NAME

ssyevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

SYNOPSIS

  SUBROUTINE SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, 
 *      LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER N, LDA, LWORK, LIWORK, INFO
  INTEGER IWORK(*)
  REAL A(LDA,*), W(*), WORK(*)

  SUBROUTINE SSYEVD_64( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, 
 *      LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 N, LDA, LWORK, LIWORK, INFO
  INTEGER*8 IWORK(*)
  REAL A(LDA,*), W(*), WORK(*)

F95 INTERFACE

  SUBROUTINE SYEVD( JOBZ, UPLO, [N], A, [LDA], W, [WORK], [LWORK], 
 *       [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: N, LDA, LWORK, LIWORK, INFO
  INTEGER, DIMENSION(:) :: IWORK
  REAL, DIMENSION(:) :: W, WORK
  REAL, DIMENSION(:,:) :: A

  SUBROUTINE SYEVD_64( JOBZ, UPLO, [N], A, [LDA], W, [WORK], [LWORK], 
 *       [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: N, LDA, LWORK, LIWORK, INFO
  INTEGER(8), DIMENSION(:) :: IWORK
  REAL, DIMENSION(:) :: W, WORK
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void ssyevd(char jobz, char uplo, int n, float *a, int lda, float *w, int *info);

void ssyevd_64(char jobz, char uplo, long n, float *a, long lda, float *w, long *info);

PURPOSE

ssyevd computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

Because of large use of BLAS of level 3, SSYEVD needs N**2 more workspace than SSYEVX.

ARGUMENTS

JOBZ (input)

 = 'N':  Compute eigenvalues only;

 = 'V':  Compute eigenvalues and eigenvectors.

UPLO (input)

 = 'U':  Upper triangle of A is stored;

 = 'L':  Lower triangle of A is stored.

N (input)
The order of the matrix A. N > = 0.
A (input/output)
On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO ='L') or the upper triangle (if UPLO ='U') of A, including the diagonal, is destroyed.
LDA (input)
The leading dimension of the array A. LDA > = max(1,N).
W (output)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace)
dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. If N < = 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
IWORK (workspace)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
The dimension of the array IWORK. If N < = 1, LIWORK must be at least 1. If JOBZ = 'N' and N > 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.

INFO (output)

 = 0:  successful exit

 < 0:  if INFO  = -i, the i-th argument had an illegal value

 > 0:  if INFO  = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

FURTHER DETAILS

Based on contributions by

   Jeff Rutter, Computer Science Division, University of California
   at Berkeley, USA

Modified by Francoise Tisseur, University of Tennessee.