# Tutorial7 - 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 Function Class in the Steema.TeeChart.Functions namespace and inherit Function's [#FunctionPeriod Period property]. TeeChart Pro offers following list of predefined functions: 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.

### Adding a Function

With the TeeChart Editor, on the First Chart page, select the Add button as if to add a new Series to the Chart. In the TeeChart Gallery choose the Functions tab to select the Function you require. Each Function is presented as a Line Series, you may change the Series Type associated with the Function later by choosing the Change button on the first Chart Page. Function definitions are easily changed afterwards on the Datasource page of the Function Series. Here, just as easily, you may change the definition of a normal Series that you have added to the Chart to that of a Function (Function is really a definition of datasource, not a definition of Series Type).

The image below shows the Datasource page when editing a Function. The Line Series (Title "line2") is defined. The left listbox at the bottom of the Datasource page shows other Series in the Chart available for input (here "line1"). Assuming we start with a completely empty Chart here are the steps in code to build a simple Series-Function related Chart.

```[C#] private void Form1_Load(object sender, System.EventArgs e)               //Add a data Series             Line line1 = new Line(tChart1.Chart);              //Populate it with data (here random)             line1.FillSampleValues(10);              //Add a series to be used for an Average Function             Line line2 = new Line(tChart1.Chart);              //Define the Function Type for the new Series             Steema.TeeChart.Functions.Average average1 = new Steema.TeeChart.Functions.Average();             line2.Function = average1;              //Define the Datasource for the new Function Series             line2.DataSource = 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.Function.Period = 2;             line2.CheckDataSource();           [VB.Net] Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load         'Add a data Series         Dim Line1 As New Steema.TeeChart.Styles.Line(TChart1.Chart)                  'Populate it with data (here random)         Line1.FillSampleValues(10)          'Add a series to be used for an Average Function         Dim Line2 As New Steema.TeeChart.LineSeries(TChart1.Chart)          'Define the Function Type for the new Series         Dim Average1 As New Steema.TeeChart.Functions.Average()         Line2.Function = Average1          'Define the Datasource for the new Function Series         Line2.DataSource = 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.Function.Period = 2         Line2.CheckDataSource() End Sub
```

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

```[C#] private void button1_Click(object sender, System.EventArgs e)                      //Let's change to 2D for visibility             tChart1.Aspect.View3D = false;             //Add another Series to be used for a 2nd Function              Line line3 = new Line(tChart1.Chart);             //Define the Function Type for the new Series              Steema.TeeChart.Functions.High high1 = new Steema.TeeChart.Functions.High();             line3.Function = high1;             //Define the Datasource for the new Function Series              //Use the existing Function (Series2) as input              line3.DataSource = tChart1.Series;             //Leave the Period at default 0 (No Period set) to draw              //A line at Highest of all points of the Average Function            [VB.Net] Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click         'Let's change to 2D for visibility         TChart1.Aspect.View3D = False         'Add another Series to be used for a 2nd Function          Dim Line3 As New Steema.TeeChart.LineSeries(TChart1.Chart)         'Define the Function Type for the new Series          Dim High1 As New Steema.TeeChart.Functions.High()         Line3.Function = High1         'Define the Datasource for the new Function Series          'Use the existing Function (Series2) as input          Line3.DataSource = TChart1.Series(1)         'Leave the Period at default 0 (No Period set) to draw          'A line at Highest of all points of the Average Function  End Sub
```

### Defining a datasource

The examples in the previous section highlight the use of Datasource for populating a Function by code. Series use datasource for defining the input for a Function or to define a Series ADO.NET datasource (see the Tutorial about accessing databases).

Using the TeeChart Editor, after adding a Function, the Function Series' Datasource page will show a list of available series for inclusion in the function definition. Here you may change the Function Type you wish to apply to the Series and select Series from the Left listBox "Available" and add them to the right Listbox,"Selected".

Datasource by code uses the Series.Datasource property.

