def spline_data(file):
""" The "spline_data" function takes 1 argument :
- file: string, the name of the file which contains the data to load
Returns 8 values given by the function "calculate_spline_data", just with the name of the file in argument.
"""
(nUpper, nLower, ix, iy) = load_foil(file)
nUpper = int(nUpper[0])
nLower = int(nLower[0])
return calculate_spline_data(ix, iy, nUpper, nLower)
def spline_data(file):
""" The "spline_data" function takes 1 argument :
- file: string, the name of the file which contains the data to load
Returns 8 values given by the function "calculate_spline_data", just with the name of the file in argument.
"""
(nUpper,nLower,ix,iy) = load_foil(file)
nUpper=int(nUpper[0])
nLower=int(nLower[0])
return calculate_spline_data(ix, iy, nUpper, nLower)
def wings_interpolation(filename, eps=0.001):
""" The "wings_interpolation" function takes 2 arguments :
- filename: string, the name of the file to load
- eps: real, step for x
Returns tables of cubic-spline interpolated values y, for x from 0 to 1 (step eps), for the upper and lower part.
"""
(nUpper, nLower, ix, iy) = load_foil(filename)
nUpper = int(nUpper[0])
nLower = int(nLower[0])
return splint_improved(ix, iy, nUpper, nLower, eps)
def wings_interpolation(filename,eps=0.001):
""" The "wings_interpolation" function takes 2 arguments :
- filename: string, the name of the file to load
- eps: real, step for x
Returns tables of cubic-spline interpolated values y, for x from 0 to 1 (step eps), for the upper and lower part.
"""
(nUpper,nLower,ix,iy) = load_foil(filename)
nUpper=int(nUpper[0])
nLower=int(nLower[0])
return splint_improved(ix, iy, nUpper, nLower, eps)
def get_foil(a, b, N, file):
(dim, ex, ey, ix, iy) = load_foil(file)
pas = (b - a) / N
ex2 = [a + pas * k for k in range(N + 1)]
ey2 = [splint(ex, ey, x) for x in ex2]
ix2 = [a + pas * k for k in range(N + 1)]
iy2 = [splint(ix, iy, x) for x in ix2]
return ex2, ey2, ix2, iy2
def test_foil():
file = "foil.txt"
(dim, ex, ey, ix, iy) = load_foil(file)
(ex2, ey2, ix2, iy2) = get_foil(0, 1, 100, file)
plt.axis('equal')
plt.plot(ex, ey, 'o')
plt.plot(ix, iy, 'o')
plt.plot(ex2, ey2)
plt.plot(ix2, iy2)
plt.show()
def test_wing(filename, eps=0.001):
""" The "test_wing" function takes 2 arguments :
- filename: string, the name of the file to load
- eps: real, step for x
Checks that every yTable data are consonant with the yUpper and yLower arrays data
"""
(nx1, nx2, xTable, yTable) = load_foil(filename)
nUpper = int(nx1[0])
nLower = int(nx2[0])
yUpper, yLower = splint_improved(xTable, yTable, nUpper, nLower, eps)
x = [0]
i = 0
while (x[i] < 1):
x += [x[i] + eps]
i += 1
x = x[:(len(yUpper))]
for i in range(nUpper):
if (xTable[i] in x):
assert (yTable[i] in yUpper)
for i in range(nUpper, nLower, 1):
if (xTable[i] in x):
assert (yTable[i] in yLower)
print("Test interpolation : PASSED.")
def test_wing(filename, eps=0.001):
""" The "test_wing" function takes 2 arguments :
- filename: string, the name of the file to load
- eps: real, step for x
Checks that every yTable data are consonant with the yUpper and yLower arrays data
"""
(nx1,nx2,xTable,yTable) = load_foil(filename)
nUpper=int(nx1[0])
nLower=int(nx2[0])
yUpper,yLower = splint_improved(xTable, yTable, nUpper, nLower, eps)
x=[0]
i=0
while (x[i]<1):
x+=[x[i]+eps]
i+=1
x=x[:(len(yUpper))]
for i in range (nUpper):
if (xTable[i] in x):
assert(yTable[i] in yUpper)
for i in range (nUpper,nLower,1):
if (xTable[i] in x):
assert(yTable[i] in yLower)
print("Test interpolation : PASSED.")
