Actual source code: jbearing2.c
1: /*
2: Include "petsctao.h" so we can use TAO solvers
3: Include "petscdmda.h" so that we can use distributed arrays (DMs) for managing
4: Include "petscksp.h" so we can set KSP type
5: the parallel mesh.
6: */
8: #include <petsctao.h>
9: #include <petscdmda.h>
11: static char help[]=
12: "This example demonstrates use of the TAO package to \n\
13: solve a bound constrained minimization problem. This example is based on \n\
14: the problem DPJB from the MINPACK-2 test suite. This pressure journal \n\
15: bearing problem is an example of elliptic variational problem defined over \n\
16: a two dimensional rectangle. By discretizing the domain into triangular \n\
17: elements, the pressure surrounding the journal bearing is defined as the \n\
18: minimum of a quadratic function whose variables are bounded below by zero.\n\
19: The command line options are:\n\
20: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
21: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
22: \n";
24: /*T
25: Concepts: TAO^Solving a bound constrained minimization problem
26: Routines: TaoCreate();
27: Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
28: Routines: TaoSetHessianRoutine();
29: Routines: TaoSetVariableBounds();
30: Routines: TaoSetMonitor(); TaoSetConvergenceTest();
31: Routines: TaoSetInitialVector();
32: Routines: TaoSetFromOptions();
33: Routines: TaoSolve();
34: Routines: TaoDestroy();
35: Processors: n
36: T*/
38: /*
39: User-defined application context - contains data needed by the
40: application-provided call-back routines, FormFunctionGradient(),
41: FormHessian().
42: */
43: typedef struct {
44: /* problem parameters */
45: PetscReal ecc; /* test problem parameter */
46: PetscReal b; /* A dimension of journal bearing */
47: PetscInt nx,ny; /* discretization in x, y directions */
49: /* Working space */
50: DM dm; /* distributed array data structure */
51: Mat A; /* Quadratic Objective term */
52: Vec B; /* Linear Objective term */
53: } AppCtx;
55: /* User-defined routines */
56: static PetscReal p(PetscReal xi, PetscReal ecc);
57: static PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *,Vec,void *);
58: static PetscErrorCode FormHessian(Tao,Vec,Mat, Mat, void *);
59: static PetscErrorCode ComputeB(AppCtx*);
60: static PetscErrorCode Monitor(Tao, void*);
61: static PetscErrorCode ConvergenceTest(Tao, void*);
63: int main(int argc, char **argv)
64: {
65: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
66: PetscInt Nx, Ny; /* number of processors in x- and y- directions */
67: PetscInt m; /* number of local elements in vectors */
68: Vec x; /* variables vector */
69: Vec xl,xu; /* bounds vectors */
70: PetscReal d1000 = 1000;
71: PetscBool flg,testgetdiag; /* A return variable when checking for user options */
72: Tao tao; /* Tao solver context */
73: KSP ksp;
74: AppCtx user; /* user-defined work context */
75: PetscReal zero = 0.0; /* lower bound on all variables */
77: /* Initialize PETSC and TAO */
78: PetscInitialize(&argc, &argv,(char *)0,help);if (ierr) return ierr;
80: /* Set the default values for the problem parameters */
81: user.nx = 50; user.ny = 50; user.ecc = 0.1; user.b = 10.0;
82: testgetdiag = PETSC_FALSE;
84: /* Check for any command line arguments that override defaults */
85: PetscOptionsGetInt(NULL,NULL,"-mx",&user.nx,&flg);
86: PetscOptionsGetInt(NULL,NULL,"-my",&user.ny,&flg);
87: PetscOptionsGetReal(NULL,NULL,"-ecc",&user.ecc,&flg);
88: PetscOptionsGetReal(NULL,NULL,"-b",&user.b,&flg);
89: PetscOptionsGetBool(NULL,NULL,"-test_getdiagonal",&testgetdiag,NULL);
91: PetscPrintf(PETSC_COMM_WORLD,"\n---- Journal Bearing Problem SHB-----\n");
92: PetscPrintf(PETSC_COMM_WORLD,"mx: %D, my: %D, ecc: %g \n\n",user.nx,user.ny,(double)user.ecc);
94: /* Let Petsc determine the grid division */
95: Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
97: /*
98: A two dimensional distributed array will help define this problem,
99: which derives from an elliptic PDE on two dimensional domain. From
100: the distributed array, Create the vectors.
101: */
102: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.nx,user.ny,Nx,Ny,1,1,NULL,NULL,&user.dm);
103: DMSetFromOptions(user.dm);
104: DMSetUp(user.dm);
106: /*
107: Extract global and local vectors from DM; the vector user.B is
108: used solely as work space for the evaluation of the function,
109: gradient, and Hessian. Duplicate for remaining vectors that are
110: the same types.
111: */
112: DMCreateGlobalVector(user.dm,&x); /* Solution */
113: VecDuplicate(x,&user.B); /* Linear objective */
115: /* Create matrix user.A to store quadratic, Create a local ordering scheme. */
116: VecGetLocalSize(x,&m);
117: DMCreateMatrix(user.dm,&user.A);
119: if (testgetdiag) {
120: MatSetOperation(user.A,MATOP_GET_DIAGONAL,NULL);
121: }
123: /* User defined function -- compute linear term of quadratic */
124: ComputeB(&user);
126: /* The TAO code begins here */
128: /*
129: Create the optimization solver
130: Suitable methods: TAOGPCG, TAOBQPIP, TAOTRON, TAOBLMVM
131: */
132: TaoCreate(PETSC_COMM_WORLD,&tao);
133: TaoSetType(tao,TAOBLMVM);
135: /* Set the initial vector */
136: VecSet(x, zero);
137: TaoSetInitialVector(tao,x);
139: /* Set the user function, gradient, hessian evaluation routines and data structures */
140: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*) &user);
142: TaoSetHessianRoutine(tao,user.A,user.A,FormHessian,(void*)&user);
144: /* Set a routine that defines the bounds */
145: VecDuplicate(x,&xl);
146: VecDuplicate(x,&xu);
147: VecSet(xl, zero);
148: VecSet(xu, d1000);
149: TaoSetVariableBounds(tao,xl,xu);
151: TaoGetKSP(tao,&ksp);
152: if (ksp) {
153: KSPSetType(ksp,KSPCG);
154: }
156: PetscOptionsHasName(NULL,NULL,"-testmonitor",&flg);
157: if (flg) {
158: TaoSetMonitor(tao,Monitor,&user,NULL);
159: }
160: PetscOptionsHasName(NULL,NULL,"-testconvergence",&flg);
161: if (flg) {
162: TaoSetConvergenceTest(tao,ConvergenceTest,&user);
163: }
165: /* Check for any tao command line options */
166: TaoSetFromOptions(tao);
168: /* Solve the bound constrained problem */
169: TaoSolve(tao);
171: /* Free PETSc data structures */
172: VecDestroy(&x);
173: VecDestroy(&xl);
174: VecDestroy(&xu);
175: MatDestroy(&user.A);
176: VecDestroy(&user.B);
178: /* Free TAO data structures */
179: TaoDestroy(&tao);
180: DMDestroy(&user.dm);
181: PetscFinalize();
182: return ierr;
183: }
185: static PetscReal p(PetscReal xi, PetscReal ecc)
186: {
187: PetscReal t=1.0+ecc*PetscCosScalar(xi);
188: return (t*t*t);
189: }
191: PetscErrorCode ComputeB(AppCtx* user)
192: {
194: PetscInt i,j,k;
195: PetscInt nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
196: PetscReal two=2.0, pi=4.0*atan(1.0);
197: PetscReal hx,hy,ehxhy;
198: PetscReal temp,*b;
199: PetscReal ecc=user->ecc;
201: nx=user->nx;
202: ny=user->ny;
203: hx=two*pi/(nx+1.0);
204: hy=two*user->b/(ny+1.0);
205: ehxhy = ecc*hx*hy;
207: /*
208: Get local grid boundaries
209: */
210: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
211: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
213: /* Compute the linear term in the objective function */
214: VecGetArray(user->B,&b);
215: for (i=xs; i<xs+xm; i++) {
216: temp=PetscSinScalar((i+1)*hx);
217: for (j=ys; j<ys+ym; j++) {
218: k=xm*(j-ys)+(i-xs);
219: b[k]= - ehxhy*temp;
220: }
221: }
222: VecRestoreArray(user->B,&b);
223: PetscLogFlops(5.0*xm*ym+3.0*xm);
225: return 0;
226: }
228: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *fcn,Vec G,void *ptr)
229: {
230: AppCtx* user=(AppCtx*)ptr;
232: PetscInt i,j,k,kk;
233: PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
234: PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
235: PetscReal hx,hy,hxhy,hxhx,hyhy;
236: PetscReal xi,v[5];
237: PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
238: PetscReal vmiddle, vup, vdown, vleft, vright;
239: PetscReal tt,f1,f2;
240: PetscReal *x,*g,zero=0.0;
241: Vec localX;
243: nx=user->nx;
244: ny=user->ny;
245: hx=two*pi/(nx+1.0);
246: hy=two*user->b/(ny+1.0);
247: hxhy=hx*hy;
248: hxhx=one/(hx*hx);
249: hyhy=one/(hy*hy);
251: DMGetLocalVector(user->dm,&localX);
253: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
254: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
256: VecSet(G, zero);
257: /*
258: Get local grid boundaries
259: */
260: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
261: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
263: VecGetArray(localX,&x);
264: VecGetArray(G,&g);
266: for (i=xs; i< xs+xm; i++) {
267: xi=(i+1)*hx;
268: trule1=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc)) / six; /* L(i,j) */
269: trule2=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc)) / six; /* U(i,j) */
270: trule3=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc)) / six; /* U(i+1,j) */
271: trule4=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc)) / six; /* L(i-1,j) */
272: trule5=trule1; /* L(i,j-1) */
273: trule6=trule2; /* U(i,j+1) */
275: vdown=-(trule5+trule2)*hyhy;
276: vleft=-hxhx*(trule2+trule4);
277: vright= -hxhx*(trule1+trule3);
278: vup=-hyhy*(trule1+trule6);
279: vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
281: for (j=ys; j<ys+ym; j++) {
283: row=(j-gys)*gxm + (i-gxs);
284: v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
286: k=0;
287: if (j>gys) {
288: v[k]=vdown; col[k]=row - gxm; k++;
289: }
291: if (i>gxs) {
292: v[k]= vleft; col[k]=row - 1; k++;
293: }
295: v[k]= vmiddle; col[k]=row; k++;
297: if (i+1 < gxs+gxm) {
298: v[k]= vright; col[k]=row+1; k++;
299: }
301: if (j+1 <gys+gym) {
302: v[k]= vup; col[k] = row+gxm; k++;
303: }
304: tt=0;
305: for (kk=0;kk<k;kk++) {
306: tt+=v[kk]*x[col[kk]];
307: }
308: row=(j-ys)*xm + (i-xs);
309: g[row]=tt;
311: }
313: }
315: VecRestoreArray(localX,&x);
316: VecRestoreArray(G,&g);
318: DMRestoreLocalVector(user->dm,&localX);
320: VecDot(X,G,&f1);
321: VecDot(user->B,X,&f2);
322: VecAXPY(G, one, user->B);
323: *fcn = f1/2.0 + f2;
325: PetscLogFlops((91 + 10.0*ym) * xm);
326: return 0;
328: }
330: /*
331: FormHessian computes the quadratic term in the quadratic objective function
332: Notice that the objective function in this problem is quadratic (therefore a constant
333: hessian). If using a nonquadratic solver, then you might want to reconsider this function
334: */
335: PetscErrorCode FormHessian(Tao tao,Vec X,Mat hes, Mat Hpre, void *ptr)
336: {
337: AppCtx* user=(AppCtx*)ptr;
339: PetscInt i,j,k;
340: PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
341: PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
342: PetscReal hx,hy,hxhy,hxhx,hyhy;
343: PetscReal xi,v[5];
344: PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
345: PetscReal vmiddle, vup, vdown, vleft, vright;
346: PetscBool assembled;
348: nx=user->nx;
349: ny=user->ny;
350: hx=two*pi/(nx+1.0);
351: hy=two*user->b/(ny+1.0);
352: hxhy=hx*hy;
353: hxhx=one/(hx*hx);
354: hyhy=one/(hy*hy);
356: /*
357: Get local grid boundaries
358: */
359: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
360: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
361: MatAssembled(hes,&assembled);
362: if (assembled) {MatZeroEntries(hes);}
364: for (i=xs; i< xs+xm; i++) {
365: xi=(i+1)*hx;
366: trule1=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc)) / six; /* L(i,j) */
367: trule2=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc)) / six; /* U(i,j) */
368: trule3=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc)) / six; /* U(i+1,j) */
369: trule4=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc)) / six; /* L(i-1,j) */
370: trule5=trule1; /* L(i,j-1) */
371: trule6=trule2; /* U(i,j+1) */
373: vdown=-(trule5+trule2)*hyhy;
374: vleft=-hxhx*(trule2+trule4);
375: vright= -hxhx*(trule1+trule3);
376: vup=-hyhy*(trule1+trule6);
377: vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
378: v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
380: for (j=ys; j<ys+ym; j++) {
381: row=(j-gys)*gxm + (i-gxs);
383: k=0;
384: if (j>gys) {
385: v[k]=vdown; col[k]=row - gxm; k++;
386: }
388: if (i>gxs) {
389: v[k]= vleft; col[k]=row - 1; k++;
390: }
392: v[k]= vmiddle; col[k]=row; k++;
394: if (i+1 < gxs+gxm) {
395: v[k]= vright; col[k]=row+1; k++;
396: }
398: if (j+1 <gys+gym) {
399: v[k]= vup; col[k] = row+gxm; k++;
400: }
401: MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES);
403: }
405: }
407: /*
408: Assemble matrix, using the 2-step process:
409: MatAssemblyBegin(), MatAssemblyEnd().
