Difference between revisions of "ApCoCoA-1:Num.SVD"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Num.SVD</title> | <title>Num.SVD</title> | ||
| − | <short_description> | + | <short_description>Singular value decomposition of a matrix.</short_description> |
<syntax> | <syntax> | ||
| − | Num.SVD(A: | + | Num.SVD(A:MAT):[U:MAT,S:MAT,VT:MAT] |
</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. | |
<itemize> | <itemize> | ||
<item>@param <em>A</em> The matrix we want to decompose.</item> | <item>@param <em>A</em> The matrix we want to decompose.</item> | ||
| − | <item>@return This function returns a list of three matrices which form the singular value decomposition of the input matrix. The list produced is [U, S, VT]. | + | <item>@return This function returns a list of three matrices which form the singular value decomposition of the input matrix. The list produced is [U, S, VT].</item> |
| − | </item> | ||
</itemize> | </itemize> | ||
| Line 35: | Line 34: | ||
<seealso> | <seealso> | ||
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
| − | <see> | + | <see>Num.QR</see> |
| − | <see> | + | <see>Num.EigenValues</see> |
| − | <see> | + | <see>Num.EigenValuesAndVectors</see> |
| − | <see> | + | <see>Num.EigenValuesAndAllVectors</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
| + | <type>matrix</type> | ||
</types> | </types> | ||
<key>numerical.svd</key> | <key>numerical.svd</key> | ||
| + | <key>svd</key> | ||
| + | <key>num.svd</key> | ||
<wiki-category>Package_numerical</wiki-category> | <wiki-category>Package_numerical</wiki-category> | ||
</command> | </command> | ||
Revision as of 16:53, 23 April 2009
Num.SVD
Singular value decomposition of a matrix.
Syntax
Num.SVD(A:MAT):[U:MAT,S:MAT,VT: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.
@param A The matrix we want to decompose.
@return This function returns a list of three matrices which form the singular value decomposition of the input matrix. The list produced is [U, S, VT].
Example
D:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10]]); Num.SVD(D); ------------------------------- [Mat([ [-2608957845014309/4503599627370496, 3400715993947695/4503599627370496, -1196230415249177/4503599627370496, -5542055005031021/36028797018963968], [-4803191187447087/18014398509481984, 4289880920686871/36028797018963968, 3813211715037953/9007199254740992, 7724713654272699/9007199254740992], [-7645273287337725/18014398509481984, -5741692259075309/36028797018963968, 3381220959856661/4503599627370496, -540919752203371/1125899906842624], [-5789886178591733/9007199254740992, -2813340077166513/4503599627370496, -7780633724302695/18014398509481984, 3606131681355807/36028797018963968] ]), Mat([ [1164315100749939/35184372088832, 4798366071344577/281474976710656, 3788674137264815/1125899906842624] ]), Mat([ [-8521591816535737/18014398509481984, -3744869794805223/9007199254740992, -6996513907843673/9007199254740992], [-3002889242741505/4503599627370496, -7337996657000815/18014398509481984, 2810636692253967/4503599627370496], [-5187087952406809/9007199254740992, 915526145687749/1125899906842624, -6091132379868651/72057594037927936] ])] -------------------------------
See also
