/*----------------------------------------------------------------*/
bool NOMAD::Directions::compute_one_direction ( NOMAD::Direction & dir,
int mesh_index,
int halton_index )
{
dir.clear();
// categorical variables: do nothing:
if ( _is_categorical )
return false;
/*-------------------------------*/
/* binary variables */
/* (we use a random direction) */
/*-------------------------------*/
if ( _is_binary ) {
dir.reset ( _nc , 0.0 );
dir.set_type ( NOMAD::GPS_BINARY );
dir[NOMAD::RNG::rand()%_nc] = (NOMAD::RNG::rand()%2) ? -1.0 : 1.0;
}
/*----------------*/
/* Ortho-MADS */
/*----------------*/
else if ( _is_orthomads ) {
if ( !_primes )
ortho_mads_init ( _halton_seed );
dir.reset ( _nc , 0.0 );
dir.set_type ( NOMAD::ORTHO_1 );
NOMAD::Double alpha_t_l;
if ( !compute_halton_dir ( halton_index , mesh_index , alpha_t_l , dir ) )
return false;
// }
}
/*-------------*/
/* LT-MADS 1 */
/*-------------*/
else {
if ( !_lt_initialized)
lt_mads_init();
int hat_i;
dir = *get_bl ( mesh_index , NOMAD::LT_1 , hat_i );
}
return true;
}
/*-----------------------------------------------------------------------------*/
bool NOMAD::Directions::compute_dir_on_unit_sphere ( NOMAD::Direction & random_dir ) const
{
int i;
NOMAD::Double norm,d;
for ( i = 0 ; i < _nc ; ++i )
random_dir[i]=NOMAD::RNG::normal_rand(0,1);
norm=random_dir.norm();
if ( norm==0 )
return false;
for ( i = 0 ; i < _nc ; ++i )
random_dir[i]/=norm;
return true;
}
/*----------------------------------------------------------------*/
void NOMAD::Directions::householder ( const NOMAD::Direction & halton_dir ,
bool complete_to_2n ,
NOMAD::Direction ** H ) const
{
int i , j;
NOMAD::Double norm2 = halton_dir.squared_norm() , v , h2i;
for ( i = 0 ; i < _nc ; ++i ) {
h2i = 2 * halton_dir[i];
for ( j = 0 ; j < _nc ; ++j ) {
// H[i]:
(*H[i])[j] = v = (i==j) ? norm2 - h2i * halton_dir[j] : - h2i * halton_dir[j];
// -H[i]:
if ( complete_to_2n )
(*H[i+_nc])[j] = -v;
}
}
}
/*---------------------------------------------------------*/
bool NOMAD::Directions::compute_halton_dir ( int halton_index ,
int mesh_index ,
NOMAD::Double & alpha_t_l ,
NOMAD::Direction & halton_dir ) const
{
alpha_t_l.clear();
int i;
NOMAD::Double d , norm = 0.0;
NOMAD::Point b ( _nc );
for ( i = 0 ; i < _nc ; ++i )
{
d = Directions::get_phi ( halton_index , _primes[i] );
b[i] = 2*d - 1.0;
norm += b[i].pow2();
}
norm = norm.sqrt();
// desired squared norm for q:
NOMAD::direction_type hdt = halton_dir.get_type();
NOMAD::Double target = ( hdt == NOMAD::ORTHO_2N || hdt == NOMAD::ORTHO_NP1_QUAD || hdt == NOMAD::ORTHO_NP1_NEG ) ?
pow ( NOMAD::Mesh::get_mesh_update_basis() , abs(mesh_index) / 2.0 ) :
pow ( NOMAD::Mesh::get_mesh_update_basis() , abs(mesh_index) );
NOMAD::Double x = target.sqrt();
NOMAD::Double fx = eval_ortho_norm ( x , norm , b , halton_dir );
NOMAD::Double y = 1.0 , fy , delta_x , abs_dx , min , delta_min , diff , eps;
bool inc , possible , set_eps = false;
int cnt = 0;
while ( fx != target )
{
// safety test:
if ( ++cnt > 1000 )
{
#ifdef DEBUG
_out << std::endl << "Warning (" << "Directions.cpp" << ", " << __LINE__
<< "): could not compute Halton direction for (t="
<< halton_index << ", ell=" << mesh_index
<< ")" << std::endl << std::endl;
#endif
alpha_t_l.clear();
halton_dir.clear();
return false;
}
if ( set_eps )
{
eps = 1e-8;
set_eps = false;
}
else
eps = 0.0;
inc = ( fx < target );
possible = false;
min = 1e+20;
for ( i = 0 ; i < _nc ; ++i )
{
if ( b[i] != 0.0 )
{
if ( b[i] > 0.0 )
{
if ( inc )
diff = 0.5+eps;
else
diff = -0.5-eps;
}
else
{
if ( inc )
diff = -0.5-eps;
else
diff = 0.5+eps;
}
delta_x = norm * ( halton_dir[i] + diff) / b[i] - x;
y = x + delta_x;
if ( y > 0 )
{
abs_dx = delta_x.abs();
if ( abs_dx < min )
{
min = abs_dx;
delta_min = delta_x;
possible = true;
}
}
}
}
if ( !possible ) {
#ifdef DEBUG
_out << std::endl << "Warning (" << "Directions.cpp" << ", " << __LINE__
<< "): could not compute Halton direction for (t="
<< halton_index << ", ell=" << mesh_index << ")"
<< std::endl << std::endl;
#endif
alpha_t_l.clear();
halton_dir.clear();
return false;
}
y = x + delta_min;
fy = eval_ortho_norm ( y , norm , b , halton_dir );
if ( fx == fy ) {
set_eps = true;
continue;
}
if ( fy==target )
break;
if ( inc && fy > target && fx > 0 ) {
eval_ortho_norm ( x , norm , b , halton_dir );
break;
}
if ( !inc && fy < target && fy > 0 )
break;
x = y;
fx = fy;
}
alpha_t_l = y;
return true;
}
/// Reset the infeasible successful direction.
void reset_infeas_success_dir ( void ) const { _infeas_success_dir.clear(); }
/*---------------------------------------------------------*/
void NOMAD::Variable_Group::get_directions ( std::list<NOMAD::Direction> & dirs ,
NOMAD::poll_type poll ,
const NOMAD::Point & poll_center ,
int mesh_index ,
const NOMAD::Direction & feas_success_dir ,
const NOMAD::Direction & infeas_success_dir )
{
int nc = static_cast<int>(_var_indexes.size());
// vectors are of size nc :
// ------------------------
if ( nc == poll_center.size() ) {
_directions->compute ( dirs ,
poll ,
poll_center ,
mesh_index ,
-1 ,
feas_success_dir ,
infeas_success_dir );
return;
}
// construct vectors of size nc from vectors of size < nc :
// --------------------------------------------------------
std::set<int>::const_iterator it ;
int i = 0;
NOMAD::Point new_poll_center ( nc );
NOMAD::Direction new_fsd , new_isd;
if ( feas_success_dir.is_defined() )
new_fsd = NOMAD::Direction ( nc , 0.0 , feas_success_dir.get_type() );
if ( infeas_success_dir.is_defined() )
new_isd = NOMAD::Direction ( nc , 0.0 , infeas_success_dir.get_type() );
for ( it = _var_indexes.begin() ; it != _var_indexes.end() ; ++it )
{
new_poll_center[i] = poll_center[*it];
if ( feas_success_dir.is_defined() )
new_fsd[i] = feas_success_dir [*it];
if ( infeas_success_dir.is_defined() )
new_isd[i] = infeas_success_dir[*it];
++i;
}
_directions->compute ( dirs ,
poll ,
new_poll_center ,
mesh_index ,
-1 ,
new_fsd ,
new_isd );
}