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asteTest.py
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""" Generates data to show the effect of rescaling. Low density basisfunctions used. """
import pandas
import os
import logging
from rbf import *
import basisfunctions, testfunctions
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
from mpl_toolkits import mplot3d
import time
import mesh
import math
from random import randint
from scipy import spatial
from halton import *
import vtk
import matplotlib.tri as mtri
import mesh_io
from mpi4py import MPI
'''
############################################################
IMPORTANT!
1. Eigenvalue decomposition does not work with 100x100 input matrix - too large for memory
2. Difficult to run global input mesh with 100x100
############################################################
'''
my_Rank = MPI.COMM_WORLD.rank
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
print("Size and rank: ", size, rank)
useHaltonIn = 0
useHaltonOut = 0
useVTKIn = 1
useVTKOut = 1
useChebyIn = 0
useChebyOut = 0
useStructuredGrid = 0
class Mesh:
"""
A Mesh consists of:
- Points: A list of tuples of floats representing coordinates of points
- Cells: A list of tuples of ints representing mesh elements
- Pointdata: A list of floats representing data values at the respective point
"""
def __init__(self, points = None, cells = None, cell_types = None, pointdata = None):
if points is not None:
self.points = points
else:
self.points = []
if cells is not None:
assert(cell_types is not None)
self.cells = cells
self.cell_types = cell_types
else:
self.cells = []
self.cell_types = []
if pointdata is not None:
self.pointdata = pointdata
else:
self.pointdata = []
def __str__(self):
return "Mesh with {} Points and {} Cells ({} Cell Types)".format(len(self.points), len(self.cells), len(self.cell_types))
def read_mesh(filename):
points, cells, cell_types, pointdata = mesh_io.read_mesh(filename)
#print("Points: ", len(points))
#print("Point data: ", pointdata)
return Mesh(points, cells, cell_types, pointdata)
#print("Hi, I'm process: ", rank)
#print(MPI.COMM_WORLD.rank)
#if (MPI.COMM_WORLD.rank == 0):
# print("This is the master rank")
#Xtest = np.outer(np.linspace(-2, 2, 100), np.ones(100))
#Ytest = Xtest.copy().T # transpose
#Xtest, Ytest = np.meshgrid(Xtest, Ytest)
#Ztest = np.cos(Xtest ** 2 + Ytest ** 2)
#fig = plt.figure()
#ax = fig.gca(projection='3d')
#ax.set_title('Test grid')
#ax.plot_surface(Xtest, Ytest, Ztest,cmap='viridis',linewidth=0,edgecolor='black')
#plt.show()
if (useVTKIn == 1):
input_mesh_name = "Mesh/Plate/l1Data.vtk"
#input_mesh_name = "Mesh/Turbine/out-0.005.vtk"
input_mesh = read_mesh(input_mesh_name)
print("Number of input points: ", len(input_mesh.points))
nPointsInput = len(input_mesh.points)
in_mesh = np.random.random((len(input_mesh.points),2))
in_mesh_local_LOOCV_error = np.random.random((len(input_mesh.points),2))
in_mesh_global = np.random.random((len(input_mesh.points),2))
if (useVTKOut == 1):
#output_mesh_name = "Mesh/Plate/l3Data.vtk"
output_mesh_name = "Mesh/Plate/l3Data.vtk"
output_mesh = read_mesh(output_mesh_name)
print("Number of output points: ", len(output_mesh.points))
nPointsOutput = len(output_mesh.points)
out_mesh = np.random.random((len(output_mesh.points),2))
out_mesh_global = np.random.random((len(output_mesh.points),2))
out_mesh_Combined = np.random.random((len(output_mesh.points),2))
out_mesh_Split = np.random.random((len(output_mesh.points),2))
if (useHaltonIn == 1):
nPointsInput = 5000
print("Number of Halton input points: ", nPointsInput)
in_mesh = np.random.random((nPointsInput,2))
in_mesh_local_LOOCV_error = np.random.random((nPointsInput,2))
in_mesh_global = np.random.random((nPointsInput,2))
haltonPoints = halton_sequence(nPointsInput, 2)
for i in range(0,nPointsInput):
in_mesh[i,0] = haltonPoints[0][i]
in_mesh[i,1] = haltonPoints[1][i]
in_mesh_global[i,0] = haltonPoints[0][i]
in_mesh_global[i,1] = haltonPoints[1][i]
if (useHaltonOut == 1):
nPointsOutput = 6
print("Number of Halton output points: ", nPointsOutput)
out_mesh = np.random.random((nPointsOutput,2))
out_mesh_global = np.random.random((nPointsOutput,2))
out_mesh_Combined = np.random.random((nPointsOutput,2))
out_mesh_Split = np.random.random((nPointsOutput,2))
haltonPoints = halton_sequence(nPointsOutput, 2)
for i in range(0,nPointsOutput):
out_mesh[i,0] = haltonPoints[0][i]
out_mesh[i,1] = haltonPoints[1][i]
out_mesh_global[i,0] = haltonPoints[0][i]
out_mesh_global[i,1] = haltonPoints[1][i]
out_mesh_Combined[i,0] = haltonPoints[0][i]
out_mesh_Combined[i,1] = haltonPoints[1][i]
out_mesh_Split[i,0] = haltonPoints[0][i]
out_mesh_Split[i,1] = haltonPoints[1][i]
if (useChebyIn == 1):
nPointsInput = 4900
M = math.ceil(math.sqrt(nPointsInput))
in_mesh = np.random.random((nPointsInput,2))
in_mesh_local_LOOCV_error = np.random.random((nPointsInput,2))
in_mesh_global = np.random.random((nPointsInput,2))
print("Number of In Chebyshev points in x,y: ", M)
x = np.cos (np.pi * np.arange(M + 1) / M)
for i in range(0,M):
for j in range(0,M):
in_mesh[j+(i*M),0] = 0.5*(np.cos (np.pi * (j) / M))
in_mesh[j+(i*M),1] = 0.5*(np.cos (np.pi * (i) / M))
in_mesh_global[j+(i*M),0] = 0.5*(np.cos (np.pi * (j) / M))
in_mesh_global[j+(i*M),1] = 0.5*(np.cos (np.pi * (i) / M))
if (useChebyOut == 1):
nPointsOutput = 3600
N = math.ceil(math.sqrt(nPointsOutput))
out_mesh = np.random.random((nPointsOutput,2))
out_mesh_global = np.random.random((nPointsOutput,2))
out_mesh_Combined = np.random.random((nPointsOutput,2))
out_mesh_Split = np.random.random((nPointsOutput,2))
print("Number of Out Chebyshev points in x,y: ", N)
y = np.cos (np.pi * np.arange(N + 1) / N)
for i in range(0,N):
for j in range(0,N):
out_mesh[j+(i*N),0] = 0.5*(np.cos (np.pi * (j) / N))
out_mesh[j+(i*N),1] = 0.5*(np.cos (np.pi * (i) / N))
out_mesh_global[j+(i*N),0] = 0.5*(np.cos (np.pi * (j) / N))
out_mesh_global[j+(i*N),1] = 0.5*(np.cos (np.pi * (i) / N))
out_mesh_Combined[j+(i*N),0] = 0.5*(np.cos (np.pi * (j) / N))
out_mesh_Combined[j+(i*N),1] = 0.5*(np.cos (np.pi * (i) / N))
out_mesh_Split[j+(i*N),0] = 0.5*(np.cos (np.pi * (j) / N))
out_mesh_Split[j+(i*N),1] = 0.5*(np.cos (np.pi * (i) / N))
start = time.time()
######################################################
######################################################
'''
Define the parameters of in and out meshes
'''
######################################################
######################################################
#inLenTotal = 60 #now xMesh
#outLenTotal = 45 # now yMesh
xInMesh = 4
yInMesh = 4
xOutMesh = 1
yOutMesh = 1
xMin = 0
xMax = 1
yMin = 0
yMax = 1
TotalXLength = xMax - xMin
TotalYLength = yMax - yMin
alphaInX = TotalXLength/xInMesh
alphaInY = TotalYLength/yInMesh
alphaOutX = TotalXLength/xOutMesh
alphaOutY = TotalYLength/yOutMesh
InedgeLengthX = 3.0
InedgeLengthY = 3.0
OutedgeLengthX = 3.0
OutedgeLengthY = 3.0
InxMinLength = 0.0
InyMinLength = 0.0
OutxMinLength = 0.0
OutyMinLength = 0.0
#alpha = TotalXLength/inLenTotal
domainXLenghtMin = 0.0
domainXLenghtMax = 3.0
domainLength = domainXLenghtMax - domainXLenghtMin
######################################################
######################################################
'''
Define which problems to solve:
Global - Regular
Global - Rational
Local - Regular
Local - Rational
'''
regularGlobal = 1
rationalGlobal = 0
regularLocal = 0
rationalLocal = 0
######################################################
######################################################
######################################################
######################################################
'''
How many blocks in each direction to break problem into
'''
######################################################
######################################################
# Domain decomposition. Grid mesh size/domainDecompo must be integer value
xDomainDecomposition = 3
yDomainDecomposition = 3
totalLocalDomains = xDomainDecomposition*yDomainDecomposition
xStep = TotalXLength/xDomainDecomposition
yStep = TotalYLength/yDomainDecomposition
xGridStepIn = xInMesh/xDomainDecomposition
yGridStepIn = yInMesh/yDomainDecomposition
xGridStepOut = xOutMesh/xDomainDecomposition
yGridStepOut = yOutMesh/yDomainDecomposition
#inLen = int(inLenTotal/domainDecomposition)
#outLen = int(outLenTotal/domainDecomposition)
#inLen = 20
#outLen = 30
#### Even numbers only!!!!
xBoundaryExtension = 0.2
yBoundaryExtension = 0.2
#edgeLengthX = InedgeLengthX/domainDecomposition
#edgeLengthY = InedgeLengthY/domainDecomposition
xMinLength = xMin
yMinLength = yMin
globalRegularL2Error = 0
globalRationalL2Error = 0
######################################################
######################################################
######################################################
xInMesh += 1
yInMesh += 1
xOutMesh += 1
yOutMesh += 1
#in_size = np.linspace(xMinLength, edgeLengthX + xMinLength, inLenTotal)
#out_size = np.linspace(yMinLength, edgeLengthY + yMinLength, outLenTotal)
out_mesh_Combined_value = []
out_mesh_Split_value = []
inputScaling = 1.0
outputScaling = 1.0
if (useStructuredGrid == 1):
print("Total number in input mesh vertices: ", xInMesh*yInMesh)
print("Total number in output mesh vertices: ", xOutMesh*yOutMesh)
nPointsInput = xInMesh*yInMesh
nPointsOutput = xOutMesh*yOutMesh
in_mesh = np.random.random(((xInMesh*yInMesh),2))
in_mesh_global = np.random.random(((xInMesh*yInMesh),2))
in_mesh_local_LOOCV_error = np.random.random(((xInMesh*yInMesh),2))
out_mesh = np.random.random((xOutMesh*yOutMesh,2))
out_mesh_global = np.random.random((xOutMesh*yOutMesh,2))
out_mesh_Combined = np.random.random((xOutMesh*yOutMesh,2))
out_mesh_Split = np.random.random((xOutMesh*yOutMesh,2))
out_mesh_Combined_value = []
out_mesh_Split_value = []
for j in range(0,yInMesh):
for i in range(0,xInMesh):
#in_mesh[j+i*inLenTotal,0] = (InedgeLengthX/inLenTotal)*j
#in_mesh[j+i*inLenTotal,1] = (InedgeLengthY/inLenTotal)*i
in_mesh[i+j*xInMesh,0] = pow(alphaInX*i,inputScaling)
in_mesh[i+j*xInMesh,1] = pow(alphaInY*j,inputScaling)
in_mesh_global[i+j*xInMesh,0] = pow(alphaInX*i,inputScaling)
in_mesh_global[i+j*xInMesh,1] = pow(alphaInY*j,inputScaling)
#print("Original inmesh length: ", jj)
for j in range(0,yOutMesh):
for i in range(0,xOutMesh):
#out_mesh[j+i*outLenTotal,0] = (OutedgeLengthX/outLenTotal)*j + OutxMinLength
out_mesh[i+j*xOutMesh,0] = pow(alphaOutX*i,outputScaling)
out_mesh[i+j*xOutMesh,1] = pow(alphaOutY*j,outputScaling)
out_mesh_global[i+j*xOutMesh,0] = pow(alphaOutX*i,outputScaling)
out_mesh_global[i+j*xOutMesh,1] = pow(alphaOutY*j,outputScaling)
out_mesh_Combined[i+j*xOutMesh,0] = pow(alphaOutX*i,outputScaling)
out_mesh_Combined[i+j*xOutMesh,1] = pow(alphaOutY*j,outputScaling)
out_mesh_Split[i+j*xOutMesh,0] = pow(alphaOutX*i,outputScaling)
out_mesh_Split[i+j*xOutMesh,1] = pow(alphaOutY*j,outputScaling)
if (useVTKIn == 1):
for j in range(0,len(input_mesh.points)):
#if(input_mesh.points[j][2] > -10):
in_mesh[j,0] = pow(input_mesh.points[j][0] + 0.0,inputScaling)
in_mesh[j,1] = pow(input_mesh.points[j][1] + 0.0,inputScaling)
in_mesh_global[j,0] = pow(input_mesh.points[j][0] + 0.0,inputScaling)
in_mesh_global[j,1] = pow(input_mesh.points[j][1] + 0.0,inputScaling)
#else:
# in_mesh[j,0] = pow(input_mesh.points[j][0] + 0.5,inputScaling)*0.00001
# in_mesh[j,1] = pow(input_mesh.points[j][1] + 0.5,inputScaling)*0.00001
# in_mesh_global[j,0] = pow(input_mesh.points[j][0] + 0.5,inputScaling)*0.00001
# in_mesh_global[j,1] = pow(input_mesh.points[j][1] + 0.5,inputScaling)*0.00001
#print("Original inmesh length: ", jj)
if (useVTKOut == 1):
for j in range(0,len(output_mesh.points)):
#out_mesh[j+i*outLenTotal,0] = (OutedgeLengthX/outLenTotal)*j + OutxMinLength
#if(output_mesh.points[j][2] > -10):
out_mesh[j,0] = pow(output_mesh.points[j][0] + 0.0,outputScaling)
out_mesh[j,1] = pow(output_mesh.points[j][1] + 0.0,outputScaling)
out_mesh_global[j,0] = pow(output_mesh.points[j][0] + 0.0,outputScaling)
out_mesh_global[j,1] = pow(output_mesh.points[j][1] + 0.0,outputScaling)
out_mesh_Combined[j,0] = pow(output_mesh.points[j][0] + 0.0,outputScaling)
out_mesh_Combined[j,1] = pow(output_mesh.points[j][1] + 0.0,outputScaling)
out_mesh_Split[j,0] = pow(output_mesh.points[j][0] + 0.0,outputScaling)
