Spline::Spline(const Point input[], int inputLength) :
params(new Param[inputLength]),
c(¶ms[0]),
paramsLength(inputLength)
{
assert(inputLength > 2);
std::vector<double> dxs(inputLength - 1);
std::vector<double> ms(inputLength - 1);
// Get consecutive differences and slopes
for (int i = 0; i < inputLength - 1; i++)
{
assert(input[i].x < input[i + 1].x);
const double dx = input[i + 1].x - input[i].x;
const double dy = input[i + 1].y - input[i].y;
dxs[i] = dx;
ms[i] = dy/dx;
}
// Get degree-1 coefficients
params[0].c = ms[0];
for (int i = 1; i < inputLength - 1; i++)
{
const double m = ms[i - 1];
const double mNext = ms[i];
if (m * mNext <= 0) {
params[i].c = 0.0;
} else {
const double dx = dxs[i - 1];
const double dxNext = dxs[i];
const double common = dx + dxNext;
params[i].c = 3.0 * common / ((common + dxNext) / m + (common + dx) / mNext);
}
}
params[inputLength - 1].c = ms[inputLength - 2];
// Get degree-2 and degree-3 coefficients
for (int i = 0; i < inputLength - 1; i++)
{
params[i].x1 = input[i].x;
params[i].x2 = input[i + 1].x;
params[i].d = input[i].y;
const double c1 = params[i].c;
const double m = ms[i];
const double invDx = 1.0 / dxs[i];
const double common = c1 + params[i + 1].c - m - m;
params[i].b = (m - c1 - common) * invDx;
params[i].a = common * invDx * invDx;
}
// Fix the value ranges, because we interpolate outside original bounds if necessary.
params[0].x1 = std::numeric_limits<double>::min();
params[inputLength - 2].x2 = std::numeric_limits<double>::max();
}
arma::field<arma::Cube<double>> Softmax::backProp(const arma::field<arma::Cube<double>>& deltas) {
arma::field<arma::Cube<double>> dxs(deltas.size());
for (unsigned int i=0; i<deltas.size(); ++i) {
const arma::Col<double>& y = mYs[i];
arma::Mat<double> jacobian = -y*y.t();
jacobian.diag() = y%(1.0-y);
arma::Col<double> delta = deltas[i];
arma::Col<double> dx = jacobian*delta;
dxs[i] = arma::Cube<double>((const double*) dx.begin(), 1, 1, dx.size());
}
return dxs;
}
