Difference between revisions of "ApCoCoA-1:Num.SVD"
From ApCoCoAWiki
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<short_description>singular value decomposition of a matrix</short_description> | <short_description>singular value decomposition of a matrix</short_description> | ||
<syntax> | <syntax> | ||
| − | $numerical.SVD(A:Matrix):[ | + | $numerical.SVD(A:Matrix):[U:Matrix,S:Matrix,VT:Matrix] |
</syntax> | </syntax> | ||
<description> | <description> | ||
{{ApCoCoAServer}} Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support. | {{ApCoCoAServer}} Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support. | ||
| − | This function returns a list of three matrices which form the singular | + | <itemize> |
| + | <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 <formula>[U, S, VT]</formula>. | value decomposition of the input matrix. The list produced is <formula>[U, S, VT]</formula>. | ||
| − | + | </item> | |
| + | </itemize> | ||
<example> | <example> | ||
Revision as of 16:42, 22 April 2009
Numerical.SVD
singular value decomposition of a matrix
Syntax
$numerical.SVD(A:Matrix):[U:Matrix,S:Matrix,VT:Matrix]
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. Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.
@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 <formula>[U, S, VT]</formula>.
Example
D:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10]]); $numerical.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
Numerical.EigenValuesAndVectors
Numerical.EigenValuesAndAllVectors
