Affine2Main<AF_iAF>& Affine2Main<AF_iAF>::operator*=(const Interval& y) {
if ( (!is_actif())||
y.is_empty()||
y.is_unbounded() ) {
*this = itv()*y;
} else {
double yVal0;
int i;
//std::cout << "in * "<<y<<std::endl;
//saxpy(y.mid(), Affine2Main<AF_iAF>(), 0.0, y.rad(), true, false, false, true);
yVal0 = y.mid();
// RES = X%(0) * res
for (i=0; i<=_n;i++) {
_elt._val[i] *=yVal0;
}
//_elt._err *= (fabs(yVal0)+Interval(y.rad()));
_elt._err *= (abs(y).ub());
{
bool b = (_elt._err.ub()<POS_INFINITY);
for (i=0;i<=_n;i++) {
b &= (abs(_elt._val[i]).ub()<POS_INFINITY);
}
if (!b) {
*this = Interval::ALL_REALS;
}
}
}
return *this;
}
Affine2Main<AF_iAF>::Affine2Main(const Affine2Main<AF_iAF>& x) :
_n (x._n),
_elt (NULL ,x._elt._err ) {
if (is_actif()) {
_elt._val =new Interval[x.size() + 1];
for (int i = 0; i <= x.size(); i++){
_elt._val[i] = x._elt._val[i];
}
}
}
Affine2Main<AF_iAF>& Affine2Main<AF_iAF>::operator*=(const Interval& y) {
if ( (!is_actif())||
y.is_empty()||
y.is_unbounded() ) {
*this = itv()*y;
} else {
*this *= Affine2Main<AF_iAF>(size(),0,y);
}
return *this;
}
Affine2Main<AF_iAF> Affine2Main<AF_iAF>::operator-() const {
Affine2Main<AF_iAF> res;
res._n = _n;
res._elt._err = _elt._err;
if (is_actif()) {
res._elt._val = new Interval[_n+1];
for (int i = 0; i <= _n; i++) {
res._elt._val[i] = (-_elt._val[i]);
}
}
return res;
}
const Interval Affine2Main<AF_iAF>::itv() const {
if (is_actif()) {
Interval res(_elt._val[0]);
Interval pmOne(-1.0, 1.0);
for (int i = 1; i <= _n; i++){
res += (_elt._val[i] * pmOne);
}
res += _elt._err * pmOne;
return res;
} else {
return _elt._err;
}
}
Affine2Main<AF_iAF>& Affine2Main<AF_iAF>::sqr(const Interval itv) {
// std::cout << "in sqr "<<std::endl;
bool b = (!(itv.is_empty()||itv.is_unbounded()));
if ( (!is_actif())||
itv.is_empty()||
itv.is_unbounded()||
(itv.diam() < AF_EC()) ) {
*this = pow(itv,2);
} else {
Interval Sx, Sx2, x0;
Sx = 0; Sx2 = 0; x0 = 0;
// compute the error
for (int i = 1; i <= _n; i++) {
Sx2 += _elt._val[i]*_elt._val[i];
Sx += abs(_elt._val[i]);
}
// compute 2*_elt._val[0]*(*this)
x0 = _elt._val[0];
_elt._val[0] = x0*x0;
// compute 2*_elt._val[0]*(*this)
for (int i = 1; i <= _n; i++) {
_elt._val[i] *= (2*x0);
}
_elt._val[0] += 0.5 *Sx2;
_elt._err = (2*abs(x0) * _elt._err - 0.5 * Sx2) + pow((_elt._err+Sx),2);
{
bool b = (_elt._err.ub()<POS_INFINITY);
for (int i=0;i<=_n;i++) {
b &= (abs(_elt._val[i]).ub()<POS_INFINITY);
}
if (!b) {
*this = Interval::ALL_REALS;
}
}
}
// std::cout << "out sqr "<<std::endl;
return *this;
}
Affine2Main<AF_iAF>& Affine2Main<AF_iAF>::operator*=(const Affine2Main<AF_iAF>& y) {
// std::cout << "in *= "<< *this <<std::endl;
if (is_actif() && (y.is_actif())) {
if (_n==y.size()) {
Interval Sx, Sy, Sxy, Sz, xVal0,tmp;
int i;
Interval * xTmp;
xTmp = new Interval[_n + 1];
Sx=0.0; Sy=0.0; Sxy=0.0; Sz=0.0; xVal0=0.0; tmp =0.0;
for (i = 1; i <= _n; i++) {
tmp =_elt._val[i]*y._elt._val[i];
Sz += tmp;
Sxy += abs(tmp);
Sx += abs(_elt._val[i]);
Sy += abs(y._elt._val[i]);
}
xVal0 = _elt._val[0];
// RES = X%T(0) * res
for (i = 0; i <= _n; i++) {
_elt._val[i] *= y._elt._val[0];
}
// Xtmp = X%T(0) * Y
xTmp[0] = 0.0;
for (i = 1; i <= _n; i++) {
xTmp[i] = xVal0*y._elt._val[i];
}
//RES = RES + Xtmp = ( Y%(0) * X ) + ( X%T(0) * Y - X%T(0)*Y%(0) )
for (i = 0; i <= _n; i++) {
_elt._val[i] += xTmp[i];
}
_elt._val[0] += 0.5 *Sz ;
_elt._err = abs(y._elt._val[0]) * _elt._err + abs(xVal0) * y._elt._err +(_elt._err+Sx)*(y._elt._err+Sy)- 0.5 * Sxy;
{
bool b = (_elt._err.ub()<POS_INFINITY);
for (i=0;i<=_n;i++) {
b &= (abs(_elt._val[i]).ub()<POS_INFINITY);
}
if (!b) {
*this = Interval::ALL_REALS;
}
}
delete[] xTmp;
} else {
if (_n>y.size()) {
*this *= y.itv();
} else {
Interval tmp1 = this->itv();
*this = y;
*this *= tmp1;
}
}
} else {
*this = itv()*y.itv();
}
// std::cout << "out *= "<< *this<<std::endl;
return *this;
}
Affine2Main<AF_iAF>& Affine2Main<AF_iAF>::saxpy(double alpha, const Affine2Main<AF_iAF>& y, double beta, double ddelta, bool B1, bool B2, bool B3, bool B4) {
//std::cout << "saxpy IN " << alpha << " x " << *this << " + " << y << " + "<< beta << " +error " << ddelta << " / "<< B1 << B2 << B3 << B4 << std::endl;
int i;
// std::cout << "in saxpy alpha=" << alpha << " beta= " << beta << " delta = " << ddelta << std::endl;
if (is_actif()) {
if (B1) { // multiply by a scalar alpha
if (alpha==0.0) {
for (i=0; i<=_n;i++) {
_elt._val[i]=0;
}
_elt._err = 0;
}
else if ((fabs(alpha)) < POS_INFINITY) {
for (i=0; i<=_n;i++) {
_elt._val[i] *= alpha;
}
_elt._err *= fabs(alpha);
}
else {
*this = itv()*alpha;
}
}
if (B2) { // add a affine2 form y
if (y.is_actif()) {
if (_n==y._n) {
for(i=0;i<=_n;i++) {
_elt._val[i] +=y._elt._val[i];
}
_elt._err += y._elt._err;
} else {
if (_n>y.size()) {
*this += y.itv();
} else {
Interval tmp1 = itv();
*this = y;
*this += tmp1;
}
}
}
else { // y is not a valid affine2 form. So we add y.itv() such as an interval
*this = itv()+y.itv();
}
}
if (B3) { //add a constant beta
if ((fabs(beta))<POS_INFINITY) {
_elt._val[0] += beta;
}
else {
*this = itv()+beta;
}
}
if (B4) { // add an error ddelta
if ((fabs(ddelta))<POS_INFINITY) {
_elt._err += fabs(ddelta);
}
else {
*this = itv()+Interval(-1,1)*ddelta;
}
}
if (_elt._val != NULL) {
bool b = (_elt._err.ub()<POS_INFINITY);
for (i=0;i<=_n;i++) {
b &= (abs(_elt._val[i]).ub()<POS_INFINITY);
}
if (!b) {
*this = Interval::ALL_REALS;
}
}
} else {
if (B1) { //scalar alpha
*this = itv()* alpha;
}
if (B2) { // add y
*this = itv()+ y.itv();
}
if (B3) { //constant beta
*this = itv()+ beta;
}
if (B4) { // error delta
*this = itv()+Interval(-1,1)*ddelta;;
}
}
// std::cout << " saxpy OUT x= "<< *this<<std::endl;
return *this;
}