vendor/scs/src/cones.c in scs-0.2.3 vs vendor/scs/src/cones.c in scs-0.3.0
- old
+ new
@@ -1,82 +1,118 @@
#include "cones.h"
-
#include "linalg.h"
#include "scs.h"
#include "scs_blas.h" /* contains BLAS(X) macros and type info */
#include "util.h"
-#define CONE_RATE (2)
-#define CONE_TOL (1e-8)
-#define CONE_THRESH (1e-6)
+#define CONE_TOL (1e-9)
+#define CONE_THRESH (1e-8)
#define EXP_CONE_MAX_ITERS (100)
+#define BOX_CONE_MAX_ITERS (25)
#define POW_CONE_MAX_ITERS (20)
+/* In the box cone projection we penalize the `t` term additionally by this
+ * factor. This encourages the `t` term to stay close to the incoming `t` term,
+ * which should provide better convergence since typically the `t` term does
+ * not appear in the linear system other than `t = 1`. Setting to 1 is
+ * the vanilla projection.
+ */
+#define BOX_T_SCALE (1.)
+
+/* Box cone limits (+ or -) taken to be INF */
+#define MAX_BOX_VAL (1e15)
+
#ifdef USE_LAPACK
-void BLAS(syevr)(const char *jobz, const char *range, const char *uplo,
- blas_int *n, scs_float *a, blas_int *lda, scs_float *vl,
- scs_float *vu, blas_int *il, blas_int *iu, scs_float *abstol,
- blas_int *m, scs_float *w, scs_float *z, blas_int *ldz,
- blas_int *isuppz, scs_float *work, blas_int *lwork,
- blas_int *iwork, blas_int *liwork, blas_int *info);
-void BLAS(syr)(const char *uplo, const blas_int *n, const scs_float *alpha,
- const scs_float *x, const blas_int *incx, scs_float *a,
- const blas_int *lda);
+void BLAS(syev)(const char *jobz, const char *uplo, blas_int *n, scs_float *a,
+ blas_int *lda, scs_float *w, scs_float *work, blas_int *lwork,
+ blas_int *info);
+blas_int BLAS(syrk)(const char *uplo, const char *trans, const blas_int *n,
+ const blas_int *k, const scs_float *alpha,
+ const scs_float *a, const blas_int *lda,
+ const scs_float *beta, scs_float *c, const blas_int *ldc);
void BLAS(scal)(const blas_int *n, const scs_float *sa, scs_float *sx,
const blas_int *incx);
-scs_float BLAS(nrm2)(const blas_int *n, scs_float *x, const blas_int *incx);
#endif
-static scs_int get_sd_cone_size(scs_int s) { return (s * (s + 1)) / 2; }
+/* set the vector of rho y terms, based on scale and cones */
+void SCS(set_rho_y_vec)(const ScsCone *k, scs_float scale, scs_float *rho_y_vec,
+ scs_int m) {
+ scs_int i, count = 0;
+ /* f cone */
+ for (i = 0; i < k->z; ++i) {
+ /* set rho_y small for z, similar to rho_x term, since z corresponds to
+ * dual free cone, this effectively decreases penalty on those entries
+ * and lets them be determined almost entirely by the linear system solve
+ */
+ rho_y_vec[i] = 1.0 / (1000. * scale);
+ }
+ count += k->z;
+ /* others */
+ for (i = count; i < m; ++i) {
+ rho_y_vec[i] = 1.0 / scale;
+ }
+ /* Note, if updating this to use different scales for other cones (e.g. box)
+ * then you must be careful to also include the effect of the rho_y_vec
+ * in the cone projection operator.
+ */
+
+ /* Increase rho_y_vec for the t term in the box cone */
+ if (k->bsize) {
+ rho_y_vec[k->z + k->l] *= BOX_T_SCALE;
+ }
+}
+
+static inline scs_int get_sd_cone_size(scs_int s) {
+ return (s * (s + 1)) / 2;
+}
+
/*
* boundaries will contain array of indices of rows of A corresponding to
* cone boundaries, boundaries[0] is starting index for cones of size strictly
- * larger than 1
- * returns length of boundaries array, boundaries malloc-ed here so should be
- * freed
+ * larger than 1, boundaries malloc-ed here so should be freed.