a = (xa[khi] - x) / h
b = (x - xa[klo]) / h
return a * ya[klo] + b * ya[khi] + (((a**3) - a) * y2a[klo] + (
(b**3) - b) * y2a[khi]) * (h * h) / 6.0
# Return the spline function passing through each provided point where
# xa is the array containing the x coordinate of each point
# ya is the array containing the y coordinate of each point
# n is the number of points
def spline_fun(xa, ya, n):
y2 = spline(xa, ya, n)
return lambda x: splint(xa, ya, y2, n, x)
if __name__ == "__main__":
(dim, ex, ey, ix, iy) = lf.load_foil("k1.dat")
espline = spline_fun(ex, ey, int(dim[0]))
ispline = spline_fun(ix, iy, int(dim[1]))
r = np.arange(0, 1.00001, 0.001)
mp.plot(r, list(map(espline, r)), linewidth=1.0)
mp.plot(ex, ey, marker='.', linestyle="None")
mp.plot(r, list(map(ispline, r)), linewidth=1.0)
mp.plot(ix, iy, marker='.', linestyle="None")
mp.axis('equal')
mp.title("Cubic spline interpolation of the airfoil")
mp.show()
-f is a cubic-spline interpolating g
-n is the length of x
Returns average of relatives error between f and y
"""
cpt = 0.0
for i in range(0, n):
if (y[i] > 1e-6):
cpt = cpt + (f(x[i]) - y[i]) / y[i]
cpt = cpt / n
return cpt
#---------------------------------------------------
#-------Airfoil refinment, application--------------
#---------------------------------------------------
(ex, ey, ix, iy) = foil.load_foil("goe281.dat")
plt.plot(ex, ey)
plt.plot(ix, iy)
plt.title("Wing curve goe281 without spline")
#plt.axis([-0.1,1.1,-0.1,1.1])
plt.savefig("goe281_no_spline")
plt.show()
#Taille des tableaux de points de l'aile
#e correspond à extrados
#i correspond à intrados
ne = ex.shape[0]
ni = ix.shape[0]
#On prend les dérivées premières comme nulles
yp1 = 0.0
-x is an array containing abscissae
-y is an array containing the values of g(x). y[i] = g(x[i])
-f is a cubic-spline interpolating g
-n is the length of x
Returns average of relatives error between f and y
"""
cpt = 0.0
for i in range(0,n):
if( y[i] > 1e-6 ):
cpt = cpt + (f(x[i]) - y[i])/y[i]
cpt = cpt / n
return cpt
#---------------------------------------------------
#-------Airfoil refinment, application--------------
#---------------------------------------------------
(ex,ey,ix,iy) = foil.load_foil("goe281.dat")
plt.plot(ex,ey)
plt.plot(ix,iy)
plt.title("Wing curve goe281 without spline")
#plt.axis([-0.1,1.1,-0.1,1.1])
plt.savefig("goe281_no_spline")
plt.show()
#Taille des tableaux de points de l'aile
#e correspond à extrados
#i correspond à intrados
ne = ex.shape[0]
ni = ix.shape[0]
#On prend les dérivées premières comme nulles
yp1 = 0.0
# Import
import os
import sys
import numpy as np
import matplotlib.pyplot as mp
import load_foil as fl
# Constante globale
epsilon = 0.1**2
# Variable globale (chargee a partir de foilload)
(ex, ey, ix, iy) = fl.load_foil('BACNLF.DAT');
# Aile extrados
def extrados(ix, iy):
extrados_x = [];
extrados_y = [];
for i in range(0, ix.size-1):
if(iy[i]>=0):
extrados_x.append(ix[i]);
extrados_y.append(iy[i]);
return (extrados_x, extrados_y);
# Aile intrados
def intrados(ix, iy):
intrados_x = [];
intrados_y = [];
for i in range(0, ix.size-1):
if(iy[i]<=0):
intrados_x.append(ix[i]);
intrados_y.append(iy[i]);
## Import
import numpy as np
import matplotlib.pyplot as mp
import load_foil as fl
# Constantes
eps = 0.1 ** 2
(ex, ey, ix, iy) = fl.load_foil("BACNLF.DAT")
# Fonction mettant en equation les polynomes interpolateurs de lagrange
def lagrange_polynomial(x1, x2, y1, y2):
def lagrange(x):
A = (x - x2) / (x1 - x2)
B = (x - x1) / (x2 - x1)
C = y1 * A + y2 * B
return C
return lagrange
# Fonction permettant de mettre en place es derivees
def lagrange_derivative(x1, x2, y1, y2):
def deriv(x):
A = 1 / (x1 - x2)
B = 1 / (x2 - x1)
C = y1 * A + y2 * B
return C
return deriv
