#!/usr/bin/python
## example9_8
import numpy as np
from householder import *
a = np.array([[ 7.0, 2.0, 3.0, -1.0],\
[ 2.0, 8.0, 5.0, 1.0], \
[ 3.0, 5.0, 12.0, 9.0], \
[-1.0, 1.0, 9.0, 7.0]])
d, c = householder(a)
print("Principal diagonal {d}:\n", d)
print("\nSubdiagonal {c}:\n", c)
print("\nTransformation matrix [P]:")
print(computeP(a))
input("\nPress return to exit")
## example9_14
from householder import *
from eigenvals3 import *
from inversePower3 import *
from numarray import array, zeros, Float64, matrixmultiply
N = 3 # Number of eigenvalues requested
a = array([[ 11.0, 2.0, 3.0, 1.0, 4.0], \
[ 2.0, 9.0, 3.0, 5.0, 2.0], \
[ 3.0, 3.0, 15.0, 4.0, 3.0], \
[ 1.0, 5.0, 4.0, 12.0, 4.0], \
[ 4.0, 2.0, 3.0, 4.0, 17.0]])
xx = zeros((len(a), N), type=Float64)
d, c = householder(a) # Tridiagonalize [A]
p = computeP(a) # Compute transformation matrix
lambdas = eigenvals3(d, c, N) # Compute eigenvalues
for i in range(N):
s = lambdas[i] * 1.0000001 # Shift very close to eigenvalue
lam, x = inversePower3(d, c, s) # Compute eigenvector [x]
xx[:, i] = x # Place [x] in array [xx]
xx = matrixmultiply(p, xx) # Recover eigenvectors of [A]
print "Eigenvalues:\n", lambdas
print "\nEigenvectors:\n", xx
raw_input("Press return to exit")
#!usr/bin/env python from auxFuncSLE import * from householder import * from givens import * from gramSchmidt import * A = [[12, -51, 4], [6, 167, -68], [-4, 24, -41]] # gramSchmidt print "\nMetodo Gram Schmidt" Q, R = gramSchmidt(A) print "\tMatrix Q" printMatrix(Q) print "\tMatrix R" printMatrix(R) # householder print "\nMetodo Householder" Q, R = householder(A) print "\tMatrix Q" printMatrix(Q) print "\tMatrix R" printMatrix(R) # givens print "\nMetodo Givens" Q, R = givens(A) print "\tMatrix Q" printMatrix(Q) print "\tMatrix R" printMatrix(R) print
## example9_8
from numarray import array,matrixmultiply
from householder import *
a = array([[ 7.0, 2.0, 3.0, -1.0], \
[ 2.0, 8.0, 5.0, 1.0], \
[ 3.0, 5.0, 12.0, 9.0], \
[-1.0, 1.0, 9.0, 7.0]])
d,c = householder(a)
print "Principal diagonal {d}:\n", d
print "\nSubdiagonal {c}:\n",c
print "\nTransformation matrix [P]:"
print computeP(a)
raw_input("\nPress return to exit")
## example9_14
from householder import *
from eigenvals3 import *
from inversePower3 import *
from numarray import array,zeros,Float64,matrixmultiply
N = 3 # Number of eigenvalues requested
a = array([[ 11.0, 2.0, 3.0, 1.0, 4.0], \
[ 2.0, 9.0, 3.0, 5.0, 2.0], \
[ 3.0, 3.0, 15.0, 4.0, 3.0], \
[ 1.0, 5.0, 4.0, 12.0, 4.0], \
[ 4.0, 2.0, 3.0, 4.0, 17.0]])
xx = zeros((len(a),N),type=Float64)
d,c = householder(a) # Tridiagonalize [A]
p = computeP(a) # Compute transformation matrix
lambdas = eigenvals3(d,c,N) # Compute eigenvalues
for i in range(N):
s = lambdas[i]*1.0000001 # Shift very close to eigenvalue
lam,x = inversePower3(d,c,s) # Compute eigenvector [x]
xx[:,i] = x # Place [x] in array [xx]
xx = matrixmultiply(p,xx) # Recover eigenvectors of [A]
print "Eigenvalues:\n",lambdas
print "\nEigenvectors:\n",xx
raw_input("Press return to exit")