MPTrapezoidIntegral




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Integrates a CustomFunction object using the Mid Point TrapezoidIntegral method.

Given a target accuracy tolerance, the integral of the generic function f() between the LowerLimit and UpperLimit is calculated by means of the trapezoid formula.

The function to be integrated must have been previously created via the CustomFunction() function.

This CustomFunction() would have returned a string 'KEY' which is to be passed to the 'FuncKey' parameter of this function.



Note: Within Excel, the function is named - CT.FUNC.MPTrapezoidIntegral


High level graphic of MPTrapezoidIntegral() function with parameters. Blue square node is the actual function with the parameters ordered.



Parameter Description


  1. FuncKey parameter

    Key value an already created CustomFunction object.
  2. tolerance parameter

    The tolerance to use for this integration (ie - 0.0001).
  3. LowerLimit parameter

    The lower limit of integration.
  4. UpperLimit parameter

    The Upper limit of integration.


Extended information

Function Syntax

VB Syntax 


Double CTUtils.MPTrapezoidIntegral( _
String FuncKey, _
Double tolerance, _
Long LowerLimit, _
Long UpperLimit)


Excel Spreadsheet Syntax 


=CT.FUNC.MPTrapezoidIntegral(
Excel String Cell FuncKey,
Excel Numeric Cell tolerance,
Excel Numeric Cell LowerLimit,
Excel Numeric Cell UpperLimit)


C++ Syntax 


static double MPTrapezoidIntegral(
std::string FuncKey,
double tolerance,
long LowerLimit,
long UpperLimit);


DotNET Syntax 


System.Double CTUtilsSA.MPTrapezoidIntegral(
System.String FuncKey,
System.Double tolerance,
System.Int32 LowerLimit,
System.Int32 UpperLimit);

Parameter data types

ArgNameArgTypeIsKey
FuncKeyStringTRUE
toleranceDoubleFALSE
LowerLimitLongFALSE
UpperLimitLongFALSE

Example Inputs

The first column represents the name of the parameters. The second column specifies whether the parameters are optional or not. Finally the last column provides some sample input data.
Function call input string-keys are always in the format : "NAME.EXTTAG.TICKER" The "EXTTAG.TICKER" part is determined from the output of other, capetools, object creation functions.


ArgNameIsOptional (Excel only)Example
FuncKeyFALSEFuncKeyNAME.EXTTAG.TICKER (from a function call)
toleranceFALSE0.001
LowerLimitFALSE0
UpperLimitFALSE1


Example function usage


The C# example below contains all the sub-function calls leading up to this function call. As a result, the example can contain a lot of code.

The VB.NET, J#, C++.NET, Java, Excel VBA, Visual Basic 6 (via COM) and C++ examples below contain function code stubs for the calls leading up to this function call. However, the function call for this function is displayed.
You can easily reproduce the stub functions code from the C# example.


If you are accessing this functrion via the MiniXL libraries, this function is present within the CT.QL.Utils20 MiniXL Excel Addin.

Within our Excel Example Addin Generator, we have used the following QuantTools sub-functions in order to prepare the arguments needed to call the MPTrapezoidIntegral() function. If you are executing this function via the MiniXL libraries, the module addin name, (in brackets, to the right of the sub-functions listed below), indicates the MiniXL library in which the sub-function is held. You will need to load this library into your Excel session (along with any other libraries that the sub-function call within the addin requires (ie - CT.QT.Utils20 addin in almost all cases) in order for the example to compute successfully.

These are the financial QuantTools sub-function calls that are used within the examples :





The objects generated by these sub-functions are inter-connected in the following way :




The following four examples demostrate calling this function within a Microsoft .NET environment

The following four examples demostrate calling this function within a non .NET environment

The following is a sample output from executing the MPTrapezoidIntegral() function call


-5.46632388794492

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