Open source FMZ Quant TA library, learn to use (with JavascriptPythonC++ versions)

The code is the best commentary, how can you say you know how to use an indicator if you don't know how it is generated.
The following code is handcrafted by myself when I transitioned from being a programmer to the finance industry, without any copy-pasting. I hope it will be helpful for beginners.

            javascript
            
            
var Std = {
    _skip: function(arr, period) {
        var j = 0;
        for (var k = 0; j < arr.length; j++) {
            if (!isNaN(arr[j]))
                k++;
            if (k == period)
                break;
        }
        return j;
    },
    _sum: function(arr, num) {
        var sum = 0.0;
        for (var i = 0; i < num; i++) {
            if (!isNaN(arr[i])) {
                sum += arr[i];
            }
        }
        return sum;
    },

    _avg: function(arr, num) {
        var n = 0;
        var sum = 0.0;
        for (var i = 0; i < num; i++) {
            if (!isNaN(arr[i])) {
                sum += arr[i];
                n++;
            }
        }
        return sum / n;
    },

    _zeros: function(len) {
        var n = [];
        for (var i = 0; i < len; i++) {
            n.push(0.0);
        }
        return n;
    },

    _set: function(arr, start, end, value) {
        var e = Math.min(arr.length, end);
        for (var i = start; i < e; i++) {
            arr[i] = value;
        }
    },

    _diff: function(a, b) {
        var d = [];
        for (var i = 0; i < b.length; i++) {
            if (isNaN(a[i]) || isNaN(b[i])) {
                d.push(NaN);
            } else {
                d.push(a[i] - b[i]);
            }
        }
        return d;
    },
    _move_diff: function(a) {
        var d = [];
        for (var i = 1; i < a.length; i++) {
            d.push(a[i] - a[i - 1]);
        }
        return d;
    },
    _sma: function(S, period) {
        var R = Std._zeros(S.length);
        var j = Std._skip(S, period);
        Std._set(R, 0, j, NaN);
        if (j < S.length) {
            var sum = 0;
            for (var i = j; i < S.length; i++) {
                if (i == j) {
                    sum = Std._sum(S, i + 1);
                } else {
                    sum += S[i] - S[i - period];
                }
                R[i] = sum / period;
            }
        }
        return R;
    },

    _smma: function(S, period) {
        var R = Std._zeros(S.length);
        var j = Std._skip(S, period);
        Std._set(R, 0, j, NaN);
        if (j < S.length) {
            R[j] = Std._avg(S, j + 1);
            for (var i = j + 1; i < S.length; i++) {
                R[i] = (R[i - 1] * (period - 1) + S[i]) / period;
            }
        }
        return R;
    },
    _ema: function(S, period) {
        var R = Std._zeros(S.length);
        var multiplier = 2.0 / (period + 1);
        var j = Std._skip(S, period);
        Std._set(R, 0, j, NaN);
        if (j < S.length) {
            R[j] = Std._avg(S, j + 1);
            for (var i = j + 1; i < S.length; i++) {
                R[i] = ((S[i] - R[i - 1]) * multiplier) + R[i - 1];
            }
        }
        return R;
    },
    _cmp: function(arr, start, end, cmpFunc) {
        var v = arr[start];
        for (var i = start; i < end; i++) {
            v = cmpFunc(arr[i], v);
        }
        return v;
    },
    _filt: function(records, n, attr, iv, cmpFunc) {
        if (records.length < 2) {
            return NaN;
        }
        var v = iv;
        var pos = n !== 0 ? records.length - Math.min(records.length - 1, n) - 1 : 0;
        for (var i = records.length - 2; i >= pos; i--) {
            if (typeof(attr) !== 'undefined') {
                v = cmpFunc(v, records[i][attr]);
            } else {
                v = cmpFunc(v, records[i]);
            }
        }
        return v;
    },
    _ticks: function(records) {
        if (records.length === 0) {
            return [];
        }
        var ticks = [];
        if (typeof(records[0].Close) !== 'undefined') {
            for (var i = 0; i < records.length; i++) {
                ticks.push(records[i].Close);
            }
        } else {
            ticks = records;
        }
        return ticks;
    },
};

var TA = {
    Highest: function(records, n, attr) {
        return Std._filt(records, n, attr, Number.MIN_VALUE, Math.max);
    },
    Lowest: function(records, n, attr) {
        return Std._filt(records, n, attr, Number.MAX_VALUE, Math.min);
    },

    MA: function(records, period) {
        period = typeof(period) === 'undefined' ? 9 : period;
        return Std._sma(Std._ticks(records), period);
    },
    SMA: function(records, period) {
        period = typeof(period) === 'undefined' ? 9 : period;
        return Std._sma(Std._ticks(records), period);
    },

    EMA: function(records, period) {
        period = typeof(period) === 'undefined' ? 9 : period;
        return Std._ema(Std._ticks(records), period);
    },

    MACD: function(records, fastEMA, slowEMA, signalEMA) {
        fastEMA = typeof(fastEMA) === 'undefined' ? 12 : fastEMA;
        slowEMA = typeof(slowEMA) === 'undefined' ? 26 : slowEMA;
        signalEMA = typeof(signalEMA) === 'undefined' ? 9 : signalEMA;
        var ticks = Std._ticks(records);
        var slow = Std._ema(ticks, slowEMA);
        var fast = Std._ema(ticks, fastEMA);
        // DIF
        var dif = Std._diff(fast, slow);
        // DEA
        var signal = Std._ema(dif, signalEMA);
        var histogram = Std._diff(dif, signal);
        return [dif, signal, histogram];
    },

    BOLL: function(records, period, multiplier) {
        period = typeof(period) === 'undefined' ? 20 : period;
        multiplier = typeof(multiplier) === 'undefined' ? 2 : multiplier;
        var S = Std._ticks(records);
        for (var j = period - 1; j < S.length && isNaN(S[j]); j++);
        var UP = Std._zeros(S.length);
        var MB = Std._zeros(S.length);
        var DN = Std._zeros(S.length);
        Std._set(UP, 0, j, NaN);
        Std._set(MB, 0, j, NaN);
        Std._set(DN, 0, j, NaN);
        var sum = 0;
        for (var i = j; i < S.length; i++) {
            if (i == j) {
                for (var k = 0; k < period; k++) {
                    sum += S[k];
                }
            } else {
                sum = sum + S[i] - S[i - period];
            }
            var ma = sum / period;
            var d = 0;
            for (var k = i + 1 - period; k <= i; k++) {
                d += (S[k] - ma) * (S[k] - ma);
            }
            var stdev = Math.sqrt(d / period);
            var up = ma + (multiplier * stdev);
            var dn = ma - (multiplier * stdev);
            UP[i] = up;
            MB[i] = ma;
            DN[i] = dn;
        }
        // upper, middle, lower
        return [UP, MB, DN];
    },

    KDJ: function(records, n, k, d) {
        n = typeof(n) === 'undefined' ? 9 : n;
        k = typeof(k) === 'undefined' ? 3 : k;
        d = typeof(d) === 'undefined' ? 3 : d;

        var RSV = Std._zeros(records.length);
        Std._set(RSV, 0, n - 1, NaN);
        var K = Std._zeros(records.length);
        var D = Std._zeros(records.length);
        var J = Std._zeros(records.length);

        var hs = Std._zeros(records.length);
        var ls = Std._zeros(records.length);
        for (var i = 0; i < records.length; i++) {
            hs[i] = records[i].High;
            ls[i] = records[i].Low;
        }

        for (var i = 0; i < records.length; i++) {
            if (i >= (n - 1)) {
                var c = records[i].Close;
                var h = Std._cmp(hs, i - (n - 1), i + 1, Math.max);
                var l = Std._cmp(ls, i - (n - 1), i + 1, Math.min);
                RSV[i] = 100 * ((c - l) / (h - l));
                K[i] = (1 * RSV[i] + (k - 1) * K[i - 1]) / k;
                D[i] = (1 * K[i] + (d - 1) * D[i - 1]) / d;
            } else {
                K[i] = D[i] = 50;
                RSV[i] = 0;
            }
            J[i] = 3 * K[i] - 2 * D[i];
        }
        // remove prefix
        for (var i = 0; i < n - 1; i++) {
            K[i] = D[i] = J[i] = NaN;
        }
        return [K, D, J];
    },

    RSI: function(records, period) {
        period = typeof(period) === 'undefined' ? 14 : period;
        var i;
        var n = period;
        var rsi = Std._zeros(records.length);
        Std._set(rsi, 0, rsi.length, NaN);
        if (records.length < n) {
            return rsi;
        }
        var ticks = Std._ticks(records);
        var deltas = Std._move_diff(ticks);
        var seed = deltas.slice(0, n);
        var up = 0;
        var down = 0;
        for (i = 0; i < seed.length; i++) {
            if (seed[i] >= 0) {
                up += seed[i];
            } else {
                down += seed[i];
            }
        }
        up /= n;
        down = -(down /= n);
        var rs = down != 0 ? up / down : 0;
        rsi[n] = 100 - 100 / (1 + rs);
        var delta = 0;
        var upval = 0;
        var downval = 0;
        for (i = n + 1; i < ticks.length; i++) {
            delta = deltas[i - 1];
            if (delta > 0) {
                upval = delta;
                downval = 0;
            } else {
                upval = 0;
                downval = -delta;
            }
            up = (up * (n - 1) + upval) / n;
            down = (down * (n - 1) + downval) / n;
            rs = up / down;
            rsi[i] = 100 - 100 / (1 + rs);
        }
        return rsi;
    },
    OBV: function(records) {
        if (records.length === 0) {
            return [];
        }
        if (typeof(records[0].Close) === 'undefined') {
            throw "argument must KLine";
        }
        var R = [];
        for (var i = 0; i < records.length; i++) {
            if (i === 0) {
                R[i] = records[i].Volume;
            } else if (records[i].Close >= records[i - 1].Close) {
                R[i] = R[i - 1] + records[i].Volume;
            } else {
                R[i] = R[i - 1] - records[i].Volume;
            }
        }
        return R;
    },
    ATR: function(records, period) {
        if (records.length === 0) {
            return [];
        }
        if (typeof(records[0].Close) === 'undefined') {
            throw "argument must KLine";
        }
        period = typeof(period) === 'undefined' ? 14 : period;
        var R = Std._zeros(records.length);
        var sum = 0;
        var n = 0;
        for (var i = 0; i < records.length; i++) {
            var TR = 0;
            if (i == 0) {
                TR = records[i].High - records[i].Low;
            } else {
                TR = Math.max(records[i].High - records[i].Low, Math.abs(records[i].High - records[i - 1].Close), Math.abs(records[i - 1].Close - records[i].Low));
            }
            sum += TR;
            if (i < period) {
                n = sum / (i + 1);
            } else {
                n = (((period - 1) * n) + TR) / period;
            }
            R[i] = n;
        }
        return R;
    },
    Alligator: function(records, jawLength, teethLength, lipsLength) {
        jawLength = typeof(jawLength) === 'undefined' ? 13 : jawLength;
        teethLength = typeof(teethLength) === 'undefined' ? 8 : teethLength;
        lipsLength = typeof(lipsLength) === 'undefined' ? 5 : lipsLength;
        var ticks = [];
        for (var i = 0; i < records.length; i++) {
            ticks.push((records[i].High + records[i].Low) / 2);
        }
        return [
            [NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN].concat(Std._smma(ticks, jawLength)), // jaw (blue)
            [NaN, NaN, NaN, NaN, NaN].concat(Std._smma(ticks, teethLength)), // teeth (red)
            [NaN, NaN, NaN].concat(Std._smma(ticks, lipsLength)), // lips (green)
        ];
    },
    CMF: function(records, periods) {
        periods = periods || 20;
        var ret = [];
        var sumD = 0;
        var sumV = 0;
        var arrD = [];
        var arrV = [];
        for (var i = 0; i < records.length; i++) {
            var d = (records[i].High == records[i].Low) ? 0 : (2 * records[i].Close - records[i].Low - records[i].High) / (records[i].High - records[i].Low) * records[i].Volume;
            arrD.push(d);
            arrV.push(records[i].Volume);
            sumD += d;
            sumV += records[i].Volume;
            if (i >= periods) {
                sumD -= arrD.shift();
                sumV -= arrV.shift();
            }
            ret.push(sumD / sumV);
        }
        return ret;
    }
};

            python
            
            
import math

class Std:
    @staticmethod
    def _skip(arr, period):
        k = 0
        for j in xrange(0, len(arr)):
            if arr[j] is not None:
                k+=1
            if k == period:
                break
        return j

