def test_get_banded():
A = np.array([[2.0, 3.0],
[5.0, 7.0]])
B = get_banded(A, 1, 2)
B_ref = np.array([
[0.0, 3.0],
[2.0, 7.0],
[5.0, 0.0]
])
assert np.allclose(B, B_ref)
with pytest.raises(ValueError):
get_banded(np.array([[1], [2]]), 1, 1)
def test_get_banded_F_padded():
A = np.array([[2.0, 3.0],
[5.0, 7.0]])
B = get_banded(A, 1, 2, order='F', padded=True)
B_ref = np.array([
[0.0, 0.0],
[0.0, 3.0],
[2.0, 7.0],
[5.0, 0.0]
])
assert np.allclose(B, B_ref)
def test_ReactionDiffusion__only_1_species_diffusion_3bins(log):
# Diffusion without reaction
# 3 bins
t0 = 3.0
logy, logt = log
D = 17.0
y0 = np.array([23.0, 27.0, 37.0])
N = 3
x = [5.0, 7.0, 13.0, 15.0]
xc = [4.0, 6.0, 10.0, 14.0, 16.0]
nstencil = 3
rd = ReactionDiffusion(1, [], [], [], D=[D], x=x, N=N, logy=logy,
logt=logt, lrefl=False, rrefl=False,
nstencil=nstencil)
assert np.allclose(rd.xc, xc)
w = [1/16, -1/8, 1/16] # finite diff. weights for 2nd order deriv
for i in range(N):
assert np.allclose(rd.D_weight[i*nstencil:(i+1)*nstencil], w)
J = D*(w[0]*y0[0] + w[1]*y0[1] + w[2]*y0[2])
fref = np.array([J, J, J])
if logy:
fref /= y0
if logt:
fref *= t0
if logy:
jref = D*np.array([ # jref[i, k] = ...
[w[k]*y0[k]/y0[i] if k != i else -1/y0[k]*sum([
w[j]*y0[j] if j != k else 0 for j in range(3)
]) for k in range(3)] for i in range(3)
])
jref[0, 2] = 0.0 # dense_jac_rmaj only computes banded approx.
jref[2, 0] = 0.0 # same as above.
else:
jref = D*np.array([[w[k] if abs(k-i) < 2 else 0.0 for
k in range(3)] for i in range(3)])
if logt:
jref *= t0
y = rd.logb(y0) if logy else y0
t = rd.logb(t0) if logt else t0
_test_f_and_dense_jac_rmaj(rd, t, y, fref, jref)
jout_bnd = np.zeros((4, 3), order='F')
rd.banded_jac_cmaj(t, y, jout_bnd)
jref_bnd = get_banded(jref, 1, 3)
assert np.allclose(jout_bnd[1:, :], jref_bnd)
def test_ReactionDiffusion__3_reactions_4_species_5_bins_k_factor(
geom_refl):
# UNSUPPORTED since `bin_k_factor` was replaced with `fields`
# if a real world scenario need per bin modulation of binary
# reactions and the functionality is reintroduced, this test
# is useful
from sympy import finite_diff_weights
geom, refl = geom_refl
lrefl, rrefl = refl
# r[0]: A + B -> C
# r[1]: D + C -> D + A + B
# r[2]: B + B -> D
# r[0] r[1] r[2]
stoich_active = [[0, 1], [2, 3], [1, 1]]
stoich_prod = [[2], [0, 1, 3], [3]]
n = 4
N = 5
D = np.array([2.6, 3.7, 5.11, 7.13])*213
y0 = np.array([
2.5, 1.2, 3.2, 4.3,
2.7, 0.8, 1.6, 2.4,
3.1, 0.3, 1.5, 1.8,
3.3, 0.6, 1.6, 1.4,
3.6, 0.9, 1.7, 1.2
]).reshape((5, 4))
x = np.array([11.0, 13.3, 17.0, 23.2, 29.8, 37.2])
xc_ = x[:-1]+np.diff(x)/2
xc_ = [x[0]-(xc_[0]-x[0])]+list(xc_)+[x[-1]+(x[-1]-xc_[-1])]
assert len(xc_) == 7
k = [31.0, 37.0, 41.0]
# (r[0], r[1]) modulations over bins
modulated_rxns = [0, 1]
modulation = [[i+3 for i in range(N)],
[i+4 for i in range(N)]]
nstencil = 3
nsidep = 1
rd = ReactionDiffusion(
4, stoich_active, stoich_prod, k, N, D=D, x=x,
geom=geom, nstencil=nstencil, lrefl=lrefl,
rrefl=rrefl, modulated_rxns=modulated_rxns,
modulation=modulation)
assert np.allclose(xc_, rd.xc)
lb = stencil_pxci_lbounds(nstencil, N, lrefl, rrefl)
if lrefl:
if rrefl:
assert lb == [0, 1, 2, 3, 4]
else:
assert lb == [0, 1, 2, 3, 3]
else:
if rrefl:
assert lb == [1, 1, 2, 3, 4]
else:
assert lb == [1, 1, 2, 3, 3]
assert lb == list(map(rd._stencil_bi_lbound, range(N)))
pxci2bi = pxci_to_bi(nstencil, N)
assert pxci2bi == [0, 0, 1, 2, 3, 4, 4]
assert pxci2bi == list(map(rd._xc_bi_map, range(N+2)))
