void ncp_pathsearch(NonlinearComplementarityProblem* problem, double* z, double* F, int *info , SolverOptions* options)
{
/* Main step of the algorithm:
* - compute jacobians
* - call modified lemke
*/
unsigned int n = problem->n;
unsigned int preAlloc = options->iparam[SICONOS_IPARAM_PREALLOC];
int itermax = options->iparam[SICONOS_IPARAM_MAX_ITER];
double merit_norm = 1.0;
double nn_tol = options->dparam[SICONOS_DPARAM_TOL];
int nbiter = 0;
/* declare a LinearComplementarityProblem on the stack*/
LinearComplementarityProblem lcp_subproblem;
lcp_subproblem.size = n;
/* do some allocation if required
* - nabla_F (used also as M for the LCP subproblem)
* - q for the LCP subproblem
*
* Then fill the LCP subproblem
*/
if (!preAlloc || (preAlloc && !options->internalSolvers))
{
options->internalSolvers = (SolverOptions *) malloc(sizeof(SolverOptions));
solver_options_set(options->internalSolvers, SICONOS_LCP_PIVOT);
options->numberOfInternalSolvers = 1;
SolverOptions * lcp_options = options->internalSolvers;
/* We always allocation once and for all since we are supposed to solve
* many LCPs */
lcp_options->iparam[SICONOS_IPARAM_PREALLOC] = 1;
/* set the right pivot rule */
lcp_options->iparam[SICONOS_IPARAM_PIVOT_RULE] = SICONOS_LCP_PIVOT_PATHSEARCH;
/* set the right stacksize */
lcp_options->iparam[SICONOS_IPARAM_PATHSEARCH_STACKSIZE] = options->iparam[SICONOS_IPARAM_PATHSEARCH_STACKSIZE];
}
assert(problem->nabla_F);
lcp_subproblem.M = problem->nabla_F;
if (!preAlloc || (preAlloc && !options->dWork))
{
options->dWork = (double *) malloc(4*n*sizeof(double));
}
lcp_subproblem.q = options->dWork;
double* x = &options->dWork[n];
double* x_plus = &options->dWork[2*n];
double* r = &options->dWork[3*n];
NMS_data* data_NMS;
functions_LSA* functions;
if (!preAlloc || (preAlloc && !options->solverData))
{
options->solverData = malloc(sizeof(pathsearch_data));
pathsearch_data* solverData = (pathsearch_data*) options->solverData;
/* do all the allocation */
solverData->data_NMS = create_NMS_data(n, NM_DENSE, options->iparam, options->dparam);
solverData->lsa_functions = (functions_LSA*) malloc(sizeof(functions_LSA));
solverData->data_NMS->set = malloc(sizeof(positive_orthant));
data_NMS = solverData->data_NMS;
functions = solverData->lsa_functions;
/* for use in NMS; only those 3 functions are called */
init_lsa_functions(functions, &FB_compute_F_ncp, &ncp_FB);
functions->compute_H = &FB_compute_H_ncp;
set_set_id(data_NMS->set, SICONOS_SET_POSITIVE_ORTHANT);
/* fill ls_data */
data_NMS->ls_data->compute_F = functions->compute_F;
data_NMS->ls_data->compute_F_merit = functions->compute_F_merit;
data_NMS->ls_data->z = NULL; /* XXX to check -- xhub */
data_NMS->ls_data->zc = NMS_get_generic_workV(data_NMS->workspace, n);
data_NMS->ls_data->F = NMS_get_F(data_NMS->workspace, n);
data_NMS->ls_data->F_merit = NMS_get_F_merit(data_NMS->workspace, n);
data_NMS->ls_data->desc_dir = NMS_get_dir(data_NMS->workspace, n);
/** \todo this value should be settable by the user with a default value*/
data_NMS->ls_data->alpha_min = fmin(data_NMS->alpha_min_watchdog, data_NMS->alpha_min_pgrad);
data_NMS->ls_data->data = (void*)problem;
data_NMS->ls_data->set = data_NMS->set;
