static int ATL_trmvLT
(
const enum ATLAS_DIAG Diag,
const int nb,
ATL_CINT N,
const TYPE *A,
ATL_CINT lda,
TYPE *X,
ATL_CINT incX
)
/*
* RETURNS: 0 if TRMV was performed, non-zero if nothing done
*/
{
static void (*trmvK)(ATL_CINT, const TYPE*, ATL_CINT, const TYPE*, TYPE*);
void (*gemv)(ATL_CINT, ATL_CINT, const SCALAR, const TYPE*, ATL_CINT,
const TYPE*, ATL_CINT, const SCALAR, TYPE*, ATL_CINT);
void *vp;
TYPE *x, *y;
const size_t opsize = (N*N+N+N)*sizeof(TYPE)SHIFT;
size_t t0;
#ifdef TCPLX
size_t N2=N+N, lda2 = lda+lda;
TYPE one[2] = {ATL_rone, ATL_rzero};
#else
#define N2 N
#define lda2 lda
#define one ATL_rone
#endif
const size_t incA = ((size_t)lda+1)*(nb SHIFT);
ATL_CINT Nnb = ((N-1)/nb)*nb, Nr = N-Nnb;
ATL_INT j;
if (N < nb+nb)
return(1);
if (opsize > MY_CE)
gemv = Mjoin(PATL,gemvT);
else
gemv = (opsize <= ATL_MulBySize(ATL_L1elts)) ? Mjoin(PATL,gemvT_L1) :
Mjoin(PATL,gemvT_L2);
trmvK = (Diag == AtlasNonUnit) ? ATL_trmvLTNk : ATL_trmvLTUk;
/*
* If X is aligned to Cachelen wt inc=1, use it as y
*/
t0 = (size_t) X;
if (incX == 1 && (ATL_MulByCachelen(ATL_DivByCachelen(t0)) == t0))
{
ATL_INT i;
vp = malloc(ATL_Cachelen+ATL_MulBySize(N));
if (!vp)
return(2);
x = ATL_AlignPtr(vp);
y = X;
for (i=0; i < N2; i++)
{
x[i] = X[i];
X[i] = ATL_rzero;
}
}
else /* allocate both X and Y */
{
vp = malloc((ATL_Cachelen+ATL_MulBySize(N))<<1);
if (!vp)
return(3);
x = ATL_AlignPtr(vp);
y = x + N2;
y = ATL_AlignPtr(y);
Mjoin(PATL,copy)(N, X, incX, x, 1);
Mjoin(PATL,zero)(N, y, 1);
}
for (j=0; j < Nnb; j += nb, A += incA)
{
#ifdef TCPLX
const register size_t j2=j+j, nb2=nb+nb;
#else
#define j2 j
#define nb2 nb
#endif
trmvK(nb, A, lda, x+j2, y+j2);
gemv(N-j-nb, nb, one, A+nb2, lda, x+j2+nb2, 1, one, y+j2, 1);
#ifndef TCPLX
#undef j2
#undef nb2
#endif
}
#ifdef TCPLX
j += j;
#endif
trmvK(Nr, A, lda, x+j, y+j);
if (y != X)
Mjoin(PATL,copy)(N, y, 1, X, incX);
free(vp);
return(0);
}
void ATL_her(const enum ATLAS_UPLO Uplo, ATL_CINT N, const TYPE alpha,
const TYPE *X, ATL_CINT incX, TYPE *A, ATL_CINT lda)
{
const TYPE calpha[2] = {alpha, ATL_rzero};
void *vp=NULL;
TYPE *x, *xt;
ATL_r1kern_t gerk;
ATL_INT CacheElts;
const int ALP1 = (alpha == ATL_rone);
int COPYX, COPYXt;
int mu, nu, minM, minN, alignX, alignXt, FNU, ALIGNX2A;
if (N < 1 || (alpha == ATL_rzero))
return;
/*
* For very small problems, avoid overhead of func calls & data copy
*/
if (N < 50)
{
Mjoin(PATL,refher)(Uplo, N, alpha, X, incX, A, lda);
return;
}
/*
* Determine the GER kernel to use, and its parameters
*/
gerk = ATL_GetR1Kern(N-ATL_s1L_NU, ATL_s1L_NU, A, lda, &mu, &nu,
&minM, &minN, &alignX, &ALIGNX2A, &alignXt,
&FNU, &CacheElts);
/*
