int RandFourierMap(int nKernelType, const fvec& x, const std::vector<fvec> &W, const fvec &b, fvec &result)
{
int nErrCode = 0;
if(W.empty() || b.empty())
{
return 1;
}
int nKernelRank = W[0].size();
switch(nKernelType)
{
case RAND_KERNEL_RBF:
for(int rank_idx = 0; rank_idx < nKernelRank; ++rank_idx)
{
float sum = 0.0;
for(int dim_idx = 0; dim_idx < x.size(); ++dim_idx)
{
sum += W[dim_idx][rank_idx] * x[dim_idx];
}
result.push_back(sqrt(2.0 / nKernelRank) * cos(sum + b[rank_idx]));
}
break;
default:
nErrCode = 1;
}
return nErrCode;
}
int RandFourierFactorize(int nKernelType, int nKernelRank, float fGamma, const std::vector<fvec>& X, std::vector<fvec> &G, std::vector<fvec> &W, fvec &b)
{
int nErrCode = 0;
int m = X.size();
if(m == 0)
{
return nErrCode;
}
int dim = X[0].size();
G.clear();
W.clear();
b.clear();
//generate random features
dlib::rand r;
std::ostringstream seed;
seed << (unsigned int) time(0);
r.set_seed(seed.str());
switch(nKernelType)
{
case RAND_KERNEL_RBF:
for(int ind = 0; ind < dim; ++ind)
{
fvec tmp_vec;
for(int rank_idx = 0; rank_idx < nKernelRank; ++rank_idx)
{
tmp_vec.push_back(r.get_random_gaussian() * fGamma);
}
W.push_back(tmp_vec);
}
for(int ind = 0; ind < nKernelRank; ++ind)
{
b.push_back(r.get_random_float() * 2.0 * PI);
}
for(int ind = 0; ind < m; ++ind)
{
fvec tmp_vec;
RandFourierMap(nKernelType, X[ind], W, b, tmp_vec);
G.push_back(tmp_vec);
}
break;
default:
//unknown kernel type
//printf("unknown type\n");
nErrCode = 1;
break;
};
return nErrCode;
}
void search2(fvec &stat, ivec &sel_id, int &marg_id, const fvec &S, const fmat &Sigma, const int &mc){
int ns = S.size();
//find best marginal SNP
int id = -1;
double max_stat = -1.0;
for(int j = 0; j < ns; ++j){
double s = S[j] * S[j] / Sigma[j][j];
if(s > max_stat){
max_stat = s;
id = j;
}
}
stat = fvec(1, max_stat);
assert(id >= 0 && id < ns);
sel_id = ivec(1, id);
marg_id = id;
if(ns == 1){
return;
}
//find best pair
int id1 = -1;
int id2 = -1;
max_stat = -1.0;
for(int j = 0; j < ns; ++j){
for(int k = j + 1; k < ns; ++k){
double a = Sigma[j][j];
double b = Sigma[j][k];
double d = Sigma[k][k];
double stat = (d * S[j] * S[j] - 2 * b * S[j] * S[k] + a * S[k] * S[k]) / (a * d - b * b);
if(stat > max_stat){
max_stat = stat;
id1 = j;
id2 = k;
}
}
}
stat.push_back(max_stat);
assert(id1 >= 0 && id1 < ns);
assert(id2 >= 0 && id2 < ns);
sel_id = ivec(1, id1);
sel_id.push_back(id2);
if(ns == 2){
return;
}
dmat inv_Sigma22(mc + 1, dvec(mc + 1, .0));
double a = Sigma[id1][id1];
double b = Sigma[id1][id2];
double d = Sigma[id2][id2];
double e = a * d - b * b;
inv_Sigma22[0][0] = d / e;
inv_Sigma22[0][1] = -b / e;
inv_Sigma22[1][0] = inv_Sigma22[0][1];
inv_Sigma22[1][1] = a / e;
dvec S2(mc + 1, .0);
S2[0] = S[id1];
S2[1] = S[id2];
vector<bool> used(ns, false);
used[id1] = true;
used[id2] = true;
double w = max_stat;
for(int j = 2; j <= mc; ++j){//j is the number of SNPs being selected
dvec v(j, .0); // v = (Sigma22)^-1 S2
for(int i = 0; i < j; ++i){
v[i] = .0;
for(int k = 0; k < j; ++k){
v[i] += inv_Sigma22[i][k] * S2[k];
}
}
max_stat = -1.0;
double max_qf2 = -1.0;
id = -1;
for(int k = 0; k < ns; ++k){
if(used[k]){
continue;
}
double S1 = S[k];
double qf1 = .0; //qf1 = sigma12 (Sigma22)^-1 S2
double qf2 = .0; //qf2 = sigma12 (Sigma22)^-1 sigma21
for(int l = 0; l < j; ++l){
qf1 += Sigma[k][sel_id[l]] * v[l];
double tmp = .0; // tmp = the l-th column of sigma12 (Sigma22)^-1
for(int t = 0; t < j; ++t){
tmp += Sigma[k][sel_id[t]] * inv_Sigma22[t][l];
}
qf2 += tmp * Sigma[sel_id[l]][k];
}
double stat = w + (S1 * S1 - 2.0 * S1 * qf1 + qf1 * qf1)/(Sigma[k][k] - qf2);
if(stat > max_stat){
max_stat = stat;
id = k;
max_qf2 = qf2;
}
}
w = max_stat;
stat.push_back(max_stat);
sel_id.push_back(id);
used[id] = true;
S2[j] = S[id];
inv_Sigma22[j][j] = 1.0 / (Sigma[id][id] - max_qf2);
dvec tmp(j, .0);
for(int l = 0; l < j; ++l){
inv_Sigma22[j][l] = .0;
for(int t = 0; t < j; ++t){
inv_Sigma22[j][l] += Sigma[id][sel_id[t]] * inv_Sigma22[t][l];
}
inv_Sigma22[j][l] *= -inv_Sigma22[j][j];
inv_Sigma22[l][j] = inv_Sigma22[j][l];
}
for(int l = 0; l < j; ++l){
for(int t = 0; t < j; ++t){
inv_Sigma22[l][t] += inv_Sigma22[l][j] * inv_Sigma22[t][j] / inv_Sigma22[j][j];
}
}
}
}
