The eigensystem analysis subroutines are described in this chapter.
The eigensystem analysis subroutines provide solutions to the algebraic
eigensystem analysis problem Az = wz
and the generalized eigensystem analysis problem
Az = wBz ( Table 117). Many of the eigensystem analysis
subroutines use the algorithms presented in Linear Algebra by
Wilkinson and Reinsch [93] or use adaptations of EISPACK routines, as described in
the EISPACK Guide Lecture Notes in Computer Science in reference
[81] or in the EISPACK Guide Extension Lecture Notes in
Computer Science in reference [55]. (EISPACK is available from the sources listed in
reference [49].)
Table 117. List of Eigensystem Analysis Subroutines
| Descriptive Name | Short- Precision Subroutine | Long- Precision Subroutine | Page |
|---|---|---|---|
| Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix |
SGEEV CGEEV |
DGEEV ZGEEV | SGEEV, DGEEV, CGEEV, and ZGEEV--Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix |
| Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix |
SSPEV CHPEV |
DSPEV ZHPEV | SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix |
| Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix |
SSPSV CHPSV |
DSPSV ZHPSV | SSPSV, DSPSV, CHPSV, and ZHPSV--Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix |
| Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Eigensystem, Az=wBz, where A and B Are Real General Matrices | SGEGV | DGEGV | SGEGV and DGEGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Eigensystem, Az=wBz, where A and B Are Real General Matrices |
| Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Symmetric Eigensystem, Az=wBz, where A Is Real Symmetric and B Is Real Symmetric Positive Definite | SSYGV | DSYGV | SSYGV and DSYGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Symmetric Eigensystem, Az=wBz, where A Is Real Symmetric and B Is Real Symmetric Positive Definite |