data_NMS->ls_data->sigma = options->dparam[SICONOS_DPARAM_NMS_SIGMA];
/* data_NMS->ls_data->searchtype is set in the NMS code */
}
else
{
pathsearch_data* solverData = (pathsearch_data*) options->solverData;
data_NMS = solverData->data_NMS;
functions = solverData->lsa_functions;
}
/* initial value for ref_merit */
problem->compute_F(problem->env, n, z, F);
functions->compute_F_merit(problem, z, F, data_NMS->ls_data->F_merit);
data_NMS->ref_merit = .5 * cblas_ddot(n, data_NMS->ls_data->F_merit, 1, data_NMS->ls_data->F_merit, 1);
data_NMS->merit_bestpoint = data_NMS->ref_merit;
cblas_dcopy(n, z, 1, NMS_checkpoint_0(data_NMS, n), 1);
cblas_dcopy(n, z, 1, NMS_checkpoint_T(data_NMS, n), 1);
cblas_dcopy(n, z, 1, NMS_bestpoint(data_NMS, n), 1);
/* -------------------- end init ---------------------------*/
int nms_failed = 0;
double err = 10*nn_tol;
/* to check the solution */
LinearComplementarityProblem lcp_subproblem_check;
int check_lcp_solution = 1; /* XXX add config for that */
double normal_norm2_newton_point;
/* F is already computed here at z */
while ((err > nn_tol) && (nbiter < itermax) && !nms_failed)
{
int force_watchdog_step = 0;
int force_d_step_merit_check = 0;
double check_ratio = 0.0;
nbiter++;
/* update M, q and r */
/* First find x */
ncp_pathsearch_compute_x_from_z(n, z, F, x);
pos_part(n, x, x_plus); /* update x_plus */
ncp_pathsearch_update_lcp_data(problem, &lcp_subproblem, n, x_plus, x, r);
if (check_lcp_solution)
{
lcp_subproblem_check.size = n;
lcp_subproblem_check.M = problem->nabla_F;
lcp_subproblem_check.q = lcp_subproblem.q;
//cblas_dcopy(n, x, 1, lcp_subproblem_check.q , 1);
//prodNumericsMatrix(n, n, -1.0, problem->nabla_F, x_plus, 0.0, lcp_subproblem.q);
}
double norm_r2 = cblas_ddot(n, r, 1, r, 1);
if (norm_r2 < DBL_EPSILON*DBL_EPSILON) /* ||r|| < 1e-15 */
{
DEBUG_PRINTF("ncp_pathsearch :: ||r|| = %e < %e; path search procedure was successful!\n", norm_r2, DBL_EPSILON*DBL_EPSILON);
(*info) = 0;
ncp_compute_error(n, z, F, nn_tol, &err); /* XXX F should be up-to-date, we should check only CC*/
break;
}
/* end update M, q and r */
lcp_pivot_covering_vector(&lcp_subproblem, x_plus, x, info, options->internalSolvers, r);
switch (*info)
{
case LCP_PIVOT_SUCCESS:
DEBUG_PRINT("ncp_pathsearch :: path search procedure was successful!\n");
if (check_lcp_solution)
{
double err_lcp = 0.0;
cblas_daxpy(n, 1.0, r, 1, lcp_subproblem_check.q, 1);
lcp_compute_error(&lcp_subproblem_check, x_plus, x, 1e-14, &err_lcp);
double local_tol = fmax(1e-14, DBL_EPSILON*sqrt(norm_r2));
printf("ncp_pathsearch :: lcp solved with error = %e; local_tol = %e\n", err_lcp, local_tol);
//assert(err_lcp < local_tol && "ncp_pathsearch :: lcp solved with very bad precision");
if (err_lcp > local_tol)
{
printf("ncp_pathsearch :: lcp solved with very bad precision\n");
NM_display(lcp_subproblem.M);
printf("z r q x_plus\n");
for (unsigned i = 0; i < n; ++i) printf("%e %e %e %e\n", z[i], r[i], lcp_subproblem.q[i], x_plus[i]);
options->internalSolvers->iparam[SICONOS_IPARAM_PIVOT_RULE] = 0;
lcp_pivot(&lcp_subproblem, x_plus, x, info, options->internalSolvers);
options->internalSolvers->iparam[SICONOS_IPARAM_PIVOT_RULE] = SICONOS_LCP_PIVOT_PATHSEARCH;
