• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

sspevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

SYNOPSIS

  SUBROUTINE SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, 
 *      LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER N, LDZ, LWORK, LIWORK, INFO
  INTEGER IWORK(*)
  REAL AP(*), W(*), Z(LDZ,*), WORK(*)

  SUBROUTINE SSPEVD_64( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, 
 *      IWORK, LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 N, LDZ, LWORK, LIWORK, INFO
  INTEGER*8 IWORK(*)
  REAL AP(*), W(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE SPEVD( JOBZ, UPLO, [N], AP, W, Z, [LDZ], WORK, [LWORK], 
 *       [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: N, LDZ, LWORK, LIWORK, INFO
  INTEGER, DIMENSION(:) :: IWORK
  REAL, DIMENSION(:) :: AP, W, WORK
  REAL, DIMENSION(:,:) :: Z

  SUBROUTINE SPEVD_64( JOBZ, UPLO, [N], AP, W, Z, [LDZ], WORK, [LWORK], 
 *       [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO
  INTEGER(8), DIMENSION(:) :: IWORK
  REAL, DIMENSION(:) :: AP, W, WORK
  REAL, DIMENSION(:,:) :: Z

C INTERFACE

#include <sunperf.h>

void sspevd(char jobz, char uplo, int n, float *ap, float *w, float *z, int ldz, float *work, int lwork, int *info);

void sspevd_64(char jobz, char uplo, long n, float *ap, float *w, float *z, long ldz, float *work, long lwork, long *info);

PURPOSE

sspevd computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. 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.

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.

• AP (input/output)
  On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j < =i < =n.

  On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A.

• W (output)
  If INFO = 0, the eigenvalues in ascending order.

• Z (output)
  If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced.

• LDZ (input)
  The leading dimension of the array Z. LDZ > = 1, and if JOBZ = 'V', LDZ > = max(1,N).

• WORK (output)
  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. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 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 JOBZ = 'N' or 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.