40 lines
1.2 KiB
Python
40 lines
1.2 KiB
Python
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import numpy as np
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from math import nan
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def Schenk_Brandenberger_S9_Aufg2(A, A_approx, b, b_approx):
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cond_A = np.linalg.cond(A,np.inf)
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norm_A_minus_A_approx = np.linalg.norm((A-A_approx),np.inf)
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norm_A = np.linalg.norm(A,np.inf)
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norm_b_minus_b_approx = np.linalg.norm((b-b_approx),np.inf)
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norm_b = np.linalg.norm(b,np.inf)
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x = np.linalg.solve(A,b)
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x_approx = np.linalg.solve(A_approx,b_approx)
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dxmax = (cond_A/(1-(cond_A*(norm_A_minus_A_approx/norm_A))))*((norm_A_minus_A_approx/norm_A)+(norm_b_minus_b_approx/norm_b))
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dxobs = np.linalg.norm((x-x_approx),np.inf)/np.linalg.norm(x,np.inf)
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if(cond_A*(norm_A_minus_A_approx/norm_A)) >= 1:
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dxmax = nan
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return [x, x_approx, dxmax, dxobs]
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if __name__ == '__main__':
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# Werte aus Aufgabe 1
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A = np.array([[20, 30, 10],
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[10, 17, 6],
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[2, 3, 2]])
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A_approx = A - 0.1
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b = np.array([[5720],
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[3300],
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[836]])
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b_approx = b + 100
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print(b_approx)
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[x, x_approx, dxmax, dxobs] = Schenk_Brandenberger_S9_Aufg2(A, A_approx, b, b_approx)
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print("Value x: ")
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print(x)
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print("X approx with error: ")
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print(x_approx)
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print("dx max: ", dxmax)
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print("dx obs: ", dxobs)
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