hpddm.optionParseArgs(opt, args, 2, ctypes.cast(val, ctypes.POINTER(ctypes.c_char_p)), ctypes.cast(desc, ctypes.POINTER(ctypes.c_char_p)))
val = None
desc = None
appArgs()
o, connectivity, dof, Mat, MatNeumann, d, f, sol, mu = generate(rankWorld, sizeWorld)
status = 0
if sizeWorld > 1:
A = hpddm.schwarzCreate(Mat, o, connectivity)
hpddm.schwarzMultiplicityScaling(A, d)
hpddm.schwarzInitialize(A, d)
if mu != 0:
hpddm.schwarzScaledExchange(A, f)
else:
mu = 1
if hpddm.optionSet(opt, b'schwarz_coarse_correction'):
nu = ctypes.c_ushort(int(hpddm.optionVal(opt, b'geneo_nu')))
if nu.value > 0:
if hpddm.optionApp(opt, b'nonuniform'):
nu.value += max(int(-hpddm.optionVal(opt, b'geneo_nu') + 1), (-1)**rankWorld * rankWorld)
threshold = hpddm.underlying(max(0, hpddm.optionVal(opt, b'geneo_threshold')))
hpddm.schwarzSolveGEVP(A, MatNeumann, ctypes.byref(nu), threshold)
addr = hpddm.optionAddr(opt, b'geneo_nu')
addr.contents.value = nu.value
else:
nu = 1
deflation = numpy.ones((dof, nu), order = 'F', dtype = hpddm.scalar)
hpddm.setVectors(hpddm.schwarzPreconditioner(A), nu, deflation)
hpddm.initializeCoarseOperator(hpddm.schwarzPreconditioner(A), nu)
hpddm.schwarzBuildCoarseOperator(A, hpddm.MPI_Comm.from_address(MPI._addressof(MPI.COMM_WORLD)))
hpddm.schwarzCallNumfact(A)
if rankWorld != 0:
if sizeWorld > 1:
A = hpddm.schwarzCreate(Mat, o, connectivity)
hpddm.schwarzMultiplicityScaling(A, d)
hpddm.schwarzInitialize(A, d)
if mu != 0:
hpddm.schwarzScaledExchange(A, f)
else:
mu = 1
if hpddm.optionSet(opt, b'schwarz_coarse_correction'):
addr = hpddm.optionAddr(opt, b'geneo_nu')
nu = ctypes.c_ushort(int(addr.contents.value))
if nu.value > 0:
if hpddm.optionApp(opt, b'nonuniform'):
addr.contents.value += max(int(-addr.contents.value + 1), (-1)**rankWorld * rankWorld)
hpddm.schwarzSolveGEVP(A, MatNeumann)
nu = int(hpddm.optionVal(opt, b'geneo_nu'))
else:
nu = 1
deflation = numpy.ones((dof, nu), order = 'F', dtype = hpddm.scalar)
hpddm.setVectors(hpddm.schwarzPreconditioner(A), nu, deflation)
hpddm.initializeCoarseOperator(hpddm.schwarzPreconditioner(A), nu)
hpddm.schwarzBuildCoarseOperator(A, hpddm.MPI_Comm.from_address(MPI._addressof(MPI.COMM_WORLD)))
hpddm.schwarzCallNumfact(A)
if rankWorld != 0:
hpddm.optionRemove(opt, b'verbosity')
comm = hpddm.getCommunicator(hpddm.schwarzPreconditioner(A))
it = hpddm.solve(A, f, sol, comm)
storage = numpy.empty(2 * mu, order = 'F', dtype = hpddm.underlying)
hpddm.schwarzComputeResidual(A, sol, f, storage)
if rankWorld == 0:
for nu in xrange(mu):
lu = scipy.sparse.linalg.spilu(csr.tocsc(), drop_tol = hpddm.optionApp(opt, b'drop_tol'), fill_factor = hpddm.optionApp(opt, b'fill_factor'))
@hpddm.precondFunc
def precond(y, x, n, m):
if m == 1:
x._shape_ = (n,)
y._shape_ = (n,)
x = numpy.ctypeslib.as_array(x, (n,))
y = numpy.ctypeslib.as_array(y, (n,))
else:
x._shape_ = (m, n)
y._shape_ = (m, n)
x = numpy.ctypeslib.as_array(x, (m, n)).transpose()
y = numpy.ctypeslib.as_array(y, (m, n)).transpose()
x[:] = lu.solve(y[:])
if hpddm.optionVal(opt, b'krylov_method') == 1:
hpddm.BGMRES(Mat, precond, f, sol)
else:
hpddm.GMRES(Mat, precond, f, sol)
status = 0
nrmb = numpy.linalg.norm(f, axis = 0)
tmp = numpy.empty_like(f)
hpddm.csrmv(Mat, sol, tmp)
tmp -= f
nrmAx = numpy.linalg.norm(tmp, axis = 0)
if mu == 1:
nrmb = [ nrmb ]
nrmAx = [ nrmAx ]
for nu in xrange(mu):
if nu == 0:
def generate(rankWorld, sizeWorld):
opt = hpddm.optionGet()
Nx = int(hpddm.optionApp(opt, b'Nx'))
Ny = int(hpddm.optionApp(opt, b'Ny'))
overlap = int(hpddm.optionApp(opt, b'overlap'))
mu = int(hpddm.optionApp(opt, b'generate_random_rhs'))
sym = bool(hpddm.optionApp(opt, b'symmetric_csr'))
xGrid = int(math.sqrt(sizeWorld))
while sizeWorld % xGrid != 0:
--xGrid
yGrid = int(sizeWorld / xGrid)
y = int(rankWorld / xGrid)
x = rankWorld - xGrid * y
iStart = max(x * int(Nx / xGrid) - overlap, 0)
iEnd = min((x + 1) * int(Nx / xGrid) + overlap, Nx)
jStart = max(y * int(Ny / yGrid) - overlap, 0)
jEnd = min((y + 1) * int(Ny / yGrid) + overlap, Ny)
ndof = (iEnd - iStart) * (jEnd - jStart)
nnz = ndof * 3 - (iEnd - iStart) - (jEnd - jStart)
if not(sym):
nnz = 2 * nnz - ndof
sol = numpy.zeros(ndof if mu == 0 else (ndof, mu), order = 'F', dtype = hpddm.scalar)
f = numpy.empty_like(sol)
xdim = [ 0.0, 10.0 ]
ydim = [ 0.0, 10.0 ]
dx = (xdim[1] - xdim[0]) / float(Nx)
dy = (ydim[1] - ydim[0]) / float(Ny)
if mu == 0:
Nf = 3
xsc = [ 6.5, 2.0, 7.0 ]
ysc = [ 8.0, 7.0, 3.0 ]
rsc = [ 0.3, 0.3, 0.4 ]
asc = [ 0.3, 0.2, -0.1 ]
k = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
frs = 1.0
for n in xrange(Nf):
(xdist, ydist) = [ xdim[0] + dx * (i + 0.5) - xsc[n], ydim[0] + dy * (j + 0.5) - ysc[n] ]
if math.sqrt(xdist * xdist + ydist * ydist) <= rsc[n]:
frs -= asc[n] * math.cos(0.5 * math.pi * xdist / rsc[n]) * math.cos(0.5 * math.pi * ydist / rsc[n])
f[k] = frs
k += 1
else:
f[:] = numpy.random.random_sample((ndof, mu))
if hpddm.scalar == numpy.complex64 or hpddm.scalar == numpy.complex128:
f[:] += numpy.random.random_sample((ndof, mu)) * 1j
d = numpy.ones(ndof, dtype = hpddm.underlying)
o = []
connectivity = []
if jStart != 0:
if iStart != 0:
o.append(rankWorld - xGrid - 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iStart + 2 * overlap):
connectivity[-1][k] = i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(overlap - j):
d[i + j + j * (iEnd - iStart)] = j / float(overlap)
for i in xrange(j):
d[i + j * (iEnd - iStart)] = i / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[i + j * (iEnd - iStart)] = j / float(overlap)
o.append(rankWorld - xGrid)
connectivity.append([None] * 2 * overlap * (iEnd - iStart))
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iEnd):
connectivity[-1][k] = i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(iStart + overlap, iEnd - overlap):
d[i - iStart + (iEnd - iStart) * j] = j / float(overlap)
if iEnd != Nx:
o.append(rankWorld - xGrid + 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for i in xrange(2 * overlap):
for j in xrange(2 * overlap):
connectivity[-1][k] = (iEnd - iStart) * (i + 1) - 2 * overlap + j
k += 1
for j in xrange(0, overlap):
for i in xrange(overlap - j):
d[(iEnd - iStart) * (j + 1) - overlap + i] = j / float(overlap)
for i in xrange(j):
d[(iEnd - iStart) * (j + 1) - i - 1] = i / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[(iEnd - iStart) * (j + 1) - overlap + i] = j / float(overlap)
if iStart != 0:
o.append(rankWorld - 1)
connectivity.append([None] * 2 * overlap * (jEnd - jStart))
k = 0
for i in xrange(jStart, jEnd):
for j in xrange(2 * overlap):
connectivity[-1][k] = j + (i - jStart) * (iEnd - iStart)
k += 1
for i in xrange(jStart + (jStart != 0) * overlap, jEnd - (jEnd != Ny) * overlap):
for j in xrange(overlap):
d[j + (i - jStart) * (iEnd - iStart)] = j / float(overlap)
if iEnd != Nx:
o.append(rankWorld + 1)
connectivity.append([None] * 2 * overlap * (jEnd - jStart))
k = 0
for i in xrange(jStart, jEnd):
for j in xrange(2 * overlap):
connectivity[-1][k] = (iEnd - iStart) * (i + 1 - jStart) - 2 * overlap + j
k += 1
for i in xrange(jStart + (jStart != 0) * overlap, jEnd - (jEnd != Ny) * overlap):
for j in xrange(overlap):
d[(iEnd - iStart) * (i + 1 - jStart) - j - 1] = j / float(overlap)
if jEnd != Ny:
if iStart != 0:
o.append(rankWorld + xGrid - 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iStart + 2 * overlap):
connectivity[-1][k] = ndof - 2 * overlap * (iEnd - iStart) + i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(overlap - j):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) * j] = i / float(overlap)
for i in xrange(overlap - j, overlap):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) * j] = (overlap - 1 - j) / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[ndof - overlap * (iEnd - iStart) + (iEnd - iStart) * j + i] = (overlap - j - 1) / float(overlap)
o.append(rankWorld + xGrid);
connectivity.append([None] * 2 * overlap * (iEnd - iStart))
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iEnd):
connectivity[-1][k] = ndof - 2 * overlap * (iEnd - iStart) + i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(iStart + overlap, iEnd - overlap):
d[ndof - overlap * (iEnd - iStart) + i - iStart + (iEnd - iStart) * j] = (overlap - 1 - j) / float(overlap)
if iEnd != Nx:
o.append(rankWorld + xGrid + 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iStart + 2 * overlap):
connectivity[-1][k] = ndof - 2 * overlap * (iEnd - iStart) + i - iStart + (iEnd - iStart) * j + (iEnd - iStart - 2 * overlap)
k += 1
for j in xrange(overlap):
for i in xrange(j, overlap):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) * (j + 1) - overlap] = (overlap - 1 - i) / float(overlap)
