void ai_eval_hexes( int x, int y, int range, int(*eval_func)(int,int,void*), void *ctx )
{
List *list = list_create( LIST_NO_AUTO_DELETE, LIST_NO_CALLBACK );
AI_Pos *pos;
int i, nx, ny;
/* gather and handle all positions by breitensuche.
use AUX mask to mark visited positions */
map_clear_mask( F_AUX );
list_add( list, ai_create_pos( x, y ) ); mask[x][y].aux = 1;
list_reset( list );
while ( list->count > 0 ) {
pos = list_dequeue( list );
if ( !eval_func( pos->x, pos->y, ctx ) ) {
free( pos );
break;
}
for ( i = 0; i < 6; i++ )
if ( get_close_hex_pos( pos->x, pos->y, i, &nx, &ny ) )
if ( !mask[nx][ny].aux && get_dist( x, y, nx, ny ) <= range ) {
list_add( list, ai_create_pos( nx, ny ) );
mask[nx][ny].aux = 1;
}
free( pos );
}
list_delete( list );
}
RGBColor
ImplicitSurface::trace_ray(const Ray& ray) const{
//float range = 10.83;
float range = 3.79;
range *= range;
float vres = (*world_ptr).vp.vres;
float hres = (*world_ptr).vp.hres;
const float x = (ray.o.x + hres/2) / hres * range;
const float y = (ray.o.y + vres/2) / vres * range;
float eval = eval_func(x, y);
return RGBColor(eval, eval, eval);
//return white;
}
// min
int min_node(int depth, int side, XY *move)
{
int best = INFINITY, value;
int nmoves;
XY moves[MOVENUM], opp[MOVENUM];
int pre_board[8][8];
int i;
if (depth == DEPTH)
return eval_func();
// 手を生成
nmoves = generate_moves(side, moves);
// 手がないとき
if (nmoves == 0)
{
if (generate_moves(-side, opp) == 0) // 相手もおけないときは終了
return get_terminal_value();
else // 違うときはパス
moves[nmoves++] = PASSMOVE;
}
// たどっていく
for (i = 0; i < nmoves; i++)
{
memcpy(pre_board, board, sizeof(board)); // 盤面の保存
place_disk(side, moves[i]); // 一手進める
// 再帰(recursive)
value = max_node(depth + 1, -side, move);
memcpy(board, pre_board, sizeof(board)); // 戻す
// 値の更新
if (value <= best)
{
best = value;
if (depth == 0)
*move = moves[i];
}
}
return best;
}
Value eval(const Tree& tree, const Params& params, void* p, Cost* limit) {
switch (tree.expr_id().type) {
case Expr::Term: {
return eval_term(tree.expr_id().index, params, p, limit);
}
case Expr::Func: {
Args args;
for (const Tree& child : tree.children())
args.push_back(eval(child, params, p, limit));
return eval_func(tree.expr_id().index, args, p, limit);
}
case Expr::Select: {
unsigned branch =
eval_select(tree.expr_id().index, params, p, limit);
assert(branch < tree.children().size());
return eval(tree.children()[branch], params, p, limit);
}
case Expr::Invalid:
throw std::logic_error("Invalid expression");
}
assert(false);
}
namespace GiNaC {
//////////
// Hermite polynomials H_n(x)
//////////
static ex hermite_evalf(const ex& n, const ex& x, PyObject* parent)
{
if (not is_exactly_a<numeric>(x)
or not is_exactly_a<numeric>(n))
return hermite(n,x).hold();
// see http://dlmf.nist.gov/18.5.E13
numeric numn = ex_to<numeric>(n);
numeric numx = ex_to<numeric>(x);
std::vector<numeric> numveca, numvecb;
numveca.push_back(numn / *_num_2_p);
numveca.push_back(*_num1_2_p + (numn / *_num_2_p));
return pow(numx * (*_num2_p), numn) * hypergeometric_pFq(numveca, numvecb, -pow(numx, *_num2_p).inverse(), parent);
}
static ex hermite_eval(const ex& n, const ex& x)
{
if (is_exactly_a<numeric>(x)) {
numeric numx = ex_to<numeric>(x);
if (numx.is_zero())
if (n.info(info_flags::integer)
and n.info(info_flags::odd))
return _ex0;
if (is_exactly_a<numeric>(n) and numx.info(info_flags::inexact))
return hermite_evalf(n, x, nullptr);
}
if (not is_exactly_a<numeric>(n))
return hermite(n, x).hold();
numeric numn = ex_to<numeric>(n);
if (not numn.info(info_flags::integer) or numn < 0)
throw std::runtime_error("hermite_eval: The index n must be a nonnegative integer");
if (numn.is_zero())
return _ex1;
// apply the formula from http://oeis.org/A060821
// T(n, k) = ((-1)^((n-k)/2))*(2^k)*n!/(k!*((n-k)/2)!) if n-k is even and >=0, else 0.
// sequentially for all viable k. Effectively there is the recurrence
// T(n, k) = -(k+2)*(k+1)/(2*(n-k)) * T(n, k+2), with T(n, n) = 2^n
numeric coeff = _num2_p->power(numn);
ex sum = _ex0;
int fac = 1;
while (numn >= 0) {
sum = sum + power(x, numn) * coeff;
coeff /= *_num_4_p;
coeff *= numn;
--numn;
coeff *= numn;
--numn;
coeff /= fac++;
}
return sum;
}
static ex hermite_deriv(const ex& n, const ex & x, unsigned deriv_param)
{
if (deriv_param == 0)
throw std::runtime_error("derivative w.r.t. to the index is not supported yet");
return _ex2 * n * hermite(n-1, x).hold();
}
REGISTER_FUNCTION(hermite, eval_func(hermite_eval).
evalf_func(hermite_evalf).
derivative_func(hermite_deriv).
latex_name("H"));
//////////
// Gegenbauer (ultraspherical) polynomials C^a_n(x)
//////////
static ex gegenb_evalf(const ex& n, const ex &a, const ex& x, PyObject* parent)
{
if (not is_exactly_a<numeric>(x)
or not is_exactly_a<numeric>(a)
or not is_exactly_a<numeric>(n))
return gegenbauer(n,a,x).hold();
// see http://dlmf.nist.gov/18.5.E9
numeric numn = ex_to<numeric>(n);
numeric numx = ex_to<numeric>(x);
numeric numa = ex_to<numeric>(a);
numeric num2a = numa * (*_num2_p);
std::vector<numeric> numveca, numvecb;
numveca.push_back(-numn);
numveca.push_back(numn + num2a);
numvecb.push_back(numa + (*_num1_2_p));
numeric factor = numn + num2a - (*_num1_p);
factor = factor.binomial(numn);
return factor * hypergeometric_pFq(numveca, numvecb, ((*_num1_p)-numx)/(*_num2_p), parent);
}
static ex gegenb_eval(const ex& n, const ex &a, const ex& x)
{
numeric numa = 1;
if (is_exactly_a<numeric>(x)) {
numeric numx = ex_to<numeric>(x);
if (is_exactly_a<numeric>(n)
and is_exactly_a<numeric>(a)
and numx.info(info_flags::inexact))
return gegenb_evalf(n, a, x, nullptr);
}
if (not is_exactly_a<numeric>(n))
return gegenbauer(n, a, x).hold();
numeric numn = ex_to<numeric>(n);
if (not numn.info(info_flags::integer) or numn < 0)
throw std::runtime_error("gegenb_eval: The index n must be a nonnegative integer");
if (numn.is_zero())
return _ex1;
if (numn.is_equal(*_num1_p))
return _ex2 * a * x;
if (is_exactly_a<numeric>(a)) {
numa = ex_to<numeric>(a);
if (numa.is_zero())
return _ex0; // C_n^0(x) = 0
}
if (not is_exactly_a<numeric>(a) or numa < 0) {
ex p = _ex1;
ex sum = _ex0;
ex sign = _ex1;
ex aa = _ex1;
unsigned long nn = numn.to_long();
sign = - 1;
for (unsigned long k=0; k<=nn/2; k++) {
sign *= - 1;
aa = a;
p = 1;
// rising factorial (a)_{n-k}
for (unsigned long i=0; i<nn-k; i++) {
p *= aa;
aa = aa + 1;
}
p /= numeric(k).factorial();
p /= numeric(nn-2*k).factorial();
sum += pow(2*x, nn-2*k) * p * sign;
}
return sum;
}
// from here on see flint2/fmpq_poly/gegenbauer_c.c
numeric numer = numa.numer();
numeric denom = numa.denom();
numeric t = numn.factorial();
numeric overall_denom = pow(denom, numn) * t;
unsigned long nn = numn.to_long();
numeric p = t / (numeric(nn/2).factorial());
if ((nn%2) != 0u)
p *= *_num2_p;
if ((nn&2) != 0u)
p = -p;
for (unsigned long k=0; k < nn-nn/2; k++) {
p *= numer;
numer += denom;
}
p *= denom.power(nn/2);
ex sum = _ex0;
if ((nn%2) != 0u)
sum += x*p;
else
sum += p;
for (long k=nn/2-1; k>=0; --k) {
p *= numer;
p *= 4*(k+1);
p *= *_num_1_p;
p /= denom;
p /= nn-2*k-1;
p /= nn-2*k;
sum += pow(x, nn-2*k) * p;
numer += denom;
}
return sum / overall_denom;
}
static ex gegenb_deriv(const ex& n, const ex & a, const ex & x, unsigned deriv_param)
{
if (deriv_param == 0)
throw std::runtime_error("derivative w.r.t. to the index is not supported yet");
if (deriv_param == 1)
throw std::runtime_error("derivative w.r.t. to the second index is not supported yet");
return _ex2 * a * gegenbauer(n-1, a+1, x).hold();
}
REGISTER_FUNCTION(gegenbauer, eval_func(gegenb_eval).
evalf_func(gegenb_evalf).
derivative_func(gegenb_deriv).
latex_name("C"));
} // namespace GiNaC
static ex exp_imag_part(const ex & x)
{
return exp(GiNaC::real_part(x))*sin(GiNaC::imag_part(x));
}
static ex exp_conjugate(const ex & x)
{
// conjugate(exp(x))==exp(conjugate(x))
return exp(x.conjugate());
}
REGISTER_FUNCTION(exp, eval_func(exp_eval).
evalf_func(exp_evalf).
expand_func(exp_expand).
derivative_func(exp_deriv).
real_part_func(exp_real_part).
imag_part_func(exp_imag_part).
conjugate_func(exp_conjugate).
latex_name("\\exp"))
//////////
// natural logarithm
//////////
static ex log_evalf(const ex & x)
{
if (is_exactly_a<numeric>(x))
return log(ex_to<numeric>(x));
return log(x).hold();
}
case info_flags::negint:
case info_flags::nonnegint:
case info_flags::has_indices:
return arg.info(inf);
}
return false;
}
static bool conjugate_info(const ex & arg, unsigned inf)
{
return func_arg_info(arg, inf);
}
REGISTER_FUNCTION(conjugate_function, eval_func(conjugate_eval).
evalf_func(conjugate_evalf).
expl_derivative_func(conjugate_expl_derivative).
info_func(conjugate_info).
print_func<print_latex>(conjugate_print_latex).
conjugate_func(conjugate_conjugate).
real_part_func(conjugate_real_part).
imag_part_func(conjugate_imag_part).
set_name("conjugate","conjugate"))
//////////
// real part
//////////
static ex real_part_evalf(const ex & arg)
{
if (is_exactly_a<numeric>(arg)) {
return ex_to<numeric>(arg).real();
/*
**
** void setup_spop(EVOLDATA ev, MATRIX fSearchPop, VECTOR fRefProbDist,
** MATRIX fRefPop, MATRIX fLC, MATRIX fDC)
**
** Sets up the search population by performing the initial evaluations.
**
** Assumes that ref. population is already setup and SORTED
**
*/
void setup_spop(EVOLDATA ev, MATRIX fSearchPop, VECTOR fRefProbDist,
MATRIX fRefPop, MATRIX fLC, MATRIX fDC)
{
int i, j, k, iSelIndex;
float fRandVal;
float fTempVec[MAXVECTOR];
int iFlag;
for (i=1; i<=ev.iSearchPopSize; i++)
{
eval_func(fSearchPop[i], ev.iNumTestCase, ev); /* simple evaluation */
/* now, pick a reference vector at RANDOM (0) or ORDERED (1) */
if (ev.iSelRefPoint == RANDOM)
iSelIndex = (int)randgen(1.0, (float)ev.iRefPopSize);
else
{
fRandVal = randgen(0.0, 1.0);
k=1;
while (fRandVal >= fRefProbDist[k])
k++;
if (k >= ev.iRefPopSize) k = 1;
iSelIndex = k;
}
/* move from search to reference */
k = 0; iFlag = FALSE; fRandVal = 0.0;
if (ev.iRepairMethod == RANDOM)
do
{
fRandVal = randgen(0.0, 1.0);
for (j=1; j<=ev.iNumVars; j++)
fTempVec[j] = fRandVal*fSearchPop[i][j] +
(1-fRandVal)*fRefPop[iSelIndex][j];
iFlag = check_all(ev, fTempVec, fLC, fDC);
k++;
} while ((iFlag == FALSE) && (k < 100));
else if (ev.iRepairMethod == DETERMINISTIC)
do
{
fRandVal = 1.0/power(2.0, k);
for (j=1; j<=ev.iNumVars; j++)
fTempVec[j] = fRandVal*fSearchPop[i][j] +
(1-fRandVal)*fRefPop[iSelIndex][j];
iFlag = check_all(ev, fTempVec, fLC, fDC);
k++;
} while ((iFlag == FALSE) && (k < 20));
/* if no feasible Z, Z = Y */
if (iFlag == FALSE)
for (j=1; j<=ev.iNumVars; j++)
fTempVec[j] = fRefPop[iSelIndex][j];
/* now, evaluate Z */
eval_func(fTempVec, ev.iNumTestCase, ev);
/* if Z better than Y, replace Y by Z */
switch(ev.iObjFnType)
{
case MAX:
if (fTempVec[0] > fRefPop[iSelIndex][0])
for (j=0; j<=ev.iNumVars; j++)
fRefPop[iSelIndex][j] = fTempVec[j];
break;
case MIN:
if (fTempVec[0] < fRefPop[iSelIndex][0])
for (j=0; j<=ev.iNumVars; j++)
fRefPop[iSelIndex][j] = fTempVec[j];
break;
default:
break;
}
/* eval(X) = eval(Z) */
fSearchPop[i][0] = fTempVec[0];
/* if probability allows, replace X by Z as well */
fRandVal = randgen(0.0, 1.0);
if (fRandVal < ev.fReplRatio)
for (j=0; j<=ev.iNumVars; j++)
fSearchPop[i][j] = fTempVec[j];
}
}