Squashed 'third_party/osqp/' content from commit 33454b3e23

Change-Id: I056df0582ca06664e86554c341a94c47ab932001
git-subtree-dir: third_party/osqp
git-subtree-split: 33454b3e236f1f44193bfbbb6b8c8e71f8f04e9a
Signed-off-by: Austin Schuh <austin.linux@gmail.com>
diff --git a/src/auxil.c b/src/auxil.c
new file mode 100644
index 0000000..89c7de7
--- /dev/null
+++ b/src/auxil.c
@@ -0,0 +1,1067 @@
+#include "osqp.h" // For OSQP rho update
+#include "auxil.h"
+#include "proj.h"
+#include "lin_alg.h"
+#include "constants.h"
+#include "scaling.h"
+#include "util.h"
+
+/***********************************************************
+* Auxiliary functions needed to compute ADMM iterations * *
+***********************************************************/
+#if EMBEDDED != 1
+c_float compute_rho_estimate(OSQPWorkspace *work) {
+  c_int   n, m;                       // Dimensions
+  c_float pri_res, dua_res;           // Primal and dual residuals
+  c_float pri_res_norm, dua_res_norm; // Normalization for the residuals
+  c_float temp_res_norm;              // Temporary residual norm
+  c_float rho_estimate;               // Rho estimate value
+
+  // Get problem dimensions
+  n = work->data->n;
+  m = work->data->m;
+
+  // Get primal and dual residuals
+  pri_res = vec_norm_inf(work->z_prev, m);
+  dua_res = vec_norm_inf(work->x_prev, n);
+
+  // Normalize primal residual
+  pri_res_norm  = vec_norm_inf(work->z, m);           // ||z||
+  temp_res_norm = vec_norm_inf(work->Ax, m);          // ||Ax||
+  pri_res_norm  = c_max(pri_res_norm, temp_res_norm); // max (||z||,||Ax||)
+  pri_res      /= (pri_res_norm + OSQP_DIVISION_TOL); // Normalize primal
+                                                      // residual (prevent 0
+                                                      // division)
+
+  // Normalize dual residual
+  dua_res_norm  = vec_norm_inf(work->data->q, n);     // ||q||
+  temp_res_norm = vec_norm_inf(work->Aty, n);         // ||A' y||
+  dua_res_norm  = c_max(dua_res_norm, temp_res_norm);
+  temp_res_norm = vec_norm_inf(work->Px, n);          // ||P x||
+  dua_res_norm  = c_max(dua_res_norm, temp_res_norm); // max(||q||,||A' y||,||P
+                                                      // x||)
+  dua_res      /= (dua_res_norm + OSQP_DIVISION_TOL); // Normalize dual residual
+                                                      // (prevent 0 division)
+
+
+  // Return rho estimate
+  rho_estimate = work->settings->rho * c_sqrt(pri_res / dua_res);
+  rho_estimate = c_min(c_max(rho_estimate, RHO_MIN), RHO_MAX);     // Constrain
+                                                                   // rho values
+  return rho_estimate;
+}
+
+c_int adapt_rho(OSQPWorkspace *work) {
+  c_int   exitflag; // Exitflag
+  c_float rho_new;  // New rho value
+
+  exitflag = 0;     // Initialize exitflag to 0
+
+  // Compute new rho
+  rho_new = compute_rho_estimate(work);
+
+  // Set rho estimate in info
+  work->info->rho_estimate = rho_new;
+
+  // Check if the new rho is large or small enough and update it in case
+  if ((rho_new > work->settings->rho * work->settings->adaptive_rho_tolerance) ||
+      (rho_new < work->settings->rho /  work->settings->adaptive_rho_tolerance)) {
+    exitflag                 = osqp_update_rho(work, rho_new);
+    work->info->rho_updates += 1;
+  }
+
+  return exitflag;
+}
+
+void set_rho_vec(OSQPWorkspace *work) {
+  c_int i;
+
+  work->settings->rho = c_min(c_max(work->settings->rho, RHO_MIN), RHO_MAX);
+
+  for (i = 0; i < work->data->m; i++) {
+    if ((work->data->l[i] < -OSQP_INFTY * MIN_SCALING) &&
+        (work->data->u[i] > OSQP_INFTY * MIN_SCALING)) {
+      // Loose bounds
+      work->constr_type[i] = -1;
+      work->rho_vec[i]     = RHO_MIN;
+    } else if (work->data->u[i] - work->data->l[i] < RHO_TOL) {
+      // Equality constraints
+      work->constr_type[i] = 1;
+      work->rho_vec[i]     = RHO_EQ_OVER_RHO_INEQ * work->settings->rho;
+    } else {
+      // Inequality constraints
+      work->constr_type[i] = 0;
+      work->rho_vec[i]     = work->settings->rho;
+    }
+    work->rho_inv_vec[i] = 1. / work->rho_vec[i];