for i in xrange(j):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) * (j + 1) - overlap] = (overlap - 1 - j) / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) * (j + 1) - overlap] = (overlap - j - 1) / float(overlap)
ia = numpy.empty(ndof + 1, dtype = ctypes.c_int)
ja = numpy.empty(nnz, dtype = ctypes.c_int)
a = numpy.empty(nnz, dtype = hpddm.scalar)
ia[0] = (hpddm.numbering.value == b'F')
ia[ndof] = nnz + (hpddm.numbering.value == b'F')
if sym:
k = 0
nnz = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
a[nnz] = -1 / (dy * dy)
ja[nnz] = k - int(Nx / xGrid) + (hpddm.numbering.value == b'F')
nnz += 1
if i > iStart:
a[nnz] = -1 / (dx * dx)
ja[nnz] = k - (hpddm.numbering.value == b'C')
nnz += 1
a[nnz] = 2 / (dx * dx) + 2 / (dy * dy)
ja[nnz] = k + (hpddm.numbering.value == b'F')
nnz += 1
k += 1
ia[k] = nnz + (hpddm.numbering.value == b'F')
else:
k = 0
nnz = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
a[nnz] = -1 / (dy * dy)
ja[nnz] = k - int(Nx / xGrid) + (hpddm.numbering.value == b'F')
nnz += 1
if i > iStart:
a[nnz] = -1 / (dx * dx)
ja[nnz] = k - (hpddm.numbering.value == b'C')
nnz += 1
a[nnz] = 2 / (dx * dx) + 2 / (dy * dy)
ja[nnz] = k + (hpddm.numbering.value == b'F')
nnz += 1
if i < iEnd - 1:
a[nnz] = -1 / (dx * dx)
ja[nnz] = k + 1 + (hpddm.numbering.value == b'F')
nnz += 1
if j < jEnd - 1:
a[nnz] = -1 / (dy * dy)
ja[nnz] = k + int(Nx / xGrid) + (hpddm.numbering.value == b'F')
nnz += 1
k += 1
ia[k] = nnz + (hpddm.numbering.value == b'F')
if sizeWorld > 1 and hpddm.optionSet(opt, b'schwarz_coarse_correction') and hpddm.optionVal(opt, b'geneo_nu') > 0:
if sym:
nnzNeumann = 2 * nnz - ndof
iNeumann = numpy.empty_like(ia)
jNeumann = numpy.empty(nnzNeumann, dtype = ctypes.c_int)
aNeumann = numpy.empty(nnzNeumann, dtype = hpddm.scalar)
iNeumann[0] = (hpddm.numbering.value == b'F')
iNeumann[ndof] = nnzNeumann + (hpddm.numbering.value == b'F')
k = 0
nnzNeumann = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
aNeumann[nnzNeumann] = -1 / (dy * dy) + (-1 / (dx * dx) if i == iStart else 0)
jNeumann[nnzNeumann] = k - int(Nx / xGrid) + (hpddm.numbering.value == b'F')
nnzNeumann += 1
if i > iStart:
aNeumann[nnzNeumann] = -1 / (dx * dx) + (-1 / (dy * dy) if j == jStart else 0)
jNeumann[nnzNeumann] = k - (hpddm.numbering.value == b'C')
nnzNeumann += 1
aNeumann[nnzNeumann] = 2 / (dx * dx) + 2 / (dy * dy)
jNeumann[nnzNeumann] = k + (hpddm.numbering.value == b'F')
nnzNeumann += 1
if i < iEnd - 1:
aNeumann[nnzNeumann] = -1 / (dx * dx) + (-1 / (dy * dy) if j == jEnd - 1 else 0)
jNeumann[nnzNeumann] = k + 1 + (hpddm.numbering.value == b'F')
nnzNeumann += 1
if j < jEnd - 1:
aNeumann[nnzNeumann] = -1 / (dy * dy) + (-1 / (dx * dx) if i == iEnd - 1 else 0)
jNeumann[nnzNeumann] = k + int(Nx / xGrid) + (hpddm.numbering.value == b'F')
nnzNeumann += 1
k += 1
iNeumann[k] = nnzNeumann + (hpddm.numbering.value == b'F')
