def test_n_jac_diags(n_jac_diags):
N, n, nstencil = 10, 1, 7
rd = ReactionDiffusion(n, [], [], [], N=N, nstencil=nstencil,
n_jac_diags=n_jac_diags, D=[9])
assert np.allclose(rd.xcenters,
[.05, .15, .25, .35, .45, .55, .65, .75, .85, .95])
y0 = np.ones(N)
# Dense
jref_cdns = np.zeros((n*N, n*N), order='F')
jout_cdns = np.zeros((n*N, n*N), order='F')
sm = SymRD.from_rd(rd)
sm.dense_jac(0.0, y0.flatten(), jref_cdns)
rd.dense_jac_cmaj(0.0, y0.flatten(), jout_cdns)
assert np.allclose(jout_cdns, jref_cdns)
# Banded
jref_cbnd = rd.alloc_jout(order='F', pad=0)
jout_cbnd = rd.alloc_jout(order='F')
sm.banded_jac(0.0, y0.flatten(), jref_cbnd)
rd.banded_jac_cmaj(0.0, y0.flatten(), jout_cbnd)
assert np.allclose(jout_cbnd[rd.n*rd.n_jac_diags:, :], jref_cbnd)
# Compressed
jref_cmprs = rd.alloc_jout_compressed()
jout_cmprs = rd.alloc_jout_compressed()
sm.compressed_jac(0.0, y0.flatten(), jref_cmprs)
rd.compressed_jac_cmaj(0.0, y0.flatten(), jout_cmprs)
assert np.allclose(jout_cmprs, jref_cmprs)
def test_ReactionDiffusion__only_1_species_diffusion_7bins(log):
# Diffusion without reaction
N = 7
nstencil = 5
nsidep = (nstencil-1)//2
t0 = 3.0
logy, logt = log
D = 2.0
y0 = np.array([12, 8, 11, 5, 7, 4, 9], dtype=np.float64)
x = np.array([3, 5, 13, 17, 23, 25, 35, 37], dtype=np.float64)
rd = ReactionDiffusion(1, [], [], [], D=[D], x=x,
logy=logy, logt=logt, nstencil=nstencil,
lrefl=False, rrefl=False)
weights = [
[951/8800, -716/2475, 100/297, -75/352, 311/5400],
[321/8800, -161/2475, 7/297, 3/352, -19/5400],
[-39/8800, 109/2475, -127/1485, 87/1760, -19/5400],
[-2/693, 38/675, -129/1100, 7/108, -1/1050],
[0, 9/160, -7/72, 2/45, -1/288],
[-8/1575, 9/400, 0, -19/450, 25/1008],
[16/315, -9/32, 31/72, -13/45, 179/2016]
]
assert np.allclose(rd.D_weight, np.array(weights).flatten())
lb = stencil_pxci_lbounds(nstencil, N)
yi = pxci_to_bi(nstencil, N)
fref = np.array([sum([D*weights[i][j]*y0[yi[j+lb[i]]] for j
in range(nstencil)]) for i in range(N)])
if logy:
fref /= y0
if logt:
fref *= t0
jref = np.zeros((N, N))
for i in range(N):
for j in range(max(0, i-1), min(N, i+2)):
if logy:
if j == i+1 or j == i-1:
for k in range(nstencil):
if yi[k+lb[i]] == j:
jref[i, j] += D*weights[i][k]*y0[j]/y0[i]
else: # j == i
assert i == j
for k in range(nstencil):
cyi = yi[k+lb[i]]
if i == cyi:
continue
jref[i, i] -= D*weights[i][k]*y0[cyi]/y0[i]
else:
if i-1 <= j and j <= i+1:
jref[i, j] = D*weights[i][j-lb[i]+nsidep]
if logt:
jref *= t0
t = rd.logb(t0) if logt else t0
y = rd.logb(y0) if logy else y0
_test_f_and_dense_jac_rmaj(rd, t, y, fref, jref)
jout_bnd = np.zeros((4, N), order='F')
rd.banded_jac_cmaj(t, y, jout_bnd)
jref_bnd = get_banded(jref, 1, N)
assert np.allclose(jout_bnd[1:, :], jref_bnd)
# compressed_jac_cmaj actually use all diagonals
rd = ReactionDiffusion(1, [], [], [], D=[D], x=x,
logy=logy, logt=logt, nstencil=nstencil,
lrefl=False, rrefl=False, n_jac_diags=2)
jout_cmprs = rd.alloc_jout_compressed()
rd.compressed_jac_cmaj(t, y, jout_cmprs)
from block_diag_ilu import Compressed_from_dense
jref2 = np.zeros((N, N))
for i in range(N):
for j in range(max(0, i-2), min(N, i+3)):
if logy:
if i-2 <= j <= i+2:
if i == j:
for k in range(nstencil):
cyi = yi[k+lb[i]]
if i == cyi:
continue
jref2[i, i] -= D*weights[i][k]*y0[cyi]/y0[i]
else:
for k in range(nstencil):
if yi[k+lb[i]] == j:
jref2[i, j] += D*weights[i][k]*y0[j]/y0[i]
else:
if i-2 <= j <= i+2:
jref2[i, j] = D*weights[i][j-lb[i]+nsidep]
if logt:
jref2 *= t0
jref_cmprs = Compressed_from_dense(jref2, N, 1, nsidep).data
assert np.allclose(jout_cmprs, jref_cmprs)
