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

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<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/>
Calculates the QR decomposition of a matrix using Lapack.
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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> Matrix A</item>
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<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>
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<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>
 
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</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

Introduction to CoCoAServer

Num.SVD

Num.EigenValues

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors