fix mistake in formula of Q in QR-split

qr.py

@@ -16,8 +16,12 @@ def givens_rotation(A, i, j):
         np.ndarray: Rotation Matrix ``J`` as above.
     """
     # TODO
-    c = abs(A[j][j]) / ((A[i][j] ** 2 + A[j][j] ** 2) ** 0.5)
-    s = abs(A[i][j]) / ((A[i][j] ** 2 + A[j][j] ** 2) ** 0.5)
+    if abs(A[j][j]) == 0.0:
+        p = ((A[i][j] ** 2 + A[j][j] ** 2) ** 0.5)
+    else:
+        p = np.sign(A[j][j]) * ((A[i][j] ** 2 + A[j][j] ** 2) ** 0.5)
+    c = A[j][j] / p
+    s = A[i][j] / p
     n, m = np.shape(A)
     J = np.eye(n)
     J[j][j] = c
@@ -99,7 +103,15 @@ def main():
     Hier kann beliebiger Testcode stehen, der bei der Korrektur vollständig
     ignoriert wird.
     """
-    pass
+    arr1 = np.array(([3, -4], [3, 5]))
+    J1 = givens_rotation(arr1, 1, 0)
+    arr2 = np.array(([3, 4], [3, 5]))
+    J2 = givens_rotation(arr2, 1, 0)
+    Q, R = qr_decompose(arr1)
+    print(f"J1= {J1}")
+    print(f"J2= {J2}")
+    print(f"J1*arr= {np.dot(J1, arr1)}")
+    print(f"J2*arr= {np.dot(J2, arr2)}")
 
 
 if __name__ == "__main__": main()
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