# Tutorial 7 - Working with Functions

## Function Types

### Function characteristics

A TeeChart Pro Function is a Series, that can be of almost any Series Type, to which an algebraic function is applied and for which the datasource is another Chart Series.

All Functions derive from the Functions Component and inherit Functions.

TeeChart Pro includes the following list of predefined functions. Please see the TeeChart Editor Gallery and Helpfile for a full list of all Function Types:

 Function Type No. of inputs Description Add Unlimited Plots sum of inputs ADX Unlimited Average Unlimited The Average Function will calculate the average of every group of Period points Count Unlimited Divide Unlimited The Divide Function plots inputs divided in descending order of inclusion High Unlimited The High Function plots high point of inputs Low Unlimited The Low Function plots low point of inputs Multiply Unlimited The Multiply Function plots value of inputs multiplied Subtract Unlimited Plots value of inputs subtracted in descending order of inclusion Mode 1 The mode function returns the source series value that is repeated more times. Median 1 Calculates the median value of the source series values. Count 1 Draws horizontal line at Y position that is defined by the number of points in underlying Series. Subset of Pro version only functions Bollinger 1 The Bollinger Function uses simple or exponential moving average to constructs Bollinger Trading Bands Curve Fitting 1 Draws fitted polynomial through data inputs using the TypeFitting formula Exponential Average 1 Exponential average based on Weight Exponential Moving Average 1 Exponential moving average based on Weight Exponential Trend 1 Draws best exponential trend line through points in input series MACD 1 Moving Average Convergence Divergence Momentum 1 Each Y value is the current point Y value less the last Period point Y value Momentum Division 1 Each Y values is the current point Y value divided by the last Period point Y Value, expressed in percents Moving Average 1 The Moving Average Function will calculate the simple or weighted average of every group of Period points Root Mean Square Unlimited The Root Mean Square Function plots RMS value of inputs Relative Strength Index 1 RSI Function calculates a percent value based on financial data. Depending on TRSISyle type different formula will be used to calculate RSI value Standard Deviation 1 Maps the Standard Deviation (or Complete Standard Deviation) of every group of Period points Stochastic 1 Trend 1 Draws best trend line through points of input Series

Several Function types support only one input Series. However it is possible to chain link Functions, thus, for example, taking

the average of several Series in your Chart to create an Average Function Series, then identify the Trend of the average by

using the Average Function as the input to the Trend Function.

Each Function is presented as a Line Series, you may change the Series Type associated with the Function later.

Assuming we start with a completely empty Chart here are the steps in code to build a simple Series-Function related Chart.

```private function Load() {
\$line1 = new Line(\$tChart1->getChart());
//Populate it with data (here random)
\$line1->fillSampleValues(10);
//Add a series to be used for an Average Function
\$line2 = new Line(\$tChart1->getChart());
//Define the Function Type for the new Series
\$average1 = new Average();
\$line2->setFunction(\$average1);
//Define the Datasource for the new Function Series
\$line2->setDataSource(\$line1);
//*Note - When populating your input Series manually you will need to
//use the Checkdatasource method
//- See the section entitled Defining a Datasource
//Change the Period of the Function so that it groups averages
//every 2 Points
\$line2->getFunction()->setPeriod(2);
\$line2->checkDataSource();
}
```
```
```

We can add another Function to tell us something about the previous Function

```//Let us change to 2D for visibility
\$tChart1->getAspect()->setView3D(false);
//Add another Series to be used for a 2nd Function
\$line3 = new Line(\$tChart1->getChart());
//Define the Function Type for the new Series
\$high1 = High();
\$line3->setFunction(\$high1);
//Define the Datasource for the new Function Series
//Use the existing Function (Series2) as input
\$line3->setDataSource(\$tChart1->getSeries(1));
//Leave the Period at default 0 (No Period set) to draw
//A line at Highest of all points of the Average Function
```

### Defining a datasource

The examples in the previous section highlight the use of Datasource for poulating a Function by code. Series use Datasource for

defining the input for a Function or to define a Series Dataset datasource (see the Tutorial about accessing databases).

Datasource by code uses the Series->Datasource property.

Example

Suppose we have 2 data Series in a Chart. We add a Function composed of the average of the 2 Series:

```require_once "../sources/TChart.php";
\$tChart1 = new TChart(600,450);
\$tChart1->getAspect()->setView3D(false);
\$bar1->fillSampleValues(10);
\$bar2->fillSampleValues(10);
}
```
```
```
```public function button1_click() {
\$line1 = new Line(\$tChart1->getChart());
\$average3 = new Average();
\$tmpDataSource = Array(\$bar1,\$bar2);
\$line1->setFunction(\$tmpDataSource);
\$line1->setDataSource(\$bar1);
\$line1->getMarks()->setVisible(true);
}
```

We add points to the 2 Series:

```public function button1_click() {
for(\$i = 0; \$i < 10;   \$i)
}

```

Notice that the Function doesn't display. You need to use the checkDataSource method to read in values for the Function.

```\$tChart1->getSeries(2)->checkDataSource();
```

Function definitions may be changed at runtime to allocate a new Function to the Series simply by redefining the

Series.DataSource method:

```public function button3_click() {
\$cumulative1 = Cumulative();
\$tChart1->getSeries(2)->setFunction(\$cumulative1);
```

### Function Period

Period is an important method for working with Functions because the Period defines the range of points across which a Function

is cyclically applied.

