def test_non_constant(Nx, sparse, ordinal):
x = de.Chebyshev('x', Nx, interval=(0, 5))
d = de.Domain([
x,
])
prob = de.EVP(d, ['y', 'yx', 'yxx', 'yxxx'], 'sigma')
prob.add_equation(
"dx(yxxx) -0.02*x*x*yxx -0.04*x*yx + (0.0001*x*x*x*x - 0.02)*y - sigma*y = 0"
)
prob.add_equation("dx(yxx) - yxxx = 0")
prob.add_equation("dx(yx) - yxx = 0")
prob.add_equation("dx(y) - yx = 0")
prob.add_bc("left(y) = 0")
prob.add_bc("right(y) = 0")
prob.add_bc("left(yx) = 0")
prob.add_bc("right(yx) = 0")
EP = Eigenproblem(prob, use_ordinal=ordinal)
EP.solve(sparse=sparse)
indx = EP.evalues_good.argsort()
five_evals = EP.evalues_good[indx][0:5]
print("First five good eigenvalues are: ")
print(five_evals)
print(five_evals[-1])
reference = np.array([
0.86690250239956 + 0j, 6.35768644786998 + 0j, 23.99274694653769 + 0j,
64.97869559403952 + 0j, 144.2841396045761 + 0j
])
assert np.allclose(reference, five_evals, rtol=1e-4)
c01 = d.new_field(name='c01')
xx = x.grid()
# this is not a reasonable way to do this; it's just to test non-constant coefficients
c3['g'] = -0.02 * xx**2
c1['g'] = -0.04 * xx
c01['g'] = 0.0001 * xx**4
prob.parameters['c3'] = c3
prob.parameters['c1'] = c1
prob.parameters['c01'] = c01
prob.parameters['c02'] = -0.02
prob.add_equation("dx(yxxx) + c3*yxx + c1*yx + (c01 + c02)*y - sigma*y = 0")
prob.add_equation("dx(yxx) - yxxx = 0")
prob.add_equation("dx(yx) - yxx = 0")
prob.add_equation("dx(y) - yx = 0")
prob.add_bc("left(y) = 0")
prob.add_bc("right(y) = 0")
prob.add_bc("left(yx) = 0")
prob.add_bc("right(yx) = 0")
EP = Eigenproblem(prob, sparse=False)
EP.solve()
EP.reject_spurious()
indx = EP.evalues_good.argsort()
print("First five good eigenvalues are: ")
print(EP.evalues_good[indx][0:5])
logger.info("grid generation time: {:10.5f} sec".format(end - start))
crit = cf.crit_finder(polish_roots=False)
if comm.rank == 0:
logger.info("critical Rm = {:10.5f}, Q = {:10.5f}".format(
crit[1], crit[0]))
# create plot of critical parameter space
pax, cax = cf.plot_crit()
fig = pax.figure
# add an interpolated critical line
x_lim = cf.parameter_grids[0][0, np.isfinite(cf.roots)]
x_hires = np.linspace(x_lim[0], x_lim[-1], 100)
pax.plot(x_hires, cf.root_fn(x_hires), color='k')
fig.savefig('{}.png'.format(file_name), dpi=300)
# plot the spectrum for the critical mode
logger.info("solving dense eigenvalue problem for critical parameters")
EP.solve(parameters={"Q": crit[0], "Rm": crit[1]}, sparse=False)
ax = EP.plot_spectrum()
# mark critical mode
eps = 1e-2
mask = np.abs(EP.evalues.real) < eps
ax.scatter(EP.evalues[mask].real, EP.evalues[mask].imag, c='red')
ax.figure.savefig('mri_critical_spectrum.png', dpi=300)
# plot drift ratio for critical mode
ax = EP.plot_drift_ratios()
ax.figure.savefig('mri_critical_drift_ratios.png', dpi=300)