PetscErrorCode FluidFieldDivergence(FluidField f)
{
DALocalInfo info;
Vec u,v,w; // Local, ghosted vectors
PetscErrorCode ierr;
PetscFunctionBegin;
PetscLogEventBegin(EVENT_FluidFieldDivergence,0,0,0,0);
// PetscLogEventRegister(&EVENT_FluidFieldDivergence,"FluidFieldDivergence", 0);
ierr = DAGetLocalInfo(f->da,&info); CHKERRQ(ierr);
ierr = DAGetLocalVector(f->da,&u); CHKERRQ(ierr);
ierr = DAGetLocalVector(f->da,&v); CHKERRQ(ierr);
ierr = DAGlobalToLocalBegin(f->da,f->u,INSERT_VALUES,u); CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd( f->da,f->u,INSERT_VALUES,u); CHKERRQ(ierr);
ierr = DAGlobalToLocalBegin(f->da,f->v,INSERT_VALUES,v); CHKERRQ(ierr);
//TODO: interleaving work with communication here a possible source of optimization?
ierr = DAGlobalToLocalEnd( f->da,f->v,INSERT_VALUES,v); CHKERRQ(ierr);
if( f->is3D )
{
ierr = DAGetLocalVector(f->da,&w); CHKERRQ(ierr);
ierr = DAGlobalToLocalBegin(f->da,f->w,INSERT_VALUES,w); CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd( f->da,f->w,INSERT_VALUES,w); CHKERRQ(ierr);
FluidFieldDivergence_3D(info, f->d, u, v, w, f->div);
ierr = DARestoreLocalVector(f->da,&w); CHKERRQ(ierr);
} else {
FluidFieldDivergence_2D(info, f->d, u, v, f->div);
}
ierr = DARestoreLocalVector(f->da,&u); CHKERRQ(ierr);
ierr = DARestoreLocalVector(f->da,&v); CHKERRQ(ierr);
PetscLogEventEnd(EVENT_FluidFieldDivergence,0,0,0,0);
PetscFunctionReturn(0);
}
PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
{
PetscErrorCode ierr;
DMMG dmmg = (DMMG)ctx;
AppCtx *user = (AppCtx*)dmmg->user;
DA da2 = (DA)dmmg->dm;
DALocalInfo info2;
Field2 **x2,**f2;
Vec X2;
PetscFunctionBegin;
ierr = DAGetLocalInfo(da2,&info2);CHKERRQ(ierr);
/* Get local vectors to hold ghosted parts of X */
ierr = DAGetLocalVector(da2,&X2);CHKERRQ(ierr);
ierr = DAGlobalToLocalBegin(da2,X,INSERT_VALUES,X2);CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd(da2,X,INSERT_VALUES,X2);CHKERRQ(ierr);
/* Access the array inside of X1 */
ierr = DAVecGetArray(da2,X2,(void**)&x2);CHKERRQ(ierr);
/* Access the subvectors in F.
These are not ghosted so directly access the memory locations in F */
ierr = DAVecGetArray(da2,F,(void**)&f2);CHKERRQ(ierr);
/* Evaluate local user provided function */
ierr = FormFunctionLocal2(&info2,0,x2,f2,(void**)user);CHKERRQ(ierr);
ierr = DAVecRestoreArray(da2,F,(void**)&f2);CHKERRQ(ierr);
ierr = DAVecRestoreArray(da2,X2,(void**)&x2);CHKERRQ(ierr);
ierr = DARestoreLocalVector(da2,&X2);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeFunction(SNES snes,Vec x,Vec f,void *ctx) {
PetscInt i,Mx,xs,xm; PetscScalar *xx,*ff,hx; DA da = (DA) ctx; Vec xlocal;
DAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
hx = 1.0/(PetscReal)(Mx-1);
DAGetLocalVector(da,&xlocal);DAGlobalToLocalBegin(da,x,INSERT_VALUES,xlocal); DAGlobalToLocalEnd(da,x,INSERT_VALUES,xlocal);
DAVecGetArray(da,xlocal,&xx); DAVecGetArray(da,f,&ff);
DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
for (i=xs; i<xs+xm; i++) {
if (i == 0 || i == Mx-1) ff[i] = xx[i]/hx;
else ff[i] = (2.0*xx[i] - xx[i-1] - xx[i+1])/hx - hx*PetscExpScalar(xx[i]);
}
DAVecRestoreArray(da,xlocal,&xx); DARestoreLocalVector(da,&xlocal);DAVecRestoreArray(da,f,&ff);
return 0;}
static PetscErrorCode TestQ2Q1DA( void )
{
DA Q2_da,Q1_da,cda;
PetscInt mx,my,mz;
Vec coords,gcoords,gcoords2;
PetscErrorCode ierr;
mx=7;
my=11;
mz=13;
ierr=DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,mx,my,mz,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,3,2,0,0,0,&Q2_da);CHKERRQ(ierr);
ierr = DASetUniformCoordinates(Q2_da,-1.0,1.0,-2.0,2.0,-3.0,3.0);CHKERRQ(ierr);
ierr = DAGetCoordinates(Q2_da,&coords);CHKERRQ(ierr);
ierr = DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,mx,my,mz,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,3,1,0,0,0,&Q1_da);CHKERRQ(ierr);
ierr = DASetCoordinates(Q1_da,coords);CHKERRQ(ierr);
ierr = VecDestroy(coords);CHKERRQ(ierr);
/* Get ghost coordinates one way */
ierr = DAGetGhostedCoordinates(Q1_da,&gcoords);CHKERRQ(ierr);
/* And another */
ierr = DAGetCoordinates(Q1_da,&coords);CHKERRQ(ierr);
ierr = DAGetCoordinateDA(Q1_da,&cda);CHKERRQ(ierr);
ierr = DAGetLocalVector(cda,&gcoords2);CHKERRQ(ierr);
ierr = DAGlobalToLocalBegin(cda,coords,INSERT_VALUES,gcoords2);CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd(cda,coords,INSERT_VALUES,gcoords2);CHKERRQ(ierr);