*/
-scs_int SCS(get_cone_boundaries)(const ScsCone *k, scs_int **boundaries) {
- scs_int i, count = 0;
- scs_int len = 1 + k->qsize + k->ssize + k->ed + k->ep + k->psize;
- scs_int *b = (scs_int *)scs_calloc(len, sizeof(scs_int));
- b[count] = k->f + k->l;
- count += 1;
- if (k->qsize > 0) {
- memcpy(&b[count], k->q, k->qsize * sizeof(scs_int));
+scs_int SCS(set_cone_boundaries)(const ScsCone *k, scs_int **cone_boundaries) {
+ scs_int i, s_cone_sz, count = 0;
+ scs_int cone_boundaries_len =
+ 1 + k->qsize + k->ssize + k->ed + k->ep + k->psize;
+ scs_int *b = (scs_int *)scs_calloc(cone_boundaries_len, sizeof(scs_int));
+ /* cones that can be scaled independently */
+ b[count] = k->z + k->l + k->bsize;
+ count += 1; /* started at 0 now move to first entry */
+ for (i = 0; i < k->qsize; ++i) {
+ b[count + i] = k->q[i];
}
count += k->qsize;
for (i = 0; i < k->ssize; ++i) {
- b[count + i] = get_sd_cone_size(k->s[i]);
+ s_cone_sz = get_sd_cone_size(k->s[i]);
+ b[count + i] = s_cone_sz;
}
- count += k->ssize;
+ count += k->ssize; /* add ssize here not ssize * (ssize + 1) / 2 */
+ /* exp cones */
for (i = 0; i < k->ep + k->ed; ++i) {
b[count + i] = 3;
}
count += k->ep + k->ed;
+ /* power cones */
for (i = 0; i < k->psize; ++i) {
b[count + i] = 3;
}
count += k->psize;
- *boundaries = b;
- return len;
+ /* other cones */
+ *cone_boundaries = b;
+ return cone_boundaries_len;
}
static scs_int get_full_cone_dims(const ScsCone *k) {
- scs_int i, c = 0;
- if (k->f) {
- c += k->f;
- }
- if (k->l) {
- c += k->l;
- }
- if (k->qsize && k->q) {
+ scs_int i, c = k->z + k->l + k->bsize;
+ if (k->qsize) {
for (i = 0; i < k->qsize; ++i) {
c += k->q[i];
}
}
- if (k->ssize && k->s) {
+ if (k->ssize) {
for (i = 0; i < k->ssize; ++i) {
c += get_sd_cone_size(k->s[i]);
}
}
if (k->ed) {
@@ -96,53 +132,65 @@
if (get_full_cone_dims(k) != d->m) {
scs_printf("cone dimensions %li not equal to num rows in A = m = %li\n",
(long)get_full_cone_dims(k), (long)d->m);
return -1;
}
- if (k->f && k->f < 0) {
- scs_printf("free cone error\n");
+ if (k->z && k->z < 0) {
+ scs_printf("free cone dimension error\n");
return -1;
}
if (k->l && k->l < 0) {
- scs_printf("lp cone error\n");
+ scs_printf("lp cone dimension error\n");
return -1;
}
+ if (k->bsize) {
+ if (k->bsize < 0) {
+ scs_printf("box cone dimension error\n");
+ return -1;
+ }
+ for (i = 0; i < k->bsize - 1; ++i) {
+ if (k->bl[i] > k->bu[i]) {
+ scs_printf("infeasible: box lower bound larger than upper bound\n");
+ return -1;
+ }
+ }
+ }
if (k->qsize && k->q) {
if (k->qsize < 0) {
- scs_printf("soc cone error\n");
+ scs_printf("soc cone dimension error\n");
return -1;
}
for (i = 0; i < k->qsize; ++i) {
if (k->q[i] < 0) {
- scs_printf("soc cone error\n");
+ scs_printf("soc cone dimension error\n");
return -1;
}
}
}
if (k->ssize && k->s) {
if (k->ssize < 0) {
- scs_printf("sd cone error\n");
+ scs_printf("sd cone dimension error\n");
return -1;
}
for (i = 0; i < k->ssize; ++i) {
if (k->s[i] < 0) {
- scs_printf("sd cone error\n");
+ scs_printf("sd cone dimension error\n");
return -1;
}
}
}
if (k->ed && k->ed < 0) {
- scs_printf("ep cone error\n");
+ scs_printf("ep cone dimension error\n");
return -1;
}
if (k->ep && k->ep < 0) {
- scs_printf("ed cone error\n");
+ scs_printf("ed cone dimension error\n");
return -1;
}
if (k->psize && k->p) {
if (k->psize < 0) {
- scs_printf("power cone error\n");
+ scs_printf("power cone dimension error\n");
return -1;
}
for (i = 0; i < k->psize; ++i) {
if (k->p[i] < -1 || k->p[i] > 1) {
scs_printf("power cone error, values must be in [-1,1]\n");
@@ -151,18 +199,10 @@
}
}
return 0;
}
-char *SCS(get_cone_summary)(const ScsInfo *info, ScsConeWork *c) {
- char *str = (char *)scs_malloc(sizeof(char) * 64);
- sprintf(str, "\tCones: avg projection time: %1.2es\n",
- c->total_cone_time / (info->iter + 1) / 1e3);
- c->total_cone_time = 0.0;
- return str;
-}
-
void SCS(finish_cone)(ScsConeWork *c) {
#ifdef USE_LAPACK
if (c->Xs) {
scs_free(c->Xs);
}
@@ -173,135 +213,140 @@
scs_free(c->e);
}
if (c->work) {
scs_free(c->work);
}
- if (c->iwork) {
- scs_free(c->iwork);
- }
#endif
+ if (c->s) {
+ scs_free(c->s);
+ }
+ if (c->bu) {
