Task: LU decomposition







Python: from pprint import pprint

def matrixMul(A, B):
    TB = zip(*B)
    return [[sum(ea*eb for ea,eb in zip(a,b)) for b in TB] for a in A]

def pivotize(m):
    
    n = len(m)
    ID = [[float(i == j) for i in xrange(n)] for j in xrange(n)]
    for j in xrange(n):
        row = max(xrange(j, n), key=lambda i: abs(m[i][j]))
        if j != row:
            ID[j], ID[row] = ID[row], ID[j]
    return ID

def lu(A):
    
    n = len(A)
    L = [[0.0] * n for i in xrange(n)]
    U = [[0.0] * n for i in xrange(n)]
    P = pivotize(A)
    A2 = matrixMul(P, A)
    for j in xrange(n):
        L[j][j] = 1.0
        for i in xrange(j+1):
            s1 = sum(U[k][j] * L[i][k] for k in xrange(i))
            U[i][j] = A2[i][j] - s1
        for i in xrange(j, n):
            s2 = sum(U[k][j] * L[i][k] for k in xrange(j))
            L[i][j] = (A2[i][j] - s2) / U[j][j]
    return (L, U, P)

a = [[1, 3, 5], [2, 4, 7], [1, 1, 0]]
for part in lu(a):
    pprint(part, width=19)
    print
print
b = [[11,9,24,2],[1,5,2,6],[3,17,18,1],[2,5,7,1]]
for part in lu(b):
    pprint(part)
    print


VB: 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