+  }
+}
+
+c_int update_rho_vec(OSQPWorkspace *work) {
+  c_int i, exitflag, constr_type_changed;
+
+  exitflag            = 0;
+  constr_type_changed = 0;
+
+  for (i = 0; i < work->data->m; i++) {
+    if ((work->data->l[i] < -OSQP_INFTY * MIN_SCALING) &&
+        (work->data->u[i] > OSQP_INFTY * MIN_SCALING)) {
+      // Loose bounds
+      if (work->constr_type[i] != -1) {
+        work->constr_type[i] = -1;
+        work->rho_vec[i]     = RHO_MIN;
+        work->rho_inv_vec[i] = 1. / RHO_MIN;
+        constr_type_changed  = 1;
+      }
+    } else if (work->data->u[i] - work->data->l[i] < RHO_TOL) {
+      // Equality constraints
+      if (work->constr_type[i] != 1) {
+        work->constr_type[i] = 1;
+        work->rho_vec[i]     = RHO_EQ_OVER_RHO_INEQ * work->settings->rho;
+        work->rho_inv_vec[i] = 1. / work->rho_vec[i];
+        constr_type_changed  = 1;
+      }
+    } else {
+      // Inequality constraints
+      if (work->constr_type[i] != 0) {
+        work->constr_type[i] = 0;
+        work->rho_vec[i]     = work->settings->rho;
+        work->rho_inv_vec[i] = 1. / work->settings->rho;
+        constr_type_changed  = 1;
+      }
+    }
+  }
+
+  // Update rho_vec in KKT matrix if constraints type has changed
+  if (constr_type_changed == 1) {
+    exitflag = work->linsys_solver->update_rho_vec(work->linsys_solver,
+                                                   work->rho_vec);
+  }
+
+  return exitflag;
+}
+
+#endif // EMBEDDED != 1
+
+
+void swap_vectors(c_float **a, c_float **b) {
+  c_float *temp;
+
+  temp = *b;
+  *b   = *a;
+  *a   = temp;
+}
+
+void cold_start(OSQPWorkspace *work) {
+  vec_set_scalar(work->x, 0., work->data->n);
+  vec_set_scalar(work->z, 0., work->data->m);
+  vec_set_scalar(work->y, 0., work->data->m);
+}
+
+static void compute_rhs(OSQPWorkspace *work) {
+  c_int i; // Index
+
+  for (i = 0; i < work->data->n; i++) {
+    // Cycle over part related to x variables
+    work->xz_tilde[i] = work->settings->sigma * work->x_prev[i] -
+                        work->data->q[i];
+  }
+
+  for (i = 0; i < work->data->m; i++) {
+    // Cycle over dual variable in the first step (nu)
+    work->xz_tilde[i + work->data->n] = work->z_prev[i] - work->rho_inv_vec[i] *
+                                        work->y[i];
+  }
+}
+
+void update_xz_tilde(OSQPWorkspace *work) {
+  // Compute right-hand side
+  compute_rhs(work);
+
+  // Solve linear system
+  work->linsys_solver->solve(work->linsys_solver, work->xz_tilde);
+}
+
+void update_x(OSQPWorkspace *work) {
+  c_int i;
+
+  // update x
+  for (i = 0; i < work->data->n; i++) {
+    work->x[i] = work->settings->alpha * work->xz_tilde[i] +
+                 ((c_float)1.0 - work->settings->alpha) * work->x_prev[i];
+  }
+
+  // update delta_x
+  for (i = 0; i < work->data->n; i++) {
+    work->delta_x[i] = work->x[i] - work->x_prev[i];
+  }
+}
+
+void update_z(OSQPWorkspace *work) {
+  c_int i;
+
+  // update z
+  for (i = 0; i < work->data->m; i++) {
+    work->z[i] = work->settings->alpha * work->xz_tilde[i + work->data->n] +
+                 ((c_float)1.0 - work->settings->alpha) * work->z_prev[i] +
+                 work->rho_inv_vec[i] * work->y[i];
+  }
+
+  // project z
+  project(work, work->z);
+}
+
+void update_y(OSQPWorkspace *work) {
+  c_int i; // Index
+
+  for (i = 0; i < work->data->m; i++) {
+    work->delta_y[i] = work->rho_vec[i] *
+                       (work->settings->alpha *
+                        work->xz_tilde[i + work->data->n] +
+                        ((c_float)1.0 - work->settings->alpha) * work->z_prev[i] -
+                        work->z[i]);
+    work->y[i] += work->delta_y[i];
+  }
+}
+
+c_float compute_obj_val(OSQPWorkspace *work, c_float *x) {
+  c_float obj_val;
+
+  obj_val = quad_form(work->data->P, x) +
+            vec_prod(work->data->q, x, work->data->n);
+
+  if (work->settings->scaling) {
+    obj_val *= work->scaling->cinv;
+  }
+
+  return obj_val;
+}
+
+c_float compute_pri_res(OSQPWorkspace *work, c_float *x, c_float *z) {
+  // NB: Use z_prev as working vector
+  // pr = Ax - z