+ scs_free(c->bu);
+ }
+ if (c->bl) {
+ scs_free(c->bl);
+ }
if (c) {
scs_free(c);
}
}
char *SCS(get_cone_header)(const ScsCone *k) {
char *tmp = (char *)scs_malloc(sizeof(char) * 512);
- scs_int i, soc_vars, soc_blks, sd_vars, sd_blks;
- sprintf(tmp, "Cones:");
- if (k->f) {
- sprintf(tmp + strlen(tmp), "\tprimal zero / dual free vars: %li\n",
- (long)k->f);
+ scs_int i, soc_vars, sd_vars;
+ sprintf(tmp, "cones: ");
+ if (k->z) {
+ sprintf(tmp + strlen(tmp), "\t z: primal zero / dual free vars: %li\n",
+ (long)k->z);
}
if (k->l) {
- sprintf(tmp + strlen(tmp), "\tlinear vars: %li\n", (long)k->l);
+ sprintf(tmp + strlen(tmp), "\t l: linear vars: %li\n", (long)k->l);
}
+ if (k->bsize) {
+ sprintf(tmp + strlen(tmp), "\t b: box cone vars: %li\n", (long)(k->bsize));
+ }
soc_vars = 0;
- soc_blks = 0;
if (k->qsize && k->q) {
- soc_blks = k->qsize;
for (i = 0; i < k->qsize; i++) {
soc_vars += k->q[i];
}
- sprintf(tmp + strlen(tmp), "\tsoc vars: %li, soc blks: %li\n",
- (long)soc_vars, (long)soc_blks);
+ sprintf(tmp + strlen(tmp), "\t q: soc vars: %li, qsize: %li\n",
+ (long)soc_vars, (long)k->qsize);
}
sd_vars = 0;
- sd_blks = 0;
if (k->ssize && k->s) {
- sd_blks = k->ssize;
for (i = 0; i < k->ssize; i++) {
sd_vars += get_sd_cone_size(k->s[i]);
}
- sprintf(tmp + strlen(tmp), "\tsd vars: %li, sd blks: %li\n", (long)sd_vars,
- (long)sd_blks);
+ sprintf(tmp + strlen(tmp), "\t s: psd vars: %li, ssize: %li\n",
+ (long)sd_vars, (long)k->ssize);
}
if (k->ep || k->ed) {
- sprintf(tmp + strlen(tmp), "\texp vars: %li, dual exp vars: %li\n",
+ sprintf(tmp + strlen(tmp), "\t e: exp vars: %li, dual exp vars: %li\n",
(long)(3 * k->ep), (long)(3 * k->ed));
}
if (k->psize && k->p) {
- sprintf(tmp + strlen(tmp), "\tprimal + dual power vars: %li\n",
+ sprintf(tmp + strlen(tmp), "\t p: primal + dual power vars: %li\n",
(long)(3 * k->psize));
}
return tmp;
}
-static scs_int is_simple_semi_definite_cone(scs_int *s, scs_int ssize) {
- scs_int i;
- for (i = 0; i < ssize; i++) {
- if (s[i] > 2) {
- return 0; /* false */
- }
- }
- return 1; /* true */
-}
-
static scs_float exp_newton_one_d(scs_float rho, scs_float y_hat,
- scs_float z_hat) {
- scs_float t = MAX(-z_hat, 1e-6);
- scs_float f, fp;
+ scs_float z_hat, scs_float w) {
+ scs_float t_prev, t = MAX(w - z_hat, MAX(-z_hat, 1e-9));
+ scs_float f = 1., fp = 1.;
scs_int i;
for (i = 0; i < EXP_CONE_MAX_ITERS; ++i) {
+ t_prev = t;
f = t * (t + z_hat) / rho / rho - y_hat / rho + log(t / rho) + 1;
fp = (2 * t + z_hat) / rho / rho + 1 / t;
t = t - f / fp;
if (t <= -z_hat) {
- return 0;
+ t = -z_hat;
+ break;
} else if (t <= 0) {
- return z_hat;
- } else if (ABS(f) < CONE_TOL) {
+ t = 0;
break;
+ } else if (ABS(t - t_prev) < CONE_TOL) {
+ break;
+ } else if (SQRTF(f * f / fp) < CONE_TOL) {
+ break;
}
}
+ if (i == EXP_CONE_MAX_ITERS) {
+ scs_printf("warning: exp cone newton step hit maximum %i iters\n", (int)i);
+ scs_printf("rho=%1.5e; y_hat=%1.5e; z_hat=%1.5e; w=%1.5e; f=%1.5e, "
+ "fp=%1.5e, t=%1.5e, t_prev= %1.5e\n",
+ rho, y_hat, z_hat, w, f, fp, t, t_prev);
+ }
return t + z_hat;
}
-static void exp_solve_for_x_with_rho(scs_float *v, scs_float *x,
- scs_float rho) {
- x[2] = exp_newton_one_d(rho, v[1], v[2]);
+static void exp_solve_for_x_with_rho(const scs_float *v, scs_float *x,
+ scs_float rho, scs_float w) {
+ x[2] = exp_newton_one_d(rho, v[1], v[2], w);
x[1] = (x[2] - v[2]) * x[2] / rho;
x[0] = v[0] - rho;
}
-static scs_float exp_calc_grad(scs_float *v, scs_float *x, scs_float rho) {
- exp_solve_for_x_with_rho(v, x, rho);
+static scs_float exp_calc_grad(const scs_float *v, scs_float *x, scs_float rho,
+ scs_float w) {
+ exp_solve_for_x_with_rho(v, x, rho, w);
if (x[1] <= 1e-12) {
return x[0];
}
return x[0] + x[1] * log(x[1] / x[2]);
}
-static void exp_get_rho_ub(scs_float *v, scs_float *x, scs_float *ub,
+static void exp_get_rho_ub(const scs_float *v, scs_float *x, scs_float *ub,
scs_float *lb) {
*lb = 0;
*ub = 0.125;
- while (exp_calc_grad(v, x, *ub) > 0) {
+ while (exp_calc_grad(v, x, *ub, v[1]) > 0) {
*lb = *ub;
(*ub) *= 2;
}
}
/* project onto the exponential cone, v has dimension *exactly* 3 */
static scs_int proj_exp_cone(scs_float *v) {
