Actual source code: jbearing2.c
petsc-3.5.4 2015-05-23
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: TaoGetConvergedReason(); 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: TaoConvergedReason reason;
76: KSP ksp;
77: AppCtx user; /* user-defined work context */
78: PetscReal zero=0.0; /* lower bound on all variables */
80: /* Initialize PETSC and TAO */
81: PetscInitialize( &argc, &argv,(char *)0,help );
83: /* Set the default values for the problem parameters */
84: user.nx = 50; user.ny = 50; user.ecc = 0.1; user.b = 10.0;
86: /* Check for any command line arguments that override defaults */
87: PetscOptionsGetInt(NULL,"-mx",&user.nx,&flg);
88: PetscOptionsGetInt(NULL,"-my",&user.ny,&flg);
89: PetscOptionsGetReal(NULL,"-ecc",&user.ecc,&flg);
90: PetscOptionsGetReal(NULL,"-b",&user.b,&flg);
93: PetscPrintf(PETSC_COMM_WORLD,"\n---- Journal Bearing Problem SHB-----\n");
94: PetscPrintf(PETSC_COMM_WORLD,"mx: %D, my: %D, ecc: %g \n\n",user.nx,user.ny,(double)user.ecc);
96: /* Let Petsc determine the grid division */
97: Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
99: /*
100: A two dimensional distributed array will help define this problem,
101: which derives from an elliptic PDE on two dimensional domain. From
102: the distributed array, Create the vectors.
103: */
104: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,
105: user.nx,user.ny,Nx,Ny,1,1,NULL,NULL,
106: &user.dm);
108: /*
109: Extract global and local vectors from DM; the vector user.B is
110: used solely as work space for the evaluation of the function,
111: gradient, and Hessian. Duplicate for remaining vectors that are
112: the same types.
113: */
114: DMCreateGlobalVector(user.dm,&x); /* Solution */
115: VecDuplicate(x,&user.B); /* Linear objective */
118: /* Create matrix user.A to store quadratic, Create a local ordering scheme. */
119: VecGetLocalSize(x,&m);
120: DMCreateMatrix(user.dm,&user.A);
122: /* User defined function -- compute linear term of quadratic */
123: ComputeB(&user);
125: /* The TAO code begins here */
127: /*
128: Create the optimization solver
129: Suitable methods: TAOGPCG, TAOBQPIP, TAOTRON, TAOBLMVM
130: */
131: TaoCreate(PETSC_COMM_WORLD,&tao);
132: 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,"-testmonitor",&flg);
157: if (flg) {
158: TaoSetMonitor(tao,Monitor,&user,NULL);
159: }
160: PetscOptionsHasName(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: TaoGetConvergedReason(tao,&reason);
172: if (reason <= 0) {
173: PetscPrintf(PETSC_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
174: }
176: /* Free PETSc data structures */
177: VecDestroy(&x);
178: VecDestroy(&xl);
179: VecDestroy(&xu);
180: MatDestroy(&user.A);
181: VecDestroy(&user.B);
182: /* Free TAO data structures */
183: TaoDestroy(&tao);
185: DMDestroy(&user.dm);
187: PetscFinalize();
189: return 0;
190: }
193: static PetscReal p(PetscReal xi, PetscReal ecc)
194: {
195: PetscReal t=1.0+ecc*PetscCosScalar(xi);
196: return (t*t*t);
197: }
201: PetscErrorCode ComputeB(AppCtx* user)
202: {
204: PetscInt i,j,k;
205: PetscInt nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
206: PetscReal two=2.0, pi=4.0*atan(1.0);
207: PetscReal hx,hy,ehxhy;
208: PetscReal temp,*b;
209: PetscReal ecc=user->ecc;
211: nx=user->nx;
212: ny=user->ny;
213: hx=two*pi/(nx+1.0);
214: hy=two*user->b/(ny+1.0);
215: ehxhy = ecc*hx*hy;
218: /*
219: Get local grid boundaries
220: */
221: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
222: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
224: /* Compute the linear term in the objective function */
225: VecGetArray(user->B,&b);
226: for (i=xs; i<xs+xm; i++){
227: temp=PetscSinScalar((i+1)*hx);
228: for (j=ys; j<ys+ym; j++){
229: k=xm*(j-ys)+(i-xs);
230: b[k]= - ehxhy*temp;
231: }
232: }
233: VecRestoreArray(user->B,&b);
234: PetscLogFlops(5*xm*ym+3*xm);
236: return 0;
237: }
241: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *fcn,Vec G,void *ptr)
242: {
243: AppCtx* user=(AppCtx*)ptr;
245: PetscInt i,j,k,kk;
246: PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
247: PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
248: PetscReal hx,hy,hxhy,hxhx,hyhy;
249: PetscReal xi,v[5];
250: PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
251: PetscReal vmiddle, vup, vdown, vleft, vright;
252: PetscReal tt,f1,f2;
253: PetscReal *x,*g,zero=0.0;
254: Vec localX;
256: nx=user->nx;
257: ny=user->ny;
258: hx=two*pi/(nx+1.0);
259: hy=two*user->b/(ny+1.0);
260: hxhy=hx*hy;
261: hxhx=one/(hx*hx);
262: hyhy=one/(hy*hy);
264: DMGetLocalVector(user->dm,&localX);
266: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
267: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
269: VecSet(G, zero);
270: /*
271: Get local grid boundaries
272: */
273: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
274: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
276: VecGetArray(localX,&x);
277: VecGetArray(G,&g);
279: for (i=xs; i< xs+xm; i++){
