# Solve poisson's equation by `scipy.sparse.linalg.splu`
# and `scipy.sparse.linagl.spsolve`.
A = poisson.getA().toarray()
b = poisson.getRHS()
print(f"A:\n{A}")
print(f"b:\n{b}")
lu = sp.linalg.splu(A)
x_lu = lu.solve(b)
x = sp.linalg.spsolve(A, b)
if not np.all(np.isclose(x_lu, x)):
raise ArithmeticError
# Show result
mesh.plot_image(x)
plt.title("Solved by `scipy.sparse.linalg.spsolve`")
print(f"x:\n{x}")
# Solve Poisson's equation using Quantum Annealing (Direct QPU).
# Construct a DirectSolver instance
solver = bl_lstsq.DirectSolver(A, b)
# Set sampler and parameters for DirectSolver.solve method
sampler = EmbeddingComposite(
DWaveSampler(solver={'qpu': True},
postprocess="sampling")) # use postprocess
# sampler = SimulatedAnnealingSampler()
sampling_params = {
"num_reads": 1000,
"chain_strength": 100,
norm_bins = np.arange(num_discrete_value) + 0.5
norm_bins = np.insert(norm_bins, 0, np.min(norm_bins) - 1.0)
cbar_ticklabels = np.array([low_param_value, high_param_value])
norm = mpl.colors.BoundaryNorm(norm_bins, num_discrete_value, clip=True)
formatter = mpl.ticker.FuncFormatter(lambda x, pos: cbar_ticklabels[norm(x)])
cbar_ticks = norm_bins[:-1] + (norm_bins[1:] - norm_bins[:-1]) / 2
models = [bin_model_params, result["bin_model_params"]]
titles = ["Synthetic Resistivity Model", "Predicted Resistivity Model"]
for i in range(2):
fig = plt.figure(figsize=(9, 4))
ax1 = fig.add_axes([0.14, 0.17, 0.68, 0.7])
im = mesh.plot_image(models[i],
ax=ax1,
grid=False,
pcolor_opts={
"norm": norm,
"cmap": cmap
})
ax1.set_title(titles[i])
ax1.set_xlabel("x (m)")
ax1.set_ylabel("z (m)")
ax2 = fig.add_axes([0.84, 0.17, 0.03, 0.7])
cbar = fig.colorbar(im[0], cax=ax2, format=formatter, ticks=cbar_ticks)
cbar.set_label(r"$\rho$ ($\Omega$*m)", rotation=270, labelpad=15, size=12)
mpl.rcdefaults()
# Compare predicted and observed responses
pred_resp = dwinv.utils.fwd_modeling(fwd_model, result["bin_model_params"],
(low_param_value, high_param_value))
with np.printoptions(precision=8, suppress=True):