scs_int i;
scs_float ub, lb, rho, g, x[3];
scs_float r = v[0], s = v[1], t = v[2];
- scs_float tol = CONE_TOL; /* iter < 0 ? CONE_TOL : MAX(CONE_TOL, 1 /
- POWF((iter + 1), CONE_RATE)); */
/* v in cl(Kexp) */
if ((s * exp(r / s) - t <= CONE_THRESH && s > 0) ||
(r <= 0 && s == 0 && t >= 0)) {
return 0;
}
/* -v in Kexp^* */
- if ((-r < 0 && r * exp(s / r) + exp(1) * t <= CONE_THRESH) ||
- (-r == 0 && -s >= 0 && -t >= 0)) {
+ if ((r > 0 && r * exp(s / r) + exp(1) * t <= CONE_THRESH) ||
+ (r == 0 && s <= 0 && t <= 0)) {
memset(v, 0, 3 * sizeof(scs_float));
return 0;
}
/* special case with analytical solution */
@@ -312,42 +357,42 @@
}
/* iterative procedure to find projection, bisects on dual variable: */
exp_get_rho_ub(v, x, &ub, &lb); /* get starting upper and lower bounds */
for (i = 0; i < EXP_CONE_MAX_ITERS; ++i) {
- rho = (ub + lb) / 2; /* halfway between upper and lower bounds */
- g = exp_calc_grad(v, x, rho); /* calculates gradient wrt dual var */
+ rho = (ub + lb) / 2; /* halfway between upper and lower bounds */
+ g = exp_calc_grad(v, x, rho, x[1]); /* calculates gradient wrt dual var */
if (g > 0) {
lb = rho;
} else {
ub = rho;
}
- if (ub - lb < tol) {
+ if (ub - lb < CONE_TOL) {
break;
}
}
- /*
-#if EXTRA_VERBOSE > 0
- scs_printf("exponential cone proj iters %i\n", i);
+#if VERBOSITY > 10
+ scs_printf("exponential cone proj iters %i\n", (int)i);
#endif
- */
+ if (i == EXP_CONE_MAX_ITERS) {
+ scs_printf("warning: exp cone outer step hit maximum %i iters\n", (int)i);
+ scs_printf("r=%1.5e; s=%1.5e; t=%1.5e\n", r, s, t);
+ }
v[0] = x[0];
v[1] = x[1];
v[2] = x[2];
return 0;
}
static scs_int set_up_sd_cone_work_space(ScsConeWork *c, const ScsCone *k) {
-#ifdef USE_LAPACK
scs_int i;
+#ifdef USE_LAPACK
blas_int n_max = 0;
- scs_float eig_tol = 1e-8;
blas_int neg_one = -1;
- blas_int m = 0;
blas_int info = 0;
scs_float wkopt = 0.0;
-#if EXTRA_VERBOSE > 0
+#if VERBOSITY > 0
#define _STR_EXPAND(tok) #tok
#define _STR(tok) _STR_EXPAND(tok)
scs_printf("BLAS(func) = '%s'\n", _STR(BLAS(func)));
#endif
/* eigenvector decomp workspace */
@@ -357,152 +402,76 @@
}
}
c->Xs = (scs_float *)scs_calloc(n_max * n_max, sizeof(scs_float));
c->Z = (scs_float *)scs_calloc(n_max * n_max, sizeof(scs_float));
c->e = (scs_float *)scs_calloc(n_max, sizeof(scs_float));
- c->liwork = 0;
- BLAS(syevr)
- ("Vectors", "All", "Lower", &n_max, c->Xs, &n_max, SCS_NULL, SCS_NULL,
- SCS_NULL, SCS_NULL, &eig_tol, &m, c->e, c->Z, &n_max, SCS_NULL, &wkopt,
- &neg_one, &(c->liwork), &neg_one, &info);
+ /* workspace query */
+ BLAS(syev)
+ ("Vectors", "Lower", &n_max, c->Xs, &n_max, SCS_NULL, &wkopt, &neg_one,
+ &info);
if (info != 0) {
- scs_printf("FATAL: syevr failure, info = %li\n", (long)info);
+ scs_printf("FATAL: syev failure, info = %li\n", (long)info);
return -1;
}
- c->lwork = (blas_int)(wkopt + 0.01); /* 0.01 for int casting safety */
+ c->lwork = (blas_int)(wkopt + 1); /* +1 for int casting safety */
c->work = (scs_float *)scs_calloc(c->lwork, sizeof(scs_float));
- c->iwork = (blas_int *)scs_calloc(c->liwork, sizeof(blas_int));
- if (!c->Xs || !c->Z || !c->e || !c->work || !c->iwork) {
+ if (!c->Xs || !c->Z || !c->e || !c->work) {
return -1;
}
return 0;
#else
- scs_printf(
- "FATAL: Cannot solve SDPs with > 2x2 matrices without linked "
- "blas+lapack libraries\n");
- scs_printf(
- "Install blas+lapack and re-compile SCS with blas+lapack library "
- "locations\n");
- return -1;
-#endif
-}
-
-ScsConeWork *SCS(init_cone)(const ScsCone *k) {
- ScsConeWork *c = (ScsConeWork *)scs_calloc(1, sizeof(ScsConeWork));
-#if EXTRA_VERBOSE > 0
- scs_printf("init_cone\n");
-#endif
- c->total_cone_time = 0.0;
- if (k->ssize && k->s) {
- if (!is_simple_semi_definite_cone(k->s, k->ssize) &&
- set_up_sd_cone_work_space(c, k) < 0) {
- SCS(finish_cone)(c);
- return SCS_NULL;
+ for (i = 0; i < k->ssize; i++) {
+ if (k->s[i] > 1) {
+ scs_printf(
+ "FATAL: Cannot solve SDPs without linked blas+lapack libraries\n");
+ scs_printf(
+ "Install blas+lapack and re-compile SCS with blas+lapack library "
+ "locations\n");
+ return -1;
}
}
-#if EXTRA_VERBOSE > 0
- scs_printf("init_cone complete\n");
-#ifdef MATLAB_MEX_FILE
