Technical Analysis Indicator Library

Calculate a vector directly with the ta module function wma:

use ta
close = 7.2 6.97 7.08 6.74 6.49 5.9 6.26 5.9 5.35 5.63
x = wma(close, 5);

In the following example, we first construct a table with data of 2 stocks, then conduct a calculation within each group:

close = 7.2 6.97 7.08 6.74 6.49 5.9 6.26 5.9 5.35 5.63 3.81 3.935 4.04 3.74 3.7 3.33 3.64 3.31 2.69 2.72
date = (2020.03.02 + 0..4 join 7..11).take(20)
symbol = take(`F,10) join take(`GPRO,10)
t = table(symbol, date, close)

Apply ta module function wma for each of these two stocks:

update t set wma = wma(close, 5) context by symbol

Some ta module functions return results with multiple columns, such as function bBands.

Example 1:

close = 7.2 6.97 7.08 6.74 6.49 5.9 6.26 5.9 5.35 5.63
low, mid, high = bBands(close, 5, 2, 2, 2);

Example 2:

close = 7.2 6.97 7.08 6.74 6.49 5.9 6.26 5.9 5.35 5.63 3.81 3.935 4.04 3.74 3.7 3.33 3.64 3.31 2.69 2.72
date = (2020.03.02 + 0..4 join 7..11).take(20)
symbol = take(`F,10) join take(`GPRO,10)
t = table(symbol, date, close) 
select *, bBands(close, 5, 2, 2, 2) as `high`mid`low from t context by symbol;

symbol date       close high     mid      low
------ ---------- ----- -------- -------- --------
F      2020.03.02 7.2
F      2020.03.03 6.97
F      2020.03.04 7.08
F      2020.03.05 6.74
F      2020.03.06 6.49  7.292691 6.786    6.279309
F      2020.03.09 5.9   7.294248 6.454    5.613752
F      2020.03.10 6.26  7.134406 6.328667 5.522927
F      2020.03.11 5.9   6.789441 6.130667 5.471892
F      2020.03.12 5.35  6.601667 5.828    5.054333
F      2020.03.13 5.63  6.319728 5.711333 5.102939
GPRO   2020.03.02 3.81
GPRO   2020.03.03 3.935
GPRO   2020.03.04 4.04
GPRO   2020.03.05 3.74
GPRO   2020.03.06 3.7   4.069365 3.817333 3.565302
GPRO   2020.03.09 3.33  4.133371 3.645667 3.157962
GPRO   2020.03.10 3.64  4.062941 3.609333 3.155726
GPRO   2020.03.11 3.31  3.854172 3.482667 3.111162
GPRO   2020.03.12 2.69  3.915172 3.198    2.480828
GPRO   2020.03.13 2.72  3.738386 2.993333 2.24828

In DolphinDB:

use ta
close = 7.2 6.97 7.08 6.74 6.49 5.9 6.26 5.9 5.35 5.63
close = take(close, 1000000)
timer x = wma(close, 5);

The ta module function wma takes 3 milliseconds to calculate for a vector with 1,000,000 elements.

The corresponding Python script is as follows:

close = np.array([7.2,6.97,7.08,6.74,6.49,5.9,6.26,5.9,5.35,5.63,5.01,5.01,4.5,4.47,4.33])
close = np.tile(close,100000)

import time
start_time = time.time()
x = talib.WMA(close, 5)
print("--- %s seconds ---" % (time.time() - start_time))

The TA-Lib function WMA takes 11 milliseconds, which is 3.7 times as long as ta module function wma.

n=1000000
close = rand(1.0, n)
date = take(2017.01.01 + 1..1000, n)
symbol = take(1..1000, n).sort!()
t = table(symbol, date, close)
timer update t set wma = wma(close, 5) context by symbol;

The ta module function wma takes 17 milliseconds to calculate for all groups.

The corresponding Python script is as follows:

close = np.random.uniform(size=1000000)
symbol = np.sort(np.tile(np.arange(1,1001),1000))
date = np.tile(pd.date_range('2017-01-02', '2019-09-28'),1000)
df = pd.DataFrame(data={'symbol': symbol, 'date': date, 'close': close})

import time
start_time = time.time()
df["wma"] = df.groupby("symbol").apply(lambda df: talib.WMA(df.close, 5)).to_numpy()
print("--- %s seconds ---" % (time.time() - start_time))

The TA-Lib function WMA takes 535 milliseconds to calculate for all groups, which is 31.5 times as long as ta module function wma.

If the input vector of TA-Lib functions starts with null values, the calculation starts from the first non-null position. The ta module uses the same strategy.

In both TA-Lib and ta module, for a rolling or cumulative window function with window length k, the first (k-1) elements of each group in the output vector are null values. If there is a null value after the first non-null element in a group, the result for this null position and all subsequent positions in the group may be null in TA-Lib. In comparison, the results are not null values for these positions in ta module unless the amount of non-null data in the window is not enough for calculation (e.g., when there is only one non-null value in a window to calculate the variance).

DolphinDB script and result:

close = [99.9, NULL, 84.69, 31.38, 60.9, 83.3, 97.26, 98.67]
ta::var(close, 5, 1);

[,,,,670.417819,467.420569,539.753584,644.748976]

Python script and result:

close = np.array([99.9, np.nan, 84.69, 31.38, 60.9, 83.3, 97.26, 98.67])
talib.VAR(close, 5, 1)

array([nan, nan, nan, nan, nan, nan, nan, nan])

As the first element of the vector 'close' is not null and the second element is null, the result is null on all positions. In short, only when all null values, if any, concentrate on the starting positions are the results of TA-Lib and ta module functions identical on all positions.

Many TA-Lib functions use iterations where the current position value is a linear function of the previous position value and the current input: r[n] = coeff * r[n-1] + input[n]. For this type of calculation, DolphinDB introduces function iterate for vectorized iteration to avoid the use of loops.

def ema(close, timePeriod) {
1 	n = close.size()
2	b = ifirstNot(close)
3	start = b + timePeriod
4	if(b < 0 || start > n) return array(DOUBLE, n, n, NULL)
5	init = close.subarray(:start).avg()
6	coeff = 1 - 2.0/(timePeriod+1)
7	ret = iterate(init, coeff, close.subarray(start:)*(1 - coeff))
8	return array(DOUBLE, start - 1, n, NULL).append!(init).append!(ret)
}

The script above is the definition of ta module function ema. Line 5 calculates the mean of the first window as the initial value of the iterative sequence. Line 6 defines the iteration coefficient. Line 7 uses the highly-efficient DolphinDB built-in function iterate to calculate the ema sequence. To calculate the ema sequence with window length of 10 for a vector with 1,000,000 elements, TA-Lib takes 7.4 milliseconds while ta module takes only 5.0 milliseconds.

DolphinDB offers various built-in moving window functions including mcount, mavg, msum, mmax, mmin, mimax, mimin, mmed, mpercentile, mrank, mmad, mbeta, mcorr, mcovar, mstd and mvar. These moving window functions have been fully optimized. The complexity of most of them is O(n) which means performance is independent of window length.

Some TA-Lib functions can be implemented with DolphinDB moving window functions. For example, TA-Lib function VAR is population variance, whereas DolphinDB function mvar is sample variance. The ta module function var is implemented in the following script:

def var(close, timePeriod, nddev){
1	n = close.size()
2	b = close.ifirstNot()
3	if(b < 0 || b + timePeriod > n) return array(DOUBLE, n, n, NULL)
4	mobs =  mcount(close, timePeriod)
5	return (mvar(close, timePeriod) * (mobs - 1) \ mobs).fill!(timePeriod - 1 + 0:b, NULL)
}

When conducting operations such as slicing, joining or appending on a vector, a large amount of data may be replicated. Data replication is usually more time consuming than many simple calculations. Here are some examples about how to reduce data replication.

• For Math Transform and Math Operators functions in TA-Lib, you can use the corresponding DolphinDB built-in functions. For examples, functions SQRT, LN and SUM in TA-Lib correspond to DolphinDB functions sqrt, log and msum, respectively.
• The following TA-Lib functions have not been implemented in the ta module: all Pattern Recognition and Cycle Indicators functions, as well as HT_TRENDLINE (Hilbert Transform-Instantaneous Trendline), ADOSC (Chaikin A / D Oscillator), MAMA (MESA Adaptive Moving Average), SAR (Parabolic SAR) and SAREXT (Parabolic SAR-Extended).