NAME¶
ZHPMV - perform the matrix-vector operation y := alpha*A*x + beta*y,
SYNOPSIS¶
- SUBROUTINE ZHPMV
- ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO COMPLEX*16 AP( *
), X( * ), Y( * )
PURPOSE¶
ZHPMV performs the matrix-vector operation
where alpha and beta are scalars, 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.
- 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.
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. Note that the imaginary
parts of the diagonal elements need not be set and are assumed to be zero.
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.
- BETA - COMPLEX*16 .
- On entry, BETA specifies the scalar beta. When BETA is supplied as zero
then Y need not be set on input. 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. On exit, Y is overwritten by the updated
vector y.
- INCY - INTEGER.
- On entry, INCY specifies the increment for the elements of Y. INCY must
not be zero. Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy
Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard
Hanson, Sandia National Labs.