library: libGraf #include "TGraphSmooth.h"

# TGraphSmooth

class description - source file - inheritance tree (.pdf)

## class TGraphSmooth : public TNamed

| Inheritance Chart:
`TObject`
| <- | `TNamed`
| <- | `TGraphSmooth` |

        public:

                          TGraphSmooth()
                          TGraphSmooth(const char* name)
                          TGraphSmooth(const TGraphSmooth&)
                  virtual ~TGraphSmooth()
                  TGraph* Approx(TGraph* grin, Option_t* option = "linear", Int_t nout = 50, Double_t* xout = 0, Double_t yleft = 0, Double_t yright = 0, Int_t rule = 0, Double_t f = 0, Option_t* ties = "mean")
          static Double_t Approx1(Double_t v, Double_t f, Double_t* x, Double_t* y, Int_t n, Int_t iKind, Double_t Ylow, Double_t Yhigh)
                     void Approxin(TGraph* grin, Int_t iKind, Double_t& Ylow, Double_t& Yhigh, Int_t rule, Int_t iTies)
              static void BDRksmooth(Double_t* x, Double_t* y, Int_t n, Double_t* xp, Double_t* yp, Int_t np, Int_t kernel, Double_t bw)
              static void BDRsmooth(Int_t n, Double_t* x, Double_t* y, Double_t* w, Double_t span, Int_t iper, Double_t vsmlsq, Double_t* smo, Double_t* acvr)
              static void BDRsupsmu(Int_t n, Double_t* x, Double_t* y, Double_t* w, Int_t iper, Double_t span, Double_t alpha, Double_t* smo, Double_t* sc)
           static TClass* Class()
          virtual TClass* IsA() const
                     void Lowess(Double_t* x, Double_t* y, Int_t n, Double_t* ys, Double_t span, Int_t iter, Double_t delta)
              static void Lowest(Double_t* x, Double_t* y, Int_t n, Double_t& xs, Double_t& ys, Int_t nleft, Int_t nright, Double_t* w, Bool_t userw, Double_t* rw, Bool_t& ok)
            TGraphSmooth& operator=(const TGraphSmooth&)
              static void Psort(Double_t* x, Int_t n, Int_t k)
              static void Rank(Int_t n, Double_t* a, Int_t* index, Int_t* rank, Bool_t down = kTRUE)
             static Int_t Rcmp(Double_t x, Double_t y)
             virtual void ShowMembers(TMemberInspector& insp, char* parent)
                     void Smoothin(TGraph* grin)
                  TGraph* SmoothKern(TGraph* grin, Option_t* option = "normal", Double_t bandwidth = 0.5, Int_t nout = 100, Double_t* xout = 0)
                  TGraph* SmoothLowess(TGraph* grin, Option_t* option = "", Double_t span = 0.67, Int_t iter = 3, Double_t delta = 0)
                  TGraph* SmoothSuper(TGraph* grin, Option_t* option = "", Double_t bass = 0, Double_t span = 0, Bool_t isPeriodic = kFALSE, Double_t* w = 0)
             virtual void Streamer(TBuffer& b)
                     void StreamerNVirtual(TBuffer& b)

### Data Members

        protected:

             Int_t fNin   Number of input points
             Int_t fNout  Number of output points
           TGraph* fGin   Input graph
           TGraph* fGout  Output graph
          Double_t fMinX  Minimum value of array X
          Double_t fMaxX  Maximum value of array X

## Class Description

     TGraphSmooth

     A helper class to smooth TGraph
     see examples in $ROOTSYS/tutorials/motorcycle.C and approx.C

    ______________________________________________________________________

TGraphSmooth(): TNamed()

    *-*-*-*-*-*-*-*-*Default GraphSmooth constructor *-*-*-*-*-*-*-*-*-*-*
                     ===============================

TGraphSmooth(const char *name): TNamed(name,"")

    *-*-*-*-*-*-*-*-*GraphSmooth constructor *-*-*-*-*-*-*-*-*-*-*-*-*-*-*
                     =======================

~TGraphSmooth()

    *-*-*-*-*-*-*-*-*GraphSmooth destructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
                     ======================

void Smoothin(TGraph *grin)

    *-*-*-*-*-*-*-*-*Sort input data points*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
                     ======================

TGraph* SmoothKern(TGraph *grin, Option_t *option, Double_t bandwidth, Int_t nout, Double_t *xout)

    *-*-*-*-*-*-*-*-*Smooth data with Kernel smoother*-*-*-*-*-*-*-*-*-*-*
                     ================================

     Smooth grin with the Nadaraya-Watson kernel regression estimate.

     Arguments:
     grin:      input graph

     option:    the kernel to be used: "box", "normal"
     bandwidth: the bandwidth. The kernels are scaled so that their quartiles
                (viewed as probability densities) are at +/- 0.25*bandwidth.
     nout:      If xout is not specified, interpolation takes place at equally
                spaced points spanning the interval [min(x), max(x)], where
                nout = max(nout, number of input data).
     xout:      an optional set of values at which to evaluate the fit

void BDRksmooth(Double_t *x, Double_t *y, Int_t n, Double_t *xp, Double_t *yp, Int_t np, Int_t kernel, Double_t bw)

    *-*-*-*-*-*-*-*-*Smooth data with specified kernel*-*-*-*-*-*-*-*-*-*-*
    *-*              =================================

       Based on R function ksmooth: Translated to C++ by C. Stratowa
       (R source file: ksmooth.c by B.D.Ripley Copyright (C) 1998)

    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

TGraph* SmoothLowess(TGraph *grin, Option_t *option , Double_t span, Int_t iter, Double_t delta)

    *-*-*-*-*-*-*-*-*Smooth data with Lowess smoother*-*-*-*-*-*-*-*-*-*-*
                     ================================

     This function performs the computations for the LOWESS smoother
     (see the reference below). Lowess returns the output points
     x and y which give the coordinates of the smooth.

     Arguments:
     grin:  Input graph

     span:  the smoother span. This gives the proportion of points in the plot
            which influence the smooth at each value.
            Larger values give more smoothness.
     iter:  the number of robustifying iterations which should be performed.
            Using smaller values of iter will make lowess run faster.
     delta: values of x which lie within delta of each other replaced by a
            single value in the output from lowess.
            For delta = 0, delta will be calculated.

     References:
     Cleveland, W. S. (1979) Robust locally weighted regression and smoothing
            scatterplots. J. Amer. Statist. Assoc. 74, 829-836.
     Cleveland, W. S. (1981) LOWESS: A program for smoothing scatterplots
            by robust locally weighted regression.
            The American Statistician, 35, 54.
                     ==================

void Lowess(Double_t *x, Double_t *y, Int_t n, Double_t *ys, Double_t span, Int_t iter, Double_t delta)

    *-*-*-*-*-*-*-*-*Lowess regression smoother*-*-*-*-*-*-*-*-*-*-*-*-*-*
                     ==========================
       Based on R function clowess: Translated to C++ by C. Stratowa
       (R source file: lowess.c by R Development Core Team (C) 1999-2001)

    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

void Lowest(Double_t *x, Double_t *y, Int_t n, Double_t &xs, Double_t &ys, Int_t nleft, Int_t nright, Double_t *w, Bool_t userw, Double_t *rw, Bool_t &ok)

    *-*-*-*-*-*-*-*-*Fit value at x[i] *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
                     =================
      Based on R function lowest: Translated to C++ by C. Stratowa
      (R source file: lowess.c by R Development Core Team (C) 1999-2001)

    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

TGraph* SmoothSuper(TGraph *grin, Option_t *, Double_t bass, Double_t span, Bool_t isPeriodic, Double_t *w)

    *-*-*-*-*-*-*-*-*Smooth data with Super smoother*-*-*-*-*-*-*-*-*-*-*-*
                     ===============================

     Smooth the (x, y) values by Friedman's ``super smoother''.

