def multiply_PiT_v(self, nu, mu, lut, v):
r"""Multiply the matrix :math:`\mathbf{P_i}^{\mathrm{T}}` by a vector
:math:`\underline{v}` from the right. Do not construct the matrix explicitly.
:param nu: The list :math:`\nu_i`.
:param mu: The list :math:`\mu_i`.
:param lut: The lookup table.
:param v: The vector :math:`\underline{v} \in \mathbb{C}^{n(D,i)}`.
"""
res = zeros(nu.shape[0], dtype=v.dtype)
for i in range(len(mu)):
res[lut[mu[i]]] = 1.0 / sqrt(multinomial(mu[i])) * v[i]
return res
def multiply_PiT_v(self, nu, mu, lut, v):
r"""Multiply the matrix :math:`\mathbf{P_i}^{\mathrm{T}}` by a vector
:math:`\underline{v}` from the right. Do not construct the matrix explicitly.
:param nu: The list :math:`\nu_i`.
:param mu: The list :math:`\mu_i`.
:param lut: The lookup table.
:param v: The vector :math:`\underline{v} \in \mathbb{C}^{n(D,i)}`.
"""
res = zeros(nu.shape[0], dtype=v.dtype)
for i in range(len(mu)):
res[lut[mu[i]]] = 1.0 / sqrt(multinomial(mu[i])) * v[i]
return res
def multiply_Pi_v(self, nu, mu, lut, v):
r"""Multiply the matrix :math:`\mathbf{P_i}` by a vector :math:`\underline{v}`
from the right. Do not construct the matrix explicitly.
:param nu: The list :math:`\nu_i`.
:param mu: The list :math:`\mu_i`.
:param lut: The lookup table.
:param v: The vector :math:`\underline{v} \in \mathcal{X}_i`.
"""
res = zeros(len(mu), dtype=v.dtype)
for i in range(len(mu)):
res[i] = sqrt(multinomial(mu[i])) * v[lut[mu[i]][0]]
return res
def multiply_Pi_v(self, nu, mu, lut, v):
r"""Multiply the matrix :math:`\mathbf{P_i}` by a vector :math:`\underline{v}`
from the right. Do not construct the matrix explicitly.
:param nu: The list :math:`\nu_i`.
:param mu: The list :math:`\mu_i`.
:param lut: The lookup table.
:param v: The vector :math:`\underline{v} \in \mathcal{X}_i`.
"""
res = zeros(len(mu), dtype=v.dtype)
for i in range(len(mu)):
res[i] = sqrt(multinomial(mu[i])) * v[lut[mu[i]][0]]
return res
