Actual source code: eptorsion3.c
1: /*$Id: eptorsion.c, v 1.1 2002/08/08 10:30 lopezca@mauddib.mcs.anl.gov $*/
3: /* Program usage: mpirun -np <proc> eptorsion [-help] [all TAO options] */
5: /*
6: Include "tao.h" so we can use TAO solvers.
7: petscda.h for distributed array
8: ad_deriv.h for AD gradient
9: */
11: #include "petscda.h"
12: #include "tao.h"
13: #include "taodaapplication.h"
15: static char help[] = "This example is based on the Elastic-Plastic Torsion (dept)\n\
16: problem from the MINPACK-2 test suite.\n\
17: The command line options are:\n\
18: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
19: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
20: -nlevels <nlevels>, where <nlevels> = number of levels in multigrid\n\
21: -byelement, if computation is made by functions on rectangular elements\n\
22: -adic, if AD is used (AD is not used by default)\n\
23: -u1 <u1>, where <u1> = upper limit in the 1st coordinate direction\n\
24: -u2 <u2>, where <u2> = upper limit in the 2nd coordinate direction\n\
25: -par <param>, where <param> = angle of twist per unit length\n\n";
27: /*T
28: Concepts: TAO - Solving a bounded minimization problem
29: Routines: TaoInitialize(); TaoFinalize();
30: Routines: TaoCreate(); TaoDestroy();
31: Routines: DAApplicationCreate(); DAApplicationDestroy();
32: Routines: DAAppSetVariableBoundsRoutine();
33: Routines: DAAppSetElementObjectiveAndGradientRoutine();
34: Routines: DAAppSetElementHessianRoutine();
35: Routines: DAAppSetObjectiveAndGradientRoutine();
36: Routines: DAAppSetADElementFunctionGradient();
37: Routines: DAAppSetHessianRoutine();
38: Routines: TaoSetOptions();
39: Routines: TaoGetSolutionStatus(); TaoDAAppSolve();
40: Routines: DAAppSetMonitor(); TaoView();
41: Routines: DAAppGetSolution();
42: Routines: DAAppGetInterpolationMatrix();
43: Processors: n
44: T*/
46: /*
47: User-defined application context - contains data needed by the
48: application-provided call-back routines.
49: */
50: typedef struct {
51: InactiveDouble param;
52: InactiveDouble hx, hy; /* increment size in both directions */
53: InactiveDouble area; /* area of the triangles */
54: } ADFGCtx;
56: typedef struct {
57: PetscReal param; /* 'c' parameter */
58: PetscReal u1, u2; /* domain upper limits (lower limits = 0) */
59: double hx, hy; /* increment size in both directions */
60: double area; /* area of the triangles */
61: ADFGCtx fgctx; /* Used only when an ADIC generated gradient is used */
62: } AppCtx;
63: int ad_EPTorsLocalFunction(int[2], DERIV_TYPE[4], DERIV_TYPE*, void*);
65: /* User-defined routines found in this file */
66: static int AppCtxInitialize(void *ptr);
67: static int FormInitialGuess(DA, Vec);
69: static int EPTorsLocalFunctionGradient(int[2], double x[4], double *f, double g[4], void *ptr);
70: static int EPTorsLocalHessian(int[2], double x[4], double H[4][4], void *ptr);
72: static int WholeEPTorsFunctionGradient(TAO_APPLICATION,DA,Vec,double *,Vec,void*);
73: static int WholeEPTorsHessian(TAO_APPLICATION,DA,Vec,Mat,void*);
75: static int DASetBounds(TAO_APPLICATION, DA, Vec, Vec, void*);
77: static int MyGridMonitorBefore(TAO_APPLICATION, DA, int, void *);
82: int main( int argc, char **argv ) {
84: int info; /* used to check for functions returning nonzeros */
85: int mx,my,Nx,Ny;
86: double ff,gnorm;
87: int iter, nlevels; /* multigrid levels */
88: DA DAarray[20];
89: Vec X;
90: PetscTruth flg, PreLoad = PETSC_TRUE; /* flags */
91: TaoMethod method = "tao_gpcg"; /* minimization method */
92: AppCtx user; /* user-defined work context */
93: TAO_SOLVER tao; /* TAO_SOLVER solver context */
94: TAO_APPLICATION EPTorsApp; /* The PETSc application */
95: TaoTerminateReason reason;
96: KSP ksp;
97: PC pc;
99: /* Initialize TAO */
100: PetscInitialize(&argc, &argv, (char *)0, help);
101: TaoInitialize(&argc, &argv, (char *)0, help);
103: PreLoadBegin(PreLoad,"Solve");
104:
105: info = AppCtxInitialize((void*)&user); CHKERRQ(info);
107: nlevels=5;
108: info = PetscOptionsGetInt(PETSC_NULL,"-nlevels",&nlevels,&flg); CHKERRQ(info);
109: mx = my = 11; /* these correspond to 10 segments on each dimension */
110: info = PetscOptionsGetInt(TAO_NULL, "-mx", &mx, &flg); CHKERRQ(info);
111: info = PetscOptionsGetInt(TAO_NULL, "-my", &my, &flg); CHKERRQ(info);
112: if (PreLoadIt == 0) {
113: nlevels = 1; mx = 11; my = 11; }
115: PetscPrintf(MPI_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n\n");
117: /* Let PETSc determine the vector distribution */
118: Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
120: /* Create distributed array (DA) to manage parallel grid and vectors */
121: info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,mx,
122: my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&DAarray[0]); CHKERRQ(info);
123: for (iter=1;iter<nlevels;iter++){
124: info = DARefine(DAarray[iter-1],PETSC_COMM_WORLD,&DAarray[iter]); CHKERRQ(info);
125: }
127: /* Create TAO solver and set desired solution method */
128: info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info);
129: info = TaoApplicationCreate(PETSC_COMM_WORLD,&EPTorsApp); CHKERRQ(info);
130: info = TaoAppSetDAApp(EPTorsApp, DAarray, nlevels ); CHKERRQ(info);
131: /* Sets routines for function, gradient and bounds evaluation */
132: info = DAAppSetVariableBoundsRoutine(EPTorsApp,DASetBounds,(void *)&user); CHKERRQ(info);
134: info = PetscOptionsHasName(TAO_NULL, "-byelement", &flg); CHKERRQ(info);
135: if (flg) {
137: /* Sets routines for function and gradient evaluation, element by element */
138: info = PetscOptionsHasName(TAO_NULL, "-adic", &flg); CHKERRQ(info);
139: if (flg) {
140: info = DAAppSetADElementFunctionGradient(EPTorsApp,ad_EPTorsLocalFunction,192,(void *)&user.fgctx); CHKERRQ(info);
141: } else {
142: info = DAAppSetElementObjectiveAndGradientRoutine(EPTorsApp,EPTorsLocalFunctionGradient,42,(void *)&user); CHKERRQ(info);
143: }
144: /* Sets routines for Hessian evaluation, element by element */
145: info = DAAppSetElementHessianRoutine(EPTorsApp,EPTorsLocalHessian,6,(void*)&user); CHKERRQ(info);
147: } else {
149: /* Sets routines for function and gradient evaluation, all in one routine */
150: info = DAAppSetObjectiveAndGradientRoutine(EPTorsApp,WholeEPTorsFunctionGradient,(void *)&user); CHKERRQ(info);
152: /* Sets routines for Hessian evaluation, all in one routine */
153: info = DAAppSetHessianRoutine(EPTorsApp,WholeEPTorsHessian,(void*)&user); CHKERRQ(info);
154:
155: }
157: info = DAAppSetBeforeMonitor(EPTorsApp,MyGridMonitorBefore,(void*)&user); CHKERRQ(info);
158: info = PetscOptionsHasName(TAO_NULL,"-tao_monitor", &flg); CHKERRQ(info);
159: if (flg){
160: info = DAAppPrintInterpolationError(EPTorsApp); CHKERRQ(info);
161: info = DAAppPrintStageTimes(EPTorsApp); CHKERRQ(info);
162: }
163: info = TaoAppSetRelativeTolerance(EPTorsApp,1.0e-6); CHKERRQ(info);
164: info = TaoSetTolerances(tao,0,0,0,0); CHKERRQ(info);
165: info = TaoSetGradientTolerances(tao,0,0,0); CHKERRQ(info);
167: info = TaoAppGetKSP(EPTorsApp,&ksp);CHKERRQ(info);