ierr = CompareGhostedCoords(gcoords,gcoords2);CHKERRQ(ierr);
ierr = DARestoreLocalVector(cda,&gcoords2);CHKERRQ(ierr);
ierr = DADestroy(cda);CHKERRQ(ierr);
ierr = VecScale(coords,10.0);CHKERRQ(ierr);
ierr = VecScale(gcoords,10.0);CHKERRQ(ierr);
ierr = DAGetGhostedCoordinates(Q1_da,&gcoords2);CHKERRQ(ierr);
ierr = CompareGhostedCoords(gcoords,gcoords2);CHKERRQ(ierr);
ierr = VecDestroy(coords);CHKERRQ(ierr);
ierr = VecDestroy(gcoords2);CHKERRQ(ierr);
ierr = VecDestroy(gcoords);CHKERRQ(ierr);
ierr = DADestroy(Q2_da);CHKERRQ(ierr);
ierr = DADestroy(Q1_da);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeJacobian(SNES snes,Vec x,Mat *J,Mat *B,MatStructure *flag,void *ctx){
DA da = (DA) ctx; PetscInt i,Mx,xm,xs; PetscScalar hx,*xx; Vec xlocal;
DAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
hx = 1.0/(PetscReal)(Mx-1);
DAGetLocalVector(da,&xlocal);DAGlobalToLocalBegin(da,x,INSERT_VALUES,xlocal); DAGlobalToLocalEnd(da,x,INSERT_VALUES,xlocal);
DAVecGetArray(da,xlocal,&xx);
DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
for (i=xs; i<xs+xm; i++) {
if (i == 0 || i == Mx-1) { MatSetValue(*J,i,i,1.0/hx,INSERT_VALUES);}
else {
MatSetValue(*J,i,i-1,-1.0/hx,INSERT_VALUES);
MatSetValue(*J,i,i,2.0/hx - hx*PetscExpScalar(xx[i]),INSERT_VALUES);
MatSetValue(*J,i,i+1,-1.0/hx,INSERT_VALUES);
}
}
MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY); MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY); *flag = SAME_NONZERO_PATTERN;
DAVecRestoreArray(da,xlocal,&xx);DARestoreLocalVector(da,&xlocal);
return 0;}
PetscErrorCode FormFunction1(SNES snes,Vec X,Vec F,void *ctx)
{
PetscErrorCode ierr;
DMMG dmmg = (DMMG)ctx;
AppCtx *user = (AppCtx*)dmmg->user;
DA da1 = (DA)dmmg->dm;
DALocalInfo info1;
Field1 **x1,**f1;
Vec X1;
Field2 **x2;
PetscFunctionBegin;
ierr = DAGetLocalInfo(da1,&info1);CHKERRQ(ierr);
/* Get local vectors to hold ghosted parts of X */
ierr = DAGetLocalVector(da1,&X1);CHKERRQ(ierr);
ierr = DAGlobalToLocalBegin(da1,X,INSERT_VALUES,X1);CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd(da1,X,INSERT_VALUES,X1);CHKERRQ(ierr);
/* Access the arrays inside X1 */
ierr = DAVecGetArray(da1,X1,(void**)&x1);CHKERRQ(ierr);
/* Access the subvectors in F.
These are not ghosted so directly access the memory locations in F */
ierr = DAVecGetArray(da1,F,(void**)&f1);CHKERRQ(ierr);
/* Evaluate local user provided function */
if (user->nsolve){
x2 = user->x2;
ierr = FormFunctionLocal1(&info1,x1,x2,f1,(void**)user);CHKERRQ(ierr);
} else {
ierr = FormFunctionLocal1(&info1,x1,0,f1,(void**)user);CHKERRQ(ierr);
}
ierr = DAVecRestoreArray(da1,F,(void**)&f1);CHKERRQ(ierr);
ierr = DAVecRestoreArray(da1,X1,(void**)&x1);CHKERRQ(ierr);
ierr = DARestoreLocalVector(da1,&X1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int FormBratuFunction(SNES snes, Vec v, Vec f, void* ctx)
{
UserBratuCtx* bratu = (UserBratuCtx *) ctx;
DA da = bratu->da;
double lambda = bratu->lambda;
double h = bratu->h;
Vec lv;
int i,j;
int lli, llj, ni, nj;
const double **varr;
double **fvarr;
DAGetCorners(da, &lli, &llj, 0, &ni, &nj, 0);
DAGetLocalVector(da, &lv);
DAGlobalToLocalBegin(da, v, INSERT_VALUES, lv);
DAGlobalToLocalEnd(da, v, INSERT_VALUES,lv);
DAVecGetArray(da, lv, (void**) &varr);
DAVecGetArray(da, f, (void**) &fvarr);
for(j=llj; j<llj+nj; j++){
for(i=lli; i<lli+ni; i++){
if(i==0 || j==0 ||i=bratu->n+1 || j==bratu->n+1){
fvarr[j][i] = 0.0;
}
else{
fvarr[j][i] = -(varr[j-1][i] + varr[j][i-1] + varr[j+1][i] + varr[j][i+1] - 4*varr[j][i])/(h*h) - lambda*exp(varr[j][i]);
}
}
}
DAVecRestoreArray(da, f, (void**) &fvarr);
DAVecRestoreArray(da, lv, (void**) &varr);
DARestoreLocalVector(da, &lv);
return 0;
}
/*
WholeMSurfFunctionGradient - Evaluates function and gradient over the
whole grid
Input:
daapplication - TAO application object
da - distributed array
X - the current point, at which the function and gradient are evaluated
ptr - user-defined application context
Output:
f - value of the objective funtion at X
G - gradient at X
*/
static int WholeMSurfFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) {
AppCtx *user = (AppCtx*)ptr;
Vec localX, localG;
PetscInt i, j;
int info;
PetscInt xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
double **x, **g;
double floc = 0.0;
PetscScalar zero = 0.0;
double hx, hy, area;
double dvdx, dvdy, flow, fup;
