/*******************************************************************
Copyright (C) 2017, 2020 AMPL Optimization, Inc.; written by David M. Gay.

Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that
both that the copyright notice and this permission notice and warranty
disclaimer appear in supporting documentation.

The author and AMPL Optimization, Inc. disclaim all warranties with
regard to this software, including all implied warranties of
merchantability and fitness.  In no event shall the author be liable
for any special, indirect or consequential damages or any damages
whatsoever resulting from loss of use, data or profits, whether in an
action of contract, negligence or other tortious action, arising out
of or in connection with the use or performance of this software.
*******************************************************************/

#include "jacpdim.h"

#ifdef __cplusplus
extern "C" {
#endif

 static void
hv_fwd(expr *e)
{
	argpair *da, *dae;
	expr *e1, **ep;
	real dO;

	for(; e; e = e->fwd) {
	    e->aO = e->adO = 0;
	    switch(e->a) {

		case Hv_timesR:
		case Hv_binaryR:
			e->dO.r = e->R.e->dO.r * e->dR;
			break;

		case Hv_timesLR:
		case Hv_binaryLR:
		case Hv_divLR:
			e->dO.r = e->L.e->dO.r*e->dL + e->R.e->dO.r*e->dR;
			break;

		case Hv_timesL:
		case Hv_unary:
			e->dO.r = e->L.e->dO.r * e->dL;
			break;

		case Hv_vararg:
		case Hv_if:
			if ((e1 = ((expr_va *)e)->valf)) {
				hv_fwd(e1);
				e->dO.r = ((expr_va *)e)->vale->dO.r;
				}
			else if ((e1 = ((expr_va *)e)->val) && e1->op != f_OPNUM)
				e->dO.r = e1->dO.r;
			else
				e->dO.r = 0;
			break;

		case Hv_plterm:
			e->dO.r = e->dL * e->R.e->dO.r;
			break;

		case Hv_sumlist:
			ep = e->R.ep;
			for(dO = 0; (e1 = *ep); ep++)
				dO += e1->dO.r;
			e->dO.r = dO;
			break;

		case Hv_func:
			da = ((expr_f *)e)->da;
			dae = ((expr_f *)e)->dae;
			for(dO = 0; da < dae; da++)
				dO += da->e->dO.r * *da->u.v;
			e->dO.r = dO;
			break;

		case Hv_negate:
			e->dO.r = -e->L.e->dO.r;
			break;

		case Hv_plusR:
			e->dO.r = e->R.e->dO.r;
			break;

		case Hv_plusL:
			e->dO.r = e->L.e->dO.r;
			break;

		case Hv_plusLR:
			e->dO.r = e->L.e->dO.r + e->R.e->dO.r;
			break;

		case Hv_minusR:
			e->dO.r = -e->R.e->dO.r;
			break;

		case Hv_minusLR:
			e->dO.r = e->L.e->dO.r - e->R.e->dO.r;
			break;

		default:/*DEBUG*/
			fprintf(Stderr, "bad e->a = %d in hv_fwd\n", e->a);
			exit(1);
		}
	    }
	}

 static void
func_back(expr_f *f)
{
	argpair *da, *da1, *dae;
	expr *e;
	real **fh;
	real aO, adO, t;

	fh = f->fh;
	aO = f->aO;
	adO = f->adO;
	da = f->da;
	for(dae = f->dae; da < dae; da++) {
		e = da->e;
		e->adO += (t = *da->u.v) * adO;
		e->aO += t * aO;
		t = adO*e->dO.r;
		for(da1 = f->da; da1 < dae; da1++) {
			e = da1->e;
			e->aO += t * **fh++;
			}
		}
	}

 static void
funnel_back(ASL_pfgh *asl, cexp *c, expr_v *v, real t)
{
	expr_v **vp, **vp1, **vpe;
	hes_fun *hf;
	ograd *og;
	real *g, *h;
	real aO, adO;

	aO = v->aO = t;
	adO = v->adO;
	hf = c->hfun;
	if ((og = hf->og)) {
		do {
			v = var_e + og->varno;
			v->adO += (t = og->coef) * adO;
			v->aO += t*aO;
			}
			while((og = og->next));
		return;
		}
	g = hf->grdhes;
	h = g + hf->n;
	vp = hf->vp;
	vpe = vp + hf->n;
	do {
		v = *vp++;
		v->adO += (t = *g++) * adO;
		v->aO += t*aO;
		t = adO * v->dO.r;
		vp1 = hf->vp;
		do (*vp1++)->aO += t * *h++;
		   while(vp1 < vpe);
		}
		while(vp < vpe);
	}

 static void
hv_back(expr *e)
{
	expr *e1, **ep, *e2;
	real adO, t1, t2;

	if (!e || (!e->aO && !e->adO))
		return;
	for(; e; e = e->bak)
	    switch(e->a) {
		case Hv_binaryR:
			e1 = e->R.e;
			e1->adO += e->adO * e->dR;
			e1->aO += e->aO * e->dR  +  e->adO * e1->dO.r * e->dR2;
			break;

		case Hv_binaryLR:
			e1 = e->L.e;
			e2 = e->R.e;
			adO = e->adO;
			t1 = adO * e1->dO.r;
			t2 = adO * e2->dO.r;
			e1->aO  += e->aO*e->dL + t1*e->dL2 + t2*e->dLR;
			e2->aO  += e->aO*e->dR + t1*e->dLR + t2*e->dR2;
			e1->adO += adO * e->dL;
			e2->adO += adO * e->dR;
			break;

		case Hv_divLR:
			e1 = e->L.e;
			e2 = e->R.e;
			adO = e->adO;
			t1 = adO * e1->dO.r;
			t2 = adO * e2->dO.r;
			e1->aO  += e->aO*e->dL + t2*e->dLR;
			e2->aO  += e->aO*e->dR + t1*e->dLR + t2*e->dR2;
			e1->adO += adO * e->dL;
			e2->adO += adO * e->dR;
			break;

		case Hv_unary:
			e1 = e->L.e;
			e1->adO += e->adO * e->dL;
			e1->aO  += e->aO * e->dL  +  e->adO * e1->dO.r * e->dL2;
			break;

