def cubesplineinterp(f, df, a, b, N):
# split on sections
x = sectionbreak(a, b, N)
step = ((b - a) / N)
# find m for twice continuous
M = np.zeros((N, N))
M[0, 0] = 1
M[N - 1, N - 1] = 1
for i, row in enumerate(M[1:-1]):
i += 1
row[i - 1] = 1
row[i] = 4
row[i + 1] = 1
b = [df(x[0])] + [(3 / step) * (f(x[i + 1]) - f(x[i - 1]))
for i, p in enumerate(x[1:-1])] + [df(x[-1])]
b = np.array(b)
m = np.linalg.solve(M, b)
print(m)
print(df(x))
m = df(x)
# find coefficient of poly
splines = []
for i, val in enumerate(x[:-1]):
A = [[x[i]**3, x[i]**2, x[i], 1]]
A += [[x[i + 1]**3, x[i + 1]**2, x[i + 1], 1]]
A += [[3 * x[i]**2, 2 * x[i], 1, 0]]
A += [[3 * x[i + 1]**2, 2 * x[i + 1], 1, 0]]
A = np.array(A)
b = [f(x[i]), f(x[i + 1]), m[i], m[i + 1]]
b = np.array(b)
#print(b)
splines.append(np.linalg.solve(A, b))
return [x, splines]
def main():
# N - number of points
N = 5
a, b = -2, 3
x, splines = cubesplineinterp(f, df, a, b, N)
# plot spline interp
plt.subplot(211)
for i, val in enumerate(x[:-1]):
st = np.arange(x[i], x[i + 1], 0.01)
plt.plot(st, Poly(splines[i]).eval(st))
a, b = -2, 2
x = np.linspace(a, b, 100)
plt.subplot(212)
plt.plot(x, f(x))
plt.show()
c = np.array(c, ndmin=1, copy=0)
x2 = x * 2
if len(c) == 1:
c0 = c[0]
c1 = 0
elif len(c) == 2:
c0 = c[0]
c1 = c[1]
else:
nd = len(c)
c0 = c[-2]
c1 = c[-1]
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = c[-i] - c1 * (2 * (nd - 1))
c1 = tmp + c1 * x2
return c0 + c1 * x2
x = np.linspace(-2, 2, 19)
coef = list((hermfit(x, f(x), 10)))
print(f(x))
s = np.arange(-2, 2, 0.01)
y = [evalpol(r, coef) for r in s]
plt.plot(s, hermval(s, coef))
plt.show()
from interpolation import f, newton_interpolation_f, chebyshev_range, np
import matplotlib.pyplot as plt
# Number of points
n = 30
# Interpolation function range
range_start = 2
range_end = 10
step_size = (range_end - range_start) / n
# X and Y values calculation using chebyshev polynomial
x_range_cheb = chebyshev_range(n, range_start, range_end)
y_range_cheb = [f(x) for x in x_range_cheb]
# Made interpolation function
interpol_f = newton_interpolation_f(x_range_cheb, y_range_cheb)
# Shows f(x) and interpolation graphs
plt.plot(np.arange(range_start, range_end, 0.01), [f(x) for x in np.arange(range_start, range_end, 0.01)], 'b',
label='f(x)')
plt.plot(np.arange(range_start, range_end, 0.01), [interpol_f(x) for x in np.arange(range_start, range_end, 0.01)], 'r',
label=f'{n} points interpolation function')
plt.scatter(x_range_cheb, y_range_cheb, color='g', label='Interpolation points')
plt.title('f(x) interpolation using Chebyshev x')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.grid(True)
plt.legend()
def main():
x = np.linspace(-2, 2, 4)
seg = np.arange(-2, 2, 0.01)
plt.plot(seg, newton_polynomial(x, f(x), seg))
plt.show()