lcp_compute_error(&lcp_subproblem_check, x_plus, x, 1e-14, &err_lcp);
printf("ncp_pathsearch :: lcp resolved with error = %e; local_tol = %e\n", err_lcp, local_tol);
}
/* XXX missing recompute x ?*/
/* recompute the normal norm */
problem->compute_F(problem->env, n, x_plus, r);
cblas_daxpy(n, -1.0, x, 1, r, 1);
normal_norm2_newton_point = cblas_ddot(n, r, 1, r, 1);
if (normal_norm2_newton_point > norm_r2)
{
printf("ncp_pathsearch :: lcp successfully solved, but the norm of the normal map increased! %e > %e\n", normal_norm2_newton_point, norm_r2);
//assert(normal_norm2_newton_point <= norm_r2);
}
else
{
printf("ncp_pathsearch :: lcp successfully solved, norm of the normal map decreased! %e < %e\n", normal_norm2_newton_point, norm_r2);
//check_ratio = norm_r2/normal_norm2_newton_point;
}
if (50*normal_norm2_newton_point < norm_r2)
{
force_d_step_merit_check = 1;
}
else if (10*normal_norm2_newton_point < norm_r2)
{
// check_ratio = sqrt(norm_r2/normal_norm2_newton_point);
}
}
break;
case LCP_PIVOT_RAY_TERMINATION:
DEBUG_PRINT("ncp_pathsearch :: ray termination, let's fastened your seat belt!\n");
break;
case LCP_PATHSEARCH_LEAVING_T:
DEBUG_PRINT("ncp_pathsearch :: leaving t, fastened your seat belt!\n");
DEBUG_PRINTF("ncp_pathsearch :: max t value = %e\n", options->internalSolvers->dparam[2]); /* XXX fix 2 */
/* try to retry solving the problem */
/* XXX keep or not ? */
/* recompute the normal norm */
problem->compute_F(problem->env, n, x_plus, r);
cblas_daxpy(n, -1.0, x, 1, r, 1);
normal_norm2_newton_point = cblas_ddot(n, r, 1, r, 1);
if (normal_norm2_newton_point > norm_r2)
{
printf("ncp_pathsearch :: lcp successfully solved, but the norm of the normal map increased! %e > %e\n", normal_norm2_newton_point, norm_r2);
//assert(normal_norm2_newton_point <= norm_r2);
}
else
{
printf("ncp_pathsearch :: lcp successfully solved, norm of the normal map decreased! %e < %e\n", normal_norm2_newton_point, norm_r2);
check_ratio = 5.0*norm_r2/normal_norm2_newton_point;
}
if (options->internalSolvers->dparam[2] > 1e-5) break;
memset(x_plus, 0, sizeof(double) * n);
problem->compute_F(problem->env, n, x_plus, r);
ncp_pathsearch_compute_x_from_z(n, x_plus, r, x);
ncp_pathsearch_update_lcp_data(problem, &lcp_subproblem, n, x_plus, x, r);
lcp_pivot_covering_vector(&lcp_subproblem, x_plus, x, info, options->internalSolvers, r);
if (*info == LCP_PIVOT_SUCCESS)
{
DEBUG_PRINT("ncp_pathsearch :: Lemke start worked !\n");
double err_lcp = 0.0;
cblas_daxpy(n, 1.0, r, 1, lcp_subproblem_check.q, 1);
lcp_compute_error(&lcp_subproblem_check, x_plus, x, 1e-14, &err_lcp);
double local_tol = fmax(1e-14, DBL_EPSILON*sqrt(norm_r2));
printf("ncp_pathsearch :: lcp solved with error = %e; local_tol = %e\n", err_lcp, local_tol);
assert(err_lcp < local_tol);
}
else
{
NM_display(lcp_subproblem.M);
printf("z r q x_plus\n");
for (unsigned i = 0; i < n; ++i) printf("%e %e %e %e\n", z[i], r[i], lcp_subproblem.q[i], x_plus[i]);
DEBUG_PRINT("ncp_pathsearch :: Lemke start did not succeeded !\n");
lcp_pivot_diagnose_info(*info);
if (*info == LCP_PATHSEARCH_LEAVING_T)
{
DEBUG_PRINTF("ncp_pathsearch :: max t value after Lemke start = %e\n", options->internalSolvers->dparam[2]);
