Contents

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

NAME

     chegst - reduce  a  complex  Hermitian-definite  generalized
     eigenproblem to standard form

SYNOPSIS

     SUBROUTINE CHEGST(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)

     CHARACTER * 1 UPLO
     COMPLEX A(LDA,*), B(LDB,*)
     INTEGER ITYPE, N, LDA, LDB, INFO

     SUBROUTINE CHEGST_64(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)

     CHARACTER * 1 UPLO
     COMPLEX A(LDA,*), B(LDB,*)
     INTEGER*8 ITYPE, N, LDA, LDB, INFO

  F95 INTERFACE
     SUBROUTINE HEGST(ITYPE, UPLO, N, A, [LDA], B, [LDB], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:,:) :: A, B
     INTEGER :: ITYPE, N, LDA, LDB, INFO

     SUBROUTINE HEGST_64(ITYPE, UPLO, N, A, [LDA], B, [LDB], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:,:) :: A, B
     INTEGER(8) :: ITYPE, N, LDA, LDB, INFO

  C INTERFACE
     #include <sunperf.h>

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

     void chegst_64(long itype, char uplo, long  n,  complex  *a,
               long lda, complex *b, long ldb, long *info);

PURPOSE

     chegst  reduces  a  complex  Hermitian-definite  generalized
     eigenproblem to standard form.

     If ITYPE = 1, the problem is A*x = lambda*B*x,
     and   A   is   overwritten    by    inv(U**H)*A*inv(U)    or
     inv(L)*A*inv(L**H)
     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**H  or
     L**H*A*L.

     B must have been previously factorized as U**H*U  or  L*L**H
     by CPOTRF.

ARGUMENTS

     ITYPE (input)
               =     1:     compute     inv(U**H)*A*inv(U)     or
               inv(L)*A*inv(L**H);
               = 2 or 3: compute U*A*U**H or L**H*A*L.

     UPLO (input)
               = 'U':  Upper triangle of A is  stored  and  B  is
               factored as U**H*U; = 'L':  Lower triangle of A is
               stored and B is factored as L*L**H.

     N (input) The order of the matrices A and B.  N >= 0.

     A (input/output)
               On entry, the Hermitian 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,
               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 tri-
               angular 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 factoriza-
               tion of B, as returned by CPOTRF.

     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 ille-
               gal value