tStart method

Future<num> tStart(num gamma, { List<num> deltaPosition = const <num>[], int sampleSize = 200, })

Returns the temperature at which the expectation value of the acceptance probability of up-hill transitions approaches gamma.

Note: The algorithm converges only for gamma in the range: 0 < gamma < 1.

Implementation

Future<num> tStart(
  num gamma, {
  List<num> deltaPosition = const <num>[],
  int sampleSize = 200,
}) async {
  if (gamma <= 0 || gamma >= 1) {
    throw ErrorOf<EnergyField>(
        message: 'Error in function optimalTemperature',
        invalidState: 'Found \'gamma\': $gamma.',
        expectedState: 'Expected: 0 < gamma < 1.');
  }
  if (deltaPosition.isEmpty) {
    deltaPosition = size / 4;
  }
  final transitions = this.transitions(
    deltaPosition,
    sampleSize: sampleSize,
  );

  final deltaE = transitions.last - transitions.first;

  /// First estimate of the initial temperature.
  var optTemperature = deltaE.stdDev() / (-log(gamma));
  num gammaEstimate = 0;

  var counter = 0;

  // Rescaling transition energies
  final transitionsGS = transitions.first.min();
  for (var i = 0; i < sampleSize; ++i) {
    transitions.first[i] -= transitionsGS;
    transitions.last[i] -= transitionsGS;
  }
  do {
    gammaEstimate = _gammaStart(transitions, optTemperature);
    optTemperature = optTemperature *
        pow(
          log(gammaEstimate) / log(gamma),
          0.2,
        );
    ++counter;
    //print('gamma: $gammaEstimate temperature: $optTemperature');
  } while ((gammaEstimate - gamma).abs() > gamma * 1e-3 && counter < 100);
  return optTemperature;
}