Difference between revisions of "ApCoCoA-1:Num.SVD"
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<title>Num.SVD</title> | <title>Num.SVD</title> | ||
<short_description>Computes the singular value decomposition of a matrix.</short_description> | <short_description>Computes the singular value decomposition of a matrix.</short_description> | ||
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[Mat([ | [Mat([ | ||
| − | [ | + | ["-0.473", "-0.666", "-0.575"], |
| − | [ | + | ["-0.415", "-0.407", "0.813"], |
| − | [ | + | ["-0.776", "0.624", "-0.084"] |
]), Mat([ | ]), Mat([ | ||
| − | [ | + | ["33.091", "17.047", "3.365"] |
]), Mat([ | ]), Mat([ | ||
| − | [ | + | ["-0.579", "-0.266", "-0.424", "-0.642"], |
| − | [ | + | ["0.755", "0.119", "-0.159", "-0.624"], |
| − | [ | + | ["-0.265", "0.423", "0.750", "-0.431"], |
| − | [ | + | ["-0.153", "0.857", "-0.480", "0.100"] |
])] | ])] | ||
------------------------------- | ------------------------------- | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | <see>Num.QR</see> | + | <see>ApCoCoA-1:Num.QR|Num.QR</see> |
| − | <see>Num.SingularValues</see> | + | <see>ApCoCoA-1:Num.SingularValues|Num.SingularValues</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> | ||
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<key>svd</key> | <key>svd</key> | ||
<key>num.svd</key> | <key>num.svd</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.SVD
Computes the 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.
This command computes the singular value decomposition of the given matrix A. Let A be a (m x n) matrix. Then A is decomposed into the product of an orthogonal (m x m) matrix U, a transposed matrix VT of an orthogonal (n x n) matrix V and a real (m x n) matrix S, which contains the singular values of the matrix A.
@param A The matrix we want to decompose.
@return A list of three matrices [U, S, VT] such that A=U*S*VT.
Example
D:=[[1,2,7,18],[2,4,9,12],[23,8,9,10]]; Dec(Num.SVD(D),3); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [Mat([ ["-0.473", "-0.666", "-0.575"], ["-0.415", "-0.407", "0.813"], ["-0.776", "0.624", "-0.084"] ]), Mat([ ["33.091", "17.047", "3.365"] ]), Mat([ ["-0.579", "-0.266", "-0.424", "-0.642"], ["0.755", "0.119", "-0.159", "-0.624"], ["-0.265", "0.423", "0.750", "-0.431"], ["-0.153", "0.857", "-0.480", "0.100"] ])] -------------------------------
See also
