def refine_validate(sigma=5, beta=1, b=0, t0=0.5, h=0.1, tau=pow(0.1, 2) / 2):
grid1 = twoddir(h=(tau, h), rx=((0, 0.2), (-4, 4)))
grid1.set_active_int_plus_top()
grid1.set_bc(hom.barenblatt(grid1, t0, sigma))
soln1 = diffusion(grid1, b, beta, sigma)
soln1.calculate()
diff1 = trivgrid(
array([[
hom._barenblatt(t0 + t, x + b * t, grid1.u.ndim - 1, sigma)
for x in grid1.x[1]
] for t in grid1.x[0]]) - soln1.g.u)
print(
'sigma: {:f}, beta: {:f}, b: {:f}, h1: {:f}, tau1: {:f}, L_2 Error: {:f}, L_inf Error: {:f}\n'
.format(sigma, beta, b, h, tau, diff1.l2_norm(), diff1.max_norm()))
grid2 = twoddir(h=(tau / 2, h / 2), rx=((0, 0.2), (-4, 4)))
grid2.set_active_int_plus_top()
grid2.set_bc(hom.barenblatt(grid2, t0, sigma))
soln2 = diffusion(grid2, b, beta, sigma)
soln2.calculate()
diff2 = trivgrid(
array([[
hom._barenblatt(t0 + t, x + b * t, grid2.u.ndim - 1, sigma)
for x in grid2.x[1]
] for t in grid2.x[0]]))
print(
'sigma: {:f}, beta: {:f}, b: {:f}, h2: {:f}, tau2: {:f}, L_2 Error: {:f}, L_inf Error: {:f}\n'
.format(sigma, beta, b, h / 2, tau / 2, diff2.l2_norm(),
diff2.max_norm()))
def test_twodir_set_xprod():
grid = uniform.twoddir((0.01, 0.1), ((0, 1), (0, 1)))
l = map(
tuple,
numpy.transpose(numpy.indices(grid.u.shape)).reshape(
(numpy.prod(grid.nx), 2)))
for i in l:
grid.u[i] = numpy.prod(grid.ind_to_x(i))
assert True
def test_twodir_set_linorder():
grid = uniform.twoddir((0.01, 0.1), ((0, 1), (0, 1)))
l = map(
tuple,
numpy.transpose(numpy.indices(grid.u.shape)).reshape(
(numpy.prod(grid.nx), 2)))
j = 0
for i in l:
grid.u[i] = j
j = j + 1
assert True
def test_ft(): gamma = 1 sigma = 2 beta = 1 b = -5 grid = twoddir((0.0005, 0.1), ((0, 0.01), (-2, 2))) grid.set_active_int_plus_top() grid.set_bc(hom.dd_xpowalpha(grid, gamma, cutoff=True)) def ffn(x, t, u, ux, uxx): return sigma * pow(u, sigma - 1) * uxx + (sigma * (sigma - 1) * pow(u, sigma - 2) + b * beta * pow(u, beta - 1)) * ux # soln = ft(grid, ffn) # soln.calculate() assert True sp2 = tr(grid, 0.1) assert True
def output_validate(dir_out,
sigma=5,
beta=1,
b=0,
t0=0.5,
h=0.1,
tau=pow(0.1, 2) / 2):
dir_with_data = path.join(dir_out, 'sigma=' + str(sigma),
'beta=' + str(beta))
if not path.isdir(dir_with_data):
os.makedirs(dir_with_data)
gridp = twoddir(h=(tau, h), rx=((0, 0.2), (-4, 4)))
gridp.set_active_int_plus_top()
gridp.set_bc(hom.barenblatt(gridp, t0, sigma))
soln = diffusion(gridp, b, beta, sigma)
soln.calculate()
grcomp = trivgrid(
array([[
hom._barenblatt(t0 + i, j + b * i, gridp.u.ndim - 1, sigma)
for j in gridp.x[1]
] for i in gridp.x[0]]))
savetxt(path.join(dir_with_data, 'xv.dat'),
gridp.x[1],
delimiter=',',
fmt='%10.5f')
savetxt(path.join(dir_with_data, 'tv.dat'),
gridp.x[0],
delimiter=',',
fmt='%10.5f')
savetxt(path.join(dir_with_data, 'u_approx.dat'),
soln.g.u,
delimiter=',',
fmt='%10.5f')
savetxt(path.join(dir_with_data, 'u_exact.dat'),
grcomp.u,
delimiter=',',
fmt='%10.5f')
savetxt(path.join(dir_with_data, 'u_diff.dat'),
grcomp.u - soln.g.u,
delimiter=',',
fmt='%10.5f')
def do_sweep(basedir, sigma, nbeta, ngamma, dx = 1e-2, dt = 4e-3):
dirWithRun = path.join(basedir, 'run'+str(sigma))
if not path.isdir(dirWithRun):
os.makedirs(dirWithRun)
b = 0.01
threshold1 = 1e-1
threshold2 = 1e-2
with open(path.join(dirWithRun, 'results.dat'), 'w') as f:
f.write('sigma,b,beta,gamma,diff_' + str(threshold1) + ',diff_' + str(threshold2) + '\n')
for beta in linspace(0,1,nbeta):
for gamma in linspace(0.9,1.8,ngamma):
grid = twoddir(h=(dt, dx), rx = [(0, 0.01), (-2, 2)])
for (j, xj) in enumerate(grid.x[1]):
grid.u[0, j] = hom._negxpowalpha(xj, gamma)
soln = diffusion(grid,b,beta,sigma)
gridout = soln.calculate()
sp2 = tr(soln.g, threshold1)
sp3 = tr(soln.g, threshold2)
f.write(str(sigma) + "," + str(b) + "," + str(beta) + "," + str(gamma) + "," + str(sp2.rex[-1] - sp2.rex[0]) + "," + str(sp3.rex[-1] - sp3.rex[0]) + "\n")
def test_twodir_barenblatt():
grid = uniform.twoddir((0.0005, 0.1), ((0, 0.01), (-2, 2)))
grid.set_active_int_plus_top()
grid.set_bc(hom.barenblatt(grid, 1, 2))
def test_twodir_xpowalpha():
grid = uniform.twoddir((0.005, 0.1), ((0, 1), (0, 1)))
grid.set_active_int_plus_top()
grid.set_bc(hom.dd_xpowalpha(grid, 1.0 / 3, cutoff=True))
assert True