sspevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
SUBROUTINE SSPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER N, LDZ, LWORK, LIWORK, INFO INTEGER IWORK(*) REAL AP(*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE SSPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER*8 N, LDZ, LWORK, LIWORK, INFO INTEGER*8 IWORK(*) REAL AP(*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE SPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER :: N, LDZ, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: AP, W, WORK REAL, DIMENSION(:,:) :: Z SUBROUTINE SPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: AP, W, WORK REAL, DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void sspevd(char jobz, char uplo, int n, float *ap, float *w, float *z, int ldz, int *info); void sspevd_64(char jobz, char uplo, long n, float *ap, float *w, float *z, long ldz, long *info);
Oracle Solaris Studio Performance Library sspevd(3P)
NAME
sspevd - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
SYNOPSIS
SUBROUTINE SSPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO)
CHARACTER*1 JOBZ, UPLO
INTEGER N, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL AP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO)
CHARACTER*1 JOBZ, UPLO
INTEGER*8 N, LDZ, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL AP(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO)
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, LDZ, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: AP, W, WORK
REAL, DIMENSION(:,:) :: Z
SUBROUTINE SPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO)
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: AP, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sspevd(char jobz, char uplo, int n, float *ap, float *w, float *z,
int ldz, int *info);
void sspevd_64(char jobz, char uplo, long n, float *ap, float *w, float
*z, long ldz, long *info);
PURPOSE
sspevd computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage. If eigenvectors are desired,
it uses a divide and conquer algorithm.
The divide and conquer algorithm 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 dig-
its, but we know of none.
ARGUMENTS
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
AP (input/output)
Real array, dimension (N*(N+1)/2) On entry, the upper or
lower triangle of the symmetric matrix A, packed columnwise
in a linear array. The j-th column of A is stored in the
array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the diag-
onal and first subdiagonal of T overwrite the corresponding
elements of A.
W (output)
Real array, dimension (N) If INFO = 0, the eigenvalues in
ascending order.
Z (output)
Real array, dimension (LDZ, N) If JOBZ = 'V', then if INFO =
0, Z contains the orthonormal eigenvectors of the matrix A,
with the i-th column of Z holding the eigenvector associated
with W(i). If JOBZ = 'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
Real array, dimension (LWORK) On exit, if INFO = 0, WORK(1)
returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. If N <= 1,
LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK
must be at least 2*N. If JOBZ = 'V' and N > 1, LWORK must be
at least 1 + 6*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)
Integer array, dimension (LIWORK) On exit, if INFO = 0,
IWORK(1) returns the optimal LIWORK.
LIWORK (input)
The dimension of the array IWORK. If JOBZ = 'N' or N <= 1,
LIWORK must be at least 1. If JOBZ = 'V' and 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: if INFO = i, the algorithm failed to converge; i off-
diagonal elements of an intermediate tridiagonal form did not
converge to zero.
7 Nov 2015 sspevd(3P)