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_f(rd, t, y, fref=None):
fout = rd.alloc_fout()
rd.f(t, np.asarray(y, dtype=np.float64), fout)
if fref is None:
fref = fout
else:
assert np.allclose(fout, fref)
if isinstance(rd, SymRD):
return
_test_f(SymRD.from_rd(rd), t, y, fref)
def test_SymRD():
rd = SymRD(2, [[0]], [[1]], k=[5.0])
fout = rd.alloc_fout()
rd.f(0, [7, 3], fout)
assert np.allclose(fout, [-5*7, 5*7])
jout = rd.alloc_jout(banded=False)
rd.dense_jac_rmaj(0, [7, 3], jout)
assert np.allclose(jout, [[-5.0, 0.0], [5.0, 0.0]])
def _test_dense_jac_rmaj(rd, t, y, jref=None):
jout = rd.alloc_jout(banded=False, order='C')
rd.dense_jac_rmaj(t, np.asarray(y, dtype=np.float64), jout)
atol = 2e-13
rtol = 2e-13
if jref is None:
jref = jout
else:
# Not perfect Jacobian
# only nearest neighbour
# assert np.allclose(jout, jref)
# ...hence:
for ri in range(rd.ny):
for ci in range(max(0, ri-rd.n), min(rd.ny, ri+rd.n+1)):
out, ref = jout[ri, ci], jref[ri, ci]
assert abs(out - ref) < atol + rtol*abs(ref)
if isinstance(rd, SymRD):
return
_test_dense_jac_rmaj(SymRD.from_rd(rd), t, y, jref)
def integrate_rd(tend=1e2, A0=1.0, B0=0.0, C0=0.0, k1=0.04, k2=1e4, k3=3e7,
t0=1e2, nt=100, N=1, nstencil=3, logt=False, logy=False,
plot=False, savefig='None', verbose=False, dump_expr='False',
use_chempy=False, D=2e-3):
if N == 1:
init_conc = (A0, B0, C0)
else:
init_conc = np.tile((A0, B0, C0), (N, 1))
init_conc /= np.linspace(1, 2, N).reshape((N, 1))**.5
rsys = ReactionSystem(get_reactions((k1, k2, k3)), 'ABC')
if verbose:
print([str(_) for _ in rsys.rxns])
if use_chempy:
from chempy.kinetics.ode import get_odesys
odesys = get_odesys(rsys, include_params=True)
if N != 1:
raise ValueError("ChemPy does not support diffusion")
odesys.integrate(np.logspace(log10(t0), log10(tend)), init_conc)
if plot:
odesys.plot_result(xscale='log', yscale='log')
result = None
else:
rd = ReactionDiffusion.from_ReactionSystem(
rsys, N=N, nstencil=1 if N == 1 else nstencil, logt=logt,
logy=logy, D=[D/2, D/3, D/5])
if dump_expr.lower() not in ('false', '0'):
from chemreac.symbolic import SymRD
import sympy as sp
cb = {'latex': sp.latex,
'ccode': sp.ccode}.get(dump_expr.lower(), str)
srd = SymRD.from_rd(rd, k=sp.symbols('k:3'))
print('dydx:')
print('\n'.join(map(cb, srd._f)))
print('jac:')
for ri, row in enumerate(srd.jacobian.tolist()):
for ci, expr in enumerate(row):
if expr == 0:
continue
print(ri, ci, cb(expr))
return None
if t0 == 0 and logt:
t0 = 1e-3*suggest_t0(rd, init_conc)
if verbose:
print("Using t0 = %12.5g" % t0)
t = np.logspace(np.log10(t0), np.log10(tend), nt)
print(t[0], t[-1])
integr = run(rd, init_conc, t)
if verbose:
import pprint
pprint.pprint(integr.info)
if plot:
if N == 1:
plot_C_vs_t(integr, xscale='log', yscale='log')
else:
import matplotlib.pyplot as plt
for idx, name in enumerate('ABC', 1):
plt.subplot(1, 3, idx)
rgb = [.5, .5, .5]
rgb[idx-1] = 1
plot_faded_time(integr, name, rgb=rgb, log_color=True)
result = integr
if plot:
save_and_or_show_plot(savefig=savefig)
return result
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)