- mexEvalString("drawnow;");
+ return 0;
#endif
-#endif
- return c;
}
-static scs_int project_2x2_sdc(scs_float *X) {
- scs_float a, b, d, l1, l2, x1, x2, rad;
- scs_float sqrt2 = SQRTF(2.0);
- a = X[0];
- b = X[1] / sqrt2;
- d = X[2];
-
- if (ABS(b) < 1e-6) { /* diagonal matrix */
- X[0] = MAX(a, 0);
- X[1] = 0;
- X[2] = MAX(d, 0);
- return 0;
- }
-
- rad = SQRTF((a - d) * (a - d) + 4 * b * b);
- /* l1 >= l2 always, since rad >= 0 */
- l1 = 0.5 * (a + d + rad);
- l2 = 0.5 * (a + d - rad);
-
-#if EXTRA_VERBOSE > 0
- scs_printf(
- "2x2 SD: a = %4f, b = %4f, (X[1] = %4f, X[2] = %4f), d = %4f, "
- "rad = %4f, l1 = %4f, l2 = %4f\n",
- a, b, X[1], X[2], d, rad, l1, l2);
-#endif
-
- if (l2 >= 0) { /* both eigs positive already */
- return 0;
- }
- if (l1 <= 0) { /* both eigs negative, set to 0 */
- X[0] = 0;
- X[1] = 0;
- X[2] = 0;
- return 0;
- }
-
- /* l1 pos, l2 neg */
- x1 = 1 / SQRTF(1 + (l1 - a) * (l1 - a) / b / b);
- x2 = x1 * (l1 - a) / b;
-
- X[0] = l1 * x1 * x1;
- X[1] = (l1 * x1 * x2) * sqrt2;
- X[2] = l1 * x2 * x2;
- return 0;
-}
-
/* size of X is get_sd_cone_size(n) */
static scs_int proj_semi_definite_cone(scs_float *X, const scs_int n,
ScsConeWork *c) {
/* project onto the positive semi-definite cone */
#ifdef USE_LAPACK
- scs_int i;
- blas_int one = 1;
- blas_int m = 0;
+ scs_int i, first_idx;
blas_int nb = (blas_int)n;
+ blas_int ncols_z;
blas_int nb_plus_one = (blas_int)(n + 1);
- blas_int cone_sz = (blas_int)(get_sd_cone_size(n));
-
+ blas_int one_int = 1;
+ scs_float zero = 0., one = 1.;
scs_float sqrt2 = SQRTF(2.0);
- scs_float sqrt2Inv = 1.0 / sqrt2;
+ scs_float sqrt2_inv = 1.0 / sqrt2;
scs_float *Xs = c->Xs;
scs_float *Z = c->Z;
scs_float *e = c->e;
scs_float *work = c->work;
- blas_int *iwork = c->iwork;
blas_int lwork = c->lwork;
- blas_int liwork = c->liwork;
-
- scs_float eig_tol = CONE_TOL; /* iter < 0 ? CONE_TOL : MAX(CONE_TOL, 1 /
- POWF(iter + 1, CONE_RATE)); */
- scs_float zero = 0.0;
blas_int info = 0;
- scs_float vupper = 0.0;
+ scs_float sq_eig_pos;
+
#endif
+
if (n == 0) {
return 0;
}
if (n == 1) {
- if (X[0] < 0.0) {
- X[0] = 0.0;
- }
+ X[0] = MAX(X[0], 0.);
return 0;
}
- if (n == 2) {
- return project_2x2_sdc(X);
- }
+
#ifdef USE_LAPACK
- memset(Xs, 0, n * n * sizeof(scs_float));
- /* expand lower triangular matrix to full matrix */
+ /* copy lower triangular matrix into full matrix */
for (i = 0; i < n; ++i) {
memcpy(&(Xs[i * (n + 1)]), &(X[i * n - ((i - 1) * i) / 2]),
(n - i) * sizeof(scs_float));
}
/*
@@ -510,68 +479,63 @@
see http://www.seas.ucla.edu/~vandenbe/publications/mlbook.pdf pg 3
*/
/* scale diags by sqrt(2) */
BLAS(scal)(&nb, &sqrt2, Xs, &nb_plus_one); /* not n_squared */
- /* max-eig upper bounded by frobenius norm */
- vupper = 1.1 * sqrt2 *
- BLAS(nrm2)(&cone_sz, X,
- &one); /* mult by factor to make sure is upper bound */
- vupper = MAX(vupper, 0.01);
-#if EXTRA_VERBOSE > 0
- SCS(print_array)(Xs, n * n, "Xs");
- SCS(print_array)(X, get_sd_cone_size(n), "X");
-#endif
/* Solve eigenproblem, reuse workspaces */
- BLAS(syevr)
- ("Vectors", "VInterval", "Lower", &nb, Xs, &nb, &zero, &vupper, SCS_NULL,
- SCS_NULL, &eig_tol, &m, e, Z, &nb, SCS_NULL, work, &lwork, iwork, &liwork,
- &info);
-#if EXTRA_VERBOSE > 0
+ BLAS(syev)("Vectors", "Lower", &nb, Xs, &nb, e, work, &lwork, &info);
if (info != 0) {
- scs_printf("WARN: LAPACK syevr error, info = %i\n", info);
+ scs_printf("WARN: LAPACK syev error, info = %i\n", info);
+ if (info < 0) {
+ return info;
+ }
}
- scs_printf("syevr input parameter dump:\n");
- scs_printf("nb = %li\n", (long)nb);
- scs_printf("lwork = %li\n", (long)lwork);
- scs_printf("liwork = %li\n", (long)liwork);
- scs_printf("vupper = %f\n", vupper);
- scs_printf("eig_tol = %e\n", eig_tol);
- SCS(print_array)(e, m, "e");
- SCS(print_array)(Z, m * n, "Z");
-#endif
- if (info < 0) {
- return -1;
+
+ first_idx = -1;
+ /* e is eigvals in ascending order, find first entry > 0 */
+ for (i = 0; i < n; ++i) {
+ if (e[i] > 0) {
+ first_idx = i;
+ break;
+ }
}
- memset(Xs, 0, n * n * sizeof(scs_float));
- for (i = 0; i < m; ++i) {
- scs_float a = e[i];
- BLAS(syr)("Lower", &nb, &a, &(Z[i * n]), &one, Xs, &nb);
