zspr(l) [redhat man page]

ZSPR(l) 								 )								   ZSPR(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	UPLO

	   INTEGER	INCX, N

	   COMPLEX*16	ALPHA

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

PURPOSE

       ZSPR  performs the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A, where alpha is a complex scalar, x is an n element vector and A
       is an n by n symmetric matrix, supplied in packed form.

ARGUMENTS

       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, 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, 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  symmetric
	      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 symmetric 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.

LAPACK version 3.0						   15 June 2000 							   ZSPR(l)

CSPMV(l)								 )								  CSPMV(l)

NAME

       CSPMV - perform the matrix-vector operation  y := alpha*A*x + beta*y,

SYNOPSIS

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

	   CHARACTER	 UPLO

	   INTEGER	 INCX, INCY, N

	   COMPLEX	 ALPHA, BETA

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

PURPOSE

       CSPMV  performs	the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A
       is an n by n symmetric matrix, supplied in packed form.

ARGUMENTS

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

       AP     - COMPLEX array, 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  symmetric
	      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 symmet-
	      ric  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.  Unchanged on exit.

       X      - COMPLEX array, 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
	      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 array, 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.

LAPACK version 3.0						   15 June 2000 							  CSPMV(l)