Actual source code: jbearing2.c
petsc-3.7.7 2017-09-25
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*);
65: int main( int argc, char **argv )
66: {
67: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
68: PetscInt Nx, Ny; /* number of processors in x- and y- directions */
69: PetscInt m; /* number of local elements in vectors */
70: Vec x; /* variables vector */
71: Vec xl,xu; /* bounds vectors */
72: PetscReal d1000 = 1000;
73: PetscBool flg; /* A return variable when checking for user options */
74: Tao tao; /* Tao solver context */
75: KSP ksp;
76: AppCtx user; /* user-defined work context */
77: PetscReal zero=0.0; /* lower bound on all variables */
79: /* Initialize PETSC and TAO */
80: PetscInitialize( &argc, &argv,(char *)0,help );
82: /* Set the default values for the problem parameters */
83: user.nx = 50; user.ny = 50; user.ecc = 0.1; user.b = 10.0;
85: /* Check for any command line arguments that override defaults */
86: PetscOptionsGetInt(NULL,NULL,"-mx",&user.nx,&flg);
87: PetscOptionsGetInt(NULL,NULL,"-my",&user.ny,&flg);
88: PetscOptionsGetReal(NULL,NULL,"-ecc",&user.ecc,&flg);
89: PetscOptionsGetReal(NULL,NULL,"-b",&user.b,&flg);
92: PetscPrintf(PETSC_COMM_WORLD,"\n---- Journal Bearing Problem SHB-----\n");
93: PetscPrintf(PETSC_COMM_WORLD,"mx: %D, my: %D, ecc: %g \n\n",user.nx,user.ny,(double)user.ecc);
95: /* Let Petsc determine the grid division */
96: Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
98: /*
99: A two dimensional distributed array will help define this problem,
100: which derives from an elliptic PDE on two dimensional domain. From
101: the distributed array, Create the vectors.
102: */
103: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,
104: user.nx,user.ny,Nx,Ny,1,1,NULL,NULL,
105: &user.dm);
107: /*
108: Extract global and local vectors from DM; the vector user.B is
109: used solely as work space for the evaluation of the function,
110: gradient, and Hessian. Duplicate for remaining vectors that are
111: the same types.
112: */
113: DMCreateGlobalVector(user.dm,&x); /* Solution */
114: VecDuplicate(x,&user.B); /* Linear objective */
117: /* Create matrix user.A to store quadratic, Create a local ordering scheme. */
118: VecGetLocalSize(x,&m);
119: DMCreateMatrix(user.dm,&user.A);
121: /* User defined function -- compute linear term of quadratic */
122: ComputeB(&user);
124: /* The TAO code begins here */
126: /*
127: Create the optimization solver
128: Suitable methods: TAOGPCG, TAOBQPIP, TAOTRON, TAOBLMVM
129: */
130: TaoCreate(PETSC_COMM_WORLD,&tao);
131: TaoSetType(tao,TAOBLMVM);
134: /* Set the initial vector */
135: VecSet(x, zero);
136: TaoSetInitialVector(tao,x);
138: /* Set the user function, gradient, hessian evaluation routines and data structures */
139: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*) &user);
141: TaoSetHessianRoutine(tao,user.A,user.A,FormHessian,(void*)&user);
143: /* Set a routine that defines the bounds */
144: VecDuplicate(x,&xl);
145: VecDuplicate(x,&xu);
146: VecSet(xl, zero);
147: VecSet(xu, d1000);
148: TaoSetVariableBounds(tao,xl,xu);
150: TaoGetKSP(tao,&ksp);
151: if (ksp) {
152: KSPSetType(ksp,KSPCG);
153: }
155: PetscOptionsHasName(NULL,NULL,"-testmonitor",&flg);
156: if (flg) {
157: TaoSetMonitor(tao,Monitor,&user,NULL);
158: }
159: PetscOptionsHasName(NULL,NULL,"-testconvergence",&flg);
160: if (flg) {
161: TaoSetConvergenceTest(tao,ConvergenceTest,&user);
162: }
164: /* Check for any tao command line options */
165: TaoSetFromOptions(tao);
167: /* Solve the bound constrained problem */
168: TaoSolve(tao);
170: /* Free PETSc data structures */
171: VecDestroy(&x);
