static void setSolution(Data * d, Work * w, Sol * sol, Info * info) {
idxint l = d->n + d->m + 1;
setx(d, w, sol);
sety(d, w, sol);
sets(d, w, sol);
if (info->statusVal == 0 || info->statusVal == SOLVED) {
pfloat tau = w->u[l - 1];
pfloat kap = ABS(w->v[l - 1]);
if (tau > INDETERMINATE_TOL && tau > kap) {
info->statusVal = solved(d, sol, info, tau);
} else {
if (calcNorm(w->u, l) < INDETERMINATE_TOL * SQRTF((pfloat) l)) {
info->statusVal = indeterminate(d, sol, info);
} else {
pfloat bTy = innerProd(d->b, sol->y, d->m);
pfloat cTx = innerProd(d->c, sol->x, d->n);
if (bTy < cTx) {
info->statusVal = infeasible(d, sol, info);
} else {
info->statusVal = unbounded(d, sol, info);
}
}
}
} else if (info->statusVal == INFEASIBLE) {
info->statusVal = infeasible(d, sol, info);
} else {
info->statusVal = unbounded(d, sol, info);
}
}
static idxint converged(Data * d, Work * w, struct residuals * r, idxint iter) {
pfloat nmpr, nmdr, tau, kap, *x, *y, cTx, nmAxs, bTy, nmATy, rpri, rdua, gap;
idxint n = d->n, m = d->m;
if (iter % CONVERGED_INTERVAL != 0) {
return 0;
}
x = w->u;
y = &(w->u[n]);
tau = ABS(w->u[n + m]);
kap = ABS(w->v[n + m]) / (d->NORMALIZE ? (d->SCALE * w->sc_c * w->sc_b) : 1);
r->tau = tau;
r->kap = kap;
/* requires mult by A:
nmpr = calcPrimalResid(d, w, w->u, &(w->v[n]), ABS(w->u[n + m]), &nmAxs);
*/
/* does not require mult by A: */
nmpr = fastCalcPrimalResid(d, w, &nmAxs);
cTx = innerProd(x, d->c, n) / (d->NORMALIZE ? (d->SCALE * w->sc_c * w->sc_b) : 1);
r->resPri = cTx < 0 ? w->nm_c * nmAxs / -cTx : NAN;
if (r->resPri < d->EPS) {
return UNBOUNDED;
}
nmdr = calcDualResid(d, w, y, tau, &nmATy);
bTy = innerProd(y, d->b, m) / (d->NORMALIZE ? (d->SCALE * w->sc_c * w->sc_b) : 1);
r->resDual = bTy < 0 ? w->nm_b * nmATy / -bTy : NAN;
if (r->resDual < d->EPS) {
return INFEASIBLE;
}
r->cTx = cTx / tau;
r->bTy = bTy / tau;
r->relGap = NAN;
rpri = nmpr / (1 + w->nm_b) / tau;
rdua = nmdr / (1 + w->nm_c) / tau;
gap = ABS(cTx + bTy) / (tau + ABS(cTx) + ABS(bTy));
if (tau > kap) {
r->resPri = rpri;
r->resDual = rdua;
r->relGap = gap;
}
return (MAX(MAX(rpri,rdua),gap) < d->EPS ? SOLVED : 0);
}
// Feature transformation to PCA, whitening or Fisher subspace
void MQDFTEST::featureTrans( unsigned char* ftr, int dim, float* input )
{
float *shx;
shx = new float [dim];
powerTrans( ftr, dim, power, shx );
int i;
for( i=0; i<dim; i++ )
shx[i] -= gmean[i]; // shift with respect to gross mean
int j;
float proj, euclid;
if( residual )
{
euclid = 0;
for( i=0; i<dim; i++ )
euclid += shx[i]*shx[i];
}
for( j=0; j<redDim; j++ )
{
proj = innerProd( shx, trbasis+j*dim, dim );
if( residual )
euclid -= proj*proj;
input[j] = proj*dscale1 ;
}
if( residual )
input[redDim] = euclid*dscale1*dscale1 ;
delete []shx;
}
static void updateWork(Data * d, Work * w, Sol * sol) {
/* before normalization */
idxint n = d->n;
idxint m = d->m;
w->nm_b = calcNorm(d->b, m);
w->nm_c = calcNorm(d->c, n);
#ifdef EXTRAVERBOSE
printArray(d->b, d->m, "b");
scs_printf("pre-normalized norm b = %4f\n", calcNorm(d->b, d->m));
printArray(d->c, d->n, "c");
scs_printf("pre-normalized norm c = %4f\n", calcNorm(d->c, d->n));
#endif
if (d->NORMALIZE) {
normalizeBC(d, w);
#ifdef EXTRAVERBOSE
printArray(d->b, d->m, "bn");
scs_printf("sc_b = %4f\n", w->sc_b);
scs_printf("post-normalized norm b = %4f\n", calcNorm(d->b, d->m));
printArray(d->c, d->n, "cn");
scs_printf("sc_c = %4f\n", w->sc_c);
scs_printf("post-normalized norm c = %4f\n", calcNorm(d->c, d->n));
#endif
}
if (d->WARM_START) {
warmStartVars(d, w, sol);
} else {
coldStartVars(d, w);
}
memcpy(w->h, d->c, n * sizeof(pfloat));
memcpy(&(w->h[d->n]), d->b, m * sizeof(pfloat));
memcpy(w->g, w->h, (n + m) * sizeof(pfloat));
solveLinSys(d, w->p, w->g, NULL, -1);
scaleArray(&(w->g[d->n]), -1, m);
w->gTh = innerProd(w->h, w->g, n + m);
}
/* status < 0 indicates failure */
static idxint projectLinSys(Data * d, Work * w, idxint iter) {
/* ut = u + v */
idxint n = d->n, m = d->m, l = n + m + 1, status;
memcpy(w->u_t, w->u, l * sizeof(pfloat));
addScaledArray(w->u_t, w->v, l, 1.0);
scaleArray(w->u_t, d->RHO_X, n);
addScaledArray(w->u_t, w->h, l - 1, -w->u_t[l - 1]);
addScaledArray(w->u_t, w->h, l - 1, -innerProd(w->u_t, w->g, l - 1) / (w->gTh + 1));
scaleArray(&(w->u_t[n]), -1, m);
status = solveLinSys(d, w->p, w->u_t, w->u, iter);
w->u_t[l - 1] += innerProd(w->u_t, w->h, l - 1);
return status;
}
static void getInfo(Data * d, Work * w, Sol * sol, Info * info) {
pfloat cTx, bTy, nmAxs, nmATy, nmpr, nmdr;
pfloat * x = sol->x, *y = sol->y, *s = sol->s;
/* unNomalized */
nmpr = calcPrimalResid(d, w, x, s, 1, &nmAxs); /* pr = Ax + s - b */
nmdr = calcDualResid(d, w, y, 1, &nmATy); /* dr = A'y + c */
cTx = innerProd(x, d->c, d->n);
bTy = innerProd(y, d->b, d->m);
if (d->NORMALIZE) {
cTx /= (d->SCALE * w->sc_c * w->sc_b);
bTy /= (d->SCALE * w->sc_c * w->sc_b);
}
info->pobj = cTx;
info->dobj = -bTy;
if (info->statusVal == SOLVED) {
info->relGap = ABS(cTx + bTy) / (1 + ABS(cTx) + ABS(bTy));
info->resPri = nmpr / (1 + w->nm_b);
info->resDual = nmdr / (1 + w->nm_c);
} else {
if (info->statusVal == UNBOUNDED) {
info->dobj = NAN;
info->relGap = NAN;
info->resPri = w->nm_c * nmAxs / -cTx;
info->resDual = NAN;
scaleArray(x, -1 / cTx, d->n);
scaleArray(s, -1 / cTx, d->m);
info->pobj = -1;
} else {
info->pobj = NAN;
info->relGap = NAN;
info->resPri = NAN;
info->resDual = w->nm_b * nmATy / -bTy;
scaleArray(y, -1 / bTy, d->m);
info->dobj = -1;
}
}
}
static void cgCustom(Data *d, Work *w, const double * s, int max_its, double tol) {
/* solves (I+A'A)x = b */
/* warm start cg with s */
int i = 0, n = d->n;
double *x = w->p->x;
double *p = w->p->p; // cg direction
double *Ap = w->p->Ap; // updated CG direction
double *r = w->p->r; // cg residual
double *G = w->p->G; // Gram matrix
double alpha, beta, rsnew=0;
if (s==NULL) {
memset(x,0,n*sizeof(double));
}
else {
memcpy(x,s,n*sizeof(double));
cblas_dsymv(CblasColMajor, CblasUpper,n, -1, G, n, x,1, 1, r, 1);
//b_dsymv('U', n, -1, G, n, x,1, 1, r, 1);
}
memcpy(p, r, n*sizeof(double));
//double rsold=cblas_dnrm2(n,r,1);
double rsold=calcNorm(r,n);
for (i=0; i< max_its; i++) {
cblas_dsymv(CblasColMajor, CblasUpper,n, 1, G, n, p, 1, 0, Ap, 1);
//b_dsymv('U', n, 1, G, n, p, 1, 0, Ap, 1);
//beta = cblas_ddot(n, p, 1, Ap, 1);
beta = innerProd(p,Ap,n);
alpha=(rsold*rsold)/beta;
addScaledArray(x,p,n,alpha);
//cblas_daxpy(n,alpha,p,1,x,1);
addScaledArray(r,Ap,n,-alpha);
//cblas_daxpy(n,-alpha,Ap,1,r,1);
//rsnew=cblas_dnrm2(n,r,1);
rsnew=calcNorm(r,n);
if (rsnew<tol) {
break;
}
scaleArray(p,(rsnew*rsnew)/(rsold*rsold),n);
//cblas_dscal(n,(rsnew*rsnew)/(rsold*rsold),p,1);
addScaledArray(p,r,n,1);
//cblas_daxpy(n,1,r,1,p,1);
rsold=rsnew;
}
//printf("terminating cg residual = %4f, took %i itns\n",rsnew,i);
}
static scs_int pcg(const AMatrix * A, const Settings * stgs, Priv * pr, const scs_float * s, scs_float * b, scs_int max_its,
scs_float tol) {
scs_int i, n = A->n;
scs_float ipzr, ipzrOld, alpha;
scs_float *p = pr->p; /* cg direction */
scs_float *Gp = pr->Gp; /* updated CG direction */
scs_float *r = pr->r; /* cg residual */
scs_float *z = pr->z; /* for preconditioning */
scs_float *M = pr->M; /* inverse diagonal preconditioner */
if (s == NULL) {
memcpy(r, b, n * sizeof(scs_float));
memset(b, 0, n * sizeof(scs_float));
} else {
matVec(A, stgs, pr, s, r);
addScaledArray(r, b, n, -1);
scaleArray(r, -1, n);
memcpy(b, s, n * sizeof(scs_float));
}
/* check to see if we need to run CG at all */
if (calcNorm(r, n) < MIN(tol, 1e-18)) {
return 0;
}
applyPreConditioner(M, z, r, n, &ipzr);
memcpy(p, z, n * sizeof(scs_float));
for (i = 0; i < max_its; ++i) {
matVec(A, stgs, pr, p, Gp);
alpha = ipzr / innerProd(p, Gp, n);
addScaledArray(b, p, n, alpha);
addScaledArray(r, Gp, n, -alpha);
if (calcNorm(r, n) < tol) {
#if EXTRAVERBOSE > 0
scs_printf("tol: %.4e, resid: %.4e, iters: %li\n", tol, calcNorm(r, n), (long) i+1);
#endif
return i + 1;
}
ipzrOld = ipzr;
applyPreConditioner(M, z, r, n, &ipzr);
scaleArray(p, ipzr / ipzrOld, n);
addScaledArray(p, z, n, 1);
}
return i;
}
void MQDFTEST::MQDF( float* ftr, int dim, float* eudist, short* preIdx, int rank1, float* qdmin, short* index, int rankNum )
{
int k;
for( k=0; k<rankNum; k++ )
qdmin[k] = (float)1E12+k;
float euclid;
float* shx;
shx = new float [dim];
int cls, i, m;
float proj;
float qdist, tdist;
int pos, kt;
for( int ri=0; ri<rankN1; ri++ )
{
if( preIdx )
cls = preIdx[ri];
else
cls = ri;
for( i=0; i<dim; i++ )
shx[i] = (float)ftr[i]-means[cls*dim+i];
if( preIdx )
euclid = eudist[ri];
else
{
euclid = 0;
for( i=0; i<dim; i++ )
euclid += shx[i]*shx[i];
}
qdist = loglambda[cls];
kt = knum[cls]; // truncated knum
if( kt==dim )
kt -= 1;
for( m=0; m<kt; m++ )
{
proj = innerProd( shx, phi[cls]+m*dim, dim );
euclid -= proj*proj;
qdist += proj*proj/lambda[cls][m];
tdist = qdist+euclid/lambda[cls][m+1]; // increasing sequence
if( tdist>=qdmin[rankNum-1] )
break;
}
qdist = tdist;
if( qdist<qdmin[rankNum-1] )
{
pos = posAscd( qdist, qdmin, rankNum );
for( k=rankNum-1; k>pos; k-- )
{
qdmin[k] = qdmin[k-1];
index[k] = index[k-1];
}
qdmin[pos] = qdist;
index[pos] = cls;
}
}
delete shx;
}
int main(int argc, char **argv) {
scs_int n, m, col_nnz, nnz, i, q_total, q_num_rows, max_q;
Cone * k;
Data * d;
Sol * sol, * opt_sol;
Info info = { 0 };
scs_float p_f, p_l;
int seed = 0;
/* default parameters */
p_f = 0.1;
p_l = 0.3;
seed = time(SCS_NULL);
switch (argc) {
case 5:
seed = atoi(argv[4]);
/* no break */
case 4:
p_f = atof(argv[2]);
p_l = atof(argv[3]);
/* no break */
case 2:
n = atoi(argv[1]);
break;
default:
scs_printf("usage:\t%s n p_f p_l s\n"