		case Hv_vararg:
		case Hv_if:
			if ((e1 = ((expr_va *)e)->vale)) {
				e1->aO = e->aO;
				e1->adO = e->adO;
				hv_back(e1);
				}
			else {
				e1 = ((expr_va *)e)->val;
				if (e1->op != f_OPNUM) {
					e1->aO += e->aO;
					e1->adO += e->adO;
					}
				}
			break;

		case Hv_plterm:
			e->R.e->aO += e->dL * e->aO;
			break;

		case Hv_sumlist:
			ep = e->R.ep;
			t1 = e->aO;
			t2 = e->adO;
			while((e1 = *ep++)) {
				e1->aO += t1;
				e1->adO += t2;
				}
			break;

		case Hv_func:
			func_back((expr_f *)e);
			break;

		case Hv_negate:
			e1 = e->L.e;
 neg_end:
			e1->aO -= e->aO;
			e1->adO -= e->adO;
			break;

		case Hv_plusR:
			e1 = e->R.e;
			goto plus_end;

		case Hv_plusL:
			e1 = e->L.e;
 plus_end:
			e1->aO += e->aO;
			e1->adO += e->adO;
			break;

		case Hv_plusLR:
			e1 = e->L.e;
			e1->aO += t1 = e->aO;
			e1->adO += t2 = e->adO;
			e1 = e->R.e;
			e1->aO += t1;
			e1->adO += t2;
			break;

		case Hv_minusR:
			e1 = e->R.e;
			goto neg_end;

		case Hv_minusLR:
			e1 = e->L.e;
			e1->aO += t1 = e->aO;
			e1->adO += t2 = e->adO;
			e1 = e->R.e;
			e1->aO -= t1;
			e1->adO -= t2;
			break;

		case Hv_timesR:
			e1 = e->R.e;
			e1->adO += e->adO * (t1 = e->dR);
			e1->aO += e->aO * t1;
			break;

		case Hv_timesL:
			e1 = e->L.e;
			e1->adO += e->adO * (t1 = e->dL);
			e1->aO  += e->aO * t1;
			break;

		case Hv_timesLR:
			e1 = e->L.e;
			e2 = e->R.e;
			adO = e->adO;
			e1->aO  += e->aO*e->dL  +  adO * e2->dO.r;
			e2->aO  += e->aO*e->dR  +  adO * e1->dO.r;
			e1->adO += adO * e->dL;
			e2->adO += adO * e->dR;
			break;

		default:/*DEBUG*/
			fprintf(Stderr, "bad e->a = %d in hv_back\n", e->a);
			exit(1);
		}
	}

 static void
hv_fwd0(ASL_pfgh *asl, cexp *c, expr_v *v)
{
	expr_v **vp, **vpe;
	hes_fun *hf;
	int i;
	linarg *la;
	linpart *L, *Le;
	ograd *og;
	real *g, x;

	v->aO = v->adO = 0;
	if ((hf = c->hfun)) {
		x = 0;
		if ((og = hf->og))
			do x += og->coef * var_e[og->varno].dO.r;
			while((og = og->next));
		else {
			g = hf->grdhes;
			vp = hf->vp;
			vpe = vp + hf->n;
			do x += *g++ * (*vp++)->dO.r;
			   while(vp < vpe);
			}
		}
	else if (c->ef) {
		hv_fwd(c->ef);
		x = c->ee->dO.r;
		}
	else if (c->e->op != f_OPNUM)
		x = c->e->dO.r;
	else
		x = 0;
	if ((la = c->la)) {
		i = c - asl->I.cexps2_;
		x += asl->P.dv[i].scale * la->v->dO.r;
		}

	else if ((L = c->L)) {
		for(Le = L + c->nlin; L < Le; L++)
			x += L->fac * ((expr_v*)L->v.vp)->dO.r;
		}
	v->dO.r = x;
	}

 static void
hfg_fwd(expr *e)
{
	expr *e1;

	for(; e; e = e->fwd) {
		e->aO = 0;
		switch(e->a) {
		  case Hv_vararg:
		  case Hv_if:
			if ((e1 = ((expr_va *)e)->valf))
				hfg_fwd(e1);
		  }
		}
	}

 static void
hfg_back(expr *e)
{
	expr *e1, **ep;
	real aO;

	if (!e || !e->aO)
		return;
	for(; e; e = e->bak)
	    switch(e->a) {
		case Hv_timesR:
		case Hv_binaryR:
			e->R.e->aO += e->aO * e->dR;
			break;

		case Hv_binaryLR:
		case Hv_timesLR:
		case Hv_divLR:
			aO = e->aO;
			e->L.e->aO += aO * e->dL;
			e->R.e->aO += aO * e->dR;
			break;

		case Hv_unary:
		case Hv_timesL:
			e->L.e->aO += e->aO * e->dL;
			break;

		case Hv_vararg:
		case Hv_if:
			if ((e1 = ((expr_va *)e)->vale)) {
				e1->aO = e->aO;
				hfg_back(e1);
				}
			else {
				e1 = ((expr_va *)e)->val;
				if (e1->op != f_OPNUM)
					e1->aO += e->aO;
				}
			break;

		case Hv_plterm:
			e->R.e->aO += e->dL * e->aO;
			break;

		case Hv_sumlist:
			ep = e->R.ep;
			aO = e->aO;
			while((e1 = *ep++))
				e1->aO += aO;
			break;

		case Hv_func:
			func_back((expr_f *)e);
			break;

		case Hv_negate:
			e->L.e->aO -= e->aO;
			break;

		case Hv_plusR:
			e->R.e->aO += e->aO;
			break;

		case Hv_plusL:
			e->L.e->aO += e->aO;
			break;

		case Hv_plusLR:
			e->L.e->aO += aO = e->aO;
			e->R.e->aO += aO;
			break;

		case Hv_minusR:
			e->R.e->aO -= e->aO;
			break;

		case Hv_minusLR:
			e->L.e->aO += aO = e->aO;
			e->R.e->aO -= aO;
			break;