172: VecDestroy(&xl);
173: VecDestroy(&xu);
174: MatDestroy(&user.A);
175: VecDestroy(&user.B);
176: /* Free TAO data structures */
177: TaoDestroy(&tao);
179: DMDestroy(&user.dm);
181: PetscFinalize();
183: return 0;
184: }
187: static PetscReal p(PetscReal xi, PetscReal ecc)
188: {
189: PetscReal t=1.0+ecc*PetscCosScalar(xi);
190: return (t*t*t);
191: }
195: PetscErrorCode ComputeB(AppCtx* user)
196: {
198: PetscInt i,j,k;
199: PetscInt nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
200: PetscReal two=2.0, pi=4.0*atan(1.0);
201: PetscReal hx,hy,ehxhy;
202: PetscReal temp,*b;
203: PetscReal ecc=user->ecc;
205: nx=user->nx;
206: ny=user->ny;
207: hx=two*pi/(nx+1.0);
208: hy=two*user->b/(ny+1.0);
209: ehxhy = ecc*hx*hy;
212: /*
213: Get local grid boundaries
214: */
215: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
216: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
218: /* Compute the linear term in the objective function */
219: VecGetArray(user->B,&b);
220: for (i=xs; i<xs+xm; i++){
221: temp=PetscSinScalar((i+1)*hx);
222: for (j=ys; j<ys+ym; j++){
223: k=xm*(j-ys)+(i-xs);
224: b[k]= - ehxhy*temp;
225: }
226: }
227: VecRestoreArray(user->B,&b);
228: PetscLogFlops(5*xm*ym+3*xm);
230: return 0;
231: }
235: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *fcn,Vec G,void *ptr)
236: {
237: AppCtx* user=(AppCtx*)ptr;
239: PetscInt i,j,k,kk;
240: PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
241: PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
242: PetscReal hx,hy,hxhy,hxhx,hyhy;
243: PetscReal xi,v[5];
244: PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
245: PetscReal vmiddle, vup, vdown, vleft, vright;
246: PetscReal tt,f1,f2;
247: PetscReal *x,*g,zero=0.0;
248: Vec localX;
250: nx=user->nx;
251: ny=user->ny;
252: hx=two*pi/(nx+1.0);
253: hy=two*user->b/(ny+1.0);
254: hxhy=hx*hy;
255: hxhx=one/(hx*hx);
256: hyhy=one/(hy*hy);
258: DMGetLocalVector(user->dm,&localX);
260: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
261: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
263: VecSet(G, zero);
264: /*
265: Get local grid boundaries
266: */
267: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
268: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
270: VecGetArray(localX,&x);
271: VecGetArray(G,&g);
273: for (i=xs; i< xs+xm; i++){
274: xi=(i+1)*hx;
275: trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
276: trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
277: trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
278: trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
279: trule5=trule1; /* L(i,j-1) */
280: trule6=trule2; /* U(i,j+1) */
282: vdown=-(trule5+trule2)*hyhy;
283: vleft=-hxhx*(trule2+trule4);
284: vright= -hxhx*(trule1+trule3);
285: vup=-hyhy*(trule1+trule6);
286: vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
288: for (j=ys; j<ys+ym; j++){
290: row=(j-gys)*gxm + (i-gxs);
291: v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
293: k=0;
294: if (j>gys){
295: v[k]=vdown; col[k]=row - gxm; k++;
296: }
298: if (i>gxs){
299: v[k]= vleft; col[k]=row - 1; k++;
300: }
302: v[k]= vmiddle; col[k]=row; k++;
304: if (i+1 < gxs+gxm){
305: v[k]= vright; col[k]=row+1; k++;
306: }
308: if (j+1 <gys+gym){
309: v[k]= vup; col[k] = row+gxm; k++;
310: }
311: tt=0;
312: for (kk=0;kk<k;kk++){
313: tt+=v[kk]*x[col[kk]];
314: }
315: row=(j-ys)*xm + (i-xs);
316: g[row]=tt;
318: }
320: }
322: VecRestoreArray(localX,&x);
323: VecRestoreArray(G,&g);
325: DMRestoreLocalVector(user->dm,&localX);
327: VecDot(X,G,&f1);
328: VecDot(user->B,X,&f2);
329: VecAXPY(G, one, user->B);
330: *fcn = f1/2.0 + f2;
