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from scipy import *
from scipy.sparse.linalg import lobpcg
from symeig import symeig
from pylab import plot, show, legend, xlabel, ylabel
set_printoptions(precision=3,linewidth=90)
import time
def test(n):
x = arange(1,n+1)
B = diag(1./x)
y = arange(n-1,0,-1)
z = arange(2*n-1,0,-2)
A = diag(z)-diag(y,-1)-diag(y,1)
return A,B
def as2d( ar ):
if ar.ndim == 2:
return ar
else: # Assume 1!
aux = nm.array( ar, copy = False )
aux.shape = (ar.shape[0], 1)
return aux
def precond(x):
y= linalg.cho_solve((LorU, lower),x)
return as2d(y)
m = 10 # Blocksize
N = array(([128,256,512,1024,2048])) # Increasing matrix size
data1=[]
data2=[]
for n in N:
print '******', n
A,B = test(n) # Mikota pair
X = rand(n,m)
X = linalg.orth(X)
tt = time.clock()
(LorU, lower) = linalg.cho_factor(A, lower=0, overwrite_a=0)
eigs,vecs = lobpcg.lobpcg(X,A,B,operatorT = precond,
residualTolerance = 1e-4, maxIterations = 40)
data1.append(time.clock()-tt)
eigs = sort(eigs)
print
print 'Results by LOBPCG'
print
print n,eigs
tt = time.clock()
w,v=symeig(A,B,range=(1,m))
data2.append(time.clock()-tt)
print
print 'Results by symeig'
print
print n, w
xlabel(r'Size $n$')
ylabel(r'Elapsed time $t$')
plot(N,data1,label='LOBPCG')
plot(N,data2,label='SYMEIG')
legend()
show()
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