from shenfun.matrixbase import SpectralMatrix, SpectralMatDict
from shenfun.la import TDMA_O
from . import bases
CD = bases.CompactDirichlet
CN = bases.CompactNeumann
L = bases.Orthogonal
[docs]
class BLLmat(SpectralMatrix):
r"""Mass matrix :math:`B=(b_{kj}) \in \mathbb{R}^{M \times N}`, where
.. math::
b_{kj}=(La_j, La_k)_w,
:math:`La_k \in` :class:`.laguerre.bases.Orthogonal` and test and trial spaces have
dimensions of M and N, respectively.
"""
[docs]
def assemble(self, method):
test, trial = self.testfunction, self.trialfunction
assert isinstance(test[0], L)
assert isinstance(trial[0], L)
return {0: 1}
[docs]
def solve(self, b, u=None, axis=0, constraints=()):
if u is not None:
u[:] = b
u /= (self.scale*self[0])
return u
else:
b /= (self.scale*self[0])
return b
[docs]
def matvec(self, v, c, format=None, axis=0):
c[:] = v
self.scale_array(c, self.scale*self[0])
return c
[docs]
class BCDCDmat(SpectralMatrix):
r"""Mass matrix :math:`B=(b_{kj}) \in \mathbb{R}^{M \times N}`, where
.. math::
b_{kj}=(\phi_j, \phi_k)_w,
:math:`\phi_k \in` :class:`.laguerre.bases.CompactDirichlet` and test and trial spaces have
dimensions of M and N, respectively.
"""
[docs]
def assemble(self, method):
test, trial = self.testfunction, self.trialfunction
assert isinstance(test[0], CD)
assert isinstance(trial[0], CD)
d = {0:2., 1: -1., -1:-1.}
return d
[docs]
def get_solver(self):
return TDMA_O
[docs]
class ACDCDmat(SpectralMatrix):
r"""Stiffness matrix :math:`BA=(a_{kj}) \in \mathbb{R}^{M \times N}`, where
.. math::
a_{kj}=(\phi'_j, \phi'_k)_w,
:math:`\phi_k \in` :class:`.laguerre.bases.CompactDirichlet` and test and trial spaces have
dimensions of M and N, respectively.
"""
[docs]
def assemble(self, method):
test, trial = self.testfunction, self.trialfunction
assert isinstance(test[0], CD)
assert isinstance(trial[0], CD)
d = {0: 0.5,
1: 0.25,
-1: 0.25}
return d
[docs]
def get_solver(self):
return TDMA_O
mat = SpectralMatDict({
#((CD, 0), (CD, 0)): BCDCDmat,
#((CD, 1), (CD, 1)): ACDCDmat,
((L, 0), (L, 0)): BLLmat
})