def tridiagonal_solver(d, e, eigenvectors=True):
"""Calculates the eigenvalues and eigenvectors of a tridiagonal and
symmetric matrix.
Parameters
----------
d : a numpy array with ndim = 1.
The elements of the diagonal of the tridiagonal matrix.
e : a numpy array with ndim = 1.
The off-diagonal elements of the tridiagonal matrix.
eigenvectors : a bool (optional).
Whether you want to calculate the eigenvectors.
Returns
-------
evals : a numpy array with ndim = 1.
The eigenvalues.
evecs : a numpy array with ndim = 2.
The eigenvectors.
Raises
------
TridiagonalException
if `d` and `e` have different sizes.
"""
if (d.size != e.size + 1):
raise TridiagonalException("d, and e have different sizes")
num_evals = d.size
evals = np.empty(num_evals)
evecs = np.empty((num_evals, num_evals))
r = lamRange(d, e, num_evals)
assert (len(r) == num_evals + 1)
evals = eigenvals3(d, e, num_evals)
if eigenvectors:
for i in range(num_evals):
evals[i], evecs[:, i] = inversePower3(d, e, 1.00000001 * evals[i])
#
# An alternative that uses the brakets from lamRange:
#
# if eigenvectors:
# for i in range(num_evals):
# s = (r[i] + r[i+1])/2.0
# evals[i], evecs[:, i] = inversePower3(d, e, s)
# else:
# evals = eigenvals3(d, e, num_evals)
return evals, evecs
def tridiagonal_solver(d, e, eigenvectors = True):
"""Calculates the eigenvalues and eigenvectors of a tridiagonal and
symmetric matrix.
Parameters
----------
d : a numpy array with ndim = 1.
The elements of the diagonal of the tridiagonal matrix.
e : a numpy array with ndim = 1.
The off-diagonal elements of the tridiagonal matrix.
eigenvectors : a bool (optional).
Whether you want to calculate the eigenvectors.
Returns
-------
evals : a numpy array with ndim = 1.
The eigenvalues.
evecs : a numpy array with ndim = 2.
The eigenvectors.
Raises
------
TridiagonalException
if `d` and `e` have different sizes.
"""
if (d.size != e.size + 1):
raise TridiagonalException("d, and e have different sizes")
num_evals = d.size
evals = np.empty(num_evals)
evecs = np.empty((num_evals, num_evals))
r = lamRange(d, e, num_evals)
assert(len(r) == num_evals +1)
evals = eigenvals3(d, e, num_evals)
if eigenvectors:
for i in range(num_evals):
evals[i], evecs[:, i] = inversePower3(d, e, 1.00000001*evals[i])
#
# An alternative that uses the brakets from lamRange:
#
# if eigenvectors:
# for i in range(num_evals):
# s = (r[i] + r[i+1])/2.0
# evals[i], evecs[:, i] = inversePower3(d, e, s)
# else:
# evals = eigenvals3(d, e, num_evals)
return evals, evecs
## 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/python
## example9_12
import numpy as np
from eigenvals3 import *
N = 3
n = 100
d = np.ones(n) * 2.0
c = np.ones(n - 1) * (-1.0)
lambdas = eigenvals3(d, c, N)
print(lambdas)
raw_input("\nPress return to exit")
## example9_12
from numarray import ones, Float64
from eigenvals3 import *
N = 3
n = 100
d = ones((n)) * 2.0
c = ones((n - 1)) * (-1.0)
lambdas = eigenvals3(d, c, N)
print lambdas
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")