     Arguments:
     grin: graph for smoothing

     span: the fraction of the observations in the span of the running lines
            smoother, or 0 to choose this by leave-one-out cross-validation.
     bass: controls the smoothness of the fitted curve.
            Values of up to 10 indicate increasing smoothness.
     isPeriodic: if TRUE, the x values are assumed to be in [0, 1]
            and of period 1.
     w:     case weights

     Details:
     supsmu is a running lines smoother which chooses between three spans for
     the lines. The running lines smoothers are symmetric, with k/2 data points
     each side of the predicted point, and values of k as 0.5 * n, 0.2 * n and
     0.05 * n, where n is the number of data points. If span is specified,
     a single smoother with span span * n is used.

     The best of the three smoothers is chosen by cross-validation for each
     prediction. The best spans are then smoothed by a running lines smoother
     and the final prediction chosen by linear interpolation.

     The FORTRAN code says: ``For small samples (n < 40) or if there are
     substantial serial correlations between observations close in x - value,
     then a prespecified fixed span smoother (span > 0) should be used.
     Reasonable span values are 0.2 to 0.4.''

     References:
     Friedman, J. H. (1984) SMART User's Guide.
               Laboratory for Computational Statistics,
               Stanford University Technical Report No. 1.

     Friedman, J. H. (1984) A variable span scatterplot smoother.
               Laboratory for Computational Statistics,
               Stanford University Technical Report No. 5.
                     ==================

void BDRsupsmu(Int_t n, Double_t *x, Double_t *y, Double_t *w, Int_t iper, Double_t span, Double_t alpha, Double_t *smo, Double_t *sc)

    *-*-*-*-*-*-*-*-*Friedmannīs super smoother *-*-*-*-*-*-*-*-*-*-*-*-*-*
                     ==========================

      super smoother (Friedman, 1984).

      version 10/10/84

      coded  and copywrite (c) 1984 by:

                             Jerome H. Friedman
                          department of statistics
                                    and
                     stanford linear accelerator center
                             stanford university

      all rights reserved.

      input:
         n : number of observations (x,y - pairs).
         x(n) : ordered abscissa values.
         y(n) : corresponding ordinate (response) values.
         w(n) : weight for each (x,y) observation.
         iper : periodic variable flag.
            iper=1 => x is ordered interval variable.
            iper=2 => x is a periodic variable with values
                      in the range (0.0,1.0) and period 1.0.
         span : smoother span (fraction of observations in window).
                span=0.0 => automatic (variable) span selection.
         alpha : controls high frequency (small span) penality
                 used with automatic span selection (bass tone control).
                 (alpha.le.0.0 or alpha.gt.10.0 => no effect.)
      output:
        smo(n) : smoothed ordinate (response) values.
      scratch:
        sc(n,7) : internal working storage.

      note:
         for small samples (n < 40) or if there are substantial serial
         correlations between observations close in x - value, then
         a prespecified fixed span smoother (span > 0) should be
         used. reasonable span values are 0.2 to 0.4.

     current implementation:
       Based on R function supsmu: Translated to C++ by C. Stratowa
       (R source file: ppr.f by B.D.Ripley Copyright (C) 1994-97)

    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

void BDRsmooth(Int_t n, Double_t *x, Double_t *y, Double_t *w, Double_t span, Int_t iper, Double_t vsmlsq, Double_t *smo, Double_t *acvr)

    *-*-*-*-*-*-*-*-* Function for super smoother *-*-*-*-*-*-*-*-*-*-*-*
                     ============================

       Based on R function supsmu: Translated to C++ by C. Stratowa
       (R source file: ppr.f by B.D.Ripley Copyright (C) 1994-97)

    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

void Approxin(TGraph *grin, Int_t /*iKind*/, Double_t &Ylow, Double_t &Yhigh, Int_t rule, Int_t iTies)

