Difference between revisions of "ApCoCoA-1:Num.EigenValuesAndAllVectors"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
| − | <title> | + | <title>Num.EigenValuesAndAllVectors</title> |
| − | <short_description>eigenvalues and left and right eigenvectors of a matrix</short_description> | + | <short_description>Computes eigenvalues and left and right eigenvectors of a matrix</short_description> |
<syntax> | <syntax> | ||
| − | + | Num.EigenValuesAndAllVectors(A:Matrix):[B:Matrix, C:Matrix, D:Matrix, E:Matrix, F: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 | + | This function returns a List of five matrices, containing numerical approximation to A's eigenvalues and right and left eigenvectors. |
| − | + | The input matrix A has to be a square matrix! | |
| − | + | The output [B:Matrix, C:Matrix, D:Matrix, E:Matrix, F:Matrix] contains a matrix B, where each column contains one of A's eigenvalues. The first row contains the eigenvalue's real part, the second row the imaginary. | |
| − | The output | + | The matrices C, D, E and F all have the same dimensions as A. Column j of matrix C contains the real part of the right eigenvector corresponding to eigenvalue j and column j of matrix D contains the imaginary part of the right eigenvector correspsonding to eigenvalue j. The matrices E and F store the left eigenvectors in the same way as C and D. |
| − | The | ||
<example> | <example> | ||
A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); | A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); | ||
| − | + | Dec(Num.EigenValuesAndAllVectors(A),3); | |
| − | -- CoCoAServer: computing Cpu Time = 0. | + | -- CoCoAServer: computing Cpu Time = 0.016 |
------------------------------- | ------------------------------- | ||
[Mat([ | [Mat([ | ||
| − | [ | + | ["28.970", "-13.677", "0.353", "0.353"], |
| − | [0, 0, | + | ["0", "0", "3.051", "-3.051"] |
]), Mat([ | ]), Mat([ | ||
| − | [ | + | ["0.538", "-0.600", "0.389", "0.389"], |
| − | [ | + | ["0.311", "-0.222", "-0.442", "-0.442"], |
| − | [ | + | ["0.427", "0.174", "0.050", "0.050"], |
| − | [ | + | ["0.656", "0.748", "0", "0"] |
]), Mat([ | ]), Mat([ | ||
| − | [ | + | ["0", "0", "-0.174", "0.174"], |
| − | [ | + | ["0", "0", "0.139", "-0.139"], |
| − | [ | + | ["0", "0", "0.265", "-0.265"], |
| − | [ | + | ["0", "0", "-0.727", "0.727"] |
| + | ]), Mat([ | ||
| + | ["0.394", "-0.581", "0.260", "0.260"], | ||
| + | ["0.435", "-0.442", "-0.547", "-0.547"], | ||
| + | ["0.763", "0.621", "0", "0"], | ||
| + | ["0.268", "0.281", "0.046", "0.046"] | ||
| + | ]), Mat([ | ||
| + | ["0", "0", "-0.031", "0.031"], | ||
| + | ["0", "0", "-0.301", "0.301"], | ||
| + | ["0", "0", "0.680", "-0.680"], | ||
| + | ["0", "0", "-0.274", "0.274"] | ||
])] | ])] | ||
------------------------------- | ------------------------------- | ||
| Line 45: | Line 54: | ||
<type>cocoaserver</type> | <type>cocoaserver</type> | ||
</types> | </types> | ||
| − | <key> | + | <key>Num.EigenValuesAndAllVectors</key> |
| − | <key> | + | <key>EigenValuesAndAllVectors</key> |
<wiki-category>Package_Numerical</wiki-category> | <wiki-category>Package_Numerical</wiki-category> | ||
</command> | </command> | ||
Revision as of 13:54, 30 March 2009
Num.EigenValuesAndAllVectors
Computes eigenvalues and left and right eigenvectors of a matrix
Syntax
Num.EigenValuesAndAllVectors(A:Matrix):[B:Matrix, C:Matrix, D:Matrix, E:Matrix, F: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.
This function returns a List of five matrices, containing numerical approximation to A's eigenvalues and right and left eigenvectors.
The input matrix A has to be a square matrix!
The output [B:Matrix, C:Matrix, D:Matrix, E:Matrix, F:Matrix] contains a matrix B, where each column contains one of A's eigenvalues. The first row contains the eigenvalue's real part, the second row the imaginary. The matrices C, D, E and F all have the same dimensions as A. Column j of matrix C contains the real part of the right eigenvector corresponding to eigenvalue j and column j of matrix D contains the imaginary part of the right eigenvector correspsonding to eigenvalue j. The matrices E and F store the left eigenvectors in the same way as C and D.
Example
A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); Dec(Num.EigenValuesAndAllVectors(A),3); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- [Mat([ ["28.970", "-13.677", "0.353", "0.353"], ["0", "0", "3.051", "-3.051"] ]), Mat([ ["0.538", "-0.600", "0.389", "0.389"], ["0.311", "-0.222", "-0.442", "-0.442"], ["0.427", "0.174", "0.050", "0.050"], ["0.656", "0.748", "0", "0"] ]), Mat([ ["0", "0", "-0.174", "0.174"], ["0", "0", "0.139", "-0.139"], ["0", "0", "0.265", "-0.265"], ["0", "0", "-0.727", "0.727"] ]), Mat([ ["0.394", "-0.581", "0.260", "0.260"], ["0.435", "-0.442", "-0.547", "-0.547"], ["0.763", "0.621", "0", "0"], ["0.268", "0.281", "0.046", "0.046"] ]), Mat([ ["0", "0", "-0.031", "0.031"], ["0", "0", "-0.301", "0.301"], ["0", "0", "0.680", "-0.680"], ["0", "0", "-0.274", "0.274"] ])] -------------------------------
See also
Numerical.EigenValuesAndVectors
