Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

Overview of the Eigensystem Analysis and Singular Value Analysis Subroutines

The eigensystems analysis and singular value analysis subroutines provide solutions to the algebraic eigensystem analysis problem for real symmetric matrices and complex Hermitian matrices and the real symmetric and complex Hermitian positive definite generalized eigensystem analysis problem. |In addition, subroutines to reduce real symmetric and complex |Hermitian matrices, real symmetric and complex Hermitian positive definite |generalized eigenproblems, and real general matrices to condensed form are |provided. These subroutines include a subset of the ScaLAPACK subroutines. See references [19] and [20].

Note:: These subroutines are designed in accordance with the proposed ScaLAPACK standard. If these subroutines do no comply with the standard as approved, IBM will consider updating them to do so. If IBM updates these subroutines, the update could require modifications of the calling application program.

Table 101. List of Eigensystem Analysis and Singular Value Analysis Subroutines

Descriptive Name	Long-Precision Subroutine	Page
Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Matrix	PDSYEVX PZHEEVX	PDSYEVX and PZHEEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Matrix
Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem	PDSYGVX PZHEGVX	PDSYGVX and PZHEGVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem
Reduce a Real Symmetric or Complex Hermitian Matrix to Tridiagonal Form	PDSYTRD PZHETRD	PDSYTRD and PZHETRD--Reduce a Real Symmetric or Complex Hermitian Matrix to Tridiagonal Form
Reduce a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem to Standard Form	PDSYGST PZHEGST	PDSYGST and PZHEGST--Reduce a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem to Standard Form
Reduce a General Matrix to Upper Hessenberg Form	PDGEHRD	PDGEHRD--Reduce a General Matrix to Upper Hessenberg Form
Reduce a General Matrix to Bidiagonal Form	PDGEBRD	PDGEBRD--Reduce a General Matrix to Bidiagonal Form

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