+
+  mat_vec(work->data->A, x, work->Ax, 0); // Ax
+  vec_add_scaled(work->z_prev, work->Ax, z, work->data->m, -1);
+
+  // If scaling active -> rescale residual
+  if (work->settings->scaling && !work->settings->scaled_termination) {
+    return vec_scaled_norm_inf(work->scaling->Einv, work->z_prev, work->data->m);
+  }
+
+  // Return norm of the residual
+  return vec_norm_inf(work->z_prev, work->data->m);
+}
+
+c_float compute_pri_tol(OSQPWorkspace *work, c_float eps_abs, c_float eps_rel) {
+  c_float max_rel_eps, temp_rel_eps;
+
+  // max_rel_eps = max(||z||, ||A x||)
+  if (work->settings->scaling && !work->settings->scaled_termination) {
+    // ||Einv * z||
+    max_rel_eps =
+      vec_scaled_norm_inf(work->scaling->Einv, work->z, work->data->m);
+
+    // ||Einv * A * x||
+    temp_rel_eps = vec_scaled_norm_inf(work->scaling->Einv,
+                                       work->Ax,
+                                       work->data->m);
+
+    // Choose maximum
+    max_rel_eps = c_max(max_rel_eps, temp_rel_eps);
+  } else { // No unscaling required
+    // ||z||
+    max_rel_eps = vec_norm_inf(work->z, work->data->m);
+
+    // ||A * x||
+    temp_rel_eps = vec_norm_inf(work->Ax, work->data->m);
+
+    // Choose maximum
+    max_rel_eps = c_max(max_rel_eps, temp_rel_eps);
+  }
+
+  // eps_prim
+  return eps_abs + eps_rel * max_rel_eps;
+}
+
+c_float compute_dua_res(OSQPWorkspace *work, c_float *x, c_float *y) {
+  // NB: Use x_prev as temporary vector
+  // NB: Only upper triangular part of P is stored.
+  // dr = q + A'*y + P*x
+
+  // dr = q
+  prea_vec_copy(work->data->q, work->x_prev, work->data->n);
+
+  // P * x (upper triangular part)
+  mat_vec(work->data->P, x, work->Px, 0);
+
+  // P' * x (lower triangular part with no diagonal)
+  mat_tpose_vec(work->data->P, x, work->Px, 1, 1);
+
+  // dr += P * x (full P matrix)
+  vec_add_scaled(work->x_prev, work->x_prev, work->Px, work->data->n, 1);
+
+  // dr += A' * y
+  if (work->data->m > 0) {
+    mat_tpose_vec(work->data->A, y, work->Aty, 0, 0);
+    vec_add_scaled(work->x_prev, work->x_prev, work->Aty, work->data->n, 1);
+  }
+
+  // If scaling active -> rescale residual
+  if (work->settings->scaling && !work->settings->scaled_termination) {
+    return work->scaling->cinv * vec_scaled_norm_inf(work->scaling->Dinv,
+                                                     work->x_prev,
+                                                     work->data->n);
+  }
+
+  return vec_norm_inf(work->x_prev, work->data->n);
+}
+
+c_float compute_dua_tol(OSQPWorkspace *work, c_float eps_abs, c_float eps_rel) {
+  c_float max_rel_eps, temp_rel_eps;
+
+  // max_rel_eps = max(||q||, ||A' y|, ||P x||)
+  if (work->settings->scaling && !work->settings->scaled_termination) {
+    // || Dinv q||
+    max_rel_eps = vec_scaled_norm_inf(work->scaling->Dinv,
+                                      work->data->q,
+                                      work->data->n);
+
+    // || Dinv A' y ||
+    temp_rel_eps = vec_scaled_norm_inf(work->scaling->Dinv,
+                                       work->Aty,
+                                       work->data->n);
+    max_rel_eps = c_max(max_rel_eps, temp_rel_eps);
+
+    // || Dinv P x||
+    temp_rel_eps = vec_scaled_norm_inf(work->scaling->Dinv,
+                                       work->Px,
+                                       work->data->n);
+    max_rel_eps = c_max(max_rel_eps, temp_rel_eps);
+
+    // Multiply by cinv
+    max_rel_eps *= work->scaling->cinv;
+  } else { // No scaling required
+    // ||q||
+    max_rel_eps = vec_norm_inf(work->data->q, work->data->n);
+
+    // ||A'*y||
+    temp_rel_eps = vec_norm_inf(work->Aty, work->data->n);
+    max_rel_eps  = c_max(max_rel_eps, temp_rel_eps);
+
+    // ||P*x||
+    temp_rel_eps = vec_norm_inf(work->Px, work->data->n);
+    max_rel_eps  = c_max(max_rel_eps, temp_rel_eps);
+  }
+
+  // eps_dual
+  return eps_abs + eps_rel * max_rel_eps;
+}
+
+c_int is_primal_infeasible(OSQPWorkspace *work, c_float eps_prim_inf) {
+  // This function checks for the primal infeasibility termination criteria.