* Determine if we need to copy the vectors
*/
COPYX = (incX != 1);
if (!COPYX) /* may still need to copy due to alignment issues */
{
/*
* ATL_Cachelen is the highest alignment that can be requested, so
* make X's % with Cachelen match that of A if you want A & X to have
* the same alignment
*/
if (ALIGNX2A)
{
size_t t1 = (size_t) A, t2 = (size_t) X;
COPYX = (t1 - ATL_MulByCachelen(ATL_DivByCachelen(t1))) !=
(t2 - ATL_MulByCachelen(ATL_DivByCachelen(t2)));
}
else if (alignX)
{
size_t t1 = (size_t) X;
COPYX = ((t1/alignX)*alignX != t1);
}
}
vp = malloc((ATL_Cachelen+ATL_MulBySize(N))*(1+COPYX));
if (!vp)
{
Mjoin(PATL,refher)(Uplo, N, alpha, X, incX, A, lda);
return;
}
xt = ATL_AlignPtr(vp);
if (COPYX)
{
x = xt + N+N;
x = ALIGNX2A ? ATL_Align2Ptr(x, A) : ATL_AlignPtr(x);
Mjoin(PATL,copy)(N, X, incX, x, 1);
}
else
x = (TYPE*) X;
if (ALP1)
Mjoin(PATL,copyConj)(N, X, incX, xt, 1);
else
Mjoin(PATL,moveConj)(N, calpha, X, incX, xt, 1);
if (Uplo == AtlasUpper)
Mjoin(PATL,her_kU)(gerk, N, alpha, x, xt, A, lda);
else
Mjoin(PATL,her_kL)(gerk, N, alpha, x, xt, A, lda);
if (vp)
free(vp);
}
void ATL_gemv
(ATL_CINT M, ATL_CINT N, const SCALAR alpha0, const TYPE *A, ATL_CINT lda,
const TYPE *X, ATL_CINT incX, const SCALAR beta0, TYPE *Y, ATL_CINT incY)
/*
* y = alpha*A*x + beta*y, A is MxN, len(X) = N, len(Y) = M
*/
{
ATL_mvkern_t mvnk, mvnk_b1, mvnk_b0;
void *vp=NULL;
TYPE *x = (TYPE*)X, *y = (TYPE*)Y, *p;
size_t t1, t2;
ATL_INT m, Nm, nr, CacheElts, mb, imb, incy=1;
int mu, nu, alignX, alignY, ALIGNY2A, ForceNU, COPYX, COPYY, APPLYALPHAX;
int minM, minN, DOTBASED;
#ifdef TREAL
#define one ATL_rone
#define Zero ATL_rzero
TYPE alpha = alpha0, beta = beta0;
const int ALPHA_IS_ONE = (alpha0 == ATL_rone);
#else
TYPE one[2] = {ATL_rone, ATL_rzero}, *alpha=(TYPE*)alpha0;
TYPE Zero[2] = {ATL_rzero, ATL_rzero};
TYPE *beta = (TYPE*) beta0;
const int ALPHA_IS_ONE = (alpha0[0] == ATL_rone && alpha[1] == ATL_rzero);
#endif
if (M < 1 || N < 1) /* F77BLAS doesn't scale in either case */
return;
if (SCALAR_IS_ZERO(alpha)) /* No contrib from alpha*A*x */
{
if (!SCALAR_IS_ONE(beta))
{
if (SCALAR_IS_ZERO(beta))
Mjoin(PATL,zero)(M, Y, incY);
else
Mjoin(PATL,scal)(M, beta, Y, incY);
}
return;
}
/*
* ATLAS's mvn kernels loop over M in inner loop, which is bad news if M is
* very small. Call code that requires no copy of X & Y for these degenerate
* cases
*/
if (M < 16)
{
Mjoin(PATL,mvnk_Mlt16)(M, N, alpha0, A, lda, X, incX, beta0, Y, incY);
return;
}
/*
* Get mvnk kernel pointer along with any usage guidelines, and use the
* optimized CacheElts to compute the correct blocking factor
* For no transpose, X alignment args really apply to Y, and vice versa.
