Schenk_Brandenberger_S8_Aufg2.py

@@ -32,38 +32,23 @@ def Serie8_Aufg2(A):
     R = A
 
     for j in np.arange(0,n-1):
-        # erzeuge Nullen in R in der j-ten Spalte unterhalb der Diagonalen:
-        #a = (Q @ A)[j:,j:][:,0]
-        a = np.copy((Q @ A)[j:,j:][:,0]).reshape(n-j,1)
-        e = np.eye(n-j)[:,0].reshape(n-j,1)
+        a = np.copy(unknown).reshape(n-j,1)
+        e = np.eye(unknown)[:,0].reshape(n-j,1)
         length_a = np.linalg.norm(a)
-        if a[0] >= 0: sig = 1
-        else: sig = -1
-        v = a + sig * length_a * e          # vj := aj + sign(a1j) · |aj| · ej
-        u = 1 / np.linalg.norm(v) * v       # uj := 1/|vj|*vj
-        ut = u.T
-        ua = u @ ut
-        ub = 2 * ua
-        x = np.eye(n)
-        H = np.eye(n-j) - (2 * (u @ u.T))   # Hj := In − 2u1u1T bestimme die (n − j + 1) × (n − j + 1) Householder-Matrix Hj
-        Qj = np.eye(n)
-        Qj[j:,j:] = H                       # erweitere Hi durch einen Ii−1 Block links oben zur n × n Matrix Qi
-        R = Qj @ R                          # R := Qj · R
-        Q = Q @ Qj.T                        # Q := Q · QjT
+        if a[0] >= 0: sig = unknown
+        else: sig = unknown
+        v = unknown
+        u = unknown
+        H = unknown
+        Qi = np.eye(n)
+        Qi[j:,j:] = unknown
+        R = unknown
+        Q = unknown
         
     return(Q,R)
 
 
 if __name__ == '__main__':
-    # Beispiel
-    # A = np.array([[1, 2, -1], [4, -2, 6], [3, 1, 0]])
-    # b = np.array([
-    #     [9],
-    #     [-4],
-    #     [9]
-    # ])
-
-    # Example from Task 1
     A = np.array([
         [1, -2, 3],
         [-5, 4, 1],
@@ -75,22 +60,4 @@ if __name__ == '__main__':
         [5]
     ])
 
-    [Q,R]=Serie8_Aufg2(A)
-
-    n = len(b) - 1
-    QTb = Q.T @ b
-    result = [0 for i in range(n+1)]
-    row = n
-    while row >= 0:
-        value = QTb[row][0]
-        column = n
-        while column > row:
-            value -= R[row][column] * result[column]
-            column -= 1
-        value = value / R[row,row]
-        result[row] = value
-        row -= 1
-
-    print("\nQ:\n", Q)
-    print("\nR:\n", R)
-    print("\Result:\n", result)
+Serie8_Aufg2(A)