Newton’s Method¶

Contents: rhea_newton.h
rhea_newton_check.h

`rhea_newton.h` [source]¶

Typedefs

typedef void (*rhea_newton_data_initialize_fn_t)(ymir_vec_t *solution, void *data)¶

RHEA_NEWTON

Nonlinear solver using Newton’s method. Initializes user data of the nonlinear problem to be able to run the Newton solver.

Param solution:: [in] Solution vector (may be NULL)
Param data:: [in] User data

typedef void (*rhea_newton_data_finalize_fn_t)(ymir_vec_t *solution, void *data)¶

Clears user data of the nonlinear problem after the Newton solve.

Param data:: [in] User data

typedef double (*rhea_newton_evaluate_objective_fn_t)(ymir_vec_t *solution, void *data, double *obj_comp)¶

Evaluates the objective functional.

Param solution:: [in] Current solution vector (may be NULL)
Param data:: [in] User data
Return:: Value of objective functional

typedef void (*rhea_newton_compute_negative_gradient_fn_t)(ymir_vec_t *neg_gradient, ymir_vec_t *solution, void *data)¶

Computes the negative gradient of the objective functional.

Param neg_gradient:: [out] Negative gradient vector
Param solution:: [in] Current solution vector (may be NULL)
Param data:: [in] User data

typedef double (*rhea_newton_compute_norm_of_gradient_fn_t)(ymir_vec_t *neg_gradient, void *data, double *grad_norm_comp)¶

Computes the norm of the gradient.

Param neg_gradient:: [in] Negative gradient vector
Param data:: [in] User data
Param norm_comp:: [out] Components of the gradient norm
Return:: Norm of the gradient vector

typedef void (*rhea_newton_apply_hessian_fn_t)(ymir_vec_t *out, ymir_vec_t *in, void *data)¶

Applies the Hessian operator to a vector.

Param out:: [out] Result of Hessian application
Param in:: [in] Input vector
Param data:: [in] User data

typedef int (*rhea_newton_solve_hessian_system_fn_t)(ymir_vec_t *step, ymir_vec_t *neg_gradient, const int lin_iter_max, const double lin_res_norm_rtol, const int nonzero_initial_guess, void *data, int *lin_iter_count)¶

Applies inexact inverse of the Hessian operator.

Param step:: [out] Newton step
Param neg_gradient:: [in] Negative gradient vector (serves as RHS)
Param lin_iter_max:: [in] Max #iterations for iterative solver
Param lin_res_norm_rtol:: [in] Relative tolerance for iterative solver
Param nonzero_initial_guess:: [in] Flag if initial guess is nonzero
Param data:: [in] User data
Param lin_iter_count:: [out] Number of iterations taken
Return:: Stopping reason

typedef double (*rhea_newton_modify_step_fn_t)(ymir_vec_t *step, ymir_vec_t *solution, const int iter, void *data)¶

Modfies the Newton step after it has been.computed.

Param [in/out]:: step Newton step (previously computed)
Param solution:: [in] Current solution vector
Param iter:: [in] Iteration number of Newton’s method
Param data:: [in] User data
Return:: Step length modification factor

typedef void (*rhea_newton_update_operator_fn_t)(ymir_vec_t *solution, void *data)¶

Updates the nonlinear operator at the current solution vector.

Param solution:: [in] Current solution vector (may be NULL)
Param data:: [in] User data

typedef void (*rhea_newton_update_hessian_fn_t)(ymir_vec_t *solution, ymir_vec_t *step_vec, const double step_length, void *data)¶

Updates the Hessian operator at the current solution vector.

Param solution:: [in] Current solution vector (may be NULL)
Param step_vec:: [in] Recent step vector, which (together with step length) resulted in current solution (may be NULL)
Param step_length:: [in] Step length corresponding to step vector
Param data:: [in] User data

typedef void (*rhea_newton_modify_hessian_system_fn_t)(ymir_vec_t *neg_gradient, ymir_vec_t *solution, void *data)¶

Modifies the Hessian system before launching the solver for this system.

