EIGENVEC

The EIGENVEC function computes the eigenvectors of an n-by-n real, non-symmetric array using Inverse Subspace Iteration. Use ELMHES and HQR to find the eigenvalues of an n-by-n real, nonsymmetric array.

This routine is written in the IDL language. Its source code can be found in the file eigenvec.pro in the lib subdirectory of the IDL distribution.

Syntax

Result = EIGENVEC( A, Eval [, /DOUBLE] [, ITMAX=value] [, RESIDUAL=variable] )

Return Value

This function returns a complex array with a column dimension equal to n and a row dimension equal to the number of eigenvalues.

Arguments

A

An n-by-n nonsymmetric, single- or double-precision floating-point array.

EVAL

An n-element complex vector of eigenvalues.

Keywords

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

ITMAX

The maximum number of iterations allowed in the computation of each eigenvector. The default value is 4.

RESIDUAL

Use this keyword to specify a named variable that will contain the residuals for each eigenvalue/eigenvector (l/x) pair. The residual is based on the definition Ax - lx = 0 and is an array of the same size and type as that returned by the function. The rows of this array correspond to the residuals for each eigenvalue/eigenvector pair.

Examples

; Define an n-by-n real, nonsymmetric array: 
A = [[1.0, -2.0, -4.0,  1.0], $ 
     [0.0, -2.0,  3.0,  4.0], $ 
     [2.0, -6.0, -1.0,  4.0], $ 
     [3.0, -3.0,  1.0, -2.0]] 
; Compute the eigenvalues of A using double-precision complex 
; arithmetic and print the result: 
eval = HQR(ELMHES(A), /DOUBLE) 
PRINT, 'Eigenvalues: ' 
PRINT, eval 
evec = EIGENVEC(A, eval, RESIDUAL = residual) 
 
; Print the eigenvectors: 
PRINT, 'Eigenvectors:' 
PRINT, evec[*,0], evec[*,1], evec[*,2], evec[*,3] 

IDL prints:

Eigenvalues: 
(  0.26366255, -6.1925899)(  0.26366255, 6.1925899) 
(  -4.9384492,  0.0000000)(  0.41112406, 0.0000000) 
Eigenvectors: 
( 0.0076733129,  -0.42912489)(  0.40651652,  0.32973069) 
(   0.54537624,  -0.28856257)(  0.33149359, -0.22632585) 
(  -0.42145884, -0.081113711)(  0.23867007,  0.46584824) 
(  -0.39497143,   0.47402647)( -0.28990600,  0.27760747) 
(  -0.54965842,    0.0000000)( -0.18401243,   0.0000000) 
(  -0.58124548,    0.0000000)(  0.57111192,   0.0000000) 
(   0.79297048,    0.0000000)(  0.50289130,   0.0000000) 
( -0.049618509,    0.0000000)(  0.34034720,   0.0000000) 

You can check the accuracy of each eigenvalue/eigenvector (l/x) pair by printing the residual array. All residual values should be floating-point zeros.

Version History

Introduced: 4.0

See Also

ELMHES, HQR, LA_EIGENVEC, TRIQL, TRIRED