RSI vs Wilder's RSI Calculation Problems

I am having trouble getting a smoothed RSI. The below picture is from freestockcharts.com. The calculation uses this code.

public static double CalculateRsi(IEnumerable<double> closePrices)
{
    var prices = closePrices as double[] ?? closePrices.ToArray();

    double sumGain = 0;
    double sumLoss = 0;
    for (int i = 1; i < prices.Length; i++)
    {
        var difference = prices[i] - prices[i - 1];
        if (difference >= 0)
        {
            sumGain += difference;
        }
        else
        {
            sumLoss -= difference;
        }
    }

    if (sumGain == 0) return 0;
    if (Math.Abs(sumLoss) < Tolerance) return 100;

    var relativeStrength = sumGain / sumLoss;

    return 100.0 - (100.0 / (1 + relativeStrength));
}

https://stackoverflow.com/questions/...th-index-using-some-programming-language-js-c

This seems to be the pure RSI with no smoothing. How does a smoothed RSI get calculated? I have tried changing it to fit the definitions of the these two sites however the output was not correct. It was barely smoothed.

(I don't have enough rep to post links)

tc2000 -> Indicators -> RSI_and_Wilder_s_RSI (Wilder's smoothing = Previous MA value + (1/n periods * (Close - Previous MA)))

priceactionlab -> wilders-cutlers-and-harris-relative-strength-index (RS = EMA(Gain(n), n)/EMA(Loss(n), n))

Can someone actually do the calculation with some sample data?

Wilder's RSI vs RSI

In order to calculate the RSI, you need a period to calculate it with. As noted on Wikipedia, 14 is used quite often.

So the calculation steps would be as follows:

Period 1 - 13, RSI = 0

Period 14:

AverageGain = TotalGain / PeriodCount;
AverageLoss = TotalLoss / PeriodCount;
RS = AverageGain / AverageLoss;
RSI = 100 - 100 / (1 + RS);

Period 15 - to period (N):

if (Period(N)Change > 0
  AverageGain(N) = ((AverageGain(N - 1) * (PeriodCount - 1)) + Period(N)Change) / PeriodCount;
else
  AverageGain(N) = (AverageGain(N - 1) * (PeriodCount - 1)) / PeriodCount;

if (this.Change < 0)
  AverageLoss(N) = ((AverageLoss(N - 1) * (PeriodCount - 1)) + Math.Abs(Period(N)Change)) / PeriodCount;
else
  AverageLoss(N) = (AverageLoss(N - 1) * (PeriodCount - 1)) / PeriodCount;

RS = AverageGain / AverageLoss;
RSI = 100 - (100 / (1 + RS));