    @staticmethod
    def _sum(arr, num):
        s = 0.0
        for i in xrange(0, num):
            if arr[i] is not None:
                s += arr[i]
        return s

    @staticmethod
    def _avg(arr, num):
        if len(arr) == 0:
            return 0
        s = 0.0
        n = 0
        for i in xrange(0, min(len(arr), num)):
            if arr[i] is not None:
                s += arr[i]
                n += 1
        if n == 0:
            return 0
        return s / n

    @staticmethod
    def _zeros(n):
        return [0.0] * n 

    @staticmethod
    def _set(arr, start, end, value):
        for i in xrange(start, min(len(arr), end)):
            arr[i] = value

    @staticmethod
    def _diff(a, b):
        d = [None] * len(b)
        for i in xrange(0, len(b)):
            if a[i] is not None and b[i] is not None:
                d[i] = a[i] - b[i]
        return d

    @staticmethod
    def _move_diff(a):
        d = [None] * (len(a)-1)
        for i in xrange(1, len(a)):
            d[i-1] = a[i] - a[i-1]
        return d

    @staticmethod
    def _cmp(arr, start, end, cmpFunc):
        v = arr[start]
        for i in xrange(start, end):
            v = cmpFunc(arr[i], v)
        return v

    @staticmethod
    def _filt(records, n, attr, iv, cmpFunc):
        if len(records) < 2:
            return None
        v = iv
        pos = 0
        if n != 0:
            pos = len(records) - min(len(records)-1, n) - 1
        for i in xrange(len(records)-2, pos-1, -1):
            if records[i] is not None:
                if attr is not None:
                    v = cmpFunc(v, records[i][attr])
                else:
                    v = cmpFunc(v, records[i])
        return v

    @staticmethod
    def _ticks(records):
        if len(records) == 0:
            return []
        if 'Close' not in records[0]:
            return records

        ticks = [None] * len(records)
        for i in xrange(0, len(records)):
            ticks[i] = records[i]['Close']
        return ticks

    @staticmethod
    def _sma(S, period):
        R = Std._zeros(len(S))
        j = Std._skip(S, period)
        Std._set(R, 0, j, None)
        if j < len(S):
            s = 0
            for i in xrange(j, len(S)):
                if i == j:
                    s = Std._sum(S, i+1)
                else:
                    s += S[i] - S[i-period]
                R[i] = s / period
        return R

    @staticmethod
    def _smma(S, period):
        R = Std._zeros(len(S))
        j = Std._skip(S, period)
        Std._set(R, 0, j, None)
        if j < len(S):
            R[j] = Std._avg(S, j+1)
            for i in xrange(j+1, len(S)):
                R[i] = (R[i-1] * (period-1) + S[i]) / period
        return R

    @staticmethod
    def _ema(S, period):
        R = Std._zeros(len(S))
        multiplier = 2.0 / (period + 1)
        j = Std._skip(S, period)
        Std._set(R, 0, j, None)
        if j < len(S):
            R[j] = Std._avg(S, j+1)
            for i in xrange(j+1, len(S)):
                R[i] = ((S[i] - R[i-1] ) * multiplier) + R[i-1]
        return R

class TA:
    @staticmethod
    def Highest(records, n, attr=None):
        return Std._filt(records, n, attr, 5e-324, max)

    @staticmethod
    def Lowest(records, n, attr=None):
        return Std._filt(records, n, attr, 1.7976931348623157e+308, min)

    @staticmethod
    def MA(records, period=9):
        return Std._sma(Std._ticks(records), period)

    @staticmethod
    def SMA(records, period=9):
        return Std._sma(Std._ticks(records), period)

    @staticmethod
    def EMA(records, period=9):
        return Std._ema(Std._ticks(records), period)

    @staticmethod
    def MACD(records, fastEMA=12, slowEMA=26, signalEMA=9):
        ticks = Std._ticks(records)
        slow = Std._ema(ticks, slowEMA)
        fast = Std._ema(ticks, fastEMA)
        # DIF
        dif = Std._diff(fast, slow)
        # DEA
        signal = Std._ema(dif, signalEMA)
        histogram = Std._diff(dif, signal)
        return [ dif, signal, histogram]

