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
def apply(self, wf):
"""
Applies the composite operator to a wavefunction.
Applies each of the operator components that form the composite
operator and sums up the results.
Parameters
----------
wf : A Wavefunction
The wavefunction you want to apply the operator.
Returns
-------
result : a Wavefunction
The wavefunction resulting of the operation. It has the same
shape (i.e. is in the same Hilbert space) as the one passed as
argument.
Raises
------
DMRGException
if self.list_of_components is empty.
Examples
--------
>>> import numpy as np
>>> from dmrg101.core.operators import CompositeOperator
>>> from dmrg101.core.wavefunction import Wavefunction
>>> wf = Wavefunction(2, 2)
>>> wf.randomize()
>>> identity_operator = CompositeOperator(2, 2)
>>> identity_operator.add(np.eye(2, 2), np.eye(2, 2))
>>> new_wf = identity_operator.apply(wf)
>>> np.array_equal(new_wf.as_matrix, wf.as_matrix)
True
"""
if not self.list_of_components:
raise DMRGException("Composite operator is empty.")
result = Wavefunction(self.left_dim, self.right_dim)
result.set_to_zero()
for component in self.list_of_components:
result.as_matrix += component.apply(wf).as_matrix
return result
def apply(self, wf):
"""
Applies the composite operator to a wavefunction.
Applies each of the operator components that form the composite
operator and sums up the results.
Parameters
----------
wf : A Wavefunction
The wavefunction you want to apply the operator.
Returns
-------
result : a Wavefunction
The wavefunction resulting of the operation. It has the same
shape (i.e. is in the same Hilbert space) as the one passed as
argument.
Raises
------
DMRGException
if self.list_of_components is empty.
Examples
--------
>>> import numpy as np
>>> from dmrg101.core.operators import CompositeOperator
>>> from dmrg101.core.wavefunction import Wavefunction
>>> wf = Wavefunction(2, 2)
>>> wf.randomize()
>>> identity_operator = CompositeOperator(2, 2)
>>> identity_operator.add(np.eye(2, 2), np.eye(2, 2))
>>> new_wf = identity_operator.apply(wf)
>>> np.array_equal(new_wf.as_matrix, wf.as_matrix)
True
"""
if not self.list_of_components:
raise DMRGException("Composite operator is empty.")
result = Wavefunction(self.left_dim, self.right_dim)
result.set_to_zero()
for component in self.list_of_components:
result.as_matrix += component.apply(wf).as_matrix
return result
