def test_coefficient_vector(self):
mesh = (np.arange(3), np.arange(10, 12))
G = Grid.Grid(mesh, initializer=lambda *x: 0.0)
# print G
F = FD.FiniteDifferenceEngineADI(G,
coefficients={
(0, 1): lambda t, *x: 1
})
op = self.F.operators[(0, 1)]
op.D.data[op.D.data != 0] = op.D.data[op.D.data != 0]**0
op.D = todia(op.D)
# diamat = op.D
# densemat = diamat.todense()
# f0 = lambda t, *x: x[0]
# f1 = lambda t, *x: x[1]
f = lambda t, *x: x
vec = F.coefficient_vector(f, 0, 0)
ref = np.tile(mesh[0], G.shape[1]), np.repeat(mesh[1], G.shape[0])
npt.assert_array_equal(ref, vec, "Failed when focused on dim: %i", 0)
vec = F.coefficient_vector(f, 0, 1)
ref = np.repeat(mesh[0], G.shape[1]), np.tile(mesh[1], G.shape[0])
npt.assert_array_equal(ref, vec, "Failed when focused on dim: %i", 1)
def apWithRes(A, U, R, blocks=1):
A = todia(A)
d = foldMatFor(A, blocks)
diagonalize = d.dot
undiagonalize = d.todense().I.dot
ret = undiagonalize(diagonalize(A).dot(U)) + R
return d, ret
def test_migrate_01(self):
B = self.F.operators[(0,1)]
B.D = utils.todia(B.D.tocoo().todia())
ref = B.copy()
B = BOG.BandedOperator(B, "test 01")
B = B.immigrate("test 01")
npt.assert_array_equal(ref.D.todense(), B.D.todense())
assert ref == B
def solveWithRes(A, U, R, blocks=1):
A = todia(A)
d = foldMatFor(A, blocks)
diagonalize = compose(todia, d.dot)
# undiagonalize = compose(lambda x: x.A[0], d.todense().I.dot)
diaA = diagonalize(A)
ret = diaA.todense().I.dot(d.dot(U-R)).A[0]
return ret
def test_copy_csr(self):
ref = self.F.operators[(0,1)]
tst = BOG.BandedOperator(ref).copy().immigrate()
ref.D = utils.todia(ref.D.tocoo().todia())
# fp(ref.D)
# print
# fp(tst.D)
# print
# fp(tst.D - ref.D)
npt.assert_array_equal(ref.D.todense(), tst.D.todense())
npt.assert_equal(tst, ref)
def setUp(self):
loops = 200
blocks = 2
decimals = 12
self.loops = loops
self.blocks = blocks
self.decimals = decimals
mat = np.matrix("""
-1.5 0.5 2 0 0;
-1 2 -1 0 0;
0 -1 2 -1 0;
0 0 -1 2 -1;
0 0 -1.5 0.5 2""").A
diamat = todia(scipy.sparse.dia_matrix(mat))
x = foldMatFor(diamat, 1).todense().A
topx = x.copy()
bottomx = x.copy()
topx[-1,-2] = 0
bottomx[0,1] = 0
x, topx, bottomx = map(todia, [x, topx, bottomx])
topblockx = scipy.sparse.block_diag([topx]*blocks)
bottomblockx = scipy.sparse.block_diag([bottomx]*blocks)
blockx = todia(scipy.sparse.block_diag([x]*blocks))
self.blockxI = blockx.todense().I.A
self.topblockxI = topblockx.todense().I.A
self.bottomblockxI = bottomblockx.todense().I.A
npt.assert_array_equal(todia(topblockx.dot(bottomblockx)).data, blockx.data)
blockdiamat = todia(scipy.sparse.block_diag([diamat]*blocks))
blocktridiamat = todia(blockx.dot(blockdiamat))
topblocktridiamat = todia(topblockx.dot(blockdiamat))
bottomblocktridiamat = todia(bottomblockx.dot(blockdiamat))
self.blockdiamat = blockdiamat
self.blockx = blockx
self.topblockx = topblockx
self.bottomblockx = bottomblockx
self.blocktridiamat = blocktridiamat
self.topblocktridiamat = topblocktridiamat
self.bottomblocktridiamat = bottomblocktridiamat
self.vec = np.random.random(mat.shape[1]*blocks)
self.B = FD.BandedOperator((blockdiamat.data, (2, 1, 0, -1, -2)), inplace=False)
self.B.blocks = blocks
def test_coefficient_vector(self):
mesh = (np.arange(3), np.arange(10, 12))
G = Grid.Grid(mesh, initializer=lambda *x: 0.0)
# print G
F = FD.FiniteDifferenceEngineADI(G, coefficients={(0, 1): lambda t, *x: 1})
op = self.F.operators[(0, 1)]
op.D.data[op.D.data != 0] = op.D.data[op.D.data != 0] ** 0
op.D = todia(op.D)
# diamat = op.D
# densemat = diamat.todense()
# f0 = lambda t, *x: x[0]
# f1 = lambda t, *x: x[1]
f = lambda t, *x: x
vec = F.coefficient_vector(f, 0, 0)
ref = np.tile(mesh[0], G.shape[1]), np.repeat(mesh[1], G.shape[0])
npt.assert_array_equal(ref, vec, "Failed when focused on dim: %i", 0)
vec = F.coefficient_vector(f, 0, 1)
ref = np.repeat(mesh[0], G.shape[1]), np.tile(mesh[1], G.shape[0])
npt.assert_array_equal(ref, vec, "Failed when focused on dim: %i", 1)
def test_combine_dimensional_operators_1(self):
if self.F.operators[1].solve_banded_offsets[1] != 2:
print self.skipTest(
"Using first order boundary approximation. Top is tridiag.")
