def exec_sample():
n = 10
matrix = lil_matrix((n, n), dtype='float64')
for i in range(n - 1):
matrix[(i, i + 1)] = 1
matrix[(i + 1, i)] = 1
# Equivalent to the following n by n matrix
# 0 1 0 0 .. 0 0
# 1 0 1 0 .. 0 0
# 0 1 0 1 .. 0 0
# 0 0 1 0 .. 0 0
# : : : : : :
# 0 0 0 0 .. 0 1
# 0 0 0 0 .. 1 0
# Its eigenvalues are 2*cos(k*pi/(n+1)), where k = 1, 2, ... , n.
# So k = 1 is the largest one and k = n is the smallest one.
engine = PyLanczos(csr_matrix(matrix),
True) # True to calculate the largest eigenvalue.
eigval, eigvec, itern = engine.run()
print("Eigenvalue: {}".format(eigval))
print("Eigenvector: {}".format(eigvec))
print("Iteration count: {}".format(itern))
def test_simple_matrix(self):
matrix = np.array([[2, 1, 1], [1, 2, 1], [1, 1, 2]], dtype='float64')
engine = PyLanczos(matrix, True)
eigval, eigvec, itern = engine.run()
np.testing.assert_almost_equal(eigval, 4.0)
sign = np.sign(eigvec[0])
correct_eigvec = sign / np.sqrt(len(matrix)) * np.array([1, 1, 1])
np.testing.assert_allclose(eigvec, correct_eigvec)
def exec_sample():
matrix = np.array([[2.0, 1.0, 1.0],
[1.0, 2.0, 1.0],
[1.0, 1.0, 2.0]])
engine = PyLanczos(matrix, True) # True to calculate the maximum eigenvalue.
eigval, eigvec, itern = engine.run()
print("Eigenvalue: {}".format(eigval))
print("Eigenvector: {}".format(eigvec))
print("Iteration count: {}".format(itern))
def test_complex_matrix(self):
matrix = np.array([[0, 1j, 1], [-1j, 0, 1j], [1, -1j, 0]],
dtype='complex128')
engine = PyLanczos(matrix, False)
eigval, eigvec, itern = engine.run()
np.testing.assert_almost_equal(eigval, -2.0)
phase = np.angle(eigvec[0])
correct_eigvec = np.array([1, 1j, -1])
correct_eigvec = np.exp(
1j * phase) / np.linalg.norm(correct_eigvec) * correct_eigvec
np.testing.assert_allclose(eigvec, correct_eigvec)
def test_sparse_matrix_numpy(self):
n = 10
matrix = np.zeros((n, n), dtype='float64')
for i in range(n - 1):
matrix[i, i + 1] = -1
matrix[i + 1, i] = -1
engine = PyLanczos(matrix, False)
eigval, eigvec, itern = engine.run()
np.testing.assert_almost_equal(eigval, -2.0 * np.cos(np.pi / (n + 1)))
sign = np.sign(eigvec[0])
correct_eigvec = sign * np.sin(
(1 + np.array(range(n))) * np.pi / (n + 1))
correct_eigvec /= np.linalg.norm(correct_eigvec)
np.testing.assert_allclose(eigvec, correct_eigvec)
def test_sparse_matrix_dynamic(self):
n = 10
def mv_mul(v_in, v_out):
for i in range(n - 1):
v_out[i] += -1.0 * v_in[i + 1]
v_out[i + 1] += -1.0 * v_in[i]
engine = PyLanczos.create_custom(mv_mul, n, 'float64', False)
eigval, eigvec, itern = engine.run()
np.testing.assert_almost_equal(eigval, -2.0 * np.cos(np.pi / (n + 1)))
sign = np.sign(eigvec[0])
correct_eigvec = sign * np.sin(
(1 + np.array(range(n))) * np.pi / (n + 1))
correct_eigvec /= np.linalg.norm(correct_eigvec)
np.testing.assert_allclose(eigvec, correct_eigvec)
def test_unsupported_dtype(self):
matrix = np.array([[2, 1, 1], [1, 2, 1], [1, 1, 2]], dtype='int64')
with self.assertRaises(Exception):
PyLanczos(matrix, True)
import numpy as np
from pylanczos import PyLanczos
if __name__ == "__main__":
matrix = np.array([[2.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 1.0, 2.0]])
engine = PyLanczos(matrix,
True) # True to calculate the maximum eigenvalue.
eigval, eigvec, itern = engine.run()
print("Eigenvalue: {}".format(eigval))
print("Eigenvector: {}".format(eigvec))