Actual source code: minsurf2.c
1: /*$Id: minsurf2.c 1.80 05/05/11 08:44:55-05:00 sarich@zorak.(none) $*/
3: /* Program usage: mpirun -np <proc> minsurf2 [-help] [all TAO options] */
5: /*
6: Include "tao.h" so we can use TAO solvers.
7: petscda.h for distributed array
8: */
9: #include "petscda.h"
10: #include tao.h
12: static char help[] =
13: "This example demonstrates use of the TAO package to \n\
14: solve an unconstrained minimization problem. This example is based on a \n\
15: problem from the MINPACK-2 test suite. Given a rectangular 2-D domain and \n\
16: boundary values along the edges of the domain, the objective is to find the\n\
17: surface with the minimal area that satisfies the boundary conditions.\n\
18: The command line options are:\n\
19: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
20: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
21: -start <st>, where <st> =0 for zero vector, <st> >0 for random start, and <st> <0 \n\
22: for an average of the boundary conditions\n\n";
24: /*T
25: Concepts: TAO - Solving an unconstrained minimization problem
26: Routines: TaoInitialize(); TaoFinalize();
27: Routines: TaoCreate(); TaoDestroy();
28: Routines: TaoApplicationCreate(); TaoAppDestroy();
29: Routines: TaoAppSetInitialSolutionVec();
30: Routines: TaoAppSetObjectiveAndGradientRoutine();
31: Routines: TaoAppSetHessianMat(); TaoAppSetHessianRoutine();
32: Routines: TaoSetOptions();
33: Routines: TaoGetKSP(); TaoSolveApplication();
34: Routines: TaoAppSetMonitor(); TaoView();
35: Routines: TaoAppGetSolutionVec();
36: Processors: 1
37: T*/
39: /*
40: User-defined application context - contains data needed by the
41: application-provided call-back routines, FormFunctionGradient()
42: and FormHessian().
43: */
44: typedef struct {
45: int mx, my; /* discretization in x, y directions */
46: double *bottom, *top, *left, *right; /* boundary values */
47: DA da; /* distributed array data structure */
48: Mat H; /* Hessian */
49: ISColoring iscoloring;
50: } AppCtx;
53: /* -------- User-defined Routines --------- */
55: static int MSA_BoundaryConditions(AppCtx*);
56: static int MSA_InitialPoint(AppCtx*,Vec);
57: int QuadraticH(AppCtx*,Vec,Mat);
58: int FormFunctionGradient(TAO_APPLICATION,Vec,double *,Vec,void*);
59: int FormGradient(TAO_APPLICATION,Vec,Vec,void*);
60: int FormHessian(TAO_APPLICATION,Vec,Mat*,Mat*,MatStructure *,void*);
61: int My_Monitor(TAO_APPLICATION, void *);
65: int main( int argc, char **argv )
66: {
67: int info; /* used to check for functions returning nonzeros */
68: int Nx, Ny; /* number of processors in x- and y- directions */
69: int iter; /* iteration information */
70: double ff,gnorm;
71: Vec x; /* solution, gradient vectors */
72: PetscTruth flg, viewmat; /* flags */
73: PetscTruth fddefault, fdcoloring; /* flags */
74: KSP ksp; /* Krylov subspace method */
75: TaoMethod method = "tao_nls"; /* minimization method */
76: TaoTerminateReason reason;
77: TAO_SOLVER tao; /* TAO_SOLVER solver context */
78: TAO_APPLICATION minsurfapp; /* The PETSc application */
79: AppCtx user; /* user-defined work context */
81: /* Initialize TAO */
82: PetscInitialize( &argc, &argv,(char *)0,help );
83: TaoInitialize( &argc, &argv,(char *)0,help );
85: /* Specify dimension of the problem */
86: user.mx = 10; user.my = 10;
88: /* Check for any command line arguments that override defaults */
89: info = PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,&flg); CHKERRQ(info);
90: info = PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,&flg); CHKERRQ(info);
92: PetscPrintf(MPI_COMM_WORLD,"\n---- Minimum Surface Area Problem -----\n");
93: PetscPrintf(MPI_COMM_WORLD,"mx: %d my: %d \n\n",user.mx,user.my);
96: /* Let PETSc determine the vector distribution */
97: Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
99: /* Create distributed array (DA) to manage parallel grid and vectors */
100: info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,user.mx,
101: user.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.da); CHKERRQ(info);
102:
104: /* Create TAO solver and set desired solution method. Create an TAO application structure */
105: info = TaoCreate(PETSC_COMM_WORLD,method,&tao); CHKERRQ(info);
106: info = TaoApplicationCreate(PETSC_COMM_WORLD,&minsurfapp); CHKERRQ(info);
108: /*
109: Extract global vector from DA for the vector of variables -- PETSC routine
110: Compute the initial solution -- application specific, see below
111: Set this vector for use by TAO -- TAO routine
112: */
113: info = DACreateGlobalVector(user.da,&x); CHKERRQ(info);
114: info = MSA_BoundaryConditions(&user); CHKERRQ(info);
115: info = MSA_InitialPoint(&user,x); CHKERRQ(info);
116: info = TaoAppSetInitialSolutionVec(minsurfapp,x); CHKERRQ(info);
118: /*
119: Initialize the Application context for use in function evaluations -- application specific, see below.
