/****************************************************************
Copyright (C) 1997-1998, 2000-2001 Lucent Technologies
All Rights Reserved

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, and that the name of Lucent or any of its entities
not be used in advertising or publicity pertaining to
distribution of the software without specific, written prior
permission.

LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES 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 "asl_pfgh.h"

 static void
#ifdef KR_headers
hv_fwd(asl, e) ASL_pfgh *asl; register expr *e;
#else
hv_fwd(ASL_pfgh *asl, register expr *e)
#endif
{
	expr *e1, **ep;
	real dO;
	de *d;
	derp *D, *D1;

	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;
			break;

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

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

		case Hv_vararg:
			e->dO.r = 0;
			for(d = ((expr_va*)e)->L.d; d->e; d++) {
				if (e1 = d->ef) {
					hv_fwd(asl, e1);
					e->dO.r += d->ee->dO.r;
					}
				else if (e1 = d->e)
					e->dO.r += e1->dO.r;
				}
			if (!((expr_va*)e)->val && (D = ((expr_va*)e)->R.D)) {
				D->a.rp = adjoints_nv1;
				D1 = ((expr_va*)e)->d0;
				d = ((expr_va*)e)->L.d;
				((expr_va*)e)->val = d->e;
				do {
					D->next = d->d;
					while(D->next != D1)
						D = D->next;
					d->dlast = D;
					++d;
					}
					while(d->e);
				((expr_va*)e)->next = asl->P.valist;
				asl->P.valist = (expr_va*)e;
				}
			break;

		case Hv_if:
			e->dO.r = 0;
			if (e1 = ((expr_if*)e)->Tf) {
				hv_fwd(asl, e1);
				e->dO.r = ((expr_if *)e)->Te->dO.r;
				}
			else if (e1 = ((expr_if*)e)->T)
				e->dO.r = e1->dO.r;
			if (e1 = ((expr_if*)e)->Ff) {
				hv_fwd(asl, e1);
				e->dO.r += ((expr_if *)e)->Fe->dO.r;
				}
			else if (e1 = ((expr_if*)e)->F)
				e->dO.r += e1->dO.r;
			if (!((expr_if*)e)->val && (D = ((expr_if*)e)->D)) {
				((expr_if*)e)->val = ((expr_if*)e)->T;
				D->a.rp = adjoints_nv1;
				D1 = ((expr_if*)e)->d0;
				D->next = ((expr_if*)e)->dT;
				while(D->next != D1)
					D = D->next;
				((expr_if*)e)->dTlast = D;
				D->next = ((expr_if*)e)->dF;
				((expr_if*)e)->next = asl->P.iflist;
				asl->P.iflist = (expr_if*)e;
				}
			break;

		case Hv_plterm:
			e->dO.r = 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:
			e->dO.r = 1.;
			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
#ifdef KR_headers
func_back(f) expr_f *f;
#else
func_back(expr_f *f)
#endif
{
	argpair *da, *da1, *dae;
	expr *e;
	real aO, adO, t;

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

 static void
#ifdef KR_headers
hv_back(e) register expr *e;
#else
hv_back(register expr *e)
#endif
{
	register expr *e1, **ep, *e2;
	real adO, t1, t2;
	de *d;

	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;
			e1->aO += e->aO  +  e->adO * e1->dO.r;
			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 + t1 + t2;
			e2->aO  += e->aO + t1 + t2;
			e1->adO += adO;
			e2->adO += adO;
			break;

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

		case Hv_vararg:
			for(d = ((expr_va*)e)->L.d; d->e; d++) {
				if (e1 = d->ee) {
					e1->aO = e->aO;
					e1->adO = e->adO;
					hv_back(e1);
					}
				else {
					e1 = d->e;
					if (e1->op != f_OPNUM) {
						e1->aO = e->aO;
						e1->adO = e->adO;
						}
					}
				}
			break;

		case Hv_if:
			if (e1 = ((expr_if *)e)->Te) {
				e1->aO = e->aO;
				e1->adO = e->adO;
				hv_back(e1);
				}
			else {
				e1 = ((expr_if *)e)->T;
				if (e1->op != f_OPNUM) {
					e1->aO = e->aO;
					e1->adO = e->adO;
					}
				}
			if (e1 = ((expr_if *)e)->Fe) {
				e1->aO = e->aO;
				e1->adO = e->adO;
				hv_back(e1);
				}
			else {
				e1 = ((expr_if *)e)->F;
				if (e1->op != f_OPNUM) {
					e1->aO = e->aO;
					e1->adO = e->adO;
					}
				}
			break;

		case Hv_plterm:
			e->R.e->aO += 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;
			e1->aO += e->aO;
			break;

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

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

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

 static void
#ifdef KR_headers
hv_fwd0(asl, c, v) ASL_pfgh *asl; register cexp *c; register expr_v *v;
#else
hv_fwd0(ASL_pfgh *asl, register cexp *c, register expr_v *v)
#endif
{
	register linpart *L, *Le;
	real x;

	v->aO = v->adO = 0;
	if (c->ef) {
		hv_fwd(asl, c->ef);
		x = c->ee->dO.r;
		}
	else if (c->e->op != f_OPNUM)
		x = c->e->dO.r;
	else
		x = 0;
	if (L = c->L)
		for(Le = L + c->nlin; L < Le; L++)
			x += ((expr_v*)L->v.vp)->dO.r;
	v->dO.r = x;
	}

 static void
#ifdef KR_headers
pshv_prod1(asl, r, nobj, ow, y) ASL_pfgh *asl; range *r; int nobj, ow, y;
#else
pshv_prod1(ASL_pfgh *asl, range *r, int nobj, int ow, int y)
#endif
{
	int *cei, *cei0, *ceie, i;
	linarg *la, **lap, **lap1, **lape;
	linpart *L, *Le;
	expr_v *v;
	cexp *c;
	expr *e;
	real *s;
	psb_elem *b;

	s = asl->P.dOscratch;
	lap = lap1 = r->lap;
	lape = lap + r->n;
	while(lap1 < lape) {
		la = *lap1++;
		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 (!ow && i != nobj)
				continue;
			}
		else if (!y)
			continue;
		if (e = b->D.ef) {
			hv_fwd(asl, e);
			e = b->D.ee;
			e->aO = 0;
			e->adO = 1.;
			hv_back(e);
			}
		else if ((e = b->D.e)->op != f_OPNUM) {
			e->aO = 0;
			e->adO = 1.;
			}
		}
	while(cei > cei0) {
		i = *--cei;
		c = cexps + i;
		v = asl->P.vp[i];
		if (v->aO && (L = c->L))
		    for(Le = L + c->nlin; L < Le; L++)
			((expr_v*)L->v.vp)->aO++;
		if (e = c->ee) {
			e->aO = 1.;
			e->adO = v->adO;
			hv_back(e);
			}
		else if ((e = c->e)->op != f_OPNUM) {
			e->aO = 1.;
			e->adO = v->adO;
			}
		}
	}

#ifdef __cplusplus
extern "C" {
static int compar(const void*, const void*);
}
#endif

 static int
#ifdef KR_headers
compar(a, b) char *a, *b;
#else
compar(const void *a, const void *b)
#endif
{ return *(int*)a - *(int*)b; }

#undef nzc
#undef asl
#undef del_mblk
#define del_mblk(b,c) Del_mblk_ASL(a,b,(Char*)(c))

 static void
#ifdef KR_headers
new_Hesoprod(asl, L, R, coef) ASL_pfgh *asl; ograd *L, *R; real coef;
#else
new_Hesoprod(ASL_pfgh *asl, ograd *L, ograd *R, real coef)
#endif
{
	Hesoprod *h, **hp, *h1, *h2;
	int kh;
	Char **mblk_free;

	ACQUIRE_DTOA_LOCK(HESOPROD_LOCK);
	if (!(h = asl->P.hop_free)) {
		mblk_free = asl->mblk_free;
		kh = asl->P.khesoprod;
		while(kh < 8 && !mblk_free[kh])
			kh++;
		asl->P.khesoprod = kh;
		h = h1 = (Hesoprod *)new_mblk(kh);
		h2 = h + (sizeof(Char*) << kh)/sizeof(Hesoprod) - 1;
		while(h1 < h2)
			h1 = h1->next = h1 + 1;
		h1->next = 0;
		}
	asl->P.hop_free = h->next;
	FREE_DTOA_LOCK(HESOPROD_LOCK);
	h->left = L;
	h->right = R;
	h->coef = coef;
	hp = asl->P.otodo + R->varno;
	h->next = *hp;
	*hp = h;
	}

 static void
#ifdef KR_headers
del_Hesoprod(asl, x) ASL_pfgh *asl; Hesoprod *x;
#else
del_Hesoprod(ASL_pfgh *asl, Hesoprod *x)
#endif
{
	x->next = asl->P.hop_free;
	asl->P.hop_free = x;
	}

 static real *
#ifdef KR_headers
saveog(asl, no, noe, y, kp) ASL_pfgh *asl; int no; int noe; int y; int *kp;
#else
saveog(ASL_pfgh *asl, int no, int noe, int y, int *kp)
#endif
{
	real *o, *ogsave;
	int i, k, n;
	ps_func *p, *pe;
	psg_elem *g, *ge;
	ograd *og;

	n = 0;
	if (asl->P.nobjgroups)
		for(i = no; i < noe; i++) {
			p = asl->P.ops + i;
			g = p->g;
			for(ge = g + p->ng; g < ge; g++)
				for(og = g->og; og; og = og->next)
					n++;
			}
	if (asl->P.ncongroups && y) {
		p = asl->P.cps;
		for(pe = p + n_con; p < pe; p++)
			for(g = p->g, ge = g + p->ng; g < ge; g++)
				for(og = g->og; og; og = og->next)
					n++;
		}
	if (!n)
		return 0;
	k = *kp = htcl(n*sizeof(real));
	o = ogsave = (real*)new_mblk(k);
	if (asl->P.nobjgroups)
		for(i = no; i < noe; i++) {
			p = asl->P.ops + i;
			g = p->g;
			for(ge = g + p->ng; g < ge; g++)
				for(og = g->og; og; og = og->next)
					*o++ = og->coef;
			}
	if (asl->P.ncongroups && y) {
		p = asl->P.cps;
		for(pe = p + n_con; p < pe; p++)
			for(g = p->g, ge = g + p->ng; g < ge; g++)
				for(og = g->og; og; og = og->next)
					*o++ = og->coef;
		}
	return ogsave;
	}

 static void
#ifdef KR_headers
restog(asl, ogsave, no, noe, y, k) ASL_pfgh *asl; real *ogsave; int no; int noe; int y; int k;
#else
restog(ASL_pfgh *asl, real *ogsave, int no, int noe, int y, int k)
#endif
{
	real *o = ogsave;
	int i;
	ps_func *p, *pe;
	psg_elem *g, *ge;
	ograd *og;

	if (asl->P.nobjgroups)
		for(i = no; i < noe; i++) {
			p = asl->P.ops + i;
			g = p->g;
			for(ge = g + p->ng; g < ge; g++)
				for(og = g->og; og; og = og->next)
					og->coef = *o++;
			}
	if (asl->P.ncongroups && y) {
		p = asl->P.cps;
		for(pe = p + n_con; p < pe; p++)
			for(g = p->g, ge = g + p->ng; g < ge; g++)
				for(og = g->og; og; og = og->next)
					og->coef = *o++;
		}
	Del_mblk_ASL((ASL*)asl, k, ogsave);
	}

 static fint
#ifdef KR_headers
bothadj(asl, spi) ASL_pfgh *asl; SputInfo *spi;
#else
bothadj(ASL_pfgh *asl, SputInfo *spi)
#endif
{
	/* Adjust to compute both triangles of Hessian */
	fint i, i0, i1, j, k, k0, L, n, n1, nod, nz;
	int kz, *z, *z0, *z1;
	fint *hcs, *hr, *hre, *hrn, *hrn0, *ucs, *ulc, *uli;

	n = n_var;
	if ((nod = spi->nod) >= 0) {
		if (!nod)
			return 0;
		goto done;
		}
	n1 = n + 1;
	hcs = spi->hcolstarts;
	nod = nz = hcs[n] - hcs[0];
	hr = spi->hrownos - 1;
	i = i0 = Fortran;
	for(j = i + n; i < j; i++, hcs++) {
		hr += k = hcs[1] - hcs[0];
		if (k && *hr == i)
			--nod;
		}
	/* nod = number of off-diagonal elements in upper triangle */
	if (!(spi->nod = nod))
		return 0;	/* diagonal Hessian */
	nz += nod;
	spi->khinfob = kz = htcl((nz+2*(nod+n1))*sizeof(fint));
	spi->ulinc0 = uli = (fint*)new_mblk(kz);
	spi->hcs[1] = hcs = uli + n1;
	spi->hrn[1] = hrn0 = hcs + n1;
	spi->ulcopy0 = ulc = hrn0 + nz;
	z = z0 = (int*)new_mblk(kz = htcl(n*sizeof(int)));
	z1 = z - Fortran;
	ucs = spi->hcs[0];
	hre = spi->hrn[0];
	for(i = i0; i < j; i++, ucs++) {
		hr = hre;
		hre += *z++ = ucs[1] - ucs[0];
		while(hr < hre)
			if ((k = *hr++) != i)
				z1[k]++;
		}
	ucs = spi->hcs[0];
	hre = spi->hrn[0];
	*uli++ = 0;
	for(i = k = i0; i < j; i++, ucs++) {
		hr = hre;
		hre += L = ucs[1] - ucs[0];
		*hcs++ = k;
		k0 = k - i0;
		hrn = hrn0 + k0;
		*uli++ = z1[i] - L;
		k += z1[i];
		z1[i] = k0 + L;
		while(hr < hre)
			if ((i1 = *hrn++ = *hr++) != i) {
				*ulc++ = k0++;
				hrn0[*ulc++ = z1[i1]++] = i;
				}
		}
	*hcs = k;
	spi->ulcend = ulc;
	Del_mblk_ASL((ASL*)asl, kz, z0);
	spi->ulinc = spi->ulinc0;
	spi->ulcopy = spi->ulcopy0;
 done:
	spi->hrownos = spi->hrn[1];
	spi->hcolstarts = spi->hcs[1];
	return nod;
	}

 static void
#ifdef KR_headers
upper_to_lower(asl, spi, nz) ASL_pfgh *asl; SputInfo *spi; fint nz;
#else
upper_to_lower(ASL_pfgh *asl, SputInfo *spi, fint nz)
#endif
{	/* convert upper to lower triangular */

	fint *cs, *hcolstarts, *hrownos, *rn;
	int f, i, j, j1, j2, k, n;
	int *rs, *u0, *utoL, *z;

	f = Fortran;
	n = n_var;
	hrownos = spi->hrownos;
	hcolstarts = spi->hcolstarts;
	k = htcl((nz + n + 1)*sizeof(fint));
	rn = spi->hrownos = spi->ulinc0 = (fint*)new_mblk(k);
	spi->khinfob = k;
	spi->hcolstarts = cs = rn + nz;
	k = htcl((n+nz)*sizeof(int));
	rs = (int*)new_mblk(k);
	z = rs + n;
	memset(rs, 0, n*sizeof(fint));
	for(i = 0; i < nz; i++)
		rs[hrownos[i]-f]++;
	for(i = j = 0; i < n; i++) {
		cs[i] = j + f;
		j1 = rs[i];
		rs[i] = j;
		j += j1;
		}
	cs[n] = nz + f;
	j1 = hcolstarts[1] - f;
	for(i = j = 0; i < nz; i++) {
		while(i >= j1)
			j1 = hcolstarts[++j + 1] - f;
		rn[z[i] = rs[hrownos[i]-f]++] = j + f;
		}
	for(i = j = 0; i < nz; i++) {
		if ((j1 = z[i]) <= i) {
			if (j1 < 0)
				z[i] = -(j1 + 1);
			continue;
			}
		j += 3;
		while((j2 = z[j1]) != i) {
			z[j1] = -(j2 + 1);
			j++;
			j1 = j2;
			}
		}
	if (j) {
		j += 2;
		j1 = htcl(j*sizeof(int));
		spi->uptolow = utoL = (int*)new_mblk(j1);
		*utoL++ = j1;
		for(i = 0; i < nz; i++) {
			if ((j = z[i]) <= i)
				continue;
			u0 = utoL++;
			*utoL++ = i;
			*utoL++ = j;
			while((j2 = z[j]) != i) {
				z[j] = -(j2 + 1);
				j = *utoL++ = j2;
				}
			*u0 = (utoL - u0) - 1;
			}
		*utoL = 0;
		}
	Del_mblk_ASL((ASL*)asl, k, rs);
	}

 fint
#ifdef KR_headers
sphes_setup_ASL(a, pspi, nobj, ow, y, uptri) ASL *a; SputInfo **pspi;
			int nobj, ow, y, uptri;
#else
sphes_setup_ASL(ASL *a, SputInfo **pspi, int nobj, int ow, int y, int uptri)
#endif
{
	int i, j, k, khinfo, kog, kz, n, n1, nhinfo, no, noe, nqslim, nzc;
	int rfilter, robjno;
	int *ui, *zc, *zci;
	linarg *la, **lap, **lap1, **lape;
	expr_v *v;
	range *r, *r0, **rp, **rtodo;
	real *ogsave, *s, *si, t;
	ograd *og, *og1, **ogp, **ogpe;
	Hesoprod *hop, *hop1, **otodo, **otodoi, **otodoj;
	uHeswork *uhw, *uhwi, **utodo, **utodoi, **utodoj;
	fint *hcolstarts, *hr, *hre, *hrownos, rv, *tf;
	derp *D1;
	de *d;
	psb_elem *b;
	psg_elem *g, *ge;
	ps_func *p, *pe;
	ASL_pfgh *asl;
	expr_va *valist;
	expr_if *iflist;
	SputInfo *spi, *spi1;

	asl = pscheck_ASL(a, "sphes_setup");
	if (!pspi)
		pspi = &asl->i.sputinfo_;
	if (nobj >= 0 && nobj < n_obj) {
		robjno = -2 - nobj;
		rfilter = n_obj > 1 || !y && n_con > 0;
		ow = 0;
		no = nobj;
		noe = no + 1;
		}
	else {
		robjno = nobj = -1;
		rfilter = !ow && n_obj > 0 || !y && n_con > 0;
		no = noe = 0;
		if (ow) {
			noe = n_obj;
			ow = 1;
			}
		}
	if (y)
		y = 1;
	n = n_var;
	if (spi = *pspi) {
		if (spi->ow == ow && spi->y == y && spi->nobj == nobj
		 && spi->uptri == uptri)
			goto done;
		del_mblk(spi->khinfo, spi);
		if (spi->ulinc0)
			del_mblk(spi->khinfob, spi->ulinc0);
		if (ui = spi->uptolow)
			del_mblk(*ui, ui);
		*pspi = 0;
		}
	if (!asl->P.hes_setup_called)
		(*asl->p.Hesset)(a, 1, 0, nlo, 0, nlc);
	asl->P.hes_setup_called = 3;
	asl->P.iflist = 0;
	asl->P.valist = 0;
	otodo = otodoi = asl->P.otodo;
	rtodo = asl->P.rtodo;
	utodo = utodoi = asl->P.utodo;
	s = asl->P.dOscratch;
	nqslim = n >> 3;
	kz = htcl(2*sizeof(int)*n);
	zc = (int*)new_mblk_ASL(a, kz);
	zci = zc + n;
	memset(zc, 0, n*sizeof(int));
	n1 = n + 1;
	khinfo = htcl((2*n + 30)*sizeof(fint) + sizeof(SputInfo));
	spi = (SputInfo*)new_mblk_ASL(a, khinfo);
	hcolstarts = (fint*)(spi+1);
	hr = hrownos = hcolstarts + n1;
	nhinfo = ((sizeof(Char*)<<khinfo) - sizeof(SputInfo)) / sizeof(fint);
	hre = hr + (nhinfo - n1);
	r0 = (range*)&asl->P.rlist;
	for(r = asl->P.rlist.next; r != r0; r = r->rlist.next) {
		if ((j = r->n) <= 0)
			continue;
		if (rfilter) {
			for(b = r->refs; b; b = b->next) {
				if (b->conno >= 0) {
					if (y)
						goto keep;
					}
				else if (b->conno == robjno)
					goto keep;
				}
			continue;
			}
 keep:
		i = r->lasttermno;
		rp = rtodo + i;
		r->hnext = *rp;
		*rp = r;
		}
	ogsave = asl->P.npsgcomp ? saveog(asl, no, noe, y, &kog) : 0;
	if (asl->P.nobjgroups)
		for(i = no; i < noe; i++) {
			p = asl->P.ops + i;
			g = p->g;
			for(ge = g + p->ng; g < ge; g++)
			    if (og = g->og) {
				do og->coef = 1; while(og = og->next);
				og = g->og;
				new_Hesoprod(asl, og, og, 1.);
				}
			}
	if (asl->P.ncongroups && y) {
		p = asl->P.cps;
		for(pe = p + n_con; p < pe; p++)
			for(g = p->g, ge = g + p->ng; g < ge; g++)
			    if (og = g->og) {
				do og->coef = 1; while(og = og->next);
				og = g->og;
				new_Hesoprod(asl, og, og, 1.);
				}
		}
	for(i = 0; i < n; i++) {
		nzc = 0;
		rp = rtodo;
		uhwi = *utodoi;
		*utodoi++ = 0;
		while(r = *rp) {
			rp = &r->hnext;
			lap = r->lap;
			lape = lap + r->n;
			if (r->n >= r->nv) {
				k = htcl(sizeof(uHeswork)
					+ (r->n - 1)*sizeof(ograd*));
				uhw = (uHeswork *)new_mblk_ASL(a, k);
				uhw->k = k;
				uhw->next = uhwi;
				uhwi = uhw;
				uhw->r = r;
				uhw->ui = ui = r->ui;
				uhw->uie = ui + r->nv;
				ogp = uhw->ogp;
				while(lap < lape)
					*ogp++ = (*lap++)->nz;
				}
			else {
				si = s;
				while(lap < lape) {
					*si = 1;
					pshv_prod1(asl, r, nobj, ow, y);
					*si++ = 0;
					lap1 = lap++;
					la = *lap1++;
					og = la->nz;
					v = la->v;
					if (t = v->aO)
						new_Hesoprod(asl,og,og,t);
					while(lap1 < lape) {
					    la = *lap1++;
					    v = la->v;
					    if (t = v->aO) {
						og1 = la->nz;
						new_Hesoprod(asl,og,og1,t);
						new_Hesoprod(asl,og1,og,t);
						}
					    }
					}
				}
			}
		*rtodo++ = 0;	/* reset */
		while(uhw = uhwi) {
			uhwi = uhwi->next;
			si = s;
			ogp = uhw->ogp;
			r = uhw->r;
			ogpe = ogp + r->n;
			si = s;
			do {
				if ((og = *ogp) && og->varno == i)
					*si = 1.; /* og->coef til 20080629 */
				si++;
				} while(++ogp < ogpe);
			pshv_prod1(asl, r, nobj, ow, y);

			lap = r->lap;
			lape = lap + r->n;
			do {
				la = *lap++;
				if (la->v->aO)
					for(og = la->nz; og; og = og->next)
						if ((j = og->varno) <= i
						 && !zc[j]++)
							zci[nzc++] = j;
				}
				while(lap < lape);

			ogp = uhw->ogp;
			si = s;
			do {
				if ((og = *ogp) && og->varno == i) {
					*si = 0;
					*ogp = og->next;
					}
				si++;
				} while(++ogp < ogpe);
			if ((ui = ++uhw->ui) >= uhw->uie)
				del_mblk(uhw->k, uhw);
			else {
				utodoj = utodo + *ui;
				uhw->next = *utodoj;
				*utodoj = uhw;
				}
			}

		hop1 = *otodoi;
		*otodoi++ = 0;
		while(hop = hop1) {
			hop1 = hop->next;
			og = hop->left;
			og1 = hop->right;
			while((j = og->varno) <= i) {
				if (!zc[j]++)
					zci[nzc++] = j;
				if (!(og = og->next))
					break;
				}
			if (og = og1->next) {
				hop->right = og;
				otodoj = otodo + og->varno;
				hop->next = *otodoj;
				*otodoj = hop;
				}
			else
				del_Hesoprod(asl,hop);
			}
		hcolstarts[i] = hr - hrownos;
		if (nzc > hre - hr) {
			k = khinfo++;
			spi1 = (SputInfo*)new_mblk_ASL(a, khinfo);
			tf = (fint*)(spi1+1);
			memcpy(tf, hcolstarts, (hr - hcolstarts)*sizeof(fint));
			del_mblk(k, spi);
			spi = spi1;
			hcolstarts = tf;
			hrownos = tf + n1;
			hr = hrownos + hcolstarts[i];
			nhinfo = ((sizeof(Char*)<<khinfo) - sizeof(SputInfo))
				/ sizeof(fint);
			hre = hrownos + (nhinfo - n1);
			}
		if (nzc > nqslim) {
			for(j = 0; j < n; j++)
				if (zc[j])
					zc[*hr++ = j] = 0;
			}
		else {
			if (nzc > 1)
				qsort(zci, nzc, sizeof(int), compar);
			for(j = 0; j < nzc; j++)
				zc[*hr++ = zci[j]] = 0;
			}
		}
	for(valist = asl->P.valist; valist; valist = valist->next) {
		D1 = valist->d0;
		for(d = valist->L.d; d->e; d++)
			d->dlast->next = D1;
		}
	for(iflist = asl->P.iflist; iflist; iflist = iflist->next)
		iflist->dTlast->next = iflist->d0;
	hcolstarts[n] = hr - hrownos;
	if (j = Fortran) {
		for(i = 0; i <= n; i++)
			hcolstarts[i] += j;
		i = (int)(hcolstarts[n] - j);
		while(i)
			hrownos[--i] += j;
		}
	spi->hcs[0] = hcolstarts;
	spi->hrn[0] = hrownos;
	spi->nod = -1;
	spi->ulcend = 0;
	spi->khinfo = khinfo;
	spi->nobj = nobj;
	spi->ow = ow;
	spi->y = y;
	spi->uptri = uptri;
	*pspi = spi;
	if (ogsave)
		restog(asl, ogsave, no, noe, y, kog);
	spi->ulinc0 = spi->ulinc = spi->ulcopy = 0;
	spi->uptolow = 0;
	del_mblk(kz, zc);
 done:
	spi->hrownos = spi->hrn[0];
	spi->hcolstarts = hcolstarts = spi->hcs[0];
	rv = hcolstarts[n] - hcolstarts[0];
	switch(uptri) {
	  case 0:
		rv += bothadj(asl, spi);
		break;
	  case 2:
		upper_to_lower(asl, spi, rv);
	  }
	return rv;
	}

 void
#ifdef KR_headers
sphes_ASL(a, pspi, H, nobj, ow, y) ASL *a; SputInfo **pspi; real *H; int nobj; real *ow, *y;
#else
sphes_ASL(ASL *a, SputInfo **pspi, real *H, int nobj, real *ow, real *y)
#endif
{
	/* sparse upper triangle of Hessian */

	int i, j, k, kh, n, no, noe, *ui;
	linarg *la, **lap, **lap1, **lape;
	expr_v *v;
	range *r, *r0, **rp, **rtodo;
	real *Hi, *H0, *H00;
	real *cscale, *owi, *s, *si, t, t1, *vsc0, *vsc1, *vsc, *y1;
	ograd *og, *og1, **ogp, **ogpe;
	Hesoprod *hop, *hop1, **otodo, **otodoi, **otodoj;
	uHeswork *uhw, *uhwi, **utodo, **utodoi, **utodoj;
	fint *hcs, *hr, *uli;
	psg_elem *g, *ge;
	ps_func *p, *pe;
	ASL_pfgh *asl;
	SputInfo *spi;

	asl = pscheck_ASL(a, "sputhes");
	xpsg_check_ASL(asl, nobj, ow, y);
	if (!pspi)
		pspi = &a->i.sputinfo_;
	i = j = 0;
	if (y)
		j = 1;
	if (nobj >= 0 && nobj < n_obj) {
		no = nobj;
		noe = no + 1;
		owi = ow ? ow + no : &edag_one_ASL;
		ow = 0;
		}
	else {
		nobj = -1;
		no = noe = 0;
		if (owi = ow) {
			noe = n_obj;
			i = 1;
			}
		}
	if (asl->P.hes_setup_called != 3)
		sphes_setup_ASL(a, pspi, nobj, ow != 0, y != 0, 0);
	spi = *pspi;
	if (spi->nobj != nobj || spi->ow != i || spi->y != j) {
		fprintf(Stderr,
		 "\nsphes() call inconsistent with previous sphsetup()\n");
		exit(1);
		}
	otodo = otodoi = asl->P.otodo;
	rtodo = asl->P.rtodo;
	utodo = utodoi = asl->P.utodo;
	s = asl->P.dOscratch;
	n = n_var;
	Hi = H0 = (real*)new_mblk_ASL(a, kh = htcl(n*sizeof(real)));
	memset(Hi, 0, n * sizeof(real));
	H0 -= Fortran;
	r0 = (range*)&asl->P.rlist;
	for(r = asl->P.rlist.next; r != r0; r = r->rlist.next) {
		if ((j = r->n) <= 0)
			continue;
		i = r->lasttermno;
		rp = rtodo + i;
		r->hnext = *rp;
		*rp = r;
		}
	if (asl->P.nobjgroups)
	    for(; no < noe; no++)
		if (t = *owi++) {
		    p = asl->P.ops + no;
		    g = p->g;
		    for(ge = g + p->ng; g < ge; g++)
			if (t1 = t*g->g2)
				for(og = g->og; og; og = og->next)
					if (og->coef) {
						new_Hesoprod(asl, og, og, t1);
						break;
						}
		}
	if (asl->P.ncongroups && y) {
		cscale = asl->i.lscale;
		p = asl->P.cps;
		y1 = y;
		for(pe = p + n_con; p < pe; p++, y1++)
			if (t = cscale ? *cscale++ * *y1 : *y1)
				for(g = p->g, ge = g + p->ng; g < ge; g++)
				    if (t1 = t*g->g2)
					for(og = g->og; og; og = og->next)
					    if (og->coef) {
						new_Hesoprod(asl, og, og, t1);
						break;
						}
		}
	hcs = spi->hcs[0];
	hr  = spi->hrn[0];
	uli = spi->ulinc;
	H00 = H;
	if (vsc = asl->i.vscale) {
		vsc0 = vsc - Fortran;
		vsc1 = vsc;
		}
	for(i = 0; i < n; i++) {
		rp = rtodo;
		uhwi = *utodoi;
		*utodoi++ = 0;
		while(r = *rp) {
			rp = &r->hnext;
			lap = r->lap;
			lape = lap + r->n;
			if (r->n >= r->nv) {
				k = htcl(sizeof(uHeswork)
					+ (r->n - 1)*sizeof(ograd*));
				uhw = (uHeswork *)new_mblk_ASL(a, k);
				uhw->k = k;
				uhw->next = uhwi;
				uhwi = uhw;
				uhw->r = r;
				uhw->ui = ui = r->ui;
				uhw->uie = ui + r->nv;
				ogp = uhw->ogp;
				while(lap < lape)
					*ogp++ = (*lap++)->nz;
				}
			else {
				si = s;
				while(lap < lape) {
					*si = 1;
					pshv_prod_ASL(asl, r, nobj, ow, y);
					*si++ = 0;
					lap1 = lap++;
					la = *lap1++;
					og = la->nz;
					v = la->v;
					if (t = v->aO)
						new_Hesoprod(asl,og,og,t);
					while(lap1 < lape) {
					    la = *lap1++;
					    v = la->v;
					    if (t = v->aO) {
						og1 = la->nz;
						new_Hesoprod(asl,og,og1,t);
						new_Hesoprod(asl,og1,og,t);
						}
					    }
					}
				}
			}
		*rtodo++ = 0;	/* reset */
		while(uhw = uhwi) {
			uhwi = uhwi->next;
			si = s;
			ogp = uhw->ogp;
			r = uhw->r;
			ogpe = ogp + r->n;
			si = s;
			do {
				if ((og = *ogp) && og->varno == i)
					*si = og->coef;
				si++;
				} while(++ogp < ogpe);
			pshv_prod_ASL(asl, r, nobj, ow, y);

			lap = r->lap;
			lape = lap + r->n;
			do {
				la = *lap++;
				if (t = la->v->aO)
					for(og = la->nz; og; og = og->next)
						if ((j = og->varno) <= i)
							Hi[j] += t*og->coef;
				}
				while(lap < lape);

			ogp = uhw->ogp;
			si = s;
			do {
				if ((og = *ogp) && og->varno == i) {
					*si = 0;
					*ogp = og->next;
					}
				si++;
				} while(++ogp < ogpe);
			if ((ui = ++uhw->ui) >= uhw->uie)
				del_mblk(uhw->k, uhw);
			else {
				utodoj = utodo + *ui;
				uhw->next = *utodoj;
				*utodoj = uhw;
				}
			}

		hop1 = *otodoi;
		*otodoi++ = 0;
		while(hop = hop1) {
			hop1 = hop->next;
			og = hop->left;
			og1 = hop->right;
			t = hop->coef * og1->coef;
			while((j = og->varno) <= i) {
				Hi[j] += t*og->coef;
				if (!(og = og->next))
					break;
				}
			if (og = og1->next) {
				hop->right = og;
				otodoj = otodo + og->varno;
				hop->next = *otodoj;
				*otodoj = hop;
				}
			else
				del_Hesoprod(asl,hop);
			}
		k = (int)(hcs[1] - hcs[0]);
		hcs++;
		if (uli)
			H += *uli++;
		if (vsc) {
			t = *vsc1++;
			while(--k >= 0) {
				j = (int)*hr++;
				*H++ = t * vsc0[j] * H0[j];
				H0[j] = 0;
				}
			}
		else
			while(--k >= 0) {
				*H++ = H0[j = (int)*hr++];
				H0[j] = 0;
				}
		}
	del_mblk(kh, Hi);
	H = H00;
	if (hr = spi->ulcopy)
		for(uli = spi->ulcend; hr < uli; hr += 2)
			H[hr[1]] = H[hr[0]];
	else if (ui = spi->uptolow)
		while(k = *++ui) {
			t = H[j = *++ui];
			while(--k) {
				t1 = H[i = *++ui];
				H[i] = t;
				t = t1;
				}
			H[j] = t;
			}
	}