		default:/*DEBUG*/
			fprintf(Stderr, "bad e->a = %d in hfg_back\n", e->a);
			exit(1);
		}
	}

 static void
funnelhes(ASL_pfgh *asl)
{
	cexp *c;
	expr *e;
	expr_v *v, **vp, **vp1, **vpe;
	hes_fun *hf;
	int n;
	real *g, *h;

	x0kind &= ~ASL_need_funnel;
	for(hf = asl->I.hesthread; hf; hf = hf->hfthread) {
		if (hf->og)
			continue;
		n = hf->n;
		g = hf->grdhes;
		h = g + n;
		c = hf->c;
		vp = hf->vp;
		vpe = vp + n;

		do (*vp++)->aO = 0;
		   while(vp < vpe);

		hfg_fwd(c->ef);
		e = c->ee;
		e->aO = 1;
		hfg_back(e);

		vp = hf->vp;
		do {
			v = *vp++;
			*g++ = v->aO;
			v->dO.r = v->aO = v->adO = 0;
			}
			while(vp < vpe);

		vp = hf->vp;
		do {
			v = *vp++;
			v->dO.r = 1;
			if ((e = c->ef))
				hv_fwd(e);
			if ((e = c->ee)) {
				e->aO = 0;
				e->adO = 1;
				hv_back(e);
				}
			else if ((e = c->e)->op != f_OPNUM) {
				e->aO = 0;
				e->adO = 1;
				}
			v->dO.r = 0;
			vp1 = hf->vp;
			do {
				v = *vp1++;
				*h++ = v->aO;
				v->aO = v->adO = 0;
				}
				while(vp1 < vpe);
			}
			while(vp < vpe);
		}
	}

 static void
hvp0comp_ASL(ASL_pfgh *asl, real *hv, const real *p, int nobj, const real *ow, const real *y)
	/* p = direction */
	/* y = Lagrange multipliers */
	/* hv = result */
{
	cexp *c, *c1, *ce;
	const real *p1;
	expr *e;
	expr_v *v, *x, *x0, *xe;
	int *dvsp0, i, i0, i1, n, nc, no, noe;
	linarg *la;
	linpart *L, *Le;
	ograd *og;
	ps_func *f, *f0;
	psb_elem *b, *be;
	psg_elem *g, *ge;
	real *cscale, t, t2;

#ifdef IGNORE_BOGUS_WARNINGS
	c1 = ce = 0;
	dvsp0 = 0;
	i1 = 0;
#endif

	if (x0kind & ASL_need_funnel)
		funnelhes(asl);
	if (nobj >= 0 && nobj < n_obj) {
		ow = ow ? ow + nobj : &edag_one_ASL;
		no = nobj;
		noe = no + 1;
		}
	else {
		no = noe = 0;
		if (ow)
			noe = n_obj;
		}
	n = c_vars >= o_vars ? c_vars : o_vars;
	for(la = asl->P.lalist; la; la = la->lnext) {
		og = la->nz;
		t = p[og->varno]*og->coef;
		while((og = og->next))
			t += p[og->varno]*og->coef;
		x = la->v;
		x->dO.r = t;
		x->aO = x->adO = 0;
		}
	p1 = p;
	x = x0 = var_e;
	for(xe = x + n; x < xe; x++) {
		x->dO.r = *p1++;
		x->aO = x->adO = 0.;
		}
	if (asl->P.ncom) {
		x = var_ex;
		dvsp0 = asl->P.dvsp0;
		c = cexps;
		i0 = *dvsp0;
		for(ce = c1 = c + asl->P.ncom; c < ce; c++) {
			for(i1 = *++dvsp0; i0 < i1; i0++)
				hv_fwd0(asl, c1++, asl->P.vp[i0]);
			hv_fwd0(asl, c, x++);
			}
		}
	if (!y || (nc = n_con) <= 0)
		goto no_y;
	cscale = asl->i.lscale;
	f0 = asl->P.cps;
	for(i = 0; i < nc; ++i) {
	    if ((t2 = y[i])) {
		if (cscale)
			t2 *= cscale[i];
		f = f0 + i;
		for(b = f->b, be = b + f->nb; b < be; b++) {
			if ((e = b->D.ef)) {
				hv_fwd(e);
				e = b->D.ee;
				e->aO = 0;
				e->adO = t2;
				hv_back(e);
				}
			else if ((e = b->D.e)->op != f_OPNUM) {
				e->aO = 0;
				e->adO = t2;
				}
			}
		for(g = f->g, ge = g + f->ng; g < ge; g++) {
			for(b = g->E, be = b + g->ns; b < be; b++) {
				if ((e = b->D.ef)) {
					hv_fwd(e);
					e = b->D.ee;
					e->aO = 0;
					e->adO = t2*g->g1;
					hv_back(e);
					}
				else if ((e = b->D.e)->op != f_OPNUM) {
					e->aO = 0;
					e->adO = t2*g->g1;
					}
				}
			if (g->g2) {
				t = 0.;
				for(og = g->og; og; og = og->next)
					t += og->coef * p[og->varno];
				t *= t2*g->g2;
				for(og = g->og; og; og = og->next)
					x0[og->varno].aO += t*og->coef;
				}
			}
		}
	    }
 no_y:
	for(; no < noe; no++) {
	    if ((t2 = *ow++)) {
		f = asl->P.ops + no;
		for(b = f->b, be = b + f->nb; b < be; b++) {
			if ((e = b->D.ef)) {
				hv_fwd(e);
				e = b->D.ee;
				e->aO = 0;
				e->adO = t2;
				hv_back(e);
				}
			else if ((e = b->D.e)->op != f_OPNUM) {
				e->aO = 0;
				e->adO = t2;
				}
			}
		for(g = f->g, ge = g + f->ng; g < ge; g++) {
			for(b = g->E, be = b + g->ns; b < be; b++) {
				if ((e = b->D.ef)) {
					hv_fwd(e);
					e = b->D.ee;
					e->aO = 0;
					e->adO = t2*g->g1;
					hv_back(e);
					}
				else if ((e = b->D.e)->op != f_OPNUM) {
					e->aO = 0;
					e->adO = t2*g->g1;
					}
				}
			if (g->g2) {
				t = 0.;
				for(og = g->og; og; og = og->next)
					t += og->coef * p[og->varno];
				t *= t2*g->g2;
				for(og = g->og; og; og = og->next)
					x0[og->varno].aO += t*og->coef;
				}
			}
		}
	    }
	if (asl->P.ncom) {
	    for(c = cexps; c < ce--; ) {
		for(i0 = *--dvsp0; i0 < i1; ) {
			v = asl->P.vp[--i1];
			--c1;
			if ((t = v->aO) && (L = c1->L))
				for(Le = L + c1->nlin; L < Le; L++)
					((expr_v*)L->v.vp)->aO += t * L->fac;
			if (c1->hfun)
				funnel_back(asl, c1, v, t);
			else if ((e = c1->ee)) {
				e->aO = t;
				e->adO = v->adO;
				hv_back(e);
				}
			else if ((e = c1->e)->op != f_OPNUM) {
				e->aO = t;
				e->adO = v->adO;
				}
			}
		if ((t = (--x)->aO) && (L = ce->L))
			for(Le = L + ce->nlin; L < Le; L++)
				((expr_v*)L->v.vp)->aO += t * L->fac;
		if (ce->hfun)
			funnel_back(asl, ce, x, t);
		else if ((e = ce->ee)) {
			e->aO = t;
			e->adO = x->adO;
			hv_back(e);
			}
		else if ((e = ce->e)->op != f_OPNUM) {
			e->aO = t;
			e->adO = x->adO;
			}
		}
	    }
	x = var_e;
	for(la = asl->P.lalist; la; la = la->lnext)
		if ((t = la->v->aO)) {
			og = la->nz;
			do x[og->varno].aO += t*og->coef;
				while((og = og->next));
			}
	while(x < xe)
		*hv++ = (x++)->aO;
	}