120: Set routines for function and gradient evaluation
121: */
122: info = TaoAppSetObjectiveAndGradientRoutine(minsurfapp,FormFunctionGradient,(void *)&user); CHKERRQ(info);
124: /*
125: Given the command line arguments, calculate the hessian with either the user-
126: provided function FormHessian, or the default finite-difference driven Hessian
127: functions
128: */
129: info = PetscOptionsHasName(PETSC_NULL,"-tao_fddefault",&fddefault);CHKERRQ(info);
130: info = PetscOptionsHasName(PETSC_NULL,"-tao_fdcoloring",&fdcoloring);CHKERRQ(info);
132: if (fdcoloring) {
133: info = TaoAppSetColoring(minsurfapp, user.iscoloring); CHKERRQ(info);
134: info = TaoAppSetHessianRoutine(minsurfapp,TaoAppDefaultComputeHessianColor,(void *)&user); CHKERRQ(info);
135: } else if (fddefault){
136: info = TaoAppSetHessianRoutine(minsurfapp,TaoAppDefaultComputeHessian,(void *)&user); CHKERRQ(info);
137: } else {
138: info = TaoAppSetHessianRoutine(minsurfapp,FormHessian,(void *)&user); CHKERRQ(info);
139: }
141: /*
142: Create a matrix data structure to store the Hessian and set
143: the Hessian evalution routine.
144: Set the matrix structure to be used for Hessian evalutions
145: */
146: info = DAGetMatrix(user.da,MATAIJ,&user.H);CHKERRQ(info);
147: info = DAGetColoring(user.da,IS_COLORING_GHOSTED,&user.iscoloring);
148: CHKERRQ(info);
149: info = MatSetOption(user.H,MAT_SYMMETRIC); CHKERRQ(info);
151: info = TaoAppSetHessianMat(minsurfapp,user.H,user.H); CHKERRQ(info);
153: /*
154: If my_monitor option is in command line, then use the user-provided
155: monitoring function
156: */
157: info = PetscOptionsHasName(PETSC_NULL,"-my_monitor",&viewmat); CHKERRQ(info);
158: if (viewmat){
159: info = TaoAppSetMonitor(minsurfapp,My_Monitor,TAO_NULL); CHKERRQ(info);
160: }
162: /* Check for any tao command line options */
163: info = TaoSetOptions(minsurfapp,tao); CHKERRQ(info);
165: /* Limit the number of iterations in the KSP linear solver */
166: info = TaoGetKSP(tao,&ksp); CHKERRQ(info);
167: if (ksp) { /* Modify the PETSc KSP structure */
168: info = KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,user.mx*user.my);
169: CHKERRQ(info);
170: }
172: /* SOLVE THE APPLICATION */
173: info = TaoSolveApplication(minsurfapp,tao); CHKERRQ(info);
175: /* Get information on termination */
176: info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
177: if (reason <= 0 ){
178: PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
179: PetscPrintf(MPI_COMM_WORLD," Iterations: %d, Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm);
180: }
182: /*
183: To View TAO solver information use
184: info = TaoView(tao); CHKERRQ(info);
185: */
187: /* Free TAO data structures */
188: info = TaoDestroy(tao); CHKERRQ(info);
189: info = TaoAppDestroy(minsurfapp); CHKERRQ(info);
191: /* Free PETSc data structures */
192: info = VecDestroy(x); CHKERRQ(info);
193: info = MatDestroy(user.H); CHKERRQ(info);
194: info = ISColoringDestroy(user.iscoloring);CHKERRQ(info);
195: PetscFree(user.bottom);
196: PetscFree(user.top);
197: PetscFree(user.left);
198: PetscFree(user.right);
199: info = DADestroy(user.da); CHKERRQ(info);
201: /* Finalize TAO */
202: TaoFinalize();
203: PetscFinalize();
204:
205: return 0;
206: }
210: int FormGradient(TAO_APPLICATION taoapp, Vec X, Vec G,void *userCtx){
211: int info;
212: double fcn;
213: TaoFunctionBegin;
214: info = FormFunctionGradient(taoapp,X,&fcn,G,userCtx);CHKERRQ(info);
215: TaoFunctionReturn(0);
216: }
218: /* -------------------------------------------------------------------- */
221: /* FormFunctionGradient - Evaluates the function and corresponding gradient.
