# TH1*¶

继承 public TNamed, public TAttLine, public TAttFill, public TAttMarker

TH1C : histograms with one byte per channel. Maximum bin content = 127

TH1S : histograms with one short per channel. Maximum bin content = 32767

TH1I : histograms with one int per channel. Maximum bin content = 2147483647

TH1F : histograms with one float per channel. Maximum precision 7 digits

TH1D : histograms with one double per channel. Maximum precision 14 digits

```
The TH*C classes also inherit from the array class TArrayC.
The TH*S classes also inherit from the array class TArrayS.
The TH*I classes also inherit from the array class TArrayI.
The TH*F classes also inherit from the array class TArrayF.
The TH*D classes also inherit from the array class TArrayD.
```

When an histogram is created, a reference to it is automatically added to the list of in-memory objects for the current file or directory. This default behaviour can be changed by:

```
h->SetDirectory(0); // for the current histogram h
TH1::AddDirectory(kFALSE); // sets a global switch disabling the reference
```

When the histogram is deleted, the reference to it is removed from the list of objects in memory. When a file is closed, all histograms in memory associated with this file are automatically deleted.

All histogram types support either fix or variable bin sizes. 2-D histograms may have fix size bins along X and variable size bins along Y or vice-versa. The functions to fill, manipulate, draw or access histograms are identical in both cases.

Convention for numbering bins

For all histogram types: nbins, xlow, xup

```
bin = 0; underflow bin
bin = 1; first bin with low-edge xlow INCLUDED
bin = nbins; last bin with upper-edge xup EXCLUDED
bin = nbins+1; overflow bin
```

## class¶

```
// TH1 status bits
enum {
kNoStats = BIT(9), // don't draw stats box
kUserContour = BIT(10), // user specified contour levels
//kCanRebin = BIT(11), // FIXME DEPRECATED - to be removed, replaced by SetCanExtend / CanExtendAllAxes
kLogX = BIT(15), // X-axis in log scale
kIsZoomed = BIT(16), // bit set when zooming on Y axis
kNoTitle = BIT(17), // don't draw the histogram title
kIsAverage = BIT(18), // Bin contents are average (used by Add)
kIsNotW = BIT(19) // Histogram is forced to be not weighted even when the histogram is filled with weighted different than 1.
};
// size of statistics data (size of array used in GetStats()/ PutStats )
// s[0] = sumw s[1] = sumw2
// s[2] = sumwx s[3] = sumwx2
// s[4] = sumwy s[5] = sumwy2 s[6] = sumwxy
// s[7] = sumwz s[8] = sumwz2 s[9] = sumwxz s[10] = sumwyz
// s[11] = sumwt s[12] = sumwt2 (11 and 12 used only by TProfile3D)
enum {
kNstat = 13 // size of statistics data (up to TProfile3D)
};
virtual ~TH1();
virtual Bool_t Add(TF1 *h1, Double_t c1=1, Option_t *option="");
/// Performs the operation: this = this + c1*f1
/// if errors are defined (see TH1::Sumw2), errors are also recalculated.
/// By default, the function is computed at the centre of the bin.
/// if option "I" is specified (1-d histogram only), the integral of the
/// function in each bin is used instead of the value of the function at
/// the centre of the bin.
/// Only bins inside the function range are recomputed.
/// IMPORTANT NOTE: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Add
/// The function return kFALSE if the Add operation failed
virtual Bool_t Add(const TH1 *h1, Double_t c1=1);//该函数是将h1直方图进行c1倍的放大或缩小后加到当前直方图中。
/// Performs the operation: this = this + c1*h1
/// If errors are defined (see TH1::Sumw2), errors are also recalculated.
/// Note that if h1 has Sumw2 set, Sumw2 is automatically called for this
/// if not already set.
/// Note also that adding histogram with labels is not supported, histogram will be
/// added merging them by bin number independently of the labels.
/// For adding histogram with labels one should use TH1::Merge
/// SPECIAL CASE (Average/Efficiency histograms)
/// For histograms representing averages or efficiencies, one should compute the average
/// of the two histograms and not the sum. One can mark a histogram to be an average
/// histogram by setting its bit kIsAverage with
/// myhist.SetBit(TH1::kIsAverage);
/// Note that the two histograms must have their kIsAverage bit set
/// IMPORTANT NOTE1: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Add
/// IMPORTANT NOTE2: if h1 has a normalisation factor, the normalisation factor
/// is used , ie this = this + c1*factor*h1
/// Use the other TH1::Add function if you do not want this feature
/// The function return kFALSE if the Add operation failed
virtual Bool_t Add(const TH1 *h, const TH1 *h2, Double_t c1=1, Double_t c2=1); // *MENU* 将 h1 放大或缩小 c1 倍加上 h2 放大或缩小 c2 倍相加赋给 h。
/// Replace contents of this histogram by the addition of h1 and h2.
///this = c1*h1 + c2*h2
///if errors are defined (see TH1::Sumw2), errors are also recalculated
///Note that if h1 or h2 have Sumw2 set, Sumw2 is automatically called for this
///if not already set.
///Note also that adding histogram with labels is not supported, histogram will be
///added merging them by bin number independently of the labels.
///For adding histogram ith labels one should use TH1::Merge
/// SPECIAL CASE (Average/Efficiency histograms)
/// For histograms representing averages or efficiencies, one should compute the average
/// of the two histograms and not the sum. One can mark a histogram to be an average
/// histogram by setting its bit kIsAverage with
/// myhist.SetBit(TH1::kIsAverage);
/// Note that the two histograms must have their kIsAverage bit set
/// IMPORTANT NOTE: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Add
/// ANOTHER SPECIAL CASE : h1 = h2 and c2 < 0
/// do a scaling this = c1 * h1 / (bin Volume)
/// The function returns kFALSE if the Add operation failed
virtual void AddBinContent(Int_t bin);//在第 bin 个 bin 上计数加一。
virtual void AddBinContent(Int_t bin, Double_t w);/// Increment bin content by a weight w.
static void AddDirectory(Bool_t add=kTRUE);
/// Sets the flag controlling the automatic add of histograms in memory
/// By default (fAddDirectory = kTRUE), histograms are automatically added
/// to the list of objects in memory.
/// Note that one histogram can be removed from its support directory
/// by calling h->SetDirectory(0) or h->SetDirectory(dir) to add it
/// to the list of objects in the directory dir.
/// NOTE that this is a static function. To call it, use;
/// TH1::AddDirectory
static Bool_t AddDirectoryStatus();///static function: cannot be inlined on Windows/NT
virtual void Browse(TBrowser *b);/// Browe the Histogram object.
virtual Bool_t CanExtendAllAxes() const;/// returns true if all axes are extendable
virtual Double_t Chi2Test(const TH1* h2, Option_t *option = "UU", Double_t *res = 0) const;
/// chi^{2} test for comparing weighted and unweighted histograms
/// Function: Returns p-value. Other return values are specified by the 3rd parameter
/// \param[in] h2 the second histogram
/// \param[in] option
/// - "UU" = experiment experiment comparison (unweighted-unweighted)
/// - "UW" = experiment MC comparison (unweighted-weighted). Note that
/// the first histogram should be unweighted
/// - "WW" = MC MC comparison (weighted-weighted)
/// - "NORM" = to be used when one or both of the histograms is scaled
/// but the histogram originally was unweighted
/// - by default underflows and overlows are not included:
/// * "OF" = overflows included
/// * "UF" = underflows included
/// - "P" = print chi2, ndf, p_value, igood
/// - "CHI2" = returns chi2 instead of p-value
/// - "CHI2/NDF" = returns #chi^{2}/ndf
/// \param[in] res not empty - computes normalized residuals and returns them in this array
/// The current implementation is based on the papers chi^{2} test for comparison
/// of weighted and unweighted histograms" in Proceedings of PHYSTAT05 and
/// "Comparison weighted and unweighted histograms", arXiv:physics/0605123
/// by N.Gagunashvili. This function has been implemented by Daniel Haertl in August 2006.
/// Introduction:
/// A frequently used technique in data analysis is the comparison of
/// histograms. First suggested by Pearson [1] the #chi^{2} test of
/// homogeneity is used widely for comparing usual (unweighted) histograms.
/// This paper describes the implementation modified #chi^{2} tests
/// for comparison of weighted and unweighted histograms and two weighted
/// histograms [2] as well as usual Pearson's #chi^{2} test for
/// comparison two usual (unweighted) histograms.
/// Overview:
/// Comparison of two histograms expect hypotheses that two histograms
/// represent identical distributions. To make a decision p-value should
/// be calculated. The hypotheses of identity is rejected if the p-value is
/// lower then some significance level. Traditionally significance levels
/// 0.1, 0.05 and 0.01 are used. The comparison procedure should include an
/// analysis of the residuals which is often helpful in identifying the
/// bins of histograms responsible for a significant overall #chi^{2} value.
/// Residuals are the difference between bin contents and expected bin
/// contents. Most convenient for analysis are the normalized residuals. If
/// hypotheses of identity are valid then normalized residuals are
/// approximately independent and identically distributed random variables
/// having N(0,1) distribution. Analysis of residuals expect test of above
/// mentioned properties of residuals. Notice that indirectly the analysis
/// of residuals increase the power of #chi^{2} test.
/// Methods of comparison:
/// #chi^{2} test for comparison two (unweighted) histograms:
/// Let us consider two histograms with the same binning and the number
/// of bins equal to r. Let us denote the number of events in the ith bin
/// in the first histogram as ni and as mi in the second one. The total
/// number of events in the first histogram is equal to:
/// \f[
/// N = \sum_{i=1}^{r} n_{i}
/// \f]
/// and
/// \f[
/// M = \sum_{i=1}^{r} m_{i}
/// \f]
/// in the second histogram. The hypothesis of identity (homogeneity) [3]
/// is that the two histograms represent random values with identical
/// distributions. It is equivalent that there exist r constants p1,...,pr,
/// such that
/// \f[
///\sum_{i=1}^{r} p_{i}=1
/// \f]
/// and the probability of belonging to the ith bin for some measured value
/// in both experiments is equal to pi. The number of events in the ith
/// bin is a random variable with a distribution approximated by a Poisson
/// probability distribution
/// \f[
///\frac{e^{-Np_{i}}(Np_{i})^{n_{i}}}{n_{i}!}
/// \f]
///for the first histogram and with distribution
/// \f[
///\frac{e^{-Mp_{i}}(Mp_{i})^{m_{i}}}{m_{i}!}
/// \f]
/// for the second histogram. If the hypothesis of homogeneity is valid,
/// then the maximum likelihood estimator of pi, i=1,...,r, is
/// \f[
///\hat{p}_{i}= \frac{n_{i}+m_{i}}{N+M}
/// \f]
/// and then
/// \f[
/// X^{2} = \sum_{i=1}^{r}\frac{(n_{i}-N\hat{p}_{i})^{2}}{N\hat{p}_{i}} + \sum_{i=1}^{r}\frac{(m_{i}-M\hat{p}_{i})^{2}}{M\hat{p}_{i}} =\frac{1}{MN} \sum_{i=1}^{r}\frac{(Mn_{i}-Nm_{i})^{2}}{n_{i}+m_{i}}
/// \f]
/// has approximately a \f$ \chi^{2}_{(r-1)} \f$ distribution [3].
/// The comparison procedure can include an analysis of the residuals which
/// is often helpful in identifying the bins of histograms responsible for
/// a significant overall #chi^{2} value. Most convenient for
/// analysis are the adjusted (normalized) residuals [4]
/// \f[
/// r_{i} = \frac{n_{i}-N\hat{p}_{i}}{\sqrt{N\hat{p}_{i}}\sqrt{(1-N/(N+M))(1-(n_{i}+m_{i})/(N+M))}}
/// \f]
/// If hypotheses of homogeneity are valid then residuals ri are
/// approximately independent and identically distributed random variables
/// having N(0,1) distribution. The application of the #chi^{2} test has
/// restrictions related to the value of the expected frequencies Npi,
/// Mpi, i=1,...,r. A conservative rule formulated in [5] is that all the
/// expectations must be 1 or greater for both histograms. In practical
/// cases when expected frequencies are not known the estimated expected
/// frequencies \f$ M\hat{p}_{i}, N\hat{p}_{i}, i=1,...,r \f$ can be used.
/// Unweighted and weighted histograms comparison:
/// A simple modification of the ideas described above can be used for the
/// comparison of the usual (unweighted) and weighted histograms. Let us
/// denote the number of events in the ith bin in the unweighted
/// histogram as ni and the common weight of events in the ith bin of the
/// weighted histogram as wi. The total number of events in the
/// unweighted histogram is equal to
///\f[
/// N = \sum_{i=1}^{r} n_{i}
///\f]
/// and the total weight of events in the weighted histogram is equal to
///\f[
/// W = \sum_{i=1}^{r} w_{i}
///\f]
/// Let us formulate the hypothesis of identity of an unweighted histogram
/// to a weighted histogram so that there exist r constants p1,...,pr, such
/// that
///\f[
/// \sum_{i=1}^{r} p_{i} = 1
///\f]
/// for the unweighted histogram. The weight wi is a random variable with a
/// distribution approximated by the normal probability distribution
/// \f$ N(Wp_{i},\sigma_{i}^{2}) \f$ where \f$ \sigma_{i}^{2} \f$ is the variance of the weight wi.
/// If we replace the variance \f$ \sigma_{i}^{2} \f$
/// with estimate \f$ s_{i}^{2} \f$ (sum of squares of weights of
/// events in the ith bin) and the hypothesis of identity is valid, then the
/// maximum likelihood estimator of pi,i=1,...,r, is
///\f[
/// \hat{p}_{i} = \frac{Ww_{i}-Ns_{i}^{2}+\sqrt{(Ww_{i}-Ns_{i}^{2})^{2}+4W^{2}s_{i}^{2}n_{i}}}{2W^{2}}
///\f]
/// We may then use the test statistic
///\f[
/// X^{2} = \sum_{i=1}^{r} \frac{(n_{i}-N\hat{p}_{i})^{2}}{N\hat{p}_{i}} + \sum_{i=1}^{r} \frac{(w_{i}-W\hat{p}_{i})^{2}}{s_{i}^{2}}
///\f]
/// and it has approximately a \f$ \sigma^{2}_{(r-1)} \f$ distribution [2]. This test, as well
/// as the original one [3], has a restriction on the expected frequencies. The
/// expected frequencies recommended for the weighted histogram is more than 25.
/// The value of the minimal expected frequency can be decreased down to 10 for
/// the case when the weights of the events are close to constant. In the case
/// of a weighted histogram if the number of events is unknown, then we can
/// apply this recommendation for the equivalent number of events as
///\f[
/// n_{i}^{equiv} = \frac{ w_{i}^{2} }{ s_{i}^{2} }
///\f]
/// The minimal expected frequency for an unweighted histogram must be 1. Notice
/// that any usual (unweighted) histogram can be considered as a weighted
/// histogram with events that have constant weights equal to 1.
/// The variance \f$ z_{i}^{2} \f$ of the difference between the weight wi
/// and the estimated expectation value of the weight is approximately equal to:
///\f[
/// z_{i}^{2} = Var(w_{i}-W\hat{p}_{i}) = N\hat{p}_{i}(1-N\hat{p}_{i})\left(\frac{Ws_{i}^{2}}{\sqrt{(Ns_{i}^{2}-w_{i}W)^{2}+4W^{2}s_{i}^{2}n_{i}}}\right)^{2}+\frac{s_{i}^{2}}{4}\left(1+\frac{Ns_{i}^{2}-w_{i}W}{\sqrt{(Ns_{i}^{2}-w_{i}W)^{2}+4W^{2}s_{i}^{2}n_{i}}}\right)^{2}
///\f]
/// The residuals
///\f[
/// r_{i} = \frac{w_{i}-W\hat{p}_{i}}{z_{i}}
///\f]
/// have approximately a normal distribution with mean equal to 0 and standard
/// deviation equal to 1.
/// Two weighted histograms comparison:
/// Let us denote the common weight of events of the ith bin in the first
/// histogram as w1i and as w2i in the second one. The total weight of events
/// in the first histogram is equal to
///\f[
/// W_{1} = \sum_{i=1}^{r} w_{1i}
///\f]
/// and
///\f[
/// W_{2} = \sum_{i=1}^{r} w_{2i}
///\f]
/// in the second histogram. Let us formulate the hypothesis of identity of
/// weighted histograms so that there exist r constants p1,...,pr, such that
///\f[
/// \sum_{i=1}^{r} p_{i} = 1
///\f]
/// and also expectation value of weight w1i equal to W1pi and expectation value
/// of weight w2i equal to W2pi. Weights in both the histograms are random
/// variables with distributions which can be approximated by a normal
/// probability distribution \f$ N(W_{1}p_{i},\sigma_{1i}^{2}) \f$ for the first histogram
/// and by a distribution \f$ N(W_{2}p_{i},\sigma_{2i}^{2}) \f$ for the second.
/// Here \f$ \sigma_{1i}^{2} \f$ and \f$ \sigma_{2i}^{2} \f$ are the variances
/// of w1i and w2i with estimators \f$ s_{1i}^{2} \f$ and \f$ s_{2i}^{2} \f$ respectively.
/// If the hypothesis of identity is valid, then the maximum likelihood and
/// Least Square Method estimator of pi,i=1,...,r, is
///\f[
/// \hat{p}_{i} = \frac{w_{1i}W_{1}/s_{1i}^{2}+w_{2i}W_{2} /s_{2i}^{2}}{W_{1}^{2}/s_{1i}^{2}+W_{2}^{2}/s_{2i}^{2}}
///\f]
/// We may then use the test statistic
///\f[
/// X^{2} = \sum_{i=1}^{r} \frac{(w_{1i}-W_{1}\hat{p}_{i})^{2}}{s_{1i}^{2}} + \sum_{i=1}^{r} \frac{(w_{2i}-W_{2}\hat{p}_{i})^{2}}{s_{2i}^{2}} = \sum_{i=1}^{r} \frac{(W_{1}w_{2i}-W_{2}w_{1i})^{2}}{W_{1}^{2}s_{2i}^{2}+W_{2}^{2}s_{1i}^{2}}
///\f]
/// and it has approximately a \f$ \chi^{2}_{(r-1)} \f$ distribution [2].
/// The normalized or studentised residuals [6]
///\f[
/// r_{i} = \frac{w_{1i}-W_{1}\hat{p}_{i}}{s_{1i}\sqrt{1 - \frac{1}{(1+W_{2}^{2}s_{1i}^{2}/W_{1}^{2}s_{2i}^{2})}}}
///\f]
/// have approximately a normal distribution with mean equal to 0 and standard
/// deviation 1. A recommended minimal expected frequency is equal to 10 for
/// the proposed test.
/// Numerical examples:
/// The method described herein is now illustrated with an example.
/// We take a distribution
///\f[
/// \phi(x) = \frac{2}{(x-10)^{2}+1} + \frac{1}{(x-14)^{2}+1} (1)
///\f]
/// defined on the interval [4,16]. Events distributed according to the formula
/// (1) are simulated to create the unweighted histogram. Uniformly distributed
/// events are simulated for the weighted histogram with weights calculated by
/// formula (1). Each histogram has the same number of bins: 20. Fig.1 shows
/// the result of comparison of the unweighted histogram with 200 events
/// (minimal expected frequency equal to one) and the weighted histogram with
/// 500 events (minimal expected frequency equal to 25)
/// Begin_Macro
/// ../../../tutorials/math/chi2test.C
/// End_Macro
/// Fig 1. An example of comparison of the unweighted histogram with 200 events
/// and the weighted histogram with 500 events:
/// a) unweighted histogram;
/// b) weighted histogram;
/// c) normalized residuals plot;
/// d) normal Q-Q plot of residuals.
/// The value of the test statistic \f$ \chi^{2} \f$ is equal to
/// 21.09 with p-value equal to 0.33, therefore the hypothesis of identity of
/// the two histograms can be accepted for 0.05 significant level. The behavior
/// of the normalized residuals plot (see Fig. 1c) and the normal Q-Q plot
/// (see Fig. 1d) of residuals are regular and we cannot identify the outliers
/// or bins with a big influence on \f$ \chi^{2} \f$.
/// The second example presents the same two histograms but 17 events was added
/// to content of bin number 15 in unweighted histogram. Fig.2 shows the result
/// of comparison of the unweighted histogram with 217 events (minimal expected
/// frequency equal to one) and the weighted histogram with 500 events (minimal
/// expected frequency equal to 25)
///Begin_Macro
/// ../../../tutorials/math/chi2test.C(17)
///End_Macro
/// Fig 2. An example of comparison of the unweighted histogram with 217 events
/// and the weighted histogram with 500 events:
/// a) unweighted histogram;
/// b) weighted histogram;
/// c) normalized residuals plot;
/// d) normal Q-Q plot of residuals.
/// The value of the test statistic \f$ \chi^{2} \f$ is equal to
/// 32.33 with p-value equal to 0.029, therefore the hypothesis of identity of
/// the two histograms is rejected for 0.05 significant level. The behavior of
/// the normalized residuals plot (see Fig. 2c) and the normal Q-Q plot (see
/// Fig. 2d) of residuals are not regular and we can identify the outlier or
/// bin with a big influence on \f$ \chi^{2} \f$.
virtual Double_t Chi2TestX(const TH1* h2, Double_t &chi2, Int_t &ndf, Int_t &igood,Option_t *option = "UU", Double_t *res = 0) const;
/// The computation routine of the Chisquare test. For the method description,
/// see Chi2Test() function.
/// \return p-value
/// \param[in] h2 the second histogram
/// \param[in] option
/// - "UU" = experiment experiment comparison (unweighted-unweighted)
/// - "UW" = experiment MC comparison (unweighted-weighted). Note that the first
/// histogram should be unweighted
/// - "WW" = MC MC comparison (weighted-weighted)
/// - "NORM" = if one or both histograms is scaled
/// - "OF" = overflows included
/// - "UF" = underflows included
/// by default underflows and overflows are not included
/// \param[out] igood test output
/// - igood=0 - no problems
/// - For unweighted unweighted comparison
/// - igood=1'There is a bin in the 1st histogram with less than 1 event'
/// - igood=2'There is a bin in the 2nd histogram with less than 1 event'
/// - igood=3'when the conditions for igood=1 and igood=2 are satisfied'
/// - For unweighted weighted comparison
/// - igood=1'There is a bin in the 1st histogram with less then 1 event'
/// - igood=2'There is a bin in the 2nd histogram with less then 10 effective number of events'
/// - igood=3'when the conditions for igood=1 and igood=2 are satisfied'
/// - For weighted weighted comparison
/// - igood=1'There is a bin in the 1st histogram with less then 10 effective
/// number of events'
/// - igood=2'There is a bin in the 2nd histogram with less then 10 effective
/// number of events'
/// - igood=3'when the conditions for igood=1 and igood=2 are satisfied'
/// \param[out] chi2 chisquare of the test
/// \param[out] ndf number of degrees of freedom (important, when both histograms have the same empty bins)
/// \param[out] res normalized residuals for further analysis
virtual Double_t Chisquare(TF1 * f1, Option_t *option = "") const;
/// Compute and return the chisquare of this histogram with respect to a function
/// The chisquare is computed by weighting each histogram point by the bin error
/// By default the full range of the histogram is used.
/// Use option "R" for restricting the chisquare calculation to the given range of the function
virtual void ClearUnderflowAndOverflow();
/// Remove all the content from the underflow and overflow bins, without changing the number of entries
/// After calling this method, every undeflow and overflow bins will have content 0.0
/// The Sumw2 is also cleared, since there is no more content in the bins
virtual Double_t ComputeIntegral(Bool_t onlyPositive = false);
/// Compute integral (cumulative sum of bins)
/// The result stored in fIntegral is used by the GetRandom functions.
/// This function is automatically called by GetRandom when the fIntegral
/// array does not exist or when the number of entries in the histogram
/// has changed since the previous call to GetRandom.
/// The resulting integral is normalized to 1
/// If the routine is called with the onlyPositive flag set an error will
/// be produced in case of negative bin content and a NaN value returned
TObject* Clone(const char* newname=0) const;//克隆直方图，这里的 Close 是新开辟一块内存空间存储新直方图的，克隆之后，原始直方图的修改或删除对克隆的直方图没有影响。而TH1D *hnew =h;这个只是将新建的对象指向 h 的地址。
virtual void Copy(TObject &hnew) const;/// Copy this to newth1
/// Copy this histogram structure to newth1.
/// Note that this function does not copy the list of associated functions.
/// Use TObject::Clone to make a full copy of an histogram.
/// Note also that the histogram it will be created in gDirectory (if AddDirectoryStatus()=true)
/// or will not be added to any directory if AddDirectoryStatus()=false
/// independently of the current directory stored in the original histogram
virtual void DirectoryAutoAdd(TDirectory *);
/// Perform the automatic addition of the histogram to the given directory
/// Note this function is called in place when the semantic requires
/// this object to be added to a directory (I.e. when being read from
/// a TKey or being Cloned)
virtual Int_t DistancetoPrimitive(Int_t px, Int_t py);
/// Compute distance from point px,py to a line.
/// Compute the closest distance of approach from point px,py to elements
/// of an histogram.
/// The distance is computed in pixels units.
/// Algorithm:
/// Currently, this simple model computes the distance from the mouse
/// to the histogram contour only.
virtual Bool_t Divide(TF1 *f1, Double_t c1=1);
/// Performs the operation: this = this/(c1*f1)
/// if errors are defined (see TH1::Sumw2), errors are also recalculated.
/// Only bins inside the function range are recomputed.
/// IMPORTANT NOTE: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Divide
/// The function return kFALSE if the divide operation failed
virtual Bool_t Divide(const TH1 *h1);
/// Divide this histogram by h1.
/// this = this/h1
/// if errors are defined (see TH1::Sumw2), errors are also recalculated.
/// Note that if h1 has Sumw2 set, Sumw2 is automatically called for this
/// if not already set.
/// The resulting errors are calculated assuming uncorrelated histograms.
/// See the other TH1::Divide that gives the possibility to optionally
/// compute binomial errors.
/// IMPORTANT NOTE: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Scale
/// The function return kFALSE if the divide operation failed
virtual Bool_t Divide(const TH1 *h1, const TH1 *h2, Double_t c1=1, Double_t c2=1, Option_t *option=""); // *MENU*
/// Replace contents of this histogram by the division of h1 by h2.
/// this = c1*h1/(c2*h2)
/// If errors are defined (see TH1::Sumw2), errors are also recalculated
/// Note that if h1 or h2 have Sumw2 set, Sumw2 is automatically called for this
/// if not already set.
/// The resulting errors are calculated assuming uncorrelated histograms.
/// However, if option ="B" is specified, Binomial errors are computed.
/// In this case c1 and c2 do not make real sense and they are ignored.
/// IMPORTANT NOTE: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Divide
/// Please note also that in the binomial case errors are calculated using standard
/// binomial statistics, which means when b1 = b2, the error is zero.
/// If you prefer to have efficiency errors not going to zero when the efficiency is 1, you must
/// use the function TGraphAsymmErrors::BayesDivide, which will return an asymmetric and non-zero lower
/// error for the case b1=b2.
/// The function return kFALSE if the divide operation failed
virtual void Draw(Option_t *option="");//画图
/// Draw this histogram with options.
/// Histograms are drawn via the THistPainter class. Each histogram has
/// a pointer to its own painter (to be usable in a multithreaded program).
/// The same histogram can be drawn with different options in different pads.
/// When an histogram drawn in a pad is deleted, the histogram is
/// automatically removed from the pad or pads where it was drawn.
/// If an histogram is drawn in a pad, then filled again, the new status
/// of the histogram will be automatically shown in the pad next time
/// the pad is updated. One does not need to redraw the histogram.
/// To draw the current version of an histogram in a pad, one can use
/// h->DrawCopy();
/// This makes a clone of the histogram. Once the clone is drawn, the original
/// histogram may be modified or deleted without affecting the aspect of the
/// clone.
/// By default, TH1::Draw clears the current pad.
/// One can use TH1::SetMaximum and TH1::SetMinimum to force a particular
/// value for the maximum or the minimum scale on the plot.
/// TH1::UseCurrentStyle can be used to change all histogram graphics
/// attributes to correspond to the current selected style.
/// This function must be called for each histogram.
/// In case one reads and draws many histograms from a file, one can force
/// the histograms to inherit automatically the current graphics style
/// by calling before gROOT->ForceStyle();
/// See the THistPainter class for a description of all the drawing options.
virtual TH1 *DrawCopy(Option_t *option="", const char * name_postfix = "_copy") const;
/// Copy this histogram and Draw in the current pad.
/// Once the histogram is drawn into the pad, any further modification
/// using graphics input will be made on the copy of the histogram,
/// and not to the original object.
/// By default a postfix "_copy" is added to the histogram name. Pass an empty postfix in case
/// you want to draw an histogram with the same name
/// See Draw for the list of options
virtual TH1 *DrawNormalized(Option_t *option="", Double_t norm=1) const;
/// Draw a normalized copy of this histogram.
/// A clone of this histogram is normalized to norm and drawn with option.
/// A pointer to the normalized histogram is returned.
/// The contents of the histogram copy are scaled such that the new
/// sum of weights (excluding under and overflow) is equal to norm.
/// Note that the returned normalized histogram is not added to the list
/// of histograms in the current directory in memory.
/// It is the user's responsability to delete this histogram.
/// The kCanDelete bit is set for the returned object. If a pad containing
/// this copy is cleared, the histogram will be automatically deleted.
/// See Draw for the list of options
virtual void DrawPanel(); // *MENU* Display a panel with all histogram drawing options. See class TDrawPanelHist for example
virtual Int_t BufferEmpty(Int_t action=0);
/// Fill histogram with all entries in the buffer.
/// action = -1 histogram is reset and refilled from the buffer (called by THistPainter::Paint)
/// action = 0 histogram is reset and filled from the buffer. When the histogram is filled from the
/// buffer the value fBuffer[0] is set to a negative number (= - number of entries)
/// When calling with action == 0 the histogram is NOT refilled when fBuffer[0] is < 0
/// While when calling with action = -1 the histogram is reset and ALWAYS refilled independently if
/// the histogram was filled before. This is needed when drawing the histogram
/// action = 1 histogram is filled and buffer is deleted
/// The buffer is automatically deleted when filling the histogram and the entries is
/// larger than the buffer size
virtual void Eval(TF1 *f1, Option_t *option="");
/// Evaluate function f1 at the center of bins of this histogram.
/// If option "R" is specified, the function is evaluated only
/// for the bins included in the function range.
/// If option "A" is specified, the value of the function is added to the
/// existing bin contents
/// If option "S" is specified, the value of the function is used to
/// generate a value, distributed according to the Poisson
/// distribution, with f1 as the mean.
virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py);
/// Execute action corresponding to one event.
/// This member function is called when a histogram is clicked with the locator
/// If Left button clicked on the bin top value, then the content of this bin
/// is modified according to the new position of the mouse when it is released.
virtual void ExtendAxis(Double_t x, TAxis *axis);
/// Histogram is resized along axis such that x is in the axis range.
/// The new axis limits are recomputed by doubling iteratively
/// the current axis range until the specified value x is within the limits.
/// The algorithm makes a copy of the histogram, then loops on all bins
/// of the old histogram to fill the extended histogram.
/// Takes into account errors (Sumw2) if any.
/// The algorithm works for 1-d, 2-D and 3-D histograms.
/// The axis must be extendable before invoking this function.
/// Ex: h->GetXaxis()->SetCanExtend(kTRUE);
virtual TH1 *FFT(TH1* h_output, Option_t *option);
/// This function allows to do discrete Fourier transforms of TH1 and TH2.
/// Available transform types and flags are described below.
/// To extract more information about the transform, use the function
/// TVirtualFFT::GetCurrentTransform() to get a pointer to the current transform object.
/// \param[out] h_output histogram for the output. If a null pointer is passed, a new histogram is created
/// and returned, otherwise, the provided histogram is used and should be big enough
/// \param[in] option option parameters consists of 3 parts:
/// - option on what to return
/// - "RE" - returns a histogram of the real part of the output
/// - "IM" - returns a histogram of the imaginary part of the output
/// - "MAG"- returns a histogram of the magnitude of the output
/// - "PH" - returns a histogram of the phase of the output
/// - option of transform type
/// - "R2C" - real to complex transforms - default
/// - "R2HC" - real to halfcomplex (special format of storing output data,
/// results the same as for R2C)
/// - "DHT" - discrete Hartley transform
/// real to real transforms (sine and cosine):
/// - "R2R_0", "R2R_1", "R2R_2", "R2R_3" - discrete cosine transforms of types I-IV
/// - "R2R_4", "R2R_5", "R2R_6", "R2R_7" - discrete sine transforms of types I-IV
/// To specify the type of each dimension of a 2-dimensional real to real
/// transform, use options of form "R2R_XX", for example, "R2R_02" for a transform,
/// which is of type "R2R_0" in 1st dimension and "R2R_2" in the 2nd.
/// - option of transform flag
/// - "ES" (from "estimate") - no time in preparing the transform, but probably sub-optimal
/// performance
/// - "M" (from "measure") - some time spend in finding the optimal way to do the transform
/// - "P" (from "patient") - more time spend in finding the optimal way to do the transform
/// - "EX" (from "exhaustive") - the most optimal way is found
/// This option should be chosen depending on how many transforms of the same size and
/// type are going to be done. Planning is only done once, for the first transform of this
/// size and type. Default is "ES".
/// Examples of valid options: "Mag R2C M" "Re R2R_11" "Im R2C ES" "PH R2HC EX"
virtual Int_t Fill(Double_t x);//将数据填充进直方图
/// Increment bin with abscissa X by 1.
/// if x is less than the low-edge of the first bin, the Underflow bin is incremented
/// if x is greater than the upper edge of last bin, the Overflow bin is incremented
/// If the storage of the sum of squares of weights has been triggered,
/// via the function Sumw2, then the sum of the squares of weights is incremented
/// by 1 in the bin corresponding to x.
/// The function returns the corresponding bin number which has its content incremented by 1
virtual Int_t Fill(Double_t x, Double_t w);
/// Increment bin with abscissa X with a weight w.
/// if x is less than the low-edge of the first bin, the Underflow bin is incremented
/// if x is greater than the upper edge of last bin, the Overflow bin is incremented
/// If the weight is not equal to 1, the storage of the sum of squares of
/// weights is automatically triggered and the sum of the squares of weights is incremented
/// by w^2 in the bin corresponding to x.
/// The function returns the corresponding bin number which has its content incremented by w
virtual Int_t Fill(const char *name, Double_t w);
/// Increment bin with namex with a weight w
/// if x is less than the low-edge of the first bin, the Underflow bin is incremented
/// if x is greater than the upper edge of last bin, the Overflow bin is incremented
/// If the weight is not equal to 1, the storage of the sum of squares of
/// weights is automatically triggered and the sum of the squares of weights is incremented
/// by w^2 in the bin corresponding to x.
/// The function returns the corresponding bin number which has its content incremented by w
virtual void FillN(Int_t ntimes, const Double_t *x, const Double_t *w, Int_t stride=1);
/// Fill this histogram with an array x and weights w.
/// \param[in] ntimes number of entries in arrays x and w (array size must be ntimes*stride)
/// \param[in] x array of values to be histogrammed
/// \param[in[ w array of weighs
/// \param[in] stride step size through arrays x and w
/// If the weight is not equal to 1, the storage of the sum of squares of
/// weights is automatically triggered and the sum of the squares of weights is incremented
/// y w^2 in the bin corresponding to x.
/// if w is NULL each entry is assumed a weight=1
virtual void FillN(Int_t, const Double_t *, const Double_t *, const Double_t *, Int_t) {;}
virtual void FillRandom(const char *fname, Int_t ntimes=5000);
/// Fill histogram following distribution in function fname.
/// The distribution contained in the function fname (TF1) is integrated
/// over the channel contents for the bin range of this histogram.
/// It is normalized to 1.
/// Getting one random number implies:
/// - Generating a random number between 0 and 1 (say r1)
/// - Look in which bin in the normalized integral r1 corresponds to
/// - Fill histogram channel
/// ntimes random numbers are generated
/// One can also call TF1::GetRandom to get a random variate from a function.
virtual void FillRandom(TH1 *h, Int_t ntimes=5000);
/// Fill histogram following distribution in histogram h.
/// The distribution contained in the histogram h (TH1) is integrated
/// over the channel contents for the bin range of this histogram.
/// It is normalized to 1.
/// Getting one random number implies:
/// - Generating a random number between 0 and 1 (say r1)
/// - Look in which bin in the normalized integral r1 corresponds to
/// - Fill histogram channel ntimes random numbers are generated
/// SPECIAL CASE when the target histogram has the same binning as the source.
/// in this case we simply use a poisson distribution where
/// the mean value per bin = bincontent/integral.
virtual Int_t FindBin(Double_t x, Double_t y=0, Double_t z=0);//寻找x值对应的bin数 对一维直方图，返回 x 值所在 bin，若为二维直方图，返回 （x，y） 所在 bin，三维同理。
/// Return Global bin number corresponding to x,y,z
/// 2-D and 3-D histograms are represented with a one dimensional
/// structure. This has the advantage that all existing functions, such as
/// GetBinContent, GetBinError, GetBinFunction work for all dimensions.
/// This function tries to extend the axis if the given point belongs to an
/// under-/overflow bin AND if CanExtendAllAxes() is true.
/// See also TH1::GetBin, TAxis::FindBin and TAxis::FindFixBin
virtual Int_t FindFixBin(Double_t x, Double_t y=0, Double_t z=0) const;
/// Return Global bin number corresponding to x,y,z.
/// 2-D and 3-D histograms are represented with a one dimensional
/// structure. This has the advantage that all existing functions, such as
/// GetBinContent, GetBinError, GetBinFunction work for all dimensions.
/// This function DOES NOT try to extend the axis if the given point belongs
/// to an under-/overflow bin.
/// See also TH1::GetBin, TAxis::FindBin and TAxis::FindFixBin
virtual Int_t FindFirstBinAbove(Double_t threshold=0, Int_t axis=1) const;
/// Find first bin with content > threshold for axis (1=x, 2=y, 3=z)
/// if no bins with content > threshold is found the function returns -1.
virtual Int_t FindLastBinAbove (Double_t threshold=0, Int_t axis=1) const;
/// Find last bin with content > threshold for axis (1=x, 2=y, 3=z)
/// if no bins with content > threshold is found the function returns -1.
virtual TObject *FindObject(const char *name) const;/// search object named name in the list of functions
virtual TObject *FindObject(const TObject *obj) const;/// search object obj in the list of functions
virtual TFitResultPtr Fit(const char *formula ,Option_t *option="" ,Option_t *goption="", Double_t xmin=0, Double_t xmax=0); // *MENU*
/// Fit histogram with function fname.
/// fname is the name of an already predefined function created by TF1 or TF2
/// Predefined functions such as gaus, expo and poln are automatically
/// created by ROOT.
/// fname can also be a formula, accepted by the linear fitter (linear parts divided
/// by "++" sign), for example "x++sin(x)" for fitting "[0]*x+[1]*sin(x)"
/// This function finds a pointer to the TF1 object with name fname
/// and calls TH1::Fit(TF1 *f1,...)
virtual TFitResultPtr Fit(TF1 *f1 ,Option_t *option="" ,Option_t *goption="", Double_t xmin=0, Double_t xmax=0);
/// Fit histogram with function f1.
/// \param[in] option fit options is given in parameter option.
/// - "W" Set all weights to 1 for non empty bins; ignore error bars
/// - "WW" Set all weights to 1 including empty bins; ignore error bars
/// - "I" Use integral of function in bin, normalized by the bin volume,
/// instead of value at bin center
/// - "L" Use Loglikelihood method (default is chisquare method)
/// - "WL" Use Loglikelihood method and bin contents are not integer,
/// i.e. histogram is weighted (must have Sumw2() set)
/// - "P" Use Pearson chi2 (using expected errors instead of observed errors)
/// - "U" Use a User specified fitting algorithm (via SetFCN)
/// - "Q" Quiet mode (minimum printing)
/// - "V" Verbose mode (default is between Q and V)
/// - "E" Perform better Errors estimation using Minos technique
/// - "B" User defined parameter settings are used for predefined functions
/// like "gaus", "expo", "poln", "landau".
/// Use this option when you want to fix one or more parameters for these functions.
/// - "M" More. Improve fit results.
/// It uses the IMPROVE command of TMinuit (see TMinuit::mnimpr).
/// This algorithm attempts to improve the found local minimum by searching for a
/// better one.
/// - "R" Use the Range specified in the function range
/// - "N" Do not store the graphics function, do not draw
/// - "0" Do not plot the result of the fit. By default the fitted function
/// is drawn unless the option"N" above is specified.
/// - "+" Add this new fitted function to the list of fitted functions
/// (by default, any previous function is deleted)
/// - "C" In case of linear fitting, don't calculate the chisquare
/// (saves time)
/// - "F" If fitting a polN, switch to minuit fitter
/// - "S" The result of the fit is returned in the TFitResultPtr
/// (see below Access to the Fit Result)
/// \param[in] goption specify a list of graphics options. See TH1::Draw for a complete list of these options.
/// \param[in] xxmin range
/// \param[in] xxmax range
/// ## Setting initial conditions
/// Parameters must be initialized before invoking the Fit function.
/// The setting of the parameter initial values is automatic for the
/// predefined functions : poln, expo, gaus, landau. One can however disable
/// this automatic computation by specifying the option "B".
/// Note that if a predefined function is defined with an argument,
/// eg, gaus(0), expo(1), you must specify the initial values for
/// the parameters.
/// Note that option "I" gives better results but is slower.
/// ## Changing the fitting objective function
/// By default a chi square function is used for fitting. When option "L" (or "LL") is used
/// a Poisson likelihood function (see note below) is used.
/// The functions are defined in the header Fit/Chi2Func.h or Fit/PoissonLikelihoodFCN and they
/// are implemented using the routines FitUtil::EvaluateChi2 or FitUtil::EvaluatePoissonLogL in
/// the file math/mathcore/src/FitUtil.cxx.
/// To specify a User defined fitting function, specify option "U" and
/// call the following functions:
/// TVirtualFitter::Fitter(myhist)->SetFCN(MyFittingFunction)
/// where MyFittingFunction is of type:
/// extern void MyFittingFunction(Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag);
/// ## Chi2 Fits
/// By default a chi2 (least-square) fit is performed on the histogram. The so-called modified least-square method
/// is used where the residual for each bin is computed using as error the observed value (the bin error)
/// Chi2 = Sum{ ( y(i) - f (x(i) | p )/ e(i) )^2 }
/// where y(i) is the bin content for each bin i, x(i) is the bin center and e(i) is the bin error (sqrt(y(i) for
/// an un-weighted histogram. Bins with zero errors are excluded from the fit. See also later the note on the treatment of empty bins.
/// When using option "I" the residual is computed not using the function value at the bin center, f (x(i) | p), but the integral
/// of the function in the bin, Integral{ f(x|p)dx } divided by the bin volume
/// ## Likelihood Fits
/// When using option "L" a likelihood fit is used instead of the default chi2 square fit.
/// The likelihood is built assuming a Poisson probability density function for each bin.
/// The negative log-likelihood to be minimized is
/// NLL = Sum{ log Poisson( y(i) |{ f(x(i) | p ) ) }
/// The exact likelihood used is the Poisson likelihood described in this paper:
/// S. Baker and R. D. Cousins, “Clarification of the use of chi-square and likelihood functions in fits to histograms,”
/// Nucl. Instrum. Meth. 221 (1984) 437.
/// This method can then be used only when the bin content represents counts (i.e. errors are sqrt(N) ).
/// The likelihood method has the advantage of treating correctly bins with low statistics. In case of high
/// statistics/bin the distribution of the bin content becomes a normal distribution and the likelihood and chi2 fit
/// give the same result.
/// The likelihood method, although a bit slower, it is therefore the recommended method in case of low
/// bin statistics, where the chi2 method may give incorrect results, in particular when there are
/// several empty bins (see also below).
/// In case of a weighted histogram, it is possible to perform a likelihood fit by using the
/// option "WL". Note a weighted histogram is an histogram which has been filled with weights and it
/// contains the sum of the weight square ( TH1::Sumw2() has been called). The bin error for a weighted
/// histogram is the square root of the sum of the weight square.
/// ## Treatment of Empty Bins
/// Empty bins, which have the content equal to zero AND error equal to zero,
/// are excluded by default from the chisquare fit, but they are considered in the likelihood fit.
/// since they affect the likelihood if the function value in these bins is not negligible.
/// When using option "WW" these bins will be considered in the chi2 fit with an error of 1.
/// Note that if the histogram is having bins with zero content and non zero-errors they are considered as
/// any other bins in the fit. Instead bins with zero error and non-zero content are excluded in the chi2 fit.
/// A likelihood fit should also not be peformed on such an histogram, since we are assuming a wrong pdf for each bin.
/// In general, one should not fit an histogram with non-empty bins and zero errors, apart if all the bins have zero errors.
/// In this case one could use the option "w", which gives a weight=1 for each bin (unweighted least-square fit).
/// ## Fitting a histogram of dimension N with a function of dimension N-1
/// It is possible to fit a TH2 with a TF1 or a TH3 with a TF2.
/// In this case the option "Integral" is not allowed and each cell has
/// equal weight.
/// ## Associated functions
/// One or more object (typically a TF1*) can be added to the list
/// of functions (fFunctions) associated to each histogram.
/// When TH1::Fit is invoked, the fitted function is added to this list.
/// Given an histogram h, one can retrieve an associated function
/// with: TF1 *myfunc = h->GetFunction("myfunc");
/// ##Access to the fit result
/// The function returns a TFitResultPtr which can hold a pointer to a TFitResult object.
/// By default the TFitResultPtr contains only the status of the fit which is return by an
/// automatic conversion of the TFitResultPtr to an integer. One can write in this case directly:
/// Int_t fitStatus = h->Fit(myFunc)
/// ## Access to the fit status
/// The status of the fit can be obtained converting the TFitResultPtr to an integer
/// independently if the fit option "S" is used or not:
/// TFitResultPtr r = h->Fit(myFunc,opt);
/// Int_t fitStatus = r;
/// The fitStatus is 0 if the fit is OK (i.e no error occurred).
/// The value of the fit status code is negative in case of an error not connected with the
/// minimization procedure, for example when a wrong function is used.
/// Otherwise the return value is the one returned from the minimization procedure.
/// When TMinuit (default case) or Minuit2 are used as minimizer the status returned is :
/// fitStatus = migradResult + 10*minosResult + 100*hesseResult + 1000*improveResult.
/// TMinuit will return 0 (for migrad, minos, hesse or improve) in case of success and 4 in
/// case of error (see the documentation of TMinuit::mnexcm). So for example, for an error
/// only in Minos but not in Migrad a fitStatus of 40 will be returned.
/// Minuit2 will return also 0 in case of success and different values in migrad minos or
/// hesse depending on the error. See in this case the documentation of
/// Minuit2Minimizer::Minimize for the migradResult, Minuit2Minimizer::GetMinosError for the
/// minosResult and Minuit2Minimizer::Hesse for the hesseResult.
/// If other minimizers are used see their specific documentation for the status code returned.
/// For example in the case of Fumili, for the status returned see TFumili::Minimize.
/// ## Access to the Minimizer information during fitting
/// This function calls, the ROOT::Fit::FitObject function implemented in HFitImpl.cxx
/// which uses the ROOT::Fit::Fitter class. The Fitter class creates the objective fuction
/// (e.g. chi2 or likelihood) and uses an implementation of the Minimizer interface for minimizing
/// the function.
/// The default minimizer is Minuit (class TMinuitMinimizer which calls TMinuit).
/// The default can be set in the resource file in etc/system.rootrc. For example
/// Root.Fitter: Minuit2
/// A different fitter can also be set via ROOT::Math::MinimizerOptions::SetDefaultMinimizer
/// (or TVirtualFitter::SetDefaultFitter).
/// For example ROOT::Math::MinimizerOptions::SetDefaultMinimizer("GSLMultiMin","BFGS");
/// will set the usdage of the BFGS algorithm of the GSL multi-dimensional minimization
/// (implemented in libMathMore). ROOT::Math::MinimizerOptions can be used also to set other
/// default options, like maximum number of function calls, minimization tolerance or print
/// level. See the documentation of this class.
/// For fitting linear functions (containing the "++" sign" and polN functions,
/// the linear fitter is automatically initialized.
virtual void FitPanel(); // *MENU* Display a panel with all histogram fit options. See class TFitPanel for example
TH1 *GetAsymmetry(TH1* h2, Double_t c2=1, Double_t dc2=0);
/// Return an histogram containing the asymmetry of this histogram with h2,
/// where the asymmetry is defined as:
/// Asymmetry = (h1 - h2)/(h1 + h2) where h1 = this
/// works for 1D, 2D, etc. histograms
/// c2 is an optional argument that gives a relative weight between the two
/// histograms, and dc2 is the error on this weight. This is useful, for example,
/// when forming an asymmetry between two histograms from 2 different data sets that
/// need to be normalized to each other in some way. The function calculates
/// the errors asumming Poisson statistics on h1 and h2 (that is, dh = sqrt(h)).
/// example: assuming 'h1' and 'h2' are already filled
/// h3 = h1->GetAsymmetry(h2)
/// then 'h3' is created and filled with the asymmetry between 'h1' and 'h2';
/// h1 and h2 are left intact.
/// Note that it is the user's responsibility to manage the created histogram.
/// The name of the returned histogram will be Asymmetry_nameOfh1-nameOfh2
///
/// clone the histograms so top and bottom will have the
/// correct dimensions:
/// Sumw2 just makes sure the errors will be computed properly
/// when we form sums and ratios below.
Int_t GetBufferLength() const {return fBuffer ? (Int_t)fBuffer[0] : 0;}
Int_t GetBufferSize () const {return fBufferSize;}
const Double_t *GetBuffer() const {return fBuffer;}
static Int_t GetDefaultBufferSize();
/// static function
/// return the default buffer size for automatic histograms
/// the parameter fgBufferSize may be changed via SetDefaultBufferSize
virtual Double_t *GetIntegral();//ROOT 6 //TH1积分，当前bin值为前面所有bin的累积，然后归一化（最大值为1），返回该数组
/// Return a pointer to the array of bins integral.
/// if the pointer fIntegral is null, TH1::ComputeIntegral is called
/// The array dimension is the number of bins in the histograms
/// including underflow and overflow (fNCells)
/// the last value integral[fNCells] is set to the number of entries of
/// the histogram
TH1 *GetCumulative(Bool_t forward = kTRUE, const char* suffix = "_cumulative") const;//ROOT 6 //TH1积分，当前bin值为前面所有bin的累积。
/// Return a pointer to an histogram containing the cumulative The
/// cumulative can be computed both in the forward (default) or backward
/// direction; the name of the new histogram is constructed from
/// the name of this histogram with the suffix suffix appended.
/// The cumulative distribution is formed by filling each bin of the
/// resulting histogram with the sum of that bin and all previous
/// (forward == kTRUE) or following (forward = kFALSE) bins.
/// note: while cumulative distributions make sense in one dimension, you
/// may not be getting what you expect in more than 1D because the concept
/// of a cumulative distribution is much trickier to define; make sure you
/// understand the order of summation before you use this method with
/// histograms of dimension >= 2.
TList *GetListOfFunctions() const { return fFunctions; }
virtual Int_t GetNdivisions(Option_t *axis="X") const;
virtual Color_t GetAxisColor(Option_t *axis="X") const;
virtual Color_t GetLabelColor(Option_t *axis="X") const;
virtual Style_t GetLabelFont(Option_t *axis="X") const;
virtual Float_t GetLabelOffset(Option_t *axis="X") const;
virtual Float_t GetLabelSize(Option_t *axis="X") const;
virtual Style_t GetTitleFont(Option_t *axis="X") const;
virtual Float_t GetTitleOffset(Option_t *axis="X") const;
virtual Float_t GetTitleSize(Option_t *axis="X") const;
virtual Float_t GetTickLength(Option_t *axis="X") const;
virtual Float_t GetBarOffset() const {return Float_t(0.001*Float_t(fBarOffset));}
virtual Float_t GetBarWidth() const {return Float_t(0.001*Float_t(fBarWidth));}
virtual Int_t GetContour(Double_t *levels=0);
/// Return contour values into array levels if pointer levels is non zero
/// The function returns the number of contour levels.
/// see GetContourLevel to return one contour only
virtual Double_t GetContourLevel(Int_t level) const;/// Return value of contour number level use GetContour to return the array of all contour levels
virtual Double_t GetContourLevelPad(Int_t level) const;
/// Return the value of contour number "level" in Pad coordinates ie: if the Pad
/// is in log scale along Z it returns le log of the contour level value.
/// see GetContour to return the array of all contour levels
virtual Int_t GetBin(Int_t binx, Int_t biny=0, Int_t binz=0) const;
/// Return Global bin number corresponding to binx,y,z.
/// 2-D and 3-D histograms are represented with a one dimensional structure.
/// This has the advantage that all existing functions, such as
/// GetBinContent, GetBinError, GetBinFunction work for all dimensions.
/// In case of a TH1x, returns binx directly.
/// see TH1::GetBinXYZ for the inverse transformation.
/// Convention for numbering bins
/// For all histogram types: nbins, xlow, xup
/// bin = 0; underflow bin
/// bin = 1; first bin with low-edge xlow INCLUDED
/// bin = nbins; last bin with upper-edge xup EXCLUDED
/// bin = nbins+1; overflow bin
/// In case of 2-D or 3-D histograms, a "global bin" number is defined.
/// For example, assuming a 3-D histogram with binx,biny,binz, the function
/// Int_t bin = h->GetBin(binx,biny,binz);
/// returns a global/linearized bin number. This global bin is useful
/// to access the bin information independently of the dimension.
virtual void GetBinXYZ(Int_t binglobal, Int_t &binx, Int_t &biny, Int_t &binz) const;/// return binx, biny, binz corresponding to the global bin number globalbin. see TH1::GetBin function above
virtual Double_t GetBinCenter(Int_t bin) const;//返回该bin的中点坐标。
virtual Double_t GetBinContent(Int_t bin) const;//返回该bin的计数.
/// Return content of bin number bin.
/// Implemented in TH1C,S,F,D
/// Convention for numbering bins
/// For all histogram types: nbins, xlow, xup
/// bin = 0; underflow bin
/// bin = 1; first bin with low-edge xlow INCLUDED
/// bin = nbins; last bin with upper-edge xup EXCLUDED
/// bin = nbins+1; overflow bin
/// In case of 2-D or 3-D histograms, a "global bin" number is defined.
/// For example, assuming a 3-D histogram with binx,biny,binz, the function
/// Int_t bin = h->GetBin(binx,biny,binz);
/// returns a global/linearized bin number. This global bin is useful
/// to access the bin information independently of the dimension.
virtual Double_t GetBinContent(Int_t bin, Int_t) const { return GetBinContent(bin); }
virtual Double_t GetBinContent(Int_t bin, Int_t, Int_t) const { return GetBinContent(bin); }
virtual Double_t GetBinError(Int_t bin) const;//Return value of error associated to bin number bin. if the sum of squares of weights has been defined (via Sumw2),this function returns the sqrt(sum of w2). otherwise it returns the sqrt(contents) for this bin.
virtual Double_t GetBinError(Int_t binx, Int_t biny) const { return GetBinError(GetBin(binx, biny)); } // for 2D histograms only
virtual Double_t GetBinError(Int_t binx, Int_t biny, Int_t binz) const { return GetBinError(GetBin(binx, biny, binz)); } // for 3D histograms only
virtual Double_t GetBinErrorLow(Int_t bin) const;//Return lower error associated to bin number bin. The error will depend on the statistic option used will return the binContent - lower interval value
virtual Double_t GetBinErrorUp(Int_t bin) const;//Return upper error associated to bin number bin. The error will depend on the statistic option used will return the binContent - upper interval value
virtual EBinErrorOpt GetBinErrorOption() const { return fBinStatErrOpt; }
virtual Double_t GetBinLowEdge(Int_t bin) const;//return bin lower edge for 1D historam Better to use h1.GetXaxis().GetBinLowEdge(bin)
virtual Double_t GetBinWidth(Int_t bin) const;//返回bin的宽度。 return bin width for 1D historam Better to use h1.GetXaxis().GetBinWidth(bin)
virtual Double_t GetBinWithContent(Double_t c, Int_t &binx, Int_t firstx=0, Int_t lastx=0,Double_t maxdiff=0) const;
/// compute first binx in the range [firstx,lastx] for which
/// diff = abs(bin_content-c) <= maxdiff
/// In case several bins in the specified range with diff=0 are found
/// the first bin found is returned in binx.
/// In case several bins in the specified range satisfy diff <=maxdiff
/// the bin with the smallest difference is returned in binx.
/// In all cases the function returns the smallest difference.
/// NOTE1: if firstx <= 0, firstx is set to bin 1
/// if (lastx < firstx then firstx is set to the number of bins
/// ie if firstx=0 and lastx=0 (default) the search is on all bins.
/// NOTE2: if maxdiff=0 (default), the first bin with content=c is returned.
virtual void GetCenter(Double_t *center) const;/// Fill array with center of bins for 1D histogram Better to use h1.GetXaxis().GetCenter(center)
static Bool_t GetDefaultSumw2();
TDirectory *GetDirectory() const {return fDirectory;}
virtual Double_t GetEntries() const; //returns the number of entries
virtual Double_t GetEffectiveEntries() const;
/// number of effective entries of the histogram,
/// neff = (Sum of weights )^2 / (Sum of weight^2 )
/// In case of an unweighted histogram this number is equivalent to the
/// number of entries of the histogram.
/// For a weighted histogram, this number corresponds to the hypotetical number of unweighted entries
/// a histogram would need to have the same statistical power as this weighted histogram.
/// Note: The underflow/overflow are included if one has set the TH1::StatOverFlows flag
/// and if the statistics has been computed at filling time.
/// If a range is set in the histogram the number is computed from the given range.
virtual TF1 *GetFunction(const char *name) const;/// Return pointer to function with name. Functions such as TH1::Fit store the fitted function in the list of functions of this histogram.
virtual Int_t GetDimension() const { return fDimension; }
virtual Double_t GetKurtosis(Int_t axis=1) const;//For axis =1, 2 or 3 returns kurtosis of the histogram along x, y or z axis.Kurtosis(gaussian(0, 1)) = 0. For axis =11, 12 or 13 returns the approximate standard error of kurtosis of the histogram along x, y or z axis. Note, that since third and fourth moment are not calculated at the fill time, kurtosis and its standard error are computed bin by bin
virtual void GetLowEdge(Double_t *edge) const;/// Fill array with low edge of bins for 1D histogram Better to use h1.GetXaxis().GetLowEdge(edge)
virtual Double_t GetMaximum(Double_t maxval=FLT_MAX) const;
/// Return maximum value smaller than maxval of bins in the range,
/// unless the value has been overridden by TH1::SetMaximum,
/// in which case it returns that value. (This happens, for example,
/// when the histogram is drawn and the y or z axis limits are changed
/// To get the maximum value of bins in the histogram regardless of
/// whether the value has been overridden, use
/// h->GetBinContent(h->GetMaximumBin())
virtual Int_t GetMaximumBin() const;/// Return location of bin with maximum value in the range.
virtual Int_t GetMaximumBin(Int_t &locmax, Int_t &locmay, Int_t &locmaz) const;/// Return location of bin with maximum value in the range.
virtual Double_t GetMaximumStored() const {return fMaximum;}
virtual Double_t GetMinimum(Double_t minval=-FLT_MAX) const;
/// Return minimum value larger than minval of bins in the range,
/// unless the value has been overridden by TH1::SetMinimum,
/// in which case it returns that value. (This happens, for example,
/// when the histogram is drawn and the y or z axis limits are changed
/// To get the minimum value of bins in the histogram regardless of
/// whether the value has been overridden, use
/// h->GetBinContent(h->GetMinimumBin())
virtual Int_t GetMinimumBin() const;/// Return location of bin with minimum value in the range.
virtual Int_t GetMinimumBin(Int_t &locmix, Int_t &locmiy, Int_t &locmiz) const;/// Return location of bin with minimum value in the range.
virtual Double_t GetMinimumStored() const {return fMinimum;}
virtual Double_t GetMean(Int_t axis=1) const;//returns the mean value along axis. For axis = 1,2 or 3 returns the mean value of the histogram along X,Y or Z axis. For axis = 11, 12, 13 returns the standard error of the mean value of the histogram along X, Y or Z axis. Note that the mean value/RMS is computed using the bins in the currently defined range (see TAxis::SetRange). By default the range includes all bins from 1 to nbins included, excluding underflows and overflows. To force the underflows and overflows in the computation, one must call the static function TH1::StatOverflows(kTRUE) before filling the histogram.
virtual Double_t GetMeanError(Int_t axis=1) const;//Return standard error of mean of this histogram along the X axis. Note that the mean value/RMS is computed using the bins in the currently defined range (see TAxis::SetRange). By default the range includes all bins from 1 to nbins included, excluding underflows and overflows. To force the underflows and overflows in the computation, one must call the static function TH1::StatOverflows(kTRUE) before filling the histogram. Also note, that although the definition of standard error doesn't include the assumption of normality, many uses of this feature implicitly assume it.
virtual Int_t GetNbinsX() const {return fXaxis.GetNbins();}//获取该轴bin值
virtual Int_t GetNbinsY() const {return fYaxis.GetNbins();}
virtual Int_t GetNbinsZ() const {return fZaxis.GetNbins();}
virtual Int_t GetNcells() const {return fNcells; }//number of bins(1D), cells (2D) +U/Overflows
virtual Double_t GetNormFactor() const {return fNormFactor;}//如果没有设置将会返回0。这个因子是将直方图面积设为该因子。设置该因子参考 SetNormFactor(Double_t factor=1)。
virtual char *GetObjectInfo(Int_t px, Int_t py) const;
/// Redefines TObject::GetObjectInfo.
/// Displays the histogram info (bin number, contents, integral up to bin
/// corresponding to cursor position px,py
Option_t *GetOption() const {return fOption.Data();}
TVirtualHistPainter *GetPainter(Option_t *option="");/// return pointer to painter if painter does not exist, it is created
virtual Int_t GetQuantiles(Int_t nprobSum, Double_t *q, const Double_t *probSum=0);
/// Compute Quantiles for this histogram
/// Quantile x_q of a probability distribution Function F is defined as
/// F(x_q) = q with 0 <= q <= 1.
/// For instance the median x_0.5 of a distribution is defined as that value
/// of the random variable for which the distribution function equals 0.5:
/// F(x_0.5) = Probability(x < x_0.5) = 0.5
/// code from Eddy Offermann, Renaissance
/// \param[in] nprobSum maximum size of array q and size of array probSum (if given)
/// \param[in] probSum array of positions where quantiles will be computed.
/// - if probSum is null, probSum will be computed internally and will
/// have a size = number of bins + 1 in h. it will correspond to the
/// quantiles calculated at the lowest edge of the histogram (quantile=0) and
/// all the upper edges of the bins.
/// - if probSum is not null, it is assumed to contain at least nprobSum values.
/// \param[out] q array q filled with nq quantiles
/// \return value nq (<=nprobSum) with the number of quantiles computed
/// Note that the Integral of the histogram is automatically recomputed
/// if the number of entries is different of the number of entries when
/// the integral was computed last time. In case you do not use the Fill
/// functions to fill your histogram, but SetBinContent, you must call
/// TH1::ComputeIntegral before calling this function.
virtual Double_t GetRandom() const;//return a random number distributed according the histogram bin contents. This function checks if the bins integral exists. If not, the integral is evaluated, normalized to one. The integral is automatically recomputed if the number of entries is not the same then when the integral was computed. NB Only valid for 1-d histograms. Use GetRandom2 or 3 otherwise. If the histogram has a bin with negative content a NaN is returned
virtual void GetStats(Double_t *stats) const;
// fill the array stats from the contents of this histogram
// The array stats must be correctly dimensioned in the calling program.
// stats[0] = sumw
// stats[1] = sumw2
// stats[2] = sumwx
// stats[3] = sumwx2
// If no axis-subrange is specified (via TAxis::SetRange), the array stats is simply a copy of the statistics quantities computed at filling time.If a sub-range is specified, the function recomputes these quantities from the bin contents in the current axis range.
// Note that the mean value/RMS is computed using the bins in the currently defined range (see TAxis::SetRange). By default the range includes all bins from 1 to nbins included, excluding underflows and overflows. To force the underflows and overflows in the computation, one must call the static function TH1::StatOverflows(kTRUE) before filling the histogram.
virtual Double_t GetStdDev(Int_t axis=1) const;//returns the sigma distribution along axis
/// Returns the Standard Deviation (Sigma).
/// The Sigma estimate is computed as Sqrt((1/N)*(Sum(x_i-x_mean)^2))
/// For axis = 1,2 or 3 returns the Sigma value of the histogram along
/// X, Y or Z axis
/// For axis = 11, 12 or 13 returns the error of StdDev estimation along
/// X, Y or Z axis for Normal distribution
/// Note that the mean value/sigma is computed using the bins in the currently
/// defined range (see TAxis::SetRange). By default the range includes
/// all bins from 1 to nbins included, excluding underflows and overflows.
/// To force the underflows and overflows in the computation, one must
/// call the static function TH1::StatOverflows(kTRUE) before filling
/// the histogram.
virtual Double_t GetStdDevError(Int_t axis=1) const;
/// Return error of standard deviation estimation for Normal distribution
/// Note that the mean value/StdDev is computed using the bins in the currently
/// defined range (see TAxis::SetRange). By default the range includes
/// all bins from 1 to nbins included, excluding underflows and overflows.
/// To force the underflows and overflows in the computation, one must
/// call the static function TH1::StatOverflows(kTRUE) before filling
/// the histogram.
/// Value returned is standard deviation of sample standard deviation.
/// Note that it is an approximated value which is valid only in the case that the
/// original data distribution is Normal. The correct one would require
/// the 4-th momentum value, which cannot be accurately estimated from an histogram since
/// the x-information for all entries is not kept.
virtual Double_t GetSumOfWeights() const;//Return the sum of weights excluding under/overflows.
virtual TArrayD *GetSumw2() {return &fSumw2;}
virtual const TArrayD *GetSumw2() const {return &fSumw2;}
virtual Int_t GetSumw2N() const {return fSumw2.fN;}
Double_t GetRMS(Int_t axis=1) const { return GetStdDev(axis); }
// For axis = 1,2 or 3 returns the Sigma value of the histogram along X, Y or Z axis. For axis = 11, 12 or 13 returns the error of RMS estimation along X, Y or Z axis for Normal distribution.
// Note that the mean value/sigma is computed using the bins in the currently defined range (see TAxis::SetRange). By default the range includes all bins from 1 to nbins included, excluding underflows and overflows. To force the underflows and overflows in the computation, one must call the static function TH1::StatOverflows(kTRUE) before filling the histogram.
// Note that this function returns the Standard Deviation (Sigma) of the distribution (not RMS). The Sigma estimate is computed as Sqrt((1/N)*(Sum(x_i-x_mean)^2)). The name "RMS" was introduced many years ago (Hbook/PAW times).
Double_t GetRMSError(Int_t axis=1) const { return GetStdDevError(axis); }
// Return error of RMS estimation for Normal distribution.
// Note that the mean value/RMS is computed using the bins in the currently defined range (see TAxis::SetRange). By default the range includes all bins from 1 to nbins included, excluding underflows and overflows. To force the underflows and overflows in the computation, one must call the static function TH1::StatOverflows(kTRUE) before filling the histogram.
// Value returned is standard deviation of sample standard deviation.
Note that it is an approximated value which is valid only in the case that the original data distribution is Normal. The correct one would require the 4-th momentum value, which cannot be accurately estimated from an histogram since the x-information for all entries is not kept.
virtual Double_t GetSkewness(Int_t axis=1) const;
///For axis = 1, 2 or 3 returns skewness of the histogram along x, y or z axis.
///For axis = 11, 12 or 13 returns the approximate standard error of skewness
///of the histogram along x, y or z axis
///Note, that since third and fourth moment are not calculated
///at the fill time, skewness and its standard error are computed bin by bin
TAxis* GetXaxis() { return &fXaxis; }//返回指向该坐标轴 TAxis* 的指针，可对该轴进行设置。具体参考TAxis类的使用。
TAxis* GetYaxis() { return &fYaxis; }//返回指向该坐标轴 TAxis* 的指针，可对该轴进行设置。具体参考TAxis类的使用。
TAxis* GetZaxis() { return &fZaxis; }//返回指向该坐标轴 TAxis* 的指针，可对该轴进行设置。具体参考TAxis类的使用。
const TAxis* GetXaxis() const { return &fXaxis; }
const TAxis* GetYaxis() const { return &fYaxis; }
const TAxis* GetZaxis() const { return &fZaxis; }
virtual Double_t Integral(Option_t *option="") const;//Return integral of bin contents. Only bins in the bins range are considered. By default the integral is computed as the sum of bin contents in the range. if option "width" is specified, the integral is the sum of the bin contents multiplied by the bin width in x.
virtual Double_t Integral(Int_t binx1, Int_t binx2, Option_t *option="") const;//returns the integral of bin contents in a given bin range
///Return integral of bin contents in range [binx1,binx2]
/// By default the integral is computed as the sum of bin contents in the range.
/// if option "width" is specified, the integral is the sum of
/// the bin contents multiplied by the bin width in x.
virtual Double_t IntegralAndError(Int_t binx1, Int_t binx2, Double_t & err, Option_t *option="") const;
///Return integral of bin contents in range [binx1,binx2] and its error
/// By default the integral is computed as the sum of bin contents in the range.
/// if option "width" is specified, the integral is the sum of
/// the bin contents multiplied by the bin width in x.
/// the error is computed using error propagation from the bin errors assumming that
/// all the bins are uncorrelated
virtual Double_t Interpolate(Double_t x);//Given a point x, approximates the value via linear interpolation based on the two nearest bin centers. 获取x的y值。其值为最近两个bin线性插值。
virtual Double_t Interpolate(Double_t x, Double_t y);
virtual Double_t Interpolate(Double_t x, Double_t y, Double_t z);
Bool_t IsBinOverflow(Int_t bin) const;//Return true if the bin is overflow.
Bool_t IsBinUnderflow(Int_t bin) const;//Return true if the bin is overflow.
virtual Double_t AndersonDarlingTest(const TH1 *h2, Option_t *option="") const;
/// Statistical test of compatibility in shape between
/// this histogram and h2, using the Anderson-Darling 2 sample test.
/// The AD 2 sample test formula are derived from the paper
/// F.W Scholz, M.A. Stephens "k-Sample Anderson-Darling Test".
/// The test is implemented in root in the ROOT::Math::GoFTest class
/// It is the same formula ( (6) in the paper), and also shown in this preprint
/// http://arxiv.org/pdf/0804.0380v1.pdf
/// Binned data are considered as un-binned data
/// with identical observation happening in the bin center.
/// \param[in] option is a character string to specify options
/// - "D" Put out a line of "Debug" printout
/// - "T" Return the normalized A-D test statistic
/// - Note1: Underflow and overflow are not considered in the test
/// - Note2: The test works only for un-weighted histogram (i.e. representing counts)
/// - Note3: The histograms are not required to have the same X axis
/// - Note4: The test works only for 1-dimensional histograms
virtual Double_t AndersonDarlingTest(const TH1 *h2, Double_t &advalue) const;/// Same funciton as above but returning also the test statistic value
virtual Double_t KolmogorovTest(const TH1 *h2, Option_t *option="") const;// statistical test of compatibility in shape between two histograms
/// Statistical test of compatibility in shape between
/// this histogram and h2, using Kolmogorov test.
/// Note that the KolmogorovTest (KS) test should in theory be used only for unbinned data
/// and not for binned data as in the case of the histogram (see NOTE 3 below).
/// So, before using this method blindly, read the NOTE 3.
/// Default: Ignore under- and overflow bins in comparison
/// \param[in] option is a character string to specify options
/// - "U" include Underflows in test (also for 2-dim)
/// - "O" include Overflows (also valid for 2-dim)
/// - "N" include comparison of normalizations
/// - "D" Put out a line of "Debug" printout
/// - "M" Return the Maximum Kolmogorov distance instead of prob
/// - "X" Run the pseudo experiments post-processor with the following procedure:
/// make pseudoexperiments based on random values from the parent
/// distribution and compare the KS distance of the pseudoexperiment
/// to the parent distribution. Bin the KS distances in a histogram,
/// and then take the integral of all the KS values above the value
/// obtained from the original data to Monte Carlo distribution.
/// The number of pseudo-experiments nEXPT is currently fixed at 1000.
/// The function returns the integral.
/// (thanks to Ben Kilminster to submit this procedure). Note that
/// this option "X" is much slower.
/// The returned function value is the probability of test
/// (much less than one means NOT compatible)
/// Code adapted by Rene Brun from original HBOOK routine HDIFF
/// NOTE1
/// A good description of the Kolmogorov test can be seen at:
/// http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm
/// NOTE2
/// see also alternative function TH1::Chi2Test
/// The Kolmogorov test is assumed to give better results than Chi2Test
/// in case of histograms with low statistics.
/// NOTE3 (Jan Conrad, Fred James)
/// "The returned value PROB is calculated such that it will be
/// uniformly distributed between zero and one for compatible histograms,
/// provided the data are not binned (or the number of bins is very large
/// compared with the number of events). Users who have access to unbinned
/// data and wish exact confidence levels should therefore not put their data
/// into histograms, but should call directly TMath::KolmogorovTest. On
/// the other hand, since TH1 is a convenient way of collecting data and
/// saving space, this function has been provided. However, the values of
/// PROB for binned data will be shifted slightly higher than expected,
/// depending on the effects of the binning. For example, when comparing two
/// uniform distributions of 500 events in 100 bins, the values of PROB,
/// instead of being exactly uniformly distributed between zero and one, have
/// a mean value of about 0.56. We can apply a useful
/// rule: As long as the bin width is small compared with any significant
/// physical effect (for example the experimental resolution) then the binning
/// cannot have an important effect. Therefore, we believe that for all
/// practical purposes, the probability value PROB is calculated correctly
/// provided the user is aware that:
/// 1. The value of PROB should not be expected to have exactly the correct
/// distribution for binned data.
/// 2. The user is responsible for seeing to it that the bin widths are
/// small compared with any physical phenomena of interest.
/// 3. The effect of binning (if any) is always to make the value of PROB
/// slightly too big. That is, setting an acceptance criterion of (PROB>0.05
/// will assure that at most 5% of truly compatible histograms are rejected,
/// and usually somewhat less."
/// Note also that for GoF test of unbinned data ROOT provides also the class
/// ROOT::Math::GoFTest. The class has also method for doing one sample tests
/// (i.e. comparing the data with a given distribution).
virtual void LabelsDeflate(Option_t *axis="X");// Reduce the number of bins for the axis passed in the option to the number of bins having a label. The method will remove only the extra bins existing after the last "labeled" bin. Note that if there are "un-labeled" bins present between "labeled" bins they will not be removed.
virtual void LabelsInflate(Option_t *axis="X");//Double the number of bins for axis.Refill histogram. This function is called by TAxis::FindBin(const char *label).
virtual void LabelsOption(Option_t *option="h", Option_t *axis="X");
/// Set option(s) to draw axis with labels
/// \param[in] option
/// - "a" sort by alphabetic order
/// - ">" sort by decreasing values
/// - "<" sort by increasing values
/// - "h" draw labels horizontal
/// - "v" draw labels vertical
/// - "u" draw labels up (end of label right adjusted)
/// - "d" draw labels down (start of label left adjusted)
virtual Long64_t Merge(TCollection *list);
/// Add all histograms in the collection to this histogram.
/// This function computes the min/max for the x axis,
/// compute a new number of bins, if necessary,
/// add bin contents, errors and statistics.
/// If all histograms have bin labels, bins with identical labels
/// will be merged, no matter what their order is.
/// If overflows are present and limits are different the function will fail.
/// The function returns the total number of entries in the result histogram
/// if the merge is successful, -1 otherwise.
/// IMPORTANT remark. The axis x may have different number
/// of bins and different limits, BUT the largest bin width must be
/// a multiple of the smallest bin width and the upper limit must also
/// be a multiple of the bin width.
virtual Bool_t Multiply(TF1 *h1, Double_t c1=1);//Performs the operation: this = this*c1*f1. if errors are defined (see TH1::Sumw2), errors are also recalculated. Only bins inside the function range are recomputed. IMPORTANT NOTE: If you intend to use the errors of this histogram later you should call Sumw2 before making this operation. This is particularly important if you fit the histogram after TH1::Multiply The function return kFALSE if the Multiply operation failed.
virtual Bool_t Multiply(const TH1 *h1);// Multiply this histogram by h1. this = this*h1 If errors of this are available (TH1::Sumw2), errors are recalculated. Note that if h1 has Sumw2 set, Sumw2 is automatically called for this if not already set. IMPORTANT NOTE: If you intend to use the errors of this histogram later you should call Sumw2 before making this operation. This is particularly important if you fit the histogram after TH1::Multiply. The function return kFALSE if the Multiply operation failed
virtual Bool_t Multiply(const TH1 *h1, const TH1 *h2, Double_t c1=1, Double_t c2=1, Option_t *option=""); // *MENU* Replace contents of this histogram by multiplication of h1 by h2. this = (c1*h1)*(c2*h2) If errors of this are available (TH1::Sumw2), errors are recalculated. Note that if h1 or h2 have Sumw2 set, Sumw2 is automatically called for this if not already set. IMPORTANT NOTE: If you intend to use the errors of this histogram later you should call Sumw2 before making this operation. This is particularly important if you fit the histogram after TH1::Multiply. The function return kFALSE if the Multiply operation failed.
virtual void Paint(Option_t *option="");//Control routine to paint any kind of histograms. This function is automatically called by TCanvas::Update.(see TH1::Draw for the list of options)
virtual void Print(Option_t *option="") const;//Print some global quantities for this histogram. If option "base" is given, number of bins and ranges are also printed. If option "range" is given, bin contents and errors are also printed for all bins in the current range (default 1-->nbins). If option "all" is given, bin contents and errors are also printed for all bins including under and overflows.
virtual void PutStats(Double_t *stats);/// Replace current statistics with the values in array stats
virtual TH1 *Rebin(Int_t ngroup=2, const char*newname="", const Double_t *xbins=0); // *MENU*
/// Rebin this histogram
/// ### case 1 xbins=0
/// If newname is blank (default), the current histogram is modified and
/// a pointer to it is returned.
