zhpr(3) [debian man page]

ZHPR(3) 							   BLAS routine 							   ZHPR(3)

NAME

       ZHPR - perform the hermitian rank 1 operation   A := alpha*x*conjg( x' ) + A,

SYNOPSIS

       SUBROUTINE ZHPR ( UPLO, N, ALPHA, X, INCX, AP )

	   DOUBLE      PRECISION ALPHA

	   INTEGER     INCX, N

	   CHARACTER*1 UPLO

	   COMPLEX*16  AP( * ), X( * )

PURPOSE

       ZHPR    performs the hermitian rank 1 operation

       where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix, supplied in packed form.

PARAMETERS

       UPLO   - CHARACTER*1.
	      On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:

	      UPLO = 'U' or 'u'   The upper triangular part of A is supplied in AP.

	      UPLO = 'L' or 'l'   The lower triangular part of A is supplied in AP.

	      Unchanged on exit.

       N      - INTEGER.
	      On entry, N specifies the order of the matrix A.	N must be at least zero.  Unchanged on exit.

       ALPHA  - DOUBLE PRECISION.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX*16	 array of dimension at least
	      ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain the n element vector x.  Unchanged on exit.

       INCX   - INTEGER.
	      On entry, INCX specifies the increment for the elements of X. INCX must not be zero.  Unchanged on exit.

       AP     - COMPLEX*16	 array of DIMENSION at least
	      (  (  n*( n + 1 ) )/2 ).	Before entry with  UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian
	      matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2,  2
	      )  respectively,	and  so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix.  Before entry
	      with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially,	column	by
	      column,  so  that  AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit,
	      the array AP is overwritten by the lower triangular part of the updated matrix.  Note that the imaginary parts of the diagonal  ele-
	      ments need not be set, they are assumed to be zero, and on exit they are set to zero.

	      Level 2 Blas routine.

	      -- Written on 22-October-1986.  Jack Dongarra, Argonne National Lab.  Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag Cen-
	      tral Office.  Richard Hanson, Sandia National Labs.

BLAS routine							  16 October 1992							   ZHPR(3)

ZHPR2(3)							   BLAS routine 							  ZHPR2(3)

NAME

       ZHPR2 - perform the hermitian rank 2 operation	A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,

SYNOPSIS

       SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )

	   COMPLEX*16	ALPHA

	   INTEGER	INCX, INCY, N

	   CHARACTER*1	UPLO

	   COMPLEX*16	AP( * ), X( * ), Y( * )

PURPOSE

       ZHPR2  performs the hermitian rank 2 operation

       where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form.

PARAMETERS

       UPLO   - CHARACTER*1.
	      On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:

	      UPLO = 'U' or 'u'   The upper triangular part of A is supplied in AP.

	      UPLO = 'L' or 'l'   The lower triangular part of A is supplied in AP.

	      Unchanged on exit.

       N      - INTEGER.
	      On entry, N specifies the order of the matrix A.	N must be at least zero.  Unchanged on exit.

       ALPHA  - COMPLEX*16	.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX*16	 array of dimension at least
	      ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain the n element vector x.  Unchanged on exit.

       INCX   - INTEGER.
	      On entry, INCX specifies the increment for the elements of X. INCX must not be zero.  Unchanged on exit.

       Y      - COMPLEX*16	 array of dimension at least
	      ( 1 + ( n - 1 )*abs( INCY ) ).  Before entry, the incremented array Y must contain the n element vector y.  Unchanged on exit.

       INCY   - INTEGER.
	      On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.  Unchanged on exit.

       AP     - COMPLEX*16	 array of DIMENSION at least
	      (  (  n*( n + 1 ) )/2 ).	Before entry with  UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian
	      matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2,  2
	      )  respectively,	and  so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix.  Before entry
	      with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially,	column	by
	      column,  so  that  AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit,
	      the array AP is overwritten by the lower triangular part of the updated matrix.  Note that the imaginary parts of the diagonal  ele-
	      ments need not be set, they are assumed to be zero, and on exit they are set to zero.

	      Level 2 Blas routine.

	      -- Written on 22-October-1986.  Jack Dongarra, Argonne National Lab.  Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag Cen-
	      tral Office.  Richard Hanson, Sandia National Labs.

BLAS routine							  16 October 1992							  ZHPR2(3)