+ if (first_idx == -1) {
+ /* there are no positive eigenvalues, set X to 0 and return */
+ memset(X, 0, sizeof(scs_float) * get_sd_cone_size(n));
+ return 0;
}
- /* scale diags by 1/sqrt(2) */
- BLAS(scal)(&nb, &sqrt2Inv, Xs, &nb_plus_one); /* not n_squared */
+
+ /* Z is matrix of eigenvectors with positive eigenvalues */
+ memcpy(Z, &Xs[first_idx * n], sizeof(scs_float) * n * (n - first_idx));
+
+ /* scale Z by sqrt(eig) */
+ for (i = first_idx; i < n; ++i) {
+ sq_eig_pos = SQRTF(e[i]);
+ BLAS(scal)(&nb, &sq_eig_pos, &Z[(i - first_idx) * n], &one_int);
+ }
+
+ /* Xs = Z Z' = V E V' */
+ ncols_z = (blas_int)(n - first_idx);
+ BLAS(syrk)("Lower", "NoTrans", &nb, &ncols_z, &one, Z, &nb, &zero, Xs, &nb);
+
+ /* undo rescaling: scale diags by 1/sqrt(2) */
+ BLAS(scal)(&nb, &sqrt2_inv, Xs, &nb_plus_one); /* not n_squared */
+
/* extract just lower triangular matrix */
for (i = 0; i < n; ++i) {
memcpy(&(X[i * n - ((i - 1) * i) / 2]), &(Xs[i * (n + 1)]),
(n - i) * sizeof(scs_float));
}
+ return 0;
-#if EXTRA_VERBOSE > 0
- SCS(print_array)(Xs, n * n, "Xs");
- SCS(print_array)(X, get_sd_cone_size(n), "X");
-#endif
-
#else
- scs_printf(
- "FAILURE: solving SDP with > 2x2 matrices, but no blas/lapack "
- "libraries were linked!\n");
+ scs_printf("FAILURE: solving SDP but no blas/lapack libraries were found!\n");
scs_printf("SCS will return nonsense!\n");
SCS(scale_array)(X, NAN, n);
return -1;
#endif
- return 0;
}
static scs_float pow_calc_x(scs_float r, scs_float xh, scs_float rh,
scs_float a) {
scs_float x = 0.5 * (xh + SQRTF(xh * xh + 4 * a * (rh - r) * r));
@@ -592,10 +556,128 @@
scs_float dydr, scs_float a) {
return POWF(x, a) * POWF(y, (1 - a)) * (a * dxdr / x + (1 - a) * dydr / y) -
1;
}
+/*
+ * Routine to scale the limits of the box cone by the scaling diagonal mat D > 0
+ *
+ * want (t, s) \in K <==> (t', s') \in K'
+ *
+ * (t', s') = (d0 * t, D s) (overloading D to mean D[1:])
+ * (up to scalar scaling factor which we can ignore due to conic prooperty)
+ *
+ * K = { (t, s) | t * l <= s <= t * u, t >= 0 } =>
+ * { (t, s) | d0 * t * D l / d0 <= D s <= d0 * t D u / d0, t >= 0 } =>
+ * { (t', s') | t' * l' <= s' <= t' u', t >= 0 } = K'
+ * where l' = D l / d0, u' = D u / d0.
+ */
+static void normalize_box_cone(ScsConeWork *c, scs_float *D, scs_int bsize) {
+ scs_int j;
+ for (j = 0; j < bsize - 1; j++) {
+ if (c->bu[j] >= MAX_BOX_VAL) {
+ c->bu[j] = INFINITY;
+ } else {
+ c->bu[j] = D ? D[j + 1] * c->bu[j] / D[0] : c->bu[j];
+ }
+ if (c->bl[j] <= -MAX_BOX_VAL) {
+ c->bl[j] = -INFINITY;
+ } else {
+ c->bl[j] = D ? D[j + 1] * c->bl[j] / D[0] : c->bl[j];
+ }
+ }
+}
+
+/* project onto { (t, s) | t * l <= s <= t * u, t >= 0 }, Newton's method on t
+ tx = [t; s], total length = bsize
+ uses Moreau since \Pi_K*(tx) = \Pi_K(-tx) + tx
+*/
+static scs_float proj_box_cone(scs_float *tx, const scs_float *bl,
+ const scs_float *bu, scs_int bsize,
+ scs_float t_warm_start) {
+ scs_float *x, gt, ht, t_prev, t = t_warm_start;
+ scs_int iter, j;
+
+ if (bsize == 1) { /* special case */
+ tx[0] = MAX(tx[0], 0.0);
+ return tx[0];
+ }
+
+ x = &(tx[1]);
+
+ /* should only require about 5 or so iterations, 1 or 2 if warm-started */
+ for (iter = 0; iter < BOX_CONE_MAX_ITERS; iter++) {
+ t_prev = t;
+ /* incorporate the additional BOX_T_SCALE factor into the projection */
+ gt = BOX_T_SCALE * (t - tx[0]); /* gradient */
+ ht = BOX_T_SCALE; /* hessian */
+ for (j = 0; j < bsize - 1; j++) {
+ if (x[j] > t * bu[j]) {
+ gt += (t * bu[j] - x[j]) * bu[j]; /* gradient */
+ ht += bu[j] * bu[j]; /* hessian */
+ } else if (x[j] < t * bl[j]) {
+ gt += (t * bl[j] - x[j]) * bl[j]; /* gradient */
+ ht += bl[j] * bl[j]; /* hessian */
+ }
+ }
+ t = MAX(t - gt / MAX(ht, 1e-8), 0.); /* newton step */
+#if VERBOSITY > 3
+ scs_printf("iter %i, t_new %1.3e, t_prev %1.3e, gt %1.3e, ht %1.3e\n", iter,
+ t, t_prev, gt, ht);
+ scs_printf("ABS(gt / (ht + 1e-6)) %.4e, ABS(t - t_prev) %.4e\n",
+ ABS(gt / (ht + 1e-6)), ABS(t - t_prev));
+#endif
+ /* TODO: sometimes this check can fail (ie, declare convergence before it
+ * should) if ht is very large, which can happen with some pathological
+ * problems.
+ */
+ if (ABS(gt / MAX(ht, 1e-6)) < 1e-12 * MAX(t, 1.) ||
+ ABS(t - t_prev) < 1e-11 * MAX(t, 1.)) {
+ break;
+ }
+ }
+ if (iter == BOX_CONE_MAX_ITERS) {
+ scs_printf("warning: box cone proj hit maximum %i iters\n", (int)iter);
+ }
+ for (j = 0; j < bsize - 1; j++) {
+ if (x[j] > t * bu[j]) {
+ x[j] = t * bu[j];
+ } else if (x[j] < t * bl[j]) {
+ x[j] = t * bl[j];
+ }
+ /* x[j] unchanged otherwise */
+ }
+ tx[0] = t;
+#if VERBOSITY > 3
+ scs_printf("box cone iters %i\n", (int)iter + 1);
+#endif
+ return t;
+}
+
+/* project onto SOC of size q*/
+static void proj_soc(scs_float *x, scs_int q) {
+ if (q == 0) {
+ return;
+ }
+ if (q == 1) {
+ x[0] = MAX(x[0], 0.);
+ return;
+ }
+ scs_float v1 = x[0];
+ scs_float s = SCS(norm_2)(&(x[1]), q - 1);
+ scs_float alpha = (s + v1) / 2.0;
+
+ if (s <= v1) {
+ return;
+ } else if (s <= -v1) {
+ memset(&(x[0]), 0, q * sizeof(scs_float));
+ } else {
+ x[0] = alpha;
+ SCS(scale_array)(&(x[1]), alpha / s, q - 1);
+ }
+}
+
static void proj_power_cone(scs_float *v, scs_float a) {
scs_float xh = v[0], yh = v[1], rh = ABS(v[2]);
scs_float x = 0.0, y = 0.0, r;
scs_int i;
/* v in K_a */
@@ -633,104 +715,91 @@
v[0] = x;
v[1] = y;
v[2] = (v[2] < 0) ? -(r) : (r);
}
-/* outward facing cone projection routine, iter is outer algorithm iteration, if
- iter < 0 then iter is ignored
- warm_start contains guess of projection (can be set to SCS_NULL) */
-scs_int SCS(proj_dual_cone)(scs_float *x, const ScsCone *k, ScsConeWork *c,
- const scs_float *warm_start, scs_int iter) {
- scs_int i;
- scs_int count = (k->f ? k->f : 0);
- SCS(timer) cone_timer;
-#if EXTRA_VERBOSE > 0
- SCS(timer) proj_timer;
- SCS(tic)(&proj_timer);
-#endif
- SCS(tic)(&cone_timer);
+/* project onto the primal K cone in the paper */
+static scs_int proj_cone(scs_float *x, const ScsCone *k, ScsConeWork *c,
+ scs_int normalize) {
+ scs_int i, status;
+ scs_int count = 0;
+ if (k->z) {
+ /* project onto primal zero / dual free cone */
+ memset(x, 0, k->z * sizeof(scs_float));
+ count += k->z;
+ }
+
if (k->l) {
/* project onto positive orthant */
for (i = count; i < count + k->l; ++i) {
- if (x[i] < 0.0) {
- x[i] = 0.0;
- }
- /* x[i] = (x[i] < 0.0) ? 0.0 : x[i]; */
+ x[i] = MAX(x[i], 0.0);
}
count += k->l;
-#if EXTRA_VERBOSE > 0
- scs_printf("pos orthant proj time: %1.2es\n", SCS(tocq)(&proj_timer) / 1e3);
- SCS(tic)(&proj_timer);
-#endif
}
+ if (k->bsize) {
+ /* project onto box cone */
+ if (normalize) {
+ c->box_t_warm_start = proj_box_cone(&(x[count]), c->bl, c->bu, k->bsize,
+ c->box_t_warm_start);
+ } else {
+ c->box_t_warm_start = proj_box_cone(&(x[count]), k->bl, k->bu, k->bsize,
+ c->box_t_warm_start);
+ }
+ count += k->bsize; /* since b = (t,s), len(s) = bsize - 1 */
+ }
+
if (k->qsize && k->q) {
- /* project onto SOC */
+ /* project onto second-order cones */
for (i = 0; i < k->qsize; ++i) {
- if (k->q[i] == 0) {
- continue;
- }
- if (k->q[i] == 1) {
- if (x[count] < 0.0) {
- x[count] = 0.0;
- }
- } else {
- scs_float v1 = x[count];
- scs_float s = SCS(norm)(&(x[count + 1]), k->q[i] - 1);
- scs_float alpha = (s + v1) / 2.0;
-
- if (s <= v1) { /* do nothing */
- } else if (s <= -v1) {
- memset(&(x[count]), 0, k->q[i] * sizeof(scs_float));
- } else {
- x[count] = alpha;
- SCS(scale_array)(&(x[count + 1]), alpha / s, k->q[i] - 1);
- }
- }
+ proj_soc(&(x[count]), k->q[i]);
count += k->q[i];
}
-#if EXTRA_VERBOSE > 0
- scs_printf("SOC proj time: %1.2es\n", SCS(tocq)(&proj_timer) / 1e3);
- SCS(tic)(&proj_timer);
-#endif
}
if (k->ssize && k->s) {
- /* project onto PSD cone */
+ /* project onto PSD cones */
for (i = 0; i < k->ssize; ++i) {
-#if EXTRA_VERBOSE > 0
- scs_printf("SD proj size %li\n", (long)k->s[i]);
-#endif
- if (k->s[i] == 0) {
- continue;
+ status = proj_semi_definite_cone(&(x[count]), k->s[i], c);
+ if (status < 0) {
+ return status;
}
- if (proj_semi_definite_cone(&(x[count]), k->s[i], c) < 0) {
- return -1;
- }
count += get_sd_cone_size(k->s[i]);
}
-#if EXTRA_VERBOSE > 0
