/*$Id$*/ /* Program usage: mpirun -np <proc> minsurf2 [-help] [all TAO options] */ /* Include "tao.h" so we can use TAO solvers. petscda.h for distributed array */ #include "petscda.h" #include "tao.h" static char help[] = "This example demonstrates use of the TAO package to \n\ solve an unconstrained minimization problem. This example is based on a \n\ problem from the MINPACK-2 test suite. Given a rectangular 2-D domain and \n\ boundary values along the edges of the domain, the objective is to find the\n\ surface with the minimal area that satisfies the boundary conditions.\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\ -start <st>, where <st> =0 for zero vector, <st> >0 for random start, and <st> <0 \n\ for an average of the boundary conditions\n\n"; /*T Concepts: TAO - Solving an unconstrained minimization problem Routines: TaoInitialize(); TaoFinalize(); Routines: TaoCreate(); TaoDestroy(); Routines: TaoApplicationCreate(); TaoAppDestroy(); Routines: TaoAppSetInitialSolutionVec(); Routines: TaoAppSetObjectiveAndGradientRoutine(); Routines: TaoAppSetHessianMat(); TaoAppSetHessianRoutine(); Routines: TaoSetOptions(); Routines: TaoAppGetKSP(); TaoSolveApplication(); Routines: TaoAppSetMonitor(); TaoView(); Routines: TaoAppGetSolutionVec(); Processors: 1 T*/ /* User-defined application context - contains data needed by the application-provided call-back routines, FormFunctionGradient() and FormHessian(). */ typedef struct { int mx, my; /* discretization in x, y directions */ double *bottom, *top, *left, *right; /* boundary values */ DA da; /* distributed array data structure */ Mat H; /* Hessian */ ISColoring iscoloring; } AppCtx; /* -------- User-defined Routines --------- */ static int MSA_BoundaryConditions(AppCtx*); static int MSA_InitialPoint(AppCtx*,Vec); int QuadraticH(AppCtx*,Vec,Mat); int FormFunctionGradient(TAO_APPLICATION,Vec,double *,Vec,void*); int FormGradient(TAO_APPLICATION,Vec,Vec,void*); int FormHessian(TAO_APPLICATION,Vec,Mat*,Mat*,MatStructure *,void*); int My_Monitor(TAO_APPLICATION, void *); #undef __FUNCT__ #define __FUNCT__ "main" int main( int argc, char **argv ) { int info; /* used to check for functions returning nonzeros */ int Nx, Ny; /* number of processors in x- and y- directions */ int iter; /* iteration information */ double ff,gnorm; Vec x; /* solution, gradient vectors */ PetscTruth flg, viewmat; /* flags */ PetscTruth fddefault, fdcoloring; /* flags */ KSP ksp; /* Krylov subspace method */ TaoMethod method = "tao_nls"; /* minimization method */ TaoTerminateReason reason; TAO_SOLVER tao; /* TAO_SOLVER solver context */ TAO_APPLICATION minsurfapp; /* The PETSc application */ AppCtx user; /* user-defined work context */ /* Initialize TAO */ PetscInitialize( &argc, &argv,(char *)0,help ); TaoInitialize( &argc, &argv,(char *)0,help ); /* Specify dimension of the problem */ user.mx = 10; user.my = 10; /* Check for any command line arguments that override defaults */ info = PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,&flg); CHKERRQ(info); info = PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,&flg); CHKERRQ(info); PetscPrintf(MPI_COMM_WORLD,"\n---- Minimum Surface Area Problem -----\n"); PetscPrintf(MPI_COMM_WORLD,"mx: %d my: %d \n\n",user.mx,user.my); /* 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,user.mx, user.