Contents
ssygvd - compute all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite eigen-
problem, 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);
ssygvd computes all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite eigen-
problem, 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 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
digits, but we know of none.
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 con-
tains the upper triangular 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 con-
tains the matrix Z of eigenvectors. The eigenvec-
tors 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 con-
tains the upper triangular 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 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: SPOTRF or SSYEVD returned an error code:
<= N: if INFO = i, SSYEVD failed to converge; i
off-diagonal elements of an intermediate tridiago-
nal 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.
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA