ApCoCoA-1:Num.ProjectAVI: Difference between revisions

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   <command>
   {{Version|1}}
     <title>Numerical.ProjectAVI</title>
<command>
     <short_description>Calculates the least squares solution to the general problem Ax=b, where x are coefficients of an order ideal</short_description>
     <title>Num.ProjectAVI</title>
     <short_description>Computes the least squares solution of the general problem <tt>Ax=b</tt>, where <tt>x</tt> are coefficients of an order ideal.</short_description>
<syntax>
<syntax>
Num.ProjectAVI(Mat:Matrix, Vec:Matrix, OI:PolyList):Poly;
Num.ProjectAVI(Mat:MAT, Vec:MAT, OI:LIST):POLY
</syntax>
</syntax>
     <description>
     <description>
{{ApCoCoAServer}} Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.
<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/>
Calculates the least squares solution to the general problem Ax=b, when there is no exact solution. The solution x is interpreted as the coefficients of the terms in the order ideal.  
This command computes the least squares solution of the general problem <tt>Ax=b</tt>, if there is no exact solution. The solution <tt>x</tt> has to be interpreted as the coefficients of the terms in the order ideal.  


<itemize>
<itemize>
<item>@param <em>Mat</em> Matrix A</item>
<item>@param <em>Mat</em> Matrix <tt>A</tt></item>
<item>@param <em>Vec</em> Vector B in matrix form.</item>
<item>@param <em>Vec</em> Vector <tt>B</tt> as a matrix.</item>
<item>@param <em>OI</em> Order Ideal</item>
<item>@param <em>OI</em> Order Ideal</item>
<item>@return The least squares soltion to Ax=b interpreted as coefficients of OI.</item>
<item>@return The least squares solution of <tt>Ax=b</tt> interpreted as coefficients of <tt>OI</tt>.</item>
</itemize>
</itemize>


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     </description>
     </description>
     <seealso>
     <seealso>
       <see>Introduction to CoCoAServer</see>
       <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
     </seealso>
     </seealso>
     <types>
     <types>
       <type>apcocoaserver</type>
       <type>apcocoaserver</type>
      <type>matrix</type>
     </types>
     </types>
    <key>numerical.ProjectAVI</key>
     <key>Num.ProjectAVI</key>
     <key>Num.ProjectAVI</key>
     <key>ProjectAVI</key>
     <key>ProjectAVI</key>
     <wiki-category>Package_numerical</wiki-category>
    <key>numerical.projectavi</key>
     <wiki-category>ApCoCoA-1:Package_numerical</wiki-category>
   </command>
   </command>

Latest revision as of 13:47, 29 October 2020

This article is about a function from ApCoCoA-1.

Num.ProjectAVI

Computes the least squares solution of the general problem Ax=b, where x are coefficients of an order ideal.

Syntax

Num.ProjectAVI(Mat:MAT, Vec:MAT, OI:LIST):POLY

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 least squares solution of the general problem Ax=b, if there is no exact solution. The solution x has to be interpreted as the coefficients of the terms in the order ideal.

  • @param Mat Matrix A

  • @param Vec Vector B as a matrix.

  • @param OI Order Ideal

  • @return The least squares solution of Ax=b interpreted as coefficients of OI.


Example

Dec(Num.ProjectAVI([[1,1],[0,1],[1,1]],[[0],[1],[0]],[x,y]),2);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
["-0.99 x +1 y "]
-------------------------------

See also

Introduction to CoCoAServer