def compare_eigen_methods():
""" timing of different eigensolver methods"""
import scipy.linalg as linalg
print '\n *** diagonalize a real symmetric band matrix by different methods ***\n'
mt=mytimer.create(10)
try:
N=float(sys.argv[1])
S=float(sys.argv[2])
except:
sys.exit('supply N S (command line arguments): matrix dimension N and and number of super-diagonals S ')
np.random.seed(1)
a=np.random.random((N,N))
ab=GMatrix(np.random.random((S+1,N)),storage='upper_banded')
mt[0].start('lapack symmetric upper banded')
print ab.store+'\n',ab.eigvals()[:5]
mt[0].stop()
a=ab.restore('full')
mt[1].start('lapack symmetric full')
print a.store+'\n',a.eigvals()[:5]
mt[1].stop()
print 'lingalg'
mt[2].start('linalg general')
print np.sort(linalg.eigvals(a.m).real)[:5]
mt[2].stop()
mytimer.table()
# Schmidt orthonormalize
for m in range(M):
vk[:,m]=vk[:,m]-vk[:,:m]*(vk[:,:m].T*vk[:,m])
vk[:,m]=vk[:,m]/np.sqrt(vk[:,m].T*vk[:,m])
t[3].stop()
t[4].start('A*vk')
ek=(vk.T*A*vk).diagonal()
t[4].stop()
eguess=ek[0,0]
t[5].stop()
print ' appr.,exact',L,eguess,ev0[(np.abs(ev0-eguess)).argmin()]
print ' ---------------'
mt.table()
xlabel('Number of iterations')
ylabel('|DE/E|')
title('About as simple as it gets, folks')
axes().set_aspect('equal', 'datalim')
for m in range(M):
plot(range(kplt), eplt[:,m], '-', lw=2)
show()
def inversiter(eguess,wfguess,A,S):
vk=np.matrix(wfguess)
olu,opi=la.lu_factor(Ovr)