/*$Id: eptorsion.c, v 1.1 2002/08/08 10:30 lopezca@mauddib.mcs.anl.gov $*/ /* Program usage: mpirun -np <proc> eptorsion [-help] [all TAO options] */ /* Include "tao.h" so we can use TAO solvers. petscda.h for distributed array ad_deriv.h for AD gradient */ #include "petscda.h" #include "tao.h" #include "taodaapplication.h" static char help[] = "This example is based on the Elastic-Plastic Torsion (dept)\n\ problem from the MINPACK-2 test suite.\n\ The command line options are:\n\ -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\ -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\ -nlevels <nlevels>, where <nlevels> = number of levels in multigrid\n\ -byelement, if computation is made by functions on rectangular elements\n\ -adic, if AD is used (AD is not used by default)\n\ -u1 <u1>, where <u1> = upper limit in the 1st coordinate direction\n\ -u2 <u2>, where <u2> = upper limit in the 2nd coordinate direction\n\ -par <param>, where <param> = angle of twist per unit length\n\n"; /*T Concepts: TAO - Solving a bounded minimization problem Routines: TaoInitialize(); TaoFinalize(); Routines: TaoCreate(); TaoDestroy(); Routines: DAApplicationCreate(); DAApplicationDestroy(); Routines: DAAppSetVariableBoundsRoutine(); Routines: DAAppSetElementObjectiveAndGradientRoutine(); Routines: DAAppSetElementHessianRoutine(); Routines: DAAppSetObjectiveAndGradientRoutine(); Routines: DAAppSetADElementFunctionGradient(); Routines: DAAppSetHessianRoutine(); Routines: TaoSetOptions(); Routines: TaoGetSolutionStatus(); TaoDAAppSolve(); Routines: DAAppSetMonitor(); TaoView(); Routines: DAAppGetSolution(); Routines: DAAppGetInterpolationMatrix(); Processors: n T*/ /* User-defined application context - contains data needed by the application-provided call-back routines. */ typedef struct { InactiveDouble param; InactiveDouble hx, hy; /* increment size in both directions */ InactiveDouble area; /* area of the triangles */ } ADFGCtx; typedef struct { PetscReal param; /* 'c' parameter */ PetscReal u1, u2; /* domain upper limits (lower limits = 0) */ double hx, hy; /* increment size in both directions */ double area; /* area of the triangles */ ADFGCtx fgctx; /* Used only when an ADIC generated gradient is used */ } AppCtx; int ad_EPTorsLocalFunction(int[2], DERIV_TYPE[4], DERIV_TYPE*, void*); /* User-defined routines found in this file */ static int AppCtxInitialize(void *ptr); static int FormInitialGuess(DA, Vec); static int EPTorsLocalFunctionGradient(int[2], double x[4], double *f, double g[4], void *ptr); static int EPTorsLocalHessian(int[2], double x[4], double H[4][4], void *ptr); static int WholeEPTorsFunctionGradient(TAO_APPLICATION,DA,Vec,double *,Vec,void*); static int WholeEPTorsHessian(TAO_APPLICATION,DA,Vec,Mat,void*); static int DASetBounds(TAO_APPLICATION, DA, Vec, Vec, void*); static int MyGridMonitorBefore(TAO_APPLICATION, DA, int, void *); #undef __FUNCT__ #define __FUNCT__ "main" int main( int argc, char **argv ) { int info; /* used to check for functions returning nonzeros */ int mx,my,Nx,Ny; double ff,gnorm; int iter, nlevels; /* multigrid levels */ DA DAarray[20]; Vec X; PetscTruth flg, PreLoad = PETSC_TRUE; /* flags */ TaoMethod method = "tao_gpcg"; /* minimization method */ AppCtx user; /* user-defined work context */ TAO_SOLVER tao; /* TAO_SOLVER solver context */ TAO_APPLICATION EPTorsApp; /* The PETSc application */ TaoTerminateReason reason; /* Initialize TAO */ PetscInitialize(&argc, &argv, (char *)0, help); TaoInitialize(&argc, &argv, (char *)0, help); PreLoadBegin(PreLoad,"Solve"); info = AppCtxInitialize((void*)&user); CHKERRQ(info); nlevels=5; info = PetscOptionsGetInt(PETSC_NULL,"-nlevels",&nlevels,&flg); CHKERRQ(info); mx = my = 11; /* these correspond to 10 segments on each dimension */ info = PetscOptionsGetInt(TAO_NULL, "-mx", &mx, &flg); CHKERRQ(info); info = PetscOptionsGetInt(TAO_NULL, "-my", &my, &flg); CHKERRQ(info); if (PreLoadIt == 0) { nlevels = 1; mx = 11; my = 11; } PetscPrintf(MPI_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n\n"); /* Let PETSc determine the vector distribution */ Nx = PETSC_DECIDE; Ny = PETSC_DECIDE; /* Create distributed array (DA) to manage parallel grid and vectors */ info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,mx, my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&DAarray[0]); CHKERRQ(info); for (iter=1;iter<nlevels;iter++){ info = DARefine(DAarray[iter-1],PETSC_COMM_WORLD,&DAarray[iter]); CHKERRQ(info); } /* Create TAO solver and set desired solution method */ info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info); info = TaoApplicationCreate(PETSC_COMM_WORLD,&EPTorsApp); CHKERRQ(info); info = TaoAppSetDAApp(EPTorsApp, DAarray, nlevels ); CHKERRQ(info); /* Sets routines for function, gradient and bounds evaluation */ info = DAAppSetVariableBoundsRoutine(EPTorsApp,DASetBounds,(void *)&user); CHKERRQ(info); info = PetscOptionsHasName(TAO_NULL, "-byelement", &flg); CHKERRQ(info); if (flg) { /* Sets routines for function and gradient evaluation, element by element */ info = PetscOptionsHasName(TAO_NULL, "-adic", &flg); CHKERRQ(info); if (flg) { info = DAAppSetADElementFunctionGradient(EPTorsApp,ad_EPTorsLocalFunction,192,(void *)&user.fgctx); CHKERRQ(info); } else { info = DAAppSetElementObjectiveAndGradientRoutine(EPTorsApp,EPTorsLocalFunctionGradient,42,(void *)&user); CHKERRQ(info); } /* Sets routines for Hessian evaluation, element by element */ info = DAAppSetElementHessianRoutine(EPTorsApp,EPTorsLocalHessian,6,(void*)&user); CHKERRQ(info); } else { /* Sets routines for function and gradient evaluation, all in one routine */ info = DAAppSetObjectiveAndGradientRoutine(EPTorsApp,WholeEPTorsFunctionGradient,(void *)&user); CHKERRQ(info); /* Sets routines for Hessian evaluation, all in one routine */ info = DAAppSetHessianRoutine(EPTorsApp,WholeEPTorsHessian,(void*)&user); CHKERRQ(info); } info = DAAppSetBeforeMonitor(EPTorsApp,MyGridMonitorBefore,(void*)&user); CHKERRQ(info); info = PetscOptionsHasName(TAO_NULL,"-tao_monitor", &flg); CHKERRQ(info); if (flg){ info = DAAppPrintStageTimes(EPTorsApp); CHKERRQ(info); info = DAAppPrintInterpolationError(EPTorsApp); CHKERRQ(info); } info = TaoAppSetRelativeTolerance(EPTorsApp,1.0e-8); CHKERRQ(info); info = TaoSetTolerances(tao,0,0,0,0); CHKERRQ(info); info = TaoSetGradientTolerances(tao,0,0,0); CHKERRQ(info); /* Check for any tao command line options */ info = TaoSetOptions(EPTorsApp, tao); CHKERRQ(info); info = DAAppGetSolution(EPTorsApp,0,&X); CHKERRQ(info); info = FormInitialGuess(DAarray[0],X); CHKERRQ(info); info = DAAppSetInitialSolution(EPTorsApp,X); CHKERRQ(info); /* SOLVE THE APPLICATION */ info = TaoDAAppSolve(EPTorsApp, tao); CHKERRQ(info); /* Get information on termination */ info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info); if (reason <= 0 ){ PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n"); PetscPrintf(MPI_COMM_WORLD," Iterations: %d, Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm); } info = PetscOptionsHasName(PETSC_NULL,"-view_sol",&flg); CHKERRQ(info); if (flg){ info = DAAppGetSolution(EPTorsApp,nlevels-1,&X); CHKERRQ(info); info=VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info); } /* To View TAO solver information */ // info = TaoView(tao); CHKERRQ(info); /* Free TAO data structures */ info = TaoDestroy(tao); CHKERRQ(info); info = TaoAppDestroy(EPTorsApp); CHKERRQ(info); /* Free PETSc data structures */ for (iter=0;iter<nlevels;iter++){ info = DADestroy(DAarray[iter]); CHKERRQ(info); } PreLoadEnd(); /* Finalize TAO */ TaoFinalize(); PetscFinalize(); return 