2.1.17.5.15 ocmath_interpolate

1 Description
2 Syntax
3 Parameters
4 Return
5 Examples
6 Remark
7 See Also
8 Header to Include
9 Reference

Description

Do interpolation with mode of Linear, Spline or B-Spline.

Syntax

int ocmath_interpolate( const double * pX, double * pY, UINT nSize, const double * pSrcX, const double * pSrcY, UINT nSrcSize, int nMode = INTERP_TYPE_LINEAR, double dSmoothingFactor = 1, const double * pWeights = NULL, double * pCof = NULL, DWORD dwCntrl = 0, int nSplBoundType = 0, int iOption = OPTION_EXTRAPOLATE )

Parameters

pX: [input] pointer to X coordinate to be evaluated. size is nSize
pY: [output] pointer to the interpolation values at evaluation points. size is nSize; if pX[i] is invalid(e.g, out of the range of pSrcX[0] to pSrcX[nSrcSize-1] in linear interpolation), set pY[i] to NANUM.
nSize: [input] size of pX and pY, nSize > 0
pSrcX: [input] pointer to the X value of the curve, must be in strictly ascending order, otherwise it should be sorted before calling this function. size is nSrcSize.
pSrcY: [input] pointer to the Y value of the curve. size is nSrcSize.
nSrcSize: [input] size of pSrcX and pSrcY. if nMode = INTERP_TYPE_LINEAR, nSrcSize >= 1; otherwise nSrcSize >= 4.
nMode: [input] interpolation method. Must be one of the three modes:; INTERP_TYPE_LINEAR(linear interpolation),; INTERP_TYPE_SPLINE(cubic spline interpolation with not-a-knot boundary condition, and the not-a-knot boundary condition assume that the 3rd order derivative are continuous on the 2nd and last 2nd points),; INTERP_TYPE_BSPLINE(B-Spline curve fitting using method by Dierckx.P)
dSmoothingFactor: [input] This argument specifies the closeness to the original data. It is only useful when nMode = INTERP_TYPE_BSPLINE. dSmoothingFactor >= 0.; By means of this parameter, the user can control the tradeoff between closeness of fit and smoothness of fit of the approximation.; If dSmoothingFactor is too large, the spline will be too smooth and signal will be lost ; if it is too small the spline will pick up too much noise.; In the extreme cases the program will return an interpolating spline if dSmoothingFactor=0 and the weighted least-squares polynomial of degree 3 if s is very large.
pWeights: [input] pointer to weights, which is only used in method INTERP_TYPE_BSPLINE, by default(pWeights = NULL) all weights are 1. size is nSrcSize
pCof: [output] pointer to coefficients, which are used in method INTERP_TYPE_SPLINE and INTERP_TYPE_BSPLINE, by default(pCof = Null), size is nSrcSize
dwCntrl: [input] indicates do sorting or not before doing interpolation, when it equals OCMATH_SRCDATA_X_MONOTONIC, don't sort.
nSplBoundType: [input] enumeration, indicate the boundary condition for spline (cubic spline), 0 for natural boundary condition, 1 for not_a_knot (currently only support these 2 kinds)
iOption: [input] enumeration, specify how to extrapolate Y values in extrapolated range. Must be one of the three values:; OPTION_EXTRAPOLATE(extrapolate Y using the last two points),; OPTION_SET_MISSING(set all Y values in the extrapolated range to be missing values),; OPTION_REPEAT_LAST(use the Y value of the closest input X value for all values in the extrapolated range)

Return

OE_NOERROR: Success

OE_BAD_PARAM (error code: -18): invalid argument of nMode

OE_INT_ARG_LT (error code: -15): invalid argument of nSize of nSrcSize

OE_NOT_STRICTLY_INCREASING (error code: -17): pSrcX[i], i=0,1,...,nSrcSize-1 not strictly increasing

OE_REAL_ARG_LT(error code: -14): invalid dSmoothingFactor

OE_ALLOC_FAIL (error code: -19): memory allocation failed

OE_COEFF_CONV (error code: - 23): the iterative process has failed to converge using method INTERP_TYPE_BSPLINE. Possibly dSmoothingFactor is too small

Examples

EX1

//Assume that Active worksheet has 4 columns A,B,C and D. Column C and D are x and y data of curve. Column C is in ascending order.
//Column A is x data to be evaluated, interpolation result will be output into column B.
    void    ocmath_interpolate_ex1(double dd = 1)
    {
        int nMode = INTERP_TYPE_BSPLINE;
        double dSmoothingFactor = dd;
        Worksheet    wks = Project.ActiveLayer();
        wks.SetSize(-1, 4);
        DataRange drIn;
        drIn.Add("X", wks, 0, 0, -1, 0);
        drIn.Add("X", wks, 0, 1, -1, 1);
        drIn.Add("X", wks, 0, 2, -1, 2);
        drIn.Add("X", wks, 0, 3, -1, 3);
    
        vector vx, vy, vSrcx, vSrcy;
        drIn.GetData(&vx, 0);
        //drIn.GetData(&vy, 1);
        drIn.GetData(&vSrcx, 2);
        drIn.GetData(&vSrcy, 3);
        
        int    nSize = vx.GetSize();
        int    nSrcSize = vSrcx.GetSize();
        vy.SetSize(nSize);
        
        int iRet = ocmath_interpolate(vx, vy, nSize, vSrcx, vSrcy, nSrcSize, nMode, dSmoothingFactor);
        drIn.SetData(vy, true, 1);//interpolation result 
    }

Remark

Interpolation. Three modes are available: Linear, Spline, B-Spline.

When the mode is B-Spline, if your data, which will be interpolated or extrapolated, is in the interval of the B-Spline, this function calls B-Spline functions of nag to interpolate it, otherwise this function uses the nearest two end points to extend the B-Spline polynomial by linear interpolation.

cf. Dierckx P: an algorithm for smoothing, differentiation and integration of experimental data using spline functions, J.Comp.Appl.Maths 1 (1975) 165-184.