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t1p_fun.c
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/*
APRON Library / Taylor1+ Domain (beta version)
Copyright (C) 2009-2011 Khalil Ghorbal
*/
#include "itv_linearize.h"
#include "t1p_internal.h"
#include "t1p_representation.h"
#include "t1p_itv_utils.h"
#ifdef _USE_SDP
#include "declarations.h"
#include "vSDP.h"
#endif
#include "ap_texpr0.h"
#include "t1p_fun.h"
/* pseudo-taken from http://kiwi.emse.fr/POLE/SDA/corr-iset.html */
/* we initialize p,q with the head of each list :
* - if p and q are null pointers, we reach the halt condition;
* - if one of p or q is a null pointer, we copy the non null list;
* - else, p and q are non null pointers :
* - if nsym_index p = nsym_index q then
* * add coeff,
* * copy the index,
* * increment p and q to p->next and q->next respectively.
* - if nsym_index p < nsymindex q then
* * copy coeff and nsym_index of p,
* * increment p.
* - else :
* * copy coeff and nsym_index of q,
* * increment q.
*/
t1p_aff_t* t1p_aff_add(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* abs)
{
itv_t box; itv_init(box);
itv_t tmp; itv_init(tmp);
t1p_aff_t* res = t1p_aff_alloc_init(pr);
t1p_aaterm_t *p, *q, *ptr;
itv_add(res->c, exprA->c, exprB->c);
itv_set(box, res->c);
if (exprA->q || exprB->q) {
ptr = t1p_aaterm_alloc_init();
for(p = exprA->q, q = exprB->q; p || q;) {
if (p && q) {
if (p->pnsym->index == q->pnsym->index) {
itv_add(ptr->coeff, p->coeff, q->coeff);
ptr->pnsym = p->pnsym;
p = p->n ;
q = q->n ;
} else if (p->pnsym->index < q->pnsym->index) {
itv_set(ptr->coeff, p->coeff);
ptr->pnsym = p->pnsym;
p = p->n ;
} else {
itv_set(ptr->coeff, q->coeff);
ptr->pnsym = q->pnsym;
q = q->n ;
}
} else if (p) {
itv_set(ptr->coeff, p->coeff);
ptr->pnsym = p->pnsym;
p = p->n ;
} else {
itv_set(ptr->coeff, q->coeff);
ptr->pnsym = q->pnsym;
q = q->n ;
}
if (itv_is_zero(ptr->coeff)) {
if (!(p||q)) {
/* the last iteration */
t1p_aaterm_free(pr, ptr);
if (res->end) res->end->n = NULL;
}
} else {
/* keep this term */
if (!res->q) res->q = ptr;
res->end = ptr;
res->l++;
t1p_nsymcons_get_gamma(pr, tmp, ptr->pnsym->index, abs);
itv_mul(pr->itv, tmp, tmp, ptr->coeff);
itv_add(box, box, tmp);
if (p||q) {
/* continuing */
ptr->n = t1p_aaterm_alloc_init();
ptr=ptr->n;
}
}
}
}
itv_add(res->itv, exprA->itv, exprB->itv);
itv_meet(pr->itv, res->itv, res->itv, box);
itv_clear(box);
itv_clear(tmp);
return res;
}
t1p_aff_t* t1p_aff_sub(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* abs)
{
itv_t box; itv_init(box);
itv_t tmp; itv_init(tmp);
t1p_aff_t* res = t1p_aff_alloc_init(pr);
t1p_aaterm_t *p, *q, *ptr;
if (!itv_is_eq(exprA->c, exprB->c)) itv_sub(res->c, exprA->c, exprB->c);
itv_set(box, res->c);
if (exprA->q || exprB->q) {
ptr = t1p_aaterm_alloc_init();
for(p = exprA->q, q = exprB->q; p || q;) {
if (p && q) {
if (p->pnsym->index == q->pnsym->index) {
if (!itv_is_eq(p->coeff, q->coeff)) itv_sub(ptr->coeff, p->coeff, q->coeff);
ptr->pnsym = p->pnsym;
p = p->n ;
q = q->n ;
} else if (p->pnsym->index < q->pnsym->index) {
itv_set(ptr->coeff, p->coeff);
ptr->pnsym = p->pnsym;
p = p->n ;
} else {
itv_neg(ptr->coeff, q->coeff);
ptr->pnsym = q->pnsym;
q = q->n ;
}
} else if (p) {
itv_set(ptr->coeff, p->coeff);
ptr->pnsym = p->pnsym;
p = p->n ;
} else {
itv_neg(ptr->coeff, q->coeff);
ptr->pnsym = q->pnsym;
q = q->n ;
}
if (itv_is_zero(ptr->coeff)) {
if (!(p||q)) {
/* the last iteration */
t1p_aaterm_free(pr, ptr);
if (res->end) res->end->n = NULL;
}
} else {
/* keep this term */
if (!res->q) res->q = ptr;
res->end = ptr;
res->l++;
t1p_nsymcons_get_gamma(pr, tmp, ptr->pnsym->index, abs);
itv_mul(pr->itv, tmp, tmp, ptr->coeff);
itv_add(box, box, tmp);
if (p||q) {
/* continuing */
ptr->n = t1p_aaterm_alloc_init();
ptr=ptr->n;
} else {
/* the last iteration */
ptr->n = NULL;
}
}
}
}
itv_sub(res->itv, exprA->itv, exprB->itv);
itv_meet(pr->itv, res->itv, res->itv, box);
itv_clear(box);
itv_clear(tmp);
return res;
}
t1p_aff_t* t1p_aff_mul_itv(t1p_internal_t* pr, t1p_aff_t* src, itv_t lambda)
{
if (itv_is_zero(lambda) || t1p_aff_is_known_to_be_zero(pr, src)) {
return t1p_aff_alloc_init(pr);
} else if (t1p_aff_is_bottom(pr, src) || itv_is_bottom(pr->itv, lambda)) {
return t1p_aff_bottom(pr);
} else if (t1p_aff_is_top(pr, src) || itv_is_top(lambda)) {
return t1p_aff_top(pr);
} else {
t1p_aff_t* dst = NULL;
t1p_aaterm_t *p,*q;
q = NULL;
dst = t1p_aff_alloc_init(pr);
itv_mul(pr->itv, dst->c, lambda, src->c);
if (src->q) {
dst->q = q = t1p_aaterm_alloc_init();
for (p=src->q; p; p=p->n) {
/*if (p == src->lastu) {
dst->lastu = q;
}*/
itv_mul(pr->itv, q->coeff, lambda, p->coeff);
q->pnsym = p->pnsym;
if (p->n) {
/* continue */
q->n = t1p_aaterm_alloc_init();
q = q->n;
} else {
/* the last iteration */
dst->end = q;
}
}
}
dst->l = src->l;
itv_mul(pr->itv, dst->itv, src->itv, lambda);
return dst;
}
}
void t1p_aff_mul_itv_inplace(t1p_internal_t* pr, t1p_aff_t* exprA, itv_t lambda)
{
if (itv_is_zero(lambda) || t1p_aff_is_known_to_be_zero(pr, exprA)) {
t1p_aff_clear(pr, exprA);
} else if (t1p_aff_is_bottom(pr, exprA) || itv_is_bottom(pr->itv, lambda)) {
t1p_aff_check_free(pr, exprA);
exprA = t1p_aff_bottom(pr);
} else if (t1p_aff_is_top(pr, exprA) || itv_is_top(lambda)) {
t1p_aff_check_free(pr, exprA);
exprA = t1p_aff_top(pr);
} else {
t1p_aaterm_t *p;
itv_mul(pr->itv, exprA->c, exprA->c, lambda);
for (p=exprA->q; p; p=p->n) {
itv_mul(pr->itv, p->coeff, p->coeff, lambda);
}
itv_mul(pr->itv, exprA->itv, exprA->itv, lambda);
}
}
t1p_aff_t* t1p_aff_mul(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* env)
{
t1p_aff_t* res;
if (t1p_aff_is_known_to_be_zero(pr, exprA) || t1p_aff_is_known_to_be_zero(pr, exprB)) {
res = t1p_aff_alloc_init(pr);
} else if (t1p_aff_is_bottom(pr, exprA) || t1p_aff_is_bottom(pr, exprB)) {
res = t1p_aff_bottom(pr);
} else if (t1p_aff_is_top(pr, exprA) || t1p_aff_is_top(pr, exprB)) {
res = t1p_aff_top(pr);
} else {
itv_t box; itv_init(box);
if (env->hypercube) res = t1p_aff_mul_non_constrained(pr, exprA, exprB, env);
else res = t1p_aff_mul_constrained(pr, exprA, exprB, env);
itv_mul(pr->itv, box, exprA->itv, exprB->itv);
itv_meet(pr->itv, res->itv, res->itv, box);
itv_clear(box);
}
return res;
}
t1p_aff_t* t1p_aff_mul_constrained_backup(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* env)
{
t1p_aff_t* res = t1p_aff_alloc_init(pr);
t1p_aaterm_t *p, *q, *ptr;
itv_t itv_nlin; itv_init(itv_nlin);
int i = 0;
int SDP_dim = 0;
unsigned int dim = 0; /* compute the number of different eps */
int cond_SDP; /* use SDP or not ? */
itv_t* tmp = itv_array_alloc(5); /* to store temporary variables */
itv_t midi, devi, mid1, mid2;
itv_init(midi); itv_init(devi); itv_init(mid1); itv_init(mid2);
itv_t* gammabis = itv_array_alloc(pr->dim);
itv_middev(pr->itv, mid1, tmp[2], exprA->itv);
itv_middev(pr->itv, mid2, tmp[3], exprB->itv);
itv_mul(pr->itv, tmp[0], mid1, mid2);
itv_mul(pr->itv, tmp[1], mid1, exprB->c);
itv_mul(pr->itv, tmp[2], mid2, exprA->c);
itv_add(res->c, tmp[1], tmp[2]);
itv_sub(res->c, res->c, tmp[0]);
itv_set(res->itv, res->c);
itv_t eps_itv; itv_init(eps_itv);
/* hash table to sort noise symbols "de facon contigue".
* If we have eps1, eps2, eps4, eps5 shared between the two forms, they are seen as eps1, eps2, eps3, eps4 which optimizes the size of the SDP problem.
*/
int* hash = (int *)malloc((2+pr->dim)*sizeof(int));
int* nsym_shared;
checked_malloc(nsym_shared,int,pr->dim,abort(););
int* nsym_shared_hash;
/* si on accumule, pour chaque expression, les coeff des symboles indépendants, on rajoute 2 symboles, un pour chaque expression.
le hash prend en compte ces deux eventuels ajouts.
*/
checked_malloc(nsym_shared_hash,int,2+pr->dim,abort(););
ap_dim_t abs_dim = 0;
if (exprA->q || exprB->q) {
res->q = ptr = t1p_aaterm_alloc_init();
res->l++;
/* linear part */
for(p = exprA->q, q = exprB->q; p || q;) {
dim += 1; /* computes the number of different noise symbols */
if (p && q) {
if (p->pnsym->index == q->pnsym->index) {
itv_mul(pr->itv, tmp[3], p->coeff, mid2);
itv_mul(pr->itv, tmp[4], q->coeff, mid1);
itv_add(ptr->coeff, tmp[3], tmp[4]);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
nsym_shared[p->pnsym->index] = true;
SDP_dim++;
nsym_shared_hash[p->pnsym->index] = SDP_dim;
if (env->hypercube) itv_set(gammabis[p->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, p->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[p->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[p->pnsym->index], pr->muu);
}
}
p = p->n ;
q = q->n ;
} else if (p->pnsym->index < q->pnsym->index) {
itv_mul(pr->itv, ptr->coeff, p->coeff, mid2);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[p->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, p->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[p->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[p->pnsym->index], pr->muu);
}
}
p = p->n ;
} else {
itv_mul(pr->itv, ptr->coeff, q->coeff, mid1);
ptr->pnsym = q->pnsym;
hash[q->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[q->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, q->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[q->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[q->pnsym->index], pr->muu);
}
}
q = q->n ;
}
} else if (p) {
itv_mul(pr->itv, ptr->coeff, p->coeff, exprB->c);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[p->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, p->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[p->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[p->pnsym->index], pr->muu);
}
}
p = p->n ;
} else {
itv_mul(pr->itv, ptr->coeff, q->coeff, exprA->c);
ptr->pnsym = q->pnsym;
hash[q->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[q->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, q->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[q->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[q->pnsym->index], pr->muu);
}
}
q = q->n ;
}
/* we don't create a new aaterm if p and q are null */
if (p||q) {
ptr->n = t1p_aaterm_alloc_init();
res->l++;
ptr=ptr->n;
}
}
ptr->n = NULL;
res->end = ptr;
}
/* non linear part */
/* Calling SDP solver (non guaranteed):
* - compute different noise symboles, say "n",
* - we have "n" constraints, each is a diagonal matrix (can also be seen as 2 block matrix) of dimension 2n, containing 1 in (i,i) and (i+n,i+n) positions,
* - objectif matrix (in primal form) is a 2 block matrix of dimension 2n. First block is deduced from the non linear (quadric) part of multiplication, we zero all values of the second block,
* - objective vector (in dual form) is a one vector of dimension "n".
*/
if (exprA->q && exprB->q) {
ap_funopt_t option = ap_manager_get_funopt(pr->man, pr->funid);
cond_SDP = option.algorithm == INT_MAX ? true : false;
itv_t itv1; itv_init(itv1);
itv_t itv2; itv_init(itv2);
if (cond_SDP) {
call_sdp(pr->itv, itv1, exprA->q, exprB->q, dim, hash, true);
}
else
square_dep(pr, itv2, exprA->q, exprB->q, hash, dim, gammabis);
if (exprA == exprB) {
if (bound_sgn(itv1->inf) > 0) {bound_set_int(itv1->inf,0);}
if (bound_sgn(itv2->inf) > 0) {bound_set_int(itv2->inf,0);}
}
if (cond_SDP) itv_set(itv_nlin,itv1);
else itv_set(itv_nlin,itv2);
itv_add(res->c, res->c, itv_nlin);
itv_clear(itv1);
itv_clear(itv2);
}
/* hash may be NULL if pr->index is zero */
if (hash) {free(hash);free(nsym_shared);free(nsym_shared_hash);}
itv_array_free(gammabis, pr->dim);
itv_array_free(tmp, 5);
itv_clear(mid1);
itv_clear(mid2);
itv_clear(midi);
itv_clear(devi);
itv_clear(itv_nlin);
itv_clear(eps_itv);
return res;
}
t1p_aff_t* t1p_aff_mul_constrained(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* env)
{
t1p_aff_t* res = t1p_aff_alloc_init(pr);
t1p_aaterm_t *p, *q, *ptr;
itv_t itv_nlin; itv_init(itv_nlin);
int i = 0;
int SDP_dim = 0;
unsigned int dim = 0; /* compute the number of different eps */
int cond_SDP; /* use SDP or not ? */
itv_t* tmp = itv_array_alloc(5); /* to store temporary variables */
itv_t midi, devi, mid1, mid2;
itv_init(midi); itv_init(devi); itv_init(mid1); itv_init(mid2);
itv_t* gammabis = itv_array_alloc(pr->dim);
itv_t itv1; itv_init(itv1);
itv_t itv2; itv_init(itv2);
t1p_aff_bound(pr, itv1, exprA, env);
t1p_aff_bound(pr, itv2, exprB, env);
itv_middev(pr->itv, mid1, tmp[2], itv1);
itv_middev(pr->itv, mid2, tmp[3], itv2);
//itv_middev(pr->itv, mid1, tmp[2], exprA->itv);
//itv_middev(pr->itv, mid2, tmp[3], exprB->itv);
itv_mul(pr->itv, tmp[0], mid1, mid2);
itv_mul(pr->itv, tmp[1], mid1, exprB->c);
itv_mul(pr->itv, tmp[2], mid2, exprA->c);
itv_add(res->c, tmp[1], tmp[2]);
itv_sub(res->c, res->c, tmp[0]);
itv_set(res->itv, res->c);
itv_clear(itv1);
itv_clear(itv2);
itv_t eps_itv; itv_init(eps_itv);
/* hash table to sort noise symbols "de facon contigue".
* If we have eps1, eps2, eps4, eps5 shared between the two forms, they are seen as eps1, eps2, eps3, eps4 which optimizes the size of the SDP problem.
*/
int* hash = (int *)malloc((2+pr->dim)*sizeof(int));
int* nsym_shared;
checked_malloc(nsym_shared,int,pr->dim,abort(););
int* nsym_shared_hash;
/* si on accumule, pour chaque expression, les coeff des symboles indépendants, on rajoute 2 symboles, un pour chaque expression.
le hash prend en compte ces deux eventuels ajouts.
*/
checked_malloc(nsym_shared_hash,int,2+pr->dim,abort(););
ap_dim_t abs_dim = 0;
if (exprA->q || exprB->q) {
ptr = t1p_aaterm_alloc_init();
//res->l++;
/* linear part */
for(p = exprA->q, q = exprB->q; p || q;) {
dim += 1; /* computes the number of different noise symbols */
if (p && q) {
if (p->pnsym->index == q->pnsym->index) {
itv_mul(pr->itv, tmp[3], p->coeff, mid2);
itv_mul(pr->itv, tmp[4], q->coeff, mid1);
itv_add(ptr->coeff, tmp[3], tmp[4]);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
nsym_shared[p->pnsym->index] = true;
SDP_dim++;
nsym_shared_hash[p->pnsym->index] = SDP_dim;
if (env->hypercube) itv_set(gammabis[p->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, p->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[p->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[p->pnsym->index], pr->muu);
itv_set(eps_itv,pr->muu);
}
}
p = p->n ;
q = q->n ;
} else if (p->pnsym->index < q->pnsym->index) {
itv_mul(pr->itv, ptr->coeff, p->coeff, mid2);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[p->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, p->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[p->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[p->pnsym->index], pr->muu);
itv_set(eps_itv,pr->muu);
}
}
p = p->n ;
} else {
itv_mul(pr->itv, ptr->coeff, q->coeff, mid1);
ptr->pnsym = q->pnsym;
hash[q->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[q->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, q->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[q->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[q->pnsym->index], pr->muu);
itv_set(eps_itv,pr->muu);
}
}
q = q->n ;
}
} else if (p) {
itv_mul(pr->itv, ptr->coeff, p->coeff, mid2);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[p->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, p->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[p->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[p->pnsym->index], pr->muu);
itv_set(eps_itv,pr->muu);
}
}
p = p->n ;
} else {
itv_mul(pr->itv, ptr->coeff, q->coeff, mid1);
ptr->pnsym = q->pnsym;
hash[q->pnsym->index] = dim;
if (env->hypercube) itv_set(gammabis[q->pnsym->index], pr->muu);
else {
if (t1p_nsymcons_get_dimpos(pr, &abs_dim, q->pnsym->index, env)) {
itv_set_ap_interval(pr->itv, eps_itv, env->gamma[abs_dim]);
itv_middev(pr->itv, midi, devi, eps_itv);
itv_sub(gammabis[q->pnsym->index], eps_itv, midi);
} else {
itv_set(gammabis[q->pnsym->index], pr->muu);
itv_set(eps_itv,pr->muu);
}
}
q = q->n ;
}
if (itv_is_zero(ptr->coeff)) {
if (!(p||q)) {
/* the last iteration */
t1p_aaterm_free(pr, ptr);
if (res->end) res->end->n = NULL;
}
} else {
/* keep this term */
if (!res->q) res->q = ptr;
res->end = ptr;
res->l++;
itv_mul(pr->itv, eps_itv, eps_itv, ptr->coeff);
itv_add(res->itv, res->itv, eps_itv);
if (p||q) {
/* continuing */
ptr->n = t1p_aaterm_alloc_init();
ptr=ptr->n;
} else {
/* the last iteration */
ptr->n = NULL;
}
}
}
}
/* non linear part */
/* Calling SDP solver (non guaranteed):
* - compute different noise symboles, say "n",
* - we have "n" constraints, each is a diagonal matrix (can also be seen as 2 block matrix) of dimension 2n, containing 1 in (i,i) and (i+n,i+n) positions,
* - objectif matrix (in primal form) is a 2 block matrix of dimension 2n. First block is deduced from the non linear (quadric) part of multiplication, we zero all values of the second block,
* - objective vector (in dual form) is a one vector of dimension "n".
*/
if (exprA->q && exprB->q) {
ap_funopt_t option = ap_manager_get_funopt(pr->man, pr->funid);
cond_SDP = option.algorithm == INT_MAX ? true : false;
itv_t itv1; itv_init(itv1);
itv_t itv2; itv_init(itv2);
if (cond_SDP) {
call_sdp(pr->itv, itv1, exprA->q, exprB->q, dim, hash, true);
}
else
square_dep(pr, itv2, exprA->q, exprB->q, hash, dim, gammabis);
if (exprA == exprB) {
if (bound_sgn(itv1->inf) > 0) {bound_set_int(itv1->inf,0);}
if (bound_sgn(itv2->inf) > 0) {bound_set_int(itv2->inf,0);}
}
if (cond_SDP) itv_set(itv_nlin,itv1);
else itv_set(itv_nlin,itv2);
itv_add(res->c, res->c, itv_nlin);
itv_add(res->itv, res->itv, itv_nlin);
itv_clear(itv1);
itv_clear(itv2);
}
/* hash may be NULL if pr->index is zero */
if (hash) {free(hash);free(nsym_shared);free(nsym_shared_hash);}
itv_array_free(gammabis, pr->dim);
itv_array_free(tmp, 5);
itv_clear(mid1);
itv_clear(mid2);
itv_clear(midi);
itv_clear(devi);
itv_clear(eps_itv);
itv_clear(itv_nlin);
return res;
}
t1p_aff_t* t1p_aff_mul_non_constrained(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* env)
{
t1p_aaterm_t *p, *q, *ptr;
itv_t itv_nlin; itv_init(itv_nlin);
int i = 0;
int SDP_dim = 0;
unsigned int dim = 0; /* compute the number of different eps */
int cond_SDP; /* use SDP or not ? */
itv_t tmp; itv_init(tmp);
/* hash table to sort noise symbols "de facon contigue".
* If we have eps1, eps2, eps4, eps5 shared between the two forms, they are seen as eps1, eps2, eps3, eps4 which optimizes the size of the SDP problem.
*/
int* hash = (int *)malloc((2+pr->dim)*sizeof(int));
int* nsym_shared;
checked_malloc(nsym_shared,int,pr->dim,abort(););
int* nsym_shared_hash;
/* si on accumule, pour chaque expression, les coeff des symboles indépendants, on rajoute 2 symboles, un pour chaque expression.
le hash prend en compte ces deux eventuels ajouts.
*/
checked_malloc(nsym_shared_hash,int,2+pr->dim,abort(););
t1p_aff_t* res = t1p_aff_alloc_init(pr);
itv_mul(pr->itv, res->c, exprA->c, exprB->c);
itv_set(res->itv, res->c);
if (exprA->q || exprB->q) {
ptr = t1p_aaterm_alloc_init();
for(p = exprA->q, q = exprB->q; p || q;) {
dim += 1; /* compute the number of different noise symbols */
if (p && q) {
if (p->pnsym->index == q->pnsym->index) {
itv_mul(pr->itv, tmp, p->coeff, exprB->c);
itv_mul(pr->itv, ptr->coeff, q->coeff, exprA->c);
itv_add(ptr->coeff, ptr->coeff, tmp);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
nsym_shared[p->pnsym->index] = true;
SDP_dim++;
nsym_shared_hash[p->pnsym->index] = SDP_dim;
p = p->n ;
q = q->n ;
} else if (p->pnsym->index < q->pnsym->index) {
itv_mul(pr->itv, ptr->coeff, p->coeff, exprB->c);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
p = p->n ;
} else {
itv_mul(pr->itv, ptr->coeff, q->coeff, exprA->c);
ptr->pnsym = q->pnsym;
hash[q->pnsym->index] = dim;
q = q->n ;
}
} else if (p) {
itv_mul(pr->itv, ptr->coeff, p->coeff, exprB->c);
ptr->pnsym = p->pnsym;
hash[p->pnsym->index] = dim;
p = p->n ;
} else {
itv_mul(pr->itv, ptr->coeff, q->coeff, exprA->c);
ptr->pnsym = q->pnsym;
hash[q->pnsym->index] = dim;
q = q->n ;
}
if (itv_is_zero(ptr->coeff)) {
if (!(p||q)) {
/* the last iteration */
t1p_aaterm_free(pr, ptr);
if (res->end) res->end->n = NULL;
}
} else {
/* keep this term */
if (!res->q) res->q = ptr;
res->end = ptr;
res->l++;
t1p_nsymcons_get_gamma(pr, tmp, ptr->pnsym->index, env);
itv_mul(pr->itv, tmp, tmp, ptr->coeff);
itv_add(res->itv, res->itv, tmp);
if (p||q) {
/* continuing */
ptr->n = t1p_aaterm_alloc_init();
ptr=ptr->n;
} else {
/* the last iteration */
ptr->n = NULL;
}
}
}
}
/* non linear part */
/* Calling SDP solver (non guaranteed):
* - compute different noise symboles, say "n",
* - we have "n" constraints, each is a diagonal matrix (can also be seen as 2 block matrix) of dimension 2n, containing 1 in (i,i) and (i+n,i+n) positions,
* - objectif matrix (in primal form) is a 2 block matrix of dimension 2n. First block is deduced from the non linear (quadric) part of multiplication, we zero all values of the second block,
* - objective vector (in dual form) is a one vector of dimension "n".
*/
if (exprA->q && exprB->q) {
ap_funopt_t option = ap_manager_get_funopt(pr->man, pr->funid);
cond_SDP = option.algorithm == INT_MAX ? true : false;
itv_t itv1; itv_init(itv1);
itv_t itv2; itv_init(itv2);
if (cond_SDP) {
call_sdp(pr->itv, itv1, exprA->q, exprB->q, dim, hash, true);
/* tentative de mise en place d'un solveur garantit, to be continued ... */
// itv_t* array = itv_array_alloc(dim*(dim+1)/2);
// buildIntervalUpperTriangle(pr, array, exprA->q, exprB->q, dim, hash);
// double* phi = buildDoubleUpperTriangle(pr, array, dim);
// call_sound_sdp(dim, phi);
// free(phi);
// itv_array_free(array,(dim*(dim+1)/2));
}
else
square_dep(pr, itv2, exprA->q, exprB->q, hash, dim, NULL);
if (exprA == exprB) {
if (bound_sgn(itv1->inf) > 0) {bound_set_int(itv1->inf,0);}
if (bound_sgn(itv2->inf) > 0) {bound_set_int(itv2->inf,0);}
}
if (cond_SDP) itv_set(itv_nlin,itv1);
else itv_set(itv_nlin,itv2);
itv_add(res->c, res->c, itv_nlin);
itv_add(res->itv, res->itv, itv_nlin);
itv_clear(itv1);
itv_clear(itv2);
}
/* hash may be NULL if pr->index is zero */
if (hash) {free(hash);free(nsym_shared);free(nsym_shared_hash);}
itv_clear(tmp);
itv_clear(itv_nlin);
return res;
}
/* computes exprA/exprB.
If 0 \in exprB->itv, return top + caveat
else if exprB->itv has an infity bound return (1/exprB->itv)*exprA
else return (1/exprB)*exprA
*/
t1p_aff_t* t1p_aff_div(t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB, t1p_t* env)
{
t1p_aff_t* res;
itv_t box;
itv_t mid, dev;
itv_t a,b;
itv_t zeta, alpha, beta;
itv_t one;
itv_t tmp;
itv_init(box);
itv_init(mid); itv_init(dev);
itv_init(a); itv_init(b);
itv_init(zeta); itv_init(alpha); itv_init(beta);
itv_init(one);
itv_init(tmp);
itv_set_int(one, (long int)1);
if (itv_is_leq(tmp, exprB->itv)) {
fprintf(stderr,"(caveat) division by zero.\n");
res = t1p_aff_alloc_init(pr);
itv_set_top(res->c);
itv_set_top(res->itv);
} else if (itv_has_infty_bound(exprB->itv)) {
itv_div(pr->itv, tmp, one, exprB->itv);
res = t1p_aff_mul_itv(pr, exprA, tmp);
} else {
if (exprB->q == NULL) {
itv_div(pr->itv, tmp, one, exprB->c);
res = t1p_aff_mul_itv(pr,exprA,tmp);
} else {
if (itv_is_neg(exprB->itv)) itv_neg(box,exprB->itv);
else itv_set(box, exprB->itv);
itv_set(a,box);bound_neg(a->sup,a->inf); // a <- [box->inf,box->inf]
itv_set(b,box);bound_neg(b->inf,b->sup); // b <- [box->sup,box->sup]
itv_middev(pr->itv, mid, dev, box);
/* alpha = -1/mid^2 */
itv_mul(pr->itv, alpha, mid, mid);
itv_div(pr->itv, alpha, one, alpha);
itv_neg(alpha,alpha);
/* beta = 1/2a - 1/(a^2/2b + b/2 + a) */
itv_mul(pr->itv, tmp, a, a); // a*a
itv_div(pr->itv, tmp, tmp, b); // a*a/b
itv_mul_2exp(beta, tmp, -1); // a*a/2b
itv_mul_2exp(tmp, b, -1); // b/2
itv_add(beta, beta, tmp);
itv_add(beta, beta, a);
itv_div(pr->itv, beta, one, beta);
itv_neg(beta, beta);
itv_div(pr->itv, tmp, one, a); // 1/a
itv_mul_2exp(tmp, tmp, -1); // 1/2a
itv_add(beta, beta, tmp);
/* zeta = 2/mid + beta = 1/2a + 1/(b^2/2a + a/2 + b) + 2/(a+b) */
itv_mul(pr->itv, tmp, b, b); // b*b
itv_div(pr->itv, tmp, tmp, a); // b*b/a
itv_mul_2exp(zeta, tmp, -1); // b*b/2a
itv_mul_2exp(tmp, a, -1); // a/2
itv_add(zeta, zeta, tmp);
itv_add(zeta, zeta, b);
itv_div(pr->itv, zeta, one, zeta);
itv_div(pr->itv, tmp, one, a); // 1/a
itv_mul_2exp(tmp, tmp, -1); // 1/2a
itv_add(zeta, zeta, tmp);
itv_div(pr->itv, tmp, one, mid); // 2/(a+b)
itv_add(zeta, zeta, tmp);
t1p_aff_t* inv = t1p_aff_mul_itv(pr, exprB, alpha);
if (itv_is_neg(exprB->itv)) itv_sub(inv->c, inv->c, zeta);
else itv_add(inv->c, inv->c, zeta);
bound_set(beta->inf, beta->sup);
itv_add(inv->c, inv->c, beta);
//t1p_aff_nsym_create(pr, inv, beta);
itv_div(pr->itv, inv->itv, one, exprB->itv); /* update inv->itv */
/* x/y = x*y^{-1} */
res = t1p_aff_mul(pr,exprA,inv,env); /* inplace , boxes are needed */
//if (itv_is_neg(exprB->itv)) t1p_aff_neg_inplace(pr,res);
t1p_aff_free(pr, inv);
itv_div(pr->itv, box, exprA->itv, exprB->itv);
itv_meet(pr->itv, res->itv, res->itv, box);
}
}
itv_clear(box);
itv_clear(one);
itv_clear(a); itv_clear(b);
itv_clear(zeta); itv_clear(alpha); itv_clear(beta);
itv_clear(mid); itv_clear(dev);
itv_clear(tmp);
return res;
}
t1p_aff_t* t1p_aff_mod (t1p_internal_t* pr, t1p_aff_t* exprA, t1p_aff_t* exprB)
{
not_implemented();
}
/* a = sqrt(b) */
t1p_aff_t* t1p_aff_sqrt( t1p_internal_t* pr, t1p_aff_t* expr, t1p_t* env)
{
t1p_aff_t* res;
itv_t zero; itv_init(zero);
itv_t box; itv_init(box);
bool eval_aff = false;
if (t1p_aff_is_bottom(pr, expr)) res = t1p_aff_bottom(pr);
else if (itv_is_neg(expr->itv)) {
if (itv_is_leq(zero,expr->itv)) res = t1p_aff_alloc_init(pr);
else {
fprintf(stderr," (error) computing the square root of something negative.\n");
res = t1p_aff_bottom(pr);
}
} else if (itv_is_pos(expr->itv)) {
if (t1p_aff_is_zero(pr, expr)) {
res = t1p_aff_alloc_init(pr);
} else {
itv_set(box,expr->itv);
eval_aff = true;
}
} else {
fprintf(stderr," (caveat) computing the square root of something negative.\n");
itv_set(box,expr->itv);
bound_set_int(box->inf, 0);
eval_aff = true;
}
if (eval_aff) {
itv_t alpha, beta, zeta;
itv_t mid, dev;
itv_t one, tmp, tmp1;
itv_t a, b;
itv_init(alpha); itv_init(beta); itv_init(zeta);
itv_init(mid); itv_init(dev);
itv_init(one); itv_init(tmp); itv_init(tmp1);
itv_init(a); itv_init(b);
itv_set_int(one, 1);
itv_set(a,box);bound_neg(a->sup,a->inf); // a <- [box->inf,box->inf]
itv_set(b,box);bound_neg(b->inf,b->sup); // b <- [box->sup,box->sup]
itv_middev(pr->itv, mid, dev, box);
itv_sqrt(pr->itv, tmp, mid); // sqrt(mid)
itv_div(pr->itv, alpha, one, tmp); // 1/sqrt(mid)
itv_mul_2exp(alpha, alpha, -1);
itv_mul_2exp(beta, tmp, -1);
if (!itv_is_zero(a)) {
itv_sqrt(pr->itv, tmp1, a); // sqrt(a)
itv_sub(beta, beta, tmp1);
itv_mul(pr->itv, tmp1, a, a); // a*a
itv_div(pr->itv, tmp1, b, tmp1); // b/a*a
itv_div(pr->itv, tmp, one, a); // 1/a
itv_add(tmp, tmp1, tmp); // 1/a + b/a*a
itv_mul_2exp(tmp, tmp, 1); // 2(1/a + b/a*a)
itv_sqrt(pr->itv, tmp, tmp); // sqrt(2(1/a + b/a*a))
itv_div(pr->itv, tmp, one, tmp); // 1/sqrt(2(1/a + b/a*a))
itv_add(beta, beta, tmp);
}
itv_mul_2exp(beta, beta, -1);
itv_sqrt(pr->itv, tmp, mid); // sqrt(mid)
itv_mul_2exp(zeta, tmp, -1);
itv_sub(zeta, zeta, beta);
res = t1p_aff_mul_itv(pr, expr, alpha);
itv_add(res->c, res->c, zeta);
bound_set(beta->inf, beta->sup);
itv_add(res->c, res->c, beta);
itv_sqrt(pr->itv, res->itv, box); /* update a->itv */
itv_clear(a); itv_clear(b);
itv_clear(alpha); itv_clear(beta); itv_clear(zeta);
itv_clear(mid); itv_clear(dev);
itv_clear(one);
itv_clear(tmp); itv_clear(tmp1);
}
itv_clear(zero); itv_clear(box);
return res;
}
/* a = -b */
t1p_aff_t* t1p_aff_neg(t1p_internal_t* pr, t1p_aff_t* b)
{
t1p_aff_t* res = t1p_aff_alloc_init(pr);
t1p_aaterm_t *p, *q;
itv_neg(res->c, b->c);
res->l = b->l;
if (b->q) {
res->q = t1p_aaterm_alloc_init();
for (p=b->q, q=res->q; p->n; p=p->n) {
itv_neg(q->coeff, p->coeff);
q->pnsym = p->pnsym;
q->n = t1p_aaterm_alloc_init();
q = q->n;
}
itv_neg(q->coeff, p->coeff);
q->pnsym = p->pnsym;
res->end = q;
}
itv_neg(res->itv, b->itv);
return res;
}
void t1p_aff_neg_inplace(t1p_internal_t* pr, t1p_aff_t* b)
{
t1p_aaterm_t *p;
itv_neg(b->c, b->c);
for (p=b->q; p->n; p=p->n) {
itv_neg(p->coeff, p->coeff);
}
itv_neg(b->itv, b->itv);