dspr man page on Scientific

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DSPR(1)				 BLAS routine			       DSPR(1)

NAME
       DSPR - performs the symmetric rank 1 operation	A := alpha*x*x' + A,

SYNOPSIS
       SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)

	   DOUBLE			       PRECISION ALPHA

	   INTEGER			       INCX,N

	   CHARACTER			       UPLO

	   DOUBLE			       PRECISION AP(*),X(*)

PURPOSE
       DSPR    performs the symmetric rank 1 operation

       where alpha is a real 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 fol‐
	      lows:

	      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      - DOUBLE PRECISION 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     - DOUBLE PRECISION 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  sym‐
	      metric 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 sequen‐
	      tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
	      AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and	 a(  3,	 1  )  respec‐
	      tively,  and  so on. On exit, the array AP is overwritten by the
	      lower triangular part of the updated matrix.

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.

BLAS routine			 November 2008			       DSPR(1)
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