280: xi=(i+1)*hx;
281: trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
282: trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
283: trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
284: trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
285: trule5=trule1; /* L(i,j-1) */
286: trule6=trule2; /* U(i,j+1) */
288: vdown=-(trule5+trule2)*hyhy;
289: vleft=-hxhx*(trule2+trule4);
290: vright= -hxhx*(trule1+trule3);
291: vup=-hyhy*(trule1+trule6);
292: vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
294: for (j=ys; j<ys+ym; j++){
296: row=(j-gys)*gxm + (i-gxs);
297: v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
299: k=0;
300: if (j>gys){
301: v[k]=vdown; col[k]=row - gxm; k++;
302: }
304: if (i>gxs){
305: v[k]= vleft; col[k]=row - 1; k++;
306: }
308: v[k]= vmiddle; col[k]=row; k++;
310: if (i+1 < gxs+gxm){
311: v[k]= vright; col[k]=row+1; k++;
312: }
314: if (j+1 <gys+gym){
315: v[k]= vup; col[k] = row+gxm; k++;
316: }
317: tt=0;
318: for (kk=0;kk<k;kk++){
319: tt+=v[kk]*x[col[kk]];
320: }
321: row=(j-ys)*xm + (i-xs);
322: g[row]=tt;
324: }
326: }
328: VecRestoreArray(localX,&x);
329: VecRestoreArray(G,&g);
331: DMRestoreLocalVector(user->dm,&localX);
333: VecDot(X,G,&f1);
334: VecDot(user->B,X,&f2);
335: VecAXPY(G, one, user->B);
336: *fcn = f1/2.0 + f2;
339: PetscLogFlops((91 + 10*ym) * xm);
340: return 0;
342: }
347: /*
348: FormHessian computes the quadratic term in the quadratic objective function
349: Notice that the objective function in this problem is quadratic (therefore a constant
350: hessian). If using a nonquadratic solver, then you might want to reconsider this function
351: */
352: PetscErrorCode FormHessian(Tao tao,Vec X,Mat hes, Mat Hpre, void *ptr)
353: {
354: AppCtx* user=(AppCtx*)ptr;
356: PetscInt i,j,k;
357: PetscInt col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
358: PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
359: PetscReal hx,hy,hxhy,hxhx,hyhy;
360: PetscReal xi,v[5];
361: PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
362: PetscReal vmiddle, vup, vdown, vleft, vright;
363: PetscBool assembled;
365: nx=user->nx;
366: ny=user->ny;
367: hx=two*pi/(nx+1.0);
368: hy=two*user->b/(ny+1.0);
369: hxhy=hx*hy;
370: hxhx=one/(hx*hx);
371: hyhy=one/(hy*hy);
373: /*
374: Get local grid boundaries
375: */
376: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
377: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
378: MatAssembled(hes,&assembled);
379: if (assembled){MatZeroEntries(hes);}
381: for (i=xs; i< xs+xm; i++){
382: xi=(i+1)*hx;
383: trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
384: trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
385: trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
386: trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
387: trule5=trule1; /* L(i,j-1) */
388: trule6=trule2; /* U(i,j+1) */
390: vdown=-(trule5+trule2)*hyhy;
391: vleft=-hxhx*(trule2+trule4);
392: vright= -hxhx*(trule1+trule3);
393: vup=-hyhy*(trule1+trule6);
394: vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
395: v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
397: for (j=ys; j<ys+ym; j++){
398: row=(j-gys)*gxm + (i-gxs);
400: k=0;
401: if (j>gys){
402: v[k]=vdown; col[k]=row - gxm; k++;
403: }
405: if (i>gxs){
406: v[k]= vleft; col[k]=row - 1; k++;
407: }
409: v[k]= vmiddle; col[k]=row; k++;
411: if (i+1 < gxs+gxm){
412: v[k]= vright; col[k]=row+1; k++;
413: }
415: if (j+1 <gys+gym){
416: v[k]= vup; col[k] = row+gxm; k++;
417: }
418: MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES);
420: }
422: }
424: /*
425: Assemble matrix, using the 2-step process:
426: MatAssemblyBegin(), MatAssemblyEnd().
427: By placing code between these two statements, computations can be
428: done while messages are in transition.
429: */
430: MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY);
431: MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY);
433: /*
434: Tell the matrix we will never add a new nonzero location to the
435: matrix. If we do it will generate an error.
436: */
437: MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
438: MatSetOption(hes,MAT_SYMMETRIC,PETSC_TRUE);
440: PetscLogFlops(9*xm*ym+49*xm);
441: MatNorm(hes,NORM_1,&hx);
442: return 0;
443: }
447: PetscErrorCode Monitor(Tao tao, void *ctx)
448: {
449: PetscErrorCode ierr;
450: PetscInt its;
451: PetscReal f,gnorm,cnorm,xdiff;
452: TaoConvergedReason reason;
455: TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
456: if (!(its%5)) {
457: PetscPrintf(PETSC_COMM_WORLD,"iteration=%D\tf=%g\n",its,(double)f);
458: }
459: return(0);
460: }
464: PetscErrorCode ConvergenceTest(Tao tao, void *ctx)
465: {
466: PetscErrorCode ierr;
467: PetscInt its;
468: PetscReal f,gnorm,cnorm,xdiff;
469: TaoConvergedReason reason;
472: TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
473: if (its == 100) {
474: TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS);
475: }
476: return(0);
478: }