0; } /* main */ /*----- The following two routines MyGridMonitorBefore MyGridMonitorAfter help diplay info of iterations at every grid level */ #undef __FUNCT__ #define __FUNCT__ "MyGridMonitorBefore" static int MyGridMonitorBefore(TAO_APPLICATION myapp, DA da, int level, void *ctx) { AppCtx *user = (AppCtx*)ctx; int info,mx,my; info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL, PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info); user->hx = user->u1 / (mx - 1); user->hy = user->u2 / (my - 1); user->area = 0.5 * user->hx * user->hy; user->fgctx.hx = user->hx; user->fgctx.hy = user->hy; user->fgctx.area = user->area; user->fgctx.param = user->param; PetscPrintf(MPI_COMM_WORLD,"Grid: %d, mx: %d my: %d \n",level,mx,my); return 0; } /*------- USER-DEFINED: initialize the application context information -------*/ #undef __FUNCT__ #define __FUNCT__ "AppCtxInitialize" /* AppCtxInitialize - Sets initial values for the application context parameters Input: ptr - void user-defined application context Output: ptr - user-defined application context with the default or user-provided parameters */ static int AppCtxInitialize(void *ptr) { AppCtx *user = (AppCtx*)ptr; PetscTruth flg; /* flag for PETSc calls */ int info; /* Specify default parameters */ user->param = 25.0; user->u1 = user->u2 = 1.0; /* Check for command line arguments that override defaults */ info = PetscOptionsGetReal(TAO_NULL, "-par", &user->param, &flg); CHKERRQ(info); info = PetscOptionsGetReal(TAO_NULL, "-u1", &user->u1, &flg); CHKERRQ(info); info = PetscOptionsGetReal(TAO_NULL, "-u2", &user->u2, &flg); CHKERRQ(info); return 0; } /* AppCtxInitialize */ #undef __FUNCT__ #define __FUNCT__ "FormInitialGuess" static int FormInitialGuess(DA da, Vec X) { int info, i, j, mx, my; int xs, ys, xm, ym, xe, ye; PetscReal hx, hy, temp, val; double **x; /* Get local mesh boundaries */ info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL, PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info); hx = 1.0/(mx-1); hy = 1.0/(my-1); info = DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info); xe = xs+xm; ye = ys+ym; info = DAVecGetArray(da, X, (void**)&x); CHKERRQ(info); /* Compute initial guess over locally owned part of mesh */ for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */ temp = PetscMin(j+1,my-j)*hy; for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */ val = PetscMin((PetscMin(i+1,mx-i))*hx,temp); x[j][i] = val; } } info = DAVecRestoreArray(da, X, (void**)&x); CHKERRQ(info); return 0; } /*------- USER-DEFINED: set the upper and lower bounds for the variables -------*/ #undef __FUNCT__ #define __FUNCT__ "DASetBounds" /* FormBounds - Forms bounds on the variables Input: user - user-defined application context Output: XL - vector of lower bounds XU - vector of upper bounds */ static int DASetBounds(TAO_APPLICATION daapplication, DA da, Vec XL, Vec XU, void *ptr) { AppCtx *user = (AppCtx*)ptr; int i, j, info, xs, xm, ys, ym; double hx, hy, u1, u2, dist, d1, d2, hd, vd; double **xl, **xu; hx = user->hx; hy = user->hy; u1 = user->u1; u2 = user->u2; info = DAVecGetArray(da, XL, (void**)&xl); CHKERRQ(info); info = DAVecGetArray(da, XU, (void**)&xu); CHKERRQ(info); info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info); for (j = ys; j < ys+ym; j++){ for (i = xs; i < xs+xm; i++){ d1 = i * hx; d2 = u1 - d1; hd = PetscMin(d1,d2); d1 = j * hy; d2 = u2 - d1; vd = PetscMin(d1,d2); dist = PetscMin(hd,vd); xl[j][i] = -dist; xu[j][i] = dist; } } info = DAVecRestoreArray(da, XL, (void**)&xl); CHKERRQ(info); info = DAVecRestoreArray(da, XU, (void**)&xu); CHKERRQ(info); info = PetscLogFlops(xm * ym * 4); CHKERRQ(info); return 0; } /* DASetBounds */ #undef __FUNCT__ #define __FUNCT__ "EPTorsLocalFunctionGradient" /* EPTorsLocalFunctionGradient - Evaluates function and gradient over the local rectangular element Input: coor - vector with the indices of the position of current element in the first, second and third directions x - current point (values over the current rectangular element) df - degrees of freedom at each point ptr - user-defined application context Output: f - value of the objective funtion at the local rectangular element g - gradient of the local function */ static int EPTorsLocalFunctionGradient(int coor[2], double x[4], double *f, double g[4], void *ptr) { AppCtx *user = (AppCtx*)ptr; double fquad, flin; double hx, hy, dvdx, dvdy, area; double cdiv3, cnt; cdiv3 = user->param / 3.0; hx = user->hx; hy = user->hy; area = user->area; cnt = area * cdiv3; /* lower triangle contribution */ dvdx = (x[0] - x[1]) / hx; dvdy = (x[0] - x[2]) / hy; fquad = dvdx * dvdx + dvdy * dvdy; flin = x[0] + x[1] + x[2]; dvdx = 0.5 * dvdx * hy; dvdy = 0.5 * dvdy * hx; g[0] = dvdx + dvdy - cnt; g[1] = -dvdx - 2.0 * cnt; g[2] = -dvdy - 2.0 * cnt; /* upper triangle contribution */ dvdx = (x[3] - x[2]) / hx; dvdy = (x[3] - x[1]) / hy; fquad += dvdx * dvdx + dvdy * dvdy; flin += x[1] + x[2] + x[3]; dvdx = 0.5 * dvdx * hy; dvdy = 0.5 * dvdy * hx; g[1] += -dvdy; g[2] += -dvdx; g[3] = dvdx + dvdy - cnt; *f = area * (0.5 * fquad - flin * cdiv3); return 0; } /* EPTorsLocalFunctionGradient */ /*------- USER-DEFINED: routine to evaluate the Hessian at a local (rectangular element) level -------*/ #undef __FUNCT__ #define __FUNCT__ "EPTorsLocalHessian" /* EPTorsLocalHessian - Computes the Hessian of the local (partial) function defined over the current rectangle Input: coor - vector with the indices of the position of current element in the first, second and third directions x - current local solution (over the rectangle only) df - degrees of freedom at each point ptr - user-defined application context Output: H - Hessian matrix of the local function (wrt the four points of the rectangle only) */ static int EPTorsLocalHessian(int coor[2], double x[4], double H[4][4], void *ptr) { AppCtx *user = (AppCtx*)ptr; double hx, hy, dxdy, dydx; double diagxy, bandxy, bandyx; hx = user->hx; hy = user->hy; dxdy = hx/hy; dydx = hy/hx; diagxy = 0.5 * (dxdy + dydx); bandxy = -0.5 * dxdy; bandyx = -0.5 * dydx; /* Hessian contribution at 0,0 */ H[0][0] = diagxy; H[0][1] = H[1][0] = bandyx; H[0][2] = H[2][0] = bandxy; H[0][3] = H[3][0] = 0.0; /* Hessian contribution at 1,0 */ H[1][1] = diagxy; H[1][2] = H[2][1] = 0.0; H[1][3] = H[3][1] = bandxy; /* Hessian contribution at 0,1 */ H[2][2] = diagxy; H[2][3] = H[3][2] = bandyx; /* Hessian contribution at 1,1 */ H[3][3] = diagxy; return 0; } /* EPTorsLocalHessian */ /*------- USER-DEFINED: routine to evaluate the function and gradient at the whole grid -------*/ #undef __FUNCT__ #define __FUNCT__ "WholeEPTorsFunctionGradient" /* WholeEPTorsFunctionGradient - Evaluates function and gradient over the whole grid Input: daapplication - TAO application object da - distributed array X - the current point, at which the function and gradient are evaluated ptr - user-defined application context Output: f - value of the objective funtion at X G - gradient at X */ static int WholeEPTorsFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) { AppCtx *user = (AppCtx*)ptr; Vec localX, localG; int info, i, j; int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye; double **x, **g; double floc = 0.0; PetscScalar zero = 0.0; double fquad, flin; double hx, hy, dvdx, dvdy, area; double cdiv3, cnt; cdiv3 = user->param / 3.0; hx = user->hx; hy = user->hy; area = user->area; cnt = area * cdiv3; info = DAGetLocalVector(da, &localX); CHKERRQ(info); info = DAGetLocalVector(da, &localG); CHKERRQ(info); info = VecSet(G, zero); CHKERRQ(info); info = VecSet(localG, zero); CHKERRQ(info); info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info); info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info); info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info); info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info); info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info); info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info); xe = gxs + gxm - 1; ye = gys + gym - 1; for (j = ys; j < ye; j++) { for (i = xs; i < xe; i++) { /* lower triangle contribution */ dvdx = (x[j][i] - x[j][i+1]) / hx; dvdy = (x[j][i] - x[j+1][i]) / hy; fquad = dvdx * dvdx + dvdy * dvdy; flin = x[j][i] + x[j][i+1] + x[j+1][i]; dvdx = 0.5 * dvdx * hy; dvdy = 0.5 * dvdy * hx; g[j][i] += dvdx + dvdy - cnt; g[j][i+1] += -dvdx - 2.0 * cnt; g[j+1][i] += -dvdy - 2.0 * cnt; /* upper triangle contribution */ dvdx = (x[j+1][i+1] - x[j+1][i]) / hx; dvdy = (x[j+1][i+1] - x[j][i+1]) / hy; fquad += dvdx * dvdx + dvdy * dvdy; flin += x[j][i+1] + x[j+1][i] + x[j+1][i+1]; dvdx = 0.5 * dvdx * hy; dvdy = 0.5 * dvdy * hx; g[j][i+1] += -dvdy; g[j+1][i] += -dvdx; g[j+1][i+1] += dvdx + dvdy - cnt; floc += area * (0.5 * fquad - flin * cdiv3); } } info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); CHKERRQ(info); info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info); info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info); info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info); info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info); info = DARestoreLocalVector(da, &localX); CHKERRQ(info); info = DARestoreLocalVector(da, &localG); CHKERRQ(info); info = PetscLogFlops((xe-xs) * (ye-ys) * 47 + 2); CHKERRQ(info); return 0; } /* WholeEPTorsFunctionGradient */ /*------- USER-DEFINED: routine to evaluate the Hessian at the whole grid -------*/ #undef __FUNCT__ #define __FUNCT__ "WholeEPTorsHessian" /* WholeEPTorsHessian - Evaluates Hessian over the whole grid Input: daapplication - TAO application object da - distributed array X - the current point, at which the function and gradient are evaluated ptr - user-defined application context Output: H - Hessian at X */ static int WholeEPTorsHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) { AppCtx *user = (AppCtx*)ptr; int info, i, j, ind[4]; int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye; double smallH[4][4]; double hx, hy, dxdy, dydx; double diagxy, bandxy, bandyx; PetscTruth assembled; hx = user->hx; hy = user->hy; dxdy = hx/hy; dydx = hy/hx; diagxy = 0.5 * (dxdy + dydx); bandxy = -0.5 * dxdy; bandyx = -0.5 * dydx; info = MatAssembled(H,&assembled); CHKERRQ(info); if (assembled){info = MatZeroEntries(H); CHKERRQ(info);} info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info); info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info); xe = gxs + gxm - 1; ye = gys + gym - 1; for (j = ys; j < ye; j++) { for (i = xs; i < xe; i++) { /* Hessian contribution at 0,0 */ smallH[0][0] = diagxy; smallH[0][1] = smallH[1][0] = bandyx; smallH[0][2] = smallH[2][0] = bandxy; smallH[0][3] = smallH[3][0] = 0.0; /* Hessian contribution at 1,0 */ smallH[1][1] = diagxy; smallH[1][2] = smallH[2][1] = 0.0; smallH[1][3] = smallH[3][1] = bandxy; /* Hessian contribution at 0,1 */ smallH[2][2] = diagxy; smallH[2][3] = smallH[3][2] = bandyx; /* Hessian contribution at 1,1 */ smallH[3][3] = diagxy; ind[0] = (j-gys) * gxm + (i-gxs); ind[1] = ind[0] + 1; ind[2] = ind[0] + gxm; ind[3] = ind[2] + 1; info = MatSetValuesLocal(H,4,ind,4,ind,(PetscScalar*)smallH,ADD_VALUES); CHKERRQ(info); } } info = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info); info = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info); info = MatSetOption(H, MAT_SYMMETRIC); CHKERRQ(info); info = PetscLogFlops(6); CHKERRQ(info); return 0; } /* WholeEPTorsHessian */