LU Decomposition

Performs LU Decomposition of the current matrix object.

Syntax

MatrixObject.LU L, U, PermIndex, PermSign

Parameters

L: Optional. A matrix object variable that, on exit, will contain the reference to a matrix representing the lower triangular part of the LU decomposition.
U: Optional. A matrix object variable that, on exit, will contain the reference to a matrix representing the upper triangular part of the LU decomposition.
PermIndex: Optional. A variant variable that, on exit, will contain an array of integers representing the row permutations effected by the partial pivoting.
PermSign: Optional. Long Integer. On exit will contain +1 or -1 depending on whether the number of row interchanges was even or odd, respectively.

Remarks

LU decomposition is not possible for a singular matrix.

Partial pivoting is used, so that L x U matrix product returns the initial matrix with rows permutated according to the row permutation index which is returned in parameter PermIndex.

Error Codes

Error 1305 will be returned if the matrix is not square.

Error 1313 will be returned if the the decomposition is not possible due to the matrix being singular.

Example

This example demonstrates the use of LU method.

Private Sub MatrixLU()

Dim A As Matrix, L As Matrix, U As Matrix, R As Matrix
Dim permIndex, pSign As Long

    'first we creare a new matrix and we
    'fill it with random values
    Set A = New Matrix
    A.Size 5, 5
    A.FillRandom

    'and we print it
    Debug.Print "A= "
    Debug.Print A.GetString

    'then we perform the LU decomposition
    'perIndex() will return the row exchanges
    Set L = New Matrix
    Set U = New Matrix
    A.LU L, U, permIndex, pSign

    'and we print the results
    Debug.Print "L="
    Debug.Print L.GetString
    Debug.Print "U="
    Debug.Print U.GetString

    'now we verify the results finding
    'the product R = LxU
    Set R = L.Times(U)

    'and we rearrange rows using
    'the permutation index
    R.ReorderRows permIndex

    Debug.Print "R=LxU"
    Debug.Print R.GetString

    'please notice that R equals to
    'original matrix
End Sub

    Debug.Print "L2="
    Debug.Print L2.GetString

    'please notice that L2 equals matrix L
    '
End Sub

Output