Performs QR decomposition of the current matrix object.

Syntax

MatrixObject.QR Q, R

Parameters

Q

Optional. A matrix object variable that, upon exit, will contain the reference to a matrix representing the orthogonal part of the QR decomposition.

R

Optional. A matrix object variable that, upon exit, will contain the reference to a matrix representing the upper triangular part of the QR decomposition.

Remarks

If any of Q or R parameters is not set or omitted, this parameter will be not calculated.

Number of matrix rows must be greater or equal to number of matrix columns.

The QR method is supported only in Advanced and Advanced II editions of ShortName.

Error Codes

Error 1318 will be returned if the number of matrix rows is not equal or greater than the number of matrix columns.

Example

This example demonstrates the use of QR method.

Private Sub MatrixQR()

Dim A As New Matrix
Dim Q As New Matrix
Dim R As New Matrix
    
    'initializing matrix A
    A.Size 5, 3
    'fill with random values
    A.FillRandom
    'perform QR decomposition
    A.QR Q, R
    
    'print results
    Debug.Print "A ="
    Debug.Print A.GetString
    Debug.Print "Q ="
    Debug.Print Q.GetString
    Debug.Print "R="
    Debug.Print R.GetString
    
    'the product QxR should be equal to initial matrix
    Debug.Print "Q x R ="
    Debug.Print Q.Times(R).GetString
    
    'check that Q is orthogonal Qt x Q = 1
    'Qt = transpose of Q, 1 = identity matrix
    Debug.Print "Qt x Q ="
    Debug.Print Q.Transpose.Times(Q).GetString
    
End Sub

Output

A =
| 6.000 2.000 8.000 |
| 6.000 5.000 4.000 |
| 9.000 8.000 7.000 |
| 2.000 9.000 7.000 |
| 5.000 3.000 0.000 |

Q =
| -0.445  0.355  0.757 |
| -0.445 -0.019 -0.163 |
| -0.667 -0.091 -0.125 |
| -0.148 -0.921  0.226 |
| -0.371  0.130 -0.578 |

R=
| -13.491 -10.896 -11.045 |
|   0.000  -8.017  -4.323 |
|   0.000   0.000   6.110 |

Q x R =
| 6.000 2.000 8.000 |
| 6.000 5.000 4.000 |
| 9.000 8.000 7.000 |
| 2.000 9.000 7.000 |
| 5.000 3.000 0.000 |

Qt x Q =
| 1.000 0.000 0.000 |
| 0.000 1.000 0.000 |
| 0.000 0.000 1.000 |

See Also

Cholesky Method | LU Method | SVD Method

Applies To: Matrix | CMatrix