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