def test_padded_centers():
b = [0, 2, 6]
xc_ = padded_centers(b, 1)
assert np.allclose(xc_, [-1, 1, 4, 8])
b = np.arange(10, 21)
xc_ = padded_centers(b, 2)
print(xc_)
assert np.allclose(xc_, np.linspace(8.5, 21.5, 14))
def test_ReactionDiffusion__lrefl_7(log):
# Diffusion without reaction (7 bins)
from sympy import finite_diff_weights
lrefl, rrefl = True, False
N = 7
t0 = 3.0
logy, logt = log
D = 17.0
nstencil = 5
nsidep = (nstencil-1)//2
x = np.array([3, 5, 13, 17, 23, 25, 35, 37], dtype=np.float64)
y0 = np.array([12, 8, 11, 5, 7, 4, 9], dtype=np.float64)
xc_ = padded_centers(x, nsidep)
lb = stencil_pxci_lbounds(nstencil, N, lrefl=lrefl, rrefl=rrefl)
rd = ReactionDiffusion(1, [], [], [], D=[D], x=x, logy=logy,
logt=logt, N=N, nstencil=nstencil,
lrefl=lrefl, rrefl=rrefl)
y = rd.logb(y0) if logy else y0
t = rd.logb(t0) if logt else t0
le = nsidep if lrefl else 0
D_weight_ref = np.array([
finite_diff_weights(
2, xc_[lb[i]:lb[i]+nstencil], x0=xc_[le+i])[-1][-1]
for i in range(N)], dtype=np.float64)
assert np.allclose(rd.D_weight, D_weight_ref.flatten())
yi = pxci_to_bi(nstencil, N)
fref = D*np.array([
sum([rd.D_weight[i*nstencil+j]*y0[yi[lb[i]+j]]
for j in range(nstencil)])
for i in range(N)
])
if logy:
fref /= y0
if logt:
fref *= t0
_test_f(rd, t, y, fref)
if logy:
def cb(i, j):
if abs(i-j) > 1:
return 0 # imperfect Jacobian
elif i == j:
res = 0
for k in range(nstencil):
cyi = yi[lb[i] + k] # current y index
if cyi != i:
res -= y0[cyi]/y0[i]*rd.D_weight[i*nstencil + k]
return res
else:
res = 0
for k in range(nstencil):
cyi = yi[lb[i] + k] # current y index
if cyi == j:
res += y0[j]/y0[i]*rd.D_weight[i*nstencil + k]
return res
else:
def cb(i, j):
if abs(i-j) > 1:
return 0 # imperfect Jacobian
res = 0
for k in range(nstencil):
if yi[lb[i]+k] == j:
res += rd.D_weight[i*nstencil + k]
return res
jref = D*np.array([cb(i, j) for i, j in product(
range(N), range(N))]).reshape(N, N)
if logt:
jref *= t0
_test_dense_jac_rmaj(rd, t, y, jref)
