The code I write is for the Jacobi method of approximating eigenvalues. I still get eigenvalues of 0 for a matrix of arbitrary size, although I do not get eigenvalues of 0 by hand. I think my code puts my matrix A back somewhere on all zeros.
import numpy
from numpy import *
from math import *
from matplotlib import pyplot as plt
powermethodnorm = ()
def check_symmetric(A, rtol=1e-09, atol=1e-20):
return numpy.allclose(A, A.T, rtol=rtol, atol=atol)
def Eigenvalue_Jacobi_Method(A, tol=1.0e-15):
def Maximum_Element(A):
n = len(A)
Maximum_A = 0.0
for i in range(n - 1):
for j in range(i + 1, n):
if abs(A(i, j)) >= Maximum_A:
Maximum_A = abs(A(i, j))
k = i
l = j
return Maximum_A, k, l
def rotate(A, p, k, l):
n = len(A)
Difference_A = A(l, l) - A(k, k)
if abs(A(k, l)) < abs(Difference_A) * 1.0e-36:
t = a(k, l) / Difference_A
else:
q = Difference_A / (2 * A(k, l))
t = 1 / (abs(q) + sqrt(q ** 2 + 1))
if q < 0: t = -t
c = 1 / sqrt(t ** 2 + 1)
s = t * c
w = s / (1 + c)
r = A(k, l)
A(k, l) = 0
A(k, k) = A(k, k) - t * r
A(l, l) = A(l, l) + t * r
for i in range(k):
r = A(i, k)
A(i, k) = r - s * (A(i, l) + w * r)
A(i, l) = A(i, l) + s * (r - w * A(i, l))
for i in range(k + 1, l):
r = A(k, i)
A(k, i) = r - s * (A(i, l) + w * A(k, i))
A(i, l) = A(i, l) + s * (r - w * A(i, l))
for i in range(l + 1, n):
r = A(k, i)
A(k, i) = r - s * (A(l, i) + w * r)
A(l, i) = A(l, i) + s * (r - w * A(l, i))
for i in range(n):
r = P(i, k)
P(i, k) = r - s * (P(i, l) + w * P(i, k))
P(i, l) = P(i, l) + s * (r - w * P(i, l))
n = len(A)
Maximum_Rotations = 5 * (n**2)
P = identity(n) * 1
for i in range(Maximum_Rotations):
Maximum_A, k, l = Maximum_Element(A)
if Maximum_A < tol: return diagonal(A), P
rotate(A, P, k, l)
print('Jacobi method did not converge')
it = int(input("What is the maximum amount of iterations(For Power Method): "))
n = int(input("Enter the matrix size: "))
A = numpy.zeros((n, n))
for i in range(n):
A(i) = input().split(" ")
MatrixA = numpy.array(A)
print("A= ")
print(A)
for i in range(A.shape(0)):
row = ("{}*x{}".format(A(i, j), j + 1) for j in range(A.shape(1)))
z, x = Eigenvalue_Jacobi_Method(A, tol=1.0e-15)
print("----Jacobi Method----")
print("Eigenvalues= ", z)
As an example, the 2 by 2 matrix of
(1,2) / (2,3) should lead to eigenvalues of -.23607 and 4.23607
