Actual source code: eptorsion2.c
1: /* Program usage: mpiexec -n <proc> eptorsion2 [-help] [all TAO options] */
3: /* ----------------------------------------------------------------------
5: Elastic-plastic torsion problem.
7: The elastic plastic torsion problem arises from the determination
8: of the stress field on an infinitely long cylindrical bar, which is
9: equivalent to the solution of the following problem:
11: min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
13: where C is the torsion angle per unit length.
15: The uniprocessor version of this code is eptorsion1.c; the Fortran
16: version of this code is eptorsion2f.F.
18: This application solves the problem without calculating hessians
19: ---------------------------------------------------------------------- */
21: /*
22: Include "petsctao.h" so that we can use TAO solvers. Note that this
23: file automatically includes files for lower-level support, such as those
24: provided by the PETSc library:
25: petsc.h - base PETSc routines petscvec.h - vectors
26: petscsys.h - system routines petscmat.h - matrices
27: petscis.h - index sets petscksp.h - Krylov subspace methods
28: petscviewer.h - viewers petscpc.h - preconditioners
29: Include "petscdmda.h" so that we can use distributed arrays (DMs) for managing
30: the parallel mesh.
31: */
33: #include <petsctao.h>
34: #include <petscdmda.h>
36: static char help[] =
37: "Demonstrates use of the TAO package to solve \n\
38: unconstrained minimization problems in parallel. This example is based on \n\
39: the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.\n\
40: The command line options are:\n\
41: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
42: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
43: -par <param>, where <param> = angle of twist per unit length\n\n";
45: /*T
46: Concepts: TAO^Solving an unconstrained minimization problem
47: Routines: TaoCreate(); TaoSetType();
48: Routines: TaoSetInitialVector();
49: Routines: TaoSetObjectiveAndGradientRoutine();
50: Routines: TaoSetHessianRoutine(); TaoSetFromOptions();
51: Routines: TaoSolve();
52: Routines: TaoDestroy();
53: Processors: n
54: T*/
56: /*
57: User-defined application context - contains data needed by the
58: application-provided call-back routines, FormFunction() and
59: FormGradient().
60: */
61: typedef struct {
62: /* parameters */
63: PetscInt mx, my; /* global discretization in x- and y-directions */
64: PetscReal param; /* nonlinearity parameter */
66: /* work space */
67: Vec localX; /* local vectors */
68: DM dm; /* distributed array data structure */
69: } AppCtx;
71: PetscErrorCode FormInitialGuess(AppCtx*, Vec);
72: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
73: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
75: int main(int argc, char **argv)
76: {
77: PetscErrorCode ierr;
78: Vec x;
79: Mat H;
80: PetscInt Nx, Ny;
81: Tao tao;
82: PetscBool flg;
83: KSP ksp;
84: PC pc;
85: AppCtx user;
87: PetscInitialize(&argc, &argv, (char *)0, help);
89: /* Specify default dimension of the problem */
90: user.param = 5.0; user.mx = 10; user.my = 10;
91: Nx = Ny = PETSC_DECIDE;
93: /* Check for any command line arguments that override defaults */
94: PetscOptionsGetReal(NULL,NULL,"-par",&user.param,&flg);
95: PetscOptionsGetInt(NULL,NULL,"-my",&user.my,&flg);
96: PetscOptionsGetInt(NULL,NULL,"-mx",&user.mx,&flg);
98: PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
99: PetscPrintf(PETSC_COMM_WORLD,"mx: %D my: %D \n\n",user.mx,user.my);
101: /* Set up distributed array */
102: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.mx,user.my,Nx,Ny,1,1,NULL,NULL,&user.dm);
103: DMSetFromOptions(user.dm);
104: DMSetUp(user.dm);
106: /* Create vectors */
107: DMCreateGlobalVector(user.dm,&x);
109: DMCreateLocalVector(user.dm,&user.localX);
111: /* Create Hessian */
112: DMCreateMatrix(user.dm,&H);
113: MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE);
115: /* The TAO code begins here */
117: /* Create TAO solver and set desired solution method */
118: TaoCreate(PETSC_COMM_WORLD,&tao);
119: TaoSetType(tao,TAOCG);
121: /* Set initial solution guess */
122: FormInitialGuess(&user,x);
123: TaoSetInitialVector(tao,x);
125: /* Set routine for function and gradient evaluation */
126: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
128: TaoSetHessianRoutine(tao,H,H,FormHessian,(void*)&user);
130: /* Check for any TAO command line options */
131: TaoSetFromOptions(tao);
133: TaoGetKSP(tao,&ksp);
134: if (ksp) {
135: KSPGetPC(ksp,&pc);
136: PCSetType(pc,PCNONE);
137: }
139: /* SOLVE THE APPLICATION */
140: TaoSolve(tao);
142: /* Free TAO data structures */
143: TaoDestroy(&tao);
145: /* Free PETSc data structures */
146: VecDestroy(&x);
147: MatDestroy(&H);
149: VecDestroy(&user.localX);
150: DMDestroy(&user.dm);
152: PetscFinalize();
153: return 0;
154: }
156: /* ------------------------------------------------------------------- */
157: /*
158: FormInitialGuess - Computes an initial approximation to the solution.
