# Tutorial7 - Working with Functions

Contents

Function Types

```    Function characteristics
Defining a datasource
Function Period
Period Style
Deriving Custom 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 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[1]; //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[2].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[2].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.