+  //
+  // 1) A' * delta_y < eps * ||delta_y||
+  //
+  // 2) u'*max(delta_y, 0) + l'*min(delta_y, 0) < eps * ||delta_y||
+  //
+
+  c_int i; // Index for loops
+  c_float norm_delta_y;
+  c_float ineq_lhs = 0.0;
+
+  // Project delta_y onto the polar of the recession cone of [l,u]
+  for (i = 0; i < work->data->m; i++) {
+    if (work->data->u[i] > OSQP_INFTY * MIN_SCALING) {          // Infinite upper bound
+      if (work->data->l[i] < -OSQP_INFTY * MIN_SCALING) {       // Infinite lower bound
+        // Both bounds infinite
+        work->delta_y[i] = 0.0;
+      } else {
+        // Only upper bound infinite
+        work->delta_y[i] = c_min(work->delta_y[i], 0.0);
+      }
+    } else if (work->data->l[i] < -OSQP_INFTY * MIN_SCALING) {  // Infinite lower bound
+      // Only lower bound infinite
+      work->delta_y[i] = c_max(work->delta_y[i], 0.0);
+    }
+  }
+
+  // Compute infinity norm of delta_y (unscale if necessary)
+  if (work->settings->scaling && !work->settings->scaled_termination) {
+    // Use work->Adelta_x as temporary vector
+    vec_ew_prod(work->scaling->E, work->delta_y, work->Adelta_x, work->data->m);
+    norm_delta_y = vec_norm_inf(work->Adelta_x, work->data->m);
+  } else {
+    norm_delta_y = vec_norm_inf(work->delta_y, work->data->m);
+  }
+
+  if (norm_delta_y > OSQP_DIVISION_TOL) {
+
+    for (i = 0; i < work->data->m; i++) {
+      ineq_lhs += work->data->u[i] * c_max(work->delta_y[i], 0) + \
+                  work->data->l[i] * c_min(work->delta_y[i], 0);
+    }
+
+    // Check if the condition is satisfied: ineq_lhs < -eps
+    if (ineq_lhs < eps_prim_inf * norm_delta_y) {
+      // Compute and return ||A'delta_y|| < eps_prim_inf
+      mat_tpose_vec(work->data->A, work->delta_y, work->Atdelta_y, 0, 0);
+
+      // Unscale if necessary
+      if (work->settings->scaling && !work->settings->scaled_termination) {
+        vec_ew_prod(work->scaling->Dinv,
+                    work->Atdelta_y,
+                    work->Atdelta_y,
+                    work->data->n);
+      }
+
+      return vec_norm_inf(work->Atdelta_y, work->data->n) < eps_prim_inf * norm_delta_y;
+    }
+  }
+
+  // Conditions not satisfied -> not primal infeasible
+  return 0;
+}
+
+c_int is_dual_infeasible(OSQPWorkspace *work, c_float eps_dual_inf) {
+  // This function checks for the scaled dual infeasibility termination
+  // criteria.