223: Input Parameters:
224: . taoapp - the TAO_APPLICATION context
225: . XX - input vector
226: . userCtx - optional user-defined context, as set by TaoSetFunctionGradient()
227:
228: Output Parameters:
229: . fcn - the newly evaluated function
230: . GG - vector containing the newly evaluated gradient
231: */
232: int FormFunctionGradient(TAO_APPLICATION taoapp, Vec X, double *fcn,Vec G,void *userCtx){
234: AppCtx * user = (AppCtx *) userCtx;
235: int info,i,j;
236: int mx=user->mx, my=user->my;
237: int xs,xm,gxs,gxm,ys,ym,gys,gym;
238: double ft=0;
239: double hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy, area=0.5*hx*hy;
240: double rhx=mx+1, rhy=my+1;
241: double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
242: double df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
243: PetscScalar **g, **x;
244: Vec localX;
246: /* Get local mesh boundaries */
247: info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
249: info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
250: info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info);
252: /* Scatter ghost points to local vector */
253: info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
254: info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
256: /* Get pointers to vector data */
257: info = DAVecGetArray(user->da,localX,(void**)&x);
258: info = DAVecGetArray(user->da,G,(void**)&g);
260: /* Compute function and gradient over the locally owned part of the mesh */
261: for (j=ys; j<ys+ym; j++){
262: for (i=xs; i< xs+xm; i++){
263:
264: xc = x[j][i];
265: xlt=xrb=xl=xr=xb=xt=xc;
266:
267: if (i==0){ /* left side */
268: xl= user->left[j-ys+1];
269: xlt = user->left[j-ys+2];
270: } else {
271: xl = x[j][i-1];
272: }
274: if (j==0){ /* bottom side */
275: xb=user->bottom[i-xs+1];
276: xrb =user->bottom[i-xs+2];
277: } else {
278: xb = x[j-1][i];
279: }
280:
281: if (i+1 == gxs+gxm){ /* right side */
282: xr=user->right[j-ys+1];
283: xrb = user->right[j-ys];
284: } else {
285: xr = x[j][i+1];
286: }
288: if (j+1==gys+gym){ /* top side */
289: xt=user->top[i-xs+1];
290: xlt = user->top[i-xs];
291: }else {
292: xt = x[j+1][i];
293: }
295: if (i>gxs && j+1<gys+gym){
296: xlt = x[j+1][i-1];
297: }
298: if (j>gys && i+1<gxs+gxm){
299: xrb = x[j-1][i+1];
300: }
302: d1 = (xc-xl);
303: d2 = (xc-xr);
304: d3 = (xc-xt);
305: d4 = (xc-xb);
306: d5 = (xr-xrb);
307: d6 = (xrb-xb);
308: d7 = (xlt-xl);
309: d8 = (xt-xlt);
310:
311: df1dxc = d1*hydhx;
312: df2dxc = ( d1*hydhx + d4*hxdhy );
313: df3dxc = d3*hxdhy;
314: df4dxc = ( d2*hydhx + d3*hxdhy );