out_mesh_Split[j,1] = pow(output_mesh.points[j][1] + 0.0,outputScaling)
#else:
# out_mesh[j,0] = pow(output_mesh.points[j][0] + 0.5,outputScaling)*0.00001
# out_mesh[j,1] = pow(output_mesh.points[j][1] + 0.5,outputScaling)*0.00001
# out_mesh_global[j,0] = pow(output_mesh.points[j][0] + 0.5,outputScaling)*0.00001
# out_mesh_global[j,1] = pow(output_mesh.points[j][1] + 0.5,outputScaling)*0.00001
# out_mesh_Combined[j,0] = pow(output_mesh.points[j][0] + 0.5,outputScaling)*0.00001
# out_mesh_Combined[j,1] = pow(output_mesh.points[j][1] + 0.5,outputScaling)*0.00001
# out_mesh_Split[j,0] = pow(output_mesh.points[j][0] + 0.5,outputScaling)*0.00001
# out_mesh_Split[j,1] = pow(output_mesh.points[j][1] + 0.5,outputScaling)*0.00001
#print("Original inmesh: ", in_mesh)
#print("Original outmesh: ", out_mesh)
#print("Original outmesh length: ", kk)
#mesh_size = 1/math.sqrt(nPoints)
mesh_size = 2
shape_parameter = 4.55228/((1.0)*mesh_size)
print("mesh width: ", mesh_size)
print("shape_parameter: ", shape_parameter)
bf = basisfunctions.Gaussian(shape_parameter)
##########################################################
##########################################################
'''
Functions to test
'''
#func = lambda x,y: np.exp(-100*((0.5*pow(x-0.5,2))+(0.5*pow(y-0.5,2))))
func = lambda x,y: np.cos(10*(x+y))
## Complex sin function
lambda x,y: 0.5*np.sin(2*x*y)+(0.0000001*y)
## Complex fast sin function
lambda x,y: 0.5*np.sin(10*x*y)+(0.0000001*y)
## Rosenbrock function
lambda x,y: pow(1-x,2) + 100*pow(y-pow(x,2),2)
## Arctan function (STEP FUNCTION)
lambda x,y: np.arctan(125*(pow(pow(x-1.5,2) + pow(y-0.25,2),0.5) - 0.92))
## Unit values
lambda x,y: np.ones_like(x)
stepFunction = 0 # Apply step function values if = 1
##########################################################
##########################################################
in_vals = func(in_mesh[:,0],in_mesh[:,1])
in_vals_global = func(in_mesh[:,0],in_mesh[:,1])
in_vals_global_LOOCV_error = func(in_mesh[:,0],in_mesh[:,1])
in_vals_local_LOOCV_error = func(in_mesh[:,0],in_mesh[:,1])
out_vals = func(out_mesh[:,0],out_mesh[:,1])
out_vals_global = func(out_mesh[:,0],out_mesh[:,1])
k = 0
if (stepFunction == 1):
for j in range(0,yInMesh):
for i in range(0,xInMesh):
if (in_mesh[i+j*xInMesh,0] <= 0.5 and in_mesh[i+j*xInMesh,1] <= 0.5):
in_vals[k] = 2
if (in_mesh[i+j*xInMesh,0] <= 0.5 and in_mesh[i+j*xInMesh,1] > 0.5):
in_vals[k] = 5
if (in_mesh[i+j*xInMesh,0] > 0.5 and in_mesh[i+j*xInMesh,1] > 0.5):
in_vals[k] = 7
if (in_mesh[i+j*xInMesh,0] > 0.5 and in_mesh[i+j*xInMesh,1] <= 0.5):
in_vals[k] = 9
k += 1
k = 0
for j in range(0,yOutMesh):
for i in range(0,xOutMesh):
if (out_mesh[i+j*xOutMesh,0] <= 0.5 and out_mesh[i+j*xOutMesh,1] <= 0.5):
out_vals[k] = 2
out_vals_global[k] = 2
if (out_mesh[i+j*xOutMesh,0] <= 0.5 and out_mesh[i+j*xOutMesh,1] > 0.5):
out_vals[k] = 5
out_vals_global[k] = 5
if (out_mesh[i+j*xOutMesh,0] > 0.5 and out_mesh[i+j*xOutMesh,1] > 0.5):
out_vals[k] = 7
out_vals_global[k] = 7
if (out_mesh[i+j*xOutMesh,0] > 0.5 and out_mesh[i+j*xOutMesh,1] <= 0.5):
out_vals[k] = 9
out_vals_global[k] = 9
k += 1
out_vals_global_rational = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_global_regular = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_split_rational = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_split_regular = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_split_rational_error = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_split_regular_error = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_global_rational_error = 0*func(out_mesh[:,0],out_mesh[:,1])
out_vals_global_regular_error = 0*func(out_mesh[:,0],out_mesh[:,1])
tree = spatial.KDTree(list(zip(in_mesh[:,0],in_mesh[:,1])))
nearest_neighbors = []
singlePointTestAll = len(output_mesh.points)
start = time.time()
regError = 0
real_out_mesh = np.random.random((1,2))
kNN = 5
in_mesh_2 = np.random.random(((kNN),2))
for i in range(0,singlePointTestAll):