333: PetscLogFlops((91 + 10*ym) * xm);
334: return 0;
336: }
341: /*
342: FormHessian computes the quadratic term in the quadratic objective function
343: Notice that the objective function in this problem is quadratic (therefore a constant
344: hessian). If using a nonquadratic solver, then you might want to reconsider this function
345: */
346: PetscErrorCode FormHessian(Tao tao,Vec X,Mat hes, Mat Hpre, void *ptr)
347: {
348: AppCtx* user=(AppCtx*)ptr;
350: PetscInt i,j,k;
351: PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
352: PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
353: PetscReal hx,hy,hxhy,hxhx,hyhy;
354: PetscReal xi,v[5];
355: PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
356: PetscReal vmiddle, vup, vdown, vleft, vright;
357: PetscBool assembled;
359: nx=user->nx;
360: ny=user->ny;
361: hx=two*pi/(nx+1.0);
362: hy=two*user->b/(ny+1.0);
363: hxhy=hx*hy;
364: hxhx=one/(hx*hx);
365: hyhy=one/(hy*hy);
367: /*
368: Get local grid boundaries
369: */
370: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
371: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
372: MatAssembled(hes,&assembled);
373: if (assembled){MatZeroEntries(hes);}
375: for (i=xs; i< xs+xm; i++){
376: xi=(i+1)*hx;
377: trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
378: trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
379: trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
380: trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
381: trule5=trule1; /* L(i,j-1) */
382: trule6=trule2; /* U(i,j+1) */
384: vdown=-(trule5+trule2)*hyhy;
385: vleft=-hxhx*(trule2+trule4);
386: vright= -hxhx*(trule1+trule3);
387: vup=-hyhy*(trule1+trule6);
388: vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
389: v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
391: for (j=ys; j<ys+ym; j++){
392: row=(j-gys)*gxm + (i-gxs);
394: k=0;
395: if (j>gys){
396: v[k]=vdown; col[k]=row - gxm; k++;
397: }
399: if (i>gxs){
400: v[k]= vleft; col[k]=row - 1; k++;
401: }
403: v[k]= vmiddle; col[k]=row; k++;
405: if (i+1 < gxs+gxm){
406: v[k]= vright; col[k]=row+1; k++;
407: }
409: if (j+1 <gys+gym){
410: v[k]= vup; col[k] = row+gxm; k++;
411: }
412: MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES);
414: }
416: }
418: /*
419: Assemble matrix, using the 2-step process:
420: MatAssemblyBegin(), MatAssemblyEnd().
421: By placing code between these two statements, computations can be
422: done while messages are in transition.
423: */
424: MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY);
425: MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY);
427: /*
428: Tell the matrix we will never add a new nonzero location to the
429: matrix. If we do it will generate an error.
430: */
431: MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
432: MatSetOption(hes,MAT_SYMMETRIC,PETSC_TRUE);
434: PetscLogFlops(9*xm*ym+49*xm);
435: MatNorm(hes,NORM_1,&hx);
436: return 0;
437: }
441: PetscErrorCode Monitor(Tao tao, void *ctx)
442: {
443: PetscErrorCode ierr;
444: PetscInt its;
445: PetscReal f,gnorm,cnorm,xdiff;
446: TaoConvergedReason reason;
449: TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
450: if (!(its%5)) {
451: PetscPrintf(PETSC_COMM_WORLD,"iteration=%D\tf=%g\n",its,(double)f);
452: }
453: return(0);
454: }
458: PetscErrorCode ConvergenceTest(Tao tao, void *ctx)
459: {
460: PetscErrorCode ierr;
461: PetscInt its;
462: PetscReal f,gnorm,cnorm,xdiff;
463: TaoConvergedReason reason;
466: TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
467: if (its == 100) {
468: TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS);
469: }
470: return(0);
472: }