 static real *	/* Compute vector x0 = mat(h)*y0,	*/
		/* where h = upper triang of mat(h).	*/
dtmul(int n, real *x0, real *h, real *y0)
{
	int i;
	real *hi, t, *x, *y, *y1, yi;

	y1 = y0;
	--h;
	for(i = 0; i < n; i++) {
		hi = ++h + i;
		yi = *y1++;
		t = yi**hi;
		x = x0;
		y = y0;
		while(h < hi) {
			t += *y++**h;
			*x++ += yi**h++;
			}
		*x = t;
		}
	return x0;
	}

 void
hvpcomp_ASL(ASL *a, real *hv, const real *p, int nobj, const real *ow, const real *y)
	/* p = direction */
	/* y = Lagrange multipliers */
	/* hv = result */
{
	ASL_pfgh *asl;
	Ihinfo *ihi;
	const real *owi;
	expr_v *v;
	int kp, kw, n, no, noe, ns, nv, *ui, *uie;
	linarg *la, **lap, **lape;
	ograd *og;
	ps_func *ps, *pe;
	psg_elem *g, *ge;
	range *r;
	real *cscale, t, t1, t2, *p0, *s, *w, *wi, *x;

	ASL_CHECK(a, ASL_read_pfgh, "hvpcomp");
	if (a->i.Derrs)
		deriv2_errchk_ASL(a, 3);
	asl = (ASL_pfgh*)a;
	xpsg_check_ASL(asl, nobj, ow, y);
	nv = n_var;
	kp = htcl(nv*sizeof(real));
	p0 = 0;
	if ((s = asl->i.vscale)) {
		p0 = (real*)new_mblk(kp);
		for(n = 0; n < nv; n++)
			p0[n] = s[n] * p[n];
		p = p0;
		}
	if (!asl->P.ihdcur) {
		if (asl->P.ndhmax <= 0) {
			hvp0comp_ASL(asl,hv,p,nobj,ow,y);
			goto done;
			}
		if (!(n = asl->P.nhvprod))
			n = asl->P.ihdmin;
		if (n >= asl->P.ihdmin)
			hvpinit_ASL(a, ihd_limit, nobj, ow, y);
		}
	asl->P.nhvprod++;
	memset(hv, 0, nv*sizeof(real));
	for(la = asl->P.lalist; la; la = la->lnext) {
		og = la->nz;
		t = p[og->varno]*og->coef;
		while((og = og->next))
			t += p[og->varno]*og->coef;
		v = la->v;
		v->dO.r = t;
		v->aO = v->adO = 0;
		}
	kw = kp + 1;
	w = (real*)new_mblk(kw);
	x = w + n_var;
	s = asl->P.dOscratch;
	ns = 0;
	for(ihi = asl->P.ihi1; ihi; ihi = ihi->next) {
		r = ihi->r;
		if (ihi->hest)
		    for(; r; r = r->rlist.prev) {
			n = r->n;
			nv = r->nv;
			wi = w;
			if (n < nv) {
				lap = r->lap;
				lape = lap + n;
				do {
					og = (*lap++)->nz;
					t = p[og->varno]*og->coef;
					while((og = og->next))
						t += p[og->varno]*og->coef;
					*wi++ = t;
					}
					while(lap < lape);
				wi = dtmul(n, x, r->hest, w);
				lap = r->lap;
				do if ((t = *wi++)) {
					og = (*lap)->nz;
					do hv[og->varno] +=
						t*og->coef;
					   while((og = og->next));
					}
					while(++lap < lape);
				}
			else {
				ui = r->ui;
				uie = ui + nv;
				do *wi++ = p[*ui++];
					while(ui < uie);
				wi = dtmul(nv, x, r->hest, w);
				ui = r->ui;
				do hv[*ui++] += *wi++;
					while(ui < uie);
				}
			}
		else
		    for(; r; r = r->rlist.prev) {
			n = r->n;
			if (ns < n)
				ns = n;
			wi = s;
			lap = r->lap;
			lape = lap + n;
			do {
				og = (*lap++)->nz;
				t = p[og->varno]*og->coef;
				while((og = og->next))
					t += p[og->varno]*og->coef;
				*wi++ = t;
				}
				while(lap < lape);
			pshv_prod_ASL(asl, r, nobj, ow, y);
			lap = r->lap;
			do {
				la = *lap++;
				if ((t = la->v->aO)) {
					og = la->nz;
					do hv[og->varno] += t*og->coef;
						while((og = og->next));
					}
				}
				while(lap < lape);
			}
		}
	del_mblk(kw,w);
	wi = s + ns;
	while(wi > s)
		*--wi = 0.;
	if (asl->P.nobjgroups) {
	    if (nobj >= 0 && nobj < n_obj) {
		owi = ow ? ow + nobj : &edag_one_ASL;
		no = nobj;
		noe = no + 1;
		}
	    else {
		nobj = -1;
		no = noe = 0;
		if ((owi = ow))
			noe = n_obj;
		}
	    for(; no < noe; no++)
		if ((t = *owi++)) {
		    ps = asl->P.ops + no;
		    g = ps->g;
		    for(ge = g + ps->ng; g < ge; g++)
			if ((t2 = g->g2) && (og = g->og)) {
				t1 = p[og->varno]*og->coef;
				while((og = og->next))
					t1 += p[og->varno]*og->coef;
				t2 *= t*t1;
				og = g->og;
				do hv[og->varno] += t2*og->coef;
					while((og = og->next));
				}
		}
	    }
	if (asl->P.ncongroups && y) {
		cscale = a->i.lscale;
		ps = asl->P.cps;
		for(pe = ps + n_con; ps < pe; ps++, y++)
		    if ((t = cscale ? *cscale++ * *y : *y))
			for(g = ps->g, ge = g + ps->ng; g < ge; g++)
			    if ((t2 = g->g2) && (og = g->og)) {
				t1 = p[og->varno]*og->coef;
				while((og = og->next))
					t1 += p[og->varno]*og->coef;
				t2 *= t*t1;
				og = g->og;
				do hv[og->varno] += t2*og->coef;
					while((og = og->next));
				}
		}
	v = var_e;
	for(la = asl->P.lalist; la; la = la->lnext)
		if ((t = la->v->aO)) {
			og = la->nz;
			do v[og->varno].aO += t*og->coef;
				while((og = og->next));
			}
 done:
	if (p0) {
		del_mblk(kp, p0);
		s = asl->i.vscale;
		w = hv + n_var;
		while(hv < w)
			*hv++ *= *s++;
		}
	}

/* Variant of hvpcomp_ASL that has a final nerror argument, working
   similarly to the final nerror argument to objval_(), etc. */

 void
hvpcompe_ASL(ASL *asl, real *hv, const real *p, int nobj, const real *ow, const real *y, fint *nerror)
{
	Jmp_buf **Jp, *Jsave, b;

	Jp = !nerror || *nerror >= 0 ? &err_jmp : &err_jmp1;
	Jsave = *Jp;
	*Jp = &b;
	*nerror = 0;
	if (setjmp(b.jb))
		*nerror = 1;
	else
		hvpcomp_ASL(asl, hv, p, nobj, ow, y);
	*Jp = Jsave;
	}

 void
pshv_prod_ASL(ASL_pfgh *asl, range *r, int nobj, const real *ow, const real *y)
{
	cexp *c;
	expr *e;
	expr_v *v;
	int *cei, *cei0, *ceie, i;
	linarg *la, **lap, **lape;
	linpart *L, *Le;
	ps_func *p;
	psb_elem *b;
	psg_elem *g;
	real *cscale, *s, owi, t;

	cscale = asl->i.lscale;
	owi = 1.;
	if (nobj >= 0 && nobj < n_obj) {
		if (ow) {
			if ((owi = ow[nobj]) == 0.)
				nobj = -1;
			ow = 0;
			}
		}
	if (x0kind & ASL_need_funnel)
		funnelhes(asl);
	s = asl->P.dOscratch;
	lap = r->lap;
	lape = lap + r->n;
	while(lap < lape) {
		la = *lap++;
		v = la->v;
		v->dO.r = *s++;
		v->adO = v->aO = 0.;
		}
	if ((cei = cei0 = r->cei)) {
		i = *cei0++;
		ceie = (cei = cei0) + i;
		do {
			i = *cei++;
			hv_fwd0(asl, cexps + i, asl->P.vp[i]);
			}
			while(cei < ceie);
		}
	for(b = r->refs; b; b = b->next) {
		if ((i = b->conno) < 0) {
			i = -2 - i;
			if (i == nobj)
				t = owi;
			else if (ow) {
				if (!(t = ow[i]))
					continue;
				}
			else
				continue;
			p = asl->P.ops;
			}
		else {
			if (!y || !(t = y[i]))
				continue;
			if (cscale)
				t *= cscale[i];
			p = asl->P.cps;
			}
		if (b->groupno) {
			p += i;
			g = p->g + (b->groupno - 1);
			if (asl->P.pshv_g1)
				t *= g->g1;
			}
		if ((e = b->D.ef)) {
			hv_fwd(e);
			e = b->D.ee;
			e->aO = 0;
			e->adO = t;
			hv_back(e);
			}
		else if ((e = b->D.e)->op != f_OPNUM)
			e->adO += t;
		}
	while(cei > cei0) {
		i = *--cei;
		c = cexps + i;
		v = asl->P.vp[i];
		if ((t = v->aO) && (L = c->L)) {
		    if ((la = c->la))
			la->v->aO += t * asl->P.dv[i].scale;
		    else {
			for(Le = L + c->nlin; L < Le; L++)
				((expr_v*)L->v.vp)->aO += t * L->fac;
			}
		    }
		if (c->hfun)
			funnel_back(asl, c, v, t);
		else if ((e = c->ee)) {
			e->aO = t;
			e->adO = v->adO;
			hv_back(e);
			}
		else if ((e = c->e)->op != f_OPNUM) {
			e->aO += t;
			e->adO += v->adO;
			}
		}
	}

 void
funpset_ASL(ASL_pfgh *asl, funnel *f)
{
	cplist	*cl;
	derp	*d;

	for(; f; f = f->next) {
		memset(adjoints_nv1, 0, f->fcde.zaplen);
		cl = f->cl;
		do *cl->ca.rp = 0;
			while((cl = cl->next));
		d = f->fcde.d;
		*d->b.rp = 1.;
		do *d->a.rp += *d->b.rp * *d->c.rp;
			while((d = d->next));
		cl = f->cl;
		do *cl->cfa = *cl->ca.rp;
			while((cl = cl->next));
		}
	}

 void
hvpcompd_ASL(ASL *a, real *hv, const real *p, int co)
	/* p = direction */
	/* hv = result */
	/* co >= 0: behave like hvpcomp_ASL with nobj = -1, ow = 0, y[i] = i == co ? 1. : 0. */
	/* co < 0: behave like hvpcomp_ASL with nobj = -1 - co, ow = 0, y = 0 */
{
	ASL_pfgh *asl;
	cexp *c, *c1, *ce;
	cgrad *cg, *cg0;
	expr *e;
	expr_v *v, *x, *x0;
	int *dvsp0, i0, i1, kp, n, no, nx, oxk;
	linarg *la;
	linpart *L, *Le;
	ograd *og, *og0;
	ps_func *f;
	psb_elem *b, *be;
	psg_elem *g, *ge;
	real *s, t, t2, *p0;
	varno_t i;

#ifdef IGNORE_BOGUS_WARNINGS
	c1 = ce = 0;
	dvsp0 = 0;
	i1 = 0;
	v = 0;
	x = 0;
#endif
	ASL_CHECK(a, ASL_read_pfgh, "hvpcompi");
	asl = (ASL_pfgh*)a;
	if (x0kind == ASL_first_x) {
		if (!(s = X0))
			memset(s = Lastx, 0, n_var*sizeof(real));
		co_index = co;
		xp_check_ASL(asl, s);
		}
	nx = asl->i.nxval;
	oxk = asl->i.x_known;
	asl->i.x_known = 1;

	p0 = 0;
	cg0 = 0;
	og0 = 0;
	x0 = var_e;
	n = c_vars >= o_vars ? c_vars : o_vars;
	t2 = 1.;
	memset(hv, 0, n_var*sizeof(real));
	for(la = asl->P.lalist; la; la = la->lnext) {
		og = la->nz;
		t = p[og->varno]*og->coef;
		while((og = og->next))
			t += p[og->varno]*og->coef;
		x = la->v;
		x->dO.r = t;
		x->aO = x->adO = 0;
		}
	if (co >= 0) {
		if (co >= nlc)
			return;
		f = asl->P.cps + co;
		if (asl->i.ncxval[co] != nx)
			conpival_ASL(a, co, Lastx, 0);
		if (f->ng && f->nxval != nx)
			conpgrd_ASL(a, co, Lastx, 0, 0);
		if ((s = asl->i.lscale))
			t2 = s[co];
		cg = cg0 = Cgrad[co];
		if ((s = asl->i.vscale)) {
			kp = htcl(n*sizeof(real));
			p0 = (real*)new_mblk(kp);
			for(; cg; cg = cg->next) {
				i = cg->varno;
				x = x0 + i;
				x->dO.r = p0[i] = p[i]*s[i];
				x->aO = x->adO = 0.;
				}
			p = p0;
			}
		else {
			for(; cg; cg = cg->next) {
				i = cg->varno;
				x = x0 + i;
				x->dO.r = p[i];
				x->aO = x->adO = 0.;
				}
			}
		}
	else {
		no = -1 - co;
		if (no >= nlo)
			return;
		f = asl->P.ops + no;
		if (asl->i.ncxval[no] != nx)
			objpval_ASL(a, no, Lastx, 0);
		if (f->ng && f->nxval != nx)
			objpgrd_ASL(a, no, Lastx, 0, 0);
		og = og0 = Ograd[no];
		if ((s = asl->i.vscale)) {
			kp = htcl(n*sizeof(real));
			p0 = (real*)new_mblk(kp);
			for(; og; og = og->next) {
				i = og->varno;
				x = x0 + i;
				x->dO.r = p0[i] = p[i]*s[i];
				x->aO = x->adO = 0.;
				}
			p = p0;
			}
		else {
			for(; og; og = og->next) {
				i = og->varno;
				x = x0 + i;
				x->dO.r = p[i];
				x->aO = x->adO = 0.;
				}
			}
		}
	if (asl->i.Derrs) {
		asl->i.x_known = oxk;
		deriv_errchk_ASL(a, co, 1, 3);
		asl->i.x_known = 1;
		}
	if (asl->P.ncom) {
		x = var_ex;
		dvsp0 = asl->P.dvsp0;
		c = cexps;
		i0 = *dvsp0;
		for(ce = c1 = c + asl->P.ncom; c < ce; c++) {
			for(i1 = *++dvsp0; i0 < i1; i0++)
				hv_fwd0(asl, c1++, asl->P.vp[i0]);
			hv_fwd0(asl, c, x++);
			}
		}
	for(b = f->b, be = b + f->nb; b < be; b++) {
		if ((e = b->D.ef)) {
			hv_fwd(e);
			e = b->D.ee;
			e->aO = 0;
			e->adO = t2;
			hv_back(e);
			}
		else if ((e = b->D.e)->op != f_OPNUM) {
			e->aO = 0;
			e->adO = t2;
			}
		}
	for(g = f->g, ge = g + f->ng; g < ge; g++) {
		for(b = g->E, be = b + g->ns; b < be; b++) {
			if ((e = b->D.ef)) {
				hv_fwd(e);
				e = b->D.ee;
				e->aO = 0;
				e->adO = t2*g->g1;
				hv_back(e);
				}
			else if ((e = b->D.e)->op != f_OPNUM) {
				e->aO = 0;
				e->adO = t2*g->g1;
				}
			}
		if (g->g2) {
			t = 0.;
			for(og = g->og; og; og = og->next)
				t += og->coef * p[og->varno];
			t *= t2*g->g2;
			for(og = g->og; og; og = og->next)
				x0[og->varno].aO += t*og->coef;
			}
		}
	if (asl->P.ncom) {
	    for(c = cexps; c < ce--; ) {
		for(i0 = *--dvsp0; i0 < i1; ) {
			v = asl->P.vp[--i1];
			--c1;
			if ((t = v->aO) && (L = c1->L))
				for(Le = L + c1->nlin; L < Le; L++)
					((expr_v*)L->v.vp)->aO += t * L->fac;
			if (c1->hfun)
				funnel_back(asl, c1, v, t);
			else if ((e = c1->ee)) {
				e->aO = t;
				e->adO = v->adO;
				hv_back(e);
				}
			else if ((e = c1->e)->op != f_OPNUM) {
				e->aO = t;
				e->adO = v->adO;
				}
			}
		if ((t = (--x)->aO) && (L = ce->L))
			for(Le = L + ce->nlin; L < Le; L++)
				((expr_v*)L->v.vp)->aO += t * L->fac;
		if (ce->hfun)
			funnel_back(asl, ce, x, t);
		else if ((e = ce->ee)) {
			e->aO = t;
			e->adO = x->adO;
			hv_back(e);
			}
		else if ((e = ce->e)->op != f_OPNUM) {
			e->aO = t;
			e->adO = x->adO;
			}
		}
	    }
	x = var_e;
	for(la = asl->P.lalist; la; la = la->lnext)
		if ((t = la->v->aO)) {
			og = la->nz;
			do x[og->varno].aO += t*og->coef;
				while((og = og->next));
			}
	if ((cg = cg0)) {
		if (s) {
			while(cg) {
				i = cg->varno;
				hv[i] = s[i]*x0[i].aO;
				cg = cg->next;
				}
			}
		else {
			while(cg) {
				i = cg->varno;
				hv[i] = x0[i].aO;
				cg = cg->next;
				}
			}
		}
	else {
		og = og0;
		if (s) {
			while(og) {
				i = og->varno;
				hv[i] = s[i]*x0[i].aO;
				og = og->next;
				}
			}
		else {
			while(og) {
				i = og->varno;
				hv[i] = x0[i].aO;
				og = og->next;
				}
			}
		}
	if (p0)
		del_mblk(kp, p0);
	}

