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ROOT
Reference Guide |
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ROOT
Reference Guide |
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Principal Components Analysis (PCA)
The current implementation is based on the LINTRA package from CERNLIB by R. Brun, H. Hansroul, and J. Kubler. The class has been implemented by Christian Holm Christensen in August 2000.
In many applications of various fields of research, the treatment of large amounts of data requires powerful techniques capable of rapid data reduction and analysis. Usually, the quantities most conveniently measured by the experimentalist, are not necessarily the most significant for classification and analysis of the data. It is then useful to have a way of selecting an optimal set of variables necessary for the recognition process and reducing the dimensionality of the problem, resulting in an easier classification procedure.
This paper describes the implementation of one such method of feature selection, namely the principal components analysis. This multidimensional technique is well known in the field of pattern recognition and and its use in Particle Physics has been documented elsewhere (cf. H. Wind, Function Parameterization, CERN 72-21).
Suppose we have prototypes which are trajectories of particles, passing through a spectrometer. If one measures the passage of the particle at say 8 fixed planes, the trajectory is described by an 8-component vector:
\[ \mathbf{x} = \left(x_0, x_1, \ldots, x_7\right) \]
in 8-dimensional pattern space.
One proceeds by generating a representative tracks sample and building up the covariance matrix \(\mathsf{C}\). Its eigenvectors and eigenvalues are computed by standard methods, and thus a new basis is obtained for the original 8-dimensional space the expansion of the prototypes,
\[ \mathbf{x}_m = \sum^7_{i=0} a_{m_i} \mathbf{e}_i \quad \mbox{where} \quad a_{m_i} = \mathbf{x}^T\bullet\mathbf{e}_i \]
allows the study of the behavior of the coefficients \(a_{m_i}\) for all the tracks of the sample. The eigenvectors which are insignificant for the trajectory description in the expansion will have their corresponding coefficients \(a_{m_i}\) close to zero for all the prototypes.
On one hand, a reduction of the dimensionality is then obtained by omitting these least significant vectors in the subsequent analysis.
On the other hand, in the analysis of real data, these least significant variables(?) can be used for the pattern recognition problem of extracting the valid combinations of coordinates describing a true trajectory from the set of all possible wrong combinations.
The program described here performs this principal components analysis on a sample of data provided by the user. It computes the covariance matrix, its eigenvalues ands corresponding eigenvectors and exhibits the behavior of the principal components \(a_{m_i}\), thus providing to the user all the means of understanding their data.
Let's consider a sample of \(M\) prototypes each being characterized by \(P\) variables \(x_0, x_1, \ldots, x_{P-1}\). Each prototype is a point, or a column vector, in a \(P\)-dimensional Pattern space.
\[ \mathbf{x} = \left[\begin{array}{c} x_0\\x_1\\\vdots\\x_{P-1}\end{array}\right]\,, \]
where each \(x_n\) represents the particular value associated with the \(n\)-dimension.
Those \(P\) variables are the quantities accessible to the experimentalist, but are not necessarily the most significant for the classification purpose.
The Principal Components Method consists of applying a linear* transformation to the original variables. This transformation is described by an orthogonal matrix and is equivalent to a rotation of the original pattern space into a new set of coordinate vectors, which hopefully provide easier feature identification and dimensionality reduction.
Let's define the covariance matrix:
\[ \mathsf{C} = \left\langle\mathbf{y}\mathbf{y}^T\right\rangle \quad\mbox{where}\quad \mathbf{y} = \mathbf{x} - \left\langle\mathbf{x}\right\rangle\,, \]
and the brackets indicate mean value over the sample of \(M\) prototypes.
This matrix \(\mathsf{C}\) is real, positive definite, symmetric, and will have all its eigenvalues greater then zero. It will now be show that among the family of all the complete orthonormal bases of the pattern space, the base formed by the eigenvectors of the covariance matrix and belonging to the largest eigenvalues, corresponds to the most significant features of the description of the original prototypes.