*/
mvnk_b1 = ATL_GetMVNKern(M, N, A, lda, &mvnk_b0, &DOTBASED, &mu, &nu,
&minM, &minN, &alignY, &ALIGNY2A, &alignX,
&ForceNU, &CacheElts);
/*
* Set up to handle case where kernel requires N to be a multiple if NU
*/
if (ForceNU)
{
Nm = (N/nu)*nu;
nr = N - Nm;
}
else
{
Nm = N;
nr = 0;
}
/*
* For very small N, we can't afford the data copy, so call special case code
*/
if (N < 4 || Nm < 1)
{
Mjoin(PATL,mvnk_smallN)(M, N, alpha0, A, lda, X, incX, beta0, Y, incY);
return;
}
if (CacheElts)
{
mb = (CacheElts - 2*nu) / (2*(nu+1));
mb = (mb > mu) ? (mb/mu)*mu : M;
mb = (mb > M) ? M : mb;
}
else
mb = M;
/*
*****************************************************************************
Figure out whether vecs need be copied, and which one will be scaled by alpha
*****************************************************************************
*/
COPYX = (incX != 1);
if (!COPYX && alignX)
{
t1 = (size_t) X;
COPYX = ((t1/alignX)*alignX != t1);
}
COPYY = (incY != 1);
if (!COPYY) /* may still need to copy due to alignment issues */
{
/*
* ATL_Cachelen is the highest alignment that can be requested, so
* make X's % with Cachelen match that of A if you want A & X to have
* the same alignment
*/
if (ALIGNY2A)
{
t1 = (size_t) A;
t2 = (size_t) Y;
COPYY = (t1 - ATL_MulByCachelen(ATL_DivByCachelen(t1))) !=
(t2 - ATL_MulByCachelen(ATL_DivByCachelen(t2)));
}
else if (alignY)
{
t1 = (size_t) Y;
COPYY = ((t1/alignY)*alignY != t1);
}
}
if (COPYX != COPYY) /* if only one of them is already being copied */
APPLYALPHAX = COPYX; /* apply alpha to that one */
else if (!COPYY && !COPYX) /* nobody currently being copied means */
{ /* we'll need to force a copy to apply alpha */
APPLYALPHAX = (M < N); /* apply alpha to vector requiring least */
if (!ALPHA_IS_ONE) /* workspace if alpha != 1.0 */
{
COPYX = APPLYALPHAX;
COPYY = !APPLYALPHAX;
}
}
else /* if both are being copied anyway */
APPLYALPHAX = 0; /* apply alpha during update of Y */
if (COPYX | COPYY) /* if I need to copy either vector */
{ /* allocate & align them */
vp = malloc(ATL_MulBySize(COPYY*mb+COPYX*N) + 2*ATL_Cachelen);
/*
* If we cannot allocate enough space to copy the vectors, give up and
* call the simple loop-based implementation
*/
if (!vp)
{
Mjoin(PATL,mvnk_smallN)(M, N, alpha0, A, lda, X, incX, beta0, Y, incY);
return;
}
if (COPYX)
{
x = ATL_AlignPtr(vp);
if (APPLYALPHAX && !ALPHA_IS_ONE)
Mjoin(PATL,cpsc)(N, alpha, X, incX, x, 1);
else
Mjoin(PATL,copy)(N, X, incX, x, 1);
if (COPYY)
y = x + (N SHIFT);
}
else /* if (COPYY) known true by surrounding if */
y = vp;
if (COPYY)
{
y = (ALIGNY2A) ? ATL_Align2Ptr(y, A) : ATL_AlignPtr(y);
beta = Zero;
alpha = one;
}
}
/*
* Apply beta to Y if we aren't copying Y
*/
if (!COPYY && !SCALAR_IS_ONE(beta0))
{
if (SCALAR_IS_ZERO(beta0))
beta = Zero;
else
{
Mjoin(PATL,scal)(M, beta0, Y, incY);
beta = one;
}
}
mvnk = (COPYY || SCALAR_IS_ZERO(beta)) ? mvnk_b0 : mvnk_b1;
m = M;
do
{
imb = Mmin(mb, m);
/*
* Call optimized kernel (can be restricted or general)
*/
if (imb >= minM)
