ztpmv (l) - Linux Manuals

ztpmv: performs one of the matrix-vector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,

NAME

ZTPMV - performs one of the matrix-vector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,

SYNOPSIS

SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)

    

INTEGER INCX,N

    

CHARACTER DIAG,TRANS,UPLO

    

DOUBLE COMPLEX AP(*),X(*)

PURPOSE

ZTPMV performs one of the matrix-vector operations

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.

ARGUMENTS

UPLO - CHARACTER*1.

On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:

UPLO = aqUaq or aquaq A is an upper triangular matrix.

UPLO = aqLaq or aqlaq A is a lower triangular matrix.

Unchanged on exit.

TRANS - CHARACTER*1.

On entry, TRANS specifies the operation to be performed as follows:

TRANS = aqNaq or aqnaq x := A*x.

TRANS = aqTaq or aqtaq x := Aaq*x.

TRANS = aqCaq or aqcaq x := conjg( Aaq )*x.

Unchanged on exit.

DIAG - CHARACTER*1.

On entry, DIAG specifies whether or not A is unit triangular as follows:

DIAG = aqUaq or aquaq A is assumed to be unit triangular.

DIAG = aqNaq or aqnaq A is not assumed to be unit triangular.

Unchanged on exit.

N - INTEGER.

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

AP - COMPLEX*16 array of DIMENSION at least

( ( n*( n + 1 ) )/2 ). Before entry with UPLO = aqUaq or aquaq, the array AP must contain the upper triangular 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 = aqLaq or aqlaq, the array AP must contain the lower triangular 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 when DIAG = aqUaq or aquaq, the diagonal elements of A are not referenced, but are assumed to be unity. 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. On exit, X is overwritten with the tranformed vector x.

INCX - INTEGER.

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

FURTHER DETAILS

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.