Param [in/out]:: neg_gradient Negative gradient vector (serves as RHS)
Param solution:: [in] Current solution vector (may be NULL)
Param data:: [in] User data

typedef int (*rhea_newton_setup_poststep_fn_t)(ymir_vec_t **solution, const int iter, void *data)¶

Performs additional setup for next Newton step, e.g., AMR.

Param solution:: [in] Pointer to solution vector
Param iter:: [in] Iteration number of Newton’s method
Param data:: [in] User data
Return:: Flag whether to recompute Newton status

typedef void (*rhea_newton_output_prestep_fn_t)(ymir_vec_t *solution, ymir_vec_t *neg_gradient, const int iter, void *data)¶

Writes or prints output at the beginning of a Newton step.

Param solution:: [in] Solution vector
Param iter:: [in] Iteration number of Newton’s method
Param data:: [in] User data

typedef double (*rhea_newton_check_gradient_innerprod_fn_t)(ymir_vec_t *gradient, ymir_vec_t *perturbation, void *data)¶

Computes the inner product of the gradient and a (random) perturbation.

Param gradient:: [in] Vector on left-hand side of inner product
Param perturbation:: [in] Vector on right-hand side of inner product
Param data:: [in] User data
Return:: Value of inner product

typedef struct rhea_newton_options rhea_newton_options_t¶

typedef struct rhea_newton_problem rhea_newton_problem_t¶

Enums

enum rhea_newton_perfmon_idx_t¶

Values:

enumerator RHEA_NEWTON_PERFMON_DATA_INITIALIZE¶

enumerator RHEA_NEWTON_PERFMON_DATA_FINALIZE¶

enumerator RHEA_NEWTON_PERFMON_OBJ¶

enumerator RHEA_NEWTON_PERFMON_GRAD¶

enumerator RHEA_NEWTON_PERFMON_GRAD_NORM¶

enumerator RHEA_NEWTON_PERFMON_UPDATE_HESSIAN¶

enumerator RHEA_NEWTON_PERFMON_MODIFY_HESSIAN¶

enumerator RHEA_NEWTON_PERFMON_COMPUTE_STEP¶

enumerator RHEA_NEWTON_PERFMON_HESSIAN_SOLVE¶

enumerator RHEA_NEWTON_PERFMON_HESSIAN_APPLY¶

enumerator RHEA_NEWTON_PERFMON_SEARCH_STEP_LENGTH¶

enumerator RHEA_NEWTON_PERFMON_UPDATE_OPERATOR¶

enumerator RHEA_NEWTON_PERFMON_PRESTEP¶

enumerator RHEA_NEWTON_PERFMON_POSTSTEP¶

enumerator RHEA_NEWTON_PERFMON_N¶

Functions

void rhea_newton_add_options(rhea_newton_options_t *newton_options, ymir_options_t *opt_sup)¶: Defines options and adds them as sub-options.

void rhea_newton_get_global_options(rhea_newton_options_t *opt)¶: Gets global options values.

void rhea_newton_options_set_defaults(rhea_newton_options_t *opt)¶: Sets options to default values.

rhea_newton_problem_t *rhea_newton_problem_new(rhea_newton_compute_negative_gradient_fn_t compute_neg_gradient, rhea_newton_compute_norm_of_gradient_fn_t compute_gradient_norm, const int grad_norm_multi_components, rhea_newton_solve_hessian_system_fn_t solve_hessian_sys)¶: Creates a new nonlinear problem.

void rhea_newton_problem_destroy(rhea_newton_problem_t *nl_problem)¶: Destroys a nonlinear problem.

void rhea_newton_problem_set_vectors(ymir_vec_t *neg_gradient_vec, ymir_vec_t *step_vec, rhea_newton_problem_t *nl_problem)¶: Sets vectors required by the Newton solver.

