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#!/usr/bin/env python
__usage__ = """
To run tests locally:
python tests/test_arpack.py [-l<int>] [-v<int>]
"""
from numpy.testing import *
from numpy import array, finfo, argsort, dot, round, conj, random
from scipy.sparse.linalg.eigen.arpack import eigen_symmetric, eigen
def assert_almost_equal_cc(actual,desired,decimal=7,err_msg='',verbose=True):
# almost equal or complex conjugates almost equal
try:
assert_almost_equal(actual,desired,decimal,err_msg,verbose)
except:
assert_almost_equal(actual,conj(desired),decimal,err_msg,verbose)
def assert_array_almost_equal_cc(actual,desired,decimal=7,
err_msg='',verbose=True):
# almost equal or complex conjugates almost equal
try:
assert_array_almost_equal(actual,desired,decimal,err_msg,verbose)
except:
assert_array_almost_equal(actual,conj(desired),decimal,err_msg,verbose)
# precision for tests
_ndigits = {'f':4, 'd':12, 'F':4, 'D':12}
class TestArpack(TestCase):
def setUp(self):
self.symmetric=[]
self.nonsymmetric=[]
S1={}
S1['mat']=\
array([[ 2., 0., 0., -1., 0., -1.],
[ 0., 2., 0., -1., 0., -1.],
[ 0., 0., 2., -1., 0., -1.],
[-1., -1., -1., 4., 0., -1.],
[ 0., 0., 0., 0., 1., -1.],
[-1., -1., -1., -1., -1., 5.]])
S1['eval']=array([0,1,2,2,5,6])
self.symmetric.append(S1)
N1={}
N1['mat']=\
array([[-2., -8., 1., 2., -5.],
[ 6., 6., 0., 2., 1.],
[ 0., 4., -2., 11., 0.],
[ 1., 6., 1., 0., -4.],
[ 2., -6., 4., 9., -3]])
N1['eval']=\
array([ -5.4854094033782888+0.0j,
-2.2169058544873783+8.5966096591588261j,
-2.2169058544873783-8.5966096591588261j,
4.4596105561765107+3.8007839204319454j,
4.4596105561765107-3.8007839204319454j],'D')
self.nonsymmetric.append(N1)
class TestEigenSymmetric(TestArpack):
def get_exact_eval(self,d,typ,k,which):
eval=d['eval'].astype(typ)
ind=argsort(eval)
eval=eval[ind]
if which=='LM':
return eval[-k:]
if which=='SM':
return eval[:k]
if which=='BE':
# one ev from each end - if k is odd, extra ev on high end
l=k/2
h=k/2+k%2
low=range(len(eval))[:l]
high=range(len(eval))[-h:]
return eval[low+high]
def eval_evec(self,d,typ,k,which,**kwds):
a=d['mat'].astype(typ)
exact_eval=self.get_exact_eval(d,typ,k,which)
eval,evec=eigen_symmetric(a,k,which=which,**kwds)
# check eigenvalues
assert_array_almost_equal(eval,exact_eval,decimal=_ndigits[typ])
# check eigenvectors A*evec=eval*evec
for i in range(k):
assert_array_almost_equal(dot(a,evec[:,i]),
eval[i]*evec[:,i],
decimal=_ndigits[typ])
def test_symmetric_modes(self):
k=2
for typ in 'fd':
for which in ['LM','SM','BE']:
self.eval_evec(self.symmetric[0],typ,k,which)
def test_starting_vector(self):
k=2
for typ in 'fd':
A=self.symmetric[0]['mat']
n=A.shape[0]
v0 = random.rand(n).astype(typ)
self.eval_evec(self.symmetric[0],typ,k,which='LM',v0=v0)
class TestEigenComplexSymmetric(TestArpack):
def sort_choose(self,eval,typ,k,which):
# sort and choose the eigenvalues and eigenvectors
# both for the exact answer and that returned from ARPACK
reval=round(eval,decimals=_ndigits[typ])
ind=argsort(reval)
if which=='LM' or which=='LR':
return ind[-k:]
if which=='SM' or which=='SR':
return ind[:k]
def eval_evec(self,d,typ,k,which):
a=d['mat'].astype(typ)
# get exact eigenvalues
exact_eval=d['eval'].astype(typ)
ind=self.sort_choose(exact_eval,typ,k,which)
exact_eval=exact_eval[ind]
# compute eigenvalues
eval,evec=eigen(a,k,which=which)
ind=self.sort_choose(eval,typ,k,which)
eval=eval[ind]
evec=evec[:,ind]
# check eigenvalues
assert_array_almost_equal(eval,exact_eval,decimal=_ndigits[typ])
# check eigenvectors A*evec=eval*evec
for i in range(k):
assert_array_almost_equal(dot(a,evec[:,i]),
eval[i]*evec[:,i],
decimal=_ndigits[typ])
def test_complex_symmetric_modes(self):
k=2
for typ in 'FD':
for which in ['LM','SM','LR','SR']:
self.eval_evec(self.symmetric[0],typ,k,which)
class TestEigenNonSymmetric(TestArpack):
def sort_choose(self,eval,typ,k,which):
reval=round(eval,decimals=_ndigits[typ])
if which in ['LR','SR']:
ind=argsort(reval.real)
elif which in ['LI','SI']:
# for LI,SI ARPACK returns largest,smallest abs(imaginary) why?
ind=argsort(abs(reval.imag))
else:
ind=argsort(abs(reval))
if which in ['LR','LM','LI']:
return ind[-k:]
if which in ['SR','SM','SI']:
return ind[:k]
def eval_evec(self,d,typ,k,which,**kwds):
a=d['mat'].astype(typ)
# get exact eigenvalues
exact_eval=d['eval'].astype(typ.upper())
ind=self.sort_choose(exact_eval,typ,k,which)
exact_eval=exact_eval[ind]
# compute eigenvalues
eval,evec=eigen(a,k,which=which,**kwds)
ind=self.sort_choose(eval,typ,k,which)
eval=eval[ind]
evec=evec[:,ind]
# check eigenvalues
# check eigenvectors A*evec=eval*evec
for i in range(k):
assert_almost_equal_cc(eval[i],exact_eval[i],decimal=_ndigits[typ])
assert_array_almost_equal_cc(dot(a,evec[:,i]),
eval[i]*evec[:,i],
decimal=_ndigits[typ])
def test_nonsymmetric_modes(self):
k=2
for typ in 'fd':
for which in ['LI','LR','LM','SM','SR','SI']:
for m in self.nonsymmetric:
self.eval_evec(m,typ,k,which)
def test_starting_vector(self):
k=2
for typ in 'fd':
A=self.symmetric[0]['mat']
n=A.shape[0]
v0 = random.rand(n).astype(typ)
self.eval_evec(self.symmetric[0],typ,k,which='LM',v0=v0)
class TestEigenComplexNonSymmetric(TestArpack):
def sort_choose(self,eval,typ,k,which):
eps=finfo(typ).eps
reval=round(eval,decimals=_ndigits[typ])
if which in ['LR','SR']:
ind=argsort(reval)
elif which in ['LI','SI']:
ind=argsort(reval.imag)
else:
ind=argsort(abs(reval))
if which in ['LR','LI','LM']:
return ind[-k:]
if which in ['SR','SI','SM']:
return ind[:k]
def eval_evec(self,d,typ,k,which):
a=d['mat'].astype(typ)
# get exact eigenvalues
exact_eval=d['eval'].astype(typ.upper())
ind=self.sort_choose(exact_eval,typ,k,which)
exact_eval=exact_eval[ind]
if verbose >= 3:
print "exact"
print exact_eval
# compute eigenvalues
eval,evec=eigen(a,k,which=which)
ind=self.sort_choose(eval,typ,k,which)
eval=eval[ind]
evec=evec[:,ind]
if verbose >= 3:
print eval
# check eigenvalues
# check eigenvectors A*evec=eval*evec
for i in range(k):
assert_almost_equal_cc(eval[i],exact_eval[i],decimal=_ndigits[typ])
assert_array_almost_equal_cc(dot(a,evec[:,i]),
eval[i]*evec[:,i],
decimal=_ndigits[typ])
def test_complex_nonsymmetric_modes(self):
k=2
for typ in 'FD':
for which in ['LI','LR','LM','SI','SR','SM']:
for m in self.nonsymmetric:
self.eval_evec(m,typ,k,which)
if __name__ == "__main__":
run_module_suite()
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