    @staticmethod
    def BOLL(records, period=20, multiplier=2):
        S = Std._ticks(records)
        j = period - 1
        while j < len(S) and (S[j] is None):
            j+=1
        UP = Std._zeros(len(S))
        MB = Std._zeros(len(S))
        DN = Std._zeros(len(S))
        Std._set(UP, 0, j, None)
        Std._set(MB, 0, j, None)
        Std._set(DN, 0, j, None)
        n = 0.0
        for i in xrange(j, len(S)):
            if i == j:
                for k in xrange(0, period):
                    n += S[k]
            else:
                n = n + S[i] - S[i - period]
            ma = n / period
            d = 0
            for k in xrange(i+1-period, i+1):
                d += (S[k] - ma) * (S[k] - ma)
            stdev = math.sqrt(d / period)
            up = ma + (multiplier * stdev)
            dn = ma - (multiplier * stdev)
            UP[i] = up
            MB[i] = ma
            DN[i] = dn
        return [UP, MB, DN]

    @staticmethod
    def KDJ(records, n=9, k=3, d=3):
        RSV = Std._zeros(len(records))
        Std._set(RSV, 0, n - 1, None)
        K = Std._zeros(len(records))
        D = Std._zeros(len(records))
        J = Std._zeros(len(records))

        hs = Std._zeros(len(records))
        ls = Std._zeros(len(records))
        for i in xrange(0, len(records)):
            hs[i] = records[i]['High']
            ls[i] = records[i]['Low']

        for i in xrange(0, len(records)):
            if i >= (n - 1):
                c = records[i]['Close']
                h = Std._cmp(hs, i - (n - 1), i + 1, max)
                l = Std._cmp(ls, i - (n - 1), i + 1, min)
                RSV[i] = 100 * ((c - l) / (h - l))
                K[i] = float(1 * RSV[i] + (k - 1) * K[i - 1]) / k
                D[i] = float(1 * K[i] + (d - 1) * D[i - 1]) / d
            else:
                K[i] = D[i] = 50.0
                RSV[i] = 0.0
            J[i] = 3 * K[i] - 2 * D[i]
        # remove prefix
        for i in xrange(0, n-1):
            K[i] = D[i] = J[i] = None
        return [K, D, J]

    @staticmethod
    def RSI(records, period=14):
        n = period
        rsi = Std._zeros(len(records))
        Std._set(rsi, 0, len(rsi), None)
        if len(records) < n:
            return rsi

        ticks = Std._ticks(records)
        deltas = Std._move_diff(ticks)
        seed = deltas[:n]
        up = 0.0
        down = 0.0
        for i in xrange(0, len(seed)):
            if seed[i] >= 0:
                up += seed[i]
            else:
                down += seed[i]
        up /= n
        down /= n
        down = -down
        if down != 0:
            rs = up / down
        else:
            rs = 0
        rsi[n] = 100 - 100 / (1 + rs)
        delta = 0.0
        upval = 0.0
        downval = 0.0
        for i in xrange(n+1, len(ticks)):
            delta = deltas[i - 1]
            if delta > 0:
                upval = delta
                downval = 0.0
            else:
                upval = 0.0
                downval = -delta
            up = (up * (n - 1) + upval) / n
            down = (down * (n - 1) + downval) / n
            rs = up / down
            rsi[i] = 100 - 100 / (1 + rs)
        return rsi
    @staticmethod
    def OBV(records):
        if len(records) == 0:
            return []

        if 'Close' not in records[0]:
            raise "TA.OBV argument must KLine"

        R = Std._zeros(len(records))
        for i in xrange(0, len(records)):
            if i == 0:
                R[i] = records[i]['Volume']
            elif records[i]['Close'] >= records[i - 1]['Close']:
                R[i] = R[i - 1] + records[i]['Volume']
            else:
                R[i] = R[i - 1] - records[i]['Volume']
        return R

    @staticmethod
    def ATR(records, period=14):
        if len(records) == 0:
            return []
        if 'Close' not in records[0]:
            raise "TA.ATR argument must KLine"

        R = Std._zeros(len(records))
        m = 0.0
        n = 0.0
        for i in xrange(0, len(records)):
            TR = 0
            if i == 0:
                TR = records[i]['High'] - records[i]['Low']
            else:
                TR = max(records[i]['High'] - records[i]['Low'], abs(records[i]['High'] - records[i - 1]['Close']), abs(records[i - 1]['Close'] - records[i]['Low']))
            m += TR
            if i < period:
                n = m / (i + 1)
            else:
                n = (((period - 1) * n) + TR) / period
            R[i] = n
        return R

