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

From ApCoCoAWiki
m (replaced <quotes> tag by real quotes)
 
(8 intermediate revisions by 3 users not shown)
Line 1: Line 1:
   <command>
+
   {{Version|1}}
 +
<command>
 
     <title>Num.LeastSquaresQR</title>
 
     <title>Num.LeastSquaresQR</title>
     <short_description>Calculates the least squares solution to the general problem Ax=b</short_description>
+
     <short_description>Computes the least squares solution of the linear system of equations <tt>Ax=b</tt>.</short_description>
 
<syntax>
 
<syntax>
Num.LeastSquaresQR(Mat:MAT, Vec:MAT):MAT;
+
Num.LeastSquaresQR(Mat:MAT, Vec:MAT):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
 
<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 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.
+
This command computes the least squares solution of the linear system of equations <tt>Ax=b</tt>, if there is no exact solution. The matrix <tt>Mat</tt> must have the same number of rows as <tt>Vec</tt>.
The QR decomposition of Mat is used to find the solution.  
+
The QR decomposition of <tt>Mat</tt> is used to find the solution.  
  
 
<itemize>
 
<itemize>
<item>@param <em>Mat</em> Matrix A</item>
+
<item>@param <em>Mat</em> Matrix <tt>A</tt> of the linear system of equations.</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>@return The least squares solution to Ax=b.</item>
+
<item>@return The least squares solution to <tt>Ax=b</tt>.</item>
 
</itemize>
 
</itemize>
  
Line 21: Line 22:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Mat([
+
["-0.99", "1"]
  ["-0.99"],
 
  ["1"]
 
])
 
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
 
     </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>Num.LeastSquaresQR</key>
 
     <key>Num.LeastSquaresQR</key>
 
     <key>LeastSquaresQR</key>
 
     <key>LeastSquaresQR</key>
     <wiki-category>Package_numerical</wiki-category>
+
    <key>numerical.leastsquaresqr</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.LeastSquaresQR

Computes the least squares solution of the linear system of equations Ax=b.

Syntax

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

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 linear system of equations Ax=b, if 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 of the linear system of equations.

  • @param Vec Vector B as a matrix.

  • @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
-------------------------------
["-0.99", "1"]
-------------------------------

See also

Introduction to CoCoAServer