+  //
+  // 1) q * delta_x < eps * || delta_x ||
+  //
+  // 2) ||P * delta_x || < eps * || delta_x ||
+  //
+  // 3) -> (A * delta_x)_i > -eps * || delta_x ||,    l_i != -inf
+  //    -> (A * delta_x)_i <  eps * || delta_x ||,    u_i != inf
+  //
+
+
+  c_int   i; // Index for loops
+  c_float norm_delta_x;
+  c_float cost_scaling;
+
+  // Compute norm of delta_x
+  if (work->settings->scaling && !work->settings->scaled_termination) { // Unscale
+                                                                        // if
+                                                                        // necessary
+    norm_delta_x = vec_scaled_norm_inf(work->scaling->D,
+                                       work->delta_x,
+                                       work->data->n);
+    cost_scaling = work->scaling->c;
+  } else {
+    norm_delta_x = vec_norm_inf(work->delta_x, work->data->n);
+    cost_scaling = 1.0;
+  }
+
+  // Prevent 0 division || delta_x || > 0
+  if (norm_delta_x > OSQP_DIVISION_TOL) {
+    // Normalize delta_x by its norm
+
+    /* vec_mult_scalar(work->delta_x, 1./norm_delta_x, work->data->n); */
+
+    // Check first if q'*delta_x < 0
+    if (vec_prod(work->data->q, work->delta_x, work->data->n) <
+        cost_scaling * eps_dual_inf * norm_delta_x) {
+      // Compute product P * delta_x (NB: P is store in upper triangular form)
+      mat_vec(work->data->P, work->delta_x, work->Pdelta_x, 0);
+      mat_tpose_vec(work->data->P, work->delta_x, work->Pdelta_x, 1, 1);
+
+      // Scale if necessary
+      if (work->settings->scaling && !work->settings->scaled_termination) {
+        vec_ew_prod(work->scaling->Dinv,
+                    work->Pdelta_x,
+                    work->Pdelta_x,
+                    work->data->n);
+      }
+
+      // Check if || P * delta_x || = 0
+      if (vec_norm_inf(work->Pdelta_x, work->data->n) <
+          cost_scaling * eps_dual_inf * norm_delta_x) {
+        // Compute A * delta_x
+        mat_vec(work->data->A, work->delta_x, work->Adelta_x, 0);
+
+        // Scale if necessary
+        if (work->settings->scaling && !work->settings->scaled_termination) {
+          vec_ew_prod(work->scaling->Einv,
+                      work->Adelta_x,
+                      work->Adelta_x,
+                      work->data->m);
+        }
+
+        // De Morgan Law Applied to dual infeasibility conditions for A * x
+        // NB: Note that MIN_SCALING is used to adjust the infinity value
+        //     in case the problem is scaled.
+        for (i = 0; i < work->data->m; i++) {
+          if (((work->data->u[i] < OSQP_INFTY * MIN_SCALING) &&
+               (work->Adelta_x[i] >  eps_dual_inf * norm_delta_x)) ||
+              ((work->data->l[i] > -OSQP_INFTY * MIN_SCALING) &&
+               (work->Adelta_x[i] < -eps_dual_inf * norm_delta_x))) {
+            // At least one condition not satisfied -> not dual infeasible
+            return 0;
+          }
+        }
+
+        // All conditions passed -> dual infeasible
+        return 1;
+      }
+    }
+  }
+
+  // Conditions not satisfied -> not dual infeasible
+  return 0;
+}
+
+c_int has_solution(OSQPInfo * info){
+
+  return ((info->status_val != OSQP_PRIMAL_INFEASIBLE) &&
+      (info->status_val != OSQP_PRIMAL_INFEASIBLE_INACCURATE) &&
+      (info->status_val != OSQP_DUAL_INFEASIBLE) &&
+      (info->status_val != OSQP_DUAL_INFEASIBLE_INACCURATE) &&
+      (info->status_val != OSQP_NON_CVX));
+
+}
+
+void store_solution(OSQPWorkspace *work) {
+#ifndef EMBEDDED
+  c_float norm_vec;
+#endif /* ifndef EMBEDDED */
+
+  if (has_solution(work->info)) {
+    prea_vec_copy(work->x, work->solution->x, work->data->n); // primal
+    prea_vec_copy(work->y, work->solution->y, work->data->m); // dual
+
+    // Unscale solution if scaling has been performed
+    if (work->settings->scaling)
+      unscale_solution(work);
+  } else {
+    // No solution present. Solution is NaN
+    vec_set_scalar(work->solution->x, OSQP_NAN, work->data->n);
+    vec_set_scalar(work->solution->y, OSQP_NAN, work->data->m);
+
+#ifndef EMBEDDED
+
+    // Normalize infeasibility certificates if embedded is off
+    // NB: It requires a division
+    if ((work->info->status_val == OSQP_PRIMAL_INFEASIBLE) ||
+        ((work->info->status_val == OSQP_PRIMAL_INFEASIBLE_INACCURATE))) {
+      norm_vec = vec_norm_inf(work->delta_y, work->data->m);
+      vec_mult_scalar(work->delta_y, 1. / norm_vec, work->data->m);
+    }
+
+    if ((work->info->status_val == OSQP_DUAL_INFEASIBLE) ||
+        ((work->info->status_val == OSQP_DUAL_INFEASIBLE_INACCURATE))) {
+      norm_vec = vec_norm_inf(work->delta_x, work->data->n);
+      vec_mult_scalar(work->delta_x, 1. / norm_vec, work->data->n);
+    }
+
+#endif /* ifndef EMBEDDED */
+
+    // Cold start iterates to 0 for next runs (they cannot start from NaN)
+    cold_start(work);
+  }
+}
+
+void update_info(OSQPWorkspace *work,
+                 c_int          iter,
+                 c_int          compute_objective,
+                 c_int          polish) {
+  c_float *x, *z, *y;                   // Allocate pointers to variables
+  c_float *obj_val, *pri_res, *dua_res; // objective value, residuals
+
+#ifdef PROFILING
+  c_float *run_time;                    // Execution time
+#endif /* ifdef PROFILING */
+
+#ifndef EMBEDDED
+
+  if (polish) {
+    x       = work->pol->x;
+    y       = work->pol->y;
+    z       = work->pol->z;
+    obj_val = &work->pol->obj_val;
+    pri_res = &work->pol->pri_res;
+    dua_res = &work->pol->dua_res;
+# ifdef PROFILING
+    run_time = &work->info->polish_time;
+# endif /* ifdef PROFILING */
+  } else {
+#endif // EMBEDDED
+  x                = work->x;
+  y                = work->y;
+  z                = work->z;
+  obj_val          = &work->info->obj_val;
+  pri_res          = &work->info->pri_res;
+  dua_res          = &work->info->dua_res;
+  work->info->iter = iter; // Update iteration number
+#ifdef PROFILING
+  run_time = &work->info->solve_time;
+#endif /* ifdef PROFILING */
+#ifndef EMBEDDED
+}
+
+#endif /* ifndef EMBEDDED */
+
+
+  // Compute the objective if needed
+  if (compute_objective) {
+    *obj_val = compute_obj_val(work, x);
+  }
+
+  // Compute primal residual
+  if (work->data->m == 0) {
+    // No constraints -> Always primal feasible
+    *pri_res = 0.;
+  } else {
+    *pri_res = compute_pri_res(work, x, z);
+  }
+
+  // Compute dual residual
+  *dua_res = compute_dua_res(work, x, y);
+
+  // Update timing
+#ifdef PROFILING
+  *run_time = osqp_toc(work->timer);
+#endif /* ifdef PROFILING */
+
+#ifdef PRINTING
+  work->summary_printed = 0; // The just updated info have not been printed
+#endif /* ifdef PRINTING */
+}
+
+
+void reset_info(OSQPInfo *info) {
+#ifdef PROFILING
+
+  // Initialize info values.
+  info->solve_time = 0.0;  // Solve time to zero
+# ifndef EMBEDDED
+  info->polish_time = 0.0; // Polish time to zero
+# endif /* ifndef EMBEDDED */
+
+  // NB: We do not reset the setup_time because it is performed only once
+#endif /* ifdef PROFILING */
+
+  update_status(info, OSQP_UNSOLVED); // Problem is unsolved
+
+#if EMBEDDED != 1
+  info->rho_updates = 0;              // Rho updates are now 0
+#endif /* if EMBEDDED != 1 */
+}
+
+void update_status(OSQPInfo *info, c_int status_val) {
+  // Update status value
+  info->status_val = status_val;
+
+  // Update status string depending on status val
+  if (status_val == OSQP_SOLVED) c_strcpy(info->status, "solved");
+
+  if (status_val == OSQP_SOLVED_INACCURATE) c_strcpy(info->status,
+                                                     "solved inaccurate");
+  else if (status_val == OSQP_PRIMAL_INFEASIBLE) c_strcpy(info->status,
+                                                          "primal infeasible");
+  else if (status_val == OSQP_PRIMAL_INFEASIBLE_INACCURATE) c_strcpy(info->status,
+                                                                     "primal infeasible inaccurate");
+  else if (status_val == OSQP_UNSOLVED) c_strcpy(info->status, "unsolved");
+  else if (status_val == OSQP_DUAL_INFEASIBLE) c_strcpy(info->status,
+                                                        "dual infeasible");
+  else if (status_val == OSQP_DUAL_INFEASIBLE_INACCURATE) c_strcpy(info->status,
+                                                                   "dual infeasible inaccurate");
+  else if (status_val == OSQP_MAX_ITER_REACHED) c_strcpy(info->status,
+                                                         "maximum iterations reached");
+#ifdef PROFILING
+  else if (status_val == OSQP_TIME_LIMIT_REACHED) c_strcpy(info->status,
+                                                           "run time limit reached");
+#endif /* ifdef PROFILING */
+  else if (status_val == OSQP_SIGINT) c_strcpy(info->status, "interrupted");
+
+  else if (status_val == OSQP_NON_CVX) c_strcpy(info->status, "problem non convex");
+
+}
+
+c_int check_termination(OSQPWorkspace *work, c_int approximate) {
+  c_float eps_prim, eps_dual, eps_prim_inf, eps_dual_inf;
+  c_int   exitflag;
+  c_int   prim_res_check, dual_res_check, prim_inf_check, dual_inf_check;
+  c_float eps_abs, eps_rel;
+
+  // Initialize variables to 0
+  exitflag       = 0;
+  prim_res_check = 0; dual_res_check = 0;
+  prim_inf_check = 0; dual_inf_check = 0;
+
+  // Initialize tolerances
+  eps_abs      = work->settings->eps_abs;
+  eps_rel      = work->settings->eps_rel;
+  eps_prim_inf = work->settings->eps_prim_inf;
+  eps_dual_inf = work->settings->eps_dual_inf;
+
+  // If residuals are too large, the problem is probably non convex
+  if ((work->info->pri_res > OSQP_INFTY) ||
+      (work->info->dua_res > OSQP_INFTY)){
+    // Looks like residuals are diverging. Probably the problem is non convex!
