IMath.Mqr

Syntax

Mqr(Data: Array; Var Q: Array; Var R: Array);

Parameters

Data. Input parameter, two-dimension array.

NOTE. The input two-dimension array can have the n×m size (rectangular matrix) or n×n (square matrix).

Q. Input parameter, two-dimension array of the n×n size.

R. Output parameter, two-dimension array of the n×m size.

Description

The Mqr method returns the result of QR-decomposition of a real matrix.

Comments

QR-decomposition of matrix is presenting of matrix as a product of square orthogonal matrix Q and an upper triangular matrix R. The product of the Q·R matrices results in the source matrix.

The householder transformation is used to calculate QR decomposition.

Example

To execute the example, add a link to the MathFin system assembly.

Sub UserProc;
Var
    a: Array Of Double;
    Q, R: Array Of Double;
    i,j: Integer;
    str: String;
Begin
    a := New double[2,4];
    // Input matrix:
    a[0,0] := 1;    a[0,1] := 1;    a[0,2] := 2;        a[0,3] := 0;
    a[1,0] := 1;    a[1,1] := 0;    a[1,2] := -1.4142;  a[1,3] := 0;
    // QR-decomposition:
    math.Mqr(a, Q, R);
    Debug.WriteLine("Q =");
    For i := 0 To Q.GetUpperBound(1) Do
        str := "";
        For j := 0 To Q.GetUpperBound(2) Do
            str := str + Q[i, j].ToString + "; ";
        End For;
        Debug.WriteLine(str);
    End For;
    Debug.WriteLine("R =");
    For i := 0 To R.GetUpperBound(1) Do
        str := "";
        For j := 0 To R.GetUpperBound(2) Do
            str := str + R[i, j].ToString + "; ";
        End For;
        Debug.WriteLine(str);
    End For;
End Sub UserProc;

After executing the example the console window displays QR-decomposition of the source matrix:

Q =

-0.707106781186547; 0.707106781186547;

-0.707106781186547; -0.707106781186547;

R =

-1.41421356237309; -0.707106781186547; -0.414223152419079; 0;

0; 0.707106781186547; 2.41420397232711; 0;