- scs_printf("SD proj time: %1.2es\n", SCS(tocq)(&proj_timer) / 1e3);
- SCS(tic)(&proj_timer);
-#endif
}
if (k->ep) {
- scs_float r, s, t;
- scs_int idx;
/*
* exponential cone is not self dual, if s \in K
* then y \in K^* and so if K is the primal cone
* here we project onto K^*, via Moreau
* \Pi_C^*(y) = y + \Pi_C(-y)
*/
- SCS(scale_array)(&(x[count]), -1, 3 * k->ep); /* x = -x; */
#ifdef _OPENMP
-#pragma omp parallel for private(r, s, t, idx)
+#pragma omp parallel for
#endif
for (i = 0; i < k->ep; ++i) {
+ proj_exp_cone(&(x[count + 3 * i]));
+ }
+ count += 3 * k->ep;
+ }
+
+ if (k->ed) { /* dual exponential cone */
+ /*
+ * exponential cone is not self dual, if s \in K
+ * then y \in K^* and so if K is the primal cone
+ * here we project onto K^*, via Moreau
+ * \Pi_C^*(y) = y + \Pi_C(-y)
+ */
+ scs_int idx;
+ scs_float r, s, t;
+ SCS(scale_array)(&(x[count]), -1, 3 * k->ed); /* x = -x; */
+#ifdef _OPENMP
+#pragma omp parallel for private(r, s, t, idx)
+#endif
+ for (i = 0; i < k->ed; ++i) {
idx = count + 3 * i;
r = x[idx];
s = x[idx + 1];
t = x[idx + 2];
@@ -738,30 +807,11 @@
x[idx] -= r;
x[idx + 1] -= s;
x[idx + 2] -= t;
}
- count += 3 * k->ep;
-#if EXTRA_VERBOSE > 0
- scs_printf("EP proj time: %1.2es\n", SCS(tocq)(&proj_timer) / 1e3);
- SCS(tic)(&proj_timer);
-#endif
- }
-
- if (k->ed) {
-/* exponential cone: */
-#ifdef _OPENMP
-#pragma omp parallel for
-#endif
- for (i = 0; i < k->ed; ++i) {
- proj_exp_cone(&(x[count + 3 * i]));
- }
count += 3 * k->ed;
-#if EXTRA_VERBOSE > 0
- scs_printf("ED proj time: %1.2es\n", SCS(tocq)(&proj_timer) / 1e3);
- SCS(tic)(&proj_timer);
-#endif
}
if (k->psize && k->p) {
scs_float v[3];
scs_int idx;
@@ -770,33 +820,70 @@
pragma omp parallel for private(v, idx)
endif
*/
for (i = 0; i < k->psize; ++i) {
idx = count + 3 * i;
- if (k->p[i] <= 0) {
- /* dual power cone */
- proj_power_cone(&(x[idx]), -k->p[i]);
+ if (k->p[i] >= 0) {
+ /* primal power cone */
+ proj_power_cone(&(x[idx]), k->p[i]);
} else {
- /* primal power cone, using Moreau */
+ /* dual power cone, using Moreau */
v[0] = -x[idx];
v[1] = -x[idx + 1];
v[2] = -x[idx + 2];
- proj_power_cone(v, k->p[i]);
+ proj_power_cone(v, -k->p[i]);
x[idx] += v[0];
x[idx + 1] += v[1];
x[idx + 2] += v[2];
}
}
count += 3 * k->psize;
-#if EXTRA_VERBOSE > 0
- scs_printf("Power cone proj time: %1.2es\n", SCS(tocq)(&proj_timer) / 1e3);
- SCS(tic)(&proj_timer);
-#endif
}
/* project onto OTHER cones */
- if (c) {
- c->total_cone_time += SCS(tocq)(&cone_timer);
- }
return 0;
+}
+
+ScsConeWork *SCS(init_cone)(const ScsCone *k, const ScsScaling *scal,
+ scs_int cone_len) {
+ ScsConeWork *c = (ScsConeWork *)scs_calloc(1, sizeof(ScsConeWork));
+ c->cone_len = cone_len;
+ c->s = (scs_float *)scs_calloc(cone_len, sizeof(scs_float));
+ if (k->bsize && k->bu && k->bl) {
+ c->box_t_warm_start = 1.;
+ if (scal) {
+ c->bu = (scs_float *)scs_calloc(k->bsize - 1, sizeof(scs_float));
+ c->bl = (scs_float *)scs_calloc(k->bsize - 1, sizeof(scs_float));
+ memcpy(c->bu, k->bu, (k->bsize - 1) * sizeof(scs_float));
+ memcpy(c->bl, k->bl, (k->bsize - 1) * sizeof(scs_float));
+ /* also does some sanitizing */
+ normalize_box_cone(c, scal ? &(scal->D[k->z + k->l]) : SCS_NULL,
+ k->bsize);
+ }
+ }
+ if (k->ssize && k->s) {
+ if (set_up_sd_cone_work_space(c, k) < 0) {
+ SCS(finish_cone)(c);
+ return SCS_NULL;
+ }
+ }
+ return c;
+}
+
+/* outward facing cone projection routine
+ performs projection in-place
+ if normalize > 0 then will use normalized (equilibrated) cones if applicable.
+*/
+scs_int SCS(proj_dual_cone)(scs_float *x, const ScsCone *k, ScsConeWork *c,
+ scs_int normalize) {
+ scs_int status;
+ /* copy x, s = x */
+ memcpy(c->s, x, c->cone_len * sizeof(scs_float));
+ /* negate x -> -x */
+ SCS(scale_array)(x, -1., c->cone_len);
+ /* project -x onto cone, x -> Pi_K(-x) */
+ status = proj_cone(x, k, c, normalize);
+ /* return Pi_K*(x) = s + Pi_K(-x) */
+ SCS(add_scaled_array)(x, c->s, c->cone_len, 1.);
+ return status;
}