/*
* Computes residuals.
*
* hrx = -A'*y - G'*z; rx = hrx - c.*tau; hresx = norm(rx,2);
* hry = A*x; ry = hry - b.*tau; hresy = norm(ry,2);
* hrz = s + G*x; rz = hrz - h.*tau; hresz = norm(rz,2);
* rt = kappa + c'*x + b'*y + h'*z;
*/
void computeResiduals(pwork *w)
{
/* rx = -A'*y - G'*z - c.*tau */
if( w->p > 0 ) {
sparseMtVm(w->A, w->y, w->rx, 1, 0);
sparseMtVm(w->G, w->z, w->rx, 0, 0);
} else {
sparseMtVm(w->G, w->z, w->rx, 1, 0);
}
w->hresx = norm2(w->rx, w->n);
vsubscale(w->n, w->tau, w->c, w->rx);
/* ry = A*x - b.*tau */
if( w->p > 0 ){
sparseMV(w->A, w->x, w->ry, 1, 1);
w->hresy = norm2(w->ry, w->p);
vsubscale(w->p, w->tau, w->b, w->ry);
} else {
w->hresy = 0;
w->ry = NULL;
}
/* rz = s + G*x - h.*tau */
sparseMV(w->G, w->x, w->rz, 1, 1);
vadd(w->m, w->s, w->rz);
w->hresz = norm2(w->rz, w->m);
vsubscale(w->m, w->tau, w->h, w->rz);
/* rt = kappa + c'*x + b'*y + h'*z; */
w->cx = ddot(w->n, w->c, w->x);
w->by = w->p > 0 ? ddot(w->p, w->b, w->y) : 0.0;
w->hz = ddot(w->m, w->h, w->z);
w->rt = w->kap + w->cx + w->by + w->hz;
}
/**
* Solves the permuted KKT system and returns the unpermuted search directions.
*
* On entry, the factorization of the permuted KKT matrix, PKPt,
* is assumed to be up to date (call kkt_factor beforehand to achieve this).
* The right hand side, Pb, is assumed to be already permuted.
*
* On exit, the resulting search directions are written into dx, dy and dz,
* where these variables are permuted back to the original ordering.
*
* KKT->nitref iterative refinement steps are applied to solve the linear system.
*
* Returns the number of iterative refinement steps really taken.
*/
idxint kkt_solve(kkt* KKT, spmat* A, spmat* G, pfloat* Pb, pfloat* dx, pfloat* dy, pfloat* dz, idxint n, idxint p, idxint m, cone* C, idxint isinit, idxint nitref)
{
#if CONEMODE == 0
#define MTILDE (m+2*C->nsoc)
#else
#define MTILDE (m)
#endif
idxint i, k, l, j, kk, kItRef;
#if (defined STATICREG) && (STATICREG > 0)
idxint dzoffset;
#endif
idxint* Pinv = KKT->Pinv;
pfloat* Px = KKT->work1;
pfloat* dPx = KKT->work2;
pfloat* e = KKT->work3;
pfloat* Pe = KKT->work4;
pfloat* truez = KKT->work5;
pfloat* Gdx = KKT->work6;
pfloat* ex = e;
pfloat* ey = e + n;
pfloat* ez = e + n+p;
pfloat bnorm = 1.0 + norminf(Pb, n+p+MTILDE);
pfloat nex = 0;
pfloat ney = 0;
pfloat nez = 0;
pfloat nerr;
pfloat nerr_prev;
pfloat error_threshold = bnorm*LINSYSACC;
idxint nK = KKT->PKPt->n;
/* forward - diagonal - backward solves: Px holds solution */
LDL_lsolve2(nK, Pb, KKT->L->jc, KKT->L->ir, KKT->L->pr, Px );
LDL_dsolve(nK, Px, KKT->D);
LDL_ltsolve(nK, Px, KKT->L->jc, KKT->L->ir, KKT->L->pr);
#if PRINTLEVEL > 2
if( p > 0 ){
PRINTTEXT("\nIR: it ||ex|| ||ey|| ||ez|| (threshold: %4.2e)\n", error_threshold);
PRINTTEXT(" --------------------------------------------------\n");
} else {
PRINTTEXT("\nIR: it ||ex|| ||ez|| (threshold: %4.2e)\n", error_threshold);
