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: TaoSetSolution();
49: Routines: TaoSetObjectiveAndGradient();
50: Routines: TaoSetHessian(); 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: Vec x;
78: Mat H;
79: PetscInt Nx, Ny;
80: Tao tao;
81: PetscBool flg;
82: KSP ksp;
83: PC pc;
84: AppCtx user;
86: PetscInitialize(&argc, &argv, (char *)0, help);
88: /* Specify default dimension of the problem */
89: user.param = 5.0; user.mx = 10; user.my = 10;
90: Nx = Ny = PETSC_DECIDE;
92: /* Check for any command line arguments that override defaults */
93: PetscOptionsGetReal(NULL,NULL,"-par",&user.param,&flg);
94: PetscOptionsGetInt(NULL,NULL,"-my",&user.my,&flg);
95: PetscOptionsGetInt(NULL,NULL,"-mx",&user.mx,&flg);
97: PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
98: PetscPrintf(PETSC_COMM_WORLD,"mx: %D my: %D \n\n",user.mx,user.my);
100: /* Set up distributed array */
101: 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);
102: DMSetFromOptions(user.dm);
103: DMSetUp(user.dm);
105: /* Create vectors */
106: DMCreateGlobalVector(user.dm,&x);
108: DMCreateLocalVector(user.dm,&user.localX);
110: /* Create Hessian */
111: DMCreateMatrix(user.dm,&H);
112: MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE);
114: /* The TAO code begins here */
116: /* Create TAO solver and set desired solution method */
117: TaoCreate(PETSC_COMM_WORLD,&tao);
118: TaoSetType(tao,TAOCG);
120: /* Set initial solution guess */
121: FormInitialGuess(&user,x);
122: TaoSetSolution(tao,x);
124: /* Set routine for function and gradient evaluation */
125: TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,(void *)&user);
127: TaoSetHessian(tao,H,H,FormHessian,(void*)&user);
129: /* Check for any TAO command line options */
130: TaoSetFromOptions(tao);
132: TaoGetKSP(tao,&ksp);
133: if (ksp) {
134: KSPGetPC(ksp,&pc);
135: PCSetType(pc,PCNONE);
136: }
138: /* SOLVE THE APPLICATION */
139: TaoSolve(tao);
141: /* Free TAO data structures */
142: TaoDestroy(&tao);
144: /* Free PETSc data structures */
145: VecDestroy(&x);
146: MatDestroy(&H);
148: VecDestroy(&user.localX);
149: DMDestroy(&user.dm);
151: PetscFinalize();
152: return 0;
153: }
155: /* ------------------------------------------------------------------- */
156: /*
157: FormInitialGuess - Computes an initial approximation to the solution.
159: Input Parameters:
160: . user - user-defined application context
161: . X - vector
163: Output Parameters:
164: X - vector
165: */
166: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
167: {
168: PetscInt i, j, k, mx = user->mx, my = user->my;
169: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
170: PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;
172: /* Get local mesh boundaries */
173: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
174: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
176: /* Compute initial guess over locally owned part of mesh */
177: xe = xs+xm;
178: ye = ys+ym;
179: for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
180: temp = PetscMin(j+1,my-j)*hy;
181: for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
182: k = (j-gys)*gxm + i-gxs;
183: val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
184: VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);
185: }
186: }
187: VecAssemblyBegin(X);
188: VecAssemblyEnd(X);
189: return 0;
190: }
192: /* ------------------------------------------------------------------ */
193: /*
194: FormFunctionGradient - Evaluates the function and corresponding gradient.
196: Input Parameters:
197: tao - the Tao context
198: X - the input vector
199: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
201: Output Parameters:
202: f - the newly evaluated function
203: G - the newly evaluated gradient
204: */
205: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr)
206: {
207: AppCtx *user = (AppCtx *)ptr;
208: PetscInt i,j,k,ind;
209: PetscInt xe,ye,xsm,ysm,xep,yep;
210: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys;
211: PetscInt mx = user->mx, my = user->my;
212: PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
213: PetscReal p5 = 0.5, area, val, flin, fquad;
214: PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
215: PetscReal hx = 1.0/(user->mx + 1);
216: PetscReal hy = 1.0/(user->my + 1);
217: Vec localX = user->localX;
219: /* Initialize */
220: flin = fquad = zero;
222: VecSet(G, zero);
223: /*
224: Scatter ghost points to local vector,using the 2-step process
225: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
226: By placing code between these two statements, computations can be
227: done while messages are in transition.
