Difference between revisions of "ApCoCoA-1:Num.LeastSquaresQR"
From ApCoCoAWiki
m (replaced <quotes> tag by real quotes) |
|||
| (7 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> | + | <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): | + | 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/> | ||
| − | + | 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> | ||
| Line 21: | Line 22: | ||
-- CoCoAServer: computing Cpu Time = 0 | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
| − | + | ["-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> | ||
| Line 38: | Line 36: | ||
<key>LeastSquaresQR</key> | <key>LeastSquaresQR</key> | ||
<key>numerical.leastsquaresqr</key> | <key>numerical.leastsquaresqr</key> | ||
| − | <wiki-category>Package_numerical</wiki-category> | + | <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