315: df5dxc = d2*hydhx;
316: df6dxc = d4*hxdhy;
318: d1 *= rhx;
319: d2 *= rhx;
320: d3 *= rhy;
321: d4 *= rhy;
322: d5 *= rhy;
323: d6 *= rhx;
324: d7 *= rhy;
325: d8 *= rhx;
327: f1 = sqrt( 1.0 + d1*d1 + d7*d7);
328: f2 = sqrt( 1.0 + d1*d1 + d4*d4);
329: f3 = sqrt( 1.0 + d3*d3 + d8*d8);
330: f4 = sqrt( 1.0 + d3*d3 + d2*d2);
331: f5 = sqrt( 1.0 + d2*d2 + d5*d5);
332: f6 = sqrt( 1.0 + d4*d4 + d6*d6);
333:
334: f2 = sqrt( 1.0 + d1*d1 + d4*d4);
335: f4 = sqrt( 1.0 + d3*d3 + d2*d2);
337: ft = ft + (f2 + f4);
339: df1dxc /= f1;
340: df2dxc /= f2;
341: df3dxc /= f3;
342: df4dxc /= f4;
343: df5dxc /= f5;
344: df6dxc /= f6;
346: g[j][i] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc ) * 0.5;
347:
348: }
349: }
351: /* Compute triangular areas along the border of the domain. */
352: if (xs==0){ /* left side */
353: for (j=ys; j<ys+ym; j++){
354: d3=(user->left[j-ys+1] - user->left[j-ys+2])*rhy;
355: d2=(user->left[j-ys+1] - x[j][0]) *rhx;
356: ft = ft+sqrt( 1.0 + d3*d3 + d2*d2);
357: }
358: }
359: if (ys==0){ /* bottom side */
360: for (i=xs; i<xs+xm; i++){
361: d2=(user->bottom[i+1-xs]-user->bottom[i-xs+2])*rhx;
362: d3=(user->bottom[i-xs+1]-x[0][i])*rhy;
363: ft = ft+sqrt( 1.0 + d3*d3 + d2*d2);
364: }
365: }
367: if (xs+xm==mx){ /* right side */
368: for (j=ys; j< ys+ym; j++){
369: d1=(x[j][mx-1] - user->right[j-ys+1])*rhx;
370: d4=(user->right[j-ys]-user->right[j-ys+1])*rhy;
371: ft = ft+sqrt( 1.0 + d1*d1 + d4*d4);
372: }
373: }
374: if (ys+ym==my){ /* top side */
375: for (i=xs; i<xs+xm; i++){
376: d1=(x[my-1][i] - user->top[i-xs+1])*rhy;
377: d4=(user->top[i-xs+1] - user->top[i-xs])*rhx;
378: ft = ft+sqrt( 1.0 + d1*d1 + d4*d4);
379: }
380: }
382: if (ys==0 && xs==0){
383: d1=(user->left[0]-user->left[1])/hy;
384: d2=(user->bottom[0]-user->bottom[1])*rhx;
385: ft +=sqrt( 1.0 + d1*d1 + d2*d2);
386: }
387: if (ys+ym == my && xs+xm == mx){
388: d1=(user->right[ym+1] - user->right[ym])*rhy;
389: d2=(user->top[xm+1] - user->top[xm])*rhx;
390: ft +=sqrt( 1.0 + d1*d1 + d2*d2);
391: }
393: ft=ft*area;
394: info = MPI_Allreduce(&ft,fcn,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD);CHKERRQ(info);
396: /* Restore vectors */
397: info = DAVecRestoreArray(user->da,localX,(void**)&x);
398: info = DAVecRestoreArray(user->da,G,(void**)&g);
400: /* Scatter values to global vector */
401: info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
403: info = PetscLogFlops(67*xm*ym); CHKERRQ(info);
405: return 0;
406: }
408: /* ------------------------------------------------------------------- */
411: /*
412: FormHessian - Evaluates Hessian matrix.
