Difference between revisions of "ApCoCoA-1:Num.LeastSquaresQR"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Num.LeastSquaresQR</title> | <title>Num.LeastSquaresQR</title> | ||
| − | <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):MAT | ||
| Line 8: | Line 8: | ||
<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/> | ||
| − | + | 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 | + | <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> | ||
Revision as of 09:33, 8 July 2009
Num.LeastSquaresQR
Computes the least squares solution of the linear system of equations 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.
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 ------------------------------- Mat([ [<quotes>-0.99</quotes>], [<quotes>1</quotes>] ]) -------------------------------
See also
