void
MPC::init_f_G()
{
int numG = Gints.size();
f_G.resize(numG);
int N = max(64, 2*MaxDim+1);
vector<double> g_G_N(numG), g_G_2N(numG), g_G_4N(numG);
double g_0_N, g_0_2N, g_0_4N;
compute_g_G(g_0_N , g_G_N, 1*N);
compute_g_G(g_0_2N, g_G_2N, 2*N);
compute_g_G(g_0_4N, g_G_4N, 4*N);
// fprintf (stderr, "g_G_1N[0] = %18.14e\n", g_G_N[0]);
// fprintf (stderr, "g_G_2N[0] = %18.14e\n", g_G_2N[0]);
// fprintf (stderr, "g_G_4N[0] = %18.14e\n", g_G_4N[0]);
double volInv = 1.0/PtclRef->Lattice.Volume;
double L = PtclRef->Lattice.WignerSeitzRadius;
TinyVector<double,2> g0_12 (g_0_2N, g_0_4N);
TinyVector<double,3> g0_124 (g_0_N, g_0_2N, g_0_4N);
f_0 = extrap (N, g0_124);
app_log().precision(12);
app_log() << " Linear extrap = " << std::scientific
<< extrap (2*N, g0_12) << endl;
app_log() << " Quadratic extrap = " << std::scientific
<< f_0 << endl;
f_0 += 0.4*M_PI*L*L*volInv;
// cerr << "f_0 = " << f_0/volInv << endl;
double worst = 0.0, worstLin, worstQuad;
int iworst = 0;
for (int iG=0; iG<numG; iG++)
{
TinyVector<double,2> g_12 (g_G_2N[iG], g_G_4N[iG]);
TinyVector<double,3> g_124 (g_G_N [iG], g_G_2N[iG], g_G_4N[iG]);
double linearExtrap = extrap (2*N, g_12);
double quadExtrap = extrap (N, g_124);
double diff = std::fabs(linearExtrap - quadExtrap);
if (diff > worst)
{
worst = diff;
iworst = iG;
worstLin = linearExtrap;
worstQuad = quadExtrap;
}
f_G[iG] = quadExtrap;
double G2 = dot(Gvecs[iG], Gvecs[iG]);
double G = std::sqrt(G2);
f_G[iG] += volInv*M_PI*(4.0/G2 + 12.0/(L*L*G2*G2)*
(std::cos(G*L) - std::sin(G*L)/(G*L)));
// cerr << "f_G = " << f_G[iG]/volInv << endl;
// cerr << "f_G - 4*pi/G2= " << f_G[iG]/volInv - 4.0*M_PI/G2 << endl;
}
char buff[1000];
snprintf (buff, 1000 ,
" Worst MPC discrepancy:\n"
" Linear Extrap : %18.14e\n"
" Quadratic Extrap: %18.14e\n", worstLin, worstQuad);
app_log() << buff;
}
inline float key_extrap(float input, const vector<XObjKey>& table, int n)
{
if (table.empty()) return 0.0f;
if (table.size() == 1) return table.front().v[n];
if (table.size() == 2) return extrap(table[0].key,table[0].v[n],table[1].key,table[1].v[n],input);
vector<XObjKey>::const_iterator i = std::lower_bound(table.begin(), table.end(), input, compare_key());
vector<XObjKey>::const_iterator p1, p2;
if (i == table.end()) { p1 = i-2; p2 = i-1; }
else if (i->key == input) { return i->v[n]; }
else if (i == table.begin()) { p1 = i; p2 = i+1; }
else { p1 = i-1; p2 = i; }
return extrap(p1->key,p1->v[n],p2->key,p2->v[n], input);
}