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

NAME

dsygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form

SYNOPSIS

  SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER ITYPE, N, LDA, LDB, INFO
  DOUBLE PRECISION A(LDA,*), B(LDB,*)

  SUBROUTINE DSYGS2_64( ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 ITYPE, N, LDA, LDB, INFO
  DOUBLE PRECISION A(LDA,*), B(LDB,*)

F95 INTERFACE

  SUBROUTINE SYGS2( ITYPE, UPLO, [N], A, [LDA], B, [LDB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: ITYPE, N, LDA, LDB, INFO
  REAL(8), DIMENSION(:,:) :: A, B

  SUBROUTINE SYGS2_64( ITYPE, UPLO, [N], A, [LDA], B, [LDB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: ITYPE, N, LDA, LDB, INFO
  REAL(8), DIMENSION(:,:) :: A, B

C INTERFACE

#include <sunperf.h>

void dsygs2(int itype, char uplo, int n, double *a, int lda, double *b, int ldb, int *info);

void dsygs2_64(long itype, char uplo, long n, double *a, long lda, double *b, long ldb, long *info);

PURPOSE

dsygs2 reduces a real symmetric-definite generalized eigenproblem to standard form.

If ITYPE = 1, the problem is A*x = lambda*B*x,

and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or

B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.

B must have been previously factorized as U'*U or L*L' by SPOTRF.

ARGUMENTS

• ITYPE (input)
  

   = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');

   = 2 or 3: compute U*A*U' or L'*A*L.

• UPLO (input)
  Specifies whether the upper or lower triangular part of the symmetric matrix A is stored, and how B has been factorized. = 'U': Upper triangular

   = 'L':  Lower triangular

• 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, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

  On exit, if INFO = 0, the transformed matrix, stored in the same format as A.

• LDA (input)
  The leading dimension of the array A. LDA > = max(1,N).

• B (input)
  The triangular factor from the Cholesky factorization of B, as returned by SPOTRF.

• LDB (input)
  The leading dimension of the array B. LDB > = max(1,N).

• INFO (output)
  

   = 0:  successful exit.

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