simpsArray function

double simpsArray(Array y, { Array? x, int dx = 1, Even even = Even.last, })

Integrate y(x) using samples along the given axis and the composite Simpson's rule. If x is None, spacing of dx is assumed. If there are an even number of samples, N, then there are an odd number of intervals (N-1), but Simpson's rule requires an even number of intervals. The parameter 'even' controls how this is handled.

Parameters

• y : Array to be integrated.
• x : Optional. If given, the points at which y is sampled.
• dx : Optional. Spacing of integration points along axis of y. Only used when x is null(not informed). Default is 1.
• even : Even {avg, first, last}, optional [avg] : Average two results:1) use the first N-2 intervals with a trapezoidal rule on the last interval and 2) use the last N-2 intervals with a trapezoidal rule on the first interval. [first] : Use Simpson's rule for the first N-2 intervals with a trapezoidal rule on the last interval. [last] : Use Simpson's rule for the last N-2 intervals with a trapezoidal rule on the first interval.

References

1. "numpy.simps". https://github.com/scipy/scipy/blob/v1.3.0/scipy/integrate/quadrature.py#L384-L506. Retrieved 2019-07-31.
2. "doc numpy.simps". https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.simps.html#scipy.integrate.simps. Retrieved 2019-07-31.

Examples

var x = createArrayRange(start: 0, stop: 10);
var y = createArrayRange(start: 0, stop: 10);

print(simpsArray(y, x: x));

/* output:
40.5
*/

Implementation

double simpsArray(Array y, {Array? x, int dx = 1, Even even = Even.last}) {
  checkParamsGetRangeArray(y, x, dx);
  var result;
  var N = y.length;

  if (N % 2 == 0) {
    var val = 0.0;
    result = 0.0;

    // Compute using Simpson's rule on first intervals
    if (even == Even.avg || even == Even.first) {
      var yslice1 = y[y.length - 1];
      var yslice2 = y[y.length - 2];

      var last_dx;
      if (x != null) {
        var xslice1 = x[x.length - 1];
        var xslice2 = x[x.length - 2];
        last_dx = xslice1 - xslice2;
      }
      val += 0.5 * last_dx * (yslice1 + yslice2);
      result = _basicSimps(y, 0, N - 3, x, dx);
    }

    // Compute using Simpson's rule on last set of intervals
    if (even == Even.avg || even == Even.last) {
      var yslice1 = y[0];
      var yslice2 = y[1];

      var first_dx;
      if (x != null) {
        var xslice1 = x[0];
        var xslice2 = x[1];
        first_dx = xslice2 - xslice1;
      }
      val += 0.5 * first_dx * (yslice2 + yslice1);
      result += _basicSimps(y, 1, N - 2, x, dx);
    }

    if (even == Even.avg) {
      val /= 2.0;
      result /= 2.0;
    }

    result = result + val;
  } else {
    result = _basicSimps(y, 0, N - 2, x, dx);
  }

  return result;
}