k = arange(1,n+1)
w_ex = sort(1./(16.*pow(cos(0.5*k*pi/(n+1)),4))) # exact eigenvalues
return A,B, w_ex
m = 3 # Blocksize
#
# Large scale
#
n = 25000
A,B, w_ex = sakurai(n) # Mikota pair
X = rand(n,m)
data=[]
tt = time.clock()
eigs,vecs, resnh = lobpcg.lobpcg(X,A,B,
residualTolerance = 1e-6, maxIterations =500, retResidualNormsHistory=1)
data.append(time.clock()-tt)
print 'Results by LOBPCG for n='+str(n)
print
print eigs
print
print 'Exact eigenvalues'
print
print w_ex[:m]
print
print 'Elapsed time',data[0]
loglog(arange(1,n+1),w_ex,'b.')
xlabel(r'Number $i$')
ylabel(r'$\lambda_i$')
title('Eigenvalue distribution')
show()
def test2(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 n = 100 # Dimension A,B = test1(n) # Fixed-free elastic rod A,B = test2(n) # Mikota pair acts as a nice test since the eigenvalues are the squares of the integers n, n=1,2,... m = 20 V = rand(n,m) X = linalg.orth(V) eigs,vecs = lobpcg.lobpcg(X,A,B) eigs = sort(eigs) w,v=symeig(A,B) plot(arange(0,len(w[:m])),w[:m],'bx',label='Results by symeig') plot(arange(0,len(eigs)),eigs,'r+',label='Results by lobpcg') legend() xlabel(r'Eigenvalue $i$') ylabel(r'$\lambda_i$') show()
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
