numPts = input("Enter: ")
print "\nWhich PDE parameter? (e.g. 1.0)"
pdeParam = input("Enter: ")
print ""
exprTrueSol = sympy.exp(sympy.Symbol('x')) + (1 - sympy.Symbol('x'))
trueSol = sympy.lambdify(
(sympy.Symbol('x'), sympy.Symbol('y'), sympy.Symbol('z')),
exprTrueSol,
modules=['numpy'])
secLapBelTps = partial(secLapBelTps4Kernel, pDeParam=pdeParam)
lapBelTps = partial(lapBelTps4Kernel, pDeParam=pdeParam)
ptSet = getPtsFibonacciSphere(numPts)
collMtrx = buildSpecialSymCollMtrx(ptSet, ptSet, secLapBelTps, pdeParam)
exprRhs = computeLapBelOp(exprTrueSol, pdeParam)
rhsFct = sympy.lambdify(
(sympy.Symbol('x'), sympy.Symbol('y'), sympy.Symbol('z')),
exprRhs,
modules=['numpy'])
rhs = np.zeros(numPts + 16)
for idx in range(numPts):
rhs[idx] = rhsFct(ptSet[idx, 0], ptSet[idx, 1], ptSet[idx, 2])
lagCoeff = np.linalg.solve(collMtrx, rhs)
numEvalPts = 250
evalPtSet = getPtsFibonacciSphere(numEvalPts, 1)
from miscFcts import locLagPrecon, gmresCounter
def rhsFct(x, y, z):
return np.exp(x) * (1 - x)
print("\nHow many interpolation points? (e.g. 150)")
numPts = int(input("Enter: "))
print("\nWhich local radius? (e.g. 7.0)")
locRadius = float(input("Enter: "))
print("\nWhich GMRES tolerance? (e.g. 1e-10)")
gmresTol = float(input("Enter: "))
print("")
ptSet = getPtsFibonacciSphere(numPts)
kdTree = scipy.spatial.KDTree(ptSet)
kernelMtrx = buildKernelMtrxCond(ptSet, ptSet, tpsKernelSphere)
preconMtrx, numNeighb = locLagPrecon(ptSet, kdTree, locRadius,
buildKernelMtrxCond, tpsKernelSphere, 4)
conditionedMtrx = kernelMtrx.dot(preconMtrx)
conditionedMtrx = conditionedMtrx[0:numPts, 0:numPts]
print('Number of neighbors for localisation:')
print('\tn =', numNeighb)
print('\nEffect of preconditioner:')
print('\tcond(K) =', np.linalg.cond(kernelMtrx))
print('\tcond(KP) =', np.linalg.cond(conditionedMtrx))
from miscFcts import locLagPrecon, gmresCounter
def rhsFct(x, y, z):
return np.exp(x) * (1 - x)
print("\nHow many interpolation points? (e.g. 150)")
numPts = int(input("Enter: "))
print("\nWhich local radius? (e.g. 7.0)")
locRadius = float(input("Enter: "))
print("\nWhich GMRES tolerance? (e.g. 1e-10)")
gmresTol = float(input("Enter: "))
print("")
ptSet = getPtsFibonacciSphere(samples=numPts)
np.savetxt("ptset.txt", ptSet)
kdTree = scipy.spatial.KDTree(ptSet)
kernelMtrx = buildKernelMtrxCond(ptSet, ptSet, tpsKernelSphere)
np.savetxt("kernelMtrxCond.txt", kernelMtrx)
preconMtrx, numNeighb = locLagPrecon(ptSet, kdTree, locRadius,
buildKernelMtrxCond, tpsKernelSphere, 4)
pre = np.identity(numPts + 4)
pre[:, 0:numPts] = preconMtrx
np.savetxt("preconditioner.txt", pre)
conditionedMtrx = kernelMtrx.dot(pre)
conditionedMtrx = conditionedMtrx[0:numPts, 0:numPts]
np.savetxt("conditionedMtrx.txt", conditionedMtrx)