/*
* Initializes the solver.
*
* This function assumes that the KKT matrix K is already in the form
*
* [0 A' G']
* K = [A 0 0 ]
* [G 0 -I ]
*
* The preprocessor/codegen takes care of this, we just have to be aware
* of this implicit assumption.
*/
idxint init(pwork* w)
{
idxint i, KKT_FACTOR_RETURN_CODE;
idxint* Pinv = w->KKT->Pinv;
#if PROFILING > 1
timer tfactor, tkktsolve;
#endif
w->KKT->delta = w->stgs->delta;
/* Factor KKT matrix - this is needed in all 3 linear system solves */
#if PROFILING > 1
tic(&tfactor);
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta, &w->info->tfactor_t1, &w->info->tfactor_t2);
w->info->tfactor += toc(&tfactor);
#else
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta);
#endif
/* check if factorization was successful, exit otherwise */
if( KKT_FACTOR_RETURN_CODE != KKT_OK ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nProblem in factoring KKT system, aborting.");
#endif
return ECOS_FATAL;
}
/*
* PRIMAL VARIABLES:
* - solve xhat = arg min ||Gx-h||_2^2 such that Ax = b
* - r = h - G*xhat
* These two equations are solved by
*
* [ 0 A' G' ] [ xhat ] [ 0 ]
* [ A 0 0 ] [ y ] = [ b ]
* [ G 0 -I ] [ -r ] [ h ]
*
* and then take shat = r if alphap < 0, zbar + (1+alphap)*e otherwise
* where alphap = inf{ alpha | sbar + alpha*e >= 0 }
*/
/* Solve for RHS [0; b; h] */
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref1 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS1, w->KKT->dx1, w->KKT->dy1, w->KKT->dz1, w->n, w->p, w->m, w->C, 1, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
#if DEBUG > 0
#if PRINTLEVEL > 3
printDenseMatrix(w->KKT->dx1, w->n, 1, "dx1_init");
printDenseMatrix(w->KKT->dy1, w->p, 1, "dy1_init");
printDenseMatrix(w->KKT->dz1, w->m, 1, "dz1_init");
#endif
#endif
/* Copy out initial value of x */
for( i=0; i<w->n; i++ ){ w->x[i] = w->KKT->dx1[i]; }
/* Copy out -r into temporary variable */
for( i=0; i<w->m; i++ ){ w->KKT->work1[i] = -w->KKT->dz1[i]; }
/* Bring variable to cone */
bring2cone(w->C, w->KKT->work1, w->s );
/*
* dual variables
* solve (yhat,zbar) = arg min ||z||_2^2 such that G'*z + A'*y + c = 0
*
* we can solve this by
*
* [ 0 A' G' ] [ x ] [ -c ]
* [ A 0 0 ] [ yhat ] = [ 0 ]
* [ G 0 -I ] [ zbar ] [ 0 ]
*
* and then take zhat = zbar if alphad < 0, zbar + (1+alphad)*e otherwise
* where alphad = inf{ alpha | zbar + alpha*e >= 0 }
*/
/* Solve for RHS [-c; 0; 0] */
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref2 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS2, w->KKT->dx2, w->KKT->dy2, w->KKT->dz2, w->n, w->p, w->m, w->C, 1, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
#if DEBUG > 0
#if PRINTLEVEL > 3
printDenseMatrix(w->KKT->dx2, w->n, 1, "dx2_init");
printDenseMatrix(w->KKT->dy2, w->p, 1, "dy2_init");
printDenseMatrix(w->KKT->dz2, w->m, 1, "dz2_init");
#endif
#endif
/* Copy out initial value of y */
for( i=0; i<w->p; i++ ){ w->y[i] = w->KKT->dy2[i]; }
/* Bring variable to cone */
bring2cone(w->C, w->KKT->dz2, w->z );
/* Prepare RHS1 - before this line RHS1 = [0; b; h], after it holds [-c; b; h] */
for( i=0; i<w->n; i++){ w->KKT->RHS1[Pinv[i]] = -w->c[i]; }
/*
* other variables
*/
w->kap = 1.0;
w->tau = 1.0;
w->info->step = 0;
w->info->step_aff = 0;
w->info->dinf = 0;
w->info->pinf = 0;
return 0;
}
/*
* Initializes the solver.