+    // Terminate and report it
+    update_status(work->info, OSQP_NON_CVX);
+    work->info->obj_val = OSQP_NAN;
+    return 1;
+  }
+
+  // If approximate solution required, increase tolerances by 10
+  if (approximate) {
+    eps_abs      *= 10;
+    eps_rel      *= 10;
+    eps_prim_inf *= 10;
+    eps_dual_inf *= 10;
+  }
+
+  // Check residuals
+  if (work->data->m == 0) {
+    prim_res_check = 1; // No constraints -> Primal feasibility always satisfied
+  }
+  else {
+    // Compute primal tolerance
+    eps_prim = compute_pri_tol(work, eps_abs, eps_rel);
+
+    // Primal feasibility check
+    if (work->info->pri_res < eps_prim) {
+      prim_res_check = 1;
+    } else {
+      // Primal infeasibility check
+      prim_inf_check = is_primal_infeasible(work, eps_prim_inf);
+    }
+  } // End check if m == 0
+
+  // Compute dual tolerance
+  eps_dual = compute_dua_tol(work, eps_abs, eps_rel);
+
+  // Dual feasibility check
+  if (work->info->dua_res < eps_dual) {
+    dual_res_check = 1;
+  } else {
+    // Check dual infeasibility
+    dual_inf_check = is_dual_infeasible(work, eps_dual_inf);
+  }
+
+  // Compare checks to determine solver status
+  if (prim_res_check && dual_res_check) {
+    // Update final information
+    if (approximate) {
+      update_status(work->info, OSQP_SOLVED_INACCURATE);
+    } else {
+      update_status(work->info, OSQP_SOLVED);
+    }
+    exitflag = 1;
+  }
+  else if (prim_inf_check) {
+    // Update final information
+    if (approximate) {
+      update_status(work->info, OSQP_PRIMAL_INFEASIBLE_INACCURATE);
+    } else {
+      update_status(work->info, OSQP_PRIMAL_INFEASIBLE);
+    }
+
+    if (work->settings->scaling && !work->settings->scaled_termination) {
+      // Update infeasibility certificate
+      vec_ew_prod(work->scaling->E, work->delta_y, work->delta_y, work->data->m);
+    }
+    work->info->obj_val = OSQP_INFTY;
+    exitflag            = 1;
+  }
+  else if (dual_inf_check) {
+    // Update final information
+    if (approximate) {
+      update_status(work->info, OSQP_DUAL_INFEASIBLE_INACCURATE);
+    } else {
+      update_status(work->info, OSQP_DUAL_INFEASIBLE);
+    }
+
+    if (work->settings->scaling && !work->settings->scaled_termination) {
+      // Update infeasibility certificate
+      vec_ew_prod(work->scaling->D, work->delta_x, work->delta_x, work->data->n);
+    }
+    work->info->obj_val = -OSQP_INFTY;
+    exitflag            = 1;
+  }
+
+  return exitflag;
+}
+
+
+#ifndef EMBEDDED
+
+c_int validate_data(const OSQPData *data) {
+  c_int j, ptr;
+
+  if (!data) {
+# ifdef PRINTING
+    c_eprint("Missing data");
+# endif
+    return 1;
+  }
+
+  if (!(data->P)) {
+# ifdef PRINTING
+    c_eprint("Missing matrix P");
+# endif
+    return 1;
+  }
+
+  if (!(data->A)) {
+# ifdef PRINTING
+    c_eprint("Missing matrix A");
+# endif
+    return 1;
+  }
+
+  if (!(data->q)) {
+# ifdef PRINTING
+    c_eprint("Missing vector q");
+# endif
+    return 1;
+  }
+
+  // General dimensions Tests
+  if ((data->n <= 0) || (data->m < 0)) {
+# ifdef PRINTING
+    c_eprint("n must be positive and m nonnegative; n = %i, m = %i",
+             (int)data->n, (int)data->m);
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  // Matrix P
+  if (data->P->m != data->n) {
+# ifdef PRINTING
+    c_eprint("P does not have dimension n x n with n = %i", (int)data->n);
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (data->P->m != data->P->n) {
+# ifdef PRINTING
+    c_eprint("P is not square");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  for (j = 0; j < data->n; j++) { // COLUMN
+    for (ptr = data->P->p[j]; ptr < data->P->p[j + 1]; ptr++) {
+      if (data->P->i[ptr] > j) {  // if ROW > COLUMN
+# ifdef PRINTING
+        c_eprint("P is not upper triangular");
+# endif /* ifdef PRINTING */
+        return 1;
+      }
+    }
+  }
+
+  // Matrix A
+  if ((data->A->m != data->m) || (data->A->n != data->n)) {
+# ifdef PRINTING
+    c_eprint("A does not have dimension %i x %i", (int)data->m, (int)data->n);
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  // Lower and upper bounds
+  for (j = 0; j < data->m; j++) {
+    if (data->l[j] > data->u[j]) {
+# ifdef PRINTING
+      c_eprint("Lower bound at index %d is greater than upper bound: %.4e > %.4e",
