def cub_spl_nd(x1, y1):
roots = []
x_spline = []
y_spline = []
x_spline_range = []
for i in range(len(x1)):
f, x_domain, y_range = inter.cubicSpline(x1[i], y1[i])
x_spline.append(x_domain)
y_spline.append(y_range)
g = poly_nd_1[i](x_domain)
index = 0
h = y_range - g
root = 100
while h[index] > 0.5e-1:
if index < len(x_domain) - 1:
index = index + 1
root = x_domain[index]
else:
break
for j in range(len(x1[i]) - 1):
if root > x1[i][j] and root < x1[i][j + 1]:
#x_spline_range.append([x[i][j],x[i][j+1],x[i][j+1]-x[i][j]])
x_spline_range.append(x1[i][j + 1] - x1[i][j])
roots.append(root)
return roots, x_spline, y_spline, x_spline_range
import LeastSquares as LS
import numpy as np
from math import exp
from scipy.special import jn
import matplotlib.pyplot as plt
# Exercise 3.6
#*******************************************************************
# generate points of Bessel function J(1,x)
x = np.arange(0,12,0.5)
npts = len(x)
bess = [jn(1,i) for i in x]
# call cubic spline method from my interpolation module
xx,yy = Interp.cubicSpline(x,bess,npts,0.1)
# plot data and interpolation
plt.figure(1)
plt.plot([0,12],[0,0],'k--')
plt.plot(3.83,0,'gx',markersize=20)
plt.plot(x,bess,'bo',label='Bessel Points')
plt.plot(xx,yy,'r',label='Cubic Spline Interpolation')
plt.xlabel('x')
plt.ylabel('y')
plt.annotate('$x=3.83$',fontsize=18,xy=(0.38,0.46),xycoords='figure fraction')
plt.legend()
#*******************************************************************
# Exercise 3.10
