def matrix_rayleigh_quotient_iteration(matrix,
tol,
max_iter,
getIterCount=False):
error = tol * 10
count = 0
v_i = matrix[0]
v_i = vector_scal_mult(1 / vector_2norm(v_i), v_i)
eigenvaluenew = matrix_mult(matrix_transpose(convert_vec_mat(v_i)),
matrix_mult(matrix,
convert_vec_mat(v_i)))[0][0]
I = [[int(i == j) for i in range(len(matrix))] for j in range(len(matrix))]
while error > tol and count < max_iter:
eigenvalueold = eigenvaluenew
v_i = matrix_solve_LU(
matrix_add(matrix, matrix_scal_mult(-eigenvaluenew, I)), v_i)
v_i = vector_scal_mult(1 / vector_2norm(v_i), v_i)
eigenvaluenew = matrix_mult(matrix_transpose(convert_vec_mat(v_i)),
matrix_mult(matrix,
convert_vec_mat(v_i)))[0][0]
error = abs(eigenvaluenew - eigenvalueold)
count += 1
if getIterCount == True:
return eigenvaluenew, count
else:
return eigenvaluenew
def matrix_inverse_power_iteration(matrix,
alpha,
tol,
max_iter,
getIterCount=False):
error = tol * 10
count = 0
eigenvaluenew = 0
I = [[-int(i == j) * alpha for i in range(len(matrix))]
for j in range(len(matrix))]
v_i = matrix[0]
while error > tol and count < max_iter:
eigenvalueold = eigenvaluenew
v_i = matrix_solve_LU(matrix_add(matrix, I), v_i)
v_i = vector_scal_mult(1 / vector_2norm(v_i), v_i)
eigenvaluenew = matrix_mult(matrix_transpose(convert_vec_mat(v_i)),
matrix_mult(matrix,
convert_vec_mat(v_i)))[0][0]
count += 1
error = abs(eigenvaluenew - eigenvalueold)
if getIterCount == True:
return eigenvaluenew, count
else:
return eigenvaluenew