_SPR2,_HPR2(3F) _SPR2,_HPR2(3F)NAME
dspr2, sspr2, zhpr2, chpr2 - BLAS Level Two Symmetric Packed Matrix
Rank 2 Update
FORTRAN 77 SYNOPSIS
subroutine dspr2( uplo, n, alpha, n, incx, y, incy, ap )
character*1 uplo
integer n, incx, incy
double precision alpha
double precision ap(*), x(*), y(*)
subroutine sspr2( uplo, n, alpha, n,
character*1 uplo
integer n, incx, incy
real alpha
real ap(*), x(*), y(*)
subroutine zhpr2( uplo, n, alpha, n, incx, y, incy, ap )
character*1 uplo
integer n, incx, incy
complex*16 alpha
complex*16 ap(*), x(*), y(*)
subroutine chpr2( uplo, n, alpha, n,
character*1 uplo
integer n, incx, incy
complex alpha
complex ap(*), x(*), y(*)
C SYNOPSIS
void dspr2( uplo, n, alpha, n, incx, y, incy, ap )
MatrixTriangle uplo;
Integer n, incx, incy;
double alpha;
double (*ap)[ n ], (*x)[ n ], (*y)[ n ];
void sspr2( uplo, n, alpha, n, incx, y, incy, ap )
MatrixTriangle uplo;
Integer n, incx, incy;
float alpha;
float (*ap)[ n ], (*x)[ n ], (*y)[ n ];
void zhpr2( uplo, n, alpha, n, incx, y, incy, ap )
MatrixTriangle uplo;
Integer n, incx, incy;
Zomplex alpha;
Zomplex (*ap)[ n ], (*x)[ n ], (*y)[ n ];
void chpr2( uplo, n, alpha, n, incx, y, incy, ap )
MatrixTriangle uplo;
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_SPR2,_HPR2(3F) _SPR2,_HPR2(3F)
Integer n, incx, incy;
Complex alpha;
Complex (*ap)[ n ], (*x)[ n ], (*y)[ n ];
DESCRIPTION
dspr2 and sspr2 perform the symmetric rank 2 operation
A := alpha*x*y' + alpha*y*x' + A,
zhpr2 and chpr2 perform the hermitian rank 2 operation
A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
where alpha is a real/complex scalar, x is an n element vector and A is
an n by n symmetric/hermitian matrix, supplied in packed form.
PARAMETERS
uplo On entry, uplo specifies whether the upper or lower triangular
part of the matrix A is being supplied as follows:
FORTRAN
uplo = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
uplo = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
C
uplo = UpperTriangle Only the lower triangular part of A
is to be referenced.
uplo = LowerTriangle Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
n On entry, n specifies the the order of the matrix A. n must be
at least zero.
Unchanged on exit.
alpha specifies the scalar alpha.
Unchanged on exit.
x Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
entry, the incremented array x must contain the n element vector
x.
Unchanged on exit.
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_SPR2,_HPR2(3F) _SPR2,_HPR2(3F)
incx On entry, incx specifies the increment for the elements of x.
incx must not be zero.
Unchanged on exit.
y Array of size 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 On entry, incy specifies the increment for the elements of y.
incy must not be zero.
Unchanged on exit.
ap Array of size at least ( ( n*( n + 1 ) )/2 ).
Before entry with uplo = 'U' or 'u' or the array ap must contain
the upper triangular part of the symmetric/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' or , the array ap must
contain the lower triangular part of the symmetric/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 for the hermitian matrix the imaginary parts of the
diagonal elements need not be set, they are assumed to be zero,
and on exit they are set to zero.
Unchanged on exit.
AUTHORS
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
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