void rhea_newton_problem_set_data_fn(void *data, rhea_newton_data_initialize_fn_t data_initialize, rhea_newton_data_finalize_fn_t data_finalize, rhea_newton_problem_t *nl_problem)¶: Sets callback function for initializing the Newton solver.

void rhea_newton_problem_set_evaluate_objective_fn(rhea_newton_evaluate_objective_fn_t evaluate_objective, const int obj_multi_components, rhea_error_stats_fn_t error_stats_fn, rhea_newton_problem_t *nl_problem)¶: Sets callback function for evaluating the objective functional.

void rhea_newton_problem_set_apply_hessian_fn(rhea_newton_apply_hessian_fn_t apply_hessian, rhea_newton_problem_t *nl_problem)¶: Sets callback function for applying the Hessian.

void rhea_newton_problem_set_modify_step_fn(rhea_newton_modify_step_fn_t modify_step_vec, rhea_newton_problem_t *nl_problem)¶: Sets callback function for modfiying the Newton step after it has been.computed.

void rhea_newton_problem_set_update_fn(rhea_newton_update_operator_fn_t update_operator, rhea_newton_update_hessian_fn_t update_hessian, rhea_newton_modify_hessian_system_fn_t modify_hessian_system, rhea_newton_problem_t *nl_problem)¶: Sets callback functions for updating the nonlinear and Hessian operators.

void rhea_newton_problem_set_setup_poststep_fn(rhea_newton_setup_poststep_fn_t setup_poststep, rhea_newton_problem_t *nl_problem)¶: Sets callback functions for performing additional setup for next Newton step.

void rhea_newton_problem_set_output_fn(rhea_newton_output_prestep_fn_t output_prestep, rhea_newton_problem_t *nl_problem)¶: Sets callback function for output.

void rhea_newton_problem_set_checks(const int check_gradient, const int check_hessian, rhea_newton_problem_t *nl_problem)¶: Activates/deactivates gradient and Hessian checks.

int rhea_newton_problem_get_check_gradient(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_set_check_gradient(const int check_gradient, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_get_check_hessian(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_set_check_hessian(const int check_hessian, rhea_newton_problem_t *nl_problem)¶

ymir_vec_t **rhea_newton_problem_check_gradient_get_perturbations(int *n_vecs, rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_check_gradient_set_perturbations(ymir_vec_t **perturb_vec, const int n_vecs, rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_check_gradient_get_innerprod(rhea_newton_check_gradient_innerprod_fn_t *fn, void **data, rhea_newton_problem_t *nl_problem)¶: Gets/sets inner product for gradient check.

void rhea_newton_problem_check_gradient_set_innerprod(rhea_newton_check_gradient_innerprod_fn_t fn, void *data, rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_set_perfmon(void *perfmon, rhea_newton_problem_t *nl_problem)¶: Get/set performance monitor.

sc_MPI_Comm rhea_newton_problem_get_mpicomm(rhea_newton_problem_t *nl_problem)¶: Get/set MPI communicator.

void rhea_newton_problem_set_mpicomm(sc_MPI_Comm mpicomm, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_solve(ymir_vec_t **solution, rhea_newton_problem_t *nl_problem, rhea_newton_options_t *opt)¶: Solves a nonlinear problem with inexact Newton—Krylov.

int rhea_newton_solve_has_converged(const int stop_reason)¶

int rhea_newton_solve_get_num_iterations(rhea_newton_problem_t *nl_problem)¶

double rhea_newton_solve_get_residual_reduction(rhea_newton_problem_t *nl_problem)¶

ymir_vec_t *rhea_newton_problem_get_neg_gradient_vec(rhea_newton_problem_t *nl_problem)¶: Accesses data and callback functions of a nonlinear problem.

