def matrix_find_eigenvalues(matrix):
eigenvalues = []
eigenvalues.append(
matrix_inverse_power_iteration(matrix, 0.0, 0.00000000000001, 20000))
eigenvalues.append(matrix_power_iteration(matrix, 0.0000000001, 20000))
find_middle_eigenvalue(matrix, eigenvalues, eigenvalues[0], eigenvalues[1])
return eigenvalues
def find_middle_eigenvalue(matrix, eigenvalues, min_value, max_value):
middle = (max_value + min_value) / 2
middle_eigenvalue, count = matrix_inverse_power_iteration(
matrix, middle, 0.00000000000001, 1000, getIterCount=True)
if (
count != 1000
): #If no convergence happens after 1000 iterations, then middle is probably right inbetween the only 2 eigenvalues.
if (not abs(middle_eigenvalue - min_value) < 0.0001) and (
not abs(middle_eigenvalue - max_value) < 0.0001):
eigenvalues.append(middle_eigenvalue)
find_middle_eigenvalue(matrix, eigenvalues, min_value,
middle_eigenvalue)
find_middle_eigenvalue(matrix, eigenvalues, middle_eigenvalue,
max_value)
def hilbert_matrix_inverse_power_iteration_test():
selection = [4, 6, 8, 10]
hilbert_matrix = []
solution = []
# Create the hilbert matrices and their corresponding Q factorization matrix.
for n in selection:
hilbert_matrix.append([[1 / (1 + i + j) for i in range(n)]
for j in range(n)]) # Hilbert Matrix generator
solution.append(
matrix_inverse_power_iteration(hilbert_matrix[-1], 0,
0.0000000000001, 100000))
for i in range(0, len(selection)): # 4, 6, 8, 10
print("Smallest Eigenvalue for " + str(selection[i]) + "x" +
str(selection[i]) + ": " + str(solution[i]))
def matrix_inverse_iteration_rayleigh_quotient_compare():
for i in [10, 50, 100, 200]:
matrix = gen_sqr_diagdom_matrix(i)
#vector = [1]*i
starttime = time.time()
solution, count = matrix_inverse_power_iteration(matrix,
0,
0.0001,
10000,
getIterCount=True)
print(
str(i) + "x" + str(i) + " Inverse_Power: Time: " +
str(time.time() - starttime) + ", Iteration Count: " + str(count))
starttime = time.time()
solution, count = matrix_rayleigh_quotient_iteration(matrix,
0.0001,
10000,
getIterCount=True)
print(
str(i) + "x" + str(i) + " Rayleigh Quotient: Time: " +
str(time.time() - starttime) + ", Iteration Count: " + str(count))
def matrix_condition_number(matrix):
smallest_eigenvalue = matrix_inverse_power_iteration(
matrix, 0, 0.00000000000001, 20000)
largest_eigenvalue = matrix_power_iteration(matrix, 0.0000000001, 20000)
return abs(largest_eigenvalue / smallest_eigenvalue)
def matrix_condition_number(matrix):
largest_eigenvalue = matrix_rayleigh_quotient_iteration(
matrix, 0.00000000000001, 20000)
smallest_eigenvalue = matrix_inverse_power_iteration(
matrix, 0, 0.0000000001, 20000)
return abs(largest_eigenvalue / smallest_eigenvalue)