oldL2 = self.L2_.copy()
oldL2 = todia(oldL2.todense())
# high, low = 2, -2
# m = tuple(oldL2.offsets).index(0)
# oldL2.data = oldL2.data[m-high:m-low+1]
# oldL2.offsets = oldL2.offsets[m-high:m-low+1]
oldR2 = self.R2_.flatten()
L2 = self.F.operators[1]
# print "old"
# fp(oldL2.data)
# print
# print "new"
# fp(L2.D.data)
# print "old"
# fp(oldL2.todense())
# print
# print "new"
# fp(L2.D.todense())
# print
# print "diff"
# fp(oldL2.todense() - L2.D.todense())
npt.assert_allclose(L2.D.data, oldL2.data)
# print "old"
# print oldR2
# print
# print "new"
# print L2.R
# print "diff"
# fp(L2.R - oldR2)
npt.assert_allclose(L2.R, oldR2)
def test_combine_dimensional_operators_1(self):
if self.F.operators[1].solve_banded_offsets[1] != 2:
print self.skipTest("Using first order boundary approximation. Top is tridiag.")
oldL2 = self.L2_.copy()
oldL2 = todia(oldL2.todense())
# high, low = 2, -2
# m = tuple(oldL2.offsets).index(0)
# oldL2.data = oldL2.data[m-high:m-low+1]
# oldL2.offsets = oldL2.offsets[m-high:m-low+1]
oldR2 = self.R2_.flatten()
L2 = self.F.operators[1]
# print "old"
# fp(oldL2.data)
# print
# print "new"
# fp(L2.D.data)
# print "old"
# fp(oldL2.todense())
# print
# print "new"
# fp(L2.D.todense())
# print
# print "diff"
# fp(oldL2.todense() - L2.D.todense())
npt.assert_allclose(L2.D.data, oldL2.data)
# print "old"
# print oldR2
# print
# print "new"
# print L2.R
# print "diff"
# fp(L2.R - oldR2)
npt.assert_allclose(L2.R, oldR2)
def test_create_mixed_derivative(self):
B = self.F.simple_operators[(0,1)]
# BG = BOG.mixed_for_vector(self.F.grid.mesh[0],
# self.F.grid.mesh[1]).immigrate()
B.D = scipy.sparse.coo_matrix(B.D)
refcoo = B.D.copy()
n0 = self.F.grid.mesh[0].size
n1 = self.F.grid.mesh[1].size
compute_deltas = lambda v: np.hstack((np.nan, np.diff(v)))
d0 = compute_deltas(self.F.grid.mesh[0])
d1 = compute_deltas(self.F.grid.mesh[1])
dlen = (n1-2) * (n0-2)
sup = d1[1:n1-1] / (d1[2:n1]*(d1[1:n1-1]+d1[2:n1]))
mid = (-d1[1:n1-1] + d1[2:n1]) / (d1[1:n1-1]*d1[2:n1])
sub = -d1[2:n1] / (d1[1:n1-1]*(d1[1:n1-1]+d1[2:n1]))
supsup = np.tile(sup, n0-2)
supmid = np.tile(mid, n0-2)
supsub = np.tile(sub, n0-2)
midsup = supsup.copy()
midmid = supmid.copy()
midsub = supsub.copy()
subsup = supsup.copy()
submid = supmid.copy()
subsub = supsub.copy()
dsup = d0[1:n0-1] / (d0[2:n0]*(d0[1:n0-1]+d0[2:n0]))
dmid = (-d0[1:n0-1] + d0[2:n0]) / (d0[1:n0-1]*d0[2:n0])
dsub = -d0[2:n0] / (d0[1:n0-1]*(d0[1:n0-1]+d0[2:n0]))
dsup = np.repeat(dsup, n1-2)
dmid = np.repeat(dmid, n1-2)
dsub = np.repeat(dsub, n1-2)
supsup *= dsup
supmid *= dsup
supsub *= dsup
midsup *= dmid
midmid *= dmid
midsub *= dmid
subsup *= dsub
submid *= dsub
subsub *= dsub
tstdata = np.vstack(reversed([supsup,supmid,supsub,midsup,midmid,midsub,subsup,submid,subsub])).ravel()
B.D = utils.todia(scipy.sparse.dia_matrix(B.D))
BOG.scipy_to_cublas(B)
refdata = B.D.data[B.D.data.nonzero()].reshape((9, -1))[::-1].ravel()
BOG.cublas_to_scipy(B)
npt.assert_array_equal(tstdata, refdata)
row = np.tile(np.arange(1, n1-1), n0-2)
row += np.repeat(np.arange(1, n0-1), n1-2) * n1
row = np.tile(row, 9)
col = row.copy()
offsets = np.array([-n1-1, -n1, -n1+1, -1, 0, 1, n1-1, n1, n1+1])
col += np.repeat(offsets, dlen)
tstcoo = scipy.sparse.coo_matrix((tstdata, (row, col)), shape=2*[n0*n1])
# fp(tstcoo - B.D ,'e')
npt.assert_equal(tstcoo.todense(), refcoo.todense())