*/
idxint init(pwork* w)
{
idxint i, j, k, l, KKT_FACTOR_RETURN_CODE;
idxint* Pinv = w->KKT->Pinv;
pfloat rx, ry, rz;
#if PROFILING > 1
timer tfactor, tkktsolve;
#endif
/* set regularization parameter */
w->KKT->delta = w->stgs->delta;
/* Initialize KKT matrix */
kkt_init(w->KKT->PKPt, w->KKT->PK, w->C);
#if DEBUG > 0
dumpSparseMatrix(w->KKT->PKPt, "PKPt0.txt");
#endif
/* initialize RHS1 */
k = 0; j = 0;
for( i=0; i<w->n; i++ ){ w->KKT->RHS1[w->KKT->Pinv[k++]] = 0; }
for( i=0; i<w->p; i++ ){ w->KKT->RHS1[w->KKT->Pinv[k++]] = w->b[i]; }
for( i=0; i<w->C->lpc->p; i++ ){ w->KKT->RHS1[w->KKT->Pinv[k++]] = w->h[i]; j++; }
for( l=0; l<w->C->nsoc; l++ ){
for( i=0; i < w->C->soc[l].p; i++ ){ w->KKT->RHS1[w->KKT->Pinv[k++]] = w->h[j++]; }
#if CONEMODE == 0
w->KKT->RHS1[w->KKT->Pinv[k++]] = 0;
w->KKT->RHS1[w->KKT->Pinv[k++]] = 0;
#endif
}
#if PRINTLEVEL > 2
PRINTTEXT("Written %d entries of RHS1\n", (int)k);
#endif
/* initialize RHS2 */
for( i=0; i<w->n; i++ ){ w->KKT->RHS2[w->KKT->Pinv[i]] = -w->c[i]; }
for( i=w->n; i<w->KKT->PKPt->n; i++ ){ w->KKT->RHS2[w->KKT->Pinv[i]] = 0; }
/* get scalings of problem data */
rx = norm2(w->c, w->n); w->resx0 = MAX(1, rx);
ry = norm2(w->b, w->p); w->resy0 = MAX(1, ry);
rz = norm2(w->h, w->m); w->resz0 = MAX(1, rz);
/* Factor KKT matrix - this is needed in all 3 linear system solves */
#if PROFILING > 1
tic(&tfactor);
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta, &w->info->tfactor_t1, &w->info->tfactor_t2);
w->info->tfactor += toc(&tfactor);
#else
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta);
#endif
/* check if factorization was successful, exit otherwise */
if( KKT_FACTOR_RETURN_CODE != KKT_OK ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nProblem in factoring KKT system, aborting.");
#endif
return ECOS_FATAL;
}
/*
* PRIMAL VARIABLES:
* - solve xhat = arg min ||Gx-h||_2^2 such that Ax = b
* - r = h - G*xhat
* These two equations are solved by
*
* [ 0 A' G' ] [ xhat ] [ 0 ]
* [ A 0 0 ] [ y ] = [ b ]
* [ G 0 -I ] [ -r ] [ h ]
*
* and then take shat = r if alphap < 0, zbar + (1+alphap)*e otherwise
* where alphap = inf{ alpha | sbar + alpha*e >= 0 }
*/
/* Solve for RHS [0; b; h] */
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref1 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS1, w->KKT->dx1, w->KKT->dy1, w->KKT->dz1, w->n, w->p, w->m, w->C, 1, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
#if DEBUG > 0
#if PRINTLEVEL > 3
printDenseMatrix(w->KKT->dx1, w->n, 1, "dx1_init");
printDenseMatrix(w->KKT->dy1, w->p, 1, "dy1_init");
printDenseMatrix(w->KKT->dz1, w->m, 1, "dz1_init");
#endif
#endif
/* Copy out initial value of x */
for( i=0; i<w->n; i++ ){ w->x[i] = w->KKT->dx1[i]; }
/* Copy out -r into temporary variable */
for( i=0; i<w->m; i++ ){ w->KKT->work1[i] = -w->KKT->dz1[i]; }
/* Bring variable to cone */
bring2cone(w->C, w->KKT->work1, w->s );
/*
* dual variables
* solve (yhat,zbar) = arg min ||z||_2^2 such that G'*z + A'*y + c = 0
*
* we can solve this by
*
* [ 0 A' G' ] [ x ] [ -c ]
* [ A 0 0 ] [ yhat ] = [ 0 ]
* [ G 0 -I ] [ zbar ] [ 0 ]
*
* and then take zhat = zbar if alphad < 0, zbar + (1+alphad)*e otherwise
* where alphad = inf{ alpha | zbar + alpha*e >= 0 }
*/
/* Solve for RHS [-c; 0; 0] */
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref2 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS2, w->KKT->dx2, w->KKT->dy2, w->KKT->dz2, w->n, w->p, w->m, w->C, 1, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
#if DEBUG > 0
#if PRINTLEVEL > 3
printDenseMatrix(w->KKT->dx2, w->n, 1, "dx2_init");
printDenseMatrix(w->KKT->dy2, w->p, 1, "dy2_init");
printDenseMatrix(w->KKT->dz2, w->m, 1, "dz2_init");
#endif
#endif
/* Copy out initial value of y */
for( i=0; i<w->p; i++ ){ w->y[i] = w->KKT->dy2[i]; }
/* Bring variable to cone */
bring2cone(w->C, w->KKT->dz2, w->z );
/* Prepare RHS1 - before this line RHS1 = [0; b; h], after it holds [-c; b; h] */
for( i=0; i<w->n; i++){ w->KKT->RHS1[Pinv[i]] = -w->c[i]; }
/*
* other variables
*/
w->kap = 1.0;
w->tau = 1.0;
w->info->step = 0;
w->info->step_aff = 0;
w->info->dinf = 0;
w->info->pinf = 0;
return 0;
}
