False)
self.assertArraysAlmostEqual(r.toarray(), np.real(mx))
i = mt.safe_imag(smx, inplace=False)
self.assertArraysAlmostEqual(i.toarray(), np.imag(mx))
with self.assertRaises(NotImplementedError):
mt.safe_real(smx_lil, inplace=False)
with self.assertRaises(NotImplementedError):
mt.safe_imag(smx_lil, inplace=False)
with self.assertRaises(AssertionError):
mt.safe_real(mx, check=True)
with self.assertRaises(AssertionError):
mt.safe_imag(mx, check=True)
M = mx.copy(); M = mt.safe_real(M, inplace=True)
self.assertArraysAlmostEqual(M, np.real(mx))
M = mx.copy(); M = mt.safe_imag(M, inplace=True)
self.assertArraysAlmostEqual(M, np.imag(mx))
M = smx.copy(); M = mt.safe_real(M, inplace=True)
self.assertArraysAlmostEqual(M.toarray(), np.real(mx))
M = smx.copy(); M = mt.safe_imag(M, inplace=True)
self.assertArraysAlmostEqual(M.toarray(), np.imag(mx))
def test_fast_expm(self):
mx = np.array([[1, 2],
[2, 3]], 'd')
A = sps.csr_matrix(mx)
A, mu, m_star, s, eta = mt.expm_multiply_prep(A)
tol = 1e-6
B = np.array([1, 1], 'd')
expA = mt._custom_expm_multiply_simple_core(A, B, mu, m_star, s, tol, eta)
sp_expA = np.inner(spl.expm(mx), B)
self.assertArraysAlmostEqual(expA, sp_expA)
def test_fast_expm_raises_on_non_square(self):
nonSq = np.array([[1, 2, 4],
[2, 3, 5]], 'd')
N = sps.csr_matrix(nonSq)
with self.assertRaises(ValueError):
mt.expm_multiply_prep(N)
def test_complex_compare(self):
self.assertEqual(mt.complex_compare(1.0 + 2.0j, 1.0 + 2.0j), 0) # ==
self.assertEqual(mt.complex_compare(1.0 + 2.0j, 2.0 + 2.0j), -1) # real a < real b
self.assertEqual(mt.complex_compare(1.0 + 2.0j, 0.5 + 2.0j), +1) # real a > real b
self.assertEqual(mt.complex_compare(1.0 + 2.0j, 1.0 + 3.0j), -1) # imag a < imag b
self.assertEqual(mt.complex_compare(1.0 + 2.0j, 1.0 + 1.0j), +1) # imag a > imag b
def test_prime_factors(self):
self.assertEqual(mt.prime_factors(7), [7])
self.assertEqual(mt.prime_factors(10), [2, 5])
self.assertEqual(mt.prime_factors(12), [2, 2, 3])