#in_mesh = np.random.random(((30),2)) - 0.5
#out_mesh = 0*np.random.random(((1),2))
#in_vals = func(in_mesh[:,0],in_mesh[:,1])
#print("In Value: ", in_vals)
#mesh_size = 0.02*i + 0.02
mesh_size = 0.4
#shape_parameter = 4.55228/((1.0)*mesh_size)
shape_parameter = 3
print("mesh width: ", mesh_size)
#print("shape_parameter: ", shape_parameter)
bf = basisfunctions.Gaussian(shape_parameter)
real_out_mesh[0,0] = out_mesh[i,0]
real_out_mesh[0,1] = out_mesh[i,1]
real_out_vals = func(real_out_mesh[:,0],real_out_mesh[:,1])
queryPt = (out_mesh[0,0],out_mesh[0,1])
nnArray = tree.query(queryPt,kNN)
for j in range(0,kNN):
in_mesh_2[j,0] = in_mesh[nnArray[1][j],0]
in_mesh_2[j,1] = in_mesh[nnArray[1][j],1]
in_vals_2 = func(in_mesh_2[:,0],in_mesh_2[:,1])
if (rationalGlobal == 1):
#start = time.time()
interpRational = Rational(bf, in_mesh_2, in_vals, rescale = False)
#end = time.time()
#print("Time for Global rational inversion: ", end-start)
#start = time.time()
fr = interpRational(in_vals, out_mesh)
print("Out_value: ",fr)
print("L2 Out Rational: ", np.linalg.norm(out_vals - fr, 2))
#end = time.time()
#print("Time for Global eigen decomposition: ", end-start)
else:
print("Not running the Global Rational RBF")
fr = func(out_mesh[:,0],out_mesh[:,1])
if (regularGlobal == 1):
#start = time.time()
interp = NoneConsistent(bf, in_mesh_2, in_vals_2, rescale = False)
fr_regular = interp(real_out_mesh)
print("Out_value: ",fr_regular)
regError = regError + pow(sum(pow(real_out_vals - fr_regular,2))/len(real_out_mesh),0.5)
print("Relative L2 Out Regular: ", regError)
#print("L2 Out Regular: ", np.linalg.norm(real_out_vals - fr_regular, 2))
end = time.time()
print("Time for Global regular solve: ", i)
#start = time.time()
#print("Starting Global Regular LOOCV")
error_LOOCV = LOOCV(bf, in_mesh, in_vals, rescale = False)
errorsLOOCV = error_LOOCV()
#plt.scatter(in_mesh[:,0], in_mesh[:,1], label = "In Mesh")
#plt.scatter(out_mesh[:,0], out_mesh[:,1], label = "Out Mesh")
#plt.show()
else:
print("Not running the Global Regular RBF")
fr_regular = func(out_mesh[:,0],out_mesh[:,1])
errorsLOOCV = func(in_mesh[:,0],in_mesh[:,1])
end = time.time()
plt.scatter(in_mesh[:,0], in_mesh[:,1], label = "In Mesh")
plt.scatter(out_mesh[:,0], out_mesh[:,1], label = "Out Mesh")
plt.show()
print("Time for Global regular solve: ", end-start)
#out_vals = funcTan(out_mesh[:,0], out_mesh[:,1])
#print("out_vals: ", max(fr))
#print("Error fr= ", np.linalg.norm(out_vals - fr, 2))
#print("max fr: ", max(out_vals - fr))
#print("Error fr_regular= ", np.linalg.norm(out_vals - fr_regular, 2))
maxRegError = max(out_vals - fr_regular)
#print("max fr: ", max(out_vals - fr))
#print("max regular: ", maxRegError)
globalRegularL2Error = np.linalg.norm(out_vals - fr_regular, 2)
globalRationalL2Error = np.linalg.norm(out_vals - fr, 2)
k=0
for k in range(0,len(fr)):
out_vals_global_rational[k] = fr[k]
out_vals_global_regular[k] = fr_regular[k]
k=0
for k in range(0,len(errorsLOOCV)):
in_vals_global_LOOCV_error[k] = errorsLOOCV[k]
'''
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_title('Regular')
ax.plot_surface(Xtotal, Ytotal, Z_regular,cmap='viridis',linewidth=0,edgecolor='black')
plt.show()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_title('Rational')
ax.plot_surface(Xtotal, Ytotal, Z_rational,cmap='viridis',linewidth=0)
plt.show()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_title('Regular - error')
ax.plot_surface(Xtotal, Ytotal, Z_regular_error,cmap='viridis',linewidth=0)
plt.show()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_title('Rational - error')
#ax.set_zlim(-0.001, 0.001)
ax.plot_surface(Xtotal, Ytotal, Z_rational_error,cmap='viridis',linewidth=0)
plt.show()
'''
#Z = in_vals
# Plot the surface.
#surf = ax.plot_surface(X, Y, Z,cmap='viridis',linewidth=0)
#ax.plot_surface(X, Y, Z_regular,cmap='viridis',linewidth=0)
# Customize the z axis.
#ax.set_zlim(-4.0, 4.0)
#ax.zaxis.set_major_locator(LinearLocator(10))
#ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
# Add a color bar which maps values to colors.
#fig.colorbar(surf, shrink=0.5, aspect=5)
#ax.plot_surface(X, Y, Z_regular,cmap='viridis',linewidth=0)
#ax.plot_surface(X, Y, Z_rational,cmap='viridis',linewidth=0)
#plt.show()
#fig, axs = plt.subplots(2, 2)
#axs[0, 0].plot_surface(X, Y, Z,cmap='viridis',linewidth=0)
#axs[0, 0].set_title('Axis [0, 0]')
#axs[0, 1].plot_surface(X, Y, Z_regular,cmap='viridis',linewidth=0)
#axs[0, 1].set_title('Axis [0, 1]')
#axs[1, 0].plot_surface(X, Y, Z_rational,cmap='viridis',linewidth=0)
#axs[1, 0].set_title('Axis [1, 0]')
######################################################
######################################################
######################################################
'''
Begin local RBF
'''
print("#############################################")
print("Beginning local RBF")
print("#############################################")
######################################################
######################################################
######################################################
xGridStepInSet = xGridStepIn
yGridStepInSet = yGridStepIn
xGridStepOutSet = xGridStepOut
yGridStepOutSet = yGridStepOut
start = time.time()
domainCount= 0
for dd2 in range(0,yDomainDecomposition):
for dd1 in range(0,xDomainDecomposition):
skipLoop = int(totalLocalDomains/size)*rank + int(totalLocalDomains/size)
print(skipLoop,int(totalLocalDomains/size)*rank)
if ((domainCount > skipLoop) or (domainCount < (int(totalLocalDomains/size)*rank))):
print("Need to break on rank: ", rank)
else:
if (dd1 == 0):
shiftX = 0.0
elif (dd1 == xDomainDecomposition-1):
#shiftX = (dd1)*xStep - xBoundaryExtension*alphaInX
shiftX = (dd1)*xStep - xBoundaryExtension*xStep
else:
#shiftX = (dd1)*xStep- (xBoundaryExtension/2)*alphaInX
shiftX = (dd1)*xStep- (xBoundaryExtension/2)*xStep
if (dd2 == 0):
shiftY = 0.0
elif (dd2 == yDomainDecomposition-1):
#shiftY = (dd2)*yStep - yBoundaryExtension*alphaInY
shiftY = (dd2)*yStep - yBoundaryExtension*yStep
else:
#shiftY = (dd2)*yStep - (yBoundaryExtension/2)*alphaInY
shiftY = (dd2)*yStep - (yBoundaryExtension/2)*yStep
xMinLength = xMin + shiftX
xMaxLength = xMin + shiftX + (1+xBoundaryExtension)*xStep
yMinLength = yMin + shiftY
yMaxLength = yMin + shiftY + (1+xBoundaryExtension)*yStep
xMinLengthOut = xMin + dd1*xStep
xMaxLengthOut = xMin + dd1*xStep + xStep
yMinLengthOut = yMin + dd2*yStep
yMaxLengthOut = yMin + dd2*yStep + yStep
print("Properties: ",xMinLength,yMinLength,xMinLengthOut, yMinLengthOut,dd1,dd2)
print("Properties: ",xMaxLength,yMaxLength,xMaxLengthOut, yMaxLengthOut)
#print("Alpha X: ", alphaOutX, alphaOutY)
print("Local Domain Number: ",domainCount + 1)
if (dd1 == 0):
xMinLength -= 1.0
xMinLengthOut -= 1.0
if (dd2 == 0):
yMinLength -= 1.0
yMinLengthOut -= 1.0
if (dd1 == xDomainDecomposition-1):
xMaxLength += 1.0
xMaxLengthOut += 1.0
if (dd2 == yDomainDecomposition-1):
yMaxLength += 1.0
yMaxLengthOut += 1.0
# To create boxes for mesh
# xMinLength is the point at lowest X position, alphaInX*int(xGridStepIn+xBoundaryExtension) is the length of the block
#in_size = np.linspace(xMinLength, alphaInX*(xGridStepIn+xBoundaryExtension+1), int(xGridStepIn+xBoundaryExtension))
#print("in_size: ", in_size)
#in_size = np.linspace(xMinLength, edgeLengthX + xMinLength, inLen)
#out_size = np.linspace(yMinLength, alphaInY*(yGridStepIn+yBoundaryExtension+1), int(yGridStepIn+yBoundaryExtension))
#print("out_size: ", out_size)
#in_mesh = np.random.random((int(xGridStepIn+xBoundaryExtension)*int(yGridStepIn+yBoundaryExtension),2))
#out_mesh = np.random.random((int(xGridStepOut)*int(yGridStepOut),2))
in_mesh_list = []
inner_in_mesh_list = []
out_mesh_list = []
#print("Local domain input vertices: ", int(yGridStepIn+yBoundaryExtension)*int(xGridStepIn+xBoundaryExtension))
#for j in range(0,int(yGridStepIn+yBoundaryExtension)):
# for i in range(0,int(xGridStepIn+xBoundaryExtension)):
# in_mesh[i+j*int(xGridStepIn+xBoundaryExtension),0] = alphaInX*i + xMinLength
# in_mesh[i+j*int(xGridStepIn+xBoundaryExtension),1] = alphaInY*j + yMinLength
#if i == 0:
#print("in_mesh: ",in_mesh[i+j*int(xGridStepIn+xBoundaryExtension),0])
#print("Local domain output vertices: ", int(yGridStepOut)*int(xGridStepOut))
#for j in range(0,int(yGridStepOut)):
# for i in range(0,int(xGridStepOut)):
# out_mesh[i+j*int(xGridStepOut),0] = alphaOutX*i + xMinLengthOut
# out_mesh[i+j*int(xGridStepOut),1] = alphaOutY*j + yMinLengthOut
#if i == 0:
# print("out_mesh: ",out_mesh[j+i*outLen,0])
#print(len(out_mesh))