/* Variant of hvpcompd_ASL that has a final nerror argument, working
   similarly to the final nerror argument to objval_(), etc. */

 void
hvpcompde_ASL(ASL *asl, real *hv, const real *p, int co, fint *nerror)
{
	Jmp_buf **Jp, *Jsave, b;

	Jp = !nerror || *nerror >= 0 ? &err_jmp : &err_jmp1;
	Jsave = *Jp;
	*Jp = &b;
	*nerror = 0;
	if (setjmp(b.jb))
		*nerror = 1;
	else
		hvpcompd_ASL(asl, hv, p, co);
	*Jp = Jsave;
	}

 varno_t
hvpcomps_ASL(ASL *a, real *hv, const real *p, int co, varno_t nz, varno_t *z)
	/* p = direction */
	/* hv = result */
	/* co >= 0: behave like hvpcomp_ASL with nobj = -1, ow = 0, y[i] = i == co ? 1. : 0. */
	/* co < 0: behave like hvpcomp_ASL with nobj = -1 - co, ow = 0, y = 0 */
{
	ASL_pfgh *asl;
	cexp *c, *c1, *ce;
	cgrad *cg, *cg0;
	expr *e;
	expr_v *v, *x, *x0;
	int *dvsp0, i0, i1, kp, n, no, nx, oxk;
	linarg *la;
	linpart *L, *Le;
	ograd *og, *og0;
	ps_func *f;
	psb_elem *b, *be;
	psg_elem *g, *ge;
	real *hve, *p0, *s, t, t2, *vscale;
	varno_t F, i, rv, *ze;

#ifdef IGNORE_BOGUS_WARNINGS
	c1 = ce = 0;
	dvsp0 = 0;
	i1 = 0;
	v = 0;
	x = 0;
#endif
	ASL_CHECK(a, ASL_read_pfgh, "hvpcompi");
	asl = (ASL_pfgh*)a;
	if (x0kind == ASL_first_x) {
		if (!(s = X0))
			memset(s = Lastx, 0, n_var*sizeof(real));
		co_index = co;
		xp_check_ASL(asl, s);
		}
	nx = asl->i.nxval;
	oxk = asl->i.x_known;
	asl->i.x_known = 1;

