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|
#!/usr/bin/env python
__usage__ = """
First ensure that scipy core modules are installed.
Build interface to arpack
python setup.py build
Run tests locally:
python tests/test_arpack.py [-l<int>] [-v<int>]
"""
import sys
from numpy.testing import *
set_package_path()
from arpack import *
del sys.path[0]
import numpy
from scipy.linalg import eig,eigh,norm
class test_eigen_nonsymmetric(ScipyTestCase):
def get_a1(self,typ):
mat=numpy.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]],typ)
w=numpy.array([-2.21691+8.59661*1j,-2.21691-8.59661*1j,\
4.45961+3.80078*1j, 4.45961-3.80078*1j,\
-5.48541+0j],typ.upper())
return mat,w
def large_magnitude(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LM')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.abs(aw)
num=numpy.abs(w)
exact.sort()
num.sort()
assert_array_almost_equal(num[-k:],exact[-k:],decimal=5)
def small_magnitude(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SM')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.abs(aw)
num=numpy.abs(w)
exact.sort()
num.sort()
assert_array_almost_equal(num[:k],exact[:k],decimal=5)
def large_real(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LR')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.real(aw)
num=numpy.real(w)
exact.sort()
num.sort()
assert_array_almost_equal(num[-k:],exact[-k:],decimal=5)
def small_real(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SR')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.real(aw)
num=numpy.real(w)
exact.sort()
num.sort()
assert_array_almost_equal(num[:k],exact[:k],decimal=5)
def large_imag(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LI')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
print w
print aw
exact=numpy.imag(aw)
num=numpy.imag(w)
exact.sort()
num.sort()
assert_array_almost_equal(num[-k:],exact[-k:],decimal=5)
def small_imag(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SI')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.imag(aw)
num=numpy.imag(w)
exact.sort()
num.sort()
print num
assert_array_almost_equal(num[:k],exact[:k],decimal=5)
def check_type(self):
k=2
for typ in 'fd':
self.large_magnitude(typ,k)
self.small_magnitude(typ,k)
self.large_real(typ,k)
self.small_real(typ,k)
# Maybe my understanding of small imaginary and large imaginary
# isn't too keen. I don't understand why these return
# different answers than in the complex case (the latter seems correct)
# self.large_imag(typ,k)
# self.small_imag(typ,k)
class test_eigen_complex_nonsymmetric(ScipyTestCase):
def get_a1(self,typ):
mat=numpy.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]],typ)
w=numpy.array([-2.21691+8.59661*1j,-2.21691-8.59661*1j,\
4.45961+3.80078*1j, 4.45961-3.80078*1j,\
-5.48541+0j],typ.upper())
return mat,w
def large_magnitude(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LM')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.abs(aw)
num=numpy.abs(w)
exact.sort()
num.sort()
assert_array_almost_equal(num,exact[-k:],decimal=5)
def small_magnitude(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SM')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.abs(aw)
num=numpy.abs(w)
exact.sort()
num.sort()
assert_array_almost_equal(num,exact[:k],decimal=5)
def large_real(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LR')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.real(aw)
num=numpy.real(w)
exact.sort()
num.sort()
assert_array_almost_equal(num,exact[-k:],decimal=5)
def small_real(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SR')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.real(aw)
num=numpy.real(w)
exact.sort()
num.sort()
assert_array_almost_equal(num,exact[:k],decimal=5)
def large_imag(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LI')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.imag(aw)
num=numpy.imag(w)
exact.sort()
num.sort()
assert_array_almost_equal(num,exact[-k:],decimal=5)
def small_imag(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SI')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
exact=numpy.imag(aw)
num=numpy.imag(w)
exact.sort()
num.sort()
assert_array_almost_equal(num,exact[:k],decimal=5)
def check_type(self):
k=2
for typ in 'FD':
self.large_magnitude(typ,k)
self.small_magnitude(typ,k)
self.large_real(typ,k)
self.small_real(typ,k)
self.large_imag(typ,k)
self.small_imag(typ,k)
class test_eigen_symmetric(ScipyTestCase):
def get_a1(self,typ):
mat_a1=numpy.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.]],
typ)
w = [0,1,2,2,5,6] # eigenvalues of a1
return mat_a1,w
def large_eigenvalues(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen_symmetric(a,k,which='LM',tol=1e-7)
assert_array_almost_equal(w,aw[-k:])
def small_eigenvalues(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen_symmetric(a,k,which='SM')
assert_array_almost_equal(w,aw[:k])
def end_eigenvalues(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen_symmetric(a,k,which='BE')
exact=[aw[0],aw[-1]]
assert_array_almost_equal(w,exact)
def large_eigenvectors(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen_symmetric(a,k,which='LM')
ew,ev = eigh(a)
ind=ew.argsort()
assert_array_almost_equal(w,numpy.take(ew,ind[-k:]))
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i])
def small_eigenvectors(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen_symmetric(a,k,which='SM',tol=1e-7)
ew,ev = eigh(a)
ind=ew.argsort()
assert_array_almost_equal(w,numpy.take(ew,ind[:k]))
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i])
def end_eigenvectors(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen_symmetric(a,k,which='BE')
ew,ev = eigh(a)
ind=ew.argsort()
exact=numpy.concatenate(([ind[:k/2],ind[-k/2:]]))
assert_array_almost_equal(w,numpy.take(ew,exact))
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i])
def check_eigenvectors(self):
k=2
for typ in 'fd':
self.large_eigenvectors(typ,k)
self.small_eigenvectors(typ,k)
self.end_eigenvectors(typ,k)
def check_type(self):
k=2
for typ in 'fd':
self.large_eigenvalues(typ,k)
self.small_eigenvalues(typ,k)
self.end_eigenvalues(typ,k)
class test_eigen_complex_symmetric(ScipyTestCase):
def get_a1(self,typ):
mat_a1=numpy.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.]],
typ)
w = numpy.array([0+0j,1+0j,2+0j,2+0j,5+0j,6+0j]) # eigenvalues of a1
return mat_a1,w
def large_magnitude(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LM')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i])
aw.real.sort()
w.real.sort()
assert_array_almost_equal(w,aw[-k:])
def small_magnitude(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SM')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i])
aw.real.sort()
w.real.sort()
assert_array_almost_equal(w,aw[:k])
def large_real(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='LR')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i],decimal=5)
aw.real.sort()
w.real.sort()
assert_array_almost_equal(w,aw[-k:],decimal=5)
def small_real(self,typ,k):
a,aw = self.get_a1(typ)
w,v = eigen(a,k,which='SR')
for i in range(k):
assert_array_almost_equal(sb.dot(a,v[:,i]),w[i]*v[:,i])
aw.real.sort()
w.real.sort()
assert_array_almost_equal(w,aw[:k])
def check_complex_symmetric(self):
k=2
for typ in 'FD':
self.large_magnitude(typ,k)
self.small_magnitude(typ,k)
self.large_real(typ,k)
self.small_real(typ,k)
if __name__ == "__main__":
ScipyTest().run()
|