160: Input Parameters:
161: . user - user-defined application context
162: . X - vector
164: Output Parameters:
165: X - vector
166: */
167: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
168: {
170: PetscInt i, j, k, mx = user->mx, my = user->my;
171: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
172: PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;
175: /* Get local mesh boundaries */
176: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
177: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
179: /* Compute initial guess over locally owned part of mesh */
180: xe = xs+xm;
181: ye = ys+ym;
182: for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
183: temp = PetscMin(j+1,my-j)*hy;
184: for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
185: k = (j-gys)*gxm + i-gxs;
186: val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
187: VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);
188: }
189: }
190: VecAssemblyBegin(X);
191: VecAssemblyEnd(X);
192: return(0);
193: }
195: /* ------------------------------------------------------------------ */
196: /*
197: FormFunctionGradient - Evaluates the function and corresponding gradient.
199: Input Parameters:
200: tao - the Tao context
201: X - the input vector
202: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
204: Output Parameters:
205: f - the newly evaluated function
206: G - the newly evaluated gradient
207: */
208: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr)
209: {
210: AppCtx *user = (AppCtx *)ptr;
212: PetscInt i,j,k,ind;
213: PetscInt xe,ye,xsm,ysm,xep,yep;
214: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys;
215: PetscInt mx = user->mx, my = user->my;
216: PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
217: PetscReal p5 = 0.5, area, val, flin, fquad;
218: PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
219: PetscReal hx = 1.0/(user->mx + 1);
220: PetscReal hy = 1.0/(user->my + 1);
221: Vec localX = user->localX;
224: /* Initialize */
225: flin = fquad = zero;
227: VecSet(G, zero);
228: /*
229: Scatter ghost points to local vector,using the 2-step process
230: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
231: By placing code between these two statements, computations can be
232: done while messages are in transition.
233: */
234: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
235: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
237: /* Get pointer to vector data */
238: VecGetArray(localX,&x);
240: /* Get local mesh boundaries */
241: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
242: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
244: /* Set local loop dimensions */
245: xe = xs+xm;
246: ye = ys+ym;
247: if (xs == 0) xsm = xs-1;
248: else xsm = xs;
249: if (ys == 0) ysm = ys-1;
250: else ysm = ys;
251: if (xe == mx) xep = xe+1;
252: else xep = xe;
253: if (ye == my) yep = ye+1;
254: else yep = ye;
256: /* Compute local gradient contributions over the lower triangular elements */
257: for (j=ysm; j<ye; j++) { /* for (j=-1; j<my; j++) */
258: for (i=xsm; i<xe; i++) { /* for (i=-1; i<mx; i++) */
259: k = (j-gys)*gxm + i-gxs;
260: v = zero;
261: vr = zero;
262: vt = zero;
263: if (i >= 0 && j >= 0) v = x[k];
264: if (i < mx-1 && j > -1) vr = x[k+1];
265: if (i > -1 && j < my-1) vt = x[k+gxm];
266: dvdx = (vr-v)/hx;
267: dvdy = (vt-v)/hy;
268: if (i != -1 && j != -1) {
269: ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
270: VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);
271: }
272: if (i != mx-1 && j != -1) {
273: ind = k+1; val = dvdx/hx - cdiv3;