inCount = 0
innerInCount = 0
for i in range(0,nPointsInput):
if ((in_mesh_global[i,0] >= xMinLength) and (in_mesh_global[i,0] <= xMaxLength) and (in_mesh_global[i,1] >= yMinLength) and (in_mesh_global[i,1] <= yMaxLength)):
in_mesh_list.append(i)
if ((in_mesh_global[i,0] >= xMinLengthOut) and (in_mesh_global[i,0] <= xMaxLengthOut) and (in_mesh_global[i,1] >= yMinLengthOut) and (in_mesh_global[i,1] <= yMaxLengthOut)):
inner_in_mesh_list.append(inCount)
innerInCount += 1
inCount += 1
in_mesh = np.random.random((inCount,2))
for i in range(0,inCount):
in_mesh[i,0] = in_mesh_global[in_mesh_list[i],0]
in_mesh[i,1] = in_mesh_global[in_mesh_list[i],1]
outCount = 0
for i in range(0,nPointsOutput):
if ((out_mesh_global[i,0] >= xMinLengthOut) and (out_mesh_global[i,0] <= xMaxLengthOut) and (out_mesh_global[i,1] >= yMinLengthOut) and (out_mesh_global[i,1] <= yMaxLengthOut)):
out_mesh_list.append(i)
outCount += 1
out_mesh = np.random.random((outCount,2))
for i in range(0,outCount):
out_mesh[i,0] = out_mesh_global[out_mesh_list[i],0]
out_mesh[i,1] = out_mesh_global[out_mesh_list[i],1]
in_vals = func(in_mesh[:,0],in_mesh[:,1])
out_vals = func(out_mesh[:,0],out_mesh[:,1])
k = 0
if (rationalLocal == 1):
print("Using local Rational RBFs")
interpRational = Rational(bf, in_mesh, in_vals, rescale = False)
fr = interpRational(in_vals, out_mesh)
else:
print("NOT Using local Rational RBFs")
fr = func(out_mesh[:,0],out_mesh[:,1])
if (regularLocal == 1):
print("Using local Regular RBFs")
interp = NoneConsistent(bf, in_mesh, in_vals, rescale = False)
fr_regular = interp(out_mesh)
error_LOOCV = LOOCV(bf, in_mesh, in_vals, rescale = False)
errorsLOOCV = error_LOOCV()
else:
print("NOT Using local Regular RBFs")
fr_regular = func(out_mesh[:,0],out_mesh[:,1])
errorsLOOCV = func(in_mesh[:,0],in_mesh[:,1])
#out_vals = funcTan(out_mesh[:,0], out_mesh[:,1])
#print("out_vals: ", max(fr))
#print("Error fr= ", np.linalg.norm(out_vals - fr, 2))
#print("Error fr_regular= ", np.linalg.norm(out_vals - fr_regular, 2))
#maxRegError = max(out_vals - fr_regular)
#print("max fr: ", max(out_vals - fr))
#print("max regular: ", maxRegError)
for i in range(0,outCount):
out_vals_split_rational[out_mesh_list[i]] = fr[k]
out_vals_split_regular[out_mesh_list[i]] = fr_regular[k]
k += 1
for i in range(0,innerInCount):
in_vals_local_LOOCV_error[in_mesh_list[inner_in_mesh_list[i]]] = errorsLOOCV[inner_in_mesh_list[i]]
#for j in range(0,int(yGridStepOut)):
# for i in range(0,int(xGridStepOut)):
#Z[i,j] = out_vals[k]
#Z_split[i+int(xGridStepOutSet*dd1),j+int(yGridStepOutSet*dd2)] = fr[k]
###w = int((i+(dd1*xGridStepOutSet)) + ((j+(dd2*yGridStepOutSet))*(xOutMesh)))
#print(w)
###out_vals_split_rational[w] = fr[k]
###out_vals_split_regular[w] = fr_regular[k]
#Z_rational[i,j] = fr[k]
#Z_rational_error[i,j] = out_vals[k]- fr[k]
#Z_regular[i,j] = fr_regular[k]
#Z_regular_error[i,j] = out_vals[k]- fr_regular[k]
# k += 1
#print("j: ", j)
'''
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel('x axis')
ax.set_ylabel('y axis')
ax.set_title('Split mesh - Rational')
ax.plot_surface(Xtotal, Ytotal, Z_rational,cmap='viridis',linewidth=0,edgecolor='black')
plt.show()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel('x axis')
ax.set_ylabel('y axis')
ax.set_title('Split mesh - Regular')
ax.plot_surface(Xtotal, Ytotal, Z_regular,cmap='viridis',linewidth=0,edgecolor='black')
plt.show()
'''
domainCount += 1
end = time.time()
print("Time for decomposed problem eigen decomposition: ", end-start)
#fig = plt.figure()
#ax = fig.gca(projection='3d')
#ax.set_xlabel('Regular')
#ax.plot_surface(Xtotal, Ytotal, Z_split,cmap='viridis',linewidth=0,edgecolor='black')
#plt.show()
'''
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel('Regular Error')
ax.plot_surface(X, Y, Z_regular_error,cmap='viridis',linewidth=0)
plt.show()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel('Rational Error')
ax.plot_surface(X, Y, Z_rational_error,cmap='viridis',linewidth=0)
plt.show()
'''
global_local_rational_difference = []
global_local_regular_difference = []
k = 0
for j in range(0,nPointsOutput):
#Z_split_error[i,j] = Z_combined[i,j] - Z_split[i,j]
#Z_rational_diff[i,j] = Z_rational_global[i,j] - Z_split[i,j]
#Z_error_diff[i,j] = Z_rational_error_global[i,j] - Z_split_error[i,j]
out_vals_split_rational_error[k] = out_vals_split_rational[k] - out_vals_global[k]
out_vals_split_regular_error[k] = out_vals_split_regular[k] - out_vals_global[k]
out_vals_global_rational_error[k] = out_vals_global_rational[k] - out_vals_global[k]
