51 lines
1.2 KiB
Python
51 lines
1.2 KiB
Python
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# -*- coding: utf-8 -*-
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"""
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Created on Sat Nov 7 13:26:09 2020
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Höhere Mathematik 1, Serie 8, Gerüst für Aufgabe 2
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Description: calculates the QR factorization of A so that A = QR
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Input Parameters: A: array, n*n matrix
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Output Parameters: Q : n*n orthogonal matrix
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R : n*n upper right triangular matrix
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Remarks: none
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Example: A = np.array([[1,2,-1],[4,-2,6],[3,1,0]])
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[Q,R]=Serie8_Aufg2(A)
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@author: knaa
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"""
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def Serie8_Aufg2(A):
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import numpy as np
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A = np.copy(A) #necessary to prevent changes in the original matrix A_in
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A = A.astype('float64') #change to float
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n = np.shape(A)[0]
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if n != np.shape(A)[1]:
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raise Exception('Matrix is not square')
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Q = np.eye(n)
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R = A
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for j in np.arange(0,n-1):
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a = np.copy(???).reshape(n-j,1)
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e = np.eye(???)[:,0].reshape(n-j,1)
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length_a = np.linalg.norm(a)
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if a[0] >= 0: sig = ???
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else: sig = ???
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v = ???
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u = ???
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H = ???
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Qi = np.eye(n)
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Qi[j:,j:] = ???
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R = ???
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Q = ???
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return(Q,R)
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