    *-*-*-*-*-*-*-*-*Sort data points and eliminate double x values*-*-*-*
                     ==============================================

TGraph* Approx(TGraph *grin, Option_t *option, Int_t nout, Double_t *xout, Double_t yleft, Double_t yright, Int_t rule, Double_t f, Option_t *ties)

    *-*-*-*-*-*-*-*-*Approximate data points*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
                     =======================

     Arguments:
     grin:  graph giving the coordinates of the points to be interpolated.
            Alternatively a single plotting structure can be specified:

     option: specifies the interpolation method to be used.
            Choices are "linear" (iKind = 1) or "constant" (iKind = 2).
     nout:  If xout is not specified, interpolation takes place at n equally
            spaced points spanning the interval [min(x), max(x)], where
            nout = max(nout, number of input data).
     xout:  an optional set of values specifying where interpolation is to
            take place.
     yleft: the value to be returned when input x values less than min(x).
            The default is defined by the value of rule given below.
     yright: the value to be returned when input x values greater than max(x).
            The default is defined by the value of rule given below.
     rule:  an integer describing how interpolation is to take place outside
            the interval [min(x), max(x)]. If rule is 0 then the given yleft
            and yright values are returned, if it is 1 then 0 is returned
            for such points and if it is 2, the value at the closest data
            extreme is used.
     f:     For method="constant" a number between 0 and 1 inclusive,
            indicating a compromise between left- and right-continuous step
            functions. If y0 and y1 are the values to the left and right of
            the point then the value is y0*f+y1*(1-f) so that f=0 is
            right-continuous and f=1 is left-continuous
     ties:  Handling of tied x values. An integer describing a function with
            a single vector argument returning a single number result:
            ties = "ordered" (iTies = 0): input x are "ordered"
            ties = "mean"    (iTies = 1): function "mean"
            ties = "min"     (iTies = 2): function "min"
            ties = "max"     (iTies = 3): function "max"

     Details:
     At least two complete (x, y) pairs are required.
     If there are duplicated (tied) x values and ties is a function it is
     applied to the y values for each distinct x value. Useful functions in
     this context include mean, min, and max.
     If ties="ordered" the x values are assumed to be already ordered. The
     first y value will be used for interpolation to the left and the last
     one for interpolation to the right.

     Value:
     approx returns a graph with components x and y, containing n coordinates
     which interpolate the given data points according to the method (and rule)
     desired.

Double_t Approx1(Double_t v, Double_t f, Double_t *x, Double_t *y, Int_t n, Int_t iKind, Double_t Ylow, Double_t Yhigh)

    *-*-*-*-*-*-*-*-*Approximate one data point*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*              ==========================

       Approximate  y(v),  given (x,y)[i], i = 0,..,n-1
       Based on R function approx1: Translated to C++ by Christian Stratowa
       (R source file: approx.c by R Development Core Team (C) 1999-2001)

Int_t Rcmp(Double_t x, Double_t y)

       static function
       if (ISNAN(x))	return 1;
       if (ISNAN(y))	return -1;

void Psort(Double_t *x, Int_t n, Int_t k)

       static function
       based on R function rPsort: adapted to C++ by Christian Stratowa
       (R source file: R_sort.c by R Development Core Team (C) 1999-2001)

void Rank(Int_t n, Double_t *a, Int_t *index, Int_t *rank, Bool_t down)

       static function

### Inline Functions

                  TClass* Class()
                  TClass* IsA() const
                     void ShowMembers(TMemberInspector& insp, char* parent)
                     void Streamer(TBuffer& b)
                     void StreamerNVirtual(TBuffer& b)
             TGraphSmooth TGraphSmooth(const TGraphSmooth&)
            TGraphSmooth& operator=(const TGraphSmooth&)

Author: Christian Stratowa 30/09/2001
Last update: root/graf:$Name: $:$Id: TGraphSmooth.cxx,v 1.7 2002/12/02 18:50:02 rdm Exp $