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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.
#
# QuTIP is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# QuTIP is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with QuTIP. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright (C) 2011-2012, Paul D. Nation & Robert J. Johansson
#
###########################################################################
from qutip import *
from qutip.sparse import *
from numpy import allclose
from numpy.testing import assert_equal
import scipy,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-14,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)