def create_inner_product(self, description):
#
try:
ip_type = description["type"]
except:
# Default setting
print(
"Warning: Using fall-back inner product of type 'InhomogeneousInnerProduct'!"
)
# TODO: Maybe change to homogeneous one?
ip_type = "InhomogeneousInnerProduct"
if ip_type == "HomogeneousInnerProduct":
from WaveBlocksND.HomogeneousInnerProduct import HomogeneousInnerProduct
QE = self.create_quadrature(description["delegate"])
IP = HomogeneousInnerProduct(QE)
elif ip_type == "InhomogeneousInnerProduct":
from WaveBlocksND.InhomogeneousInnerProduct import InhomogeneousInnerProduct
QE = self.create_quadrature(description["delegate"])
IP = InhomogeneousInnerProduct(QE)
else:
raise ValueError("Unknown inner product type {}".format(ip_type))
return IP
def __init__(self, threshold=1e-8):
r"""Initialize an oracle for estimating if a specific overlap integral
:math:`\langle \Psi_k | O | \Psi_l \rangle` is approximately zero. The
oracle works by approximating :math:`\langle \Psi_k | \Psi_l \rangle`
with a Gaussian integral. If
.. math::
\langle \Psi_k | \Psi_l \rangle \approx \langle \Psi_k^G | \Psi_l^G \rangle \leq \tau
the value :math:`\langle \Psi_k | O | \Psi_l \rangle` is considered
to be zero. Of course this may fail depending on the form of the
operator :math:`O` or the basis shape :math:`\mathfrak{K}`.
.. warning::
This code is highly experimental.
:param threshold: The threshold :math:`\tau` in the Gaussian integral criterion.
The default value of :math:`10^{-8}` should be reasonable in most cases.
"""
self._threshold = threshold
self._ip = InhomogeneousInnerProduct(GaussianIntegral())
class SparsityOracleGIHAWP(SparsityOracle):
r"""This class implements an oracle by looking at Gaussian integrals.
"""
def __init__(self, threshold=1e-8):
r"""Initialize an oracle for estimating if a specific overlap integral
:math:`\langle \Psi_k | O | \Psi_l \rangle` is approximately zero. The
oracle works by approximating :math:`\langle \Psi_k | \Psi_l \rangle`
with a Gaussian integral. If
.. math::
\langle \Psi_k | \Psi_l \rangle \approx \langle \Psi_k^G | \Psi_l^G \rangle \leq \tau
the value :math:`\langle \Psi_k | O | \Psi_l \rangle` is considered
to be zero. Of course this may fail depending on the form of the
operator :math:`O` or the basis shape :math:`\mathfrak{K}`.
.. warning::
This code is highly experimental.
:param threshold: The threshold :math:`\tau` in the Gaussian integral criterion.
The default value of :math:`10^{-8}` should be reasonable in most cases.
"""
self._threshold = threshold
self._ip = InhomogeneousInnerProduct(GaussianIntegral())
def is_not_zero(self, pacbra, packet, component=None):
r"""Try to estimate if the overlap integral :math:`\langle \Psi_k | \Psi_l \rangle`
is zero or at least negligible.
:param pacbra: The packet :math:`\Psi_k` that is used for the 'bra' part.
:param packet: The packet :math:`\Psi_l` that is used for the 'ket' part.
:param component: The component of the packet that is considered.
:return: ``True`` or ``False`` whether the inner product is negligible.
"""
Q = self._ip.quadrature(pacbra, packet, diag_component=component, summed=True)
return abs(abs(Q) > self._threshold)