274: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
275: }
276: if (i != -1 && j != my-1) {
277: ind = k+gxm; val = dvdy/hy - cdiv3;
278: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
279: }
280: fquad += dvdx*dvdx + dvdy*dvdy;
281: flin -= cdiv3 * (v + vr + vt);
282: }
283: }
285: /* Compute local gradient contributions over the upper triangular elements */
286: for (j=ys; j<yep; j++) { /* for (j=0; j<=my; j++) */
287: for (i=xs; i<xep; i++) { /* for (i=0; i<=mx; i++) */
288: k = (j-gys)*gxm + i-gxs;
289: vb = zero;
290: vl = zero;
291: v = zero;
292: if (i < mx && j > 0) vb = x[k-gxm];
293: if (i > 0 && j < my) vl = x[k-1];
294: if (i < mx && j < my) v = x[k];
295: dvdx = (v-vl)/hx;
296: dvdy = (v-vb)/hy;
297: if (i != mx && j != 0) {
298: ind = k-gxm; val = - dvdy/hy - cdiv3;
299: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
300: }
301: if (i != 0 && j != my) {
302: ind = k-1; val = - dvdx/hx - cdiv3;
303: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
304: }
305: if (i != mx && j != my) {
306: ind = k; val = dvdx/hx + dvdy/hy - cdiv3;
307: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
308: }
309: fquad += dvdx*dvdx + dvdy*dvdy;
310: flin -= cdiv3 * (vb + vl + v);
311: }
312: }
314: /* Restore vector */
315: VecRestoreArray(localX,&x);
317: /* Assemble gradient vector */
318: VecAssemblyBegin(G);
319: VecAssemblyEnd(G);
321: /* Scale the gradient */
322: area = p5*hx*hy;
323: floc = area * (p5 * fquad + flin);
324: VecScale(G, area);
326: /* Sum function contributions from all processes */
327: (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);
329: PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);
331: return(0);
332: }
334: PetscErrorCode FormHessian(Tao tao, Vec X, Mat A, Mat Hpre, void*ctx)
335: {
336: AppCtx *user= (AppCtx*) ctx;
338: PetscInt i,j,k;
339: PetscInt col[5],row;
340: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
341: PetscReal v[5];
342: PetscReal hx=1.0/(user->mx+1), hy=1.0/(user->my+1), hxhx=1.0/(hx*hx), hyhy=1.0/(hy*hy), area=0.5*hx*hy;
344: /* Compute the quadratic term in the objective function */
346: /*
347: Get local grid boundaries
348: */
351: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
352: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
354: for (j=ys; j<ys+ym; j++) {
356: for (i=xs; i< xs+xm; i++) {
358: row=(j-gys)*gxm + (i-gxs);
360: k=0;
361: if (j>gys) {
362: v[k]=-2*hyhy; col[k]=row - gxm; k++;
363: }
365: if (i>gxs) {
366: v[k]= -2*hxhx; col[k]=row - 1; k++;
367: }
369: v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;
371: if (i+1 < gxs+gxm) {
372: v[k]= -2.0*hxhx; col[k]=row+1; k++;
373: }
375: if (j+1 <gys+gym) {
376: v[k]= -2*hyhy; col[k] = row+gxm; k++;
377: }
379: MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES);
381: }
382: }
383: /*
384: Assemble matrix, using the 2-step process:
385: MatAssemblyBegin(), MatAssemblyEnd().
386: By placing code between these two statements, computations can be
387: done while messages are in transition.
388: */
389: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
390: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
391: /*
392: Tell the matrix we will never add a new nonzero location to the
393: matrix. If we do it will generate an error.
394: */
395: MatScale(A,area);
396: MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
397: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
398: PetscLogFlops(9*xm*ym+49*xm);
399: return(0);
400: }
402: /*TEST
404: build:
405: requires: !complex
407: test:
408: suffix: 1
409: nsize: 2
410: args: -tao_smonitor -tao_type nls -mx 16 -my 16 -tao_gatol 1.e-4
412: TEST*/