# scipy/scipy

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 #!/usr/bin/env python """ Test functions for the sparse.linalg.eigen.lobpcg module """ from __future__ import division, print_function, absolute_import import numpy from numpy.testing import assert_almost_equal, run_module_suite from scipy import arange, ones, rand, set_printoptions, r_, diag, linalg, eye from scipy.linalg import eig from scipy.sparse.linalg.eigen.lobpcg import lobpcg set_printoptions(precision=3,linewidth=90) def ElasticRod(n): # Fixed-free elastic rod L = 1.0 le=L/n rho = 7.85e3 S = 1.e-4 E = 2.1e11 mass = rho*S*le/6. k = E*S/le A = k*(diag(r_[2.*ones(n-1),1])-diag(ones(n-1),1)-diag(ones(n-1),-1)) B = mass*(diag(r_[4.*ones(n-1),2])+diag(ones(n-1),1)+diag(ones(n-1),-1)) return A,B def MikotaPair(n): # Mikota pair acts as a nice test since the eigenvalues # are the squares of the integers n, n=1,2,... 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 compare_solutions(A,B,m): n = A.shape[0] numpy.random.seed(0) V = rand(n,m) X = linalg.orth(V) eigs,vecs = lobpcg(A, X, B=B, tol=1e-5, maxiter=30) eigs.sort() #w,v = symeig(A,B) w,v = eig(A,b=B) w.sort() assert_almost_equal(w[:int(m/2)],eigs[:int(m/2)],decimal=2) #from pylab import plot, show, legend, xlabel, ylabel #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() def test_Small(): A,B = ElasticRod(10) compare_solutions(A,B,10) A,B = MikotaPair(10) compare_solutions(A,B,10) def test_ElasticRod(): A,B = ElasticRod(100) compare_solutions(A,B,20) def test_MikotaPair(): A,B = MikotaPair(100) compare_solutions(A,B,20) def test_trivial(): n = 5 X = ones((n, 1)) A = eye(n) compare_solutions(A, None, n) if __name__ == "__main__": run_module_suite()
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