ymir_vec_t *rhea_newton_problem_get_step_vec(rhea_newton_problem_t *nl_problem)¶

void *rhea_newton_problem_get_data(rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_evaluate_objective_exists(rhea_newton_problem_t *nl_problem)¶

double rhea_newton_problem_evaluate_objective(ymir_vec_t *solution, rhea_newton_problem_t *nl_problem, double *obj_comp)¶

int rhea_newton_problem_evaluate_objective_err(double *error_mean, double *error_stddev, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_compute_gradient_norm_exists(rhea_newton_problem_t *nl_problem)¶

double rhea_newton_problem_compute_gradient_norm(ymir_vec_t *neg_gradient, rhea_newton_problem_t *nl_problem, double *grad_norm_comp)¶

int rhea_newton_problem_compute_neg_gradient_exists(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_compute_neg_gradient(ymir_vec_t *neg_gradient, ymir_vec_t *solution, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_apply_hessian_exists(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_apply_hessian(ymir_vec_t *out, ymir_vec_t *in, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_update_operator_exists(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_update_operator(ymir_vec_t *solution, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_update_hessian_exists(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_update_hessian(ymir_vec_t *solution, ymir_vec_t *step_vec, const double step_length, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_modify_hessian_system_exists(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_modify_hessian_system(ymir_vec_t *neg_gradient, ymir_vec_t *solution, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_setup_poststep_exists(rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_setup_poststep(ymir_vec_t **solution, const int iter, rhea_newton_problem_t *nl_problem)¶

int rhea_newton_problem_output_prestep_exists(rhea_newton_problem_t *nl_problem)¶

void rhea_newton_problem_output_prestep(ymir_vec_t *solution, ymir_vec_t *neg_gradient, const int iter, rhea_newton_problem_t *nl_problem)¶

double rhea_newton_problem_get_reduction_curr(rhea_newton_problem_t *nl_problem)¶: Accesses to status of a nonlinear problem.

Variables

const char *rhea_newton_perfmon_name[RHEA_NEWTON_PERFMON_N]¶

struct rhea_newton_options¶

Public Members

int nonzero_initial_guess¶

int abort_failed_step_search¶

int iter_start¶

int iter_min¶

int iter_max¶

double rtol¶

int lin_iter_max¶

int lin_rtol_init_n_iter¶

double lin_rtol_init¶

double lin_rtol_adaptive_exponent¶

double lin_rtol_adaptive_max¶

int lin_rtol_adaptive_min_active¶

double lin_rtol_adaptive_min_threshold¶

int lin_rtol_adaptive_progressive_n_iter¶

int lin_monitor_reduction¶

int init_step_search_iter_max¶

int step_search_iter_max¶

double step_length_min¶

double step_length_max¶

double step_reduction¶

double step_descend_condition_relaxation¶

int resume¶

double resume_obj_init¶

double resume_obj_prev¶

double resume_obj_reduction_prev¶

double resume_grad_norm_init¶

double resume_grad_norm_prev¶

double resume_grad_norm_reduction_prev¶

int status_verbosity¶

int print_summary¶

char *print_summary_name¶

int monitor_performance¶

`rhea_newton_check.h` [source]¶

Functions

void rhea_newton_check_gradient(ymir_vec_t *solution, ymir_vec_t *neg_gradient, int n_trials, ymir_vec_t **perturb_vec, int n_perturb_vecs, const int iter, rhea_newton_problem_t *nl_problem)¶: Checks gradient of an objective functional by comparing to the finite difference gradient of the functional.

void rhea_newton_check_hessian(ymir_vec_t *solution, ymir_vec_t *neg_gradient, int n_trials, const int iter, rhea_newton_problem_t *nl_problem)¶: Checks Hessian of an objective functional by comparing to the finite difference derivative of the functianal’s gradient.

Newton’s Method¶

rhea_newton.h [source]¶

rhea_newton_check.h [source]¶

`rhea_newton.h` [source]¶

`rhea_newton_check.h` [source]¶