nodes[i, :] = [0., 0., -i * L / (nnz - 1)]
z_[i] = -i * L / (nnz - 1)
# from constant to per segment
kr_ = [kr] * 2 * (nnz - 1)
kz_ = [kz] * 2 * (nnz - 1)
a_ = [a] * 2 * (nnz - 1)
# call back function for soil potential
soil = lambda x, y, z: p_s
# calculate fluxes within the root system
Q, b = xylem_flux.linear_system(seg, nodes, a_, kr_, kz_, rho, g, soil) #
# Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0,nnz-1]), np.array([p0,pL]))
Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0]),
np.array([p0])) # dirichlet top
Q, b = xylem_flux.bc_neumann(Q, b, [nnz - 1], [0]) # neumann tip
# plt.spy(Q)
# plt.show()
start = timeit.default_timer()
x = LA.spsolve(Q, b, use_umfpack=True) # direct
stop = timeit.default_timer()
# print ("linear system solved in", stop - start, " s")
# plot results
plt.plot(list(map(toHead, x)), z_, "r*")
plt.plot(pr, za_)
plt.xlabel("Xylem pressure (cm)")
plt.ylabel("Depth (m)")
plt.show()
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g,
soil_p2)
Q, b = xylem_flux.bc_neumann(Q, b, np.array([0]),
np.array([pot_trans]))
x = LA.spsolve(Q, b) # direct
eff_trans = xylem_flux.axial_flux0(
x, seg, nodes, kz, rho, g) # verify that eff_trans == pot_trans
print(
"using neumann ( Effective Transpiration = " + str(eff_trans) +
" m^3 s^-1)", "top potential", x[0])
if dirichlet or (x[0] < top_pot):
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g,
soil_p2)
dirichlet = True
Q, b = xylem_flux.bc_dirichlet(Q, b, np.array([0]),
np.array([top_pot]))
x = LA.spsolve(Q, b) # direct
eff_trans = xylem_flux.axial_flux0(x, seg, nodes, kz, rho, g)
dirichlet = eff_trans < pot_trans
print("using dirichlet ( Effective Transpiration = " + str(eff_trans) +
" m^3 s^-1)")
radial_flux = xylem_flux.radial_flux(
x, seg, nodes, radius, kr, soil_p2) # used to calculate the sink term
#
# 4. Sink term
#
t4 = timer.time()
sink = np.zeros(inf.n)
#
# create linear system
#
Q, b = xylem_flux.linear_system(seg, nodes, radius, kr, kz, rho, g, soil_p)
#
# apply BC
#
n0 = np.array([0]) # node indices
seg0 = np.array([0]) # segment indices
potT = np.array([-5.79e-4]) # potential Transpiration
topP = np.array([-1500]) # top potential (J/kg)
# Q, b = xylem_flux.bc_neumann(Q, b, seg0, potT, seg, nodes) # Neumann
Q, b = xylem_flux.bc_dirichlet(Q, b, n0, topP) # Dirichlet
#
# solve LS
#
t = time.time()
print("solve")
# x0 = d*np.ones(Q.shape[0]) # empirically proofen to be the best
# x, info = LA.cg(Q,b,x0=x0, tol=1e-12) # tested with CG, CGS, GMRES, BICG. CG by far the best
x = LA.spsolve(Q, b) # direct
print("fin")
# print("CG: " + str(time.time()-t) +" sec" )
print("spsolve: " + str(time.time() - t) + " sec")
#
# output