added some exercises

This commit is contained in:
Daniel Knüttel 2019-01-23 14:38:36 +01:00
parent 778fb469ee
commit 0c62b308cc
3 changed files with 60 additions and 0 deletions

20
ex_41.py Normal file
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import numpy as np
A = np.array([ [1, 5, 1]
, [5, 0, -3]
, [1, -3, 7]])
print(np.linalg.eig(A))
O = np.linalg.eig(A)[1]
D = np.zeros((3, 3))
for i, v in enumerate(np.linalg.eig(A)[0]):
D[i][i] = v
I = np.zeros((3, 3))
for i in range(3):
I[i][i] = 1
print("(2)", np.allclose(np.dot(O.T, O), I))
print("(3)", np.allclose(A, np.dot(np.dot(O, D), O.T)))
print("(4)", np.allclose(np.dot(A, A), np.dot(np.dot(O, np.dot(D, D)), O.T)))

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ex_42.py Normal file
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import numpy as np
A = np.array(
[ [0, 1, 1, 0, 0, 0]
, [1, 0, 1, 0, 1, 0]
, [1, 1, 0, 1, 0, 0]
, [0, 0, 1, 0, 1, 0]
, [0, 0, 0, 1, 0, 1]
, [0, 0, 0, 0, 1, 0]
])
eigvalues, eigvectors = np.linalg.eig(A)
l_max_i = eigvalues.argmax()
l_max = eigvalues[l_max_i]
v_max = eigvectors[l_max_i]
def some_norm(M):
return np.abs(M).max()
for k in range(1, 21):
print("some kind of error for k =", k, ":", some_norm(A**k - l_max**k * np.outer(v_max, v_max.T)))

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ex_43.py Normal file
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import numpy as np
P = np.array(
[ [1/6, 1/6, 1/6, 1/6, 1/6, 0]
, [1/6, 1/6, 1/6, 1/6, 1/6, 0]
, [1/6, 1/6, 1/6, 1/6, 1/6, 0]
, [1/6, 1/6, 1/6, 1/6, 1/6, 0]
, [1/6, 1/6, 1/6, 1/6, 1/6, 1/10]
, [1/6, 1/6, 1/6, 1/6, 1/6, 9/10]])
print(P.shape)
v = np.array([0, 1, 0, 0, 0, 0])
w = np.power(np.dot(P**4, v), 1/4)
print(w)
print(w[-1])