content: import 'package:scidart/src/numdart/numdart.dart';
  
  /// Compute the numerical accumulative integration of an Array using the trapezoidal rule.
  /// - [y] : input array to integrate
  /// - [x] : The sample points corresponding to the y values. If x is null,
  /// the sample points are assumed to be evenly spaced dx apart. The default is null.
  /// - [dx] : The spacing between sample points when x is None. The default is 1.
  /// - [initial] : optional. If given, uses this value as the first value in the returned result.
  /// Typically this value should be 0. Default is null, which means no value
  /// at x[0] is returned and return has one element less than y along the axis of integration.
  ///
  /// # References
  /// 1. "doc scipy.integrate.cumtrapz". https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.integrate.cumtrapz.html. Retrieved 2019-08-01.
  /// 2. "scipy.integrate.cumtrapz". https://github.com/scipy/scipy/blob/v0.18.1/scipy/integrate/quadrature.py#L206-L295. Retrieved 2019-08-01.
  ///
  /// # Examples
  /// ```dart
  /// var y = Array([1, 2, 3]);
  ///
  /// print(cumIntegration(y));
  /// ```
  Array cumIntegration(Array y, {Array? x, int dx = 1, double? initial}) {
    checkParamsGetRangeArray(y, x, dx);
  
    var d;
    if (x != null) {
      d = arrayDiff(x);
    } else {
      d = Array.fixed(y.length - 1, initialValue: dx.toDouble());
    }
  
    var slice1 = y.getRangeArray(0, y.length - 1);
    var slice2 = y.getRangeArray(1, y.length);
  
    var ret = arrayCumSum(d * arrayDivisionToScalar(slice1 + slice2, 2.0));
  
    if (initial != null) {
      ret = arrayConcat([arrayMultiplyToScalar(ones(1), initial), ret]);
    }
  
    return ret;
  }
  