MatNeumann = hpddm.matrixCSRCreate(ndof, ndof, nnzNeumann, aNeumann, iNeumann, jNeumann, False)
else:
aNeumann = numpy.empty_like(a)
numpy.copyto(aNeumann, a)
nnzNeumann = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
if i == iStart:
aNeumann[nnzNeumann] -= 1 / (dx * dx)
nnzNeumann += 1
if i > iStart:
if j == jStart:
aNeumann[nnzNeumann] -= 1 / (dy * dy)
nnzNeumann += 1
nnzNeumann += 1
if i < iEnd - 1:
if j == jEnd - 1:
aNeumann[nnzNeumann] -= 1 / (dy * dy)
nnzNeumann += 1
if j < jEnd - 1:
if i == iEnd - 1:
aNeumann[nnzNeumann] -= 1 / (dx * dx)
nnzNeumann += 1
MatNeumann = hpddm.matrixCSRCreate(ndof, ndof, nnzNeumann, aNeumann, ia, ja, False)
else:
MatNeumann = ctypes.POINTER(hpddm.MatrixCSR)()
Mat = hpddm.matrixCSRCreate(ndof, ndof, nnz, a, ia, ja, sym)
if sizeWorld > 1:
for k in xrange(sizeWorld):
if k == rankWorld:
print(str(rankWorld) + ':')
print(str(x) + 'x' + str(y) + ' -- [' + str(iStart) + ' ; ' + str(iEnd) + '] x [' + str(jStart) + ' ; ' + str(jEnd) + '] -- ' + str(ndof) + ', ' + str(nnz))
MPI.COMM_WORLD.Barrier()
return o, connectivity, ndof, Mat, MatNeumann, d, f, sol, mu
def generate(rankWorld, sizeWorld):
opt = hpddm.optionGet()
Nx = int(hpddm.optionApp(opt, b'Nx'))
Ny = int(hpddm.optionApp(opt, b'Ny'))
overlap = int(hpddm.optionApp(opt, b'overlap'))
mu = int(hpddm.optionApp(opt, b'generate_random_rhs'))
sym = bool(hpddm.optionApp(opt, b'symmetric_csr'))
xGrid = int(math.sqrt(sizeWorld))
while sizeWorld % xGrid != 0:
--xGrid
yGrid = int(sizeWorld / xGrid)
y = int(rankWorld / xGrid)
x = rankWorld - xGrid * y
iStart = max(x * int(Nx / xGrid) - overlap, 0)
iEnd = min((x + 1) * int(Nx / xGrid) + overlap, Nx)
jStart = max(y * int(Ny / yGrid) - overlap, 0)
jEnd = min((y + 1) * int(Ny / yGrid) + overlap, Ny)
ndof = (iEnd - iStart) * (jEnd - jStart)
nnz = ndof * 3 - (iEnd - iStart) - (jEnd - jStart)
if not (sym):
nnz = 2 * nnz - ndof
sol = numpy.zeros(ndof if mu == 0 else (ndof, mu),
order='F',
dtype=hpddm.scalar)
f = numpy.empty_like(sol)
xdim = [0.0, 10.0]
ydim = [0.0, 10.0]
dx = (xdim[1] - xdim[0]) / float(Nx)
dy = (ydim[1] - ydim[0]) / float(Ny)
if mu == 0:
Nf = 3
xsc = [6.5, 2.0, 7.0]
ysc = [8.0, 7.0, 3.0]
rsc = [0.3, 0.3, 0.4]
asc = [0.3, 0.2, -0.1]
k = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
frs = 1.0
for n in xrange(Nf):
(xdist, ydist) = [
xdim[0] + dx * (i + 0.5) - xsc[n],
ydim[0] + dy * (j + 0.5) - ysc[n]
]
if math.sqrt(xdist * xdist + ydist * ydist) <= rsc[n]:
frs -= asc[n] * math.cos(
0.5 * math.pi * xdist / rsc[n]) * math.cos(
0.5 * math.pi * ydist / rsc[n])
f[k] = frs
k += 1
else:
f[:] = numpy.random.random_sample((ndof, mu))
if hpddm.scalar == numpy.complex64 or hpddm.scalar == numpy.complex128:
f[:] += numpy.random.random_sample((ndof, mu)) * 1j
d = numpy.ones(ndof, dtype=hpddm.underlying)
o = []
connectivity = []
if jStart != 0:
if iStart != 0:
o.append(rankWorld - xGrid - 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iStart + 2 * overlap):