double areadivf;
hx = user->hx;
hy = user->hy;
area = user->area;
info = DAGetLocalVector(da, &localX); CHKERRQ(info);
info = DAGetLocalVector(da, &localG); CHKERRQ(info);
info = VecSet(G, zero); CHKERRQ(info);
info = VecSet(localG, zero); CHKERRQ(info);
info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info);
info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);
xe = gxs + gxm - 1;
ye = gys + gym - 1;
for (j = ys; j < ye; j++) {
for (i = xs; i < xe; i++) {
/* lower triangle contribution */
dvdx = (x[j][i] - x[j][i+1]) / hx;
dvdy = (x[j][i] - x[j+1][i]) / hy;
flow = sqrt( 1 + dvdx * dvdx + dvdy * dvdy );
areadivf = area / flow;
g[j][i] += (dvdx / hx + dvdy / hy) * areadivf;
g[j][i+1] += (-dvdx / hx) * areadivf;
g[j+1][i] += (-dvdy / hy) * areadivf;
/* upper triangle contribution */
dvdx = (x[j+1][i+1] - x[j+1][i]) / hx;
dvdy = (x[j+1][i+1] - x[j][i+1]) / hy;
fup = sqrt( 1 + dvdx * dvdx + dvdy * dvdy );
areadivf = area / fup;
g[j][i+1] += (-dvdy / hy) * areadivf;
g[j+1][i] += (-dvdx / hx) * areadivf;
g[j+1][i+1] += (dvdx / hx + dvdy / hy) * areadivf;
floc += area * (flow + fup);
}
}
info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); CHKERRQ(info);
info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info);
info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);
info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
info = DARestoreLocalVector(da, &localG); CHKERRQ(info);
info = PetscLogFlops((xe-xs) * (ye-ys) * 42); CHKERRQ(info);
return 0;
} /* WholeMSurfFunctionGradient */
static int TaoDA2dLoopADFunctionGradient(TAO_APPLICATION tao, DA da, Vec X, double *f, Vec G, void * ctx) {
TaoDA2D4DOFADICFGCtx *myapp = (TaoDA2D4DOFADICFGCtx*) ctx;
MPI_Comm comm;
Vec localX, localG;
int info, i, j, coor[2];
int xs, xm, mx, xe, ys, ym, ye, my;
PetscScalar zero=0.0, floc = 0.0;
DERIV_TYPE adF,*adX=myapp->adX;
Field **x,**g;
info = DAGetLocalVector(da, &localX); CHKERRQ(info);
info = DAGetLocalVector(da, &localG); CHKERRQ(info);
info = VecSet(G, zero); CHKERRQ(info);
info = VecSet(localG, zero); CHKERRQ(info);
info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info);
info = DAGetCorners(da, &xs, &ys, PETSC_NULL, &xm, &ym, PETSC_NULL); CHKERRQ(info);
xe = xs + xm;
ye = ys + ym;
for (j = ys; j < ye; j++) {
for (i = xs; i < xe; i++) {
DERIV_val(adX[0]) = x[j][i].x;
DERIV_val(adX[1]) = x[j][i].y;
DERIV_val(adX[2]) = x[j][i].vpotx;
DERIV_val(adX[3]) = x[j][i].vpoty;
DERIV_val(adX[4]) = x[j][i+1].x;
DERIV_val(adX[5]) = x[j][i+1].y;
DERIV_val(adX[6]) = x[j][i+1].vpotx;
DERIV_val(adX[7]) = x[j][i+1].vpoty;
DERIV_val(adX[8]) = x[j+1][i].x;
DERIV_val(adX[9]) = x[j+1][i].y;
DERIV_val(adX[10]) = x[j+1][i].vpotx;
DERIV_val(adX[11]) = x[j+1][i].vpoty;
DERIV_val(adX[12]) = x[j+1][i+1].x;
DERIV_val(adX[13]) = x[j+1][i+1].y;
DERIV_val(adX[14]) = x[j+1][i+1].vpotx;
DERIV_val(adX[15]) = x[j+1][i+1].vpoty;
coor[0] = i; coor[1] = j;
info = myapp->computeadicfunctiongradient(coor,adX,&adF,myapp->elementfgctx);
CHKERRQ(info);
floc += DERIV_val(adF);
g[j][i].x += DERIV_grad(adF)[0];
g[j][i].y += DERIV_grad(adF)[1];
g[j][i].vpotx += DERIV_grad(adF)[2];
g[j][i].vpoty += DERIV_grad(adF)[3];
g[j][i+1].x += DERIV_grad(adF)[4];
g[j][i+1].y += DERIV_grad(adF)[5];
g[j][i+1].vpotx += DERIV_grad(adF)[6];
g[j][i+1].vpoty += DERIV_grad(adF)[7];
g[j+1][i].x += DERIV_grad(adF)[8];
g[j+1][i].y += DERIV_grad(adF)[9];
g[j+1][i].vpotx += DERIV_grad(adF)[10];
g[j+1][i].vpoty += DERIV_grad(adF)[11];
g[j+1][i+1].x += DERIV_grad(adF)[12];
g[j+1][i+1].y += DERIV_grad(adF)[13];
g[j+1][i+1].vpotx += DERIV_grad(adF)[14];
g[j+1][i+1].vpoty += DERIV_grad(adF)[15];
}
}
info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info);
info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
info = DARestoreLocalVector(da, &localG); CHKERRQ(info);
info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);
PetscLogFlops((ye-ys)*(xe-xs)*(myapp->elementfgflops + 33));
PetscObjectGetComm((PetscObject)da,&comm); CHKERRQ(info);
info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, comm); CHKERRQ(info);
PetscFunctionReturn(0);
} /* TaoDA2dLoopADFunctionGradient */
void PETSC_STDCALL darestorelocalvector_(DM dm,Vec* g, int *__ierr ){
*__ierr = DARestoreLocalVector(
(DM)PetscToPointer((dm) ),g);
}
/* FormFunctionGradient - Evaluates the function and corresponding gradient.
