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