Example

We have 6 data points (eg. bars of a Bar Series) with values:

3, 8, 6, 2, 9 and 12

We define a Function Series with Period 0 (default) the average drawn is:

6.667

With Period set to 2 we get 3 values of average as output from the function:

5.5, 4 and 10.5

These values will plot centrally in their period range, ie. The 1st value between bars 1 and 2 of the input series, 2nd value

between bars 3 and 4, etc..

You may define Period at runtime using FunctionType.

Eg. Where Series 2 is the function series:

```\$line1->getFunction()->setPeriod(2);
```

Below are 2 Charts that highlight the effect of an applied Period

### Period Style

Period can be defined to be a range. This is very useful when using DateTime series and we want to express the "Period" of the

function as a TimeStep. The property "PeriodStyle" controls how is "Period" expressed.

For example you can now plot

the "monthly average of sales" function just using a normal "Average" function on a date-time source series and setting the

function period to "one month":

```require_once "../sources/TChart.php";
\$tChart1 = new TChart(600,450);
//Add in a Bar Series and Average Function .
\$bar = new Bar(\$tChart1->getChart());
//Populate it with data (here random)
\$bar->fillSampleValues(10);
//Add a series to be used for an Average Function
\$line2 = new Line(\$tChart1->getChart());
\$average1 = new Average();
\$line2->setFunction(\$average1);
\$tChart1->getAspect()->setView3D(false);
\$today = date_time(U);
\$bar1->getMarks()->setVisible(false);
\$bar1->getXValues()->setDateTime(true);
\$tChart1->getAxes()->getBottom()->getLabels()->setAngle(90);
for(\$i = 0; \$i < 60;   \$i)
\$days7 = 7 * 86400;
\$today = \$today   \$days7;
\$average1->setPeriodAlign(PeriodAligns::\$FIRST);
\$average1->setPeriodStyle(PeriodStyles::\$RANGE);
\$average1->setPeriod(30);
\$line1->setDataSource(\$bar1);
\$line1->checkDataSource();
}
```

This will result in several points, each one showing the "average" of each month of data in the Bar Series. It's mandatory that points in the source Series should be sorted by date when calculating functions on datetime periods. The range can also be used for non-datetime series:

```for(\$i = 0; \$i < 60;   \$i)
\$average1->setPeriodAlign(PeriodAligns::\$FIRST);
\$average1->setPeriodStyle(PeriodStyles::\$RANGE);
\$average1->setPeriod(6);
```

This will calculate an average for each group of points inside every "6" interval.
(Points with X >=6, X<6 will be used to calculate the first average, points with X >=6, X<12 will be used to calculate the second average and so on... ).
Notice this is different than calculating an average for every 6 points.

Use the Period Alignment property to align the function Points within the Series range. The following will plot the Function point at the end of a monthly Period:

``` \$average1->setPeriodAlign(PeriodAligns::\$FIRST);
\$average1->setPeriodStyle(PeriodStyles::\$RANGE);
\$average1->setPeriod(DateTime::getDaysInMonth(year,month));
```

Period = Month.TotalDays and PeriodAligns.First
As you can see from the picture below, the "average" is plotted at the end of the month.

Period = Month.TotalDays and PeriodAligns.Last
In this case the "average" is plotted at the beginning of the month.

### Deriving custom functions

Creating a new Function component is simply creating a new component derived from Functions class (it also can be derived from an existing function ). There are 2 important virtual methods in TTeeFunction that can be overridden to create a new Function type.

1) Function.Calculate: public virtual double Calculate((Series) Source,(int) First,(int) Last)

2) Function.CalculateMany: public virtual double CalculateMany((ArrayList) SourceSeries, (int) ValueIndex)

The Calculate method is used to calculate function result if only one series is datasource. CalculateMany is used to calculate function result if multiple series can be datasource.

Example : Creating new SquareSum Funtion.

Let us decide we need a SquareSum Function to return the "sum of squares".

This function can have only one datasource or multiple datasources, so we'll override the Calculate and CalculateMany methods.

public class quareSum extends Functions {

```    public function quareSum(\$c=null) {      parent::__constructor(\$c);     }
public calculate(\$sourceSeries, \$firstIndex, \$lastIndex) {
\$v = \$this->valueList(\$sourceSeries);
if (\$firstIndex == -1) {
return \$v->getTotal();
} else {
result = 0;
for (\$t = \$firstIndex; \$t <= \$lastIndex; \$t++) {
result+=sqrt(\$v->getValue(\$t));
}
return (Double)\$result;
}
}
public function calculateMany(\$sourceSeriesList,  \$valueIndex) {
\$result = 0;
for (\$t = 0; \$t < sizeof(\$sourceSeriesList); \$t++) {
\$v = \$this->valueList(\$sourceSeriesList[\$t]);
if (\$v->count > \$valueIndex) {
\$result+=sqrt(\$v->getValue(\$valueIndex));
}
}
return \$result;
}
```

The FirstIndex and EndIndex variables are used to "loop" all SourceSeries points to calculate the sum of squares.

The "ValueList" method is used to extract the mandatory Steema.TeeChart.ValueList to make the class work with Series types like HorizBarSeries where "XValues" holds the point values and not "YValues".

The "Calculate" method is used when the Series has only one Series as DataSource. When Series have more than one Series as datasources, the "CalculateMany" method is called.

"CalculateMany" will get called once for each point in the source Series, starting from zero and ending with the minimum point count of all datasources.

It is very important to understand the difference between Calculate and CalculateMany. "Calculate" is called when there is only one datasource and it's called only once. "CalculateMany" is called several times (one for each point) when there are more than one Series as datasources.