def test_HermiteCubic2(self):
t = [1, 2, 4, 5]
y = [2, 1, 4, 3]
interp = Interpolation(t, y)
exp_coeff = [[1.0, 1.0, 1.38888889, 2.0], [4.0, 4.0, 1.0, 1.0],
[3.0, 3.61111111, 4.0, 4.0]]
exp_interval = [1, 2, 4, 5]
act_coeff1, act_interval = interp.interpHermiteCubic(t, y)
#This is done for arranging the coefficients in proper order
act_coeff = []
act_coeff.append([])
act_coeff.append([])
act_coeff.append([])
act_coeff[0] = list(np.flip((act_coeff1[:, 0])))
act_coeff[1] = list(np.flip((act_coeff1[:, 1])))
act_coeff[2] = list(np.flip((act_coeff1[:, 2])))
#Checking coefficients
for i in range(0, len(act_coeff)):
for j in range(0, len(act_coeff[i])):
a = exp_coeff[i][j] - act_coeff[i][j]
b = exp_coeff[i][j]
assert (div(a, b) <= ADMISS_REL_ERR)
#checking interval
for i in range(0, len(act_interval)):
a = exp_interval[i] - act_interval[i]
b = exp_interval[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_Newton1(self):
t = [0, 1, 2]
y = [0, 1, 2]
interp = Interpolation(t, y)
exp_coeff = [0, 1, 0]
act_coeff = interp.interpNewton(t, y)
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_Newton2(self):
t = [-2, 0, 1]
y = [-27, -1, 0]
interp = Interpolation(t, y)
exp_coeff = [-27, 13.0, -4.0]
act_coeff = interp.interpNewton(t, y)
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_Lagrange2(self):
t = [-2, 0, 1]
y = [-27, -1, 0]
interp = Interpolation(t, y)
exp_coeff = [-27, -1, 0]
act_coeff = interp.interpLagrange(t, y)
print(act_coeff)
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_Monomial2(self):
t = [-2, 0, 1]
y = [-27, -1, 0]
interp = Interpolation(t, y)
exp_coeff = [-1, 5, -4]
act_coeff = np.flip(interp.interpMonomial(t, y))
print(act_coeff)
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_Monomial1(self):
t = [0, 1, 2]
y = [0, 1, 2]
interp = Interpolation(t, y)
exp_coeff = [0, 1, 0]
act_coeff = np.flip(interp.interpMonomial(t, y))
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_BSpline(self):
t = [0.0, 1.2, 1.9, 3.2, 4.0, 6.5]
y = [0.0, 2.3, 3.0, 4.3, 2.9, 3.1]
exp_coeff = [0, 2.987, -0.574, 14.670, -10.325, 3.1, 0, 0, 0, 0, 0]
interp = Interpolation(t, y)
act_coeff = interp.interpBSpline(t, y)
#Checking the coefficients
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_evalNewton2(self):
t = [-2, 0, 1]
y = [-27, -1, 0]
interp = Interpolation(t, y)
#From Matlab
MatlabC = [-27, 13.0, -4.0]
#Tests coefficients of Newton Polynomial
PythonC = interp.interpNewton(t, y)
for i in range(0, len(PythonC)):
a = PythonC[i] - MatlabC[i]
b = PythonC[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_HermiteCubic1(self):
t = [1, 3]
y = [2, 1]
interp = Interpolation(t, y)
exp_coeff = [2, 1.67, 1.33, 1.0]
exp_interval = [1, 3]
act_coeff, act_interval = interp.interpHermiteCubic(t, y)
#Checking the coefficients
for i in range(0, len(act_coeff)):
a = exp_coeff[i] - act_coeff[i]
b = exp_coeff[i]
assert (div(a, b) <= ADMISS_REL_ERR)
#Checking interval information
for i in range(0, len(act_interval)):
a = exp_interval[i] - act_interval[i]
b = exp_interval[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_evalLagrange1(self):
t = [0, 1, 2]
y = [0, 1, 2]
interp = Interpolation(t, y)
exp_coeff = interpolate.lagrange(t, y)
act_coeff = np.flip(interp.interpLagrange(t, y))
# evaluating python object
yfit_P = exp_coeff(t)
# evaluating CFS
yfit = interp.evalLagrange(y, t, t)
for i in range(0, len(yfit_P)):
a = yfit[i] - yfit_P[i]
b = yfit[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_evalMonomial2(self):
t = [-2, 0, 1]
y = [-27, -1, 0]
interp = Interpolation(t, y)
exp_coeff = interpolate.interp1d(t, y)
act_coeff = np.flip(interp.interpMonomial(t, y))
# evaluating python object
yfit_P = exp_coeff(t)
# evaluating CFS
yfit = interp.evalMonomial(np.flip(act_coeff), t)
for i in range(0, len(yfit_P)):
a = yfit[i] - yfit_P[i]
b = yfit[i]
assert (div(a, b) <= ADMISS_REL_ERR)
def test_HermiteCubic(self):
t = [1, 2, 4, 5]
y = [2, 1, 4, 3]
interp = Interpolation(t, y)
#This is from Matlab
exp_coeff = [[0.1667, 0.6667, -1.8333, 2.0000],
[-0.7500, 2.2500, 0, 1.0000],
[0.1667, -1.1667, 0, 4.0000]]
act_coeff1, act_interval = interp.interpHermiteCubic(t, y)
# This is done for arranging the coefficients in proper order
act_coeff = []
act_coeff.append([])
act_coeff.append([])
act_coeff.append([])
act_coeff[0] = list(np.flip((act_coeff1[:, 0])))
act_coeff[1] = list(np.flip((act_coeff1[:, 1])))
act_coeff[2] = list(np.flip((act_coeff1[:, 2])))
for i in range(0, len(act_coeff)):
for j in range(0, len(act_coeff[i])):
a = act_coeff[i][j] - exp_coeff[i][j]
b = act_coeff[i][j]
assert (div(a, b) <= ADMISS_REL_ERR)
# Most of them are implemented from scratch, so they are compared against python.
# Some of them use python libraries, for which Matlab is used to verify correctness.
# @date 22/12/2018
from scipy import interpolate
import numpy as np
from pytest import *
from src.Interpolation import Interpolation
from src.Regression import Regression
from src.Input import Input
ADMISS_REL_ERR = 1e-1
t = [0, 1, 2, 3]
y = [0, 1, 2, 3]
interp = Interpolation(t, y)
## @brief This method takes care of division by zero
# @details If denominator is 0, we assume div(a/b) = 0
def div(a, b):
if b == 0:
ans = 0
else:
ans = a / b
return ans
## @brief This gives the list of test cases for Correctness.
# @see {test_interpolation.py}
# @return none