Input Parameters:
. taoapp - the TAO_APPLICATION context
. XX - input vector
. userCtx - optional user-defined context, as set by TaoSetFunctionGradient()
Output Parameters:
. fcn - the newly evaluated function
. GG - vector containing the newly evaluated gradient
*/
int FormFunctionGradient(TAO_APPLICATION taoapp, Vec X, double *fcn,Vec G,void *userCtx){
AppCtx * user = (AppCtx *) userCtx;
int info;
PetscInt i,j;
PetscInt mx=user->mx, my=user->my;
PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
double ft=0;
double hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy, area=0.5*hx*hy;
double rhx=mx+1, rhy=my+1;
double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
double df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
PetscScalar **g, **x;
Vec localX;
/* Get local mesh boundaries */
info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info);
/* Scatter ghost points to local vector */
info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
/* Get pointers to vector data */
info = DAVecGetArray(user->da,localX,(void**)&x);
info = DAVecGetArray(user->da,G,(void**)&g);
/* Compute function and gradient over the locally owned part of the mesh */
for (j=ys; j<ys+ym; j++){
for (i=xs; i< xs+xm; i++){
xc = x[j][i];
xlt=xrb=xl=xr=xb=xt=xc;
if (i==0){ /* left side */
xl= user->left[j-ys+1];
xlt = user->left[j-ys+2];
} else {
xl = x[j][i-1];
}
if (j==0){ /* bottom side */
xb=user->bottom[i-xs+1];
xrb =user->bottom[i-xs+2];
} else {
xb = x[j-1][i];
}
if (i+1 == gxs+gxm){ /* right side */
xr=user->right[j-ys+1];
xrb = user->right[j-ys];
} else {
xr = x[j][i+1];
}
if (j+1==gys+gym){ /* top side */
xt=user->top[i-xs+1];
xlt = user->top[i-xs];
}else {
xt = x[j+1][i];
}
if (i>gxs && j+1<gys+gym){
xlt = x[j+1][i-1];
}
if (j>gys && i+1<gxs+gxm){
xrb = x[j-1][i+1];
}
d1 = (xc-xl);
d2 = (xc-xr);
d3 = (xc-xt);
d4 = (xc-xb);
d5 = (xr-xrb);
d6 = (xrb-xb);
d7 = (xlt-xl);
d8 = (xt-xlt);
df1dxc = d1*hydhx;
df2dxc = ( d1*hydhx + d4*hxdhy );
df3dxc = d3*hxdhy;
df4dxc = ( d2*hydhx + d3*hxdhy );
df5dxc = d2*hydhx;
df6dxc = d4*hxdhy;
d1 *= rhx;
d2 *= rhx;
d3 *= rhy;
d4 *= rhy;
d5 *= rhy;
d6 *= rhx;
d7 *= rhy;
d8 *= rhx;
f1 = sqrt( 1.0 + d1*d1 + d7*d7);
f2 = sqrt( 1.0 + d1*d1 + d4*d4);
f3 = sqrt( 1.0 + d3*d3 + d8*d8);
f4 = sqrt( 1.0 + d3*d3 + d2*d2);
f5 = sqrt( 1.0 + d2*d2 + d5*d5);
f6 = sqrt( 1.0 + d4*d4 + d6*d6);
f2 = sqrt( 1.0 + d1*d1 + d4*d4);
f4 = sqrt( 1.0 + d3*d3 + d2*d2);
ft = ft + (f2 + f4);
df1dxc /= f1;
df2dxc /= f2;
df3dxc /= f3;
df4dxc /= f4;
df5dxc /= f5;
df6dxc /= f6;
g[j][i] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc ) * 0.5;
}
}
/* Compute triangular areas along the border of the domain. */
if (xs==0){ /* left side */
for (j=ys; j<ys+ym; j++){
d3=(user->left[j-ys+1] - user->left[j-ys+2])*rhy;
d2=(user->left[j-ys+1] - x[j][0]) *rhx;
ft = ft+sqrt( 1.0 + d3*d3 + d2*d2);
}
}
if (ys==0){ /* bottom side */
for (i=xs; i<xs+xm; i++){
d2=(user->bottom[i+1-xs]-user->bottom[i-xs+2])*rhx;
d3=(user->bottom[i-xs+1]-x[0][i])*rhy;
ft = ft+sqrt( 1.0 + d3*d3 + d2*d2);
}
}
if (xs+xm==mx){ /* right side */
for (j=ys; j< ys+ym; j++){
d1=(x[j][mx-1] - user->right[j-ys+1])*rhx;
d4=(user->right[j-ys]-user->right[j-ys+1])*rhy;
ft = ft+sqrt( 1.0 + d1*d1 + d4*d4);
}
}
if (ys+ym==my){ /* top side */
for (i=xs; i<xs+xm; i++){
d1=(x[my-1][i] - user->top[i-xs+1])*rhy;
d4=(user->top[i-xs+1] - user->top[i-xs])*rhx;
ft = ft+sqrt( 1.0 + d1*d1 + d4*d4);
}
}
if (ys==0 && xs==0){
d1=(user->left[0]-user->left[1])/hy;
d2=(user->bottom[0]-user->bottom[1])*rhx;
ft +=sqrt( 1.0 + d1*d1 + d2*d2);
}
if (ys+ym == my && xs+xm == mx){
d1=(user->right[ym+1] - user->right[ym])*rhy;
d2=(user->top[xm+1] - user->top[xm])*rhx;
ft +=sqrt( 1.0 + d1*d1 + d2*d2);
}
ft=ft*area;
info = MPI_Allreduce(&ft,fcn,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD);CHKERRQ(info);
/* Restore vectors */
info = DAVecRestoreArray(user->da,localX,(void**)&x);
info = DAVecRestoreArray(user->da,G,(void**)&g);
/* Scatter values to global vector */
info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
info = PetscLogFlops(67*xm*ym); CHKERRQ(info);
return 0;
}
/*
QuadraticH - Evaluates Hessian matrix.
Input Parameters:
. user - user-defined context, as set by TaoSetHessian()
. X - input vector
Output Parameter:
. H - Hessian matrix
*/
int QuadraticH(AppCtx *user, Vec X, Mat Hessian)
{
int info;
PetscInt i,j,k;
PetscInt mx=user->mx, my=user->my;
PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
double hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
double hl,hr,ht,hb,hc,htl,hbr;
PetscScalar **x, v[7];
MatStencil col[7],row;
Vec localX;
PetscTruth assembled;
/* Get local mesh boundaries */
info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info);
/* Scatter ghost points to local vector */
info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
/* Get pointers to vector data */
info = DAVecGetArray(user->da,localX,(void**)&x);
/* Initialize matrix entries to zero */
info = MatAssembled(Hessian,&assembled); CHKERRQ(info);
if (assembled){info = MatZeroEntries(Hessian); CHKERRQ(info);}
/* Set various matrix options */
info = MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE); CHKERRQ(info);
/* Compute Hessian over the locally owned part of the mesh */
for (j=ys; j<ys+ym; j++){
for (i=xs; i< xs+xm; i++){
xc = x[j][i];
xlt=xrb=xl=xr=xb=xt=xc;
/* Left side */
if (i==0){
xl = user->left[j-ys+1];
xlt = user->left[j-ys+2];
} else {
xl = x[j][i-1];
}
if (j==0){
xb = user->bottom[i-xs+1];
xrb = user->bottom[i-xs+2];
} else {
xb = x[j-1][i];
}
if (i+1 == mx){
xr = user->right[j-ys+1];
xrb = user->right[j-ys];
} else {
xr = x[j][i+1];
}
if (j+1==my){
xt = user->top[i-xs+1];
xlt = user->top[i-xs];
}else {
xt = x[j+1][i];
}
if (i>0 && j+1<my){
xlt = x[j+1][i-1];
}
if (j>0 && i+1<mx){
xrb = x[j-1][i+1];
}
d1 = (xc-xl)/hx;
d2 = (xc-xr)/hx;
d3 = (xc-xt)/hy;
d4 = (xc-xb)/hy;
d5 = (xrb-xr)/hy;
d6 = (xrb-xb)/hx;
d7 = (xlt-xl)/hy;
d8 = (xlt-xt)/hx;
f1 = sqrt( 1.0 + d1*d1 + d7*d7);
f2 = sqrt( 1.0 + d1*d1 + d4*d4);
f3 = sqrt( 1.0 + d3*d3 + d8*d8);
f4 = sqrt( 1.0 + d3*d3 + d2*d2);
f5 = sqrt( 1.0 + d2*d2 + d5*d5);
f6 = sqrt( 1.0 + d4*d4 + d6*d6);
hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
(-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
(-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
(-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
(-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
(hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
(hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);
hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0;
row.j = j; row.i = i;
k=0;
if (j>0){
v[k]=hb;
col[k].j = j - 1; col[k].i = i;
k++;
}
if (j>0 && i < mx -1){
v[k]=hbr;
col[k].j = j - 1; col[k].i = i+1;
k++;
}
if (i>0){
v[k]= hl;
col[k].j = j; col[k].i = i-1;
k++;
}
v[k]= hc;
col[k].j = j; col[k].i = i;
k++;
if (i < mx-1 ){
v[k]= hr;
col[k].j = j; col[k].i = i+1;
k++;
}
if (i>0 && j < my-1 ){
v[k]= htl;
col[k].j = j+1; col[k].i = i-1;
k++;
}
if (j < my-1 ){
v[k]= ht;
col[k].j = j+1; col[k].i = i;
k++;
}
/*
Set matrix values using local numbering, which was defined
earlier, in the main routine.
*/
info = MatSetValuesStencil(Hessian,1,&row,k,col,v,INSERT_VALUES);
CHKERRQ(info);
}
}
/* Restore vectors */
info = DAVecRestoreArray(user->da,localX,(void**)&x);
info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
/* Assemble the matrix */
info = MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = PetscLogFlops(199*xm*ym); CHKERRQ(info);
return 0;
}
int FormFunctionGradient(TAO_APPLICATION taoapp, Vec X, double *fcn,Vec G,void *ptr)
{
AppCtx* user=(AppCtx*)ptr;
int info;
PetscInt i,j,k,kk;
PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
PetscReal hx,hy,hxhy,hxhx,hyhy;
PetscReal xi,v[5];
PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
PetscReal vmiddle, vup, vdown, vleft, vright;
PetscReal tt,f1,f2;
PetscReal *x,*g,zero=0.0;
Vec localX;
nx=user->nx;
ny=user->ny;
hx=two*pi/(nx+1.0);
hy=two*user->b/(ny+1.0);
hxhy=hx*hy;
hxhx=one/(hx*hx);
hyhy=one/(hy*hy);
info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = VecSet(G, zero); CHKERRQ(info);
/*
Get local grid boundaries
*/
info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);
info = VecGetArray(localX,&x); CHKERRQ(info);
info = VecGetArray(G,&g); CHKERRQ(info);
for (i=xs; i< xs+xm; i++){
xi=(i+1)*hx;
trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
trule5=trule1; /* L(i,j-1) */
trule6=trule2; /* U(i,j+1) */
vdown=-(trule5+trule2)*hyhy;
vleft=-hxhx*(trule2+trule4);
vright= -hxhx*(trule1+trule3);
vup=-hyhy*(trule1+trule6);
vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
for (j=ys; j<ys+ym; j++){
row=(j-gys)*gxm + (i-gxs);
v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
k=0;
if (j>gys){
v[k]=vdown; col[k]=row - gxm; k++;
}
if (i>gxs){
v[k]= vleft; col[k]=row - 1; k++;
}
v[k]= vmiddle; col[k]=row; k++;
if (i+1 < gxs+gxm){
v[k]= vright; col[k]=row+1; k++;
}
if (j+1 <gys+gym){
v[k]= vup; col[k] = row+gxm; k++;
}
tt=0;
for (kk=0;kk<k;kk++){
tt+=v[kk]*x[col[kk]];
}
row=(j-ys)*xm + (i-xs);
g[row]=tt;
}
}
info = VecRestoreArray(localX,&x); CHKERRQ(info);
info = VecRestoreArray(G,&g); CHKERRQ(info);
info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
info = VecDot(X,G,&f1); CHKERRQ(info);
info = VecDot(user->B,X,&f2); CHKERRQ(info);
info = VecAXPY(G, one, user->B); CHKERRQ(info);
*fcn = f1/2.0 + f2;
info = PetscLogFlops((91 + 10*ym) * xm); CHKERRQ(info);
return 0;
}
static PetscErrorCode BodFunctionLocal(DALocalInfo *info, Node *Hu, Node *f, AppCtx *user)
{
PetscErrorCode ierr;
PetscReal rg = user->rho * user->g, dx = user->dx;
PetscScalar *M, *Bstag, *beta,
duH, ul, u, ur, dHdx, Fl, Fr, Tl, Tr;
PetscInt i, Mx = info->mx;
Vec locBstag;
PetscFunctionBegin;
/* we need stencil width on Bstag (but not for M, beta) */
ierr = DAGetLocalVector(user->scalarda,&locBstag);CHKERRQ(ierr); /* do NOT destroy it */
ierr = DAGlobalToLocalBegin(user->scalarda,user->Bstag,INSERT_VALUES,locBstag); CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd(user->scalarda,user->Bstag,INSERT_VALUES,locBstag); CHKERRQ(ierr);
ierr = DAVecGetArray(user->scalarda,locBstag,&Bstag);CHKERRQ(ierr);
ierr = DAVecGetArray(user->scalarda,user->M,&M);CHKERRQ(ierr);
ierr = DAVecGetArray(user->scalarda,user->beta,&beta);CHKERRQ(ierr);
for (i = info->xs; i < info->xs + info->xm; i++) {
/* MASS CONT */
if (i == 0) {
/* residual at left-most point is Dirichlet cond. */
f[0].H = Hu[0].H - user->H0;
} else {
/* centered difference IS UNSTABLE:
duH = Hu[i+1].u * Hu[i+1].H - ( (i == 1) ? 0.0 : Hu[i-1].u * Hu[i-1].H );
duH *= 0.5; */
if (user->upwind1) {
/* 1st-order upwind; leftward difference because u > 0 (because dH/dx < 0) */
duH = Hu[i].u * Hu[i].H - ( (i == 1) ? 0.0 : Hu[i-1].u * Hu[i-1].H );
} else {
/* 2nd-order upwind; see Beam-Warming discussion in R. LeVeque, "Finite Volume ..." */
if (i == 1) { /* use PDE M - (uH)_x = 0 to get quadratic poly, then diff that */
duH = - dx * M[0] + 2.0 * Hu[1].u * Hu[1].H;
} else {
duH = 3.0 * Hu[i].u * Hu[i].H - 4.0 * Hu[i-1].u * Hu[i-1].H;
/* if i == 2 then u=0 so uH = 0 */
if (i >= 3) duH += Hu[i-2].u * Hu[i-2].H;
duH *= 0.5;
}
}
f[i].H = dx * M[i] - duH;
}
/* SSA */
if (i == 0) {
/* residual at left-most point is Dirichlet cond. */
f[0].u = Hu[0].u - 0.0;
} else {
/* residual: SSA eqn */
/* consecutive values of u */
ul = (i == 1) ? 0.0 : Hu[i-1].u;
u = Hu[i].u;
ur = (i == Mx-1) ? -1.1e30 : Hu[i+1].u;
/* surface slope */
if (i == 1) {
dHdx = (Hu[i+1].H - user->H0) / (2.0 * dx);
} else if (i == Mx-1) {
/* nearly 2nd-order global convergence seems to occur even with this:
dHdx = (Hu[i].H - Hu[i-1].H) / dx; */
dHdx = (3.0*Hu[i].H - 4.0*Hu[i-1].H + Hu[i-2].H) / (2.0 * dx);
} else { /* generic case */
dHdx = (Hu[i+1].H - Hu[i-1].H) / (2.0 * dx);
}
/* vertically-integrated longitudinal stress */
Fl = GetFSR(dx,user->epsilon,user->n, ul,u);
if (i == Mx-1) {
Tl = 2.0 * (Hu[i-1].H + Hu[i].H) * Bstag[i-1] * Fl;
Tr = (1.0 - user->rho / user->rhow) * user->rho * user->g * Hu[i].H * Hu[i].H;
/* exact value: Tr = 2.0 * user->Txc; */
} else {
Fr = GetFSR(dx,user->epsilon,user->n, u,ur);
Tl = (Hu[i-1].H + Hu[i].H) * Bstag[i-1] * Fl;
Tr = (Hu[i].H + Hu[i+1].H) * Bstag[i] * Fr;
}
f[i].u = (Tr - Tl) - dx * beta[i] * u - dx * rg * Hu[i].H * dHdx; /* SSA */
}
}
ierr = DAVecRestoreArray(user->scalarda,locBstag,&Bstag);CHKERRQ(ierr);
ierr = DAVecRestoreArray(user->scalarda,user->M,&M);CHKERRQ(ierr);
ierr = DAVecRestoreArray(user->scalarda,user->beta,&beta);CHKERRQ(ierr);
ierr = DARestoreLocalVector(user->scalarda,&locBstag);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static int TaoDA2dLoopADFunctionGradient(TAO_APPLICATION tao, DA da, Vec X, double *f, Vec G, void * ctx) {
TaoDA2D1DOFADICFGCtx *myapp = (TaoDA2D1DOFADICFGCtx*) ctx;
MPI_Comm comm;
Vec localX, localG;
int info, i, j, coor[2];
int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
PetscScalar **x, **g;
PetscScalar floc = 0.0;
PetscScalar zero = 0.0;
DERIV_TYPE adF,*adX=myapp->adX;
info = DAGetLocalVector(da, &localX); CHKERRQ(info);
info = DAGetLocalVector(da, &localG); CHKERRQ(info);
info = VecSet(G, zero); CHKERRQ(info);
info = VecSet(localG, zero); CHKERRQ(info);
info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info);
info = DAGetCorners(da, &xs, &ys, PETSC_NULL, &xm, &ym, PETSC_NULL); CHKERRQ(info);
info = DAGetGhostCorners(da, &gxs, &gys, PETSC_NULL, &gxm, &gym, PETSC_NULL); CHKERRQ(info);
xe = gxs + gxm - 1;
ye = gys + gym - 1;
for (j = ys; j < ye; j++) {
for (i = xs; i < xe; i++) {
DERIV_val(adX[0]) = x[j][i];
DERIV_val(adX[1]) = x[j][i+1];
DERIV_val(adX[2]) = x[j+1][i];
DERIV_val(adX[3]) = x[j+1][i+1];
coor[0] = i; coor[1] = j;
info = myapp->computeadicfunctiongradient(coor,adX,&adF,myapp->elementfgctx);
CHKERRQ(info);
floc += DERIV_val(adF);
g[j][i] += DERIV_grad(adF)[0];
g[j][i+1] += DERIV_grad(adF)[1];
g[j+1][i] += DERIV_grad(adF)[2];
g[j+1][i+1] += DERIV_grad(adF)[3];
}
}
PetscLogFlops((ye-ys)*(xe-xs)*(myapp->elementfgflops + 5));
PetscObjectGetComm((PetscObject)da,&comm); CHKERRQ(info);
info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, comm); CHKERRQ(info);
info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info);
info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);
info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
info = DARestoreLocalVector(da, &localG); CHKERRQ(info);
PetscFunctionReturn(0);
} /* TaoDA2dLoopADFunctionGradient */
/*
WholeMSurfHessian - Evaluates Hessian over the whole grid
Input:
daapplication - TAO application object
da - distributed array
X - the current point, at which the function and gradient are evaluated
ptr - user-defined application context
Output:
H - Hessian at X
*/
static int WholeMSurfHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) {
AppCtx *user = (AppCtx*)ptr;
Vec localX;
int info;
PetscInt i, j, ind[4];
PetscInt xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
double smallH[4][4];
double **x;
double hx, hy, area, byhxhx, byhyhy;
double dvdx, dvdy, flow, fup;
double areadivf, areadivf3;
PetscTruth assembled;
hx = user->hx;
hy = user->hy;
area = user->area;
byhxhx = 1.0 / (hx * hx);
byhyhy = 1.0 / (hy * hy);
info = DAGetLocalVector(da, &localX); CHKERRQ(info);
info = MatAssembled(H,&assembled); CHKERRQ(info);
if (assembled){info = MatZeroEntries(H); CHKERRQ(info);}
info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);
info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);
xe = gxs + gxm - 1;
ye = gys + gym - 1;
for (j = ys; j < ye; j++) {
for (i = xs; i < xe; i++) {
/* 0 is 0,0; 1 is 1,0; 2 is 0,1; 3 is 1,1 */
dvdx = (x[j][i] - x[j][i+1]) / hx; /* lower triangle contribution */
dvdy = (x[j][i] - x[j+1][i]) / hy;