let the prototypes be expanded on into a set of \(N\) basis vectors \(\mathbf{e}_n, n=0,\ldots,N,N+1, \ldots, P-1\)
\[ \mathbf{y}_i = \sum^N_{i=0} a_{i_n} \mathbf{e}_n, \quad i = 1, \ldots, M, \quad N < P-1 \]
The ‘best’ feature coordinates \(\mathbf{e}_n\), spanning a feature space, will be obtained by minimizing the error due to this truncated expansion, i.e.,
\[ \min\left(E_N\right) = \min\left[\left\langle\left(\mathbf{y}_i - \sum^N_{i=0} a_{i_n} \mathbf{e}_n\right)^2\right\rangle\right] \]
with the conditions:
\[ \mathbf{e}_k\bullet\mathbf{e}_j = \delta_{jk} = \left\{\begin{array}{rcl} 1 & \mbox{for} & k = j\\ 0 & \mbox{for} & k \neq j \end{array}\right. \]
Multiplying (3) by \(\mathbf{e}^T_n\) using (5), we get
\[ a_{i_n} = \mathbf{y}_i^T\bullet\mathbf{e}_n\,, \]
so the error becomes
\begin{eqnarray*} E_N &=& \left\langle\left[\sum_{n=N+1}^{P-1} a_{i_n}\mathbf{e}_n\right]^2\right\rangle\nonumber\\ &=& \left\langle\left[\sum_{n=N+1}^{P-1} \mathbf{y}_i^T\bullet\mathbf{e}_n\mathbf{e}_n\right]^2\right\rangle\nonumber\\ &=& \left\langle\sum_{n=N+1}^{P-1} \mathbf{e}_n^T\mathbf{y}_i\mathbf{y}_i^T\mathbf{e}_n\right\rangle\nonumber\\ &=& \sum_{n=N+1}^{P-1} \mathbf{e}_n^T\mathsf{C}\mathbf{e}_n \end{eqnarray*}
The minimization of the sum in (7) is obtained when each term \(\mathbf{e}_n^\mathsf{C}\mathbf{e}_n\) is minimum, since \(\mathsf{C}\) is positive definite. By the method of Lagrange multipliers, and the condition (5), we get
\[ E_N = \sum^{P-1}_{n=N+1} \left(\mathbf{e}_n^T\mathsf{C}\mathbf{e}_n - l_n\mathbf{e}_n^T\bullet\mathbf{e}_n + l_n\right) \]
The minimum condition \(\frac{dE_N}{d\mathbf{e}^T_n} = 0\) leads to the equation
\[ \mathsf{C}\mathbf{e}_n = l_n\mathbf{e}_n\,, \]
which shows that \(\mathbf{e}_n\) is an eigenvector of the covariance matrix \(\mathsf{C}\) with eigenvalue \(l_n\). The estimated minimum error is then given by
\[ E_N \sim \sum^{P-1}_{n=N+1} \mathbf{e}_n^T\bullet l_n\mathbf{e}_n = \sum^{P-1}_{n=N+1} l_n\,, \]
where \(l_n,\,n=N+1,\ldots,P\) \(l_n,\,n=N+1,\ldots,P-1\) are the eigenvalues associated with the omitted eigenvectors in the expansion (3). Thus, by choosing the \(N\) largest eigenvalues, and their associated eigenvectors, the error \(E_N\) is minimized.
The transformation matrix to go from the pattern space to the feature space consists of the ordered eigenvectors \(\mathbf{e}_1,\ldots,\mathbf{e}_P\) \(\mathbf{e}_0,\ldots,\mathbf{e}_{P-1}\) for its columns
\[ \mathsf{T} = \left[ \begin{array}{cccc} \mathbf{e}_0 & \mathbf{e}_1 & \vdots & \mathbf{e}_{P-1} \end{array}\right] = \left[ \begin{array}{cccc} \mathbf{e}_{0_0} & \mathbf{e}_{1_0} & \cdots & \mathbf{e}_{{P-1}_0}\\ \mathbf{e}_{0_1} & \mathbf{e}_{1_1} & \cdots & \mathbf{e}_{{P-1}_1}\\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{e}_{0_{P-1}} & \mathbf{e}_{1_{P-1}} & \cdots & \mathbf{e}_{{P-1}_{P-1}}\\ \end{array}\right] \]
This is an orthogonal transformation, or rotation, of the pattern space and feature selection results in ignoring certain coordinates in the transformed space.
Christian Holm August 2000, CERN
Definition at line 21 of file TPrincipal.h.
