/* Program usage: mpiexec -n 1 rosenbrock2 [-help] [all TAO options] */ /* Include "petsctao.h" so we can use TAO solvers. */ #include static char help[] = "This example demonstrates use of the TAO package to \n\ solve an unconstrained minimization problem on a single processor. We \n\ minimize the extended Rosenbrock function: \n\ sum_{i=0}^{n/2-1} (alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2) \n\ or the chained Rosenbrock function:\n\ sum_{i=0}^{n-1} alpha*(x_{i+1} - x_i^2)^2 + (1 - x_i)^2\n"; /*T Concepts: TAO^Solving an unconstrained minimization problem Routines: TaoCreate(); Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine(); Routines: TaoSetHessianRoutine(); Routines: TaoSetInitialVector(); Routines: TaoSetFromOptions(); Routines: TaoSolve(); Routines: TaoDestroy(); Processors: 1 T*/ /* User-defined application context - contains data needed by the application-provided call-back routines that evaluate the function, gradient, and hessian. */ typedef struct { PetscInt n; /* dimension */ PetscReal alpha; /* condition parameter */ PetscBool chained; } AppCtx; /* -------------- User-defined routines ---------- */ PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*); PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*); int main(int argc,char **argv) { PetscErrorCode ierr; /* used to check for functions returning nonzeros */ PetscReal zero=0.0; Vec x; /* solution vector */ Mat H; Tao tao; /* Tao solver context */ PetscBool flg, test_lmvm = PETSC_FALSE; PetscMPIInt size; /* number of processes running */ AppCtx user; /* user-defined application context */ TaoConvergedReason reason; PetscInt its, recycled_its=0, oneshot_its=0; /* Initialize TAO and PETSc */ ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); if (size >1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Incorrect number of processors"); /* Initialize problem parameters */ user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE; /* Check for command line arguments to override defaults */ ierr = PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);CHKERRQ(ierr); ierr = PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);CHKERRQ(ierr); ierr = PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);CHKERRQ(ierr); ierr = PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);CHKERRQ(ierr); /* Allocate vectors for the solution and gradient */ ierr = VecCreateSeq(PETSC_COMM_SELF,user.n,&x);CHKERRQ(ierr); ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);CHKERRQ(ierr); /* The TAO code begins here */ /* Create TAO solver with desired solution method */ ierr = TaoCreate(PETSC_COMM_SELF,&tao);CHKERRQ(ierr); ierr = TaoSetType(tao,TAOLMVM);CHKERRQ(ierr); /* Set solution vec and an initial guess */ ierr = VecSet(x, zero);CHKERRQ(ierr); ierr = TaoSetInitialVector(tao,x);CHKERRQ(ierr); /* Set routines for function, gradient, hessian evaluation */ ierr = TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);CHKERRQ(ierr); ierr = TaoSetHessianRoutine(tao,H,H,FormHessian,&user);CHKERRQ(ierr); /* Check for TAO command line options */ ierr = TaoSetFromOptions(tao);CHKERRQ(ierr); /* Solve the problem */ ierr = TaoSetTolerances(tao, 1.e-5, 0.0, 0.0);CHKERRQ(ierr); ierr = TaoSetMaximumIterations(tao, 5);CHKERRQ(ierr); ierr = TaoLMVMRecycle(tao, PETSC_TRUE);CHKERRQ(ierr); reason = TAO_CONTINUE_ITERATING; while (reason != TAO_CONVERGED_GATOL) { ierr = TaoSolve(tao);CHKERRQ(ierr); ierr = TaoGetConvergedReason(tao, &reason);CHKERRQ(ierr); ierr = TaoGetIterationNumber(tao, &its);CHKERRQ(ierr); recycled_its += its; ierr = PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");CHKERRQ(ierr); } /* Disable recycling and solve again! */ ierr = TaoSetMaximumIterations(tao, 100);CHKERRQ(ierr); ierr = TaoLMVMRecycle(tao, PETSC_FALSE);CHKERRQ(ierr); ierr = VecSet(x, zero);CHKERRQ(ierr); ierr = TaoSolve(tao);CHKERRQ(ierr); ierr = TaoGetConvergedReason(tao, &reason);CHKERRQ(ierr); if (reason != TAO_CONVERGED_GATOL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Solution failed to converge!"); ierr = TaoGetIterationNumber(tao, &oneshot_its);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_SELF, "recycled its: %D | oneshot its: %D\n", recycled_its, oneshot_its);CHKERRQ(ierr); if (recycled_its != oneshot_its) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "LMVM recycling does not work!"); ierr = TaoDestroy(&tao);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = MatDestroy(&H);CHKERRQ(ierr); ierr = PetscFinalize(); return ierr; } /* -------------------------------------------------------------------- */ /* FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X). Input Parameters: . tao - the Tao context . X - input vector . ptr - optional user-defined context, as set by TaoSetFunctionGradient() Output Parameters: . G - vector containing the newly evaluated gradient . f - function value Note: Some optimization methods ask for the function and the gradient evaluation at the same time. Evaluating both at once may be more efficient that evaluating each separately. */ PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr) { AppCtx *user = (AppCtx *) ptr; PetscInt i,nn=user->n/2; PetscErrorCode ierr; PetscReal ff=0,t1,t2,alpha=user->alpha; PetscScalar *g; const PetscScalar *x; PetscFunctionBeginUser; /* Get pointers to vector data */ ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr); ierr = VecGetArray(G,&g);CHKERRQ(ierr); /* Compute G(X) */ if (user->chained) { g[0] = 0; for (i=0; in-1; i++) { t1 = x[i+1] - x[i]*x[i]; ff += PetscSqr(1 - x[i]) + alpha*t1*t1; g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]); g[i+1] = 2*alpha*t1; } } else { for (i=0; ialpha; PetscReal v[2][2]; const PetscScalar *x; PetscBool assembled; PetscFunctionBeginUser; /* Zero existing matrix entries */ ierr = MatAssembled(H,&assembled);CHKERRQ(ierr); if (assembled) {ierr = MatZeroEntries(H);CHKERRQ(ierr);} /* Get a pointer to vector data */ ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr); /* Compute H(X) entries */ if (user->chained) { ierr = MatZeroEntries(H);CHKERRQ(ierr); for (i=0; in-1; i++) { PetscScalar t1 = x[i+1] - x[i]*x[i]; v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]); v[0][1] = 2*alpha*(-2*x[i]); v[1][0] = 2*alpha*(-2*x[i]); v[1][1] = 2*alpha*t1; ind[0] = i; ind[1] = i+1; ierr = MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);CHKERRQ(ierr); } } else { for (i=0; in/2; i++) { v[1][1] = 2*alpha; v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2; v[1][0] = v[0][1] = -4.0*alpha*x[2*i]; ind[0]=2*i; ind[1]=2*i+1; ierr = MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);CHKERRQ(ierr); } } ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr); /* Assemble matrix */ ierr = MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = PetscLogFlops(9.0*user->n/2.0);CHKERRQ(ierr); PetscFunctionReturn(0); } /*TEST build: requires: !complex test: args: -tao_type lmvm -tao_monitor requires: !single TEST*/