out_vals_global_regular_error[k] = out_vals_global_regular[k] - out_vals_global[k]
global_local_rational_difference.append(out_vals_split_rational[k] - out_vals_global_rational[k])
global_local_regular_difference.append(out_vals_split_regular[k] - out_vals_global_regular[k])
k += 1
print("Error of Global Rational RBF: ", np.linalg.norm(out_vals_global_rational_error, 2))
print("Error of Local Rational RBF sub-domains: ", np.linalg.norm(out_vals_split_rational_error, 2))
print("Max Global Rational RBF Error: ", max(abs(out_vals_global_rational_error)))
print("Max Local Rational RBF Error: ", max(abs(out_vals_split_rational_error)))
print("Error of Global Regular RBF: ", np.linalg.norm(out_vals_global_regular_error, 2))
print("Error of Local Regular RBF sub-domains: ", np.linalg.norm(out_vals_split_regular_error, 2))
print("Error of Global Regular RBF - LOOCV: ", np.linalg.norm(in_vals_global_LOOCV_error, 2))
print("Error of Local Regular RBF sub-domains - LOOCV: ", np.linalg.norm(in_vals_local_LOOCV_error, 2))
print("Max Global Regular RBF Error: ", max(abs(out_vals_global_regular_error)))
print("Max Local Regular RBF Error: ", max(abs(out_vals_split_regular_error)))
print("Interpolation error of non-boundary points for unit square")
inputMeshAppend = []
for i in range(0,nPointsInput):
if ((in_mesh_global[i,0] >= 0.1) and (in_mesh_global[i,0] <= 0.9) and (in_mesh_global[i,1] >= 0.1) and (in_mesh_global[i,1] <= 0.9)):
inputMeshAppend.append(i)
in_mesh_error_check = np.random.random((len(inputMeshAppend),2))
for i in range(0,len(inputMeshAppend)):
in_mesh_error_check[i,0] = in_mesh_global[inputMeshAppend[i],0]
in_mesh_error_check[i,1] = in_mesh_global[inputMeshAppend[i],1]
in_vals_LOOCV_regular_global_error_check = 0*func(in_mesh_error_check[:,0],in_mesh_error_check[:,1])
in_vals_LOOCV_regular_local_error_check = 0*func(in_mesh_error_check[:,0],in_mesh_error_check[:,1])
for i in range(0,len(inputMeshAppend)):
in_vals_LOOCV_regular_global_error_check[i] = in_vals_global_LOOCV_error[inputMeshAppend[i]]
in_vals_LOOCV_regular_local_error_check[i] = in_vals_local_LOOCV_error[inputMeshAppend[i]]
print("Non-boundary global - LOOCV: ", np.linalg.norm(in_vals_LOOCV_regular_global_error_check, 2))
print("Non-boundary local - LOOCV: ", np.linalg.norm(in_vals_LOOCV_regular_local_error_check, 2))
triang = mtri.Triangulation(in_mesh_global[:,0], in_mesh_global[:,1])
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.triplot(triang, c="#D3D3D3", marker='.', markerfacecolor="#DC143C",markeredgecolor="black", markersize=2)
ax.set_xlabel('X')
ax.set_ylabel('Y')
plt.show()
triang = mtri.Triangulation(out_mesh_global[:,0], out_mesh_global[:,1])
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.triplot(triang, c="#D3D3D3", marker='.', markerfacecolor="#DC143C",markeredgecolor="black", markersize=2)
ax.set_xlabel('X')
ax.set_ylabel('Y')
plt.show()
#fig = plt.figure()
#ax = fig.add_subplot(1,1,1)
#ax.triplot(triang, c="#D3D3D3", marker='.', markerfacecolor="#DC143C",
# markeredgecolor="black", markersize=10)
#ax.set_xlabel('X')
#ax.set_ylabel('Y')
#plt.show()
#isBad = np.where((out_mesh_global[:,0] < xMin+0.01) | (out_mesh_global[:,0]>xMax-0.01) | (out_mesh_global[:,1]<yMin+0.01) | (out_mesh_global[:,1]>yMax-0.01), True, False)
#mask = np.any(isBad[triang.triangles],axis=1)
#triang.set_mask(mask)
fig = plt.figure()
ax = fig.add_subplot(1,1,1, projection='3d')
ax.plot_trisurf(triang, out_vals_global, cmap='inferno_r')
ax.scatter(out_mesh_global[:,0], out_mesh_global[:,1],out_vals_global, marker='.', s=10, c="black", alpha=0.5)
ax.view_init(elev=60, azim=-45)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Out Mesh Values')
plt.show()
triang = mtri.Triangulation(in_mesh_global[:,0], in_mesh_global[:,1])
fig = plt.figure()
ax = fig.add_subplot(1,1,1, projection='3d')
ax.plot_trisurf(triang, in_vals_global, cmap='jet')
ax.scatter(in_mesh_global[:,0], in_mesh_global[:,1],in_vals_global, marker='.', s=10, c="black", alpha=0.5)
ax.view_init(elev=60, azim=-45)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('In Mesh Values')
plt.show()
triang = mtri.Triangulation(out_mesh_global[:,0], out_mesh_global[:,1])
if (regularGlobal == 1):
fig = plt.figure()
ax = fig.add_subplot(1,1,1, projection='3d')
ax.plot_trisurf(triang, out_vals_global_regular, cmap='jet')
#ax.scatter(out_mesh_global[:,0], out_mesh_global[:,1],out_vals_global_regular, marker='.', s=10, c="black", alpha=0.5)
ax.view_init(elev=60, azim=-45)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Regular RBF on Global Grid')
plt.show()