Difference between revisions of "ApCoCoA-1:Num.QR"
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| − | <command> | + | {{Version|1}} |
| + | <command> | ||
<title>Num.QR</title> | <title>Num.QR</title> | ||
<short_description>Computes the QR-decomposition of a matrix.</short_description> | <short_description>Computes the QR-decomposition of a matrix.</short_description> | ||
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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. | <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 QR-decomposition of a matrix using the external library Lapack, i.e. the matrix <tt>A</tt> will be decomposed into the product of an orthogonal matrix <tt>Q</tt> and an upper-right triangular matrix <tt>R</tt>. | |
<itemize> | <itemize> | ||
| − | <item>@param <em>A</em> | + | <item>@param <em>A</em> The matrix to decompose.</item> |
| − | <item>@return An orthogonal matrix Q and an upper-right triangular matrix R such that Q*R=A.</item> | + | <item>@return An orthogonal matrix <tt>Q</tt> and an upper-right triangular matrix <tt>R</tt> such that <tt>Q*R=A</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]); | Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]); | ||
| − | Num.QR(Points); | + | QR := Num.QR(Points); |
| + | Dec(QR[1]*QR[2],3); | ||
| + | |||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
| − | + | Mat([ | |
| − | [ | + | ["0.999", "1.999", "2.999"], |
| − | [ | + | ["1.999", "2.999", "3.999"], |
| − | [ | + | ["2.999", "3.999", "4.999"] |
| − | ]) | + | ]) |
| − | |||
| − | |||
| − | |||
| − | |||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | <see>Num.SVD</see> | + | <see>ApCoCoA-1:Num.SVD|Num.SVD</see> |
| − | <see>Num.EigenValues</see> | + | <see>ApCoCoA-1:Num.EigenValues|Num.EigenValues</see> |
| − | <see>Num.EigenValuesAndVectors</see> | + | <see>ApCoCoA-1:Num.EigenValuesAndVectors|Num.EigenValuesAndVectors</see> |
| − | <see>Num.EigenValuesAndAllVectors</see> | + | <see>ApCoCoA-1:Num.EigenValuesAndAllVectors|Num.EigenValuesAndAllVectors</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 45: | Line 45: | ||
<key>qr</key> | <key>qr</key> | ||
<key>numerical.qr</key> | <key>numerical.qr</key> | ||
| − | <wiki-category>Package_numerical</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_numerical</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:48, 29 October 2020
| This article is about a function from ApCoCoA-1. |
Num.QR
Computes the QR-decomposition of a matrix.
Syntax
Num.QR(A:MAT):[Q:MAT,R: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 QR-decomposition of a matrix using the external library Lapack, i.e. the matrix A will be decomposed into the product of an orthogonal matrix Q and an upper-right triangular matrix R.
@param A The matrix to decompose.
@return An orthogonal matrix Q and an upper-right triangular matrix R such that Q*R=A.
Example
Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]); QR := Num.QR(Points); Dec(QR[1]*QR[2],3); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Mat([ ["0.999", "1.999", "2.999"], ["1.999", "2.999", "3.999"], ["2.999", "3.999", "4.999"] ]) -------------------------------
See also