"\tcreates an SOCP with n variables where p_f fraction of rows correspond\n"
"\tto equality constraints, p_l fraction of rows correspond to LP constraints,\n"
"\tand the remaining percentage of rows are involved in second-order\n"
"\tcone constraints. the random number generator is seeded with s.\n"
"\tnote that p_f + p_l should be less than or equal to 1, and that\n"
"\tp_f should be less than .33, since that corresponds to as many equality\n"
"\tconstraints as variables.\n", argv[0]);
scs_printf("\nusage:\t%s n p_f p_l\n"
"\tdefaults the seed to the system time\n", argv[0]);
scs_printf("\nusage:\t%s n\n"
"\tdefaults to using p_f = 0.1 and p_l = 0.3\n", argv[0]);
return 0;
}
srand(seed);
scs_printf("seed : %i\n", seed);
k = scs_calloc(1, sizeof(Cone));
d = scs_calloc(1, sizeof(Data));
d->stgs = scs_calloc(1, sizeof(Settings));
sol = scs_calloc(1, sizeof(Sol));
opt_sol = scs_calloc(1, sizeof(Sol));
m = 3 * n;
col_nnz = (int) ceil(sqrt(n));
nnz = n * col_nnz;
max_q = (scs_int) ceil(3 * n / log(3 * n));
if (p_f + p_l > 1.0) {
printf("error: p_f + p_l > 1.0!\n");
return 1;
}
k->f = (scs_int) floor(3 * n * p_f);
k->l = (scs_int) floor(3 * n * p_l);
k->qsize = 0;
q_num_rows = 3 * n - k->f - k->l;
k->q = scs_malloc(q_num_rows * sizeof(scs_int));
while (q_num_rows > max_q) {
int size;
size = (rand() % max_q) + 1;
k->q[k->qsize] = size;
k->qsize++;
q_num_rows -= size;
}
if (q_num_rows > 0) {
k->q[k->qsize] = q_num_rows;
k->qsize++;
}
q_total = 0;
for (i = 0; i < k->qsize; i++) {
q_total += k->q[i];
}
k->s = SCS_NULL;
k->ssize = 0;
k->ep = 0;
k->ed = 0;
scs_printf("\nA is %ld by %ld, with %ld nonzeros per column.\n", (long) m, (long) n, (long) col_nnz);
scs_printf("A has %ld nonzeros (%f%% dense).\n", (long) nnz, 100 * (scs_float) col_nnz / m);
scs_printf("Nonzeros of A take %f GB of storage.\n", ((scs_float) nnz * sizeof(scs_float)) / POWF(2, 30));
scs_printf("Row idxs of A take %f GB of storage.\n", ((scs_float) nnz * sizeof(scs_int)) / POWF(2, 30));
scs_printf("Col ptrs of A take %f GB of storage.\n\n", ((scs_float) n * sizeof(scs_int)) / POWF(2, 30));
printf("Cone information:\n");
printf("Zero cone rows: %ld\n", (long) k->f);
printf("LP cone rows: %ld\n", (long) k->l);
printf("Number of second-order cones: %ld, covering %ld rows, with sizes\n[", (long) k->qsize, (long) q_total);
for (i = 0; i < k->qsize; i++) {
printf("%ld, ", (long) k->q[i]);
}
printf("]\n");
printf("Number of rows covered is %ld out of %ld.\n\n", (long) (q_total + k->f + k->l), (long) m);
/* set up SCS structures */
d->m = m;
d->n = n;
genRandomProbData(nnz, col_nnz, d, k, opt_sol);
setDefaultSettings(d);
scs_printf("true pri opt = %4f\n", innerProd(d->c, opt_sol->x, d->n));
scs_printf("true dua opt = %4f\n", -innerProd(d->b, opt_sol->y, d->m));
/* solve! */
scs(d, k, sol, &info);
scs_printf("true pri opt = %4f\n", innerProd(d->c, opt_sol->x, d->n));
scs_printf("true dua opt = %4f\n", -innerProd(d->b, opt_sol->y, d->m));
if (sol->x) { scs_printf("scs pri obj= %4f\n", innerProd(d->c, sol->x, d->n)); }
if (sol->y) { scs_printf("scs dua obj = %4f\n", -innerProd(d->b, sol->y, d->m)); }
freeData(d, k);
freeSol(sol);
freeSol(opt_sol);
return 0;
}