Try to solve S5

Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 5/Miguel_S5_Aufg2.py

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+#%%
+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, 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] = 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]))
+        elif i == n - 3:
+            A[i][i - 1] = h[i - 1]
+            A[i][i] = h[i - 1] + h[i]
+            z[i] = 3 * (((y[i + 1] - y[i]) / h[i]) - ((y[i] - y[i - 1]) / h[i - 1]))
+        else:
+            A[i][i - 1] = h[i - 1]
+            A[i][i] = 2 * (h[i - 1] + h[i])
+            A[i][i + 1] = h[i]
+            z[i] = 3 * (((y[i + 1] - y[i]) / h[i]) - ((y[i] - y[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)
+pyplot.scatter(xx, interpolate.CubicSpline(x, y)(xx))
+
+# %%

Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 5/Miguel_S5_Aufg3.py

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+# %%
+from Miguel_S5_Aufg2 import Miguel_S5_Aufg2
+from matplotlib import pyplot
+from numpy import array, polyfit, polyval
+from scipy import interpolate
+
+x = array([1900, 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990, 19100, 19110])
+y = array([75.995, 91.972, 105.711, 123.203, 131.669, 150.697, 179.323, 203.212, 226.505, 249.633, 281.422, 308.745])
+xx = array([17, 25, 41, 56, 72, 98, 100, 108])
+
+# a)
+
+pyplot.figure()
+Miguel_S5_Aufg2(x, y, xx)
+
+# b)
+
+pyplot.figure()
+pyplot.scatter(xx, interpolate.CubicSpline(x, y)(xx))
+
+# c) 1
+pyplot.figure()
+pyplot.scatter(xx, polyval(polyfit(x, y, deg = 11), xx))
+
+# c) 2
+x[:] -= 1900
+pyplot.figure()
+pyplot.scatter(xx, polyval(polyfit(x, y, deg = 11), xx))
+
+# %%