def dopoisson():
k = 1
N = 2
d = numpy.array([1,2,3])
g = lambda p: numpy.sin(numpy.dot(p, d))[:,numpy.newaxis, numpy.newaxis]
f = lambda p: -sum(d**2) * g(p)
points = uniformcubepoints(8)
Up = poissondirichlet(k,N,g,f, points)[:,numpy.newaxis]
up = g(points)
print math.sqrt(numpy.sum((Up - up)**2)/(len(points)))
def dopoissonmixed():
k = 3
N = 3
d = numpy.array([1,2,3])
u = lambda p: numpy.sin(numpy.dot(p, d))[:,numpy.newaxis, numpy.newaxis]
f = lambda p: -(sum(d**2) * u(p))
points = uniformcubepoints(8)
Up = mixedpoissondual(k,N, u, f, points).flatten()
up = u(points).flatten()
print Up.shape, up.shape
l2 = math.sqrt(numpy.sum((Up - up)**2)/(len(points)))
print l2
def dopoissonneumann():
k = 4
N = 3
d = numpy.array([1,2,3])
u = lambda p: numpy.sin(numpy.dot(p, d))[:,numpy.newaxis]
gn = lambda p, n: (numpy.cos(numpy.dot(p,d))*numpy.dot(n,d))[:,numpy.newaxis]
f = lambda p: -sum(d**2) * u(p)
points = uniformcubepoints(8)
Up = poissonneumann(k,N,gn, f, points) [:,numpy.newaxis]
up = u(points)
l2 = math.sqrt(numpy.sum((Up - up)**2)/(len(points)))
print l2
def tabulate():
kmax = 5
nmax = 5
points = uniformcubepoints(4)
up = logxminus111(points)
l2s = numpy.zeros((nmax,kmax))
for k in range(1,kmax+1):
for N in range(1,nmax+1):
if k==1 and N==1: break
print k,N
Up = laplacedirichlet(k,N, logxminus111, points)[:,numpy.newaxis]
l2s[k-1,N-1] = math.sqrt(numpy.sum((Up - up)**2)/(len(points)))
print l2s
c = mpl.contourf(pp[0], pp[1], ur.reshape(NP,NP) - u[:,0].reshape(NP,NP), fontsize=14, colors = None, cmap=mpl.get_cmap('Greys'))
mpl.colorbar(c, shrink=0.8)
# mpl.clabel(c, inline=1, fontsize = 14)
mpl.figure(facecolor='white')
c = mpl.contourf(pp[0], pp[1], p.reshape(NP,NP), fontsize=14, colors = None, cmap=mpl.get_cmap('Greys'))
mpl.colorbar(c, shrink=0.8)
# mpl.clabel(c, inline=1, fontsize = 14)
# mpl.show()
if __name__ == "__main__":
k = 4
N = 2
NP = 12
points = pu.uniformcubepoints(NP)
v = [[1,1,1]]
# v = [[0,0,0]]
meshevents = lambda m: pps.stokescubemesh(N, m)
# OT = 'obstructiontag'
# meshevents = lambda m: pps.cubeobstruction(m, OT)
mp = MeshPlotter()
meshevents(mp)
emm.figure(bgcolor=(1,1,1))
u, p = pps.stokespressure(k,meshevents,{pps.inputbdytag:pps.pfn(0), pps.outputbdytag:pps.pfn(1.0)}, points, False, N==1)
pt = points.reshape(NP,NP,NP,3).transpose((3,0,1,2))
ut = u.reshape(NP,NP,NP,3).transpose((3,0,1,2))
emm.quiver3d(pt[0],pt[1],pt[2], ut[0],ut[1],ut[2], opacity = 0.4)
