Name

ssymv, dsymv, chemv, zhemv − Matrix-vector product for a symmetric or hermitian matrix

FORMAT

{S,D}SYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy) {C,Z}HEMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

Arguments

uplocharacter∗1
On entry, specifies whether the upper- or lower-triangular part of the array A is referenced:

If uplo = ’U’ or ’u’, the upper-triangular part of A is referenced. 

If uplo = ’L’ or ’l’, the lower-triangular part of A is referenced. 
On exit, uplo is unchanged. 

ninteger∗4
On entry, the order of the matrix A; n >= 0.
On exit, n is unchanged. 

alphareal∗4 | real∗8 | complex∗8 | complex∗16
On entry, the scalar alpha∗.
On exit, alpha is unchanged. 

areal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a two-dimensional array with dimensions lda by n.

When uplo specifies the upper portion of the matrix, the leading n by n part of the array contains the upper-triangular part of the matrix, and the lower-triangular part of array A is not referenced. 

When uplo specifies the lower  portion of the matrix,  the leading n by n part of the array contains the lower-triangular part of the matrix, and the upper-triangular part of array A is not referenced. 

For CHEMV and ZHEMV routines,  the imaginary parts of the diagonal elements are not accessed, need not be  set, and are assumed to be zero. 
On exit, a is unchanged. 

ldainteger∗4
On entry, the first dimension of array A; lda >= MAX(1,n).
On exit, lda is unchanged. 

xreal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a one-dimensional array X of length at least (1+(n-1)∗|incx|).  Array X contains the vector x.
On exit, x is unchanged. 

incxinteger∗4
On entry, the increment for the elements of X; incx must not equal zero.
On exit, incx is unchanged. 

betareal∗4 | real∗8 | complex∗8 | complex∗16
On entry, the scalar beta.
On exit, beta is unchanged. 

yreal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a one-dimensional array Y of length at least (1+(n-1)∗|incy|).

If beta= 0, y need not be set.  If betais not equal to zero, the incremented array Y must contain the vector y. 
On exit, y is overwritten by the updated vector y. 

incyinteger∗4
On entry, the increment for the elements of Y; incy must not equal zero.
On exit, incy is unchanged. 

Description

SSYMV and DSYMV compute a matrix-vector product for a real symmetric matrix.  CHEMV and ZHEMV compute a matrix-vector product for a complex Hermitian matrix.  Both products are described by the following operation: y  = alpha∗Ax + beta∗y

alpha and beta are scalars, x and y are vectors with n elements, and A is an n by n matrix.  In the case of SSYMV and DSYMV, matrix A is a symmetric matrix and in the case of CHEMV and ZHEMV, matrix A is a Hermitian matrix. 

EXAMPLES

REAL∗8 A(100,40), X(40), Y(40), alpha, beta
N = 40
INCX = 1
INCY = 1
alpha = 1.0D0
beta = 0.0D0
LDA = 100
CALL DSYMV(’U’,N,alpha,A,LDA,X,INCX,beta,Y,INCY)

This FORTRAN code computes the product y  =  Ax where A is a symmetric matrix, of order 40, with its upper-triangular part stored.

COMPLEX∗8 A(100,40), X(40), Y(40), alpha, beta
N = 40
INCX = 1
INCY = 1
alpha = (1.0, 0.5)
beta = (0.0, 0.0)
LDA = 100
CALL CHEMV(’U’,N,alpha,A,LDA,X,INCX,beta,Y,INCY)

This FORTRAN code computes the product y  =  Ax where A is a Hermitian matrix, of order 40, with its upper-triangular part stored.