Contents
cstedc - compute all eigenvalues and, optionally, eigenvec-
tors of a symmetric tridiagonal matrix using the divide and
conquer method
SUBROUTINE CSTEDC(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO)
CHARACTER * 1 COMPZ
COMPLEX Z(LDZ,*), WORK(*)
INTEGER N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL D(*), E(*), RWORK(*)
SUBROUTINE CSTEDC_64(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 COMPZ
COMPLEX Z(LDZ,*), WORK(*)
INTEGER*8 N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL 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, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, 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, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER(8) :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: D, E, RWORK
C INTERFACE
#include <sunperf.h>
void cstedc(char compz, int n, float *d, float *e, complex
*z, int ldz, int *info);
void cstedc_64(char compz, long n, float *d, float *e, com-
plex *z, long ldz, long *info);
cstedc computes all eigenvalues and, optionally, eigenvec-
tors 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.
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 tri-
diagonal 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 tridiag-
onal matrix. On exit, E has been destroyed.
Z (input) On entry, if COMPZ = 'V', then Z contains the
unitary matrix used in the reduction to tridiago-
nal 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 (workspace)
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 (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, 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 ille-
gal value.
> 0: The algorithm failed to compute an eigen-
value while working on the submatrix lying in rows
and columns INFO/(N+1) through mod(INFO,N+1).
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA