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scs.c
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scs.c
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#include "scs.h"
#include "aa.h"
#include "ctrlc.h"
#include "glbopts.h"
#include "linalg.h"
#include "linsys.h"
#include "normalize.h"
#include "rw.h"
#include "scs_matrix.h"
#include "scs_work.h"
#include "util.h"
/* printing header */
static const char *HEADER[] = {
" iter ", " pri res ", " dua res ", " gap ",
" obj ", " scale ", " time (s)",
};
static const scs_int HSPACE = 9;
static const scs_int HEADER_LEN = 7;
static const scs_int LINE_LEN = 66;
static void free_residuals(ScsResiduals *r) {
if (r) {
scs_free(r->ax);
scs_free(r->ax_s);
scs_free(r->px);
scs_free(r->aty);
scs_free(r->ax_s_btau);
scs_free(r->px_aty_ctau);
scs_free(r);
}
}
static void free_work(ScsWork *w) {
if (w) {
scs_free(w->u);
scs_free(w->u_t);
scs_free(w->v);
scs_free(w->v_prev);
scs_free(w->rsk);
scs_free(w->h);
scs_free(w->g);
scs_free(w->b_orig);
scs_free(w->c_orig);
scs_free(w->lin_sys_warm_start);
scs_free(w->diag_r);
SCS(free_sol)(w->xys_orig);
if (w->scal) {
scs_free(w->scal->D);
scs_free(w->scal->E);
scs_free(w->scal);
}
free_residuals(w->r_orig);
if (w->stgs && w->stgs->normalize) {
SCS(free_sol)(w->xys_normalized);
free_residuals(w->r_normalized);
}
if (w->stgs) {
if (w->stgs->log_csv_filename)
scs_free((char *)w->stgs->log_csv_filename);
if (w->stgs->write_data_filename)
scs_free((char *)w->stgs->write_data_filename);
scs_free(w->stgs);
}
if (w->k) { /* deep copy */
SCS(free_cone)(w->k);
}
if (w->d) { /* deep copy */
SCS(free_data)(w->d);
}
scs_free(w);
}
}
static void print_init_header(const ScsData *d, const ScsCone *k,
const ScsSettings *stgs) {
scs_int i;
char *cone_str = SCS(get_cone_header)(k);
const char *lin_sys_method = scs_get_lin_sys_method();
#ifdef USE_LAPACK
scs_int acceleration_lookback = stgs->acceleration_lookback;
scs_int acceleration_interval = stgs->acceleration_interval;
#else
scs_int acceleration_lookback = 0;
scs_int acceleration_interval = 0;
#endif
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n\t SCS v%s - Splitting Conic Solver\n\t(c) Brendan "
"O'Donoghue, Stanford University, 2012\n",
scs_version());
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n");
scs_printf("problem: variables n: %i, constraints m: %i\n", (int)d->n,
(int)d->m);
scs_printf("%s", cone_str);
scs_free(cone_str);
scs_printf("settings: eps_abs: %.1e, eps_rel: %.1e, eps_infeas: %.1e\n"
"\t alpha: %.2f, scale: %.2e, adaptive_scale: %i\n"
"\t max_iters: %i, normalize: %i, rho_x: %.2e\n",
stgs->eps_abs, stgs->eps_rel, stgs->eps_infeas, stgs->alpha,
stgs->scale, (int)stgs->adaptive_scale, (int)stgs->max_iters,
(int)stgs->normalize, stgs->rho_x);
/* (int)stgs->warm_start); */
if (stgs->acceleration_lookback != 0) {
scs_printf("\t acceleration_lookback: %i, acceleration_interval: %i\n",
(int)acceleration_lookback, (int)acceleration_interval);
}
if (stgs->time_limit_secs) {
scs_printf("\t time_limit_secs: %.2e\n", stgs->time_limit_secs);
}
if (lin_sys_method) {
scs_printf("lin-sys: %s\n\t nnz(A): %li, nnz(P): %li\n", lin_sys_method,
(long)d->A->p[d->A->n], d->P ? (long)d->P->p[d->P->n] : 0l);
}
#ifdef MATLAB_MEX_FILE
mexEvalString("drawnow;");
#endif
}
static void populate_on_failure(scs_int m, scs_int n, ScsSolution *sol,
ScsInfo *info, scs_int status_val,
const char *msg) {
if (info) {
info->gap = NAN;
info->res_pri = NAN;
info->res_dual = NAN;
info->pobj = NAN;
info->dobj = NAN;
info->iter = -1;
info->status_val = status_val;
info->solve_time = NAN;
strcpy(info->status, msg);
}
if (sol) {
if (n > 0) {
if (!sol->x) {
sol->x = (scs_float *)scs_calloc(n, sizeof(scs_float));
}
SCS(scale_array)(sol->x, NAN, n);
}
if (m > 0) {
if (!sol->y) {
sol->y = (scs_float *)scs_calloc(m, sizeof(scs_float));
}
SCS(scale_array)(sol->y, NAN, m);
if (!sol->s) {
sol->s = (scs_float *)scs_calloc(m, sizeof(scs_float));
}
SCS(scale_array)(sol->s, NAN, m);
}
}
}
static scs_int failure(ScsWork *w, scs_int m, scs_int n, ScsSolution *sol,
ScsInfo *info, scs_int stint, const char *msg,
const char *ststr) {
scs_int status = stint;
populate_on_failure(m, n, sol, info, status, ststr);
scs_printf("Failure:%s\n", msg);
scs_end_interrupt_listener();
return status;
}
static inline scs_int _is_nan(scs_float x) {
return x != x;
}
/* given x,y,s warm start, set v = [x; s / R + y; 1]
* check for nans and set to zero if present
*/
static void warm_start_vars(ScsWork *w, ScsSolution *sol) {
scs_int n = w->d->n, m = w->d->m, i;
scs_float *v = w->v;
/* normalize the warm-start */
if (w->stgs->normalize) {
SCS(normalize_sol)(w->scal, sol);
}
for (i = 0; i < n; ++i) {
v[i] = _is_nan(sol->x[i]) ? 0. : sol->x[i];
}
for (i = 0; i < m; ++i) {
v[i + n] = sol->y[i] + sol->s[i] / w->diag_r[i + n];
v[i + n] = _is_nan(v[i + n]) ? 0. : v[i + n];
}
v[n + m] = 1.0; /* tau = 1 */
/* un-normalize so sol unchanged */
if (w->stgs->normalize) {
SCS(un_normalize_sol)(w->scal, sol);
}
}
static void compute_residuals(ScsResiduals *r, scs_int m, scs_int n) {
r->res_pri = SAFEDIV_POS(NORM(r->ax_s_btau, m), r->tau);
r->res_dual = SAFEDIV_POS(NORM(r->px_aty_ctau, n), r->tau);
r->res_unbdd_a = NAN;
r->res_unbdd_p = NAN;
r->res_infeas = NAN;
if (r->ctx_tau < 0) {
r->res_unbdd_a = SAFEDIV_POS(NORM(r->ax_s, m), -r->ctx_tau);
r->res_unbdd_p = SAFEDIV_POS(NORM(r->px, n), -r->ctx_tau);
}
if (r->bty_tau < 0) {
r->res_infeas = SAFEDIV_POS(NORM(r->aty, n), -r->bty_tau);
}
}
static void unnormalize_residuals(ScsWork *w) {
ScsResiduals *r_n = w->r_normalized; /* normalized residuals */
ScsResiduals *r = w->r_orig; /* original problem residuals */
scs_float pd = w->scal->primal_scale * w->scal->dual_scale;
/* copy vars */
r->last_iter = r_n->last_iter;
r->tau = r_n->tau;
/* mem copy arrays */
memcpy(r->ax, r_n->ax, w->d->m * sizeof(scs_float));
memcpy(r->ax_s, r_n->ax_s, w->d->m * sizeof(scs_float));
memcpy(r->ax_s_btau, r_n->ax_s_btau, w->d->m * sizeof(scs_float));
memcpy(r->aty, r_n->aty, w->d->n * sizeof(scs_float));
memcpy(r->px, r_n->px, w->d->n * sizeof(scs_float));
memcpy(r->px_aty_ctau, r_n->px_aty_ctau, w->d->n * sizeof(scs_float));
/* unnormalize */
r->kap = r_n->kap / pd;
r->bty_tau = r_n->bty_tau / pd;
r->ctx_tau = r_n->ctx_tau / pd;
r->xt_p_x_tau = r_n->xt_p_x_tau / pd;
r->xt_p_x = r_n->xt_p_x / pd;
r->ctx = r_n->ctx / pd;
r->bty = r_n->bty / pd;
r->pobj = r_n->pobj / pd;
r->dobj = r_n->dobj / pd;
r->gap = r_n->gap / pd;
SCS(un_normalize_primal)(w->scal, r->ax);
SCS(un_normalize_primal)(w->scal, r->ax_s);
SCS(un_normalize_primal)(w->scal, r->ax_s_btau);
SCS(un_normalize_dual)(w->scal, r->aty);
SCS(un_normalize_dual)(w->scal, r->px);
SCS(un_normalize_dual)(w->scal, r->px_aty_ctau);
compute_residuals(r, w->d->m, w->d->n);
}
/* calculates un-normalized residual quantities */
/* this is somewhat slow but not a bottleneck */
static void populate_residual_struct(ScsWork *w, scs_int iter) {
scs_int n = w->d->n, m = w->d->m;
/* normalized x,y,s terms */
scs_float *x = w->xys_normalized->x;
scs_float *y = w->xys_normalized->y;
scs_float *s = w->xys_normalized->s;
ScsResiduals *r = w->r_normalized; /* normalized residuals */
/* checks if the residuals are unchanged by checking iteration */
if (r->last_iter == iter) {
return;
}
r->last_iter = iter;
memcpy(x, w->u, n * sizeof(scs_float));
memcpy(y, &(w->u[n]), m * sizeof(scs_float));
memcpy(s, &(w->rsk[n]), m * sizeof(scs_float));
r->tau = ABS(w->u[n + m]);
r->kap = ABS(w->rsk[n + m]);
/**************** PRIMAL *********************/
memset(r->ax, 0, m * sizeof(scs_float));
/* ax = Ax */
SCS(accum_by_a)(w->d->A, x, r->ax);
memcpy(r->ax_s, r->ax, m * sizeof(scs_float));
/* ax_s = Ax + s */
SCS(add_scaled_array)(r->ax_s, s, m, 1.);
memcpy(r->ax_s_btau, r->ax_s, m * sizeof(scs_float));
/* ax_s_btau = Ax + s - b * tau */
SCS(add_scaled_array)(r->ax_s_btau, w->d->b, m, -r->tau);
/**************** DUAL *********************/
memset(r->px, 0, n * sizeof(scs_float));
if (w->d->P) {
/* px = Px */
SCS(accum_by_p)(w->d->P, x, r->px);
r->xt_p_x_tau = SCS(dot)(r->px, x, n);
} else {
r->xt_p_x_tau = 0.;
}
memset(r->aty, 0, n * sizeof(scs_float));
/* aty = A'y */
SCS(accum_by_atrans)(w->d->A, y, r->aty);
/* r->px_aty_ctau = Px */
memcpy(r->px_aty_ctau, r->px, n * sizeof(scs_float));
/* r->px_aty_ctau = Px + A'y */
SCS(add_scaled_array)(r->px_aty_ctau, r->aty, n, 1.);
/* r->px_aty_ctau = Px + A'y + c * tau */
SCS(add_scaled_array)(r->px_aty_ctau, w->d->c, n, r->tau);
/**************** OTHERS *****************/
r->bty_tau = SCS(dot)(y, w->d->b, m);
r->ctx_tau = SCS(dot)(x, w->d->c, n);
r->bty = SAFEDIV_POS(r->bty_tau, r->tau);
r->ctx = SAFEDIV_POS(r->ctx_tau, r->tau);
r->xt_p_x = SAFEDIV_POS(r->xt_p_x_tau, r->tau * r->tau);
r->gap = ABS(r->xt_p_x + r->ctx + r->bty);
r->pobj = r->xt_p_x / 2. + r->ctx;
r->dobj = -r->xt_p_x / 2. - r->bty;
compute_residuals(r, m, n);
if (w->stgs->normalize) {
memcpy(w->xys_orig->x, w->xys_normalized->x, n * sizeof(scs_float));
memcpy(w->xys_orig->y, w->xys_normalized->y, m * sizeof(scs_float));
memcpy(w->xys_orig->s, w->xys_normalized->s, m * sizeof(scs_float));
SCS(un_normalize_sol)(w->scal, w->xys_orig);
unnormalize_residuals(w);
}
}
static void cold_start_vars(ScsWork *w) {
scs_int l = w->d->n + w->d->m + 1;
memset(w->v, 0, l * sizeof(scs_float));
w->v[l - 1] = 1.;
}
/* utility function that computes x'Ry */
static inline scs_float dot_r(ScsWork *w, const scs_float *x,
const scs_float *y) {
scs_int i;
scs_float ip = 0.0;
for (i = 0; i < w->d->n + w->d->m; ++i) {
ip += x[i] * y[i] * w->diag_r[i];
}
return ip;
}
static scs_float root_plus(ScsWork *w, scs_float *p, scs_float *mu,
scs_float eta) {
scs_float a, b, c, tau_scale = w->diag_r[w->d->n + w->d->m];
a = tau_scale + dot_r(w, w->g, w->g);
b = dot_r(w, mu, w->g) - 2 * dot_r(w, p, w->g) - eta * tau_scale;
c = dot_r(w, p, p) - dot_r(w, p, mu);
return (-b + SQRTF(MAX(b * b - 4 * a * c, 0.))) / (2 * a);
}
/* status != 0 indicates failure */
static scs_int project_lin_sys(ScsWork *w, scs_int iter) {
scs_int n = w->d->n, m = w->d->m, l = n + m + 1, status, i;
scs_float *warm_start = SCS_NULL;
scs_float tol = -1.0; /* only used for indirect methods, overridden later */
memcpy(w->u_t, w->v, l * sizeof(scs_float));
for (i = 0; i < l - 1; ++i) {
w->u_t[i] *= (i < n ? 1 : -1) * w->diag_r[i];
}
#if INDIRECT > 0
/* compute warm start using the cone projection output */
warm_start = w->lin_sys_warm_start;
memcpy(warm_start, w->u, (l - 1) * sizeof(scs_float));
/* warm_start = u[:n] + tau * g[:n] */
SCS(add_scaled_array)(warm_start, w->g, l - 1, w->u[l - 1]);
/* use normalized residuals to compute tolerance */
tol = MIN(CG_NORM(w->r_normalized->ax_s_btau, w->d->m),
CG_NORM(w->r_normalized->px_aty_ctau, w->d->n));
/* tol ~ O(1/k^(1+eps)) guarantees convergence */
/* use warm-start to calculate tolerance rather than w->u_t, since warm_start
* should be approximately equal to the true solution */
tol = CG_TOL_FACTOR * MIN(tol, CG_NORM(warm_start, w->d->n) /
POWF((scs_float)iter + 1, CG_RATE));
tol = MAX(CG_BEST_TOL, tol);
#endif
status = scs_solve_lin_sys(w->p, w->u_t, warm_start, tol);
if (iter < FEASIBLE_ITERS) {
w->u_t[l - 1] = 1.;
} else {
w->u_t[l - 1] = root_plus(w, w->u_t, w->v, w->v[l - 1]);
}
SCS(add_scaled_array)(w->u_t, w->g, l - 1, -w->u_t[l - 1]);
return status;
}
/* Compute the [r;s;kappa] iterate
*
* rsk^{k+1} = R ( u^{k+1} + v^k - 2 * u_t^{k+1} )
*
* uses Moreau decomposition to get projection onto dual cone
* since it depends on v^k MUST be called before update_dual_vars is done
* (no effect of w->stgs->alpha here).
*/
static void compute_rsk(ScsWork *w) {
scs_int i, l = w->d->m + w->d->n + 1;
for (i = 0; i < l; ++i) {
w->rsk[i] = (w->v[i] + w->u[i] - 2 * w->u_t[i]) * w->diag_r[i];
}
}
static void update_dual_vars(ScsWork *w) {
scs_int i, l = w->d->n + w->d->m + 1;
for (i = 0; i < l; ++i) {
w->v[i] += w->stgs->alpha * (w->u[i] - w->u_t[i]);
}
}
/* status < 0 indicates failure */
static scs_int project_cones(ScsWork *w, const ScsCone *k, scs_int iter) {
scs_int i, n = w->d->n, l = w->d->n + w->d->m + 1, status;
for (i = 0; i < l; ++i) {
w->u[i] = 2 * w->u_t[i] - w->v[i];
}
/* u = [x;y;tau] */
status =
SCS(proj_dual_cone)(&(w->u[n]), w->cone_work, w->scal, &(w->diag_r[n]));
if (iter < FEASIBLE_ITERS) {
w->u[l - 1] = 1.0;
} else {
w->u[l - 1] = MAX(w->u[l - 1], 0.);
}
return status;
}
static void sety(const ScsWork *w, ScsSolution *sol) {
if (!sol->y) {
sol->y = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
}
memcpy(sol->y, &(w->u[w->d->n]), w->d->m * sizeof(scs_float));
}
/* s is contained in rsk */
static void sets(const ScsWork *w, ScsSolution *sol) {
if (!sol->s) {
sol->s = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
}
memcpy(sol->s, &(w->rsk[w->d->n]), w->d->m * sizeof(scs_float));
}
static void setx(const ScsWork *w, ScsSolution *sol) {
if (!sol->x) {
sol->x = (scs_float *)scs_calloc(w->d->n, sizeof(scs_float));
}
memcpy(sol->x, w->u, w->d->n * sizeof(scs_float));
}
static void set_solved(const ScsWork *w, ScsSolution *sol, ScsInfo *info) {
SCS(scale_array)(sol->x, SAFEDIV_POS(1.0, w->r_orig->tau), w->d->n);
SCS(scale_array)(sol->y, SAFEDIV_POS(1.0, w->r_orig->tau), w->d->m);
SCS(scale_array)(sol->s, SAFEDIV_POS(1.0, w->r_orig->tau), w->d->m);
info->gap = w->r_orig->gap;
info->res_pri = w->r_orig->res_pri;
info->res_dual = w->r_orig->res_dual;
info->pobj = w->r_orig->xt_p_x / 2. + w->r_orig->ctx;
info->dobj = -w->r_orig->xt_p_x / 2. - w->r_orig->bty;
strcpy(info->status, "solved");
info->status_val = SCS_SOLVED;
}
static void set_infeasible(const ScsWork *w, ScsSolution *sol, ScsInfo *info) {
SCS(scale_array)(sol->y, -1 / w->r_orig->bty_tau, w->d->m);
SCS(scale_array)(sol->x, NAN, w->d->n);
SCS(scale_array)(sol->s, NAN, w->d->m);
info->gap = NAN;
info->res_pri = NAN;
info->res_dual = NAN;
info->pobj = INFINITY;
info->dobj = INFINITY;
strcpy(info->status, "infeasible");
info->status_val = SCS_INFEASIBLE;
}
static void set_unbounded(const ScsWork *w, ScsSolution *sol, ScsInfo *info) {
SCS(scale_array)(sol->x, -1 / w->r_orig->ctx_tau, w->d->n);
SCS(scale_array)(sol->s, -1 / w->r_orig->ctx_tau, w->d->m);
SCS(scale_array)(sol->y, NAN, w->d->m);
info->gap = NAN;
info->res_pri = NAN;
info->res_dual = NAN;
info->pobj = -INFINITY;
info->dobj = -INFINITY;
strcpy(info->status, "unbounded");
info->status_val = SCS_UNBOUNDED;
}
/* not yet converged, take best guess */
static void set_unfinished(const ScsWork *w, ScsSolution *sol, ScsInfo *info) {
if (w->r_orig->tau > w->r_orig->kap) {
set_solved(w, sol, info);
info->status_val = SCS_SOLVED_INACCURATE;
} else if (w->r_orig->bty_tau < w->r_orig->ctx_tau) {
set_infeasible(w, sol, info);
info->status_val = SCS_INFEASIBLE_INACCURATE;
} else {
set_unbounded(w, sol, info);
info->status_val = SCS_UNBOUNDED_INACCURATE;
}
/* Append inaccurate to the status string */
if (w->time_limit_reached) {
strcat(info->status, " (inaccurate - reached time_limit_secs)");
} else if (info->iter >= w->stgs->max_iters) {
strcat(info->status, " (inaccurate - reached max_iters)");
} else {
scs_printf("ERROR: should not be in this state (1).\n");
}
}
/* sets solutions, re-scales by inner prods if infeasible or unbounded */
static void finalize(ScsWork *w, ScsSolution *sol, ScsInfo *info,
scs_int iter) {
setx(w, sol);
sety(w, sol);
sets(w, sol);
if (w->stgs->normalize) {
SCS(un_normalize_sol)(w->scal, sol);
}
populate_residual_struct(w, iter);
info->setup_time = w->setup_time;
info->iter = iter;
info->res_infeas = w->r_orig->res_infeas;
info->res_unbdd_a = w->r_orig->res_unbdd_a;
info->res_unbdd_p = w->r_orig->res_unbdd_p;
info->scale = w->stgs->scale;
info->scale_updates = w->scale_updates;
info->rejected_accel_steps = w->rejected_accel_steps;
info->accepted_accel_steps = w->accepted_accel_steps;
info->comp_slack = ABS(SCS(dot)(sol->s, sol->y, w->d->m));
if (info->comp_slack > 1e-5 * MAX(SCS(norm_inf)(sol->s, w->d->m),
SCS(norm_inf)(sol->y, w->d->m))) {
scs_printf("WARNING - large complementary slackness residual: %f\n",
info->comp_slack);
}
switch (info->status_val) {
case SCS_SOLVED:
set_solved(w, sol, info);
break;
case SCS_INFEASIBLE:
set_infeasible(w, sol, info);
break;
case SCS_UNBOUNDED:
set_unbounded(w, sol, info);
break;
case SCS_UNFINISHED: /* When SCS reaches max_iters or time_limit_secs */
set_unfinished(w, sol, info);
break;
default:
scs_printf("ERROR: should not be in this state (2).\n");
}
}
static void print_summary(ScsWork *w, scs_int i, SCS(timer) * solve_timer) {
ScsResiduals *r = w->r_orig;
scs_printf("%*i|", (int)strlen(HEADER[0]), (int)i);
scs_printf("%*.2e ", (int)HSPACE, r->res_pri);
scs_printf("%*.2e ", (int)HSPACE, r->res_dual);
scs_printf("%*.2e ", (int)HSPACE, r->gap);
/* report mid point of primal and dual objective values */
scs_printf("%*.2e ", (int)HSPACE, 0.5 * (r->pobj + r->dobj));
scs_printf("%*.2e ", (int)HSPACE, w->stgs->scale);
/* Report TOTAL time, including setup */
scs_printf("%*.2e ", (int)HSPACE,
(SCS(tocq)(solve_timer) + w->setup_time) / 1e3);
scs_printf("\n");
#if VERBOSITY > 0
scs_printf("Norm u = %4f, ", SCS(norm_2)(w->u, w->d->n + w->d->m + 1));
scs_printf("Norm u_t = %4f, ", SCS(norm_2)(w->u_t, w->d->n + w->d->m + 1));
scs_printf("Norm v = %4f, ", SCS(norm_2)(w->v, w->d->n + w->d->m + 1));
scs_printf("Norm rsk = %4f, ", SCS(norm_2)(w->rsk, w->d->n + w->d->m + 1));
scs_printf("Norm x = %4f, ", SCS(norm_2)(w->xys_orig->x, w->d->n));
scs_printf("Norm y = %4f, ", SCS(norm_2)(w->xys_orig->y, w->d->m));
scs_printf("Norm s = %4f, ", SCS(norm_2)(w->xys_orig->s, w->d->m));
scs_printf("Norm |Ax + s| = %1.2e, ", SCS(norm_2)(r->ax_s, w->d->m));
scs_printf("tau = %4f, ", w->u[w->d->n + w->d->m]);
scs_printf("kappa = %4f, ", w->rsk[w->d->n + w->d->m]);
scs_printf("|u - u_t| = %1.2e, ",
SCS(norm_diff)(w->u, w->u_t, w->d->n + w->d->m + 1));
scs_printf("res_infeas = %1.2e, ", r->res_infeas);
scs_printf("res_unbdd_a = %1.2e, ", r->res_unbdd_a);
scs_printf("res_unbdd_p = %1.2e, ", r->res_unbdd_p);
scs_printf("ctx_tau = %1.2e, ", r->ctx_tau);
scs_printf("bty_tau = %1.2e\n", r->bty_tau);
#endif
#ifdef MATLAB_MEX_FILE
mexEvalString("drawnow;");
#endif
}
static void print_header(ScsWork *w, const ScsCone *k) {
scs_int i;
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n");
for (i = 0; i < HEADER_LEN - 1; ++i) {
scs_printf("%s|", HEADER[i]);
}
scs_printf("%s\n", HEADER[HEADER_LEN - 1]);
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n");
#ifdef MATLAB_MEX_FILE
mexEvalString("drawnow;");
#endif
}
static void print_footer(ScsInfo *info) {
scs_int i;
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n");
scs_printf("status: %s\n", info->status);
scs_printf("timings: total: %1.2es = setup: %1.2es + solve: %1.2es\n",
(info->setup_time + info->solve_time) / 1e3,
info->setup_time / 1e3, info->solve_time / 1e3);
scs_printf("\t lin-sys: %1.2es, cones: %1.2es, accel: %1.2es\n",
info->lin_sys_time / 1e3, info->cone_time / 1e3,
info->accel_time / 1e3);
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n");
/* report mid point of primal and dual objective values */
scs_printf("objective = %.6f", 0.5 * (info->pobj + info->dobj));
switch (info->status_val) {
case SCS_SOLVED_INACCURATE:
case SCS_UNBOUNDED_INACCURATE:
case SCS_INFEASIBLE_INACCURATE:
scs_printf(" (inaccurate)");
default:
scs_printf("\n");
}
for (i = 0; i < LINE_LEN; ++i) {
scs_printf("-");
}
scs_printf("\n");
#ifdef MATLAB_MEX_FILE
mexEvalString("drawnow;");
#endif
}
static scs_int has_converged(ScsWork *w, scs_int iter) {
scs_float eps_abs = w->stgs->eps_abs;
scs_float eps_rel = w->stgs->eps_rel;
scs_float eps_infeas = w->stgs->eps_infeas;
scs_float grl, prl, drl;
ScsResiduals *r = w->r_orig;
scs_float *b = w->b_orig;
scs_float *c = w->c_orig;
scs_float *s = w->xys_orig->s;
if (r->tau > 0.) {
/* xt_p_x, ctx, bty already have tau divided out */
grl = MAX(MAX(ABS(r->xt_p_x), ABS(r->ctx)), ABS(r->bty));
/* s, ax, px, aty do *not* have tau divided out, so need to divide */
prl = MAX(MAX(NORM(b, w->d->m) * r->tau, NORM(s, w->d->m)),
NORM(r->ax, w->d->m)) /
r->tau;
drl = MAX(MAX(NORM(c, w->d->n) * r->tau, NORM(r->px, w->d->n)),
NORM(r->aty, w->d->n)) /
r->tau;
if (isless(r->res_pri, eps_abs + eps_rel * prl) &&
isless(r->res_dual, eps_abs + eps_rel * drl) &&
isless(r->gap, eps_abs + eps_rel * grl)) {
return SCS_SOLVED;
}
}
if (isless(r->res_unbdd_a, eps_infeas) &&
isless(r->res_unbdd_p, eps_infeas)) {
return SCS_UNBOUNDED;
}
if (isless(r->res_infeas, eps_infeas)) {
return SCS_INFEASIBLE;
}
return 0;
}
#if NO_VALIDATE == 0
static scs_int validate(const ScsData *d, const ScsCone *k,
const ScsSettings *stgs) {
if (d->m <= 0 || d->n <= 0) {
scs_printf("m and n must both be greater than 0; m = %li, n = %li\n",
(long)d->m, (long)d->n);
return -1;
}
if (d->m < d->n) {
/* scs_printf("WARN: m less than n, problem likely degenerate\n"); */
/* return -1; */
}
if (SCS(validate_lin_sys)(d->A, d->P) < 0) {
scs_printf("invalid linear system input data\n");
return -1;
}
if (SCS(validate_cones)(d, k) < 0) {
scs_printf("cone validation error\n");
return -1;
}
if (stgs->max_iters <= 0) {
scs_printf("max_iters must be positive\n");
return -1;
}
if (stgs->eps_abs < 0) {
scs_printf("eps_abs tolerance must be positive\n");
return -1;
}
if (stgs->eps_rel < 0) {
scs_printf("eps_rel tolerance must be positive\n");
return -1;
}
if (stgs->eps_infeas < 0) {
scs_printf("eps_infeas tolerance must be positive\n");
return -1;
}
if (stgs->alpha <= 0 || stgs->alpha >= 2) {
scs_printf("alpha must be in (0,2)\n");
return -1;
}
if (stgs->rho_x <= 0) {
scs_printf("rho_x must be positive (1e-3 works well).\n");
return -1;
}
if (stgs->scale <= 0) {
scs_printf("scale must be positive (1 works well).\n");
return -1;
}
if (stgs->acceleration_interval <= 0) {
scs_printf("acceleration_interval must be positive (10 works well).\n");
return -1;
}
return 0;
}
#endif
static ScsResiduals *init_residuals(const ScsData *d) {
ScsResiduals *r = (ScsResiduals *)scs_calloc(1, sizeof(ScsResiduals));
r->ax = (scs_float *)scs_calloc(d->m, sizeof(scs_float));
r->ax_s = (scs_float *)scs_calloc(d->m, sizeof(scs_float));
r->ax_s_btau = (scs_float *)scs_calloc(d->m, sizeof(scs_float));
r->px = (scs_float *)scs_calloc(d->n, sizeof(scs_float));
r->aty = (scs_float *)scs_calloc(d->n, sizeof(scs_float));
r->px_aty_ctau = (scs_float *)scs_calloc(d->n, sizeof(scs_float));
return r;
}
scs_int scs_update(ScsWork *w, scs_float *b, scs_float *c) {
SCS(timer) update_timer;
SCS(tic)(&update_timer);
if (b) {
memcpy(w->b_orig, b, w->d->m * sizeof(scs_float));
memcpy(w->d->b, b, w->d->m * sizeof(scs_float));
} else {
memcpy(w->d->b, w->b_orig, w->d->m * sizeof(scs_float));
}
if (c) {
memcpy(w->c_orig, c, w->d->n * sizeof(scs_float));
memcpy(w->d->c, c, w->d->n * sizeof(scs_float));
} else {
memcpy(w->d->c, w->c_orig, w->d->n * sizeof(scs_float));
}
/* normalize */
if (w->scal) {
SCS(normalize_b_c)(w->scal, w->d->b, w->d->c);
}
/* override setup time with update time, since the update is the 'setup' */
w->setup_time = SCS(tocq)(&update_timer);
return 0;
}
/* Sets the diag_r vector, given the scale parameters in work */
static void set_diag_r(ScsWork *w) {
scs_int i;
for (i = 0; i < w->d->n; ++i) {
w->diag_r[i] = w->stgs->rho_x;
}
/* use cone information to set R_y */
SCS(set_r_y)(w->cone_work, w->stgs->scale, &(w->diag_r[w->d->n]));
/* if modified need to SCS(enforce_cone_boundaries)(...) */
w->diag_r[w->d->n + w->d->m] =
TAU_FACTOR; /* TODO: is this the best choice? */
}
static ScsWork *init_work(const ScsData *d, const ScsCone *k,
const ScsSettings *stgs) {
ScsWork *w = (ScsWork *)scs_calloc(1, sizeof(ScsWork));
scs_int l = d->n + d->m + 1;
if (stgs->verbose) {
print_init_header(d, k, stgs);
}
if (!w) {
scs_printf("ERROR: allocating work failure\n");
return SCS_NULL;
}
/* deep copy data */
w->d = (ScsData *)scs_calloc(1, sizeof(ScsData));
SCS(deep_copy_data)(w->d, d);
d = SCS_NULL; /* for safety */
/* deep copy cone */
w->k = (ScsCone *)scs_calloc(1, sizeof(ScsCone));
SCS(deep_copy_cone)(w->k, k);
k = SCS_NULL; /* for safety */
/* deep copy settings */
w->stgs = (ScsSettings *)scs_calloc(1, sizeof(ScsSettings));
SCS(deep_copy_stgs)(w->stgs, stgs);
stgs = SCS_NULL; /* for safety */
/* allocate workspace: */
w->u = (scs_float *)scs_calloc(l, sizeof(scs_float));
w->u_t = (scs_float *)scs_calloc(l, sizeof(scs_float));
w->v = (scs_float *)scs_calloc(l, sizeof(scs_float));
w->v_prev = (scs_float *)scs_calloc(l, sizeof(scs_float));
w->rsk = (scs_float *)scs_calloc(l, sizeof(scs_float));
w->h = (scs_float *)scs_calloc((l - 1), sizeof(scs_float));
w->g = (scs_float *)scs_calloc((l - 1), sizeof(scs_float));
w->lin_sys_warm_start = (scs_float *)scs_calloc((l - 1), sizeof(scs_float));
w->diag_r = (scs_float *)scs_calloc(l, sizeof(scs_float));
/* x,y,s struct */
w->xys_orig = (ScsSolution *)scs_calloc(1, sizeof(ScsSolution));
w->xys_orig->x = (scs_float *)scs_calloc(w->d->n, sizeof(scs_float));
w->xys_orig->s = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
w->xys_orig->y = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
w->r_orig = init_residuals(w->d);
w->b_orig = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
w->c_orig = (scs_float *)scs_calloc(w->d->n, sizeof(scs_float));
if (!w->c_orig) {
scs_printf("ERROR: work memory allocation failure\n");
return SCS_NULL;
}
if (!(w->cone_work = SCS(init_cone)(w->k, w->d->m))) {
scs_printf("ERROR: init_cone failure\n");
return SCS_NULL;
}
set_diag_r(w);
if (w->stgs->normalize) {
w->xys_normalized = (ScsSolution *)scs_calloc(1, sizeof(ScsSolution));
w->xys_normalized->x = (scs_float *)scs_calloc(w->d->n, sizeof(scs_float));
w->xys_normalized->s = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
w->xys_normalized->y = (scs_float *)scs_calloc(w->d->m, sizeof(scs_float));
w->r_normalized = init_residuals(w->d);
/* this allocates memory that must be freed */
w->scal = SCS(normalize_a_p)(w->d->P, w->d->A, w->cone_work);
} else {
w->xys_normalized = w->xys_orig;
w->r_normalized = w->r_orig;
w->scal = SCS_NULL;
}
/* set w->*_orig and performs normalization if appropriate */
scs_update(w, w->d->b, w->d->c);
if (!(w->p = scs_init_lin_sys_work(w->d->A, w->d->P, w->diag_r))) {
scs_printf("ERROR: init_lin_sys_work failure\n");
return SCS_NULL;
}
if (w->stgs->acceleration_lookback) {