410: By placing code between these two statements, computations can be
411: done while messages are in transition.
412: */
413: MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY);
414: MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY);
416: /*
417: Tell the matrix we will never add a new nonzero location to the
418: matrix. If we do it will generate an error.
419: */
420: MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
421: MatSetOption(hes,MAT_SYMMETRIC,PETSC_TRUE);
423: PetscLogFlops(9.0*xm*ym+49.0*xm);
424: MatNorm(hes,NORM_1,&hx);
425: return 0;
426: }
428: PetscErrorCode Monitor(Tao tao, void *ctx)
429: {
430: PetscErrorCode ierr;
431: PetscInt its;
432: PetscReal f,gnorm,cnorm,xdiff;
433: TaoConvergedReason reason;
436: TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
437: if (!(its%5)) {
438: PetscPrintf(PETSC_COMM_WORLD,"iteration=%D\tf=%g\n",its,(double)f);
439: }
440: return(0);
441: }
443: PetscErrorCode ConvergenceTest(Tao tao, void *ctx)
444: {
445: PetscErrorCode ierr;
446: PetscInt its;
447: PetscReal f,gnorm,cnorm,xdiff;
448: TaoConvergedReason reason;
451: TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
452: if (its == 100) {
453: TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS);
454: }
455: return(0);
457: }
459: /*TEST
461: build:
462: requires: !complex
464: test:
465: args: -tao_smonitor -mx 8 -my 12 -tao_type tron -tao_gatol 1.e-5
466: requires: !single
468: test:
469: suffix: 2
470: nsize: 2
471: args: -tao_smonitor -mx 50 -my 50 -ecc 0.99 -tao_type gpcg -tao_gatol 1.e-5
472: requires: !single
474: test:
475: suffix: 3
476: nsize: 2
477: args: -tao_smonitor -mx 10 -my 16 -ecc 0.9 -tao_type bqpip -tao_gatol 1.e-4
478: requires: !single
480: test:
481: suffix: 4
482: nsize: 2
483: args: -tao_smonitor -mx 10 -my 16 -ecc 0.9 -tao_type bqpip -tao_gatol 1.e-4 -test_getdiagonal
484: output_file: output/jbearing2_3.out
485: requires: !single
487: test:
488: suffix: 5
489: args: -tao_smonitor -mx 8 -my 12 -tao_type bncg -tao_bncg_type gd -tao_gatol 1e-4
490: requires: !single
492: test:
493: suffix: 6
494: args: -tao_smonitor -mx 8 -my 12 -tao_type bncg -tao_gatol 1e-4
495: requires: !single
497: test:
498: suffix: 7
499: args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5
500: requires: !single
502: test:
503: suffix: 8
504: args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5
505: requires: !single
507: test:
508: suffix: 9
509: args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5
510: requires: !single
512: test:
513: suffix: 10
514: args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
515: requires: !single
517: test:
518: suffix: 11
519: args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
520: requires: !single
522: test:
523: suffix: 12
524: args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
525: requires: !single
527: test:
528: suffix: 13
529: args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls
530: requires: !single
532: test:
533: suffix: 14
534: args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type blmvm
535: requires: !single
537: test:
538: suffix: 15
539: args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnkls -tao_bqnk_mat_type lmvmbfgs
540: requires: !single
542: test:
543: suffix: 16
544: args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
545: requires: !single
547: test:
548: suffix: 17
549: args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls -tao_bqnls_mat_lmvm_scale_type scalar -tao_view
550: requires: !single
552: test:
553: suffix: 18
554: args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls -tao_bqnls_mat_lmvm_scale_type none -tao_view
555: requires: !single
557: test:
558: suffix: 19
559: args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5 -tao_mf_hessian
560: requires: !single
562: test:
563: suffix: 20
564: args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5 -tao_mf_hessian
565: requires: !single
567: test:
568: suffix: 21
569: args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5 -tao_mf_hessian
570: requires: !single
571: TEST*/