}
options->internalSolvers->iparam[SICONOS_IPARAM_PIVOT_RULE] = 0;
lcp_pivot(&lcp_subproblem, x_plus, x, info, options->internalSolvers);
options->internalSolvers->iparam[SICONOS_IPARAM_PIVOT_RULE] = SICONOS_LCP_PIVOT_PATHSEARCH;
double err_lcp = 0.0;
lcp_compute_error(&lcp_subproblem, x_plus, x, 1e-14, &err_lcp);
printf("ncp_pathsearch :: lemke start resolved with info = %d; error = %e\n", *info, err_lcp);
printf("x_plus x_minus\n");
for (unsigned i = 0; i < n; ++i) printf("%e %e\n", x_plus[i], x[i]);
/* recompute the normal norm */
problem->compute_F(problem->env, n, x_plus, r);
cblas_daxpy(n, -1.0, x, 1, r, 1);
double normal_norm2_newton_point = cblas_ddot(n, r, 1, r, 1);
if (normal_norm2_newton_point > norm_r2)
{
printf("ncp_pathsearch :: lcp successfully solved, but the norm of the normal map increased! %e > %e\n", normal_norm2_newton_point, norm_r2);
//assert(normal_norm2_newton_point <= norm_r2);
}
else
{
printf("ncp_pathsearch :: lcp successfully solved, norm of the normal map decreased! %.*e < %.*e\n", DECIMAL_DIG, normal_norm2_newton_point, DECIMAL_DIG, norm_r2);
}
if (100*normal_norm2_newton_point < norm_r2)
{
force_d_step_merit_check = 1;
}
}
break;
case LCP_PIVOT_NUL:
printf("ncp_pathsearch :: kaboom, kaboom still more work needs to be done\n");
lcp_pivot_diagnose_info(*info);
// exit(EXIT_FAILURE);
force_watchdog_step = 1;
break;
case LCP_PATHSEARCH_NON_ENTERING_T:
DEBUG_PRINT("ncp_pathsearch :: non entering t, something is wrong here. Fix the f****** code!\n");
assert(0 && "ncp_pathsearch :: non entering t, something is wrong here\n");
force_watchdog_step = 1;
break;
default:
printf("ncp_pathsearch :: unknown code returned by the path search\n");
exit(EXIT_FAILURE);
}
nms_failed = NMS(data_NMS, problem, functions, z, x_plus, force_watchdog_step, force_d_step_merit_check, check_ratio);
/* at this point z has been updated */
/* recompute the normal norm */
problem->compute_F(problem->env, n, z, F);
functions->compute_F_merit(problem, z, F, data_NMS->ls_data->F_merit);
/* XXX is this correct ? */
merit_norm = .5 * cblas_ddot(n, data_NMS->ls_data->F_merit, 1, data_NMS->ls_data->F_merit, 1);
ncp_compute_error(n, z, F, nn_tol, &err); /* XXX F should be up-to-date, we should check only CC*/
DEBUG_PRINTF("ncp_pathsearch :: iter = %d, ncp_error = %e; merit_norm^2 = %e\n", nbiter, err, merit_norm);
}
options->iparam[1] = nbiter;
options->dparam[1] = err;
if (nbiter == itermax)
{
*info = 1;
}
else if (nms_failed)
{
*info = 2;
}
else
{
*info = 0;
}
DEBUG_PRINTF("ncp_pathsearch procedure finished :: info = %d; iter = %d; ncp_error = %e; merit_norm^2 = %e\n", *info, nbiter, err, merit_norm);
if (!preAlloc)
{
freeNumericsMatrix(problem->nabla_F);
free(problem->nabla_F);
problem->nabla_F = NULL;
free(options->dWork);
options->dWork = NULL;
solver_options_delete(options->internalSolvers);
free(options->internalSolvers);
options->internalSolvers = NULL;
free_NMS_data(data_NMS);
free(functions);
free(options->solverData);
options->solverData = NULL;
}
}
void lcp_pivot(LinearComplementarityProblem* problem, double* u , double* s, int *info , SolverOptions* options)
{
lcp_pivot_covering_vector(problem, u, s, info, options, NULL);
}