/* TODO(HACK!) negative acceleration_lookback interpreted as type-II */
if (!(w->accel = aa_init(l, ABS(w->stgs->acceleration_lookback),
w->stgs->acceleration_lookback > 0,
w->stgs->acceleration_lookback > 0
? AA_REGULARIZATION_TYPE_1
: AA_REGULARIZATION_TYPE_2,
AA_RELAXATION, AA_SAFEGUARD_FACTOR,
AA_MAX_WEIGHT_NORM, VERBOSITY))) {
if (w->stgs->verbose) {
scs_printf("WARN: aa_init returned NULL, no acceleration applied.\n");
}
}
} else {
w->accel = SCS_NULL;
}
return w;
}
static void update_work_cache(ScsWork *w) {
/* g = (I + M)^{-1} h */
memcpy(w->g, w->h, (w->d->n + w->d->m) * sizeof(scs_float));
SCS(scale_array)(&(w->g[w->d->n]), -1., w->d->m);
scs_solve_lin_sys(w->p, w->g, SCS_NULL, CG_BEST_TOL);
return;
}
/* Reset quantities specific to current solve */
static void reset_tracking(ScsWork *w) {
w->last_scale_update_iter = 0;
w->sum_log_scale_factor = 0.;
w->n_log_scale_factor = 0;
w->scale_updates = 0;
w->time_limit_reached = 0;
/* Acceleration */
w->rejected_accel_steps = 0;
w->accepted_accel_steps = 0;
w->aa_norm = 0.;
/* Need this to force residual calc if previous solve solved at iter 0 */
w->r_normalized->last_iter = -1;
w->r_orig->last_iter = -1;
}
static scs_int update_work(ScsWork *w, ScsSolution *sol) {
reset_tracking(w);
if (w->stgs->warm_start) {
warm_start_vars(w, sol);
} else {
cold_start_vars(w);
}
/* h = [c;b] */
memcpy(w->h, w->d->c, w->d->n * sizeof(scs_float));
memcpy(&(w->h[w->d->n]), w->d->b, w->d->m * sizeof(scs_float));
update_work_cache(w);
return 0;
}
/* will update if the factor is outside of range */
scs_int should_update_r(scs_float factor, scs_int iter) {
return (factor > SQRTF(10.) || factor < 1. / SQRTF(10.));
}
static void update_scale(ScsWork *w, const ScsCone *k, scs_int iter) {
scs_int i;
scs_float factor, new_scale;
ScsResiduals *r = w->r_orig;
ScsSolution *xys = w->xys_orig;
scs_float *b = w->b_orig;
scs_float *c = w->c_orig;
scs_int iters_since_last_update = iter - w->last_scale_update_iter;
/* ||Ax + s - b * tau|| */
scs_float relative_res_pri = SAFEDIV_POS(
SCALE_NORM(r->ax_s_btau, w->d->m),
MAX(MAX(SCALE_NORM(r->ax, w->d->m), SCALE_NORM(xys->s, w->d->m)),
SCALE_NORM(b, w->d->m) * r->tau));
/* ||Px + A'y + c * tau|| */
scs_float relative_res_dual = SAFEDIV_POS(
SCALE_NORM(r->px_aty_ctau, w->d->n),
MAX(MAX(SCALE_NORM(r->px, w->d->n), SCALE_NORM(r->aty, w->d->n)),
SCALE_NORM(c, w->d->n) * r->tau));
/* higher scale makes res_pri go down faster, so increase if res_pri larger */
w->sum_log_scale_factor += log(relative_res_pri) - log(relative_res_dual);
w->n_log_scale_factor++;
/* geometric mean */
factor =
SQRTF(exp(w->sum_log_scale_factor / (scs_float)(w->n_log_scale_factor)));
/* need at least RESCALING_MIN_ITERS since last update */
if (iters_since_last_update < RESCALING_MIN_ITERS) {
return;
}
new_scale =
MIN(MAX(w->stgs->scale * factor, MIN_SCALE_VALUE), MAX_SCALE_VALUE);
if (new_scale == w->stgs->scale) {
return;
}
if (should_update_r(factor, iters_since_last_update)) {
w->scale_updates++;
w->sum_log_scale_factor = 0;
w->n_log_scale_factor = 0;
w->last_scale_update_iter = iter;
w->stgs->scale = new_scale;
/* update diag r vector */
set_diag_r(w);
/* update linear systems */
scs_update_lin_sys_diag_r(w->p, w->diag_r);
/* update pre-solved quantities */
update_work_cache(w);
/* reset acceleration so that old iterates aren't affecting new values */
if (w->accel) {
aa_reset(w->accel);
}
/* update v, using fact that rsk, u, u_t vectors should be the same */
/* solve: R^+ (v^+ + u - 2u_t) = rsk = R(v + u - 2u_t)
* => v^+ = R+^-1 rsk + 2u_t - u
*/
for (i = 0; i < w->d->n + w->d->m + 1; i++) {
w->v[i] = w->rsk[i] / w->diag_r[i] + 2 * w->u_t[i] - w->u[i];