+/*
+ * Returns a double value corresponding to the result of a dichotomy proccess with
+ * respect to a given variable/constraint (\mu in the case of a variable or \lambda in
+ * case of a constraint) and a initial value init.
+ *
+ * @param init initial value for \mu or \lambda
+ * @param diff a function that computes the differential of with respect a \mu or \lambda
+ * @param var_cnst a pointer to a variable or constraint
+ * @param min_erro a minimun error tolerated
+ *
+ * @return a double correponding to the result of the dichotomyal process
+ */
+static double dichotomy(double init, double diff(double, void *),
+ void *var_cnst, double min_error)
+{
+ double min, max;
+ double overall_error;
+ double middle;
+ double min_diff, max_diff, middle_diff;
+ double diff_0 = 0.0;
+ min = max = init;
+
+ XBT_IN();
+
+ if (init == 0.0) {
+ min = max = 0.5;
+ }
+
+ min_diff = max_diff = middle_diff = 0.0;
+ overall_error = 1;
+
+ if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
+ XBT_OUT();
+ return 0.0;
+ }
+
+ min_diff = diff(min, var_cnst);
+ max_diff = diff(max, var_cnst);
+
+ while (overall_error > min_error) {
+ XBT_CDEBUG(surf_lagrange_dichotomy,
+ "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
+ min, max, min_diff, max_diff);
+
+ if (min_diff > 0 && max_diff > 0) {
+ if (min == max) {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
+ min = min / 2.0;
+ min_diff = diff(min, var_cnst);
+ } else {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
+ max = min;
+ max_diff = min_diff;
+ }
+ } else if (min_diff < 0 && max_diff < 0) {
+ if (min == max) {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
+ max = max * 2.0;
+ max_diff = diff(max, var_cnst);
+ } else {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
+ min = max;
+ min_diff = max_diff;
+ }
+ } else if (min_diff < 0 && max_diff > 0) {
+ middle = (max + min) / 2.0;
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",
+ middle);
+
+ if ((min == middle) || (max == middle)) {
+ XBT_CWARN(surf_lagrange_dichotomy,
+ "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
+ " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
+ min, max - min, min_diff, max_diff);
+ break;
+ }
+ middle_diff = diff(middle, var_cnst);
+
+ if (middle_diff < 0) {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
+ min = middle;
+ overall_error = max_diff - middle_diff;
+ min_diff = middle_diff;
+/* SHOW_EXPR(overall_error); */
+ } else if (middle_diff > 0) {
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
+ max = middle;
+ overall_error = max_diff - middle_diff;
+ max_diff = middle_diff;
+/* SHOW_EXPR(overall_error); */
+ } else {
+ overall_error = 0;
+/* SHOW_EXPR(overall_error); */
+ }
+ } else if (min_diff == 0) {
+ max = min;
+ overall_error = 0;
+/* SHOW_EXPR(overall_error); */
+ } else if (max_diff == 0) {
+ min = max;
+ overall_error = 0;
+/* SHOW_EXPR(overall_error); */
+ } else if (min_diff > 0 && max_diff < 0) {
+ XBT_CWARN(surf_lagrange_dichotomy,
+ "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
+ xbt_abort();
+ } else {
+ XBT_CWARN(surf_lagrange_dichotomy,
+ "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
+ min_diff, max_diff);
+ xbt_abort();
+ }
+ }
+
+ XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
+ XBT_OUT();
+ return ((min + max) / 2.0);
+}
+
+static double partial_diff_lambda(double lambda, void *param_cnst)
+{
+
+ int j;
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem = NULL;
+ lmm_variable_t var = NULL;
+ lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
+ double diff = 0.0;
+ double sigma_i = 0.0;
+
+ XBT_IN();
+ elem_list = &(cnst->element_set);
+
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
+
+ xbt_swag_foreach(elem, elem_list) {
+ var = elem->variable;
+ if (var->weight <= 0)
+ continue;
+
+ XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)",
+ var);
+ // Initialize the summation variable
+ sigma_i = 0.0;
+
+ // Compute sigma_i
+ for (j = 0; j < var->cnsts_number; j++) {
+ sigma_i += (var->cnsts[j].constraint)->lambda;