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Serie8_Aufg2_Gerüst.py

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