+               (int)j, data->l[j], data->u[j]);
+# endif /* ifdef PRINTING */
+      return 1;
+    }
+  }
+
+  // TODO: Complete with other checks
+
+  return 0;
+}
+
+c_int validate_linsys_solver(c_int linsys_solver) {
+  if ((linsys_solver != QDLDL_SOLVER) &&
+      (linsys_solver != MKL_PARDISO_SOLVER)) {
+    return 1;
+  }
+
+  // TODO: Add more solvers in case
+
+  // Valid solver
+  return 0;
+}
+
+c_int validate_settings(const OSQPSettings *settings) {
+  if (!settings) {
+# ifdef PRINTING
+    c_eprint("Missing settings!");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->scaling < 0) {
+# ifdef PRINTING
+    c_eprint("scaling must be nonnegative");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if ((settings->adaptive_rho != 0) && (settings->adaptive_rho != 1)) {
+# ifdef PRINTING
+    c_eprint("adaptive_rho must be either 0 or 1");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->adaptive_rho_interval < 0) {
+# ifdef PRINTING
+    c_eprint("adaptive_rho_interval must be nonnegative");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+# ifdef PROFILING
+
+  if (settings->adaptive_rho_fraction <= 0) {
+#  ifdef PRINTING
+    c_eprint("adaptive_rho_fraction must be positive");
+#  endif /* ifdef PRINTING */
+    return 1;
+  }
+# endif /* ifdef PROFILING */
+
+  if (settings->adaptive_rho_tolerance < 1.0) {
+# ifdef PRINTING
+    c_eprint("adaptive_rho_tolerance must be >= 1");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->polish_refine_iter < 0) {
+# ifdef PRINTING
+    c_eprint("polish_refine_iter must be nonnegative");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->rho <= 0.0) {
+# ifdef PRINTING
+    c_eprint("rho must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->sigma <= 0.0) {
+# ifdef PRINTING
+    c_eprint("sigma must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->delta <= 0.0) {
+# ifdef PRINTING
+    c_eprint("delta must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->max_iter <= 0) {
+# ifdef PRINTING
+    c_eprint("max_iter must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->eps_abs < 0.0) {
+# ifdef PRINTING
+    c_eprint("eps_abs must be nonnegative");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->eps_rel < 0.0) {
+# ifdef PRINTING
+    c_eprint("eps_rel must be nonnegative");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if ((settings->eps_rel == 0.0) &&
+      (settings->eps_abs == 0.0)) {
+# ifdef PRINTING
+    c_eprint("at least one of eps_abs and eps_rel must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->eps_prim_inf <= 0.0) {
+# ifdef PRINTING
+    c_eprint("eps_prim_inf must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->eps_dual_inf <= 0.0) {
+# ifdef PRINTING
+    c_eprint("eps_dual_inf must be positive");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if ((settings->alpha <= 0.0) ||
+      (settings->alpha >= 2.0)) {
+# ifdef PRINTING
+    c_eprint("alpha must be strictly between 0 and 2");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (validate_linsys_solver(settings->linsys_solver)) {
+# ifdef PRINTING
+    c_eprint("linsys_solver not recognized");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if ((settings->verbose != 0) &&
+      (settings->verbose != 1)) {
+# ifdef PRINTING
+    c_eprint("verbose must be either 0 or 1");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if ((settings->scaled_termination != 0) &&
+      (settings->scaled_termination != 1)) {
+# ifdef PRINTING
+    c_eprint("scaled_termination must be either 0 or 1");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if (settings->check_termination < 0) {
+# ifdef PRINTING
+    c_eprint("check_termination must be nonnegative");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+
+  if ((settings->warm_start != 0) &&
+      (settings->warm_start != 1)) {
+# ifdef PRINTING
+    c_eprint("warm_start must be either 0 or 1");
+# endif /* ifdef PRINTING */
+    return 1;
+  }
+# ifdef PROFILING
+
+  if (settings->time_limit < 0.0) {
+#  ifdef PRINTING
+    c_eprint("time_limit must be nonnegative\n");
+#  endif /* ifdef PRINTING */
+    return 1;
+  }
+# endif /* ifdef PROFILING */
+
+  return 0;
+}
+
+#endif // #ifndef EMBEDDED