414: Input Parameters:
415: . taoapp - the TAO_APPLICATION context
416: . x - input vector
417: . ptr - optional user-defined context, as set by TaoSetHessian()
419: Output Parameters:
420: . H - Hessian matrix
421: . Hpre - optionally different preconditioning matrix
422: . flg - flag indicating matrix structure
424: */
425: int FormHessian(TAO_APPLICATION taoapp,Vec X,Mat *H, Mat *Hpre, MatStructure *flg, void *ptr)
426: {
427: int info;
428: AppCtx *user = (AppCtx *) ptr;
430: /* Evaluate the Hessian entries*/
431: info = QuadraticH(user,X,*H); CHKERRQ(info);
434: /* Indicate that this matrix has the same sparsity pattern during
435: successive iterations; setting this flag can save significant work
436: in computing the preconditioner for some methods. */
437: *flg=SAME_NONZERO_PATTERN;
439: return 0;
440: }
442: /* ------------------------------------------------------------------- */
445: /*
446: QuadraticH - Evaluates Hessian matrix.
448: Input Parameters:
449: . user - user-defined context, as set by TaoSetHessian()
450: . X - input vector
452: Output Parameter:
453: . H - Hessian matrix
454: */
455: int QuadraticH(AppCtx *user, Vec X, Mat Hessian)
456: {
457: int i,j,k,info;
458: int mx=user->mx, my=user->my;
459: int xs,xm,gxs,gxm,ys,ym,gys,gym;
460: double hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
461: double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
462: double hl,hr,ht,hb,hc,htl,hbr;
463: PetscScalar **x, v[7];
464: MatStencil col[7],row;
465: Vec localX;
466: PetscTruth assembled;
468: /* Get local mesh boundaries */
469: info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
471: info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
472: info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info);
474: /* Scatter ghost points to local vector */
475: info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
476: info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
478: /* Get pointers to vector data */
479: info = DAVecGetArray(user->da,localX,(void**)&x);
481: /* Initialize matrix entries to zero */
482: info = MatAssembled(Hessian,&assembled); CHKERRQ(info);
483: if (assembled){info = MatZeroEntries(Hessian); CHKERRQ(info);}
486: /* Set various matrix options */
487: info = MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES); CHKERRQ(info);
488: info = MatSetOption(Hessian,MAT_COLUMNS_SORTED); CHKERRQ(info);
489: info = MatSetOption(Hessian,MAT_ROWS_SORTED); CHKERRQ(info);
491: /* Compute Hessian over the locally owned part of the mesh */
493: for (j=ys; j<ys+ym; j++){
494:
495: for (i=xs; i< xs+xm; i++){
497: xc = x[j][i];
498: xlt=xrb=xl=xr=xb=xt=xc;
500: /* Left side */
501: if (i==0){
502: xl = user->left[j-ys+1];
503: xlt = user->left[j-ys+2];
504: } else {
505: xl = x[j][i-1];
506: }
507:
508: if (j==0){
509: xb = user->bottom[i-xs+1];
510: xrb = user->bottom[i-xs+2];
511: } else {
512: xb = x[j-1][i];
513: }
514:
515: if (i+1 == mx){
516: xr = user->right[j-ys+1];
517: xrb = user->right[j-ys];
518: } else {
519: xr = x[j][i+1];
520: }
522: if (j+1==my){
523: xt = user->top[i-xs+1];
524: xlt = user->top[i-xs];
525: }else {
526: xt = x[j+1][i];
527: }
529: if (i>0 && j+1<my){
530: xlt = x[j+1][i-1];
531: }
532: if (j>0 && i+1<mx){
533: xrb = x[j-1][i+1];
534: }
537: d1 = (xc-xl)/hx;
538: d2 = (xc-xr)/hx;
539: d3 = (xc-xt)/hy;
540: d4 = (xc-xb)/hy;
541: d5 = (xrb-xr)/hy;
542: d6 = (xrb-xb)/hx;
543: d7 = (xlt-xl)/hy;
544: d8 = (xlt-xt)/hx;
545:
546: f1 = sqrt( 1.0 + d1*d1 + d7*d7);
547: f2 = sqrt( 1.0 + d1*d1 + d4*d4);
548: f3 = sqrt( 1.0 + d3*d3 + d8*d8);
549: f4 = sqrt( 1.0 + d3*d3 + d2*d2);
550: f5 = sqrt( 1.0 + d2*d2 + d5*d5);
551: f6 = sqrt( 1.0 + d4*d4 + d6*d6);
554: hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
555: (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
556: hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
557: (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
558: ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
559: (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
560: hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
561: (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
563: hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
564: htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
566: hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
567: hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
568: (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
569: (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);
571: hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0;
573: row.j = j; row.i = i;
574: k=0;
575: if (j>0){
576: v[k]=hb;
577: col[k].j = j - 1; col[k].i = i;
578: k++;
579: }
580:
581: if (j>0 && i < mx -1){
582: v[k]=hbr;
583: col[k].j = j - 1; col[k].i = i+1;
584: k++;
585: }
586:
587: if (i>0){
588: v[k]= hl;
589: col[k].j = j; col[k].i = i-1;
590: k++;
591: }
592:
593: v[k]= hc;
594: col[k].j = j; col[k].i = i;
595: k++;
596:
597: if (i < mx-1 ){
598: v[k]= hr;
599: col[k].j = j; col[k].i = i+1;
600: k++;
601: }
602:
603: if (i>0 && j < my-1 ){
604: v[k]= htl;
605: col[k].j = j+1; col[k].i = i-1;
606: k++;
607: }
608:
609: if (j < my-1 ){
610: v[k]= ht;
611: col[k].j = j+1; col[k].i = i;
612: k++;
613: }
614:
615: /*
616: Set matrix values using local numbering, which was defined
617: earlier, in the main routine.