PRINTTEXT(" -----------------------------------------\n");
}
#endif
/* iterative refinement */
for( kItRef=0; kItRef <= nitref; kItRef++ ){
/* unpermute x & copy into arrays */
unstretch(n, p, C, Pinv, Px, dx, dy, dz);
/* compute error term */
k=0; j=0;
/* 1. error on dx*/
#if (defined STATICREG) && (STATICREG > 0)
/* ex = bx - A'*dy - G'*dz - DELTASTAT*dx */
for( i=0; i<n; i++ ){ ex[i] = Pb[Pinv[k++]] - DELTASTAT*dx[i]; }
#else
/* ex = bx - A'*dy - G'*dz */
for( i=0; i<n; i++ ){ ex[i] = Pb[Pinv[k++]]; }
#endif
if(A) sparseMtVm(A, dy, ex, 0, 0);
sparseMtVm(G, dz, ex, 0, 0);
nex = norminf(ex,n);
/* error on dy */
if( p > 0 ){
#if (defined STATICREG) && (STATICREG > 0)
/* ey = by - A*dx + DELTASTAT*dy */
for( i=0; i<p; i++ ){ ey[i] = Pb[Pinv[k++]] + DELTASTAT*dy[i]; }
#else
/* ey = by - A*dx */
for( i=0; i<p; i++ ){ ey[i] = Pb[Pinv[k++]]; }
#endif
sparseMV(A, dx, ey, -1, 0);
ney = norminf(ey,p);
}
/* --> 3. ez = bz - G*dx + V*dz_true */
kk = 0; j=0;
#if (defined STATICREG) && (STATICREG > 0)
dzoffset=0;
#endif
sparseMV(G, dx, Gdx, 1, 1);
for( i=0; i<C->lpc->p; i++ ){
#if (defined STATICREG) && (STATICREG > 0)
ez[kk++] = Pb[Pinv[k++]] - Gdx[j++] + DELTASTAT*dz[dzoffset++];
#else
ez[kk++] = Pb[Pinv[k++]] - Gdx[j++];
#endif
}
for( l=0; l<C->nsoc; l++ ){
for( i=0; i<C->soc[l].p; i++ ){
#if (defined STATICREG) && (STATICREG > 0)
ez[kk++] = i<(C->soc[l].p-1) ? Pb[Pinv[k++]] - Gdx[j++] + DELTASTAT*dz[dzoffset++] : Pb[Pinv[k++]] - Gdx[j++] - DELTASTAT*dz[dzoffset++];
#else
ez[kk++] = Pb[Pinv[k++]] - Gdx[j++];
#endif
}
#if CONEMODE == 0
ez[kk] = 0;
ez[kk+1] = 0;
k += 2;
kk += 2;
#endif
}
for( i=0; i<MTILDE; i++) { truez[i] = Px[Pinv[n+p+i]]; }
if( isinit == 0 ){
scale2add(truez, ez, C);
} else {
vadd(MTILDE, truez, ez);
}
nez = norminf(ez,MTILDE);
#if PRINTLEVEL > 2
if( p > 0 ){
PRINTTEXT(" %2d %3.1e %3.1e %3.1e\n", (int)kItRef, nex, ney, nez);
} else {
PRINTTEXT(" %2d %3.1e %3.1e\n", (int)kItRef, nex, nez);
}
#endif
/* maximum error (infinity norm of e) */
nerr = MAX( nex, nez);
if( p > 0 ){ nerr = MAX( nerr, ney ); }
/* CHECK WHETHER REFINEMENT BROUGHT DECREASE - if not undo and quit! */
if( kItRef > 0 && nerr > nerr_prev ){
/* undo refinement */
for( i=0; i<nK; i++ ){ Px[i] -= dPx[i]; }
kItRef--;
break;
}
/* CHECK WHETHER TO REFINE AGAIN */
if( kItRef == nitref || ( nerr < error_threshold ) || ( kItRef > 0 && nerr_prev < IRERRFACT*nerr ) ){
break;
}
nerr_prev = nerr;
/* permute */
for( i=0; i<nK; i++) { Pe[Pinv[i]] = e[i]; }
/* forward - diagonal - backward solves: dPx holds solution */
LDL_lsolve2(nK, Pe, KKT->L->jc, KKT->L->ir, KKT->L->pr, dPx);
LDL_dsolve(nK, dPx, KKT->D);
LDL_ltsolve(nK, dPx, KKT->L->jc, KKT->L->ir, KKT->L->pr);
/* add refinement to Px */
for( i=0; i<nK; i++ ){ Px[i] += dPx[i]; }
}
#if PRINTLEVEL > 2
PRINTTEXT("\n");
#endif
/* copy solution out into the different arrays, permutation included */
unstretch(n, p, C, Pinv, Px, dx, dy, dz);
return kItRef;
}