D_weight = []
for bi in range(N):
local_x_serie = xc_[lb[bi]:lb[bi]+nstencil]
local_x_around = xc_[nsidep+bi]
w = finite_diff_weights(
2, local_x_serie, x0=local_x_around
)
D_weight.append(w[-1][-1])
if geom == 'f':
pass
elif geom == 'c':
for wi in range(nstencil):
# first order derivative
D_weight[bi][wi] += w[-2][-1][wi]*1/local_x_around
elif geom == 's':
for wi in range(nstencil):
# first order derivative
D_weight[bi][wi] += w[-2][-1][wi]*2/local_x_around
else:
raise RuntimeError
assert np.allclose(rd.D_weight, np.array(D_weight, dtype=np.float64).flatten())
def cflux(si, bi):
f = 0.0
for k in range(nstencil):
f += rd.D_weight[bi*nstencil+k]*y0[pxci2bi[lb[bi]+k], si]
return D[si]*f
r = [
[k[0]*modulation[0][bi]*y0[bi, 0]*y0[bi, 1] for
bi in range(N)],
[k[1]*modulation[1][bi]*y0[bi, 3]*y0[bi, 2] for
bi in range(N)],
[k[2]*y0[bi, 1]**2 for bi in range(N)],
]
fref = np.array([[
-r[0][bi] + r[1][bi] + cflux(0, bi),
-r[0][bi] + r[1][bi] - 2*r[2][bi] + cflux(1, bi),
r[0][bi] - r[1][bi] + cflux(2, bi),
r[2][bi] + cflux(3, bi)
] for bi in range(N)]).flatten()
# Now let's check that the Jacobian is correctly computed.
def dfdC(bi, lri, lci):
v = 0.0
for ri in range(len(stoich_active)):
totl = (stoich_prod[ri].count(lri) -
stoich_active[ri].count(lri))
if totl == 0:
continue
actv = stoich_active[ri].count(lci)
if actv == 0:
continue
v += actv*totl*r[ri][bi]/y0[bi, lci]
return v
def jac_elem(ri, ci):
bri, bci = ri // n, ci // n
lri, lci = ri % n, ci % n
elem = 0.0
def _diffusion():
_elem = 0.0
for k in range(nstencil):
if pxci2bi[lb[bri]+k] == bci:
_elem += D[lri]*rd.D_weight[bri*nstencil+k]
return _elem
if bri == bci:
# on block diagonal
elem += dfdC(bri, lri, lci)
if lri == lci:
elem += _diffusion()
elif bri == bci - 1:
if lri == lci:
elem = _diffusion()
elif bri == bci + 1:
if lri == lci:
elem = _diffusion()
return elem
jref = np.zeros((n*N, n*N), order='C')
for ri, ci in np.ndindex(n*N, n*N):
jref[ri, ci] = jac_elem(ri, ci)
# Compare to what is calculated using our C++ callback
_test_f_and_dense_jac_rmaj(rd, 0, y0.flatten(), fref, jref)
jout_cmaj = np.zeros((n*N, n*N), order='F')
rd.dense_jac_cmaj(0.0, y0.flatten(), jout_cmaj)
assert np.allclose(jout_cmaj, jref)
ref_banded_j = get_banded(jref, n, N)
ref_banded_j_symbolic = rd.alloc_jout(order='F', pad=0)
symrd = SymRD.from_rd(rd)
symrd.banded_jac(0.0, y0.flatten(), ref_banded_j_symbolic)
assert np.allclose(ref_banded_j_symbolic, ref_banded_j)
jout_bnd_packed_cmaj = np.zeros((3*n+1, n*N), order='F')
rd.banded_jac_cmaj(0.0, y0.flatten(), jout_bnd_packed_cmaj)
if os.environ.get('plot_tests', False):
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from chemreac.util.plotting import coloured_spy
fig = plt.figure()
ax = fig.add_subplot(3, 1, 1)
coloured_spy(ref_banded_j, ax=ax)
plt.title('ref_banded_j')
ax = fig.add_subplot(3, 1, 2)
coloured_spy(jout_bnd_packed_cmaj[n:, :], ax=ax)
plt.title('jout_bnd_packed_cmaj')
ax = fig.add_subplot(3, 1, 3)
coloured_spy(ref_banded_j-jout_bnd_packed_cmaj[n:, :], ax=ax)
plt.title('diff')
plt.savefig(__file__+'.png')
assert np.allclose(jout_bnd_packed_cmaj[n:, :], ref_banded_j)
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)
def test_get_jac_row_from_banded():
n = 3
A = np.arange(n*n).reshape((n, n))
B = get_banded(A, n, 1)
assert np.allclose(get_jac_row_from_banded(B, [0], n), A[0, :])
assert np.allclose(get_jac_row_from_banded(B, [1, 2], n), A[1:, :])