168: info = KSPSetType(ksp,KSPCG); CHKERRQ(info);
169: info = KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,100);CHKERRQ(info);
170: info = KSPGetPC(ksp,&pc);CHKERRQ(info);
171: info = PCSetType(pc,PCBJACOBI);CHKERRQ(info);
173: /* Check for any tao command line options */
174: info = TaoSetOptions(EPTorsApp, tao); CHKERRQ(info);
176: info = DAAppGetSolution(EPTorsApp,0,&X); CHKERRQ(info);
177: info = FormInitialGuess(DAarray[0],X); CHKERRQ(info);
178: info = DAAppSetInitialSolution(EPTorsApp,X); CHKERRQ(info);
179:
180: /* SOLVE THE APPLICATION */
181: info = TaoDAAppSolve(EPTorsApp, tao); CHKERRQ(info);
183: /* Get information on termination */
184: info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
185: if (reason <= 0 ){
186: PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
187: PetscPrintf(MPI_COMM_WORLD," Iterations: %d, Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm);
188: }
190: info = PetscOptionsHasName(PETSC_NULL,"-view_sol",&flg); CHKERRQ(info);
191: if (flg){
192: info = DAAppGetSolution(EPTorsApp,nlevels-1,&X); CHKERRQ(info);
193: info=VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info);
194: }
196: /* To View TAO solver information */
197: // info = TaoView(tao); CHKERRQ(info);
199: /* Free TAO data structures */
200: info = TaoDestroy(tao); CHKERRQ(info);
201: info = TaoAppDestroy(EPTorsApp); CHKERRQ(info);
203: /* Free PETSc data structures */
204: for (iter=0;iter<nlevels;iter++){
205: info = DADestroy(DAarray[iter]); CHKERRQ(info);
206: }
208: PreLoadEnd();
210: /* Finalize TAO */
211: TaoFinalize();
212: PetscFinalize();
214: return 0;
215: } /* main */
219: /*----- The following two routines
220: MyGridMonitorBefore MyGridMonitorAfter
221: help diplay info of iterations at every grid level
222: */
225: static int MyGridMonitorBefore(TAO_APPLICATION myapp, DA da, int level, void *ctx) {
227: AppCtx *user = (AppCtx*)ctx;
228: int info,mx,my;
230: info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
231: PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
232: user->hx = user->u1 / (mx - 1);
233: user->hy = user->u2 / (my - 1);
234: user->area = 0.5 * user->hx * user->hy;
235: user->fgctx.hx = user->hx;
236: user->fgctx.hy = user->hy;
237: user->fgctx.area = user->area;
238: user->fgctx.param = user->param;
240: PetscPrintf(MPI_COMM_WORLD,"Grid: %d, mx: %d my: %d \n",level,mx,my);
242: return 0;
243: }
246: /*------- USER-DEFINED: initialize the application context information -------*/
249: /*
250: AppCtxInitialize - Sets initial values for the application context parameters
252: Input:
253: ptr - void user-defined application context
255: Output:
256: ptr - user-defined application context with the default or user-provided
257: parameters
258: */
259: static int AppCtxInitialize(void *ptr) {
261: AppCtx *user = (AppCtx*)ptr;
262: PetscTruth flg; /* flag for PETSc calls */
263: int info;
265: /* Specify default parameters */
266: user->param = 25.0;
267: user->u1 = user->u2 = 1.0;
269: /* Check for command line arguments that override defaults */
270: info = PetscOptionsGetReal(TAO_NULL, "-par", &user->param, &flg); CHKERRQ(info);
271: info = PetscOptionsGetReal(TAO_NULL, "-u1", &user->u1, &flg); CHKERRQ(info);
272: info = PetscOptionsGetReal(TAO_NULL, "-u2", &user->u2, &flg); CHKERRQ(info);
274: return 0;
275: } /* AppCtxInitialize */
279: static int FormInitialGuess(DA da, Vec X)
280: {
281: int info, i, j, mx, my;
282: int xs, ys, xm, ym, xe, ye;
283: PetscReal hx, hy, temp, val;
284: double **x;
