zstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
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, int *info); void zstedc_64(char compz, long n, double *d, double *e, doublecomplex *z, long ldz, long *info);
Oracle Solaris Studio Performance Library zstedc(3P)
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, int *info);
void zstedc_64(char compz, long n, double *d, double *e, doublecomplex
*z, long ldz, long *info);
PURPOSE
zstedc 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 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 DLAED3 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) 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 eigen-
vectors 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 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)
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 + 4*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 rou-
tine 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 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
7 Nov 2015 zstedc(3P)