/// If newname is not blank, the current histogram is not modified, and a
/// new histogram is returned which is a Clone of the current histogram
/// with its name set to newname.
/// The parameter ngroup indicates how many bins of this have to be merged
/// into one bin of the result.
/// If the original histogram has errors stored (via Sumw2), the resulting
/// histograms has new errors correctly calculated.
/// NOTE: If ngroup is not an exact divider of the number of bins,
/// the top limit of the rebinned histogram is reduced
/// to the upper edge of the last bin that can make a complete
/// group. The remaining bins are added to the overflow bin.
/// Statistics will be recomputed from the new bin contents.
/// ### case 2 xbins!=0
/// A new histogram is created (you should specify newname).
/// The parameter ngroup is the number of variable size bins in the created histogram.
/// The array xbins must contain ngroup+1 elements that represent the low-edges
/// of the bins.
/// If the original histogram has errors stored (via Sumw2), the resulting
/// histograms has new errors correctly calculated.
/// NOTE: The bin edges specified in xbins should correspond to bin edges
/// in the original histogram. If a bin edge in the new histogram is
/// in the middle of a bin in the original histogram, all entries in
/// the split bin in the original histogram will be transfered to the
/// lower of the two possible bins in the new histogram. This is
/// probably not what you want.
virtual TH1 *RebinX(Int_t ngroup=2, const char*newname="") { return Rebin(ngroup,newname, (Double_t*) 0); }
virtual void Rebuild(Option_t *option="");/// Using the current bin info, recompute the arrays for contents and errors
virtual void RecursiveRemove(TObject *obj);/// Recursively remove object from the list of functions
virtual void Reset(Option_t *option="");//将其清除重置
// Reset this histogram: contents, errors, etc.
// if option "ICE" is specified, resets only Integral, Contents and Errors.
// if option "ICES" is specified, resets only Integral, Contents , Errors and Statistics
// if option "M" is specified, resets also Minimum and Maximum
// The option "ICE" is used when extending the histogram (in ExtendAxis, LabelInflate, etc..)
// The option "ICES is used in combination with the buffer (see BufferEmpty and BufferFill)
virtual void ResetStats();//Reset the statistics including the number of entries and replace with values calculates from bin content. The number of entries is set to the total bin content or (in case of weighted histogram) to number of effective entries.
virtual void SavePrimitive(std::ostream &out, Option_t *option = "");/// Save primitive as a C++ statement(s) on output stream out
virtual void Scale(Double_t c1=1, Option_t *option="");//比例缩放
/// Multiply this histogram by a constant c1.
///this = c1*this
/// Note that both contents and errors(if any) are scaled.
/// This function uses the services of TH1::Add
/// IMPORTANT NOTE: If you intend to use the errors of this histogram later
/// you should call Sumw2 before making this operation.
/// This is particularly important if you fit the histogram after TH1::Scale
/// One can scale an histogram such that the bins integral is equal to
/// the normalization parameter via TH1::Scale(Double_t norm), where norm
/// is the desired normalization divided by the integral of the histogram.
/// If option contains "width" the bin contents and errors are divided
/// by the bin width.
virtual void SetAxisColor(Color_t color=1, Option_t *axis="X");
virtual void SetAxisRange(Double_t xmin, Double_t xmax, Option_t *axis="X");
virtual void SetBarOffset(Float_t offset=0.25) {fBarOffset = Short_t(1000*offset);}
virtual void SetBarWidth(Float_t width=0.5) {fBarWidth = Short_t(1000*width);}
virtual void SetBinContent(Int_t bin, Double_t content);
/// Set bin content
/// see convention for numbering bins in TH1::GetBin
/// In case the bin number is greater than the number of bins and
/// the timedisplay option is set or CanExtendAllAxes(),
/// the number of bins is automatically doubled to accommodate the new bin
virtual void SetBinContent(Int_t bin, Int_t, Double_t content) { SetBinContent(bin, content); }
virtual void SetBinContent(Int_t bin, Int_t, Int_t, Double_t content) { SetBinContent(bin, content); }
virtual void SetBinError(Int_t bin, Double_t error);/// see convention for numbering bins in TH1::GetBin
virtual void SetBinError(Int_t binx, Int_t biny, Double_t error);/// see convention for numbering bins in TH1::GetBin
virtual void SetBinError(Int_t binx, Int_t biny, Int_t binz, Double_t error);// see convention for numbering bins in TH1::GetBin
virtual void SetBins(Int_t nx, Double_t xmin, Double_t xmax);
/// Redefine x axis parameters.
/// The X axis parameters are modified.
/// The bins content array is resized
/// if errors (Sumw2) the errors array is resized
/// The previous bin contents are lost
/// To change only the axis limits, see TAxis::SetRange
virtual void SetBins(Int_t nx, const Double_t *xBins);
/// Redefine x axis parameters with variable bin sizes.
/// The X axis parameters are modified.
/// The bins content array is resized
/// if errors (Sumw2) the errors array is resized
/// The previous bin contents are lost
/// To change only the axis limits, see TAxis::SetRange
/// xBins is supposed to be of length nx+1
virtual void SetBins(Int_t nx, Double_t xmin, Double_t xmax, Int_t ny, Double_t ymin, Double_t ymax);
/// Redefine x and y axis parameters.
/// The X and Y axis parameters are modified.
/// The bins content array is resized
/// if errors (Sumw2) the errors array is resized
/// The previous bin contents are lost
/// To change only the axis limits, see TAxis::SetRange
virtual void SetBins(Int_t nx, const Double_t *xBins, Int_t ny, const Double_t *yBins);
/// Redefine x and y axis parameters with variable bin sizes.
/// The X and Y axis parameters are modified.
/// The bins content array is resized
/// if errors (Sumw2) the errors array is resized
/// The previous bin contents are lost
/// To change only the axis limits, see TAxis::SetRange
/// xBins is supposed to be of length nx+1, yBins is supposed to be of length ny+1
virtual void SetBins(Int_t nx, Double_t xmin, Double_t xmax, Int_t ny, Double_t ymin, Double_t ymax,
Int_t nz, Double_t zmin, Double_t zmax);
/// Redefine x, y and z axis parameters.
/// The X, Y and Z axis parameters are modified.
/// The bins content array is resized
/// if errors (Sumw2) the errors array is resized
/// The previous bin contents are lost
/// To change only the axis limits, see TAxis::SetRange
virtual void SetBins(Int_t nx, const Double_t *xBins, Int_t ny, const Double_t * yBins, Int_t nz,
const Double_t *zBins);
/// Redefine x, y and z axis parameters with variable bin sizes.
/// The X, Y and Z axis parameters are modified.
/// The bins content array is resized
/// if errors (Sumw2) the errors array is resized
/// The previous bin contents are lost
/// To change only the axis limits, see TAxis::SetRange
/// xBins is supposed to be of length nx+1, yBins is supposed to be of length ny+1,
/// zBins is supposed to be of length nz+1
virtual void SetBinsLength(Int_t = -1) { } //redefined in derived classes Set total number of bins including under/overflow Reallocate bin contents array
virtual void SetBinErrorOption(EBinErrorOpt type) { fBinStatErrOpt = type; }
virtual void SetBuffer(Int_t buffersize, Option_t *option="");/// set the maximum number of entries to be kept in the buffer
virtual UInt_t SetCanExtend(UInt_t extendBitMask);
/// make the histogram axes extendable / not extendable according to the bit mask
/// returns the previous bit mask specifying which axes are extendable
virtual void SetContent(const Double_t *content);/// Replace bin contents by the contents of array content
virtual void SetContour(Int_t nlevels, const Double_t *levels=0);
/// Set the number and values of contour levels.
/// By default the number of contour levels is set to 20. The contours values
/// in the array "levels" should be specified in increasing order.
/// if argument levels = 0 or missing, equidistant contours are computed
virtual void SetContourLevel(Int_t level, Double_t value);/// Set value for one contour level.
static void SetDefaultBufferSize(Int_t buffersize=1000);
/// static function to set the default buffer size for automatic histograms.
/// When an histogram is created with one of its axis lower limit greater
/// or equal to its upper limit, the function SetBuffer is automatically
/// called with the default buffer size.
static void SetDefaultSumw2(Bool_t sumw2=kTRUE);
/// static function.
/// When this static function is called with sumw2=kTRUE, all new
/// histograms will automatically activate the storage
/// of the sum of squares of errors, ie TH1::Sumw2 is automatically called.
virtual void SetDirectory(TDirectory *dir);
/// By default when an histogram is created, it is added to the list
/// of histogram objects in the current directory in memory.
/// Remove reference to this histogram from current directory and add
/// reference to new directory dir. dir can be 0 in which case the
/// histogram does not belong to any directory.
/// Note that the directory is not a real property of the histogram and
/// it will not be copied when the histogram is copied or cloned.
/// If the user wants to have the copied (cloned) histogram in the same
/// directory, he needs to set again the directory using SetDirectory to the
/// copied histograms
virtual void SetEntries(Double_t n) {fEntries = n;};
virtual void SetError(const Double_t *error);/// Replace bin errors by values in array error.
virtual void SetLabelColor(Color_t color=1, Option_t *axis="X");
virtual void SetLabelFont(Style_t font=62, Option_t *axis="X");
virtual void SetLabelOffset(Float_t offset=0.005, Option_t *axis="X");
virtual void SetLabelSize(Float_t size=0.02, Option_t *axis="X");
/*
* Set the minimum / maximum value for the Y axis (1-D histograms) or Z axis (2-D histograms)
* By default the maximum / minimum value used in drawing is the maximum / minimum value of the histogram
* plus a margin of 10%. If these functions are called, the values are used without any extra margin.
*/
virtual void SetMaximum(Double_t maximum = -1111) { fMaximum = maximum; }; // *MENU* Set the minimum / maximum value for the Y axis (1-D histograms) or Z axis (2-D histograms). By default the maximum / minimum value used in drawing is the maximum / minimum value of the histogram plus a margin of 10\%. If these functions are called, the values are used without any extra margin.
virtual void SetMinimum(Double_t minimum = -1111) { fMinimum = minimum; }; // *MENU*
virtual void SetName(const char *name); // *MENU* Change the name of this histogram. Histograms are named objects in a THashList. We must update the hashlist if we change the name. We protect this operation
virtual void SetNameTitle(const char *name, const char *title);//Change the name and title of this histogram. Histograms are named objects in a THashList. We must update the hashlist if we change the name
virtual void SetNdivisions(Int_t n=510, Option_t *axis="X");
virtual void SetNormFactor(Double_t factor=1) {fNormFactor = factor;}
virtual void SetStats(Bool_t stats=kTRUE); // *MENU*
/// Set statistics option on/off
/// By default, the statistics box is drawn.
/// The paint options can be selected via gStyle->SetOptStats.
/// This function sets/resets the kNoStats bin in the histogram object.
/// It has priority over the Style option.
virtual void SetOption(Option_t *option=" ") {fOption = option;}
virtual void SetTickLength(Float_t length=0.02, Option_t *axis="X");
virtual void SetTitleFont(Style_t font=62, Option_t *axis="X");
virtual void SetTitleOffset(Float_t offset=1, Option_t *axis="X");
virtual void SetTitleSize(Float_t size=0.02, Option_t *axis="X");
virtual void SetTitle(const char *title); // *MENU* Change (i.e. set) the title. if title is in the form "stringt;stringx;stringy;stringz" the histogram title is set to stringt, the x axis title to stringx, the y axis title to stringy, and the z axis title to stringz. To insert the character ";" in one of the titles, one should use "\#;" or "\#semicolon".
virtual void SetXTitle(const char *title) {fXaxis.SetTitle(title);}
virtual void SetYTitle(const char *title) {fYaxis.SetTitle(title);}
virtual void SetZTitle(const char *title) {fZaxis.SetTitle(title);}
virtual TH1 *ShowBackground(Int_t niter=20, Option_t *option="same"); // *MENU*
/// This function calculates the background spectrum in this histogram.
/// The background is returned as a histogram.
/// \param[in] niter number of iterations (default value = 2)
/// Increasing niter make the result smoother and lower.
/// \param[in] option may contain one of the following options
/// - to set the direction parameter
/// "BackDecreasingWindow". By default the direction is BackIncreasingWindow
/// - filterOrder-order of clipping filter (default "BackOrder2")
/// possible values= "BackOrder4" "BackOrder6" "BackOrder8"
/// - "nosmoothing" - if selected, the background is not smoothed
/// By default the background is smoothed.