286: /* Get local mesh boundaries */
287: info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
288: PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
289: hx = 1.0/(mx-1); hy = 1.0/(my-1);
291: info = DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
292: xe = xs+xm; ye = ys+ym;
294: info = DAVecGetArray(da, X, (void**)&x); CHKERRQ(info);
295: /* Compute initial guess over locally owned part of mesh */
296: for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
297: temp = PetscMin(j+1,my-j)*hy;
298: for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
299: val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
300: x[j][i] = val;
301: }
302: }
303: info = DAVecRestoreArray(da, X, (void**)&x); CHKERRQ(info);
305: return 0;
306: }
309: /*------- USER-DEFINED: set the upper and lower bounds for the variables -------*/
313: /*
314: FormBounds - Forms bounds on the variables
316: Input:
317: user - user-defined application context
319: Output:
320: XL - vector of lower bounds
321: XU - vector of upper bounds
322: */
323: static int DASetBounds(TAO_APPLICATION daapplication, DA da, Vec XL, Vec XU, void *ptr)
324: {
325: AppCtx *user = (AppCtx*)ptr;
326: int i, j, info, xs, xm, ys, ym;
327: double hx, hy, u1, u2, dist, d1, d2, hd, vd;
328: double **xl, **xu;
330: hx = user->hx;
331: hy = user->hy;
332: u1 = user->u1;
333: u2 = user->u2;
335: info = DAVecGetArray(da, XL, (void**)&xl); CHKERRQ(info);
336: info = DAVecGetArray(da, XU, (void**)&xu); CHKERRQ(info);
337: info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
339: for (j = ys; j < ys+ym; j++){
340: for (i = xs; i < xs+xm; i++){
341: d1 = i * hx; d2 = u1 - d1; hd = PetscMin(d1,d2);
342: d1 = j * hy; d2 = u2 - d1; vd = PetscMin(d1,d2);
343: dist = PetscMin(hd,vd);
344: xl[j][i] = -dist;
345: xu[j][i] = dist;
346: }
347: }
349: info = DAVecRestoreArray(da, XL, (void**)&xl); CHKERRQ(info);
350: info = DAVecRestoreArray(da, XU, (void**)&xu); CHKERRQ(info);
352: info = PetscLogFlops(xm * ym * 4); CHKERRQ(info);
353: return 0;
355: } /* DASetBounds */
360: /*
361: EPTorsLocalFunctionGradient - Evaluates function and gradient over the
362: local rectangular element
364: Input:
365: coor - vector with the indices of the position of current element
366: in the first, second and third directions
367: x - current point (values over the current rectangular element)
368: df - degrees of freedom at each point
369: ptr - user-defined application context
371: Output:
372: f - value of the objective funtion at the local rectangular element
373: g - gradient of the local function
374: */
375: static int EPTorsLocalFunctionGradient(int coor[2], double x[4], double *f, double g[4], void *ptr) {
377: AppCtx *user = (AppCtx*)ptr;
379: double fquad, flin;
380: double hx, hy, dvdx, dvdy, area;
381: double cdiv3, cnt;
383: cdiv3 = user->param / 3.0;
384: hx = user->hx;
385: hy = user->hy;
386: area = user->area;
387: cnt = area * cdiv3;
389: /* lower triangle contribution */
390: dvdx = (x[0] - x[1]) / hx;
391: dvdy = (x[0] - x[2]) / hy;
392: fquad = dvdx * dvdx + dvdy * dvdy;
393: flin = x[0] + x[1] + x[2];
395: dvdx = 0.5 * dvdx * hy;
396: dvdy = 0.5 * dvdy * hx;
397: g[0] = dvdx + dvdy - cnt;
398: g[1] = -dvdx - 2.0 * cnt;
399: g[2] = -dvdy - 2.0 * cnt;
401: /* upper triangle contribution */
402: dvdx = (x[3] - x[2]) / hx;
403: dvdy = (x[3] - x[1]) / hy;
404: fquad += dvdx * dvdx + dvdy * dvdy;
405: flin += x[1] + x[2] + x[3];
407: dvdx = 0.5 * dvdx * hy;
408: dvdy = 0.5 * dvdy * hx;
409: g[1] += -dvdy;