flow = sqrt( 1 + dvdx * dvdx + dvdy * dvdy );
dvdx = dvdx / hx;
dvdy = dvdy / hy;
areadivf = area / flow;
areadivf3 = areadivf / (flow * flow);
smallH[0][0] = areadivf * (byhxhx + byhyhy) - areadivf3 * (dvdx + dvdy) * (dvdx + dvdy);
smallH[0][1] = areadivf * (-byhxhx) + areadivf3 * (dvdx + dvdy) * (dvdx);
smallH[0][2] = areadivf * (-byhyhy) + areadivf3 * (dvdx + dvdy) * (dvdy);
smallH[0][3] = 0.0;
smallH[1][1] = areadivf * byhxhx - areadivf3 * dvdx * dvdx;
smallH[1][2] = areadivf3 * (-dvdx) * dvdy;
smallH[2][2] = areadivf * byhyhy - areadivf3 * dvdy * dvdy;
/* upper triangle contribution */
dvdx = (x[j+1][i+1] - x[j+1][i]) / hx;
dvdy = (x[j+1][i+1] - x[j][i+1]) / hy;
fup = sqrt( 1 + dvdx * dvdx + dvdy * dvdy );
dvdx = dvdx / hx;
dvdy = dvdy / hy;
areadivf = area / fup;
areadivf3 = areadivf / (fup * fup);
smallH[1][1] += areadivf * byhyhy - areadivf3 * dvdy * dvdy;
smallH[1][2] += areadivf3 * (-dvdy) * dvdx;
smallH[2][2] += areadivf * byhxhx - areadivf3 * (dvdx * dvdx);
smallH[1][3] = areadivf * (-byhyhy) + areadivf3 * (dvdx + dvdy) * dvdy;
smallH[2][3] = areadivf * (-byhxhx) + areadivf3 * (dvdx + dvdy) * dvdx;
smallH[3][3] = areadivf * (byhxhx + byhyhy) - areadivf3 * (dvdx + dvdy) * (dvdx + dvdy);
smallH[1][0] = smallH[0][1];
smallH[2][0] = smallH[0][2];
smallH[3][0] = smallH[0][3];
smallH[2][1] = smallH[1][2];
smallH[3][1] = smallH[1][3];
smallH[3][2] = smallH[2][3];
ind[0] = (j-gys) * gxm + (i-gxs);
ind[1] = ind[0] + 1;
ind[2] = ind[0] + gxm;
ind[3] = ind[2] + 1;
info = MatSetValuesLocal(H,4,ind,4,ind,(PetscScalar*)smallH,ADD_VALUES); CHKERRQ(info);
}
}
info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
info = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = MatSetOption(H, MAT_SYMMETRIC, PETSC_TRUE); CHKERRQ(info);
info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
info = PetscLogFlops((xe-xs) * (ye-ys) * 83 + 4); CHKERRQ(info);
return 0;
} /* WholeMSurfHessian */
/*
FormFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. snes - the SNES context
. x - input vector
. ctx - optional user-defined context, as set by SNESSetFunction()
Output Parameter:
. f - function vector
Note:
The user-defined context can contain any application-specific
data needed for the function evaluation.
*/
PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *ctx)
{
ApplicationCtx *user = (ApplicationCtx*) ctx;
DA da = user->da;
PetscScalar *xx,*ff,*FF,d;
PetscErrorCode ierr;
PetscInt i,M,xs,xm;
Vec xlocal;
PetscFunctionBegin;
ierr = DAGetLocalVector(da,&xlocal);CHKERRQ(ierr);
/*
Scatter ghost points to local vector, using the 2-step process
DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
By placing code between these two statements, computations can
be done while messages are in transition.
*/
ierr = DAGlobalToLocalBegin(da,x,INSERT_VALUES,xlocal);CHKERRQ(ierr);
ierr = DAGlobalToLocalEnd(da,x,INSERT_VALUES,xlocal);CHKERRQ(ierr);
/*
Get pointers to vector data.
- The vector xlocal includes ghost point; the vectors x and f do
NOT include ghost points.
- Using DAVecGetArray() allows accessing the values using global ordering
*/
ierr = DAVecGetArray(da,xlocal,&xx);CHKERRQ(ierr);
ierr = DAVecGetArray(da,f,&ff);CHKERRQ(ierr);
ierr = DAVecGetArray(da,user->F,&FF);CHKERRQ(ierr);
/*
Get local grid boundaries (for 1-dimensional DA):
xs, xm - starting grid index, width of local grid (no ghost points)
*/
ierr = DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
ierr = DAGetInfo(da,PETSC_NULL,&M,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
/*
Set function values for boundary points; define local interior grid point range:
xsi - starting interior grid index
xei - ending interior grid index
*/
if (xs == 0) { /* left boundary */
ff[0] = xx[0];
xs++;xm--;
}
if (xs+xm == M) { /* right boundary */
ff[xs+xm-1] = xx[xs+xm-1] - 1.0;
xm--;
}
/*
Compute function over locally owned part of the grid (interior points only)
*/
d = 1.0/(user->h*user->h);
for (i=xs; i<xs+xm; i++) {
ff[i] = d*(xx[i-1] - 2.0*xx[i] + xx[i+1]) + xx[i]*xx[i] - FF[i];
}
/*
Restore vectors
*/
ierr = DAVecRestoreArray(da,xlocal,&xx);CHKERRQ(ierr);
ierr = DAVecRestoreArray(da,f,&ff);CHKERRQ(ierr);
ierr = DAVecRestoreArray(da,user->F,&FF);CHKERRQ(ierr);
ierr = DARestoreLocalVector(da,&xlocal);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
