# import a prebuilt RBF function from rbf.basis import phs3 # create 5 observation points x = np.linspace(-np.pi,np.pi,5)[:,None] # find the function value at the observation points u = np.sin(x[:,0]) # create interpolation points xitp = np.linspace(-4.0,4.0,1000)[:,None] # create the coefficient matrix, where each observation point point is # an RBF center and each RBF is evaluated at the observation points A = phs3(x,x) # find the coefficients for each RBF coeff = np.linalg.solve(A,u) # create the interpolation matrix which evaluates each of the 5 RBFs # at the interpolation points Aitp = rbf.basis.phs3(xitp,x) # evaluate the interpolant at the interpolation points uitp1 = Aitp.dot(coeff) ### METHOD 2, use RBFInterpolant ### from rbf.interpolate import RBFInterpolant # This command will produce an identical interpolant to the one
[0.052,0.629],[0.373,0.63 ],[0.479,0.953],[0.49 ,0.966],
[0.503,0.952],[0.611,0.629],[0.934,0.628],[0.95 ,0.622],
[0.941,0.607],[0.692,0.397],[0.781,0.072],[0.779,0.055]])
smp = np.array([[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],
[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],
[16,17],[17,18],[18,19],[19,0]])
N = 500 # total number of nodes
nodes,smpid = menodes(N,vert,smp) # generate nodes
boundary, = (smpid>=0).nonzero() # identify boundary nodes
interior, = (smpid==-1).nonzero() # identify interior nodes
# create left-hand-side matrix and right-hand-side vector
A = np.empty((N,N))
A[interior] = phs3(nodes[interior],nodes,diff=[2,0])
A[interior] += phs3(nodes[interior],nodes,diff=[0,2])
A[boundary,:] = phs3(nodes[boundary],nodes)
d = np.empty(N)
d[interior] = -100.0
d[boundary] = 0.0
# Solve the PDE
coeff = np.linalg.solve(A,d) # solve for the RBF coefficients
itp = menodes(10000,vert,smp)[0] # interpolation points
soln = phs3(itp,nodes).dot(coeff) # evaluate at the interp points
fig,ax = plt.subplots()
p = ax.scatter(itp[:,0],itp[:,1],s=20,c=soln,edgecolor='none')
ax.set_aspect('equal')
ax.plot(nodes[:,0],nodes[:,1],'ko',markersize=4)
[0.052,0.629],[0.373,0.63 ],[0.479,0.953],[0.49 ,0.966],
[0.503,0.952],[0.611,0.629],[0.934,0.628],[0.95 ,0.622],
[0.941,0.607],[0.692,0.397],[0.781,0.072],[0.779,0.055]])
smp = np.array([[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],
[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],
[16,17],[17,18],[18,19],[19,0]])
N = 500 # total number of nodes
nodes,smpid = menodes(N,vert,smp) # generate nodes
boundary, = (smpid>=0).nonzero() # identify boundary nodes
interior, = (smpid==-1).nonzero() # identify interior nodes
# create left-hand-side matrix and right-hand-side vector
A = np.empty((N,N))
A[interior] = phs3(nodes[interior],nodes,diff=[2,0])
A[interior] += phs3(nodes[interior],nodes,diff=[0,2])
A[boundary,:] = phs3(nodes[boundary],nodes)
d = np.empty(N)
d[interior] = -100.0
d[boundary] = 0.0
# Solve the PDE
coeff = np.linalg.solve(A,d) # solve for the RBF coefficients
itp = menodes(10000,vert,smp)[0] # interpolation points
soln = phs3(itp,nodes).dot(coeff) # evaluate at the interp points
fig,ax = plt.subplots()
p = ax.scatter(itp[:,0],itp[:,1],s=20,c=soln,edgecolor='none',cmap='viridis')
ax.set_aspect('equal')
ax.plot(nodes[:,0],nodes[:,1],'ko',markersize=4)
# import a prebuilt RBF function from rbf.basis import phs3 # create 5 observation points x = np.linspace(-np.pi, np.pi, 5)[:, None] # find the function value at the observation points u = np.sin(x[:, 0]) # create interpolation points xitp = np.linspace(-4.0, 4.0, 1000)[:, None] # create the coefficient matrix, where each observation point point is # an RBF center and each RBF is evaluated at the observation points A = phs3(x, x) # find the coefficients for each RBF coeff = np.linalg.solve(A, u) # create the interpolation matrix which evaluates each of the 5 RBFs # at the interpolation points Aitp = rbf.basis.phs3(xitp, x) # evaluate the interpolant at the interpolation points uitp1 = Aitp.dot(coeff) ### METHOD 2, use RBFInterpolant ### from rbf.interpolate import RBFInterpolant # This command will produce an identical interpolant to the one
