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interpolateparametarization.py
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# class Interpolate:
# # 'Common base class for all employees'
# # empCount = 0
#
# def __init__(self,inter_method):
# self.method = inter_method
# self.w = 0
# self.v = 0
# self.xi = 0
# # self.lambda = 0
#
#
# def parameterization(self,xi, yi):
# n = xi.shape[0]
# m = xi.shape[1]
# if self.method =='NPS':
#
# A= np.zeros(shape=(m,m))
#
# for ii in range(0,m,1): # for ii =0 to m-1 with step 1; range(1,N,1)
# for jj in range(0,m,1):
# A[ii,jj] = (np.dot(xi[:,ii] - xi[:,jj],xi[:,ii] - xi[:,jj]))**(3.0/2.0)
#
# V = np.concatenate((np.ones((1,m)), xi), axis=0)
# A1 = np.concatenate((A, np.transpose(V)),axis=1)
# A2 = np.concatenate((V, np.zeros(shape=(n+1,n+1) )), axis=1)
# yi = yi[np.newaxis,:]
#
# print(yi.shape)
# b = np.concatenate([np.transpose(yi), np.zeros(shape=(n+1,1))])
# # b = np.concatenate((np.transpose(yi), np.zeros(shape=(n+1,1) )), axis=0)
# A = np.concatenate((A1,A2), axis=0)
# wv = np.linalg.solve(A,b)
# self.w = wv[:m]
# self.v = wv[m:]
# self.xi = xi
# # print(V)
#
# if self.method == "MAPS" or self.method == "MAPS2":
# a = np.ones(xi.shape[0],1)
# #a = ones(size(xi,1),1);
# lambda = 1;
# for i in range (0,20):
# # %TODO: FIX THE ITER MAX
# # % [inter_par, a] = Scale_interpar( xi,yi,a0, lambda); % method1
# # [inter_par,a] = Scale_interpar( xi,yi,a, lambda); %method2
# # inter_par{1}=inter_method;
# # lambda = lambda/2;
# # end
# # if inter_method==8
# # % keyboard
# # epsFun = yi-y0;
# # inter_par{8}=epsFun;
# # end
#
# # Scaled Polyharmonic Spline
# def Scale_interpar(xi,yi,a0, lambda0):
# #This function is for spinterpolation and finds the scaling factor for
# #polyharmonic spline interpolation
# self.lambda = lambda0;
# n = xi.shape[0]
# a0 = ones(n,1)
# self.lambda =1;
#
# return inter_par,a
#
import numpy as np
np.set_printoptions(linewidth=200, precision=5, suppress=True)
import pandas as pd;
pd.options.display.max_rows = 20;
pd.options.display.expand_frame_repr = False
import pylab as plt
class Inter_par():
def __init__(self,method="NPS", w=0, v=0, xi=0,a=0):
self.method = "NPS"
self.w=[]
self.v=[]
self.xi=[]
self.a=[]
def interpolateparameterization(xi, yi, inter_par):
n = xi.shape[0]
m = xi.shape[1]
if inter_par.method =='NPS':
A= np.zeros(shape=(m,m))
for ii in range(0,m,1): # for ii =0 to m-1 with step 1; range(1,N,1)
for jj in range(0,m,1):
A[ii,jj] = (np.dot(xi[:,ii] - xi[:,jj],xi[:,ii] - xi[:,jj]))**(3.0/2.0)
V = np.concatenate((np.ones((1,m)), xi), axis=0)
A1 = np.concatenate((A, np.transpose(V)),axis=1)
A2 = np.concatenate((V, np.zeros(shape=(n+1,n+1) )), axis=1)
#TODO Later understand the bug...
if n>1:
yi = yi[np.newaxis,:]
# print(yi.shape)
# b = np.concatenate([np.transpose(yi), np.zeros(shape=(n+1,1))])
b = np.concatenate((np.transpose(yi), np.zeros(shape=(n+1,1) )), axis=0)
# print(yi.shape)
# print('------------------------------------------------$$$$$-------------')
A = np.concatenate((A1,A2), axis=0)
# print('------------------------------------------------$$$$$-------------')
# print(A.shape)
wv = np.linalg.solve(A,b)
inter_par.w = wv[:m]
inter_par.v = wv[m:]
inter_par.xi = xi
return inter_par
# print(V)
def fun(x, alpha=0.1):
y = np.array((x[0,:]-0.45)**2.0 + alpha*(x[1,:]-0.45)**2.0)
return y.T
# return (x[0,:]-0.45)**2.0 + alpha*(x[1,:]-0.45)**2.0
inter_par = Inter_par("NPS")
xi = np.array([[0.5000 , 0.8000 , 0.5000, 0.2000, 0.5000], [0.5000, 0.5000, 0.8000, 0.5000, 0.2000]])
#xi=np.random.rand(2,3)
#x=np.array([[0.5],[0.5]])
#yi=np.random.rand(1,3)
yi=fun(xi)
print (yi)
#yi = np.array(yi)
#print(yi.shape)
#print(xi.shape)
#
inter_par = interpolateparameterization(xi, yi, inter_par)
#%%
def fun(x):
y = np.array(x-0.45)**2.0
return y
# return (x[0,:]-0.45)**2.0 + alpha*(x[1,:]-0.45)**2.0
inter_par = Inter_par("NPS")
xi = np.array([[0.5000 , 0.8000 , 0.2000, 0.6000]] )
#xi=np.random.rand(2,3)
x=np.array([[0.5]])
#yi=np.random.rand(1,3)
yi=fun(xi)
#print (yi)
##yi = np.array(yi)
#print(yi.shape)
#print(xi.shape)
inter_par = interpolateparameterization(xi, yi, inter_par)
print(inter_par.w)