def lanczos_nth_iteration(alpha, beta, lv, saved_lanczos_vectors, hamiltonian,
iteration):
"""Performs the n-th iteration for the Lanczos.
It calculates the new values for `alpha` and `beta` for this
`iteration`.
Parameters
----------
alpha : a list of doubles.
The alpha's in the Lanczos algorithm.
beta : a list of doubles.
The beta's in the Lanczos algorithm.
lv : the 3 tuple of Wavefunctions.
With the three Lanczos vectors in use.
saved_lanczos_vectors : a list of Wavefunctions.
The Lanczos vectors that are saved.
hamiltonian : a CompositeOperator
The hamiltonian you want to diagonalize.
iteration : an int
The iteration number.
Notes
-----
Postcond : The 3rd Lanczos vector in the tuple is modified. The first
two are *not*.
Raises
------
DMRGException
if `alpha.size` is not equal to `beta.size`
"""
if len(alpha) != len(beta):
DMRGException("alpha and beta have wrong sizes")
lv[2] = hamiltonian.apply(lv[1])
alpha.append(get_real(braket(lv[1], lv[2])))
lv[2].as_matrix -= (alpha[iteration] * lv[1].as_matrix +
beta[iteration - 1] * lv[0].as_matrix)
beta.append(lv[2].get_norm())
lv[2].normalize()
cycle_lanczos_vectors(lv, saved_lanczos_vectors)
assert (len(alpha) == iteration + 1)
assert (len(beta) == iteration + 1)
def lanczos_nth_iteration(alpha, beta, lv, saved_lanczos_vectors,
hamiltonian, iteration):
"""Performs the n-th iteration for the Lanczos.
It calculates the new values for `alpha` and `beta` for this
`iteration`.
Parameters
----------
alpha : a list of doubles.
The alpha's in the Lanczos algorithm.
beta : a list of doubles.
The beta's in the Lanczos algorithm.
lv : the 3 tuple of Wavefunctions.
With the three Lanczos vectors in use.
saved_lanczos_vectors : a list of Wavefunctions.
The Lanczos vectors that are saved.
hamiltonian : a CompositeOperator
The hamiltonian you want to diagonalize.
iteration : an int
The iteration number.
Notes
-----
Postcond : The 3rd Lanczos vector in the tuple is modified. The first
two are *not*.
Raises
------
DMRGException
if `alpha.size` is not equal to `beta.size`
"""
if len(alpha) != len(beta):
DMRGException("alpha and beta have wrong sizes")
lv[2] = hamiltonian.apply(lv[1])
alpha.append(get_real(braket(lv[1], lv[2])))
lv[2].as_matrix -= (alpha[iteration]*lv[1].as_matrix +
beta[iteration-1]*lv[0].as_matrix)
beta.append(lv[2].get_norm())
lv[2].normalize()
cycle_lanczos_vectors(lv, saved_lanczos_vectors)
assert(len(alpha) == iteration + 1)
assert(len(beta) == iteration + 1)
def lanczos_zeroth_iteration(alpha, beta, lv, hamiltonian):
"""Performs the zero-th iteration for the Lanczos.
The zero-th (i.e. the first at all) Lanczos iteration is slightly
different to the rest.
Parameters
----------
alpha : a list of doubles.
The alpha's in the Lanczos algorithm.
beta : a list of doubles.
The beta's in the Lanczos algorithm.
lv : a 3-tuple of numpy arrays of ndim = 2.
The Lanczos vectors.
hamiltonian : a CompositeOperator
The hamiltonian you want to diagonalize.
Returns
-------
already_the_ground_state : a bool
Whether the zeroth iteration gives you the ground state. This
happens when the initial wavefunction for the Lanczos is already
the groudn state.
Raises
------
DMRGException :
if the `alpha` or `beta` lists are not empty.
"""
if alpha and beta:
raise DMRGException("Lists not empty at zeroth Lanczos iter")
lv[1] = hamiltonian.apply(lv[0])
alpha.append(get_real(braket(lv[0], lv[1])))
lv[1].as_matrix -= alpha[0] * lv[0].as_matrix
beta.append(lv[1].get_norm())
lv[1].normalize()
assert (len(alpha) == 1)
assert (len(beta) == 1)
already_the_ground_state = (beta[0] < float_info.epsilon)
return already_the_ground_state
def lanczos_zeroth_iteration(alpha, beta, lv, hamiltonian):
"""Performs the zero-th iteration for the Lanczos.
The zero-th (i.e. the first at all) Lanczos iteration is slightly
different to the rest.
Parameters
----------
alpha : a list of doubles.
The alpha's in the Lanczos algorithm.
beta : a list of doubles.
The beta's in the Lanczos algorithm.
lv : a 3-tuple of numpy arrays of ndim = 2.
The Lanczos vectors.
hamiltonian : a CompositeOperator
The hamiltonian you want to diagonalize.
Returns
-------
already_the_ground_state : a bool
Whether the zeroth iteration gives you the ground state. This
happens when the initial wavefunction for the Lanczos is already
the groudn state.
Raises
------
DMRGException :
if the `alpha` or `beta` lists are not empty.
"""
if alpha and beta:
raise DMRGException("Lists not empty at zeroth Lanczos iter")
lv[1] = hamiltonian.apply(lv[0])
alpha.append(get_real(braket(lv[0], lv[1])))
lv[1].as_matrix -= alpha[0]*lv[0].as_matrix
beta.append(lv[1].get_norm())
lv[1].normalize()
assert(len(alpha) == 1)
assert(len(beta) == 1)
already_the_ground_state = ( beta[0] < float_info.epsilon )
return already_the_ground_state