ssygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SUBROUTINE SSYGVD(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER IWORK(*) REAL A(LDA,*), B(LDB,*), W(*), WORK(*) SUBROUTINE SSYGVD_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER*8 ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER*8 IWORK(*) REAL A(LDA,*), B(LDB,*), W(*), WORK(*) F95 INTERFACE SUBROUTINE SYGVD(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER :: ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: A, B SUBROUTINE SYGVD_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER(8) :: ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void ssygvd(int itype, char jobz, char uplo, int n, float *a, int lda, float *b, int ldb, float *w, int *info); void ssygvd_64(long itype, char jobz, char uplo, long n, float *a, long lda, float *b, long ldb, float *w, long *info);
Oracle Solaris Studio Performance Library ssygvd(3P)
NAME
ssygvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SYNOPSIS
SUBROUTINE SSYGVD(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER*1 JOBZ, UPLO
INTEGER ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL A(LDA,*), B(LDB,*), W(*), WORK(*)
SUBROUTINE SSYGVD_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER*1 JOBZ, UPLO
INTEGER*8 ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL A(LDA,*), B(LDB,*), W(*), WORK(*)
F95 INTERFACE
SUBROUTINE SYGVD(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: A, B
SUBROUTINE SYGVD_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
WORK, LWORK, IWORK, LIWORK, INFO)
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void ssygvd(int itype, char jobz, char uplo, int n, float *a, int lda,
float *b, int ldb, float *w, int *info);
void ssygvd_64(long itype, char jobz, char uplo, long n, float *a, long
lda, float *b, long ldb, float *w, long *info);
PURPOSE
ssygvd computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B
are assumed to be symmetric and B is also positive definite. If eigen-
vectors 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
ITYPE (input)
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) The order of the matrices A and B. N >= 0.
A (input/output)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu-
lar part of the matrix A. If UPLO = 'L', the leading N-by-N
lower triangular part of A contains the lower triangular part
of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized as
follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3,
Z**T*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper
triangle (if UPLO='U') or the lower triangle (if UPLO='L') of
A, including the diagonal, is destroyed.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
B (input/output)
On entry, the symmetric matrix B. If UPLO = 'U', the leading
N-by-N upper triangular part of B contains the upper triangu-
lar part of the matrix B. If UPLO = 'L', the leading N-by-N
lower triangular part of B contains the lower triangular part
of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
W (output)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. If N <= 1,
LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. If
JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*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 N <= 1,
LIWORK >= 1. If JOBZ = 'N' and N > 1, LIWORK >= 1. If JOBZ
= 'V' and N > 1, LIWORK >= 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: SPOTRF or SSYEVD returned an error code:
<= N: if INFO = i, SSYEVD failed to converge; i off-diagonal
elements of an intermediate tridiagonal form did not converge
to zero; > N: if INFO = N + i, for 1 <= i <= N, then the
leading minor of order i of B is not positive definite. The
factorization of B could not be completed and no eigenvalues
or eigenvectors were computed.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
7 Nov 2015 ssygvd(3P)