    @staticmethod
    def Alligator(records, jawLength=13, teethLength=8, lipsLength=5):
        ticks = []
        for i in xrange(0, len(records)):
            ticks.append((records[i]['High'] + records[i]['Low']) / 2)
        return [
            [None]*8+Std._smma(ticks, jawLength), # // jaw (blue)
            [None]*5+Std._smma(ticks, teethLength), # teeth (red)
            [None]*3+Std._smma(ticks, lipsLength) # lips (green)
        ]

    @staticmethod
    def CMF(records, periods=20):
        ret = []
        sumD = 0.0
        sumV = 0.0
        arrD = []
        arrV = []
        for i in xrange(0, len(records)):
            d = 0.0
            if records[i]['High'] != records[i]['Low']:
                d = (2 * records[i]['Close'] - records[i]['Low'] - records[i]['High']) / (records[i]['High'] - records[i]['Low']) * records[i]['Volume']
            arrD.append(d)
            arrV.append(records[i]['Volume'])
            sumD += d
            sumV += records[i]['Volume']
            if i >= periods:
                sumD -= arrD.pop(0)
                sumV -= arrV.pop(0)
            ret.append(sumD / sumV)
        return ret

            cpp
            
            
double _cmp_min(double a, double b) {
    return a < b ? a : b;
}

double _cmp_max(double a, double b) {
    return a > b ? a : b;
}

double _cmp_max(double a, double b, double c) {
    double d = a > b ? a : b;
    return d > c ? d : c;
}

class TAHelper {
  public:
    array<vector<double>, 3> MACD(Records &records, size_t fastEMA = 12, size_t slowEMA = 26, size_t signalEMA = 9) {
        vector<double> ticks = records.Close();
        vector<double> dif = _diff(_ema(ticks, fastEMA), _ema(ticks, slowEMA));
        vector<double> signal = _ema(dif, signalEMA);
        vector<double> histogram = _diff(dif, signal);
        return {{ dif, signal, histogram }};
    }

    array<vector<double>, 3> KDJ(Records &records, size_t n = 9, size_t k = 3, size_t d = 3) {
        size_t length = records.size();
        vector<double> RSV(length, 0);
        _set(RSV, 0, n - 1, NAN);
        vector<double> K(length, 0);
        vector<double> D(length, 0);
        vector<double> J(length, 0);

        vector<double> hs = records.High();
        vector<double> ls = records.Low();

        for (size_t i = 0; i < length; i++) {
            if (i >= size_t(n - 1)) {
                double c = records[i].Close;
                double h = _cmp(hs, i - (n - 1), i + 1, _cmp_max);
                double l = _cmp(ls, i - (n - 1), i + 1, _cmp_min);
                RSV[i] = h != l ? (100 * ((c - l) / (h - l))) : 100;
                K[i] = (1 * RSV[i] + (k - 1) * K[i - 1]) / k;
                D[i] = (1 * K[i] + (d - 1) * D[i - 1]) / d;
            } else {
                K[i] = D[i] = 50;
                RSV[i] = 0;
            }
            J[i] = 3 * K[i] - 2 * D[i];
        }
        for (size_t i = 0; i < n - 1; i++) {
            K[i] = D[i] = J[i] = NAN;
        }
        return{{ K, D, J }};
    }

    vector<double> RSI(Records &records, size_t period = 14) {
        size_t i = 0;
        size_t n = period;
        vector<double> rsi(records.size(), 0);
        _set(rsi, 0, rsi.size(), NAN);
        if (records.size() < n) {
            return rsi;
        }
        vector<double> ticks = records.Close();
        vector<double> deltas = _move_diff(ticks);
        vector<double> seed(deltas.begin(), deltas.begin() + n);
        double up = 0.0;
        double down = 0.0;
        for (i = 0; i < seed.size(); i++) {
            if (seed[i] >= 0) {
                up += seed[i];
            } else {
                down += seed[i];
            }
        }
        up /= n;
        down /= n;
        down = -down;
        double rs = down != 0 ? up / down : 0;
        rsi[n] = 100 - 100 / (1 + rs);
        double delta = 0.0;
        double upval = 0.0;
        double downval = 0.0;
        for (i = n + 1; i < ticks.size(); i++) {
            delta = deltas[i - 1];
            if (delta > 0) {
                upval = delta;
                downval = 0;
            } else {
                upval = 0;
                downval = -delta;
            }
            up = (up * (n - 1) + upval) / n;
            down = (down * (n - 1) + downval) / n;
            rs = up / down;
            rsi[i] = 100 - 100 / (1 + rs);
        }
        return rsi;
    }