mvnk(imb, Nm, A, lda, x, y);
else
Mjoin(PATL,mvnk_Mlt16)(imb, Nm, one, A, lda, x, 1, beta, y, 1);
/*
* Some kernels require N%NU=0; if so nr is remainder, do cleanup with axpy
*/
if (nr)
Mjoin(PATL,mvnk_smallN)(imb, nr, one, A+((size_t)lda)*(Nm SHIFT), lda,
x+(Nm SHIFT), 1, one, y, 1);
/*
* If we are copying Y, we have formed A*x into y, so scale it by the
* original alpha, by using axpby: Y = beta0*Y + alpha0*y
*/
if (COPYY)
Mjoin(PATL,axpby)(imb, alpha0, y, 1, beta0, Y, incY);
else
y += imb SHIFT;
A += imb SHIFT;
Y += (imb*incY)SHIFT;
m -= imb;
}
while(m);
if (vp)
free(vp);
}
void ATL_ger
(const int M, const int N, const SCALAR alpha0, const TYPE *X,
const int incX, const TYPE *Y, const int incY, TYPE *A, const int lda)
{
#ifdef ATL_CHOICE
const size_t opsize = (M*N+M+N)*sizeof(TYPE)SHIFT;
if (opsize <= ATL_MulBySize(ATL_L1elts))
Mjoin(MY_GER,_L1)(M, N, alpha0, X, incX, Y, incY, A, lda);
else if (opsize <= MY_CE)
Mjoin(MY_GER,_L2)(M, N, alpha0, X, incX, Y, incY, A, lda);
else
Mjoin(MY_GER,_OOC)(M, N, alpha0, X, incX, Y, incY, A, lda);
#else
void (*getX)(const int N, const SCALAR alpha, const TYPE *X,
const int incX, TYPE *Y, const int incY);
ATL_r1kern_t gerk;
void *vp=NULL;
TYPE *x = (TYPE*)X, *y = (TYPE*)Y;
size_t t1, t2;
ATL_INT m, Nm, nr, CacheElts, mb, imb, incy=1;
int mu, nu, alignX, alignY, ALIGNX2A, ForceNU, COPYX, COPYY, APPLYALPHAX;
int minM, minN;
#ifdef TREAL
#define one ATL_rone
TYPE alpha = alpha0;
const int ALPHA_IS_ONE = (alpha0 == ATL_rone);
#else
TYPE one[2] = {ATL_rone, ATL_rzero}, *alpha=(TYPE*)alpha0;
const int ALPHA_IS_ONE = (alpha0[0] == ATL_rone && alpha[1] == ATL_rzero);
#endif
if (M < 1 || N < 1 || SCALAR_IS_ZERO(alpha))
return;
/*
* Get gerk kernel pointer along with any usage guidelines, and use the
* optimized CacheElts to compute the correct blocking factor
*/
gerk = ATL_GetR1Kern(M, N, A, lda, &mu, &nu, &minM, &minN, &alignX,
&ALIGNX2A, &alignY, &ForceNU, &CacheElts);
if (CacheElts)
{
mb = (CacheElts - 2*nu) / (2*(nu+1));
mb = (mb > mu) ? (mb/mu)*mu : M;
mb = (mb > M) ? M : mb;
}
else
mb = M;
/*
* Set up to handle case where kernel requres N to be a multiple if NU
*/
if (ForceNU)
{
Nm = (N/nu)*nu;
nr = N - Nm;
}
else
{
Nm = N;
nr = 0;
}
/*
* For very small N, we can't afford the data copy, so call AXPY-based routine
*/
if (N < 4 || Nm < 1)
{
MY_GERK_AXPY(M, N, alpha0, X, incX, Y, incY, A, lda);
return;
}
/*
* ATLAS's GER kernels loop over M in inner loop, which is bad news if M is
* very small. Call code that requires no copy of A & B for these degenerate
* cases
*/
if (M < 16 || M < minM)
{
MY_GERK_MLT16(M, N, alpha0, X, incX, Y, incY, A, lda);
return;
}
/*
*****************************************************************************
Figure out whether vecs need be copied, and which one will be scaled by alpha
*****************************************************************************
*/
#ifdef Conj_
COPYY = 1;
#else
COPYY = (incY != 1);
if (!COPYY && alignY)
{
t1 = (size_t) Y;
COPYY = ((t1/alignY)*alignY != t1);
