def __init__(self, N, a0, alfa, beta, quad="GL"):
self.quad = quad
self.shape = (N - 4, N - 4)
SB = bases.ShenBiharmonicBasis(N, quad)
self.S = inner_product((SB, 0), (SB, 4))
self.B = inner_product((SB, 0), (SB, 0))
self.A = inner_product((SB, 0), (SB, 2))
self.a0 = a0
self.alfa = alfa
self.beta = beta
def __init__(self, N, a0, alfa, beta, quad="GL", solver="cython"):
self.quad = quad
self.solver = solver
k = arange(N)
SB = bases.ShenBiharmonicBasis(N, quad=quad)
self.S = S = inner_product((SB, 0), (SB, 4))
self.B = B = inner_product((SB, 0), (SB, 0))
self.A = A = inner_product((SB, 0), (SB, 2))
self.a0 = a0
self.alfa = alfa
self.beta = beta
if not solver == "scipy":
sii, siu, siuu = S[0], S[2], S[4]
ail, aii, aiu = A[-2], A[0], A[2]
bill, bil, bii, biu, biuu = B[-4], B[-2], B[0], B[2], B[4]
M = sii[::2].shape[0]
if hasattr(beta, "__len__"):
Ny, Nz = beta.shape
if solver == "scipy":
self.Le = Le = []
self.Lo = Lo = []
#self.AA = []
for i in range(Ny):
Lej = []
Loj = []
#AA = []
for j in range(Nz):
AA = a0*S.diags().toarray() + alfa[i, j]*A.diags().toarray() + beta[i, j]*B.diags().toarray()
Ae = AA[::2, ::2]
Ao = AA[1::2, 1::2]
Lej.append(lu_factor(Ae))
Loj.append(lu_factor(Ao))
#AA.append((a0*S + alfa*A + beta*B).diags('csr'))
Le.append(Lej)
Lo.append(Loj)
#self.AA.append(AA)
else:
self.u0 = zeros((2, M, Ny, Nz))
self.u1 = zeros((2, M, Ny, Nz))
self.u2 = zeros((2, M, Ny, Nz))
self.l0 = zeros((2, M, Ny, Nz))
self.l1 = zeros((2, M, Ny, Nz))
self.ak = zeros((2, M, Ny, Nz))
self.bk = zeros((2, M, Ny, Nz))
LUsolve.LU_Biharmonic_3D_n(a0, alfa, beta, sii, siu, siuu, ail, aii, aiu, bill, bil, bii, biu, biuu, self.u0, self.u1, self.u2, self.l0, self.l1)
LUsolve.Biharmonic_factor_pr_3D(self.ak, self.bk, self.l0, self.l1)
else:
if solver == "scipy":
#AA = a0*S.diags().toarray() + alfa*A.diags().toarray() + beta*B.diags().toarray()
#Ae = AA[::2, ::2]
#Ao = AA[1::2, 1::2]
#self.Le = lu_factor(Ae)
#self.Lo = lu_factor(Ao)
self.AA = (a0*S + alfa*A + beta*B).diags('csr')
else:
self.u0 = zeros((2, M))
self.u1 = zeros((2, M))
self.u2 = zeros((2, M))
self.l0 = zeros((2, M))
self.l1 = zeros((2, M))
self.ak = zeros((2, M))
self.bk = zeros((2, M))
LUsolve.LU_Biharmonic_1D(a0, alfa, beta, sii, siu, siuu, ail, aii, aiu, bill, bil, bii, biu, biuu, self.u0, self.u1, self.u2, self.l0, self.l1)
LUsolve.Biharmonic_factor_pr(self.ak, self.bk, self.l0, self.l1)