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test_sp_eigs.py
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test_sp_eigs.py
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# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
from qutip import *
from qutip import _version2int
from qutip.sparse import *
from numpy import allclose, isreal, iscomplex
from numpy.testing import assert_equal, run_module_suite
import scipy
import unittest
@unittest.skipIf(_version2int(scipy.__version__) < _version2int('0.10'),
'Known to fail on SciPy ' + scipy.__version__)
def test_SparseHermValsVecs():
"""
Sparse eigs Hermitian
"""
# check using number operator
N = num(10)
spvals, spvecs = N.eigenstates(sparse=True)
for k in range(10):
# check that eigvals are in proper order
assert_equal(abs(spvals[k] - k) <= 1e-13, True)
# check that eigenvectors are right and in right order
assert_equal(abs(expect(N, spvecs[k]) - spvals[k]) < 5e-14, True)
# check ouput of only a few eigenvals/vecs
spvals, spvecs = N.eigenstates(sparse=True, eigvals=7)
assert_equal(len(spvals), 7)
assert_equal(spvals[0] <= spvals[-1], True)
for k in range(7):
assert_equal(abs(spvals[k] - k) < 1e-12, True)
spvals, spvecs = N.eigenstates(sparse=True, sort='high', eigvals=5)
assert_equal(len(spvals), 5)
assert_equal(spvals[0] >= spvals[-1], True)
vals = arange(9, 4, -1)
for k in range(5):
# check that eigvals are ordered from high to low
assert_equal(abs(spvals[k] - vals[k]) < 5e-14, True)
assert_equal(abs(expect(N, spvecs[k]) - vals[k]) < 1e-14, True)
# check using random Hermitian
H = rand_herm(10)
spvals, spvecs = H.eigenstates(sparse=True)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
assert_equal(abs(expect(H, spvecs[k]) - spvals[k]) < 5e-14, True)
# check that ouput is real for Hermitian operator
assert_equal(isreal(spvals[k]), True)
def test_SparseValsVecs():
"""
Sparse eigs non-Hermitian
"""
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=True)
assert_equal(real(spvals[0]) <= real(spvals[-1]), True)
for k in range(10):
# check that eigenvectors are right and in right order
assert_equal(abs(expect(U, spvecs[k]) - spvals[k]) < 5e-14, True)
assert_equal(iscomplex(spvals[k]), True)
# check sorting
spvals, spvecs = U.eigenstates(sparse=True, sort='high')
assert_equal(real(spvals[0]) >= real(spvals[-1]), True)
# check for N-1 eigenvals
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=True, eigvals=9)
assert_equal(len(spvals), 9)
@unittest.skipIf(_version2int(scipy.__version__) < _version2int('0.10'),
'Known to fail on SciPy ' + scipy.__version__)
def test_SparseValsOnly():
"""
Sparse eigvals only Hermitian.
"""
H = rand_herm(10)
spvals = H.eigenenergies(sparse=True)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(isreal(spvals[k]), True)
spvals = H.eigenenergies(sparse=True, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = H.eigenenergies(sparse=True, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
U = rand_unitary(10)
spvals = U.eigenenergies(sparse=True)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(iscomplex(spvals[k]), True)
spvals = U.eigenenergies(sparse=True, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = U.eigenenergies(sparse=True, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
def test_DenseHermValsVecs():
"""
Dense eigs Hermitian.
"""
# check using number operator
N = num(10)
spvals, spvecs = N.eigenstates(sparse=False)
for k in range(10):
# check that eigvals are in proper order
assert_equal(abs(spvals[k] - k) < 1e-14, True)
# check that eigenvectors are right and in right order
assert_equal(abs(expect(N, spvecs[k]) - spvals[k]) < 5e-14, True)
# check ouput of only a few eigenvals/vecs
spvals, spvecs = N.eigenstates(sparse=False, eigvals=7)
assert_equal(len(spvals), 7)
assert_equal(spvals[0] <= spvals[-1], True)
for k in range(7):
assert_equal(abs(spvals[k] - k) < 1e-14, True)
spvals, spvecs = N.eigenstates(sparse=False, sort='high', eigvals=5)
assert_equal(len(spvals), 5)
assert_equal(spvals[0] >= spvals[-1], True)
vals = arange(9, 4, -1)
for k in range(5):
# check that eigvals are ordered from high to low
assert_equal(abs(spvals[k] - vals[k]) < 5e-14, True)
assert_equal(abs(expect(N, spvecs[k]) - vals[k]) < 5e-14, True)
# check using random Hermitian
H = rand_herm(10)
spvals, spvecs = H.eigenstates(sparse=False)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
assert_equal(abs(expect(H, spvecs[k]) - spvals[k]) < 5e-14, True)
# check that ouput is real for Hermitian operator
assert_equal(isreal(spvals[k]), True)
def test_DenseValsVecs():
"""
Dense eigs non-Hermitian
"""
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=False)
assert_equal(real(spvals[0]) <= real(spvals[-1]), True)
for k in range(10):
# check that eigenvectors are right and in right order
assert_equal(abs(expect(U, spvecs[k]) - spvals[k]) < 1e-14, True)
assert_equal(iscomplex(spvals[k]), True)
# check sorting
spvals, spvecs = U.eigenstates(sparse=False, sort='high')
assert_equal(real(spvals[0]) >= real(spvals[-1]), True)
# check for N-1 eigenvals
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=False, eigvals=9)
assert_equal(len(spvals), 9)
def test_DenseValsOnly():
"""
Dense eigvals only Hermitian
"""
H = rand_herm(10)
spvals = H.eigenenergies(sparse=False)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(isreal(spvals[k]), True)
spvals = H.eigenenergies(sparse=False, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = H.eigenenergies(sparse=False, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
U = rand_unitary(10)
spvals = U.eigenenergies(sparse=False)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(iscomplex(spvals[k]), True)
spvals = U.eigenenergies(sparse=False, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = U.eigenenergies(sparse=False, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
if __name__ == "__main__":
run_module_suite()