connectivity[-1][k] = i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(overlap - j):
d[i + j + j * (iEnd - iStart)] = j / float(overlap)
for i in xrange(j):
d[i + j * (iEnd - iStart)] = i / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[i + j * (iEnd - iStart)] = j / float(overlap)
o.append(rankWorld - xGrid)
connectivity.append([None] * 2 * overlap * (iEnd - iStart))
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iEnd):
connectivity[-1][k] = i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(iStart + overlap, iEnd - overlap):
d[i - iStart + (iEnd - iStart) * j] = j / float(overlap)
if iEnd != Nx:
o.append(rankWorld - xGrid + 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for i in xrange(2 * overlap):
for j in xrange(2 * overlap):
connectivity[-1][k] = (iEnd -
iStart) * (i + 1) - 2 * overlap + j
k += 1
for j in xrange(0, overlap):
for i in xrange(overlap - j):
d[(iEnd - iStart) * (j + 1) - overlap +
i] = j / float(overlap)
for i in xrange(j):
d[(iEnd - iStart) * (j + 1) - i - 1] = i / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[(iEnd - iStart) * (j + 1) - overlap +
i] = j / float(overlap)
if iStart != 0:
o.append(rankWorld - 1)
connectivity.append([None] * 2 * overlap * (jEnd - jStart))
k = 0
for i in xrange(jStart, jEnd):
for j in xrange(2 * overlap):
connectivity[-1][k] = j + (i - jStart) * (iEnd - iStart)
k += 1
for i in xrange(jStart + (jStart != 0) * overlap,
jEnd - (jEnd != Ny) * overlap):
for j in xrange(overlap):
d[j + (i - jStart) * (iEnd - iStart)] = j / float(overlap)
if iEnd != Nx:
o.append(rankWorld + 1)
connectivity.append([None] * 2 * overlap * (jEnd - jStart))
k = 0
for i in xrange(jStart, jEnd):
for j in xrange(2 * overlap):
connectivity[-1][k] = (iEnd - iStart) * (
i + 1 - jStart) - 2 * overlap + j
k += 1
for i in xrange(jStart + (jStart != 0) * overlap,
jEnd - (jEnd != Ny) * overlap):
for j in xrange(overlap):
d[(iEnd - iStart) * (i + 1 - jStart) - j -
1] = j / float(overlap)
if jEnd != Ny:
if iStart != 0:
o.append(rankWorld + xGrid - 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iStart + 2 * overlap):
connectivity[-1][k] = ndof - 2 * overlap * (
iEnd - iStart) + i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(overlap - j):
d[ndof - overlap * (iEnd - iStart) + i +
(iEnd - iStart) * j] = i / float(overlap)
for i in xrange(overlap - j, overlap):
d[ndof - overlap * (iEnd - iStart) + i +
(iEnd - iStart) * j] = (overlap - 1 - j) / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[ndof - overlap * (iEnd - iStart) + (iEnd - iStart) * j +
i] = (overlap - j - 1) / float(overlap)
o.append(rankWorld + xGrid)
connectivity.append([None] * 2 * overlap * (iEnd - iStart))
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iEnd):
connectivity[-1][k] = ndof - 2 * overlap * (
iEnd - iStart) + i - iStart + (iEnd - iStart) * j
k += 1
for j in xrange(overlap):