    vector<double> ATR(Records &records, size_t period = 14) {
        vector<double> ret;
        if (records.size() == 0) {
            return ret;
        }
        vector<double> R(records.size(), 0);
        double sum = 0.0;
        double n = 0.0;
        for (size_t i = 0; i < records.size(); i++) {
            double TR = 0.0;
            if (i == 0) {
                TR = records[i].High - records[i].Low;
            } else {
                TR = _cmp_max(records[i].High - records[i].Low, abs(records[i].High - records[i - 1].Close), abs(records[i - 1].Close - records[i].Low));
            }
            sum += TR;
            if (i < period) {
                n = sum / (i + 1);
            } else {
                n = (((period - 1) * n) + TR) / period;
            }
            R[i] = n;
        }
        return R;
    }

    vector<double> OBV(Records &records) {
        vector<double> R;
        if (records.size() == 0) {
            return R;
        }
        for (size_t i = 0; i < records.size(); i++) {
            if (i == 0) {
                R.push_back(records[i].Volume);
            } else if (records[i].Close >= records[i - 1].Close) {
                R.push_back(R[i - 1] + records[i].Volume);
            } else {
                R.push_back(R[i - 1] - records[i].Volume);
            }
        }
        return R;
    }

    vector<double> MA(Records &records, size_t period = 9) {
        return _sma(records.Close(), period);
    }

    vector<double> EMA(Records &records, size_t period = 9) {
        return _ema(records.Close(), period);
    }

    array<vector<double>, 3> BOLL(Records &records, size_t period = 20, double multiplier = 2) {
        vector<double> S = records.Close();
        size_t j = 0;
        for (j = period - 1; j < S.size() && isnan(S[j]); j++);
        vector<double> UP(S.size(), 0);
        vector<double> MB(S.size(), 0);
        vector<double> DN(S.size(), 0);
        _set(UP, 0, j, NAN);
        _set(MB, 0, j, NAN);
        _set(DN, 0, j, NAN);
        double sum = 0;
        for (size_t i = j; i < S.size(); i++) {
            if (i == j) {
                for (size_t k = 0; k < period; k++) {
                    sum += S[k];
                }
            } else {
                sum = sum + S[i] - S[i - period];
            }
            double ma = sum / period;
            double d = 0.0;
            for (size_t k = i + 1 - period; k <= i; k++) {
                d += (S[k] - ma) * (S[k] - ma);
            }
            double stdev = sqrt(d / period);
            double up = ma + (multiplier * stdev);
            double dn = ma - (multiplier * stdev);
            UP[i] = up;
            MB[i] = ma;
            DN[i] = dn;
        }
        return {{ UP, MB, DN }};
    }

    array<vector<double>, 3> Alligator(Records &records, size_t jawLength = 13, size_t teethLength = 8, size_t lipsLength = 5) {
        vector<double> ticks;
        for (size_t i = 0; i < records.size(); i++) {
            ticks.push_back((records[i].High + records[i].Low) / 2);
        }
        vector<double> jaw = _smma(ticks, jawLength);
        jaw.insert(jaw.begin(), 8, NAN);
        vector<double> teeth = _smma(ticks, teethLength);
        teeth.insert(teeth.begin(), 5, NAN);
        vector<double> lips = _smma(ticks, lipsLength);
        lips.insert(lips.begin(), 3, NAN);
        return{{ jaw, teeth, lips }};
    }

    vector<double> CMF(Records &records, size_t periods = 20) {
        vector<double> ret;
        double sumD = 0.0;
        double sumV = 0.0;
        vector<double> arrD;
        vector<double> arrV;
        for (size_t i = 0; i < records.size(); i++) {
            double d = (records[i].High == records[i].Low) ? 0 : (2 * records[i].Close - records[i].Low - records[i].High) / (records[i].High - records[i].Low) * records[i].Volume;
            arrD.push_back(d);
            arrV.push_back(records[i].Volume);
            sumD += d;
            sumV += records[i].Volume;
            if (i >= periods) {
                sumD -= arrD.front();
                arrD.erase(arrD.begin());
                sumV -= arrV.front();
                arrV.erase(arrV.begin());
            }
            ret.push_back(sumD / sumV);
        }
        return ret;
    }

