/* 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"; /* 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) { 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 */ PetscFunctionBeginUser; PetscCall(PetscInitialize(&argc, &argv, NULL, help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); PetscCheck(size == 1, 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 */ PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &user.n, &flg)); PetscCall(PetscOptionsGetReal(NULL, NULL, "-alpha", &user.alpha, &flg)); PetscCall(PetscOptionsGetBool(NULL, NULL, "-chained", &user.chained, &flg)); PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_lmvm", &test_lmvm, &flg)); /* Allocate vectors for the solution and gradient */ PetscCall(VecCreateSeq(PETSC_COMM_SELF, user.n, &x)); PetscCall(MatCreateSeqBAIJ(PETSC_COMM_SELF, 2, user.n, user.n, 1, NULL, &H)); /* The TAO code begins here */ /* Create TAO solver with desired solution method */ PetscCall(TaoCreate(PETSC_COMM_SELF, &tao)); PetscCall(TaoSetType(tao, TAOBQNLS)); /* Set solution vec and an initial guess */ PetscCall(VecSet(x, zero)); PetscCall(TaoSetSolution(tao, x)); /* Set routines for function, gradient, hessian evaluation */ PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, &user)); PetscCall(TaoSetHessian(tao, H, H, FormHessian, &user)); /* Check for TAO command line options */ PetscCall(TaoSetFromOptions(tao)); /* Solve the problem */ PetscCall(TaoSetTolerances(tao, 1.e-5, 0.0, 0.0)); PetscCall(TaoSetMaximumIterations(tao, 5)); PetscCall(TaoSetRecycleHistory(tao, PETSC_TRUE)); reason = TAO_CONTINUE_ITERATING; flg = PETSC_FALSE; PetscCall(TaoGetRecycleHistory(tao, &flg)); if (flg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Recycle: enabled\n")); while (reason != TAO_CONVERGED_GATOL) { PetscCall(TaoSolve(tao)); PetscCall(TaoGetConvergedReason(tao, &reason)); PetscCall(TaoGetIterationNumber(tao, &its)); recycled_its += its; PetscCall(PetscPrintf(PETSC_COMM_SELF, "-----------------------\n")); } /* Disable recycling and solve again! */ PetscCall(TaoSetMaximumIterations(tao, 100)); PetscCall(TaoSetRecycleHistory(tao, PETSC_FALSE)); PetscCall(VecSet(x, zero)); PetscCall(TaoGetRecycleHistory(tao, &flg)); if (!flg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Recycle: disabled\n")); PetscCall(TaoSolve(tao)); PetscCall(TaoGetConvergedReason(tao, &reason)); PetscCheck(reason == TAO_CONVERGED_GATOL, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Solution failed to converge!"); PetscCall(TaoGetIterationNumber(tao, &oneshot_its)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "-----------------------\n")); PetscCall(PetscPrintf(PETSC_COMM_SELF, "recycled its: %" PetscInt_FMT " | oneshot its: %" PetscInt_FMT "\n", recycled_its, oneshot_its)); PetscCheck(recycled_its == oneshot_its, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Recycled solution does not match oneshot solution!"); PetscCall(TaoDestroy(&tao)); PetscCall(VecDestroy(&x)); PetscCall(MatDestroy(&H)); PetscCall(PetscFinalize()); return 0; } /* -------------------------------------------------------------------- */ /* 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 than 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; PetscReal ff = 0, t1, t2, alpha = user->alpha; PetscScalar *g; const PetscScalar *x; PetscFunctionBeginUser; /* Get pointers to vector data */ PetscCall(VecGetArrayRead(X, &x)); PetscCall(VecGetArrayWrite(G, &g)); /* Compute G(X) */ if (user->chained) { g[0] = 0; for (i = 0; i < user->n - 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; i < nn; i++) { t1 = x[2 * i + 1] - x[2 * i] * x[2 * i]; t2 = 1 - x[2 * i]; ff += alpha * t1 * t1 + t2 * t2; g[2 * i] = -4 * alpha * t1 * x[2 * i] - 2.0 * t2; g[2 * i + 1] = 2 * alpha * t1; } } /* Restore vectors */ PetscCall(VecRestoreArrayRead(X, &x)); PetscCall(VecRestoreArrayWrite(G, &g)); *f = ff; PetscCall(PetscLogFlops(15.0 * nn)); PetscFunctionReturn(PETSC_SUCCESS); } /* ------------------------------------------------------------------- */ /* FormHessian - Evaluates Hessian matrix. Input Parameters: . tao - the Tao context . x - input vector . ptr - optional user-defined context, as set by TaoSetHessian() Output Parameters: . H - Hessian matrix Note: Providing the Hessian may not be necessary. Only some solvers require this matrix. */ PetscErrorCode FormHessian(Tao tao, Vec X, Mat H, Mat Hpre, void *ptr) { AppCtx *user = (AppCtx *)ptr; PetscInt i, ind[2]; PetscReal alpha = user->alpha; PetscReal v[2][2]; const PetscScalar *x; PetscBool assembled; PetscFunctionBeginUser; /* Zero existing matrix entries */ PetscCall(MatAssembled(H, &assembled)); if (assembled || user->chained) PetscCall(MatZeroEntries(H)); /* Get a pointer to vector data */ PetscCall(VecGetArrayRead(X, &x)); /* Compute H(X) entries */ if (user->chained) { for (i = 0; i < user->n - 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; PetscCall(MatSetValues(H, 2, ind, 2, ind, v[0], ADD_VALUES)); } } else { for (i = 0; i < user->n / 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; PetscCall(MatSetValues(H, 2, ind, 2, ind, v[0], INSERT_VALUES)); } } PetscCall(VecRestoreArrayRead(X, &x)); /* Assemble matrix */ PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY)); PetscCall(PetscLogFlops(9.0 * user->n / 2.0)); PetscFunctionReturn(PETSC_SUCCESS); } /*TEST build: requires: !complex test: args: -tao_type bqnls -tao_monitor requires: !single TEST*/