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

NAME

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

SYNOPSIS

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

  SUBROUTINE ZSTEDC_64( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, 
 *      LRWORK, IWORK, LIWORK, INFO)
  CHARACTER * 1 COMPZ
  DOUBLE COMPLEX Z(LDZ,*), WORK(*)
  INTEGER*8 N, LDZ, LWORK, LRWORK, LIWORK, INFO
  INTEGER*8 IWORK(*)
  DOUBLE PRECISION D(*), E(*), RWORK(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void zstedc(char compz, int n, double *d, double *e, doublecomplex *z, int ldz, double *rwork, int lrwork, int *iwork, int liwork, int *info);

void zstedc_64(char compz, long n, double *d, double *e, doublecomplex *z, long ldz, double *rwork, long lrwork, long *iwork, long liwork, long *info);

PURPOSE

zstedc computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD 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)
  

   = 'N':  Compute eigenvalues only.

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

   = 'V':  Compute eigenvectors of original Hermitian matrix
  also.  On entry, Z contains the unitary 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 unitary 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 Hermitian 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 (workspace)
  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

• LWORK (input)
  The dimension of the array WORK. If COMPZ = 'N' or 'I', or N < = 1, LWORK must be at least 1. If COMPZ = 'V' and N > 1, LWORK must be at least N*N.

  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.

• RWORK (output)
  dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

• LRWORK (input)
  The dimension of the array RWORK. If COMPZ = 'N' or N < = 1, LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK 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, LRWORK must be at least 1 + 4*N + 2*N**2 .

  If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK 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, LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK must be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or 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:  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