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.da); CHKERRQ(info); /* Create TAO solver and set desired solution method. Create an TAO application structure */ info = TaoCreate(PETSC_COMM_WORLD,method,&tao); CHKERRQ(info); info = TaoApplicationCreate(PETSC_COMM_WORLD,&minsurfapp); CHKERRQ(info); /* Extract global vector from DA for the vector of variables -- PETSC routine Compute the initial solution -- application specific, see below Set this vector for use by TAO -- TAO routine */ info = DACreateGlobalVector(user.da,&x); CHKERRQ(info); info = MSA_BoundaryConditions(&user); CHKERRQ(info); info = MSA_InitialPoint(&user,x); CHKERRQ(info); info = TaoAppSetInitialSolutionVec(minsurfapp,x); CHKERRQ(info); /* Initialize the Application context for use in function evaluations -- application specific, see below. Set routines for function and gradient evaluation */ info = TaoAppSetObjectiveAndGradientRoutine(minsurfapp,FormFunctionGradient,(void *)&user); CHKERRQ(info); /* Given the command line arguments, calculate the hessian with either the user- provided function FormHessian, or the default finite-difference driven Hessian functions */ info = PetscOptionsHasName(PETSC_NULL,"-tao_fddefault",&fddefault);CHKERRQ(info); info = PetscOptionsHasName(PETSC_NULL,"-tao_fdcoloring",&fdcoloring);CHKERRQ(info); if (fdcoloring) { info = DAGetColoring(user.da,IS_COLORING_GLOBAL,&(user.iscoloring)); CHKERRQ(info); info = TaoAppSetColoring(minsurfapp, user.iscoloring); CHKERRQ(info); info = TaoAppSetHessianRoutine(minsurfapp,TaoAppDefaultComputeHessianColor,(void *)&user); CHKERRQ(info); } else if (fddefault){ info = TaoAppSetHessianRoutine(minsurfapp,TaoAppDefaultComputeHessian,(void *)&user); CHKERRQ(info); } else { info = TaoAppSetHessianRoutine(minsurfapp,FormHessian,(void *)&user); CHKERRQ(info); } /* Create a matrix data structure to store the Hessian and set the Hessian evalution routine. Set the matrix structure to be used for Hessian evalutions */ info = DAGetMatrix(user.da,MATAIJ,&user.H);CHKERRQ(info); info = MatSetOption(user.H,MAT_SYMMETRIC); CHKERRQ(info); info = TaoAppSetHessianMat(minsurfapp,user.H,user.H); CHKERRQ(info); /* If my_monitor option is in command line, then use the user-provided monitoring function */ info = PetscOptionsHasName(PETSC_NULL,"-my_monitor",&viewmat); CHKERRQ(info); if (viewmat){ info = TaoAppSetMonitor(minsurfapp,My_Monitor,TAO_NULL); CHKERRQ(info); } /* Check for any tao command line options */ info = TaoSetOptions(minsurfapp,tao); CHKERRQ(info); /* Limit the number of iterations in the KSP linear solver */ info = TaoAppGetKSP(minsurfapp,&ksp); CHKERRQ(info); if (ksp) { /* Modify the PETSc KSP structure */ info = KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,user.mx*user.my); CHKERRQ(info); } /* SOLVE THE APPLICATION */ info = TaoSolveApplication(minsurfapp,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); } /* To View TAO solver information use info = TaoView(tao); CHKERRQ(info); */ /* Free TAO data structures */ info = TaoDestroy(tao); CHKERRQ(info); info = TaoAppDestroy(minsurfapp); CHKERRQ(info); /* Free PETSc data structures */ info = VecDestroy(x); CHKERRQ(info); info = MatDestroy(user.H); CHKERRQ(info); if (fdcoloring) { info = ISColoringDestroy(user.iscoloring);CHKERRQ(info); } info = PetscFree(user.bottom); CHKERRQ(info); info = PetscFree(user.top); CHKERRQ(info); info = PetscFree(user.left); CHKERRQ(info); info = PetscFree(user.right); CHKERRQ(info); info = DADestroy(user.da); CHKERRQ(info); /* Finalize TAO */ TaoFinalize(); PetscFinalize(); return 0; } #undef __FUNCT__ #define __FUNCT__ "FormGradient" int FormGradient(TAO_APPLICATION taoapp, Vec X, Vec G,void *userCtx){ int info; double fcn; TaoFunctionBegin; info = FormFunctionGradient(taoapp,X,&fcn,G,userCtx);CHKERRQ(info); TaoFunctionReturn(0); } /* -------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "FormFunctionGradient" /* FormFunctionGradient - Evaluates the function and corresponding gradient. Input Parameters: . taoapp - the TAO_APPLICATION context . XX - input vector . userCtx - optional user-defined context, as set by TaoSetFunctionGradient() Output Parameters: . fcn - the newly evaluated function . GG - vector containing the newly evaluated gradient */ int FormFunctionGradient(TAO_APPLICATION taoapp, Vec X, double *fcn,Vec G,void *userCtx){ AppCtx * user = (AppCtx *) userCtx; int info,i,j; int mx=user->mx, my=user->my; int xs,xm,gxs,gxm,ys,ym,gys,gym; double ft=0; double hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy, area=0.5*hx*hy; double rhx=mx+1, rhy=my+1; double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb; double df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc; PetscScalar **g, **x; Vec localX; /* Get local mesh boundaries */ info = DAGetLocalVector(user->da,&localX);CHKERRQ(info); info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info); info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info); /* Scatter ghost points to local vector */ info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info); info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info); /* Get pointers to vector data */ info = DAVecGetArray(user->da,localX,(void**)&x); info = DAVecGetArray(user->da,G,(void**)&g); /* Compute function and gradient over the locally owned part of the mesh */ for (j=ys; j<ys+ym; j++){ for (i=xs; i< xs+xm; i++){ xc = x[j][i]; xlt=xrb=xl=xr=xb=xt=xc; if (i==0){ /* left side */ xl= user->left[j-ys+1]; xlt = user->left[j-ys+2]; } else { xl = x[j][i-1]; } if (j==0){ /* bottom side */ xb=user->bottom[i-xs+1]; xrb =user->bottom[i-xs+2]; } else { xb = x[j-1][i]; } if (i+1 == gxs+gxm){ /* right side */ xr=user->right[j-ys+1]; xrb = user->right[j-ys]; } else { xr = x[j][i+1]; } if (j+1==gys+gym){ /* top side */ xt=user->top[i-xs+1]; xlt = user->top[i-xs]; }else { xt = x[j+1][i]; } if (i>gxs && j+1<gys+gym){ xlt = x[j+1][i-1]; } if (j>gys && i+1<gxs+gxm){ xrb = x[j-1][i+1]; } d1 = (xc-xl); d2 = (xc-xr); d3 = (xc-xt); d4 = (xc-xb); d5 = (xr-xrb); d6 = (xrb-xb); d7 = (xlt-xl); d8 = (xt-xlt); df1dxc = d1*hydhx; df2dxc = ( d1*hydhx + d4*hxdhy ); df3dxc = d3*hxdhy; df4dxc = ( d2*hydhx + d3*hxdhy ); df5dxc = d2*hydhx; df6dxc = d4*hxdhy; d1 *= rhx; d2 *= rhx; d3 *= rhy; d4 *= rhy; d5 *= rhy; d6 *= rhx; d7 *= rhy; d8 *= rhx; f1 = sqrt( 1.0 + d1*d1 + d7*d7); f2 = sqrt( 1.0 + d1*d1 + d4*d4); f3 = sqrt( 1.0 + d3*d3 + d8*d8); f4 = sqrt( 1.0 + d3*d3 + d2*d2); f5 = sqrt( 1.0 + d2*d2 + d5*d5); f6 = sqrt( 1.0 + d4*d4 + d6*d6); f2 = sqrt( 1.0 + d1*d1 + d4*d4); f4 = sqrt( 1.0 + d3*d3 + d2*d2); ft = ft + (f2 + f4); df1dxc /= f1; df2dxc /= f2; df3dxc /= f3; df4dxc /= f4; df5dxc /= f5; df6dxc /= f6; g[j][i] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc ) * 0.5; } } /* Compute triangular areas along the border of the domain. */ if (xs==0){ /* left side */ for (j=ys; j<ys+ym; j++){ d3=(user->left[j-ys+1] - user->left[j-ys+2])*rhy; d2=(user->left[j-ys+1] - x[j][0]) *rhx; ft = ft+sqrt( 1.0 + d3*d3 + d2*d2); } } if (ys==0){ /* bottom side */ for (i=xs; i<xs+xm; i++){ d2=(user->bottom[i+1-xs]-user->bottom[i-xs+2])*rhx; d3=(user->bottom[i-xs+1]-x[0][i])*rhy; ft = ft+sqrt( 1.0 + d3*d3 + d2*d2); } } if (xs+xm==mx){ /* right side */ for (j=ys; j< ys+ym; j++){ d1=(x[j][mx-1] - user->right[j-ys+1])*rhx; d4=(user->right[j-ys]-user->right[j-ys+1])*rhy; ft = ft+sqrt( 1.0 + d1*d1 + d4*d4); } } if (ys+ym==my){ /* top side */ for (i=xs; i<xs+xm; i++){ d1=(x[my-1][i] - user->top[i-xs+1])*rhy; d4=(user->top[i-xs+1] - user->top[i-xs])*rhx; ft = ft+sqrt( 1.0 + d1*d1 + d4*d4); } } if (ys==0 && xs==0){ d1=(user->left[0]-user->left[1])/hy; d2=(user->bottom[0]-user->bottom[1])*rhx; ft +=sqrt( 1.0 + d1*d1 + d2*d2); } if (ys+ym == my && xs+xm == mx){ d1=(user->right[ym+1] - user->right[ym])*rhy; d2=(user->top[xm+1] - user->top[xm])*rhx; ft +=sqrt( 1.0 + d1*d1 + d2*d2); } ft=ft*area; info = MPI_Allreduce(&ft,fcn,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD);CHKERRQ(info); /* Restore vectors */ info = DAVecRestoreArray(user->da,localX,(void**)&x); info = DAVecRestoreArray(user->da,G,(void**)&g); /* Scatter values to global vector */ info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info); info = PetscLogFlops(67*xm*ym); CHKERRQ(info); return 0; } /* ------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "FormHessian" /* FormHessian - Evaluates Hessian matrix. Input Parameters: . taoapp - the TAO_APPLICATION context . x - input vector . ptr - optional user-defined context, as set by TaoSetHessian() Output Parameters: . H - Hessian matrix . Hpre - optionally different preconditioning matrix . flg - flag indicating matrix structure */ int FormHessian(TAO_APPLICATION taoapp,Vec X,Mat *H, Mat *Hpre, MatStructure *flg, void *ptr) { int info; AppCtx *user = (AppCtx *) ptr; /* Evaluate the Hessian entries*/ info = QuadraticH(user,X,*H); CHKERRQ(info); /* Indicate that this matrix has the same sparsity pattern during successive iterations; setting this flag can save significant work in computing the preconditioner for some methods. */ *flg=SAME_NONZERO_PATTERN; return 0; } /* ------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "QuadraticH" /* QuadraticH - Evaluates Hessian matrix. Input Parameters: . user - user-defined context, as set by TaoSetHessian() . X - input vector Output Parameter: . H - Hessian matrix */ int QuadraticH(AppCtx *user, Vec X, Mat Hessian) { int i,j,k,info; int mx=user->mx, my=user->my; int xs,xm,gxs,gxm,ys,ym,gys,gym; double hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy; double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb; double hl,hr,ht,hb,hc,htl,hbr; PetscScalar **x, v[7]; MatStencil col[7],row; Vec localX; PetscTruth assembled; /* Get local mesh boundaries */ info = DAGetLocalVector(user->da,&localX);CHKERRQ(info); info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info); info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info); /* Scatter ghost points to local vector */ info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info); info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info); /* Get pointers to vector data */ info = DAVecGetArray(user->da,localX,(void**)&x); /* Initialize matrix entries to zero */ info = MatAssembled(Hessian,&assembled); CHKERRQ(info); if (assembled){info = MatZeroEntries(Hessian); CHKERRQ(info);} /* Set various matrix options */ info = MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES); CHKERRQ(info); info = MatSetOption(Hessian,MAT_COLUMNS_SORTED); CHKERRQ(info); info = MatSetOption(Hessian,MAT_ROWS_SORTED); CHKERRQ(info); /* Compute Hessian over the locally owned part of the mesh */ for (j=ys; j<ys+ym; j++){ for (i=xs; i< xs+xm; i++){ xc = x[j][i]; xlt=xrb=xl=xr=xb=xt=xc; /* Left side */ if (i==0){ xl = user->left[j-ys+1]; xlt = user->left[j-ys+2]; } else { xl = x[j][i-1]; } if (j==0){ xb = user->bottom[i-xs+1]; xrb = user->bottom[i-xs+2]; } else { xb = x[j-1][i]; } if (i+1 == mx){ xr = user->right[j-ys+1]; xrb = user->right[j-ys]; } else { xr = x[j][i+1]; } if (j+1==my){ xt = user->top[i-xs+1]; xlt = user->top[i-xs]; }else { xt = x[j+1][i]; } if (i>0 && j+1<my){ xlt = x[j+1][i-1]; } if (j>0 && i+1<mx){ xrb = x[j-1][i+1]; } d1 = (xc-xl)/hx; d2 = (xc-xr)/hx; d3 = (xc-xt)/hy; d4 = (xc-xb)/hy; d5 = (xrb-xr)/hy; d6 = (xrb-xb)/hx; d7 = (xlt-xl)/hy; d8 = (xlt-xt)/hx; f1 = sqrt( 1.0 + d1*d1 + d7*d7); f2 = sqrt( 1.0 + d1*d1 + d4*d4); f3 = sqrt( 1.0 + d3*d3 + d8*d8); f4 = sqrt( 1.0 + d3*d3 + d2*d2); f5 = sqrt( 1.0 + d2*d2 + d5*d5); f6 = sqrt( 1.0 + d4*d4 + d6*d6); hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+ (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2); hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+ (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4); ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+ (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4); hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+ (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2); hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6); htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3); hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) + hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) + (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) + (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4); hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0; row.j = j; row.i = i; k=0; if (j>0){ v[k]=hb; col[k].j = j - 1; col[k].i = i; k++; } if (j>0 && i < mx -1){ v[k]=hbr; col[k].j = j - 1; col[k].i = i+1; k++; } if (i>0){ v[k]= hl; col[k].j = j; col[k].i = i-1; k++; } v[k]= hc; col[k].j = j; col[k].i = i; k++; if (i < mx-1 ){ v[k]= hr; col[k].j = j; col[k].i = i+1; k++; } if (i>0 && j < my-1 ){ v[k]= htl; col[k].j = j+1; col[k].i = i-1; k++; } if (j < my-1 ){ v[k]= ht; col[k].j = j+1; col[k].i = i; k++; } /* Set matrix values using local numbering, which was defined earlier, in the main routine. */ info = MatSetValuesStencil(Hessian,1,&row,k,col,v,INSERT_VALUES); CHKERRQ(info); } } /* Restore vectors */ info = DAVecRestoreArray(user->da,localX,(void**)&x); info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info); /* Assemble the matrix */ info = MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info); info = MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info); info = PetscLogFlops(199*xm*ym); CHKERRQ(info); return 0; } /* ------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "MSA_BoundaryConditions" /* MSA_BoundaryConditions - Calculates the boundary conditions for the region. Input Parameter: . user - user-defined application context Output Parameter: . user - user-defined application context */ static int MSA_BoundaryConditions(AppCtx * user) { int i,j,k,limit=0,info,maxits=5; int xs,ys,xm,ym,gxs,gys,gxm,gym; int mx=user->mx,my=user->my; int bsize=0, lsize=0, tsize=0, rsize=0; double one=1.0, two=2.0, three=3.0, tol=1e-10; double fnorm,det,hx,hy,xt=0,yt=0; double u1,u2,nf1,nf2,njac11,njac12,njac21,njac22; double b=-0.5, t=0.5, l=-0.5, r=0.5; double *boundary; PetscTruth flg; /* Get local mesh boundaries */ info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info); info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info); bsize=xm+2; lsize=ym+2; rsize=ym+2; tsize=xm+2; info = PetscMalloc(bsize*sizeof(double),&user->bottom); CHKERRQ(info); info = PetscMalloc(tsize*sizeof(double),&user->top); CHKERRQ(info); info = PetscMalloc(lsize*sizeof(double),&user->left); CHKERRQ(info); info = PetscMalloc(rsize*sizeof(double),&user->right); CHKERRQ(info); hx= (r-l)/(mx+1); hy=(t-b)/(my+1); for (j=0; j<4; j++){ if (j==0){ yt=b; xt=l+hx*xs; limit=bsize; boundary=user->bottom; } else if (j==1){ yt=t; xt=l+hx*xs; limit=tsize; boundary=user->top; } else if (j==2){ yt=b+hy*ys; xt=l; limit=lsize; boundary=user->left; } else { //if (j==3) yt=b+hy*ys; xt=r; limit=rsize; boundary=user->right; } for (i=0; i<limit; i++){ u1=xt; u2=-yt; for (k=0; k<maxits; k++){ nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt; nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt; fnorm=sqrt(nf1*nf1+nf2*nf2); if (fnorm <= tol) break; njac11=one+u2*u2-u1*u1; njac12=two*u1*u2; njac21=-two*u1*u2; njac22=-one - u1*u1 + u2*u2; det = njac11*njac22-njac21*njac12; u1 = u1-(njac22*nf1-njac12*nf2)/det; u2 = u2-(njac11*nf2-njac21*nf1)/det; } boundary[i]=u1*u1-u2*u2; if (j==0 || j==1) { xt=xt+hx; } else { // if (j==2 || j==3) yt=yt+hy; } } } /* Scale the boundary if desired */ if (1==1){ PetscReal scl = 1.0; info = PetscOptionsGetReal(PETSC_NULL,"-bottom",&scl,&flg); CHKERRQ(info); if (flg){ for (i=0;i<bsize;i++) user->bottom[i]*=scl; } info = PetscOptionsGetReal(PETSC_NULL,"-top",&scl,&flg); CHKERRQ(info); if (flg){ for (i=0;i<tsize;i++) user->top[i]*=scl; } info = PetscOptionsGetReal(PETSC_NULL,"-right",&scl,&flg); CHKERRQ(info); if (flg){ for (i=0;i<rsize;i++) user->right[i]*=scl; } info = PetscOptionsGetReal(PETSC_NULL,"-left",&scl,&flg); CHKERRQ(info); if (flg){ for (i=0;i<lsize;i++) user->left[i]*=scl; } } return 0; } /* ------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "MSA_InitialPoint" /* MSA_InitialPoint - Calculates the initial guess in one of three ways. Input Parameters: . user - user-defined application context . X - vector for initial guess Output Parameters: . X - newly computed initial guess */ static int MSA_InitialPoint(AppCtx * user, Vec X) { int start2=-1,i,j,info; PetscReal start1=0; PetscTruth flg1,flg2; info = PetscOptionsGetReal(PETSC_NULL,"-start",&start1,&flg1); CHKERRQ(info); info = PetscOptionsGetInt(PETSC_NULL,"-random",&start2,&flg2); CHKERRQ(info); if (flg1){ /* The zero vector is reasonable */ info = VecSet(X, start1); CHKERRQ(info); } else if (flg2 && start2>0){ /* Try a random start between -0.5 and 0.5 */ PetscRandom rctx; PetscScalar np5=-0.5; info = PetscRandomCreate(PETSC_COMM_WORLD,&rctx); CHKERRQ(info); for (i=0; i<start2; i++){ info = VecSetRandom(X, rctx); CHKERRQ(info); } info = PetscRandomDestroy(rctx); CHKERRQ(info); info = VecShift(X, np5); CHKERRQ(info); } else { /* Take an average of the boundary conditions */ int xs,xm,ys,ym; int mx=user->mx,my=user->my; PetscScalar **x; /* Get local mesh boundaries */ info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info); /* Get pointers to vector data */ info = DAVecGetArray(user->da,X,(void**)&x); /* Perform local computations */ for (j=ys; j<ys+ym; j++){ for (i=xs; i< xs+xm; i++){ x[j][i] = ( ((j+1)*user->bottom[i-xs+1]+(my-j+1)*user->top[i-xs+1])/(my+2)+ ((i+1)*user->left[j-ys+1]+(mx-i+1)*user->right[j-ys+1])/(mx+2))/2.0; } } /* Restore vectors */ info = DAVecRestoreArray(user->da,X,(void**)&x); CHKERRQ(info); info = PetscLogFlops(9*xm*ym); CHKERRQ(info); } return 0; } /*-----------------------------------------------------------------------*/ #undef __FUNCT__ #define __FUNCT__ "My_Monitor" int My_Monitor(TAO_APPLICATION minsurfapp, void *ctx){ int info; Vec X; info = TaoAppGetSolutionVec(minsurfapp,&X); CHKERRQ(info); info = VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info); return 0; }