integrate method

@override IntegralResults integrate(String function)

Calculates the numerical value of the function definite integral between lowerBound and upperBound.

Implementation

@override
IntegralResults integrate(String function) {
  // Make sure to throw an exception if 'intervals' is odd
  if (intervals % 2 != 0) {
    throw const NumericalIntegrationException('There must be an even number '
        'of partitions.');
  }

  // The 'step' of the algorithm
  final h = (upperBound - lowerBound) / intervals;

  // Keeping track separatedly of the sums of the even and odd series
  var oddSum = 0.0;
  var evenSum = 0.0;

  // The list containing the various guesses of the algorithm
  final guesses = List<double>.filled(intervals, 0);

  // The first iteration
  for (var i = 1; i < intervals; i += 2) {
    oddSum += evaluateFunction(function, lowerBound + i * h);
    guesses[i] = oddSum;
  }

  // The second iteration
  for (var i = 2; i < intervals - 1; i += 2) {
    evenSum += evaluateFunction(function, lowerBound + i * h);
    guesses[i] = oddSum;
  }

  // Returning the result
  final bounds = evaluateFunction(function, lowerBound) +
      evaluateFunction(function, upperBound);

  return IntegralResults(
    guesses: guesses,
    result: (bounds + (2 * evenSum) + (4 * oddSum)) * h / 3,
  );
}