def dominant_eigen_system(matrix, iterations):
"""
Calculates the dominant eigenvalue and a dominant unit eigenvector
of a symmetric matrix using the power method.
Parameters
----------
matrix : numpy.ndarray
A symmetric matrix.
iterations : int
The number of iterations of the power method.
Returns
-------
tuple of (Int, numpy.ndarray)
Dominant eigenvalue and a dominant unit eigenvector.
The list is empty if the dominant eigenvalue is zero.
"""
row_count, col_count = matrix_size(matrix)
# Create an initial unit vector
unit_vector = np.zeros([col_count, 1])
unit_vector[0, 0] = 1
# Calculate dominant unit eigenvector
for _ in range(iterations):
product = matrix @ unit_vector
vec_length = np.linalg.norm(product)
# Reached zero eigenvalue
if vec_length < ZERO_NUMBER:
return (0, [])
unit_vector = product / vec_length
# Calculate dominant eigenvalue
eigenvalue = dot_product(matrix @ unit_vector, unit_vector)
return (eigenvalue, unit_vector)
def test_empty(self):
matrix = []
rows, columns = matrix_size(matrix)
assert rows == 0
assert columns == 0
def test_column_vector(self):
matrix = [[1], [2], [3]]
rows, columns = matrix_size(matrix)
assert rows == 3
assert columns == 1
def test_row_vector2(self):
matrix = [[1, 2, 3]]
rows, columns = matrix_size(matrix)
assert rows == 1
assert columns == 3
def test_matrix(self):
matrix = [[1, 2], [4, 5], [7, 8]]
rows, columns = matrix_size(matrix)
assert rows == 3
assert columns == 2