/// - smoothWindow - width of smoothing window, (default is "BackSmoothing3")
/// possible values= "BackSmoothing5" "BackSmoothing7" "BackSmoothing9"
/// "BackSmoothing11" "BackSmoothing13" "BackSmoothing15"
/// - "nocompton" - if selected the estimation of Compton edge
/// will be not be included (by default the compton estimation is set)
/// - "same" if this option is specified, the resulting background
/// histogram is superimposed on the picture in the current pad.
/// This option is given by default.
/// NOTE that the background is only evaluated in the current range of this histogram.
/// i.e., if this has a bin range (set via h->GetXaxis()->SetRange(binmin, binmax),
/// the returned histogram will be created with the same number of bins
/// as this input histogram, but only bins from binmin to binmax will be filled
/// with the estimated background.
virtual Int_t ShowPeaks(Double_t sigma=2, Option_t *option="", Double_t threshold=0.05); // *MENU*
/// Interface to TSpectrum::Search.
/// The function finds peaks in this histogram where the width is > sigma
/// and the peak maximum greater than threshold*maximum bin content of this.
/// For more details see TSpectrum::Search.
/// Note the difference in the default value for option compared to TSpectrum::Search
/// option="" by default (instead of "goff").
virtual void Smooth(Int_t ntimes=1, Option_t *option=""); // *MENU* Smooth bin contents of this histogram. if option contains "R" smoothing is applied only to the bins defined in the X axis range (default is to smooth all bins). Bin contents are replaced by their smooth values. Errors (if any) are not modified. the smoothing procedure is repeated ntimes (default=1)
static void SmoothArray(Int_t NN, Double_t *XX, Int_t ntimes=1);//smooth array xx, translation of Hbook routine hsmoof.F based on algorithm 353QH twice presented by J. Friedman in Proc.of the 1974 CERN School of Computing, Norway, 11-24 August, 1974.
static void StatOverflows(Bool_t flag=kTRUE);
/// if flag=kTRUE, underflows and overflows are used by the Fill functions
/// in the computation of statistics (mean value, StdDev).
/// By default, underflows or overflows are not used.
virtual void Sumw2(Bool_t flag = kTRUE);
/// Create structure to store sum of squares of weights.
/// if histogram is already filled, the sum of squares of weights
/// is filled with the existing bin contents
/// The error per bin will be computed as sqrt(sum of squares of weight)
/// for each bin.
/// This function is automatically called when the histogram is created
/// if the static function TH1::SetDefaultSumw2 has been called before.
/// If flag = false the structure is deleted
void UseCurrentStyle();///Copy current attributes from/to current style
static TH1 *TransformHisto(TVirtualFFT *fft, TH1* h_output, Option_t *option);
/// For a given transform (first parameter), fills the histogram (second parameter)
/// with the transform output data, specified in the third parameter
/// If the 2nd parameter h_output is empty, a new histogram (TH1D or TH2D) is created
/// and the user is responsible for deleting it.
/// Available options:
/// - "RE" - real part of the output
/// - "IM" - imaginary part of the output
/// - "MAG" - magnitude of the output
/// - "PH" - phase of the output
// TODO: Remove obsolete methods in v6-04
virtual Double_t GetCellContent(Int_t binx, Int_t biny) const
{ Obsolete("GetCellContent", "v6-00", "v6-04"); return GetBinContent(GetBin(binx, biny)); }
virtual Double_t GetCellError(Int_t binx, Int_t biny) const
{ Obsolete("GetCellError", "v6-00", "v6-04"); return GetBinError(binx, biny); }
virtual void RebinAxis(Double_t x, TAxis *axis)
{ Obsolete("RebinAxis", "v6-00", "v6-04"); ExtendAxis(x, axis); }
virtual void SetCellContent(Int_t binx, Int_t biny, Double_t content)
{ Obsolete("SetCellContent", "v6-00", "v6-04"); SetBinContent(GetBin(binx, biny), content); }
virtual void SetCellError(Int_t binx, Int_t biny, Double_t content)
{ Obsolete("SetCellError", "v6-00", "v6-04"); SetBinError(binx, biny, content); }
```

## code¶

```
TH1F *h1=new TH1F("stats name","title name",number of bins,min,max);
TH1F *h1=new TH1F("stats name","title name;X axis;Y axis",number of bins,min,max);
float x=gRandom->Uniform(-5.,5.);
h1->Fill(x); //均匀分布
h1->FillRandom("gaus",50000); //
h1->Draw();
```

```
//循环创建图片
TH1D h[16];
char Stringtemp[256];
for(int i=0;i<16;i++){
sprintf(Stringtemp,"h[%d]",i);//这样创建数组名不好，直接 "h%d"这样好
h[i]=new TH1D(Stringtemp,"",4096,0,4096);
}
```

```
//默认情况下，Draw 将会清空当 前Pad 再画当前直方图，如想要一个图上多个直方图，将第二个及之后的直方图 Option_t 设为 "same"。
TH1D *h=new TH1D("h","the title",60,-3.0,3.0);
TH1D *h1=new TH1D("h1","",60,-3.0,3.0);
TRandom *r =new TRandom();
for (int i = 0; i<1000; ++i)
{
h->Fill(r->Gaus());
h1->Fill(r->Gaus(1,1));
}
h->Draw();
// h1->Draw();
h1->Draw("same");
```

```
//Double_t *GetIntegral();
//Return a pointer to the array of bins integral.
//返回一个指向数组的指针，当前值为 bin 从 0到当前 bin 面积所占的比例。
int bin=60;
TH1D *h=new TH1D("h","the title",bin,-3.0,3.0);
TRandom *r =new TRandom();
for (int i = 0; i<1000; ++i)
{
h->Fill(r->Gaus());
}
double *Integral;
Integral=h->GetIntegral();
for (int i = 0; i<bin; ++i)
{
std::cout<<i<<" "<<Integral[i]<<std::endl;
}
h->Draw();
```

```
//克隆直方图，这里的 Close 是新开辟一块内存空间存储新直方图的，克隆之后，原始直方图的修改或删除对克隆的直方图没有影响。而TH1D *hnew =h;这个只是将新建的对象指向 h 的地址。
TH1D *h=new TH1D("h","the title",60,-3.0,3.0);
TRandom *r =new TRandom();
for (int i = 0; i<1000; ++i)
{
h->Fill(r->Gaus());
}
TH1D *hnew = (TH1D*)h->Clone("hnew");
// TH1D *hnew =h;
h->Reset();
hnew->Draw();
```

```
// virtual TH1 *Rebin(Int_t ngroup=2, const char*newname="", const Double_t *xbins=0);
/// examples: if h1 is an existing TH1F histogram with 100 bins
h1->Rebin(); //merges two bins in one in h1: previous contents of h1 are lost
h1->Rebin(5); //merges five bins in one in h1
TH1F *hnew = h1->Rebin(5,"hnew"); // creates a new histogram hnew merging 5 bins of h1 in one bin
/// examples: if h1 is an existing TH1F histogram with 100 bins
Double_t xbins[25] = {...} //array of low-edges (xbins[25] is the upper edge of last bin
h1->Rebin(24,"hnew",xbins); //creates a new variable bin size histogram hnew
```

```
// virtual Long64_t Merge(TCollection *list);
void atest() {
TH1F *h1 = new TH1F("h1","h1",110,-110,0);
TH1F *h2 = new TH1F("h2","h2",220,0,110);
TH1F *h3 = new TH1F("h3","h3",330,-55,55);
TRandom r;
for (Int_t i=0;i<10000;i++) {
h1->Fill(r.Gaus(-55,10));
h2->Fill(r.Gaus(55,10));
h3->Fill(r.Gaus(0,10));
}
///
TList *list = new TList;
list->Add(h1);
list->Add(h2);
list->Add(h3);
TH1F *h = (TH1F*)h1->Clone("h");
h->Reset();
h->Merge(list);
h->Draw();
}
```

```
// virtual Int_t GetQuantiles(Int_t nprobSum, Double_t *q, const Double_t *probSum=0);
Getting quantiles q from two histograms and storing results in a TGraph, a so-called QQ-plot
TGraph *gr = new TGraph(nprob);
h1->GetQuantiles(nprob,gr->GetX());
h2->GetQuantiles(nprob,gr->GetY());
gr->Draw("alp");
void quantiles() {
// demo for quantiles
const Int_t nq = 20;
TH1F *h = new TH1F("h","demo quantiles",100,-3,3);
h->FillRandom("gaus",5000);
///
Double_t xq[nq]; // position where to compute the quantiles in [0,1]
Double_t yq[nq]; // array to contain the quantiles
for (Int_t i=0;i<nq;i++) xq[i] = Float_t(i+1)/nq;
h->GetQuantiles(nq,yq,xq);
///
//show the original histogram in the top pad
TCanvas *c1 = new TCanvas("c1","demo quantiles",10,10,700,900);
c1->Divide(1,2);
c1->cd(1);
h->Draw();
///
// show the quantiles in the bottom pad
c1->cd(2);
gPad->SetGrid();
TGraph *gr = new TGraph(nq,xq,yq);
gr->SetMarkerStyle(21);
gr->Draw("alp");
}
```

```
// virtual TFitResultPtr Fit(TF1 *f1 ,Option_t *option="" ,Option_t *goption="", Double_t xmin=0, Double_t xmax=0);
/// In order to use the Range option, one must first create a function
/// with the expression to be fitted. For example, if your histogram
/// has a defined range between -4 and 4 and you want to fit a gaussian
/// only in the interval 1 to 3, you can do:
TF1 *f1 = new TF1("f1", "gaus", 1, 3);
histo->Fit("f1", "R");
/// You can specify boundary limits for some or all parameters via
f1->SetParLimits(p_number, parmin, parmax);
/// if parmin>=parmax, the parameter is fixed
/// Note that you are not forced to fix the limits for all parameters.
/// For example, if you fit a function with 6 parameters, you can do:
func->SetParameters(0, 3.1, 1.e-6, -8, 0, 100);
func->SetParLimits(3, -10, -4);
func->FixParameter(4, 0);
func->SetParLimits(5, 1, 1);
/// With this setup, parameters 0->2 can vary freely
/// Parameter 3 has boundaries [-10,-4] with initial value -8
/// Parameter 4 is fixed to 0
/// Parameter 5 is fixed to 100.
/// When the lower limit and upper limit are equal, the parameter is fixed.
/// However to fix a parameter to 0, one must call the FixParameter function.
/// If the option "S" is instead used, TFitResultPtr contains the TFitResult and behaves as a smart
/// pointer to it. For example one can do:
TFitResultPtr r = h->Fit(myFunc,"S");
TMatrixDSym cov = r->GetCovarianceMatrix(); // to access the covariance matrix
Double_t chi2 = r->Chi2(); // to retrieve the fit chi2
Double_t par0 = r->Parameter(0); // retrieve the value for the parameter 0
Double_t err0 = r->ParError(0); // retrieve the error for the parameter 0
r->Print("V"); // print full information of fit including covariance matrix
r->Write(); // store the result in a file
/// The fit parameters, error and chi2 (but not covariance matrix) can be retrieved also
/// from the fitted function.
/// If the histogram is made persistent, the list of
/// associated functions is also persistent. Given a pointer (see above)
/// to an associated function myfunc, one can retrieve the function/fit
/// parameters with calls such as:
Double_t chi2 = myfunc->GetChisquare();
Double_t par0 = myfunc->GetParameter(0); //value of 1st parameter
Double_t err0 = myfunc->GetParError(0); //error on first parameter
/// The status of the fit can be obtained converting the TFitResultPtr to an integer
/// independently if the fit option "S" is used or not:
TFitResultPtr r = h->Fit(myFunc,opt);
Int_t fitStatus = r;
/// The fitStatus is 0 if the fit is OK (i.e no error occurred).
/// The value of the fit status code is negative in case of an error not connected with the
/// minimization procedure, for example when a wrong function is used.
/// Otherwise the return value is the one returned from the minimization procedure.
/// ## Excluding points
/// Use TF1::RejectPoint inside your fitting function to exclude points
/// within a certain range from the fit. Example:
Double_t fline(Double_t *x, Double_t *par)
{
if (x[0] > 2.5 && x[0] < 3.5) {
TF1::RejectPoint();
return 0;
}
return par[0] + par[1]*x[0];
}
void exclude() {
TF1 *f1 = new TF1("f1", "[0] +[1]*x +gaus(2)", 0, 5);
f1->SetParameters(6, -1,5, 3, 0.2);
TH1F *h = new TH1F("h", "background + signal", 100, 0, 5);
h->FillRandom("f1", 2000);
TF1 *fline = new TF1("fline", fline, 0, 5, 2);
fline->SetParameters(2, -1);
h->Fit("fline", "l");
}
/// ## Warning when using the option "0"
/// When selecting the option "0", the fitted function is added to
/// the list of functions of the histogram, but it is not drawn.
/// You can undo what you disabled in the following way:
h.Fit("myFunction", "0"); // fit, store function but do not draw
h.Draw(); function is not drawn
const Int_t kNotDraw = 1<<9;
h.GetFunction("myFunction")->ResetBit(kNotDraw);
h.Draw(); // function is visible again
```