}
#endif
COPYX = (incX != 1);
if (!COPYX) /* may still need to copy due to alignment issues */
{
/*
* ATL_Cachelen is the highest alignment that can be requested, so
* make X's % with Cachelen match that of A if you want A & X to have
* the same alignment
*/
if (ALIGNX2A)
{
t1 = (size_t) A;
t2 = (size_t) X;
COPYX = (t1 - ATL_MulByCachelen(ATL_DivByCachelen(t1))) !=
(t2 - ATL_MulByCachelen(ATL_DivByCachelen(t2)));
}
else if (alignX)
{
t1 = (size_t) X;
COPYX = ((t1/alignX)*alignX != t1);
}
}
if (COPYX != COPYY) /* if only one of them is already being copied */
APPLYALPHAX = COPYX; /* apply alpha to that one */
else if (!COPYY && !COPYX) /* nobody currently being copied means */
{ /* we'll need to force a copy to apply alpha */
APPLYALPHAX = (M < N); /* apply alpha to shorter vector */
if (!ALPHA_IS_ONE) /* force copy if alpha != 1.0 */
{
COPYX = APPLYALPHAX;
COPYY = !APPLYALPHAX;
}
}
else /* if both are being copied anyway */
APPLYALPHAX = (M < N); /* apply alpha to shorter vector */
if (COPYX | COPYY) /* if I need to copy either vector */
{ /* allocate & align them */
vp = malloc(ATL_MulBySize(COPYX*mb+COPYY*N) + 2*ATL_Cachelen);
/*
* If we cannot allocate enough space to copy the vectors, give up and
* call the simple loop-based implementation
*/
if (!vp)
{
MY_GERK_AXPY(M, N, alpha0, X, incX, Y, incY, A, lda);
return;
}
if (COPYY)
{
y = ATL_AlignPtr(vp);
x = y + (N SHIFT);
x = (ALIGNX2A) ? ATL_Align2Ptr(x, A) : ATL_AlignPtr(x);
if (!APPLYALPHAX && !ALPHA_IS_ONE) /* need to apply alpha to Y */
{
#ifdef Conj_
Mjoin(PATL,moveConj)(N, alpha, Y, incY, y, 1);
#else
Mjoin(PATL,cpsc)(N, alpha, Y, incY, y, 1);
#endif
alpha = one;
}
else /* do not apply alpha */
#ifdef Conj_
Mjoin(PATL,copyConj)(N, Y, incY, y, 1);
#else
Mjoin(PATL,copy)(N, Y, incY, y, 1);
#endif
}
else if (ALIGNX2A)
x = ATL_Align2Ptr(vp, A);
else
x = ATL_AlignPtr(vp);
}
getX = (COPYX) ? Mjoin(PATL,cpsc) : NULL;
m = M;
do
{
imb = Mmin(mb, m);
if (getX) /* copy X if necessary */
getX(imb, alpha, X, incX, x, 1);
else
x = (TYPE*) X;
/*
* Call optimized kernel (can be restricted or general)
*/
if (imb > minM)
gerk(imb, Nm, x, y, A, lda);
else
Mjoin(PATL,gerk_Mlt16)(imb, Nm, one, x, 1, y, 1, A, lda);
/*
* Some kernels require N%NU=0; if so nr is remainder, do cleanup with axpy
*/
if (nr)
Mjoin(PATL,gerk_axpy)(imb, nr, one, x, 1, y+(Nm SHIFT), 1,
A+((size_t)lda)*(Nm SHIFT), lda);
A += imb SHIFT;
X += (imb*incX)SHIFT;
m -= imb;
imb = Mmin(m,mb);
}
while(m);
if (vp)
free(vp);
#endif
}
void Mjoin(PATL,hemv)
(
const enum ATLAS_UPLO Uplo,
const int N,
const SCALAR alpha,
const TYPE *A,
const int lda,
const TYPE *X,
const int incX,
const SCALAR beta,
TYPE *Y,
const int incY
)
/*
* Purpose
* =======
*
* Mjoin( PATL, hemv ) performs 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 Hermitian matrix.
*
* This is a blocked version of the algorithm. For a more detailed des-
* cription of the arguments of this function, see the reference imple-
* mentation in the ATLAS/src/blas/reference directory.