410: g[2] += -dvdx;
411: g[3] = dvdx + dvdy - cnt;
413: *f = area * (0.5 * fquad - flin * cdiv3);
415: return 0;
416: } /* EPTorsLocalFunctionGradient */
420: /*------- USER-DEFINED: routine to evaluate the Hessian
421: at a local (rectangular element) level -------*/
424: /*
425: EPTorsLocalHessian - Computes the Hessian of the local (partial) function
426: defined over the current rectangle
428: Input:
429: coor - vector with the indices of the position of current element
430: in the first, second and third directions
431: x - current local solution (over the rectangle only)
432: df - degrees of freedom at each point
433: ptr - user-defined application context
435: Output:
436: H - Hessian matrix of the local function (wrt the four
437: points of the rectangle only)
438: */
439: static int EPTorsLocalHessian(int coor[2], double x[4], double H[4][4], void *ptr) {
441: AppCtx *user = (AppCtx*)ptr;
442: double hx, hy, dxdy, dydx;
443: double diagxy, bandxy, bandyx;
445: hx = user->hx;
446: hy = user->hy;
447: dxdy = hx/hy;
448: dydx = hy/hx;
449: diagxy = 0.5 * (dxdy + dydx);
450: bandxy = -0.5 * dxdy;
451: bandyx = -0.5 * dydx;
453: /* Hessian contribution at 0,0 */
454: H[0][0] = diagxy;
455: H[0][1] = H[1][0] = bandyx;
456: H[0][2] = H[2][0] = bandxy;
457: H[0][3] = H[3][0] = 0.0;
459: /* Hessian contribution at 1,0 */
460: H[1][1] = diagxy;
461: H[1][2] = H[2][1] = 0.0;
462: H[1][3] = H[3][1] = bandxy;
464: /* Hessian contribution at 0,1 */
465: H[2][2] = diagxy;
466: H[2][3] = H[3][2] = bandyx;
468: /* Hessian contribution at 1,1 */
469: H[3][3] = diagxy;
471: return 0;
473: } /* EPTorsLocalHessian */
476: /*------- USER-DEFINED: routine to evaluate the function
477: and gradient at the whole grid -------*/
480: /*
481: WholeEPTorsFunctionGradient - Evaluates function and gradient over the
482: whole grid
484: Input:
485: daapplication - TAO application object
486: da - distributed array
487: X - the current point, at which the function and gradient are evaluated
488: ptr - user-defined application context
490: Output:
491: f - value of the objective funtion at X
492: G - gradient at X
493: */
494: static int WholeEPTorsFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) {
496: AppCtx *user = (AppCtx*)ptr;
497: Vec localX, localG;
498: int info, i, j;
499: int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
500: double **x, **g;
501: double floc = 0.0;
502: PetscScalar zero = 0.0;
504: double fquad, flin;
505: double hx, hy, dvdx, dvdy, area;
506: double cdiv3, cnt;
508: cdiv3 = user->param / 3.0;
509: hx = user->hx;
510: hy = user->hy;
511: area = user->area;
512: cnt = area * cdiv3;
514: info = DAGetLocalVector(da, &localX); CHKERRQ(info);
515: info = DAGetLocalVector(da, &localG); CHKERRQ(info);
516: info = VecSet(G, zero); CHKERRQ(info);
517: info = VecSet(localG, zero); CHKERRQ(info);
519: info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
520: info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);
522: info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
523: info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info);
525: info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
526: info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);
528: xe = gxs + gxm - 1;
529: ye = gys + gym - 1;
530: for (j = ys; j < ye; j++) {
531: for (i = xs; i < xe; i++) {
533: /* lower triangle contribution */
534: dvdx = (x[j][i] - x[j][i+1]) / hx;
535: dvdy = (x[j][i] - x[j+1][i]) / hy;
536: fquad = dvdx * dvdx + dvdy * dvdy;
