void nlopt_fill_gradient(const double * x, double * grad, void * extra) {
auto extra_info = static_cast<tuple<Enode *, box const &, bool> *>(extra);
Enode * e = get<0>(*extra_info);
box const & b = get<1>(*extra_info);
bool const polarity = get<2>(*extra_info);
unordered_map<Enode *, double> var_map;
unsigned i = 0;
vector<Enode*> forall_var_vec;
for (Enode * e : b.get_vars()) {
if (e->isForallVar()) {
var_map.emplace(e, x[i]);
i++;
forall_var_vec.push_back(e);
} else {
var_map.emplace(e, b[e].mid());
}
}
i = 0;
for (Enode * var : forall_var_vec) {
double deriv_i = deriv_enode(e->get1st(), var, var_map) - deriv_enode(e->get2nd(), var, var_map);
if (e->isGt() || e->isGeq()) {
deriv_i = - deriv_i;
}
if (!polarity) {
deriv_i = - deriv_i;
}
grad[i] = deriv_i;
i++;
}
}
double deriv_enode(Enode * const e, Enode * const v, unordered_map<Enode*, double> const & var_map) {
if (e == v) {
return 1.0;
}
if (e->isVar()) {
auto const it = var_map.find(e);
if (it == var_map.cend()) {
throw runtime_error("variable not found");
} else {
// Variable is found in var_map
return 0.0;
}
} else if (e->isConstant()) {
return 0.0;
} else if (e->isSymb()) {
throw runtime_error("eval_enode: Symb");
} else if (e->isNumb()) {
throw runtime_error("eval_enode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
double ret = 0.0;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret + deriv_enode(tmp->getCar(), v, var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret - deriv_enode(tmp->getCar(), v, var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
assert(tmp->getArity() == 1);
return (- ret);
case ENODE_ID_TIMES: {
// (f * g)' = f' * g + f * g'
if (tmp->getArity() != 2) {
throw runtime_error("deriv_enode: only support arity = 2 case for multiplication");
}
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return f_ * g + f * g_;
}
case ENODE_ID_DIV: {
// (f / g)' = (f' * g - f * g') / g^2
if (tmp->getArity() != 2) {
throw runtime_error("deriv_enode: only support arity = 2 case for division");
}
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return (f_ * g - f * g_) / (g * g);
}
case ENODE_ID_ACOS: {
// (acos f)' = -(1 / sqrt(1 - f^2)) f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return - (1 / sqrt(1 - f * f)) * f_;
}
case ENODE_ID_ASIN: {
// (asin f)' = (1 / sqrt(1 - f^2)) f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 1 / sqrt(1 - f * f) * f_;
}
case ENODE_ID_ATAN: {
// (atan f)' = (1 / (1 + f^2)) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 1 / (1 + f * f) * f_;
}
case ENODE_ID_ATAN2: {
// atan2(x,y)' = -y / (x^2 + y^2) dx + x / (x^2 + y^2) dy
// = (-y dx + x dy) / (x^2 + y^2)
assert(e->getArity() == 2);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return (-g * f_ + f * g_) / (f * f + g * g);
}
case ENODE_ID_MIN:
assert(e->getArity() == 2);
throw runtime_error("deriv_enode: no support for min");
case ENODE_ID_MAX:
assert(e->getArity() == 2);
throw runtime_error("deriv_enode: no support for max");
case ENODE_ID_MATAN:
assert(e->getArity() == 1);
throw runtime_error("deriv_enode: no support for matan");
case ENODE_ID_SAFESQRT:
assert(e->getArity() == 1);
throw runtime_error("deriv_enode: no support for safesqrt");
case ENODE_ID_SQRT: {
// (sqrt(f))' = 1/2 * 1/(sqrt(f)) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 0.5 * 1 / sqrt(f) * f_;
}
case ENODE_ID_EXP: {
// (exp f)' = (exp f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return exp(f) * f_;
}
case ENODE_ID_LOG: {
// (log f)' = f' / f
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return f_ / f;
}
case ENODE_ID_POW: {
// (f^g)' = f^g (f' * g / f + g' * ln g)
assert(e->getArity() == 2);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return pow(f, g) * (f_ * g / f + g_ * log(g));
}
case ENODE_ID_ABS: {
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
if (f > 0) {
return f_;
} else {
return - f_;
}
}
case ENODE_ID_SIN: {
// (sin f)' = (cos f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return cos(f) * f_;
}
case ENODE_ID_COS: {
// (cos f)' = - (sin f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return - sin(f) * f_;
}
case ENODE_ID_TAN: {
// (tan f)' = (1 + tan^2 f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return (1 + tan(f) * tan(f)) * f_;
}
case ENODE_ID_SINH: {
// (sinh f)' = (e^f + e^(-f))/2 * f'
// = cosh(f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return cosh(f) * f_;
}
case ENODE_ID_COSH: {
// (cosh f)' = (e^f - e^(-f))/2 * f'
// = sinh(f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return sinh(f) * f_;
}
case ENODE_ID_TANH: {
// (tanh f)' = (sech^2 f) * f'
// = (1 - tanh(f) ^ 2) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return (1 - tanh(f) * tanh(f)) * f_;
}
default:
throw runtime_error("deriv_enode: Unknown Term");
}
} else if (e->isList()) {
throw runtime_error("deriv_enode: List");
} else if (e->isDef()) {
throw runtime_error("deriv_enode: Def");
} else if (e->isEnil()) {
throw runtime_error("deriv_enode: Nil");
} else {
throw runtime_error("deriv_enode: unknown case");
}
throw runtime_error("Not implemented yet: deriv_enode");
}