*
* ---------------------------------------------------------------------
*/
{
const int BETA0 = (*beta == ATL_rzero && beta[1] == ATL_rzero);
const int BETA1 = (*beta == ATL_rone && beta[1] == ATL_rzero);
const int ALPHA1 = (*alpha == ATL_rone && alpha[1] == ATL_rzero);
const int ALPHA0 = (*alpha == ATL_rzero && alpha[1] == ATL_rzero);
if (N <= 0 || (ALPHA0 && BETA1))
return;
if (ALPHA0)
{
if (BETA0)
Mjoin(PATL,zero)(N, Y, incY);
else
Mjoin(PATL,scal)(N, beta, Y, incY);
return;
}
#ifdef USE_GEMV_BASED
if (N >= 240)
{
void *vp=NULL;
TYPE *x=(TYPE*)X, *y=Y, *xh, *yh;
const size_t tX = (size_t)X, tY = (size_t)Y, N2 = N+N;
const int COPYY = !(incY == 1 &&
(ATL_MulByCachelen(ATL_DivByCachelen(tY)) == tY));
const int COPYX = !(incX == 1 && (COPYY || ALPHA1) &&
(ATL_MulByCachelen(ATL_DivByCachelen(tX)) == tX));
const TYPE one[2] = {ATL_rone, ATL_rzero};
const TYPE *calp=one, *cbet=one;
TYPE *tp;
tp = vp = malloc((COPYX+COPYY+2)*(ATL_Cachelen+ATL_MulBySize(N)));
if (!vp)
{
Mjoin(PATL,refhemv)(Uplo, N, alpha, A, lda, X, incX, beta, Y, incY);
return;
}
yh = ATL_AlignPtr(tp);
Mjoin(PATL,zero)(N, yh, 1);
tp = yh + N2;
xh = ATL_AlignPtr(tp);
tp = xh + N2;
if (COPYX)
{
x = ATL_AlignPtr(tp);
if (COPYY || ALPHA1)
{
register ATL_INT i;
register const size_t incX2 = incX+incX;
const TYPE *xx=X;
for (i=0; i < N2; i += 2, xx += incX2)
{
xh[i] = x[i] = *xx;
xh[i+1] = -(x[i+1] = xx[1]);
}
}
else if (alpha[1] == ATL_rzero)
{
register ATL_INT i;
register const size_t incX2 = incX+incX;
register const TYPE ra=(*alpha), ia=alpha[1];
const TYPE *xx=X;
for (i=0; i < N2; i += 2, xx += incX2)
{
register TYPE rx = *xx, ix = xx[1];
x[i] = rx*ra;
x[i+1] = ix*ra;
xh[i] = rx;
xh[i+1] = -ix;
}
}
else
{
register ATL_INT i;
register const size_t incX2 = incX+incX;
register const TYPE ra=(*alpha), ia=alpha[1];
const TYPE *xx=X;
for (i=0; i < N2; i += 2, xx += incX2)
{
register TYPE rx = *xx, ix = xx[1];
x[i] = rx*ra - ix*ia;
x[i+1] = rx*ia + ix*ra;
xh[i] = rx;
xh[i+1] = -ix;
}
}
tp = x + N2;
}
else
Mjoin(PATL,copyConj)(N, X, incX, xh, 1);
if (COPYY)
{
calp = alpha;
cbet = beta;
y = ATL_AlignPtr(tp);
Mjoin(PATL,zero)(N, y, 1);
}
else if (BETA0)
Mjoin(PATL,zero)(N, y, 1);
else if (!BETA1)
Mjoin(PATL,scal)(N, beta, y, 1);
if (Uplo == AtlasLower)
ATL_symvL(Mjoin(PATL,refhemv), 120, N, A, lda, x, y, xh, yh);
else
ATL_symvU(Mjoin(PATL,refhemv), 120, N, A, lda, x, y, xh, yh);
if (COPYY)
{
Mjoin(PATL,axpbyConj)(N, alpha, yh, 1, calp, y, 1);
Mjoin(PATL,axpby)(N, one, y, 1, cbet, Y, incY);
}
else
Mjoin(PATL,axpyConj)(N, alpha, yh, 1, Y, incY);
free(vp);
return;
}
#endif
Mjoin(PATL,refhemv)(Uplo, N, alpha, A, lda, X, incX, beta, Y, incY);
}