dsygv

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:

* JOBZ (input)

* UPLO (input)

* 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)