'''What's the origin of this file? It is not ours.
Does not run because of missing mtx files, now included
changes: JP corrections to imports so it runs, comment out print
'''
from __future__ import print_function
import numpy as np
from numpy import dot, outer, random, argsort
from scipy import io, linalg, optimize
from scipy.sparse import eye as speye
import matplotlib.pyplot as plt
[docs]def R(v):
rq = dot(v.T,A*v)/dot(v.T,B*v)
res = (A*v-rq*B*v)/linalg.norm(B*v)
data.append(linalg.norm(res))
return rq
[docs]def Rp(v):
""" Gradient """
result = 2*(A*v-R(v)*B*v)/dot(v.T,B*v)
#print "Rp: ", result
return result
[docs]def Rpp(v):
""" Hessian """
result = 2*(A-R(v)*B-outer(B*v,Rp(v))-outer(Rp(v),B*v))/dot(v.T,B*v)
#print "Rpp: ", result
return result
A = io.mmread('/home/takanori/anaconda2/lib/python2.7/site-packages/statsmodels/sandbox/nos4.mtx') # clustered eigenvalues
#B = io.mmread('bcsstm02.mtx.gz')
#A = io.mmread('bcsstk06.mtx.gz') # clustered eigenvalues
#B = io.mmread('bcsstm06.mtx.gz')
n = A.shape[0]
B = speye(n,n)
random.seed(1)
v_0=random.rand(n)
print("try fmin_bfgs")
full_output = 1
data=[]
v,fopt, gopt, Hopt, func_calls, grad_calls, warnflag, allvecs = \
optimize.fmin_bfgs(R,v_0,fprime=Rp,full_output=full_output,retall=1)
if warnflag == 0:
plt.semilogy(np.arange(0,len(data)),data)
print('Rayleigh quotient BFGS',R(v))
print("fmin_bfgs OK")
print("try fmin_ncg")
#
# WARNING: the program may hangs if fmin_ncg is used
#
data=[]
v,fopt, fcalls, gcalls, hcalls, warnflag, allvecs = \
optimize.fmin_ncg(R,v_0,fprime=Rp,fhess=Rpp,full_output=full_output,retall=1)
if warnflag==0:
plt.figure()
plt.semilogy(np.arange(0,len(data)),data)
print('Rayleigh quotient NCG',R(v))