Contents

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

NAME

     zhpgst - reduce  a  complex  Hermitian-definite  generalized
     eigenproblem to standard form, using packed storage

SYNOPSIS

     SUBROUTINE ZHPGST(ITYPE, UPLO, N, AP, BP, INFO)

     CHARACTER * 1 UPLO
     DOUBLE COMPLEX AP(*), BP(*)
     INTEGER ITYPE, N, INFO

     SUBROUTINE ZHPGST_64(ITYPE, UPLO, N, AP, BP, INFO)

     CHARACTER * 1 UPLO
     DOUBLE COMPLEX AP(*), BP(*)
     INTEGER*8 ITYPE, N, INFO

  F95 INTERFACE
     SUBROUTINE HPGST(ITYPE, UPLO, N, AP, BP, [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX(8), DIMENSION(:) :: AP, BP
     INTEGER :: ITYPE, N, INFO

     SUBROUTINE HPGST_64(ITYPE, UPLO, N, AP, BP, [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX(8), DIMENSION(:) :: AP, BP
     INTEGER(8) :: ITYPE, N, INFO

  C INTERFACE
     #include <sunperf.h>

     void zhpgst(int itype, char uplo, int n, doublecomplex  *ap,
               doublecomplex *bp, int *info);

     void zhpgst_64(long itype, char uplo, long n,  doublecomplex
               *ap, doublecomplex *bp, long *info);

PURPOSE

     zhpgst  reduces  a  complex  Hermitian-definite  generalized
     eigenproblem to standard form, using packed storage.

     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 CPPTRF.

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.

     AP (input/output)
               On entry, the upper or lower triangle of the  Her-
               mitian  matrix  A,  packed  columnwise in a linear
               array.  The j-th column of  A  is  stored  in  the
               array  AP  as  follows:  if UPLO = 'U', AP(i + (j-
               1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L',  AP(i
               + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

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

     BP (input)
               The triangular factor from the Cholesky factoriza-
               tion  of  B,  stored  in  the same format as A, as
               returned by CPPTRF.

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value