for i in xrange(iStart + overlap, iEnd - overlap):
d[ndof - overlap * (iEnd - iStart) + i - iStart +
(iEnd - iStart) * j] = (overlap - 1 - j) / float(overlap)
if iEnd != Nx:
o.append(rankWorld + xGrid + 1)
connectivity.append([None] * 4 * overlap * overlap)
k = 0
for j in xrange(2 * overlap):
for i in xrange(iStart, iStart + 2 * overlap):
connectivity[-1][k] = ndof - 2 * overlap * (
iEnd - iStart) + i - iStart + (iEnd - iStart) * j + (
iEnd - iStart - 2 * overlap)
k += 1
for j in xrange(overlap):
for i in xrange(j, overlap):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) *
(j + 1) - overlap] = (overlap - 1 - i) / float(overlap)
for i in xrange(j):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) *
(j + 1) - overlap] = (overlap - 1 - j) / float(overlap)
else:
for j in xrange(overlap):
for i in xrange(overlap):
d[ndof - overlap * (iEnd - iStart) + i + (iEnd - iStart) *
(j + 1) - overlap] = (overlap - j - 1) / float(overlap)
ia = numpy.empty(ndof + 1, dtype=ctypes.c_int)
ja = numpy.empty(nnz, dtype=ctypes.c_int)
a = numpy.empty(nnz, dtype=hpddm.scalar)
ia[0] = (hpddm.numbering.value == b'F')
ia[ndof] = nnz + (hpddm.numbering.value == b'F')
if sym:
k = 0
nnz = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
a[nnz] = -1 / (dy * dy)
ja[nnz] = k - int(Nx / xGrid) + (hpddm.numbering.value
== b'F')
nnz += 1
if i > iStart:
a[nnz] = -1 / (dx * dx)
ja[nnz] = k - (hpddm.numbering.value == b'C')
nnz += 1
a[nnz] = 2 / (dx * dx) + 2 / (dy * dy)
ja[nnz] = k + (hpddm.numbering.value == b'F')
nnz += 1
k += 1
ia[k] = nnz + (hpddm.numbering.value == b'F')
else:
k = 0
nnz = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
a[nnz] = -1 / (dy * dy)
ja[nnz] = k - int(Nx / xGrid) + (hpddm.numbering.value
== b'F')
nnz += 1
if i > iStart:
a[nnz] = -1 / (dx * dx)
ja[nnz] = k - (hpddm.numbering.value == b'C')
nnz += 1
a[nnz] = 2 / (dx * dx) + 2 / (dy * dy)
ja[nnz] = k + (hpddm.numbering.value == b'F')
nnz += 1
if i < iEnd - 1:
a[nnz] = -1 / (dx * dx)
ja[nnz] = k + 1 + (hpddm.numbering.value == b'F')
nnz += 1
if j < jEnd - 1:
a[nnz] = -1 / (dy * dy)
ja[nnz] = k + int(Nx / xGrid) + (hpddm.numbering.value
== b'F')
nnz += 1
k += 1
ia[k] = nnz + (hpddm.numbering.value == b'F')
if sizeWorld > 1 and hpddm.optionSet(
opt, b'schwarz_coarse_correction') and hpddm.optionVal(
opt, b'geneo_nu') > 0:
if sym:
nnzNeumann = 2 * nnz - ndof
iNeumann = numpy.empty_like(ia)
jNeumann = numpy.empty(nnzNeumann, dtype=ctypes.c_int)
aNeumann = numpy.empty(nnzNeumann, dtype=hpddm.scalar)
iNeumann[0] = (hpddm.numbering.value == b'F')
iNeumann[ndof] = nnzNeumann + (hpddm.numbering.value == b'F')
k = 0
nnzNeumann = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
aNeumann[nnzNeumann] = -1 / (dy * dy) + (
-1 / (dx * dx) if i == iStart else 0)
jNeumann[nnzNeumann] = k - int(
Nx / xGrid) + (hpddm.numbering.value == b'F')
nnzNeumann += 1
if i > iStart:
aNeumann[nnzNeumann] = -1 / (dx * dx) + (
-1 / (dy * dy) if j == jStart else 0)
jNeumann[nnzNeumann] = k - (hpddm.numbering.value
== b'C')
nnzNeumann += 1
aNeumann[nnzNeumann] = 2 / (dx * dx) + 2 / (dy * dy)
jNeumann[nnzNeumann] = k + (hpddm.numbering.value == b'F')
nnzNeumann += 1
if i < iEnd - 1:
aNeumann[nnzNeumann] = -1 / (dx * dx) + (
-1 / (dy * dy) if j == jEnd - 1 else 0)
jNeumann[nnzNeumann] = k + 1 + (hpddm.numbering.value
== b'F')
nnzNeumann += 1
if j < jEnd - 1:
aNeumann[nnzNeumann] = -1 / (dy * dy) + (
-1 / (dx * dx) if i == iEnd - 1 else 0)
jNeumann[nnzNeumann] = k + int(
Nx / xGrid) + (hpddm.numbering.value == b'F')
nnzNeumann += 1
k += 1
iNeumann[k] = nnzNeumann + (hpddm.numbering.value == b'F')
MatNeumann = hpddm.matrixCSRCreate(ndof, ndof, nnzNeumann,
aNeumann, iNeumann, jNeumann,
False)
else:
aNeumann = numpy.empty_like(a)
numpy.copyto(aNeumann, a)
nnzNeumann = 0
for j in xrange(jStart, jEnd):
for i in xrange(iStart, iEnd):
if j > jStart:
if i == iStart:
aNeumann[nnzNeumann] -= 1 / (dx * dx)
nnzNeumann += 1
if i > iStart:
if j == jStart:
aNeumann[nnzNeumann] -= 1 / (dy * dy)
nnzNeumann += 1
nnzNeumann += 1
if i < iEnd - 1:
if j == jEnd - 1:
aNeumann[nnzNeumann] -= 1 / (dy * dy)
nnzNeumann += 1
if j < jEnd - 1:
if i == iEnd - 1:
aNeumann[nnzNeumann] -= 1 / (dx * dx)
nnzNeumann += 1
MatNeumann = hpddm.matrixCSRCreate(ndof, ndof, nnzNeumann,
aNeumann, ia, ja, False)
else:
MatNeumann = ctypes.POINTER(hpddm.MatrixCSR)()
Mat = hpddm.matrixCSRCreate(ndof, ndof, nnz, a, ia, ja, sym)
if sizeWorld > 1:
for k in xrange(sizeWorld):
if k == rankWorld:
print(str(rankWorld) + ':')
print(
str(x) + 'x' + str(y) + ' -- [' + str(iStart) + ' ; ' +
str(iEnd) + '] x [' + str(jStart) + ' ; ' + str(jEnd) +
'] -- ' + str(ndof) + ', ' + str(nnz))
MPI.COMM_WORLD.Barrier()
return o, connectivity, ndof, Mat, MatNeumann, d, f, sol, mu
appArgs()
o, connectivity, dof, Mat, MatNeumann, d, f, sol, mu = generate(
rankWorld, sizeWorld)
status = 0
if sizeWorld > 1:
A = hpddm.schwarzCreate(Mat, o, connectivity)
hpddm.schwarzMultiplicityScaling(A, d)
hpddm.schwarzInitialize(A, d)
if mu != 0:
hpddm.schwarzScaledExchange(A, f)
else:
mu = 1
if hpddm.optionSet(opt, b'schwarz_coarse_correction'):
nu = ctypes.c_ushort(int(hpddm.optionVal(opt, b'geneo_nu')))
if nu.value > 0:
if hpddm.optionApp(opt, b'nonuniform'):
nu.value += max(int(-hpddm.optionVal(opt, b'geneo_nu') + 1),
(-1)**rankWorld * rankWorld)
threshold = hpddm.underlying(
max(0, hpddm.optionVal(opt, b'geneo_threshold')))
hpddm.schwarzSolveGEVP(A, MatNeumann, ctypes.byref(nu), threshold)
addr = hpddm.optionAddr(opt, b'geneo_nu')
addr.contents.value = nu.value
else:
nu = 1
deflation = numpy.ones((dof, nu), order='F', dtype=hpddm.scalar)
hpddm.setVectors(hpddm.schwarzPreconditioner(A), nu, deflation)
hpddm.initializeCoarseOperator(hpddm.schwarzPreconditioner(A), nu)
hpddm.schwarzBuildCoarseOperator(