NAME

dstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS

  SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, 
 *      LIWORK, INFO)
  CHARACTER * 1 COMPZ
  INTEGER N, LDZ, LWORK, LIWORK, INFO
  INTEGER IWORK(*)
  DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)

  SUBROUTINE DSTEDC_64( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, 
 *      LIWORK, INFO)
  CHARACTER * 1 COMPZ
  INTEGER*8 N, LDZ, LWORK, LIWORK, INFO
  INTEGER*8 IWORK(*)
  DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE STEDC( COMPZ, N, D, E, Z, [LDZ], WORK, [LWORK], IWORK, 
 *       [LIWORK], [INFO])
  CHARACTER(LEN=1) :: COMPZ
  INTEGER :: N, LDZ, LWORK, LIWORK, INFO
  INTEGER, DIMENSION(:) :: IWORK
  REAL(8), DIMENSION(:) :: D, E, WORK
  REAL(8), DIMENSION(:,:) :: Z

  SUBROUTINE STEDC_64( COMPZ, N, D, E, Z, [LDZ], WORK, [LWORK], IWORK, 
 *       [LIWORK], [INFO])
  CHARACTER(LEN=1) :: COMPZ
  INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO
  INTEGER(8), DIMENSION(:) :: IWORK
  REAL(8), DIMENSION(:) :: D, E, WORK
  REAL(8), DIMENSION(:,:) :: Z

C INTERFACE

#include <sunperf.h>

void dstedc(char *compz, int n, double *d, double *e, double *z, int ldz, double *work, int lwork, int *iwork, int liwork, int *info);

void dstedc_64(char *compz, long n, double *d, double *e, double *z, long ldz, double *work, long lwork, long *iwork, long liwork, long *info);

PURPOSE

dstedc computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band real symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to tridiagonal form.

This code 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. See SLAED3 for details.

ARGUMENTS

COMPZ (input/output)

 = 'N':  Compute eigenvalues only.

 = 'I':  Compute eigenvectors of tridiagonal matrix also.

 = 'V':  Compute eigenvectors of original dense symmetric
matrix also.  On entry, Z contains the orthogonal
matrix used to reduce the original matrix to
tridiagonal form.

N (input)
The dimension of the symmetric tridiagonal matrix. N > = 0.
D (input/output)
On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output)
On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
Z (input/output)
On entry, if COMPZ = 'V', then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = 'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ > = 1. If eigenvectors are desired, then 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 COMPZ = 'N' or N < = 1 then LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK must be at least ( 1 + 3*N + 2*N*lg N + 3*N**2 ), where lg( N ) = smallest integer k such that 2**k > = N. If COMPZ = 'I' and N > 1 then LWORK must be at least ( 1 + 4*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 (output)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
The dimension of the array IWORK. If COMPZ = 'N' or N < = 1 then LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then LIWORK must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I' and N > 1 then 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:  The algorithm failed to compute an eigenvalue while
working on the submatrix lying in rows and columns
INFO/(N+1) through mod(INFO,N+1).

FURTHER DETAILS

Based on contributions by

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

Modified by Francoise Tisseur, University of Tennessee.