Name

sgemv, dgemv, cgemv, zgemv − Matrix-vector product for a general matrix

FORMAT

{S,D,C,Z}GEMV (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)

Arguments

transcharacter∗1
On entry, specifies the operation to be performed:

If trans = ’N’ or ’n’, the operation is y  =  alpha∗Ax + beta∗y. 

If trans = ’T’ or ’t’, the operation is y  =  alpha∗transp(A)∗x + beta∗y. 

If trans = ’C’ or ’c’, the operation is y  =  alpha∗conjug_transp(A)∗x + beta∗y. 
On exit, trans is unchanged. 

minteger∗4
On entry, the number of rows of the matrix A; m >= 0.
On exit, m is unchanged. 

ninteger∗4
On entry, the number of columns 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. The leading m by n part of the array contains the elements of the matrix A.
On exit, a is unchanged. 

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

xreal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a one-dimensional array containing the vector x.  When trans is equal to ’N’ or (1+(n-1)∗|incx|). Otherwise, the length is at least (1+(m-1)∗|incx|). 
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 containing the vector x.  When trans is equal to ’N’ or (1+(m-1)∗|incy|). Otherwise, the length is at least (1+(n-1)∗|incy|). 

If beta= 0, y need not be set.  If beta is 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

The _GEMV subprograms compute a matrix-vector product for either a general matrix or its transpose: y  =  alpha∗Ax + beta∗y
  y  =  alpha∗transp(A)∗x + beta∗y

In addition to these operations, the CGEMV and ZGEMV subprograms compute the matrix-vector product for the conjugate transpose:
  y  =  alpha∗conjug_transp(A)∗x + beta∗y

alphaand betaare scalars, x and y are vectors, and A is an m by n matrix. 

EXAMPLES

REAL∗8 A(20,20), X(20), Y(20), alpha, beta
INCX = 1
INCY = 1
LDA = 20
M = 20
N = 20
alpha = 1.0D0
beta = 0.0D0
CALL DGEMV(’T’,M,N,alpha,A,LDA,X,INCX,beta,Y,INCY)

This FORTRAN code computes the product y  =  transp(A)∗x.

COMPLEX∗8 A(20,20), X(20), Y(20), alpha, beta
INCX = 1
INCY = 1
LDA = 20
M = 20
N = 20
alpha = (1.0, 1.0)
beta = (0.0, 0.0)
CALL CGEMV(’T’,M,N,alpha,A,LDA,X,INCX,beta,Y,INCY)

This FORTRAN code computes the product y  =  transp(A)∗x.