'''
If you run this module as main, you'll get some plots.
'''
from scipy.special import kv as kv
from scipy.special import kn as kn
from matplotlib import pyplot as plt
import helper
import container
x = np.linspace( 0.0, 0.1, num=500, endpoint=True )
d = 2
if d == 2:
cot = container.Container( "square",
helper.get_mesh( "square", 100 ),
25,
gamma = 1 )
kappa = cot.kappa
factor = cot.factor
Phi1x = 1. / 2 / math.pi * kn( 0, kappa*x )
dPhi1x = -1. / 2 / math.pi * kappa * kn( 1, kappa*x )
Phi2x = cot.factor * x * kappa * kn( 1, kappa*x )
dPhi2x = -cot.factor * kappa * kappa*x * kn( 0, kappa*x )
else:
cot = container.Container( "cube",
helper.get_mesh( "cube", 99 ),
121,
gamma = 1 )
kappa = cot.kappa
tmp = -kappa * factor * kappara * (k0 * k0 + k1 * k1) / ra
return (np.sum(tmp * x0) / n ** 2, np.sum(tmp * x1) / n ** 2)
def denom2D(x0, x1, kappa, n, factor=1):
ra = np.sqrt(x0 * x0 + x1 * x1) + 1e-13
kappara = kappa * ra
tmp = factor * kappara * sp.kv(1.0, kappara) * sp.kn(0, kappara)
return 2.0 * np.sum(tmp) / n ** 2
n = 17 * 13 * 17
x0 = np.linspace(0, 1.0, n, endpoint=False)
x1 = np.linspace(-0.5, 0.5, n, endpoint=False)
X0, X1 = np.meshgrid(x0, x1)
mesh_obj = helper.get_mesh("square", 50)
alpha = 15.0
cot = container.Container("square", mesh_obj, alpha)
factor = cot.factor / 2.0 / math.pi
denom = denom2D(X0, X1, cot.kappa, n, factor=factor)
enum = np.array(enum2D(X0, X1, cot.kappa, n, factor=factor))
nx_beta = enum / denom
b = betas.Beta2DAdaptive(cot)
cb_beta = b(0.0, 0.5)
b = betas.Beta2D(cot)
fe_beta = b(0.0, 0.5)
b = betas.Beta2DRadial(cot)
def bdryBetas( mesh_name,
A,
quad,
normal,
dims ):
beta_file = "data/" + mesh_name + "/beta_" + quad + "_" + str(dims) + ".txt"
helper.empty_file( beta_file )
print beta_file
mesh_obj = helper.get_mesh( mesh_name, dims )
cot = container.Container( mesh_name,
mesh_obj,
dic[mesh_name].alpha,
quad = quad )
beta_obj = cot.chooseBeta()
if "adaptive" in quad:
for s in np.linspace( 0, 1, num=77, endpoint=True):
v = np.zeros( cot.dim )
v[-1] = s
if cot.dim == 3:
v[1] = .5
y = np.dot( A , v )
beta = beta_obj( y )
helper.add_point( beta_file,
s,
np.dot( beta, normal ) )
return
coo = mesh_obj.coordinates()
if "parallelogram" in mesh_name:
h = 1e-5
elif "square" in mesh_name:
h = 1e-9
else:
h = 1./dims
total_time = 0
counter = 0
for i in range(coo.shape[0]):
y = coo[i,:]
inv = np.linalg.solve( A, y )
doit = ( abs(inv[0]) < h )
if cot.dim == 3:
doit = doit and abs(inv[1]-0.5) < h
if doit:
counter = counter + 1
start = time.time()
beta = beta_obj( y )
total_time = total_time + time.time() - start
# print "Point = " + str( y )
# print "Beta = " + str(beta)
# print
helper.add_point( beta_file,
inv[-1],
np.dot( beta, normal ) )
print "Average time per eval = " + str(total_time/counter)