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

From ApCoCoAWiki
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   <command>
 
   <command>
     <title>Numerical.LeastSquaresQR</title>
+
     <title>Num.LeastSquaresQR</title>
 
     <short_description>Calculates the least squares solution to the general problem Ax=b</short_description>
 
     <short_description>Calculates the least squares solution to the general problem Ax=b</short_description>
 
<syntax>
 
<syntax>
Num.LeastSquaresQR(Mat:Matrix, Vec:Matrix):Matrix;
+
Num.LeastSquaresQR(Mat:MAT, Vec:MAT):MAT;
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
{{ApCoCoAServer}} Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.
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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.
 
+
<par/>
 
Calculates the least squares solution to the general problem Ax=b, when there is no exact solution. The matrix Mat must have the same number of rows as Vec.
 
Calculates the least squares solution to the general problem Ax=b, when there is no exact solution. The matrix Mat must have the same number of rows as Vec.
The QR decompostion of Mat is used to find the solution.  
+
The QR decomposition of Mat is used to find the solution.  
  
 
<itemize>
 
<itemize>
 
<item>@param <em>Mat</em> Matrix A</item>
 
<item>@param <em>Mat</em> Matrix A</item>
 
<item>@param <em>Vec</em> Vector B in matrix form.</item>
 
<item>@param <em>Vec</em> Vector B in matrix form.</item>
<item>@return The least squares soltion to Ax=b.</item>
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<item>@return The least squares solution to Ax=b.</item>
 
</itemize>
 
</itemize>
  
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       <type>apcocoaserver</type>
 
       <type>apcocoaserver</type>
 
     </types>
 
     </types>
    <key>numerical.LeastSquaresQR</key>
 
 
     <key>Num.LeastSquaresQR</key>
 
     <key>Num.LeastSquaresQR</key>
 
     <key>LeastSquaresQR</key>
 
     <key>LeastSquaresQR</key>
 
     <wiki-category>Package_numerical</wiki-category>
 
     <wiki-category>Package_numerical</wiki-category>
 
   </command>
 
   </command>

Revision as of 16:43, 23 April 2009

Num.LeastSquaresQR

Calculates the least squares solution to the general problem Ax=b

Syntax

Num.LeastSquaresQR(Mat:MAT, Vec:MAT):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.

Calculates the least squares solution to the general problem Ax=b, when there is no exact solution. The matrix Mat must have the same number of rows as Vec.

The QR decomposition of Mat is used to find the solution.

  • @param Mat Matrix A

  • @param Vec Vector B in matrix form.

  • @return The least squares solution to Ax=b.

Example

Dec(Num.LeastSquaresQR([[1,1],[0,1],[1,1]],[[0],[1],[0]]),2);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Mat([
  ["-0.99"],
  ["1"]
])
-------------------------------

See also

Introduction to CoCoAServer