66 lines
1.5 KiB
Python
66 lines
1.5 KiB
Python
#%%
|
|
from numpy import array, empty, linalg, zeros
|
|
from matplotlib import pyplot
|
|
from scipy import interpolate
|
|
|
|
def Miguel_S5_Aufg2(x, y, xx):
|
|
n = len(x)
|
|
a = empty((n - 1, 1))
|
|
b = empty((n - 1, 1))
|
|
c = empty((n, 1))
|
|
d = empty((n - 1, 1))
|
|
h = empty((n - 1, 1))
|
|
|
|
for i in range(0, n - 1):
|
|
a[i] = y[i]
|
|
h[i] = x[i + 1] - x[i]
|
|
|
|
c[0] = 0
|
|
c[n - 1] = 0
|
|
|
|
A = zeros((n - 2, n - 2))
|
|
z = empty((n - 2, 1))
|
|
|
|
for i in range(0, n - 2):
|
|
if i == 0:
|
|
A[i][0] = 2 * (h[0] + h[1])
|
|
A[i][1] = h[1]
|
|
z[i] = 3 * (((y[2] - y[1]) / h[1]) - ((y[1] - y[0]) / h[0]))
|
|
else:
|
|
A[i][i - 1] = h[i]
|
|
A[i][i] = 2 * (h[i] + h[i + 1])
|
|
z[i] = 3 * (((y[i + 2] - y[i + 1]) / h[i + 1]) - ((y[i + 1] - y[i]) / h[i]))
|
|
|
|
if i < n - 3:
|
|
A[i][i + 1] = h[i + 1]
|
|
|
|
c[1:n - 1,:] = linalg.solve(A, z)
|
|
|
|
for i in range(0, n - 1):
|
|
b[i] = ((y[i + 1] - y[i]) / h[i]) - ((h[i] / 3) * (c[i + 1] + 2 * c[i]))
|
|
d[i] = (1 / (3 * h[i])) * (c[i + 1] - c[i])
|
|
|
|
yy = empty(len(xx))
|
|
|
|
for i in range(0, len(yy)):
|
|
j = 0
|
|
value = xx[i]
|
|
|
|
while x[j] < value:
|
|
j += 1
|
|
|
|
yy[i] = y[j - 1] + b[j - 1] * (value - x[j - 1]) + c[j - 1] * (value - x[j - 1]) ** 2 + d[j - 1] * (value - x[j - 1]) ** 3
|
|
|
|
pyplot.scatter(xx, yy)
|
|
return yy
|
|
|
|
# %%
|
|
|
|
x = array([4, 6, 8, 10])
|
|
y = array([6, 3, 9, 0])
|
|
xx = array([4.5, 6.5, 9.0])
|
|
|
|
Miguel_S5_Aufg2(x, y, xx)
|
|
|
|
# %%
|