Task: LU decomposition




Go: package main

import "fmt"
    
type matrix [][]float64

func zero(n int) matrix {
    r := make([][]float64, n)
    a := make([]float64, n*n)
    for i := range r {
        r[i] = a[n*i : n*(i+1)]
    } 
    return r 
}
    
func eye(n int) matrix {
    r := zero(n)
    for i := range r {
        r[i][i] = 1
    }
    return r
}   
    
func (m matrix) print(label string) {
    if label > "" {
        fmt.Printf("%s:\n", label)
    }
    for _, r := range m {
        for _, e := range r {
            fmt.Printf(" %9.5f", e)
        }
        fmt.Println()
    }
}

func (a matrix) pivotize() matrix { 
    p := eye(len(a))
    for j, r := range a {
        max := r[j] 
        row := j
        for i := j; i < len(a); i++ {
            if a[i][j] > max {
                max = a[i][j]
                row = i
            }
        }
        if j != row {
            
            p[j], p[row] = p[row], p[j]
        }
    } 
    return p
}

func (m1 matrix) mul(m2 matrix) matrix {
    r := zero(len(m1))
    for i, r1 := range m1 {
        for j := range m2 {
            for k := range m1 {
                r[i][j] += r1[k] * m2[k][j]
            }
        }
    }
    return r
}

func (a matrix) lu() (l, u, p matrix) {
    l = zero(len(a))
    u = zero(len(a))
    p = a.pivotize()
    a = p.mul(a)
    for j := range a {
        l[j][j] = 1
        for i := 0; i <= j; i++ {
            sum := 0.
            for k := 0; k < i; k++ {
                sum += u[k][j] * l[i][k]
            }
            u[i][j] = a[i][j] - sum
        }
        for i := j; i < len(a); i++ {
            sum := 0.
            for k := 0; k < j; k++ {
                sum += u[k][j] * l[i][k]
            }
            l[i][j] = (a[i][j] - sum) / u[j][j]
        }
    }
    return
}

func main() {
    showLU(matrix{
        {1, 3, 5},
        {2, 4, 7},
        {1, 1, 0}})
    showLU(matrix{
        {11, 9, 24, 2},
        {1, 5, 2, 6},
        {3, 17, 18, 1},
        {2, 5, 7, 1}})
}

func showLU(a matrix) {
    a.print("\na")
    l, u, p := a.lu()
    l.print("l")
    u.print("u") 
    p.print("p") 
}





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