228: */
229: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
230: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
232: /* Get pointer to vector data */
233: VecGetArray(localX,&x);
235: /* Get local mesh boundaries */
236: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
237: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
239: /* Set local loop dimensions */
240: xe = xs+xm;
241: ye = ys+ym;
242: if (xs == 0) xsm = xs-1;
243: else xsm = xs;
244: if (ys == 0) ysm = ys-1;
245: else ysm = ys;
246: if (xe == mx) xep = xe+1;
247: else xep = xe;
248: if (ye == my) yep = ye+1;
249: else yep = ye;
251: /* Compute local gradient contributions over the lower triangular elements */
252: for (j=ysm; j<ye; j++) { /* for (j=-1; j<my; j++) */
253: for (i=xsm; i<xe; i++) { /* for (i=-1; i<mx; i++) */
254: k = (j-gys)*gxm + i-gxs;
255: v = zero;
256: vr = zero;
257: vt = zero;
258: if (i >= 0 && j >= 0) v = x[k];
259: if (i < mx-1 && j > -1) vr = x[k+1];
260: if (i > -1 && j < my-1) vt = x[k+gxm];
261: dvdx = (vr-v)/hx;
262: dvdy = (vt-v)/hy;
263: if (i != -1 && j != -1) {
264: ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
265: VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);
266: }
267: if (i != mx-1 && j != -1) {
268: ind = k+1; val = dvdx/hx - cdiv3;
269: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
270: }
271: if (i != -1 && j != my-1) {
272: ind = k+gxm; val = dvdy/hy - cdiv3;
273: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
274: }
275: fquad += dvdx*dvdx + dvdy*dvdy;
276: flin -= cdiv3 * (v + vr + vt);
277: }
278: }
280: /* Compute local gradient contributions over the upper triangular elements */
281: for (j=ys; j<yep; j++) { /* for (j=0; j<=my; j++) */
282: for (i=xs; i<xep; i++) { /* for (i=0; i<=mx; i++) */
283: k = (j-gys)*gxm + i-gxs;
284: vb = zero;
285: vl = zero;
286: v = zero;
287: if (i < mx && j > 0) vb = x[k-gxm];
288: if (i > 0 && j < my) vl = x[k-1];
289: if (i < mx && j < my) v = x[k];
290: dvdx = (v-vl)/hx;
291: dvdy = (v-vb)/hy;
292: if (i != mx && j != 0) {
293: ind = k-gxm; val = - dvdy/hy - cdiv3;
294: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
295: }
296: if (i != 0 && j != my) {
297: ind = k-1; val = - dvdx/hx - cdiv3;
298: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
299: }
300: if (i != mx && j != my) {
301: ind = k; val = dvdx/hx + dvdy/hy - cdiv3;
302: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
303: }
304: fquad += dvdx*dvdx + dvdy*dvdy;
305: flin -= cdiv3 * (vb + vl + v);
306: }
307: }
309: /* Restore vector */
310: VecRestoreArray(localX,&x);
312: /* Assemble gradient vector */
313: VecAssemblyBegin(G);
314: VecAssemblyEnd(G);
316: /* Scale the gradient */
317: area = p5*hx*hy;
318: floc = area * (p5 * fquad + flin);
319: VecScale(G, area);
321: /* Sum function contributions from all processes */ /* TODO: Change to PetscCallMPI() */
322: (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);
324: PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);
325: return 0;
326: }
328: PetscErrorCode FormHessian(Tao tao, Vec X, Mat A, Mat Hpre, void*ctx)
329: {
330: AppCtx *user= (AppCtx*) ctx;
331: PetscInt i,j,k;
332: PetscInt col[5],row;
333: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
334: PetscReal v[5];
335: 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;
337: /* Compute the quadratic term in the objective function */
339: /*
340: Get local grid boundaries
341: */
343: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
344: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
346: for (j=ys; j<ys+ym; j++) {
348: for (i=xs; i< xs+xm; i++) {
350: row=(j-gys)*gxm + (i-gxs);
352: k=0;
353: if (j>gys) {
354: v[k]=-2*hyhy; col[k]=row - gxm; k++;
355: }
357: if (i>gxs) {
358: v[k]= -2*hxhx; col[k]=row - 1; k++;
359: }
361: v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;
363: if (i+1 < gxs+gxm) {
364: v[k]= -2.0*hxhx; col[k]=row+1; k++;
365: }
367: if (j+1 <gys+gym) {
368: v[k]= -2*hyhy; col[k] = row+gxm; k++;
369: }
371: MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES);
373: }
374: }
375: /*
376: Assemble matrix, using the 2-step process:
377: MatAssemblyBegin(), MatAssemblyEnd().
378: By placing code between these two statements, computations can be
379: done while messages are in transition.
380: */
381: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
382: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
383: /*
384: Tell the matrix we will never add a new nonzero location to the
385: matrix. If we do it will generate an error.
386: */
387: MatScale(A,area);
388: MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
389: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
390: PetscLogFlops(9*xm*ym+49*xm);
391: return 0;
392: }
394: /*TEST
396: build:
397: requires: !complex
399: test:
400: suffix: 1
401: nsize: 2
402: args: -tao_smonitor -tao_type nls -mx 16 -my 16 -tao_gatol 1.e-4
404: TEST*/