Data commit

Task/LU-decomposition/VBA/lu-decomposition.vba

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+Option Base 1
+Private Function pivotize(m As Variant) As Variant
+    Dim n As Integer: n = UBound(m)
+    Dim im() As Double
+    ReDim im(n, n)
+    For i = 1 To n
+        For j = 1 To n
+            im(i, j) = 0
+        Next j
+        im(i, i) = 1
+    Next i
+    For i = 1 To n
+        mx = Abs(m(i, i))
+        row_ = i
+        For j = i To n
+            If Abs(m(j, i)) > mx Then
+                mx = Abs(m(j, i))
+                row_ = j
+            End If
+        Next j
+        If i <> Row Then
+            For j = 1 To n
+                tmp = im(i, j)
+                im(i, j) = im(row_, j)
+                im(row_, j) = tmp
+            Next j
+        End If
+    Next i
+    pivotize = im
+End Function
+
+Private Function lu(a As Variant) As Variant
+    Dim n As Integer: n = UBound(a)
+    Dim l() As Double
+    ReDim l(n, n)
+    For i = 1 To n
+        For j = 1 To n
+            l(i, j) = 0
+        Next j
+    Next i
+    u = l
+    p = pivotize(a)
+    a2 = WorksheetFunction.MMult(p, a)
+    For j = 1 To n
+        l(j, j) = 1#
+        For i = 1 To j
+            sum1 = 0#
+            For k = 1 To i
+                sum1 = sum1 + u(k, j) * l(i, k)
+            Next k
+            u(i, j) = a2(i, j) - sum1
+        Next i
+        For i = j + 1 To n
+            sum2 = 0#
+            For k = 1 To j
+                sum2 = sum2 + u(k, j) * l(i, k)
+            Next k
+            l(i, j) = (a2(i, j) - sum2) / u(j, j)
+        Next i
+    Next j
+    Dim res(4) As Variant
+    res(1) = a
+    res(2) = l
+    res(3) = u
+    res(4) = p
+    lu = res
+End Function
+
+Public Sub main()
+
+    a = [{1, 3, 5; 2, 4, 7; 1, 1, 0}]
+    Debug.Print "== a,l,u,p: =="
+    result = lu(a)
+    For i = 1 To 4
+        For j = 1 To UBound(result(1))
+            For k = 1 To UBound(result(1), 2)
+                Debug.Print result(i)(j, k),
+            Next k
+            Debug.Print
+        Next j
+        Debug.Print
+    Next i
+    a = [{11, 9,24, 2; 1, 5, 2, 6; 3,17,18, 1; 2, 5, 7, 1}]
+    Debug.Print "== a,l,u,p: =="
+    result = lu(a)
+    For i = 1 To 4
+        For j = 1 To UBound(result(1))
+            For k = 1 To UBound(result(1), 2)
+                Debug.Print Format(result(i)(j, k), "0.#####"),
+            Next k
+            Debug.Print
+        Next j
+        Debug.Print
+    Next i
+End Sub