618: */
619: info = MatSetValuesStencil(Hessian,1,&row,k,col,v,INSERT_VALUES);
620: CHKERRQ(info);
621:
622: }
623: }
624:
625: /* Restore vectors */
626: info = DAVecRestoreArray(user->da,localX,(void**)&x);
628: info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
630: /* Assemble the matrix */
631: info = MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
632: info = MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
634: info = PetscLogFlops(199*xm*ym); CHKERRQ(info);
635: return 0;
636: }
638: /* ------------------------------------------------------------------- */
641: /*
642: MSA_BoundaryConditions - Calculates the boundary conditions for
643: the region.
645: Input Parameter:
646: . user - user-defined application context
648: Output Parameter:
649: . user - user-defined application context
650: */
651: static int MSA_BoundaryConditions(AppCtx * user)
652: {
653: int i,j,k,limit=0,info,maxits=5;
654: int xs,ys,xm,ym,gxs,gys,gxm,gym;
655: int mx=user->mx,my=user->my;
656: int bsize=0, lsize=0, tsize=0, rsize=0;
657: double one=1.0, two=2.0, three=3.0, tol=1e-10;
658: double fnorm,det,hx,hy,xt=0,yt=0;
659: double u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
660: double b=-0.5, t=0.5, l=-0.5, r=0.5;
661: double *boundary;
662: PetscTruth flg;
664: /* Get local mesh boundaries */
665: info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
666: info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info);
668: bsize=xm+2;
669: lsize=ym+2;
670: rsize=ym+2;
671: tsize=xm+2;
673: info = PetscMalloc(bsize*sizeof(double),&user->bottom); CHKERRQ(info);
674: info = PetscMalloc(tsize*sizeof(double),&user->top); CHKERRQ(info);
675: info = PetscMalloc(lsize*sizeof(double),&user->left); CHKERRQ(info);
676: info = PetscMalloc(rsize*sizeof(double),&user->right); CHKERRQ(info);
678: hx= (r-l)/(mx+1); hy=(t-b)/(my+1);
680: for (j=0; j<4; j++){
681: if (j==0){
682: yt=b;
683: xt=l+hx*xs;
684: limit=bsize;
685: boundary=user->bottom;
686: } else if (j==1){
687: yt=t;
688: xt=l+hx*xs;
689: limit=tsize;
690: boundary=user->top;
691: } else if (j==2){
692: yt=b+hy*ys;
693: xt=l;
694: limit=lsize;
695: boundary=user->left;
696: } else { //if (j==3)
697: yt=b+hy*ys;
698: xt=r;
699: limit=rsize;
700: boundary=user->right;
701: }
703: for (i=0; i<limit; i++){
704: u1=xt;
705: u2=-yt;
706: for (k=0; k<maxits; k++){
707: nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt;
708: nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt;
709: fnorm=sqrt(nf1*nf1+nf2*nf2);
710: if (fnorm <= tol) break;
711: njac11=one+u2*u2-u1*u1;
712: njac12=two*u1*u2;
713: njac21=-two*u1*u2;
714: njac22=-one - u1*u1 + u2*u2;
715: det = njac11*njac22-njac21*njac12;
716: u1 = u1-(njac22*nf1-njac12*nf2)/det;
717: u2 = u2-(njac11*nf2-njac21*nf1)/det;
718: }
720: boundary[i]=u1*u1-u2*u2;
721: if (j==0 || j==1) {
722: xt=xt+hx;
723: } else { // if (j==2 || j==3)
724: yt=yt+hy;
725: }
726:
727: }
729: }
731: /* Scale the boundary if desired */
