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

From ApCoCoAWiki
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   <command>
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   {{Version|1}}
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<command>
 
     <title>Num.QR</title>
 
     <title>Num.QR</title>
 
     <short_description>Computes the QR-decomposition of a matrix.</short_description>
 
     <short_description>Computes the QR-decomposition of a matrix.</short_description>
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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>
 
</itemize>
 
</itemize>
  
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-------------------------------
 
-------------------------------
 
Mat([
 
Mat([
   [<quotes>0.999</quotes>, <quotes>1.999</quotes>, <quote>2.999</quotes>],
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   ["0.999", "1.999", "2.999"],
   [<quotes>1.999</quotes>, <quotes>2.999</quotes>, <quote>3.999</quotes>],
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   ["1.999", "2.999", "3.999"],
   [<quotes>2.999</quotes>, <quotes>3.999</quotes>, <quote>4.999</quotes>]
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   ["2.999", "3.999", "4.999"]
 
])
 
])
 
-------------------------------
 
-------------------------------
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     </description>
 
     </description>
 
     <seealso>
 
     <seealso>
       <see>Introduction to CoCoAServer</see>
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       <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
       <see>Num.SVD</see>
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       <see>ApCoCoA-1:Num.SVD|Num.SVD</see>
       <see>Num.EigenValues</see>
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       <see>ApCoCoA-1:Num.EigenValues|Num.EigenValues</see>
       <see>Num.EigenValuesAndVectors</see>
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       <see>ApCoCoA-1:Num.EigenValuesAndVectors|Num.EigenValuesAndVectors</see>
       <see>Num.EigenValuesAndAllVectors</see>
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       <see>ApCoCoA-1:Num.EigenValuesAndAllVectors|Num.EigenValuesAndAllVectors</see>
 
     </seealso>
 
     </seealso>
 
     <types>
 
     <types>
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     <key>qr</key>
 
     <key>qr</key>
 
     <key>numerical.qr</key>
 
     <key>numerical.qr</key>
     <wiki-category>Package_numerical</wiki-category>
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     <wiki-category>ApCoCoA-1:Package_numerical</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 13:48, 29 October 2020

This article is about a function from ApCoCoA-1.

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([
  ["0.999", "1.999", "2.999"],
  ["1.999", "2.999", "3.999"],
  ["2.999", "3.999", "4.999"]
])
-------------------------------

See also

Introduction to CoCoAServer

Num.SVD

Num.EigenValues

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors