// Inteprolation de Hardy
void computeHardy(std::vector< std::vector< float >* >* interpoleData, std::vector<std::string>* latitude, std::vector<std::string>* longitude, std::vector<std::string>* data) {
unsigned int n = data->size();
Eigen::MatrixXf A = Eigen::MatrixXf(n,n);
Eigen::VectorXf b = Eigen::VectorXf(data->size());
Eigen::VectorXf x;
float lati, longi, latj, longj, latk, longk;
float minLat, maxLat;
float minLong, maxLong;
findExtrema(minLat, maxLat, latitude);
findExtrema(minLong, maxLong, longitude);
for (unsigned int i = 0; i < n; ++i) {
for (unsigned int j = 0; j < n; ++j) {
lati = atof(latitude->at(i).c_str());
longi = atof(longitude->at(i).c_str());
latj = atof(latitude->at(j).c_str());
longj = atof(longitude->at(j).c_str());
A(i,j) = sqrt(R + pow(distance(longi,lati,longj,latj),2));
}
}
for (unsigned int i = 0; i < data->size(); ++i) {
b(i) = atof(data->at(i).c_str());
}
x = A.ldlt().solve(b);
for (int i = 0; i < resolution; ++i) {
for (int j = 0; j < resolution; ++j) {
lati = minLat + ((double(i)/(resolution-1)) * (maxLat - minLat));
longi = minLong + ((double(j)/(resolution-1)) * (maxLong - minLong));
float eval = 0.0;
for (unsigned int k = 0; k < n; ++k) {
latk = atof(latitude->at(k).c_str());
longk = atof(longitude->at(k).c_str());
eval += x(k) * sqrt(R + pow(distance(lati, longi, latk, longk),2));
}
interpoleData->at(i)->at(j) = eval;
}
}
}
bool LogisticRegressionVT::LogisticVTImpl::TestCovariate(const Matrix& Xnull,
const Vector& yVec,
const Matrix& Xcol) {
// const int n = Xnull.rows;
const int d = Xnull.cols;
const int k = Xcol.cols;
copy(Xnull, &cov); // Z = n by d = [z_1^T; z_2^T; ...]
copy(Xcol, &geno); // S = n by k = [S_1^T, S_2^T, ...]
copy(yVec, &y);
copy(this->null.GetPredicted(), &res); // n by 1
v = res.array() * (1. - res.array());
res = y - res;
Eigen::MatrixXf vsz(d, k); // \sum_i v_i S_ki Z_i = n by d matrix
Eigen::MatrixXf tmp;
// calculate U and V
const Eigen::MatrixXf& S = geno;
const Eigen::MatrixXf& Z = cov;
// U = (S.transpose() * (res.asDiagonal())).rowsum();
U = res.transpose() * S; // 1 by k matrix
// for (int i = 0; i < d; ++i) {
// vsz.col(i) = (Z * (v.array() *
// S.col().array()).matrix().asDiagonal()).rowsum();
// }
vsz = cov.transpose() * v.asDiagonal() * S; // vsz: d by k matrix
// const double zz = (v.array() *
// (Z.array().square().rowise().sum()).array()).sum();
Eigen::MatrixXf zz =
cov.transpose() * v.asDiagonal() * cov; // zz: d by d matrix
// V.size(k, 1);
// V(i, 1) = (v.array() * (S.col(i).array().square())).sum() -
// vsz.row(i).transpose() * vsz.row(i) / zz;
// }
V = (v.asDiagonal() * (S.array().square().matrix()))
.colwise()
.sum(); // - // 1 by k
tmp = ((vsz).array() * (zz.ldlt().solve(vsz)).array()).colwise().sum();
V -= tmp;
// V = (v.asDiagonal() * (S.array().square().matrix())).colwise().sum() -
// ((vsz).array() * (zz.ldlt().solve(vsz)).array()).colwise().sum();
// Uk is n by k matrix
// Uk.size(n, k);
// for (int i = 0; i < k; ++i) {
// Uk.col(i) = res * (S.col(i) - vsz.col(i).transpose()) * Z.col(i) / zz;
// }
Uk = res.asDiagonal() * (S - Z * zz.ldlt().solve(vsz));
// Vkk.size(k, k);
// for (int i = 0; i < k; ++i) {
// for (int j = 0; j <= 1; ++j) {
// Vkk(i, j) = Uk.col(i) .transpose() * Uk.col(j);
// }
// if (i != j) {
// Vkk(j, i) = Vkk(i, j);
// } else {
// if (Vkk(i,i) == 0.0) {
// return false; // variance term should be larger than zero.
// }
// }
// }
Vkk = Uk.transpose() * Uk;
Eigen::MatrixXf t = U.array() / V.array().sqrt();
Eigen::RowVectorXf tmp2 = t.row(0).cwiseAbs();
tmp2.maxCoeff(&maxIndex);
rep(-tmp2(maxIndex), k, &lower);
rep(tmp2(maxIndex), k, &upper);
makeCov(Vkk);
if (mvnorm.getBandProbFromCor(k, (double*)lower.data(), (double*)upper.data(),
(double*)cor.data(), &pvalue)) {
fprintf(stderr, "Cannot get MVN pvalue.\n");
return false;
}
copy(U, &retU);
copy(V, &retV);
copy(t, &retT);
copy(Vkk, &retCov);
pvalue = 1.0 - pvalue;
return true;
};