/** This function returns the Z error of the given FROG traces.
*
* \param Esig the current signal field.
* \param Esigp the last signal field.
*
* \returns The Z error between Esigp and Esig.
*/
TReal Zerr(const TmexArray &Esig, const TmexArray &Esigp)
{
TReal Z = 0.0;
for (size_t i = 0; i < Esig.size(); ++i)
Z += norm(Esig[i] - Esigp[i]);
return (Z/Esig.size());
}
/** \brief Calculates Esig.
*
* Calculates Esig(t,tau) given the probe and gate pulses.
*
* \param Esig the array to store the calculation in.
* \param P the probe pulse.
* \param G the gate pulse.
*/
void CalcEsig(TmexArray &Esig, const TmexArray &P, const TmexArray &G)
{
for(size_t t = 0; t<Esig.size_M(); ++t)
for(size_t tau = 0; tau<Esig.size_N(); ++tau) {
int tp = static_cast<int>(t - (tau - Esig.size_N()/2));
if (tp >= 0 && tp < static_cast<int>(G.size())) {
Esig(t,tau) = P(t) * G(tp);
}
}
}
/** Calculates the Y error.
*
* \param Esig the FROG signal field.
* \param Ew the electric field.
* \returns the Y error.
*/
TReal Zerr2_wW(const TmexArray &Esig, const TmexArray Ew)
{
TReal Z = 0.0;
for(size_t w = 0; w<Esig.size_M(); ++w)
for(size_t W = 0; W<Esig.size_N(); ++W) {
int wp = w - (W - Esig.size_N()/2);
if (wp >= 0 && wp < static_cast<int>(Ew.size())) {
Z += std::norm((Ew(W) * Ew(wp)) - Esig(w,W));
}
}
return Z/Esig.size();
}
/** Calculates the gradient of the Z error for THG.
*
* \param Esigp the magnitude replaced Esig(t,tau).
* \param Et the current best guess.
* \param dZ the gradient.
*/
void dZdE_thg(const TmexArray &Esigp, const TmexArray &Et, TmexArray &dZ)
{
int M = Esigp.size_M(); // The number of time points.
int N = Esigp.size_N(); // The number of delay points.
TReal sz = Esigp.size();
for(int t0 = 0; t0 < M; ++t0)
{
TCmplx T(0.0,0.0);
for(int tau = 0; tau < N; ++tau) {
int tp = t0 - (tau - N/2);
if (tp >= 0 && tp < M) {
T += (Et[t0] * Et[tp] * Et[tp] - Esigp(t0,tau)) * conj(Et[tp] * Et[tp]);
}
tp = t0 + (tau - N/2);
if (tp >= 0 && tp < M) {
T += 2.0 * conj(Et[tp] * Et[t0]) * (Et[tp] * Et[t0] * Et[t0] - Esigp(tp,tau));
}
}
dZ[t0] = T/sz;
}
}