537: flin = x[j][i] + x[j][i+1] + x[j+1][i];
539: dvdx = 0.5 * dvdx * hy;
540: dvdy = 0.5 * dvdy * hx;
541: g[j][i] += dvdx + dvdy - cnt;
542: g[j][i+1] += -dvdx - 2.0 * cnt;
543: g[j+1][i] += -dvdy - 2.0 * cnt;
545: /* upper triangle contribution */
546: dvdx = (x[j+1][i+1] - x[j+1][i]) / hx;
547: dvdy = (x[j+1][i+1] - x[j][i+1]) / hy;
548: fquad += dvdx * dvdx + dvdy * dvdy;
549: flin += x[j][i+1] + x[j+1][i] + x[j+1][i+1];
551: dvdx = 0.5 * dvdx * hy;
552: dvdy = 0.5 * dvdy * hx;
553: g[j][i+1] += -dvdy;
554: g[j+1][i] += -dvdx;
555: g[j+1][i+1] += dvdx + dvdy - cnt;
557: floc += area * (0.5 * fquad - flin * cdiv3);
559: }
560: }
562: info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); CHKERRQ(info);
564: info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
565: info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info);
567: info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
568: info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);
570: info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
571: info = DARestoreLocalVector(da, &localG); CHKERRQ(info);
573: info = PetscLogFlops((xe-xs) * (ye-ys) * 47 + 2); CHKERRQ(info);
574: return 0;
575: } /* WholeEPTorsFunctionGradient */
578: /*------- USER-DEFINED: routine to evaluate the Hessian
579: at the whole grid -------*/
582: /*
583: WholeEPTorsHessian - Evaluates Hessian over the whole grid
585: Input:
586: daapplication - TAO application object
587: da - distributed array
588: X - the current point, at which the function and gradient are evaluated
589: ptr - user-defined application context
591: Output:
592: H - Hessian at X
593: */
594: static int WholeEPTorsHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) {
596: AppCtx *user = (AppCtx*)ptr;
597: int info, i, j, ind[4];
598: int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
599: double smallH[4][4];
601: double hx, hy, dxdy, dydx;
602: double diagxy, bandxy, bandyx;
603: PetscTruth assembled;
605: hx = user->hx;
606: hy = user->hy;
607: dxdy = hx/hy;
608: dydx = hy/hx;
609: diagxy = 0.5 * (dxdy + dydx);
610: bandxy = -0.5 * dxdy;
611: bandyx = -0.5 * dydx;
613: info = MatAssembled(H,&assembled); CHKERRQ(info);
614: if (assembled){info = MatZeroEntries(H); CHKERRQ(info);}
617: info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
618: info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);
620: xe = gxs + gxm - 1;
621: ye = gys + gym - 1;
622: for (j = ys; j < ye; j++) {
623: for (i = xs; i < xe; i++) {
625: /* Hessian contribution at 0,0 */
626: smallH[0][0] = diagxy;
627: smallH[0][1] = smallH[1][0] = bandyx;
628: smallH[0][2] = smallH[2][0] = bandxy;
629: smallH[0][3] = smallH[3][0] = 0.0;
631: /* Hessian contribution at 1,0 */
632: smallH[1][1] = diagxy;
633: smallH[1][2] = smallH[2][1] = 0.0;
634: smallH[1][3] = smallH[3][1] = bandxy;
636: /* Hessian contribution at 0,1 */
637: smallH[2][2] = diagxy;
638: smallH[2][3] = smallH[3][2] = bandyx;
640: /* Hessian contribution at 1,1 */
641: smallH[3][3] = diagxy;
643: ind[0] = (j-gys) * gxm + (i-gxs);
644: ind[1] = ind[0] + 1;
645: ind[2] = ind[0] + gxm;
646: ind[3] = ind[2] + 1;
647: info = MatSetValuesLocal(H,4,ind,4,ind,(PetscScalar*)smallH,ADD_VALUES); CHKERRQ(info);
649: }
650: }
652: info = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
653: info = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
654: info = MatSetOption(H, MAT_SYMMETRIC); CHKERRQ(info);
657: info = PetscLogFlops(6); CHKERRQ(info);
658: return 0;
660: } /* WholeEPTorsHessian */