def __init__(self, test, trial):
from shenfun.la import PDMA
assert isinstance(test[0], SB)
assert isinstance(trial[0], SB)
N = test[0].N
k = np.arange(N, dtype=np.float)
gk = (2 * k + 3) / (2 * k + 7)
hk = -(1 + gk)
ek = 2. / (2 * k + 1)
p0 = 16 * (k[:-4] + 2)**2 * (k[:-4] + 1)**2 / (2 * k[:-4] + 5)**2 / (
2 * k[:-4] + 3)**2
p2 = 16 * (k[:-6] + 2) * (k[2:-4] + 2) * (k[:-6] + 1) * (
k[2:-4] + 1) / (2 * k[:-6] + 5) / (2 * k[2:-4] + 5) / (
2 * k[:-6] + 3) / (2 * k[2:-4] + 3)
p4 = 16 * (k[:-8] + 2) * (k[4:-4] + 2) * (k[:-8] + 1) * (
k[4:-4] + 1) / (2 * k[:-8] + 5) / (2 * k[4:-4] + 5) / (
2 * k[:-8] + 3) / (2 * k[4:-4] + 3)
d = {
0: p0 * (ek[:-4] + hk[:-4]**2 * ek[2:-2] + gk[:-4]**2 * ek[4:]),
2: p2 * ((hk[:-6] * ek[2:-4] + gk[:-6] * hk[2:-4] * ek[4:-2])),
4: p4 * (gk[:-8] * ek[4:-4])
}
d[-2] = d[2]
d[-4] = d[4]
SpectralMatrix.__init__(self, d, test, trial)
self.solve = PDMA(self)
def __init__(self, test, trial):
assert isinstance(test[0], SB)
assert isinstance(trial[0], SB)
from shenfun.la import PDMA
N = test[0].N
ck = get_ck(N, test[0].quad)
k = np.arange(N-4, dtype=np.float)
d = {4: (k[:-4]+1)/(k[:-4]+3)*np.pi/2,
2: -((k[:-2]+2)/(k[:-2]+3) + (k[:-2]+4)*(k[:-2]+1)/((k[:-2]+5)*(k[:-2]+3)))*np.pi,
0: (ck[:N-4] + 4*((k+2)/(k+3))**2 + ck[4:]*((k+1)/(k+3))**2)*np.pi/2.}
d[-2] = d[2]
d[-4] = d[4]
SpectralMatrix.__init__(self, d, test, trial)
self.solve = PDMA(self)
def __init__(self, test, trial, measure=1):
from shenfun.la import PDMA
assert isinstance(test[0], SB)
assert isinstance(trial[0], SB)
N = test[0].N
k = np.arange(N, dtype=np.float)
gk = (2*k+3)/(2*k+7)
hk = -(1+gk)
ek = 2./(2*k+1)
if test[0].quad == 'GL':
ek[-1] = 2./(N-1)
d = {0: ek[:-4] + hk[:-4]**2*ek[2:-2] + gk[:-4]**2*ek[4:],
2: hk[:-6]*ek[2:-4] + gk[:-6]*hk[2:-4]*ek[4:-2],
4: gk[:-8]*ek[4:-4]}
d[-2] = d[2]
d[-4] = d[4]
SpectralMatrix.__init__(self, d, test, trial, measure=measure)
self.solve = PDMA(self)
def __init__(self, test, trial, measure=1):
assert isinstance(test[0], SB)
assert isinstance(trial[0], SB)
from shenfun.la import PDMA
N = test[0].N
M = trial[0].N
Q = min(N, M)
ck = get_ck(Q, test[0].quad)
k = np.arange(Q-4, dtype=np.float)
d = {0: (ck[:Q-4] + 4*((k+2)/(k+3))**2 + ck[4:]*((k+1)/(k+3))**2)*np.pi/2.}
d4 = (k+1)/(k+3)*np.pi/2
d2 = -((k+2)/(k+3)+(k+4)*(k+1)/((k+5)*(k+3)))*np.pi
d[2] = d2[:dmax(N-4, M-4, 2)]
d[4] = d4[:dmax(N-4, M-4, 4)]
d[-2] = d2[:dmax(N-4, M-4, -2)]
d[-4] = d4[:dmax(N-4, M-4, -4)]
SpectralMatrix.__init__(self, d, test, trial, measure=measure)
self.solve = PDMA(self)