InterpObjectCubic1D




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Creates an one dimensional cubic-spline interpolation object.

It implements different type of end conditions: 'NotAknot' (not-a-knot), 'First' (first derivative) value and 'Second' (second derivative value).

It also implements Hyman's monotonicity constraint filter which ensures that the interpolating spline remains monotonic at the expense of the second derivative of the curve which will no longer be continuous where the filter has been applied.

If the interpolating spline is already monotonic, the Hyman filter leaves it unchanged.

See R. L. Dougherty, A. Edelman, and J. M. Hyman, 'Nonnegativity-, Monotonicity-, or Convexity-Preserving Cubic and Quintic Hermite Interpolation' Mathematics Of Computation, v.52, n.186, April 1989, pp471-pp494. Given an 'x' value, you can interpolate for the corresponding 'y' value via the InterpForValue1D() function.

Furthermore you can execute the InterpForCubic1st() or InterpForCubic2nd() functions in order to view the first and second order derivative values for a given 'x' value.



This function creates an object and returns a string-key value to represent this created object.
The TAG value of the string-key returned (second part of the key) is : "InterpCubic1D"



Note: Within Excel, the function is named - CT.INTERP.InterpObjectCubic1D


High level graphic of InterpObjectCubic1D() function with parameters. Blue square node is the actual function with the parameters ordered.



Parameter Description


  1. Key parameter

    Key Handle to be used for the new interpolation object.
  2. Reload parameter

    When creating this object for the first time, set this parameter to a positive value. Within Excel, when re-computing a worksheet where you do not wish to recreate the object, set this parameter to zero (0).
  3. XArray parameter

    X values.
  4. YArray parameter

    Y values.
  5. LeftBC parameter

    Left BoundaryCondition type. Possible values are 'NotAknot' (not-a-knot), 'First' (first derivative) value and 'Second' (second derivative value).
  6. LeftBCVal parameter

    Left BoundaryCondition value. If the 'LeftBC' parameter has been filled with either 'First' (for first derivative) or 'Second' (for second derivative) then the derivative value is entered here.
  7. RightBC parameter

    Right BoundaryCondition type. Possible values are 'NotAknot' (not-a-knot), 'First' (first derivative) value and 'Second' (second derivative value).
  8. RightBCVal parameter

    Right BoundaryCondition value. If the 'RightBC' parameter has been filled with either 'First' (for first derivative) or 'Second' (for second derivative) then the derivative value is entered here.
  9. MonoConst parameter

    Whether you wish to activate the monotonicity constraint (true) or not (false).


Extended information

Function Syntax

VB Syntax 


String CTUtils.InterpObjectCubic1D( _
String Key, _
Long Reload, _
Variant XArray, _
Variant YArray, _
String LeftBC, _
Double LeftBCVal, _
String RightBC, _
Double RightBCVal, _
Boolean MonoConst)


Excel Spreadsheet Syntax 


=CT.INTERP.InterpObjectCubic1D(
Excel String Cell Key,
Excel Numeric Cell Reload,
XLRange XArray,
XLRange YArray,
Excel String Cell LeftBC,
Excel Numeric Cell LeftBCVal,
Excel String Cell RightBC,
Excel Numeric Cell RightBCVal,
Excel Boolean Value Cell MonoConst)


C++ Syntax 


static std::string InterpObjectCubic1D(
std::string Key,
long Reload,
CTRangeDataCPP XArray,
CTRangeDataCPP YArray,
std::string LeftBC,
double LeftBCVal,
std::string RightBC,
double RightBCVal,
bool MonoConst);


DotNET Syntax 


System.String CTUtilsSA.InterpObjectCubic1D(
System.String Key,
System.Int32 Reload,
CTRangeData XArray,
CTRangeData YArray,
System.String LeftBC,
System.Double LeftBCVal,
System.String RightBC,
System.Double RightBCVal,
System.Boolean MonoConst);

Parameter data types

ArgNameArgTypeIsKey
KeyStringFALSE
ReloadLongFALSE
XArrayRangeFALSE
YArrayRangeFALSE
LeftBCStringFALSE
LeftBCValDoubleFALSE
RightBCStringFALSE
RightBCValDoubleFALSE
MonoConstBooleanFALSE

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
KeyFALSEInterpObjectCubic1D
ReloadFALSE1
XArrayFALSEInterpObjectCubic1D_XArray_Range (creates a range object)
YArrayFALSEInterpObjectCubic1D_YArray_Range (creates a range object)
LeftBCFALSENotAknot
LeftBCValTRUE0.0
RightBCFALSENotAknot
RightBCValTRUE0.0
MonoConstFALSEfalse


Example range for parameter : XArray

Within Excel, a range such as this can be passed directly into the XArray parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : XArray 


CTQL.CTRangeData InterpObjectCubic1D_XArray;


double[] arrBInterpObjectCubic1D_XArray = {
0.0,
5.0,
10.0,
15.0,
20.0,
25.0,
30.0,
35.0,
40.0,
45.0  //  Array Data

};

CTQL.DoubleVector arrInterpObjectCubic1D_XArray =
new  CTQL.DoubleVector(arrBInterpObjectCubic1D_XArray);

// Second parameter determines whether the array is a column array (false) or a row array (true)
InterpObjectCubic1D_XArray = new  CTQL.CTRangeData(arrInterpObjectCubic1D_XArray, false);

Example range for parameter : YArray

Within Excel, a range such as this can be passed directly into the YArray parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : YArray 


CTQL.CTRangeData InterpObjectCubic1D_YArray;


double[] arrBInterpObjectCubic1D_YArray = {
0.02,
0.025,
0.03,
0.035,
0.04,
0.045,
0.05,
0.055,
0.06,
0.065  //  Array Data

};

CTQL.DoubleVector arrInterpObjectCubic1D_YArray =
new  CTQL.DoubleVector(arrBInterpObjectCubic1D_YArray);

// Second parameter determines whether the array is a column array (false) or a row array (true)
InterpObjectCubic1D_YArray = new  CTQL.CTRangeData(arrInterpObjectCubic1D_YArray, false);


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 InterpObjectCubic1D() 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.


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 InterpObjectCubic1D() function call


InterpObjectCubic1D_10.InterpCubic1D.0

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