    double Highest(vector<double> records, size_t n) {
        return _filt(records, n, NAN, _cmp_max);
    }

    double Lowest(vector<double> records, size_t n) {
        return _filt(records, n, NAN, _cmp_min);
    }

    double _filt(vector<double> records, double n, double iv, double(*pfun) (double a, double b)) {
        if (records.size() < 2) {
            return NAN;
        }
        double v = iv;
        double pos = n != 0 ? records.size() - _cmp_min(records.size() - 1, n) - 1 : 0;
        for (size_t i = records.size() - 2; i >= pos; i--) {
            v = pfun(v, records[i]);
        }
        return v;
    }

    vector<double> _smma(vector<double> S, size_t period) {
        size_t length = S.size();
        vector<double> R(length, 0);
        size_t j = _skip(S, period);
        _set(R, 0, j, NAN);
        if (j < length) {
            R[j] = _avg(S, j + 1);
            for (size_t i = j + 1; i < length; i++) {
                R[i] = (R[i - 1] * (period - 1) + S[i]) / period;
            }
        }
        return R;
    }

    vector<double> _move_diff(vector<double> a) {
        vector<double> d;
        for (size_t i = 1; i < a.size(); i++) {
            d.push_back(a[i] - a[i - 1]);
        }
        return d;
    }

    vector<double> _ema(vector<double> S, size_t period) {
        size_t length = S.size();
        vector<double> R(length, 0);
        double multiplier = 2.0 / (period + 1);
        size_t j = _skip(S, period);
        _set(R, 0, j, NAN);
        if (j < length) {
            R[j] = _avg(S, j + 1);
            for (size_t i = j + 1; i < length; i++) {
                R[i] = (S[i] - R[i - 1]) * multiplier + R[i - 1];
            }
        }
        return R;
    }

    vector<double> _sma(vector<double> S, size_t period) {
        vector<double> R(S.size(), 0);
        size_t j = _skip(S, period);
        _set(R, 0, j, NAN);
        if (j < S.size()) {
            double sum = 0;
            for (size_t i = j; i < S.size(); i++) {
                if (i == j) {
                    sum = _sum(S, i + 1);
                } else {
                    if (i < period) {
                        R[i] = NAN;
                        continue;
                    }
                    sum += S[i] - S[i - period];
                }
                R[i] = sum / period;
            }
        }
        return R;
    }

    double _sum(vector<double> arr, size_t num) {
        double sum = 0.0;
        for (size_t i = 0; i < num; i++) {
            if (!isnan(arr[i])) {
                sum += arr[i];
            }
        }
        return sum;
    }

    vector<double> _diff(vector<double> a, vector<double> b) {
        vector<double> d;
        for (size_t i = 0; i < b.size(); i++) {
            if (isnan(a[i]) || isnan(b[i])) {
                d.push_back(NAN);
            } else {
                d.push_back(a[i] - b[i]);
            }
        }
        return d;
    }

    double _avg(vector<double> arr, double num) {
        size_t n = 0;
        double sum = 0.0;
        for (size_t i = 0; i < num; i++) {
            if (!isnan(arr[i])) {
                sum += arr[i];
                n++;
            }
        }
        return sum / n;
    }

    void _set(vector<double> &arr, size_t start, size_t end, double value) {
        size_t e = _cmp_min(arr.size(), end);
        for (size_t i = start; i < e; i++) {
            arr[i] = value;
        }
    }

    size_t _skip(vector<double> arr, size_t period) {
        size_t j = 0;
        for (size_t k = 0; j < arr.size(); j++) {
            if (!isnan(arr[j])) {
                k++;
            }
            if (k == period) {
                break;
            }
        }
        return j;
    }

    double _cmp(vector<double> arr, size_t start, size_t end, double(*pfun) (double a, double b)) {
        double v = arr[start];
        for (size_t i = start; i < end; i++) {
            v = pfun(arr[i], v);
        }
        return v;
    }
};

TAHelper TA;