PyLanczos is a Lanczos diagonalization library. Its core part is written in C++ as LambdaLanczos.
All samples are available here.
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, 2) # Find 2 maximum eigenpairs
eigenvalues, eigenvectors = engine.run()
print("Eigenvalue: {}".format(eigenvalues))
print("Eigenvector:")
print(eigenvectors)Note: Use of SciPy sparse matrix is recommended to take full advantage of Lanczos algorithm.
You can also attach your customized function:
tensor = np.zeros((2, 2, 2, 2), dtype='float64')
tensor[0, 0, 0, 0] = 1
# and so on...
## Matrix-vector (or tensor-matrix) multiplication function
def mv_mul(v_in, v_out):
v_in.shape = (2, 2)
v_out.shape = (2, 2)
np.einsum("ijkl, kl -> ij", tensor, v_in, out=v_out, optimize="optimal")
## Calculate an "eigenmatrix" for the 4th-order tensor.
engine = PyLanczos.create_custom(mv_mul, n, 'float64', False, 1) # Find 1 minimum eigenpair
eigenvalues, eigenmatrices = engine.run()
eigenmatrices.shape = (2, 2)
print("Eigenvalue: {}".format(eigenvalues))
print("Eigenmatrix:")
print(eigenmatrices)There is a full sample with detailed description.
pip install pylanczosC++11 compatible environment