double q_f(int df1, int df2, double f) /* ¾å¦ÎßÀѳÎΨ */
{
int i;
double cos2, sin2, prob, temp;
if (f <= 0) return 1;
if (df1 % 2 != 0 && df2 % 2 == 0)
return 1 - q_f(df2, df1, 1 / f);
cos2 = 1 / (1 + df1 * f / df2); sin2 = 1 - cos2;
if (df1 % 2 == 0) {
prob = pow(cos2, df2 / 2.0); temp = prob;
for (i = 2; i < df1; i += 2) {
temp *= (df2 + i - 2) * sin2 / i;
prob += temp;
}
return prob;
}
prob = atan(sqrt(df2 / (df1 * f)));
temp = sqrt(sin2 * cos2);
for (i = 3; i <= df1; i += 2) {
prob += temp; temp *= (i - 1) * sin2 / i;
}
temp *= df1;
for (i = 3; i <= df2; i += 2) {
prob -= temp;
temp *= (df1 + i - 2) * cos2 / i;
}
return prob * 2 / PI;
}
mat Wavefunction::q_force() {
mat q_f = zeros(n_particles, dim);
//#if NUMERICAL
#if 0
double h = 0.05;
mat r_plus = zeros(n_particles, dim);
mat r_minus = zeros(n_particles, dim);
// Initiating r_plus and r_minus.
r_plus = r_new;
r_minus = r_new;
// Calculating the Quantum Force numerically.
for (int i = 0; i < n_particles; i++) {
for (int j = 0; j < dim; j++) {
r_plus(i, j) += h;
r_minus(i, j) -= h;
q_f(i, j) = 2 * (evaluate(r_plus) - evaluate(r_minus)) / (2 * h * evaluate(r_new));
r_plus(i, j) = r_new(i, j);
r_minus(i, j) = r_new(i, j);
}
}
#else
rowvec gradient_slater;
rowvec gradient_jastrow;
double R = slater->get_ratio();
for (int i = 0; i < n_particles; i++) {
// Finding the Orbitals' gradient.
slater->compute_gradient(i);
gradient_slater = slater->get_gradient();
// Finding the Jastrow's gradient.
jas->compute_gradient(r_new, i);
gradient_jastrow = jas->get_gradient();
q_f.row(i) = 2 * (gradient_jastrow + gradient_slater)/R;
}
#endif
return q_f;
}
double p_f(int df1, int df2, double f) /* ²¼Â¦ÎßÀѳÎΨ */
{
if (f <= 0) return 0;
return q_f(df2, df1, 1 / f);
}
int Clmbr::ci_af( METHOD met, double * bds )
// using AF to calculate significance level
{
double th, sl_th, thold;
int k, numi=0, ind=0; // ind = indicator = 0 if sl was below SL, 1 if above
if( Model==M3 ) {
const double sl_inf= sl(-Inf,met,false);
const double yx = *pqy*pqx[0], y1 = *pqy*pq1[0], thzero =yx/y1;
const double ya =yx*qx1[0]-y1*qxx[0], yb =yx*q11[0]-y1*qx1[0], thk =ya/yb;
const double th1 = min(thk,thzero), th2 = max(thk,thzero);
th= min( -1., xs[0] );
th= min( th, th1 );
th *= 2, sl_th= sl( th, met, false );
int it =0;
while( fabs( sl_th - sl_inf ) > tol_sl_abs && it < 18 )
th *= 2, sl_th= sl(th,met,false), it++;
if (sl_th > SL) bds[numi++] = -Inf, ind=1;
thold= th;
if ( th1 < xs[0]) {
th = th1;
sl_th = sl( th, met, false );
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=0;
}
thold = th;
}
if ( th2 < xs[0]) {
th = th2;
sl_th = sl( th, met, false );
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=0;
}
thold = th;
}
th = xs[0];
sl_th = sl( th, met, false );
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=0;
}
thold = th;
} else {
// if Model=M1, treat regions before xs[0] and after xs[ns-1] as two seperate regions
// check region before xs[0]
th = xs[0] - 1.;
sl_th = sl( th, met, false );
if (sl_th > SL) {
bds[numi++] = -Inf;
ind=1;
}
// check first end interval
if (Model==M1) {
th = xs[1];
sl_th = sl( th, met, false );
if (sl_th > SL && ind==0) {
bds[numi++] = xs[0];
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = xs[0];
ind=0;
}
}
}
//check critical points
// (gamma*sy)^2 is monotonic between each of xs[k], 'thzero' where gamma*sy=0, 'thk' where d(gamma*sy)=0, and xs[k+1]
int ki = max(k1,0);
double yf = *pqy*q_f(xs[ki],ki);
thold = xs[ki];
for (k=ki;k<ns-2;k++)
{
const double y1 = *pqy*pq1[k+1], yx = yf + y1*xs[k];
yf = yx - y1*xs[k+1];
const double ya =yx*qx1[k+1]-y1*qxx[k+1], yb =yx*q11[k+1]-y1*qx1[k+1], thk =ya/yb, thzero =yx/y1;
const double th1 = min(thk,thzero), th2 = max(thk,thzero);
if (xs[k] < th1 && th1 < xs[k+1]) {
th = th1;
sl_th = sl( th, met, false );
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl( thold, th, met, -tol_xb );
ind=0;
}
thold = th;
}
if (xs[k] < th2 && th2 < xs[k+1]) {
th = th2;
sl_th = sl(th,met,false);
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl(thold,th,met,-tol_xb);
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl(thold,th,met,-tol_xb);
ind=0;
}
thold = th;
}
th = xs[k+1];
sl_th = sl(th,met,false);
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl(thold,th,met,-tol_xb);
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl(thold,th,met,-tol_xb);
ind=0;
}
thold = th;
}
// check final end interval
th = (xs[ns-1]+xs[ns-2])/2.;
sl_th = sl(th,met,false);
if (sl_th > SL && ind==0) {
bds[numi++] = bisect_sl(thold,xs[ns-2],met,-tol_xb);
ind=1;
}
if (sl_th < SL && ind==1) {
bds[numi++] = bisect_sl(thold,xs[ns-2],met,-tol_xb);
ind=0;
}
// check region after xs[ns-1]
th = xs[ns-1]+1.;
sl_th = sl(th,met,false);
if (sl_th > SL && ind==0) {
bds[numi++] = xs[ns-1];
bds[numi++] = Inf;
}
if (sl_th < SL && ind==1) bds[numi++] = xs[ns-1];
if (sl_th > SL && ind==1) bds[numi++] = Inf;
return numi/2;
}