Example
Suppose we have 2 data Series in a Chart added in at design-time via the TeeChart Editor. We add a Function composed of the average of the 2 Series:

```[C#] private void Form1_Load(object sender, System.EventArgs e)                      tChart1.Aspect.View3D = false;             bar1.FillSampleValues(10);             bar2.FillSampleValues(10);                   private void button1_Click(object sender, System.EventArgs e)                      Steema.TeeChart.Styles.Line line1 = new Steema.TeeChart.Styles.Line(tChart1.Chart);             Steema.TeeChart.Functions.Average average1 = new Steema.TeeChart.Functions.Average();              line1.DataSource = new object[]  this.bar2,this.bar1;             line1.Function = average1;             line1.Marks.Visible = true;            [VB.Net] Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load         TChart1.Aspect.View3D = False         Bar1.FillSampleValues(10)         Bar2.FillSampleValues(10) End Sub  Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click         Dim DataSource As New ArrayList()          DataSource.Add(Bar1)         DataSource.Add(Bar2)          Dim Line1 As New Steema.TeeChart.Styles.Line(TChart1.Chart)         Dim Average1 As New Steema.TeeChart.Functions.Average()          Line1.Function = Average1         Line1.DataSource = DataSource End Sub
```

We add points to the 2 Series:

```[C#] private void button2_Click(object sender, System.EventArgs e)                      Random rnd = new Random();             for(int i = 0; i < 10;   i)                              bar1.Add(rnd.Next(500));                 bar2.Add(rnd.Next(500));                        [VB.Net] Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click         Dim rnd As New Random()         Dim i As Integer         For i = 0 To 10             Bar1.Add(rnd.Next(500))             Bar2.Add(rnd.Next(500))         Next End Sub
```

Notice that the Function doesn't display. You need to add the Series.CheckDatasource method the the Button2_Click() event to read in values for the Function.

```[C#] tChart1.Series.CheckDataSource(); [VB.Net] TChart1.Series(2).CheckDataSource()
```

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

```[C#] private void button3_Click(object sender, System.EventArgs e)                      Steema.TeeChart.Functions.Cumulative cumulative1 = new Steema.TeeChart.Functions.Cumulative();             tChart1.Series.Function = cumulative1;           [VB.Net] Private Sub Button3_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button3.Click         Dim Cumulative1 As New Steema.TeeChart.Functions.Cumulative()         TChart1.Series(2).Function = Cumulative1 End Sub
```

### Function Period

Period is an important property for working with Functions as the Period defines the range of points across which a Function is cyclically applied.
Example

We have 6 data points (e.g. 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, i.e. The 1st value between bars 1 and 2 of the input series, 2nd value between bars 3 and 4, etc..

You may define Period by selecting the relevant Series and Function in the Datasource page and clicking the "Options" tab or you may modify Period at runtime using FunctionType.

e.g. Where line1 is the function series:

```[C#] line1.Function.Period = 2; [VB.Net] Line1.Function.Period = 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":

```[C#] private void Form1_Load(object sender, System.EventArgs e)              //Add in a BarSeries and Average Function at design-time.             Random rnd = new Random();             tChart1.Aspect.View3D = false;                           TimeSpan month = new TimeSpan(30,0,0,0);             DateTime today = DateTime.Today;              bar1.Marks.Visible = false;             bar1.XValues.DateTime = true;             tChart1.Axes.Bottom.Labels.Angle = 90;              for(int i = 0; i < 60;   i)                  today = today.AddDays(5);                 bar1.Add(today, rnd.Next(100),"",Color.Red);                           average1.PeriodAlign = Steema.TeeChart.Functions.PeriodAligns.First;             average1.PeriodStyle = Steema.TeeChart.Functions.PeriodStyles.Range;             average1.Period = month.TotalDays;             line1.DataSource = bar1;             line1.CheckDataSource();           [VB.Net] Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load         'Add in a BarSeries and Average Function at design-time.         TChart1.Aspect.View3D = False          Dim Month As New TimeSpan(30, 0, 0, 0)         Dim Today As DateTime = DateTime.Today         Dim i As Integer          Bar1.Marks.Visible = False         Bar1.XValues.DateTime = True         TChart1.Axes.Bottom.Labels.Angle = 90          For i = 0 To 60             Today = Today.AddDays(5)             Bar1.Add(Today, Rnd() * 100, "", Color.Red)         Next          Average1.PeriodAlign = Steema.TeeChart.Functions.PeriodAligns.First         Average1.PeriodStyle = Steema.TeeChart.Functions.PeriodStyles.Range         Average1.Period = Month.TotalDays         Line1.DataSource = Bar1         Line1.CheckDataSource() End Sub
```

This will result in several points, each one showing the "average" of each month of data in the BarSeries.

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:

```[C#] for(int i = 0; i < 60;   i)       bar1.Add(Convert.ToDouble(i), rnd.Next(100),"",Color.Red);  average1.PeriodAlign = Steema.TeeChart.Functions.PeriodAligns.First; average1.PeriodStyle = Steema.TeeChart.Functions.PeriodStyles.Range; average1.Period = 6;  [VB.Net] For i = 0 To 60             Bar1.Add(i, Rnd() * 100, "", Color.Red) Next Average1.PeriodAlign = Steema.TeeChart.Functions.PeriodAligns.First Average1.PeriodStyle = Steema.TeeChart.Functions.PeriodStyles.Range Average1.Period = 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:

```[C#] average1.PeriodAlign = Steema.TeeChart.Functions.PeriodAligns.First; average1.PeriodStyle = Steema.TeeChart.Functions.PeriodStyles.Range; average1.Period = month.TotalDays;  [VB.Net] Average1.PeriodAlign = Steema.TeeChart.Functions.PeriodAligns.First Average1.PeriodStyle = Steema.TeeChart.Functions.PeriodStyles.Range Average1.Period = Month.TotalDays
```

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 the Function class (it also can be derived from an existing function class). There are 2 important virtual methods in Function 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 the function result if only one series serves as the datasource. CalculateMany is used to calculate the function result if multiple series can be used as a datasource.

Example : Creating new SquareSum Funtion.

Let's 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.

fnnnt [C#]
public class SquareSum : Steema.TeeChart.Functions.Function
public SquareSum(): base()
public SquareSum(Steema.TeeChart.Chart c): base(c)

public override double Calculate(Series SourceSeries,int FirstIndex,int LastIndex)
ValueList v=ValueList(SourceSeries);
if ( FirstIndex==-1 ) return v.Total;
else
double result=0;
for (int t=FirstIndex; t<=LastIndex; t )
result =Math.Sqrt(v[t]);
return result;

public override double CalculateMany(ArrayList SourceSeriesList,int ValueIndex)
ValueList v;
double result=0;

for (int t=0; t<SourceSeriesList.Count; t )
v=ValueList((Series)SourceSeriesList[t]);
if ( v.Count>ValueIndex )
result =Math.Sqrt(v[ValueIndex]);

return result;

[VB.Net]
Public Class SquareSum
Inherits Steema.TeeChart.Functions.Function

Public Sub New()
MyBase.New()
End Sub

Public Sub New(ByVal c As Steema.TeeChart.Chart)
MyBase.New(c)
End Sub

Public Overrides Function Calculate(ByVal Source As Steema.TeeChart.Series, ByVal First As Integer, ByVal Last As Integer) As Double
Dim v As Steema.TeeChart.ValueList
Dim t As Integer
v = ValueList(Source)

If First = -1 Then
Return v.Total
Else
Dim Result As Double = 0
For t = First To t < Last
Result = Math.Sqrt(v(t))
Next
Return Result
End If
End Function

Public Overrides Function CalculateMany(ByVal SourceSeries As System.Collections.ArrayList, ByVal ValueIndex As Integer) As Double
Dim v As Steema.TeeChart.ValueList
Dim Result As Double = 0
Dim t As Integer

For t = 0 To t < SourceSeries.Count
v = ValueList(CType(SourceSeries(t), Steema.TeeChart.Series))
If v.Count > ValueIndex Then
Result = Math.Sqrt(v(ValueIndex))
End If
Next

Return Result
End Function
End Class

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 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.