	p0 = 0;
	cg0 = 0;
	og0 = 0;
	x0 = var_e;
	n = c_vars >= o_vars ? c_vars : o_vars;
	t2 = 1.;
	memset(hv, 0, n_var*sizeof(real));
	for(la = asl->P.lalist; la; la = la->lnext) {
		og = la->nz;
		t = p[og->varno]*og->coef;
		while((og = og->next))
			t += p[og->varno]*og->coef;
		x = la->v;
		x->dO.r = t;
		x->aO = x->adO = 0;
		}
	no = -1 - co;
	if (co >= 0) {
		if (co >= nlc)
			return 0;
		f = asl->P.cps + co;
		if (asl->i.ncxval[co] != nx)
			conpival_ASL(a, co, Lastx, 0);
		if (f->ng && f->nxval != nx)
			conpgrd_ASL(a, co, Lastx, 0, 0);
		if ((s = asl->i.lscale))
			t2 = s[co];
		cg = cg0 = Cgrad[co];
		if ((vscale = asl->i.vscale)) {
			kp = htcl(n*sizeof(real));
			p0 = (real*)new_mblk(kp);
			for(; cg; cg = cg->next) {
				i = cg->varno;
				x = x0 + i;
				x->dO.r = p0[i] = p[i]*vscale[i];
				x->aO = x->adO = 0.;
				}
			p = p0;
			}
		else {
			for(; cg; cg = cg->next) {
				i = cg->varno;
				x = x0 + i;
				x->dO.r = p[i];
				x->aO = x->adO = 0.;
				}
			}
		}
	else {
		if (no >= nlo)
			return 0;
		f = asl->P.ops + no;
		if (asl->i.ncxval[no] != nx)
			objpval_ASL(a, no, Lastx, 0);
		if (f->ng && f->nxval != nx)
			objpgrd_ASL(a, no, Lastx, 0, 0);
		og = og0 = Ograd[no];
		if ((vscale = asl->i.vscale)) {
			kp = htcl(n*sizeof(real));
			p0 = (real*)new_mblk(kp);
			for(; og; og = og->next) {
				i = og->varno;
				x = x0 + i;
				x->dO.r = p0[i] = p[i]*vscale[i];
				x->aO = x->adO = 0.;
				}
			p = p0;
			}
		else {
			for(; og; og = og->next) {
				i = og->varno;
				x = x0 + i;
				x->dO.r = p[i];
				x->aO = x->adO = 0.;
				}
			}
		}
	if (asl->i.Derrs) {
		asl->i.x_known = oxk;
		deriv_errchk_ASL(a, co, 1, 3);
		asl->i.x_known = 1;
		}
	if (asl->P.ncom) {
		x = var_ex;
		dvsp0 = asl->P.dvsp0;
		c = cexps;
		i0 = *dvsp0;
		for(ce = c1 = c + asl->P.ncom; c < ce; c++) {
			for(i1 = *++dvsp0; i0 < i1; i0++)
				hv_fwd0(asl, c1++, asl->P.vp[i0]);
			hv_fwd0(asl, c, x++);
			}
		}
	for(b = f->b, be = b + f->nb; b < be; b++) {
		if ((e = b->D.ef)) {
			hv_fwd(e);
			e = b->D.ee;
			e->aO = 0;
			e->adO = t2;
			hv_back(e);
			}
		else if ((e = b->D.e)->op != f_OPNUM) {
			e->aO = 0;
			e->adO = t2;
			}
		}
	for(g = f->g, ge = g + f->ng; g < ge; g++) {
		for(b = g->E, be = b + g->ns; b < be; b++) {
			if ((e = b->D.ef)) {
				hv_fwd(e);
				e = b->D.ee;
				e->aO = 0;
				e->adO = t2*g->g1;
				hv_back(e);
				}
			else if ((e = b->D.e)->op != f_OPNUM) {
				e->aO = 0;
				e->adO = t2*g->g1;
				}
			}
		if (g->g2) {
			t = 0.;
			for(og = g->og; og; og = og->next)
				t += og->coef * p[og->varno];
			t *= t2*g->g2;
			for(og = g->og; og; og = og->next)
				x0[og->varno].aO += t*og->coef;
			}
		}
	if (asl->P.ncom) {
	    for(c = cexps; c < ce--; ) {
		for(i0 = *--dvsp0; i0 < i1; ) {
			v = asl->P.vp[--i1];
			--c1;
			if ((t = v->aO) && (L = c1->L))
				for(Le = L + c1->nlin; L < Le; L++)
					((expr_v*)L->v.vp)->aO += t * L->fac;
			if (c1->hfun)
				funnel_back(asl, c1, v, t);
			else if ((e = c1->ee)) {
				e->aO = t;
				e->adO = v->adO;
				hv_back(e);
				}
			else if ((e = c1->e)->op != f_OPNUM) {
				e->aO = t;
				e->adO = v->adO;
				}
			}
		if ((t = (--x)->aO) && (L = ce->L))
			for(Le = L + ce->nlin; L < Le; L++)
				((expr_v*)L->v.vp)->aO += t * L->fac;
		if (ce->hfun)
			funnel_back(asl, ce, x, t);
		else if ((e = ce->ee)) {
			e->aO = t;
			e->adO = x->adO;
			hv_back(e);
			}
		else if ((e = ce->e)->op != f_OPNUM) {
			e->aO = t;
			e->adO = x->adO;
			}
		}
	    }
	x = var_e;
	for(la = asl->P.lalist; la; la = la->lnext)
		if ((t = la->v->aO)) {
			og = la->nz;
			do x[og->varno].aO += t*og->coef;
				while((og = og->next));
			}
	rv = 0;
	if ((ze = z))
		ze += nz;
	if ((hve = hv))
		hve += nz;
	F = Fortran;
	if ((cg = cg0)) {
		if (!hv) {
			while(cg) {
				++rv;
				if (z < ze)
					*z++ = cg->varno;
				cg = cg->next;
				}
			}
		else if (vscale) {
			while(cg) {
				++rv;
				i = cg->varno;
				if (z < ze)
					*z++ = F + i;
				if (hv < hve)
					*hv++ = vscale[i]*x0[i].aO;
				cg = cg->next;
				}
			}
		else {
			while(cg) {
				++rv;
				i = cg->varno;
				if (z < ze)
					*z++ = F + i;
				if (hv < hve)
					*hv++ = x0[i].aO;
				cg = cg->next;
				}
			}
		}
	else {
		og = Ograd[no];
		if (!hv) {
			while(og) {
				++rv;
				if (z < ze)
					*z++ = og->varno;
				og = og->next;
				}
			}
		else if (vscale) {
			while(og) {
				++rv;
				i = og->varno;
				if (z < ze)
					*z++ = F + i;
				if (hv < hve)
					*hv++ = vscale[i]*x0[i].aO;
				og = og->next;
				}
			}
		else {
			while(og) {
				++rv;
				i = og->varno;
				if (z < ze)
					*z++ = F + i;
				if (hv < hve)
					*hv++ = x0[i].aO;
				og = og->next;
				}
			}
		}
	if (p0)
		del_mblk(kp, p0);
	return rv;
	}

/* Variant of hvpcomps_ASL that has a final nerror argument, working
   similarly to the final nerror argument to objval_(), etc. */

 varno_t
hvpcompse_ASL(ASL *asl, real *hv, const real *p, int co, varno_t nz, varno_t *z, fint *nerror)
{
	Jmp_buf **Jp, *Jsave, b;
	varno_t rv;

	Jp = !nerror || *nerror >= 0 ? &err_jmp : &err_jmp1;
	Jsave = *Jp;
	*Jp = &b;
	*nerror = 0;
	rv = 0;
	if (setjmp(b.jb))
		*nerror = 1;
	else
		rv = hvpcomps_ASL(asl, hv, p, co, nz, z);
	*Jp = Jsave;
	return rv;
	}

#ifdef __cplusplus
}
#endif