/*$Id: combustion.c,v 1.1 2002/08/08 9:39 lopezca@mauddib.mcs.anl.gov $*/
/* Program usage: mpirun -np <proc> combustion [-help] [all TAO options] */
/*
Include "tao.h" so we can use TAO solvers.
petscda.h for distributed array
ad_deriv.h for AD gradient
*/
#include "petscda.h"
#include "tao.h"
#include "taodaapplication.h"
static char help[] = "Steady-State Combustion.\n\
We solve the Steady-State Combustion problem (MINPACK-2 test suite) in a 2D\n\
rectangular domain, using distributed arrays (DAs) to partition the parallel grid.\n\
The command line options include:\n\
-mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
-my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
-nlevels <nlevels>, where <nlevels> = number of levels in multigrid\n\
-byelement, if computation is made by functions on rectangular elements\n\
-adic, if AD is used (AD is not used by default)\n\
-par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
parameter lambda (0 <= par <= 6.81)\n\n";
/*T
Concepts: TAO - Solving a bounded minimization problem
Routines: TaoInitialize(); TaoFinalize();
Routines: TaoCreate(); TaoDestroy();
Routines: DAApplicationCreate(); DAApplicationDestroy();
Routines: DAAppSetVariableBoundsRoutine();
Routines: DAAppSetElementObjectiveAndGradientRoutine();
Routines: DAAppSetElementHessianRoutine();
Routines: DAAppSetObjectiveAndGradientRoutine();
Routines: DAAppSetADElementFunctionGradient();
Routines: DAAppSetHessianRoutine();
Routines: TaoAppSetOptions();
Routines: TaoGetSolutionStatus(); TaoDAAppSolve();
Routines: DAAppSetMonitor(); TaoView();
Routines: DAAppGetSolution();
Routines: DAAppGetInterpolationMatrix();
Processors: n
T*/
/*
User-defined application context - contains data needed by the
application-provided call-back routines.
*/
typedef struct {
InactiveDouble param;
InactiveDouble hx, hy; /* increment size in both directions */
InactiveDouble area; /* area of the triangles */
} ADFGCtx;
typedef struct {
PetscReal param; /* nonlinearity parameter */
double hx, hy, area; /* increments and area of the triangle */
int mx, my; /* discretization including boundaries */
ADFGCtx fgctx; /* Used only when an ADIC generated gradient is used */
} AppCtx;
int ad_CombLocalFunction(int[2], DERIV_TYPE[4], DERIV_TYPE*, void*);
/* User-defined routines foun in this file */
static int AppCtxInitialize(void *ptr);
static int FormInitialGuess(DA, Vec, AppCtx*);
static int CombLocalFunctionGradient(int[3], double x[4], double *f, double g[4], void *ptr);
static int WholeCombFunctionGradient(TAO_APPLICATION,DA,Vec,double *,Vec,void*);
static int CombLocalHessian(int[3], double x[4], double H[4][4], void *ptr);
static int WholeCombHessian(TAO_APPLICATION,DA,Vec,Mat,void*);
static int DAFixBoundary(TAO_APPLICATION, DA, Vec, Vec, void*);
static int MyGridMonitorBefore(TAO_APPLICATION, DA, int, void *);
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv ) {
int info,iter; /* used to check for functions returning nonzeros */
int Nx,Ny;
int nlevels; /* multigrid levels */
double ff,gnorm;
DA DAarray[20];
Vec X;
PetscTruth flg, PreLoad = PETSC_TRUE; /* flags */
AppCtx user; /* user-defined work context */
TaoMethod method = "tao_tron"; /* minimization method */
TAO_SOLVER tao; /* TAO_SOLVER solver context */
TAO_APPLICATION CombApp; /* The PETSc application */
TaoTerminateReason reason;
/* Initialize TAO */
PetscInitialize(&argc, &argv, (char *)0, help);
TaoInitialize(&argc, &argv, (char *)0, help);
PreLoadBegin(PreLoad,"Solve");
info = AppCtxInitialize((void*)&user); CHKERRQ(info);
nlevels=5;
info = PetscOptionsGetInt(PETSC_NULL,"-nlevels",&nlevels,&flg); CHKERRQ(info);
if (PreLoadIt == 0) {
nlevels = 1; user.mx = 11; user.my = 11;}
PetscPrintf(MPI_COMM_WORLD,"\n---- Steady-State Combustion Problem -----\n\n");
/* Let PETSc determine the vector distribution */
Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
/* Create distributed array (DA) to manage parallel grid and vectors */
info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,user.mx,
user.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&DAarray[0]); CHKERRQ(info);
for (iter=1;iter<nlevels;iter++){
info = DARefine(DAarray[iter-1],PETSC_COMM_WORLD,&DAarray[iter]); CHKERRQ(info);
}
/* Create TAO solver and set desired solution method */
info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info);
info = TaoApplicationCreate(PETSC_COMM_WORLD, &CombApp); CHKERRQ(info);
info = TaoAppSetDAApp(CombApp,DAarray,nlevels); CHKERRQ(info);
/* Sets routines for function, gradient and bounds evaluation */
info = DAAppSetVariableBoundsRoutine(CombApp,DAFixBoundary,(void *)&user); CHKERRQ(info);
info = PetscOptionsHasName(TAO_NULL, "-byelement", &flg); CHKERRQ(info);
if (flg) {
/* Sets routines for function and gradient evaluation, element by element */
info = PetscOptionsHasName(TAO_NULL, "-adic", &flg); CHKERRQ(info);
if (flg) {
info = DAAppSetADElementFunctionGradient(CombApp,ad_CombLocalFunction,228,(void *)&user.fgctx); CHKERRQ(info);
} else {
info = DAAppSetElementObjectiveAndGradientRoutine(CombApp,CombLocalFunctionGradient,51,(void *)&user); CHKERRQ(info);
}
/* Sets routines for Hessian evaluation, element by element */
info = DAAppSetElementHessianRoutine(CombApp,CombLocalHessian,21,(void*)&user); CHKERRQ(info);
} else {
/* Sets routines for function and gradient evaluation, all in one routine */
info = DAAppSetObjectiveAndGradientRoutine(CombApp,WholeCombFunctionGradient,(void *)&user); CHKERRQ(info);
/* Sets routines for Hessian evaluation, all in one routine */
info = DAAppSetHessianRoutine(CombApp,WholeCombHessian,(void*)&user); CHKERRQ(info);
}
info = DAAppSetBeforeMonitor(CombApp,MyGridMonitorBefore,(void*)&user); CHKERRQ(info);
info = DAAppPrintStageTimes(CombApp); CHKERRQ(info);
info = DAAppPrintInterpolationError(CombApp); CHKERRQ(info);
info = TaoAppSetRelativeTolerance(CombApp,1.0e-8); CHKERRQ(info);
info = TaoSetTolerances(tao,0,0,0,0); CHKERRQ(info);
info = TaoSetGradientTolerances(tao,0,0,0); CHKERRQ(info);
/* Check for any tao command line options */
info = TaoSetOptions(CombApp, tao); CHKERRQ(info);
info = DAAppGetSolution(CombApp,0,&X); CHKERRQ(info);
info = FormInitialGuess(DAarray[0],X,&user); CHKERRQ(info);
info = DAAppSetInitialSolution(CombApp,X); CHKERRQ(info);
/* SOLVE THE APPLICATION */
info = TaoDAAppSolve(CombApp, tao); CHKERRQ(info);
/* Get information on termination */
info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
if (reason <= 0 ){
PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
PetscPrintf(MPI_COMM_WORLD," Iterations: %d, Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm);
}
info = PetscOptionsHasName(PETSC_NULL,"-view_sol",&flg); CHKERRQ(info);
if (flg){
info = DAAppGetSolution(CombApp,nlevels-1,&X); CHKERRQ(info);
info=VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info);
}
/* To View TAO solver information */
// info = TaoView(tao); CHKERRQ(info);
/* Free TAO data structures */
info = TaoDestroy(tao); CHKERRQ(info);
info = TaoAppDestroy(CombApp); CHKERRQ(info);
/* Free PETSc data structures */
for (iter=0;iter<nlevels;iter++){
info = DADestroy(DAarray[iter]); CHKERRQ(info);
}
PreLoadEnd();
/* Finalize TAO */
TaoFinalize();
PetscFinalize();
return 0;
} /* main */
/*----- The following two routines
MyGridMonitorBefore MyGridMonitorAfter
help diplay info of iterations at every grid level -------*/
#undef __FUNCT__
#define __FUNCT__ "MyGridMonitorBefore"
static int MyGridMonitorBefore(TAO_APPLICATION myapp, DA da, int level, void *ctx) {
AppCtx *user = (AppCtx*)ctx;
int info,mx,my;
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);
user->mx = mx;
user->my = my;
user->hx = 1.0 / (user->mx - 1);
user->hy = 1.0 / (user->my - 1);
user->area = 0.5 * user->hx * user->hy;
user->fgctx.hx = user->hx;
user->fgctx.hy = user->hy;
user->fgctx.area = user->area;
user->fgctx.param = user->param;
PetscPrintf(MPI_COMM_WORLD,"Grid: %d, mx: %d my: %d \n",level,mx,my);
return 0;
}
/*------- USER-DEFINED: initialize the application context information -------*/
#undef __FUNCT__
#define __FUNCT__ "AppCtxInitialize"
/*
AppCtxInitialize - Sets initial values for the application context parameters
Input:
ptr - void user-defined application context
Output:
ptr - user-defined application context with the default or user-provided
parameters
*/
static int AppCtxInitialize(void *ptr) {
AppCtx *user = (AppCtx*)ptr;
PetscReal LambdaMax = 6.81, LambdaMin = 0.0; /* bounds on parameter lambda */
PetscTruth flg; /* flag for PETSc calls */
int info;
/* Specify dimension of the problem */
user->param = 5.0;
user->mx = 11;
user->my = 11;
/* Check for any command line arguments that override defaults */
info = PetscOptionsGetReal(TAO_NULL, "-par", &user->param, &flg); CHKERRQ(info);
if (user->param >= LambdaMax || user->param <= LambdaMin) {
SETERRQ(1,"Lambda is out of range.");
}
info = PetscOptionsGetInt(PETSC_NULL,"-mx",&user->mx,&flg); CHKERRQ(info);
info = PetscOptionsGetInt(PETSC_NULL,"-my",&user->my,&flg); CHKERRQ(info);
user->hx = 1.0 / (user->mx - 1);
user->hy = 1.0 / (user->my - 1);
user->area = 0.5 * user->hx * user->hy;
info = PetscLogFlops(6); CHKERRQ(info);
return 0;
} /* AppCtxInitialize */
#undef __FUNCT__
#define __FUNCT__ "FormInitialGuess"
static int FormInitialGuess(DA da, Vec X, AppCtx *ctx)
{
int info, i, j, mx, my;
int xs, ys, xm, ym, xe, ye;
PetscReal hx, hy, temp, val, lambda;
double **x;
lambda = ctx->param;
lambda = lambda/(lambda+1.0);
/* Get local mesh boundaries */
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);
hx = 1.0/(mx-1); hy = 1.0/(my-1);
info = DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
xe = xs+xm; ye = ys+ym;
info = DAVecGetArray(da, X, (void**)&x); CHKERRQ(info);
/* Compute initial guess over locally owned part of mesh */
for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
temp = PetscMin(j+1,my-j)*hy;
for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
val = lambda*sqrt(PetscMin((PetscMin(i+1,mx-i))*hx,temp));
x[j][i] = val;
}
}
info = DAVecRestoreArray(da, X, (void**)&x); CHKERRQ(info);
return 0;
}
/*------- USER-DEFINED: set the upper and lower bounds for the variables -------*/
#undef __FUNCT__
#define __FUNCT__ "DAFixBoundary"
/*
FormBounds - Forms bounds on the variables
Input:
user - user-defined application context
Output:
XL - vector of lower bounds
XU - vector of upper bounds
*/
static int DAFixBoundary(TAO_APPLICATION daapplication, DA da, Vec XL, Vec XU, void *ptr)
{
AppCtx *user = (AppCtx*)ptr;
int i, j, mx, my, info, xs, xm, ys, ym;
double lb = -TAO_INFINITY;
double ub = TAO_INFINITY;
double **xl, **xu;
mx = user->mx; /* number of points including the boundary */
my = user->my;
info = DAVecGetArray(da, XL, (void**)&xl); CHKERRQ(info);
info = DAVecGetArray(da, XU, (void**)&xu); CHKERRQ(info);
info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
/* Compute initial guess over locally owned part of the grid */
for (j = ys; j < ys+ym; j++){
for (i = xs; i < xs+xm; i++){
if (i == 0 || j == 0 || i == mx - 1 || j == my - 1) {
xl[j][i] = xu[j][i] = 0.0;
} else {
xl[j][i] = lb;
xu[j][i] = ub;
}
}
}
info = DAVecRestoreArray(da, XL, (void**)&xl); CHKERRQ(info);
info = DAVecRestoreArray(da, XU, (void**)&xu); CHKERRQ(info);
return 0;
} /* DAFixBoundary */
/*------- USER-DEFINED: routine to evaluate the function and gradient
at a local (rectangular element) level -------*/
#undef __FUNCT__
#define __FUNCT__ "CombLocalFunctionGradient"
/*
CombLocalFunctionGradient - Evaluates function and gradient over the
local rectangular element
Input:
coor - vector with the indices of the position of current element
in the first, second and third directions
x - current point (values over the current rectangular element)
ptr - user-defined application context
Output:
f - value of the objective funtion at the local rectangular element
g - gradient of the local function
*/
static int CombLocalFunctionGradient(int coor[2], double x[4], double *f, double g[4], void *ptr) {
AppCtx *user = (AppCtx*)ptr;
double lambdad3, hx, hy, area;
double fquad, fexp, dvdx, dvdy;
lambdad3 = user->param / 3.0;
hx = user->hx;
hy = user->hy;
area = user->area;
/* lower triangle contribution */
dvdx = (x[0] - x[1]) / hx;
dvdy = (x[0] - x[2]) / hy;
fquad = dvdx * dvdx + dvdy * dvdy;
fexp = exp(x[0]) + exp(x[1]) + exp(x[2]);
dvdx = 0.5 * dvdx * hy;
dvdy = 0.5 * dvdy * hx;
g[0] = dvdx + dvdy - exp(x[0]) * area * lambdad3;
g[1] = -dvdx - 2.0 * exp(x[1]) * area * lambdad3;
g[2] = -dvdy - 2.0 * exp(x[2]) * area * lambdad3;
/* upper triangle contribution */
dvdx = (x[3] - x[2]) / hx;
dvdy = (x[3] - x[1]) / hy;
fquad += dvdx * dvdx + dvdy * dvdy;
fexp += exp(x[1]) + exp(x[2]) + exp(x[3]);
dvdx = 0.5 * dvdx * hy;
dvdy = 0.5 * dvdy * hx;
g[1] += -dvdy;
g[2] += -dvdx;
g[3] = dvdx + dvdy - exp(x[3]) * area * lambdad3;
*f = area * (0.5 * fquad - lambdad3 * fexp);
return 0;
} /* CombLocalFunctionGradient */
/*------- USER-DEFINED: routine to evaluate the Hessian
at a local (rectangular element) level -------*/
#undef __FUNCT__
#define __FUNCT__ "CombLocalHessian"
/*
CombLocalHessian - Computes the Hessian of the local (partial) function
defined over the current rectangle
Input:
coor - vector with the indices of the position of current element
in the first, second and third directions
x - current local solution (over the rectangle only)
ptr - user-defined application context
Output:
H - Hessian matrix of the local function (wrt the four
points of the rectangle only)
*/
static int CombLocalHessian(int coor[2], double x[4], double H[4][4],void *ptr) {
AppCtx *user = (AppCtx*)ptr;
double hx, hy, lambdad3, area, dxdy, dydx;
double diagxy, dexp, bandxy, bandyx;
hx = user->hx;
hy = user->hy;
lambdad3 = user->param / 3.0;
area = user->area;
dxdy = hx/hy;
dydx = hy/hx;
diagxy = 0.5 * (dxdy + dydx);
bandxy = -0.5 * dxdy;
bandyx = -0.5 * dydx;
/* Hessian contribution at 0,0 */
dexp = exp(x[0]) * area * lambdad3;
H[0][0] = diagxy - dexp;
H[0][1] = H[1][0] = bandyx;
H[0][2] = H[2][0] = bandxy;
H[0][3] = H[3][0] = 0.0;
/* Hessian contribution at 1,0 */
dexp = exp(x[1]) * area * 2.0 * lambdad3;
H[1][1] = diagxy - dexp;
H[1][2] = H[2][1] = 0.0;
H[1][3] = H[3][1] = bandxy;
/* Hessian contribution at 0,1 */
dexp = exp(x[2]) * area * 2.0 * lambdad3;
H[2][2] = diagxy - dexp;
H[2][3] = H[3][2] = bandyx;
/* Hessian contribution at 1,1 */
dexp = exp(x[3]) * area * lambdad3;
H[3][3] = diagxy - dexp;
return 0;
} /* CombLocalHessian */
/*------- USER-DEFINED: routine to evaluate the function
and gradient at the whole grid -------*/
#undef __FUNCT__
#define __FUNCT__ "WholeCombFunctionGradient"
/*
WholeCombFunctionGradient - 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 WholeCombFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) {
AppCtx *user = (AppCtx*)ptr;
Vec localX, localG;
int info, i, j;
int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
double **x, **g;
double floc = 0.0;
PetscScalar zero = 0.0;
double lambdad3, hx, hy, area;
double fquad, fexp, dvdx, dvdy;
lambdad3 = user->param / 3.0;
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;
fquad = dvdx * dvdx + dvdy * dvdy;
fexp = exp(x[j][i]) + exp(x[j][i+1]) + exp(x[j+1][i]);
dvdx = 0.5 * dvdx * hy;
dvdy = 0.5 * dvdy * hx;
g[j][i] += dvdx + dvdy - exp(x[j][i]) * area * lambdad3;
g[j][i+1] += -dvdx - 2.0 * exp(x[j][i+1]) * area * lambdad3;
g[j+1][i] += -dvdy - 2.0 * exp(x[j+1][i]) * area * lambdad3;
/* 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;
fquad += dvdx * dvdx + dvdy * dvdy;
fexp += exp(x[j][i+1]) + exp(x[j+1][i]) + exp(x[j+1][i+1]);
dvdx = 0.5 * dvdx * hy;
dvdy = 0.5 * dvdy * hx;
g[j][i+1] += -dvdy;
g[j+1][i] += -dvdx;
g[j+1][i+1] += dvdx + dvdy - exp(x[j+1][i+1]) * area * lambdad3;
floc += area * (0.5 * fquad - fexp * lambdad3);
}
}
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) * 55 + 1); CHKERRQ(info);
return 0;
} /* WholeCombFunctionGradient */
/*------- USER-DEFINED: routine to evaluate the Hessian
at the whole grid -------*/
#undef __FUNCT__
#define __FUNCT__ "WholeCombHessian"
/*
WholeCombHessian - 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 WholeCombHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) {
AppCtx *user = (AppCtx*)ptr;
Vec localX;
int info, i, j, ind[4];
int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
double smallH[4][4];
double **x;
double hx, hy, lambdad3, area, dxdy, dydx;
double diagxy, dexp, bandxy, bandyx;
PetscTruth assembled;
hx = user->hx;
hy = user->hy;
lambdad3 = user->param / 3.0;
area = user->area;
dxdy = hx/hy;
dydx = hy/hx;
diagxy = 0.5 * (dxdy + dydx);
bandxy = -0.5 * dxdy;
bandyx = -0.5 * dydx;
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++) {
/* Hessian contribution at 0,0 */
dexp = exp(x[j][i]) * area * lambdad3;
smallH[0][0] = diagxy - dexp;
smallH[0][1] = smallH[1][0] = bandyx;
smallH[0][2] = smallH[2][0] = bandxy;
smallH[0][3] = smallH[3][0] = 0.0;
/* Hessian contribution at 1,0 */
dexp = exp(x[j][i+1]) * area * 2.0 * lambdad3;
smallH[1][1] = diagxy - dexp;
smallH[1][2] = smallH[2][1] = 0.0;
smallH[1][3] = smallH[3][1] = bandxy;
/* Hessian contribution at 0,1 */
dexp = exp(x[j+1][i]) * area * 2.0 * lambdad3;
smallH[2][2] = diagxy - dexp;
smallH[2][3] = smallH[3][2] = bandyx;
/* Hessian contribution at 1,1 */
dexp = exp(x[j+1][i+1]) * area * lambdad3;
smallH[3][3] = diagxy - dexp;
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); CHKERRQ(info);
info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
info = PetscLogFlops((xe-xs) * (ye-ys) * 14 + 7); CHKERRQ(info);
return 0;
} /* WholeCombHessian */