_GEMV(3F)_GEMV(3F)NAME
dgemv, sgemv, zgemv, cgemv - BLAS Level Two Matrix-Vector Product
FORTRAN 77 SYNOPSIS
subroutine dgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 trans
integer n, m, lda, incx, incy
double precision alpha, beta
double precision a( lda,*), x(*), y(*)
subroutine sgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 trans
integer n, m, lda, incx, incy
real alpha, beta
real a( lda,*), x(*), y(*)
subroutine zgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 trans
integer n, m, lda, incx, incy
double complex alpha, beta
double complex a( lda,*), x(*), y(*)
subroutine cgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
character*1 trans
integer n, m, lda, incx, incy
complex alpha, beta
complex a( lda,*), x(*), y(*)
C SYNOPSIS
void dgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTranspose trans;
Integer n, m, lda, incx, incy;
double alpha, beta;
double (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void sgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTranspose trans;
Integer n, m, lda, incx, incy;
float alpha, beta;
float (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void zgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTranspose trans;
Integer n, m, lda, incx, incy;
Zomplex alpha, beta;
Zomplex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void cgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
MatrixTranspose trans;
Integer n, m, lda, incx, incy;
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_GEMV(3F)_GEMV(3F)
Complex alpha, beta;
Complex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
DESCRIPTION
dgemv , sgemv , dgemv and cgemv perform one of the matrix-vector
operations:
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
y := alpha*conjg( A' )*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an m by n
matrix.
PARAMETERS
trans On entry, trans specifies the operation to be performed as
follows:
FORTRAN
trans = 'N' or 'n' y := alpha*A*x + beta*y.
trans = 'T' or 't' y := alpha*A'*x + beta*y.
trans = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
C
trans = NoTranspose y := alpha*A*x + beta*y.
trans = Transpose y := alpha*A'*x + beta*y.
trans = ConjugateTranspose y := alpha*conjg( A' )*x + beta**y.
Unchanged on exit.
m On entry, m specifies the number of rows of the matrix A. m must
be at least zero.
Unchanged on exit.
n On entry, n specifies the order of the matrix A. n must be at
least zero.
Unchanged on exit.
alpha On entry, 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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_GEMV(3F)_GEMV(3F)
Before entry, the leading m by n part of the array A must contain
the matrix of coefficients.
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 ) ) when trans =
'N' or 'n' or NoTranspose and at least ( 1 + ( m - 1 )*abs( incx
) ) otherwise. 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 + ( m - 1 )*abs( incy ) ) when trans =
'N' or 'n' or NoTranspose and at least ( 1 + ( n - 1 )*abs( incy
) ) otherwise.
Before entry with beta non-zero, the incremented array y must
contain the 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) ].
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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_GEMV(3F)_GEMV(3F)TUNING
Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.
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