• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dsygv - 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 DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 
 *      LDWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER ITYPE, N, LDA, LDB, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), WORK(*)

  SUBROUTINE DSYGV_64( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 
 *      LDWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 ITYPE, N, LDA, LDB, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), WORK(*)

F95 INTERFACE

  SUBROUTINE SYGV( ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, 
 *       [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: ITYPE, N, LDA, LDB, LDWORK, INFO
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: A, B

  SUBROUTINE SYGV_64( ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, 
 *       [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: ITYPE, N, LDA, LDB, LDWORK, INFO
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: A, B

C INTERFACE

#include <sunperf.h>

void dsygv(int itype, char jobz, char uplo, int n, double *a, int lda, double *b, int ldb, double *w, int *info);

void dsygv_64(long itype, char jobz, char uplo, long n, double *a, long lda, double *b, long ldb, double *w, long *info);

PURPOSE

dsygv 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.

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 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 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 positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains 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 LDWORK.

• LDWORK (input)
  The length of the array WORK. LDWORK > = max(1,3*N-1). For optimal efficiency, LDWORK > = (NB+2)*N, where NB is the blocksize for SSYTRD returned by ILAENV.

  If LDWORK = -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 LDWORK is issued by XERBLA.

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

   > 0:  SPOTRF or SSYEV returned an error code:

   < = N:  if INFO  = i, SSYEV 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.