Arguments

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Arguments

A: (input/output) REAL or COMPLEX square array, shape .
On entry, the matrix .
If ${\bf UPLO} =$ 'U', the upper triangular part of ${\bf A}$ contains the upper triangular part of matrix . If ${\bf UPLO} =$ 'L', the lower triangular part of ${\bf A}$ contains the lower triangular part of matrix .
On exit, if ${\bf JOBZ} =$ 'V', then the columns of ${\bf A}$ contain the eigenvectors, normalized as follows:

$\begin{optionarg} \item[{if ${\bf ITYPE} = 1$\ or $2$:}] $Z^H\,B\,Z = I$, \item[{if ${\bf ITYPE} = 3$:}] $Z^H\,B^{-1}\,Z = I$. \end{optionarg}$
If JOBZ = 'N', then the upper triangle (if UPLO = 'U') or the lower triangle (if UPLO = 'L') of , including the diagonal, is destroyed.
B: (input/output) REAL or COMPLEX square array, shape with $size({\bf B},1) = size({\bf A},1)$ .
On entry, the matrix . If ${\bf UPLO} =$ 'U', the upper triangular part of ${\bf B}$ contains the upper triangular part of matrix . If ${\bf UPLO} =$ 'L', the lower triangular part of ${\bf B}$ contains the lower triangular part of matrix .
On exit, if the part of ${\bf B}$ containing the matrix is overwritten by the triangular factor or of the Cholesky factorization $B = U^H\,U$ or $B = L\,L^H$ , respectively.
W: (output) REAL array, shape with $size({\bf W}) = size({\bf A},1)$ .
The eigenvalues in ascending order.
ITYPE: Optional (input) INTEGER.
Specifies the problem type to be solved:

$\begin{optionarg} \item[{= 1:}] $A z = \lambda B z$ \item[{= 2:}] $A B z = \lambda z$ \item[{= 3:}] $B A z = \lambda z$ \end{optionarg}$
Default value: 1.
JOBZ: Optional (input) CHARACTER(LEN=1).

$\begin{optionarg} \item[{= 'N':}] Compute eigenvalues only; \item[{= 'V':}] Compute eigenvalues and eigenvectors. \end{optionarg}$
Default value: 'N'.
UPLO: Optional (input) CHARACTER(LEN=1).

$\begin{optionarg} \item[{$ =$\ 'U':}] Upper triangles of $A$\ and $B$\ are stor... ...item[{$ =$\ 'L':}] Lower triangles of $A$\ and $B$\ are stored. \end{optionarg}$
Default value: 'U'.
INFO: Optional (output) INTEGER.

$\begin{infoarg} \item[{$= 0$:}] successful exit. \item[{$< 0$:}] if {\bf INFO}... ...genvectors were computed. \end{infoarg} $n$\ is the order of $A$. \end{infoarg}$
If INFO is not present and an error occurs, then the program is terminated with an error message.

References: [1] and [17,9,20].

Next: Examples Up: Generalized Symmetric Eigenvalue Problems Previous: Purpose Contents Index

Susan Blackford 2001-08-19