732: if (1==1){
733: PetscReal scl = 1.0;
735: info = PetscOptionsGetReal(PETSC_NULL,"-bottom",&scl,&flg);
736: CHKERRQ(info);
737: if (flg){
738: for (i=0;i<bsize;i++) user->bottom[i]*=scl;
739: }
741: info = PetscOptionsGetReal(PETSC_NULL,"-top",&scl,&flg);
742: CHKERRQ(info);
743: if (flg){
744: for (i=0;i<tsize;i++) user->top[i]*=scl;
745: }
747: info = PetscOptionsGetReal(PETSC_NULL,"-right",&scl,&flg);
748: CHKERRQ(info);
749: if (flg){
750: for (i=0;i<rsize;i++) user->right[i]*=scl;
751: }
753: info = PetscOptionsGetReal(PETSC_NULL,"-left",&scl,&flg);
754: CHKERRQ(info);
755: if (flg){
756: for (i=0;i<lsize;i++) user->left[i]*=scl;
757: }
758: }
759:
760: return 0;
761: }
763: /* ------------------------------------------------------------------- */
766: /*
767: MSA_InitialPoint - Calculates the initial guess in one of three ways.
769: Input Parameters:
770: . user - user-defined application context
771: . X - vector for initial guess
773: Output Parameters:
774: . X - newly computed initial guess
775: */
776: static int MSA_InitialPoint(AppCtx * user, Vec X)
777: {
778: int start2=-1,i,j,info;
779: PetscReal start1=0;
780: PetscTruth flg1,flg2;
782: info = PetscOptionsGetReal(PETSC_NULL,"-start",&start1,&flg1); CHKERRQ(info);
783: info = PetscOptionsGetInt(PETSC_NULL,"-random",&start2,&flg2); CHKERRQ(info);
785: if (flg1){ /* The zero vector is reasonable */
786:
787: info = VecSet(X, start1); CHKERRQ(info);
789: } else if (flg2 && start2>0){ /* Try a random start between -0.5 and 0.5 */
791: PetscRandom rctx; PetscScalar np5=-0.5;
793: info = PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
794: CHKERRQ(info);
795: for (i=0; i<start2; i++){
796: info = VecSetRandom(X, rctx); CHKERRQ(info);
797: }
798: info = PetscRandomDestroy(rctx); CHKERRQ(info);
799: info = VecShift(X, np5); CHKERRQ(info);
801: } else { /* Take an average of the boundary conditions */
803: int xs,xm,ys,ym;
804: int mx=user->mx,my=user->my;
805: PetscScalar **x;
806:
807: /* Get local mesh boundaries */
808: info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
809:
810: /* Get pointers to vector data */
811: info = DAVecGetArray(user->da,X,(void**)&x);
813: /* Perform local computations */
814: for (j=ys; j<ys+ym; j++){
815: for (i=xs; i< xs+xm; i++){
816: x[j][i] = ( ((j+1)*user->bottom[i-xs+1]+(my-j+1)*user->top[i-xs+1])/(my+2)+
817: ((i+1)*user->left[j-ys+1]+(mx-i+1)*user->right[j-ys+1])/(mx+2))/2.0;
818: }
819: }
820:
821: /* Restore vectors */
822: info = DAVecRestoreArray(user->da,X,(void**)&x); CHKERRQ(info);
824: info = PetscLogFlops(9*xm*ym); CHKERRQ(info);
825:
826: }
827: return 0;
828: }
830: /*-----------------------------------------------------------------------*/
833: int My_Monitor(TAO_APPLICATION minsurfapp, void *ctx){
834: int info;
835: Vec X;
837: info = TaoAppGetSolutionVec(minsurfapp,&X); CHKERRQ(info);
838: info = VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info);
839: return 0;
840: }