# Difference between revisions of "ApCoCoA-1:Num.QR"

From ApCoCoAWiki

Line 8: | Line 8: | ||

<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||

<par/> | <par/> | ||

− | + | This command computes the QR-decomposition of a matrix using the external library Lapack, i.e. the matrix <tt>A</tt> will be decomposed into the product of an orthogonal matrix <tt>Q</tt> and an upper-right triangular matrix <tt>R</tt>. | |

<itemize> | <itemize> | ||

− | <item>@param <em>A</em> | + | <item>@param <em>A</em> The matrix to decompose.</item> |

− | <item>@return An orthogonal matrix Q and an upper-right triangular matrix R such that Q*R=A.</item> | + | <item>@return An orthogonal matrix <tt>Q</tt> and an upper-right triangular matrix <tt>R</tt> such that <tt>Q*R=A</tt>.</item> |

</itemize> | </itemize> | ||

## Revision as of 11:29, 8 July 2009

## Num.QR

Computes the QR-decomposition of a matrix.

### Syntax

Num.QR(A:MAT):[Q:MAT,R:MAT]

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

This command computes the QR-decomposition of a matrix using the external library Lapack, i.e. the matrix `A` will be decomposed into the product of an orthogonal matrix `Q` and an upper-right triangular matrix `R`.

@param

*A*The matrix to decompose.@return An orthogonal matrix

`Q`and an upper-right triangular matrix`R`such that`Q*R=A`.

#### Example

Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]); QR := Num.QR(Points); Dec(QR[1]*QR[2],3); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Mat([ [<quotes>0.999</quotes>, <quotes>1.999</quotes>, <quotes>2.999</quotes>], [<quotes>1.999</quotes>, <quotes>2.999</quotes>, <quotes>3.999</quotes>], [<quotes>2.999</quotes>, <quotes>3.999</quotes>, <quotes>4.999</quotes>] ]) -------------------------------

### See also