def calculate_ground_state_wf(d, e, saved_lanczos_vectors):
"""Calculates the ground state wavefunction.
Parameters
----------
d : a numpy array with ndim = 1.
The elements of the diagonal of the tridiagonal matrix. The size
of `d`.
e : a numpy array with ndim = 1.
The off-diagonal elements of the tridiagonal matrix. The size of
`e` equals the size of `d`, and it is padded with a zero at the
end.
saved_lanczos_vectors : a list of Wavefunctions.
The Lanczos vectors that are saved.
Returns
-------
result : a Wavefunction.
The ground state function (normalized).
"""
evals, evecs = diagonalize_tridiagonal_matrix(d, e, True)
min_index = np.argsort(evals)[0]
coefficients_of_gs_in_krylov_space = evecs[:, min_index]
assert (
len(saved_lanczos_vectors) == len(coefficients_of_gs_in_krylov_space))
result = Wavefunction(saved_lanczos_vectors[0].left_dim,
saved_lanczos_vectors[0].right_dim)
result.set_to_zero()
for i in range(len(saved_lanczos_vectors)):
result.as_matrix += (coefficients_of_gs_in_krylov_space[i] *
saved_lanczos_vectors[i].as_matrix)
result.normalize()
return result
def calculate_ground_state_wf(d, e, saved_lanczos_vectors):
"""Calculates the ground state wavefunction.
Parameters
----------
d : a numpy array with ndim = 1.
The elements of the diagonal of the tridiagonal matrix. The size
of `d`.
e : a numpy array with ndim = 1.
The off-diagonal elements of the tridiagonal matrix. The size of
`e` equals the size of `d`, and it is padded with a zero at the
end.
saved_lanczos_vectors : a list of Wavefunctions.
The Lanczos vectors that are saved.
Returns
-------
result : a Wavefunction.
The ground state function (normalized).
"""
evals, evecs = diagonalize_tridiagonal_matrix(d, e, True)
min_index = np.argsort(evals)[0]
coefficients_of_gs_in_krylov_space = evecs[:, min_index]
assert(len(saved_lanczos_vectors) == len(coefficients_of_gs_in_krylov_space))
result = Wavefunction(saved_lanczos_vectors[0].left_dim,
saved_lanczos_vectors[0].right_dim)
result.set_to_zero()
for i in range(len(saved_lanczos_vectors)):
result.as_matrix += ( coefficients_of_gs_in_krylov_space[i] *
saved_lanczos_vectors[i].as_matrix )
result.normalize()
return result
