_SYMV,_HEMV(3F) _SYMV,_HEMV(3F)NAME
dsymv, ssymv, zhemv, chemv - BLAS Level Two (Symmetric/Hermitian)Matrix
- Vector Product
FORTRAN 77 SYNOPSIS
subroutine dsymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 uplo
integer n, lda, incx, incy
double precision alpha, beta
double precision a( lda,*), x(*), y(*)
subroutine ssymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 uplo
integer n, lda, incx, incy
real alpha, beta
real a( lda,*), x(*), y(*)
subroutine zhemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 uplo
integer n, lda, incx, incy
double complex alpha, beta
double complex a( lda,*), x(*), y(*)
subroutine chemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 uplo
integer n, lda, incx, incy
complex alpha, beta
complex a( lda,*), x(*), y(*)
C SYNOPSIS
void dsymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTriangle uplo;
Integer n, lda, incx, incy;
double alpha, beta;
double (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void ssymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTriangle uplo;
Integer n, lda, incx, incy;
float alpha, beta;
float (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void zhemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTriangle uplo;
Integer n, lda, incx, incy;
Zomplex alpha, beta;
Zomplex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void chemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTriangle uplo;
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_SYMV,_HEMV(3F) _SYMV,_HEMV(3F)
Integer n, lda, incx, incy;
Complex alpha, beta;
Complex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
DESCRIPTION
dsymv , ssymv , dhemv and chemv perform 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/hermitian matrix.
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' The upper triangular part of A is
being supplied.
uplo = 'L' or 'l' The lower triangular part of A is
being supplied.
C
uplo = UpperTriangle The upper triangular part of A is
being supplied.
uplo = LowerTriangle The lower triangular part of A is
being supplied
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.
a An array containing the matrix A.
FORTRAN
Array of dimension ( lda, n ).
C
A pointer to an array of size lda*n.
See note below about array storage convention for C.
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_SYMV,_HEMV(3F) _SYMV,_HEMV(3F)
Before entry with uplo = 'U' or 'u' or , the array elements
corresponding to the leading n by n upper triangular part of the
matrix A must contain the corresponding upper triangular part of
the symmetric/hermitian matrix and the strictly lower triangular
part of A is not referenced.
Before entry with uplo = 'L' or 'l' or , the array elements
corresponding to the leading n by n lower triangular part of the
array A must contain the corresponding lower triangular part of
the symmetric/hermitian matrix and the strictly upper triangular
part of A is not referenced.
Note that the imaginary parts of the diagonal elements need not
be set and are assumed to be zero.
Unchanged on exit.
lda On entry, lda specifies the first dimension of A as declared in
the calling (sub) program. lda must be at least ( k + 1 ).
Unchanged on exit.
x Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
entry, the incremented array x must contain the vector x.
Unchanged on exit.
incx On entry, incx specifies the increment for the elements of x.
incx must not be zero.
Unchanged on exit.
beta 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 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.
C ARRAY STORAGE CONVENTION
The matrices are assumed to be stored in a one dimensional C array
in an analogous fashion as a Fortran array (column major). Therefore,
the element A(i+1,j) of matrix A is stored immediately after the
element A(i,j), while A(i,j+1) is lda elements apart from A(i,j).
The element A(i,j) of the matrix can be accessed directly by reference
to a[ (j-1)*lda + (i-1) ].
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_SYMV,_HEMV(3F) _SYMV,_HEMV(3F)AUTHORS
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
TUNING
DSYMV and SSYMV are optimized and parallelized for SGI R3000 and
R4x00 platforms. For the R8000 it is optimized an parallelized
for the case when INCX = 1.
ZHEMV and CHEMV are optimized and parallelized for SGI R3000, R4x00
and R8000 platforms.
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