def eigenvals3(d, c, N):
def f(x): # f(x) = |[A] - x[I]|
p = sturmSeq(d, c, x)
return p[len(p) - 1]
lam = zeros(N)
r = lamRange(d, c, N) # Bracket eigenvalues
for i in range(N): # Solve by Brent's method
lam[i] = ridder(f, r[i], r[i + 1])
return lam
def eigenvals3(d, c, N):
def f(x): # f(x) = |[A] - x[I]|
p = sturmSeq(d, c, x)
return p[len(p) - 1]
evals = np.empty(N)
r = lamRange(d, c, N) # Bracket eigenvalues
for i in range(N): # Solve by Brent's method
assert (f(r[i]) * f(r[i + 1]) < 0.0)
evals[i] = scipy.optimize.brentq(f, r[i], r[i + 1])
return evals
def eigenvals3(d,c,N):
def f(x): # f(x) = |[A] - x[I]|
p = sturmSeq(d,c,x)
return p[len(p)-1]
lam = zeros(N)
r = lamRange(d,c,N) # Bracket eigenvalues
for i in range(N): # Solve by Brent's method
lam[i] = ridder(f,r[i],r[i+1])
return lam
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_13
from numarray import ones
from lamRange import *
from inversePower3 import *
N = 10
n = 100
d = ones((n)) * 2.0
c = ones((n - 1)) * (-1.0)
r = lamRange(d, c, N) # Bracket N smallest eigenvalues
s = (r[N - 1] + r[N]) / 2.0 # Shift to midpoint of Nth bracket
lam, x = inversePower3(d, c, s) # Inverse power method
print "Eigenvalue No.", N, " =", lam
raw_input("\nPress return to exit")
#!/usr/bin/python
## example9_13
import numpy as np
from lamRange import *
from inversePower3 import *
N = 10
n = 100
d = np.ones(n) * 2.0
c = np.ones(n - 1) * (-1.0)
r = lamRange(d, c, N)
s = (r[N - 1] + r[N]) / 2.0
lam, x = inversePower3(d, c, s) # Inverse power method
print("Eigenvalue No.", N, " =", lam)
input("\nPress return to exit")
## example9_13
from numarray import ones
from lamRange import *
from inversePower3 import *
N = 10
n = 100
d = ones((n))*2.0
c = ones((n-1))*(-1.0)
r = lamRange(d,c,N) # Bracket N smallest eigenvalues
s = (r[N-1] + r[N])/2.0 # Shift to midpoint of Nth bracket
lam,x = inversePower3(d,c,s) # Inverse power method
print "Eigenvalue No.",N," =",lam
raw_input("\nPress return to exit")
