dstedc(3P) Sun Performance Library dstedc(3P)NAMEdstedc - 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, int *info);
void dstedc_64(char compz, long n, double *d, double *e, double *z,
long ldz, long *info);
PURPOSEdstedc computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric 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 DLAED3 for details.
ARGUMENTS
COMPZ (input)
= '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) 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 refer‐
enced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1. If eigen‐
vectors are desired, then LDZ >= max(1,N).
WORK (workspace)
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 + 4*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 (workspace/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 rou‐
tine 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.
6 Mar 2009 dstedc(3P)