Public Types | |
| enum | { kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff } |
| enum | { kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) } |
| enum | EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) } |
| enum | EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) } |
Public Member Functions | |
| TPrincipal () | |
| Empty constructor. Do not use. | |
| TPrincipal (Long64_t nVariables, Option_t *opt="ND") | |
| Constructor. | |
| ~TPrincipal () override | |
| Destructor. | |
| void | AbstractMethod (const char *method) const |
| Call this function within a function that you don't want to define as purely virtual, in order not to force all users deriving from that class to implement that maybe (on their side) unused function; but at the same time, emit a run-time warning if they try to call it, telling that it is not implemented in the derived class: action must thus be taken on the user side to override it. | |
| virtual void | AddRow (const Double_t *x) |
| Add a data point and update the covariance matrix. | |
| virtual void | AppendPad (Option_t *option="") |
| Append graphics object to current pad. | |
| void | Browse (TBrowser *b) override |
| Browse the TPrincipal object in the TBrowser. | |
| ULong_t | CheckedHash () |
| Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. | |
| virtual const char * | ClassName () const |
| Returns name of class to which the object belongs. | |
| void | Clear (Option_t *option="") override |
| Clear the data in Object. | |
| TObject * | Clone (const char *newname="") const override |
| Make a clone of an object using the Streamer facility. | |
| Int_t | Compare (const TObject *obj) const override |
| Compare two TNamed objects. | |
| void | Copy (TObject &named) const override |
| Copy this to obj. | |
| virtual void | Delete (Option_t *option="") |
| Delete this object. | |
| virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
| Computes distance from point (px,py) to the object. | |
| virtual void | Draw (Option_t *option="") |
| Default Draw method for all objects. | |
| virtual void | DrawClass () const |
| Draw class inheritance tree of the class to which this object belongs. | |
| virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1). | |
| virtual void | Dump () const |
| Dump contents of object on stdout. | |
| virtual void | Error (const char *method, const char *msgfmt,...) const |
| Issue error message. | |
| virtual void | Execute (const char *method, const char *params, Int_t *error=nullptr) |
| Execute method on this object with the given parameter string, e.g. | |
| virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr) |
| Execute method on this object with parameters stored in the TObjArray. | |
| virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
| Execute action corresponding to an event at (px,py). | |
| virtual void | Fatal (const char *method, const char *msgfmt,...) const |
| Issue fatal error message. | |
| virtual void | FillBuffer (char *&buffer) |
| Encode TNamed into output buffer. | |
| virtual TObject * | FindObject (const char *name) const |
| Must be redefined in derived classes. | |
| virtual TObject * | FindObject (const TObject *obj) const |
| Must be redefined in derived classes. | |
| const TMatrixD * | GetCovarianceMatrix () const |
| Return the covariance matrix. | |
| virtual Option_t * | GetDrawOption () const |
| Get option used by the graphics system to draw this object. | |
| const TVectorD * | GetEigenValues () const |
| const TMatrixD * | GetEigenVectors () const |
| TList * | GetHistograms () const |
| virtual const char * | GetIconName () const |
| Returns mime type name of object. | |
| const TVectorD * | GetMeanValues () const |
| const char * | GetName () const override |
| Returns name of object. | |
| virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
| Returns string containing info about the object at position (px,py). | |
| virtual Option_t * | GetOption () const |
| const Double_t * | GetRow (Long64_t row) |
| Return a row of the user supplied data. | |
| const TVectorD * | GetSigmas () const |
| const char * | GetTitle () const override |
| Returns title of object. | |
| virtual UInt_t | GetUniqueID () const |
| Return the unique object id. | |
| const TVectorD * | GetUserData () const |
| virtual Bool_t | HandleTimer (TTimer *timer) |
| Execute action in response of a timer timing out. | |
| ULong_t | Hash () const override |
| Return hash value for this object. | |
| Bool_t | HasInconsistentHash () const |
| Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. | |
| virtual void | Info (const char *method, const char *msgfmt,...) const |
| Issue info message. | |
| virtual Bool_t | InheritsFrom (const char *classname) const |
| Returns kTRUE if object inherits from class "classname". | |
| virtual Bool_t | InheritsFrom (const TClass *cl) const |
| Returns kTRUE if object inherits from TClass cl. | |
| virtual void | Inspect () const |
| Dump contents of this object in a graphics canvas. | |
| void | InvertBit (UInt_t f) |
| TClass * | IsA () const override |
| Bool_t | IsDestructed () const |
| IsDestructed. | |
| virtual Bool_t | IsEqual (const TObject *obj) const |
| Default equal comparison (objects are equal if they have the same address in memory). | |
| Bool_t | IsFolder () const override |
| Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). | |
| R__ALWAYS_INLINE Bool_t | IsOnHeap () const |
| Bool_t | IsSortable () const override |
| R__ALWAYS_INLINE Bool_t | IsZombie () const |
| void | ls (Option_t *option="") const override |
| List TNamed name and title. | |
| virtual void | MakeCode (const char *filename="pca", Option_t *option="") |
Generates the file <filename>, with .C appended if it does argument doesn't end in .cxx or .C. | |
| virtual void | MakeHistograms (const char *name="pca", Option_t *option="epsdx") |
| Make histograms of the result of the analysis. | |
| virtual void | MakeMethods (const char *classname="PCA", Option_t *option="") |
Generate the file <classname>PCA.cxx which contains the implementation of two methods: | |
| virtual void | MakePrincipals () |
| Perform the principal components analysis. | |
| void | MayNotUse (const char *method) const |
| Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). | |
| virtual Bool_t | Notify () |
| This method must be overridden to handle object notification (the base implementation is no-op). | |
| void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
| Use this method to declare a method obsolete. | |
| void | operator delete (void *, size_t) |
| Operator delete for sized deallocation. | |
| void | operator delete (void *ptr) |
| Operator delete. | |
| void | operator delete (void *ptr, void *vp) |
| Only called by placement new when throwing an exception. | |
| void | operator delete[] (void *, size_t) |
| Operator delete [] for sized deallocation. | |
| void | operator delete[] (void *ptr) |
| Operator delete []. | |
| void | operator delete[] (void *ptr, void *vp) |
| Only called by placement new[] when throwing an exception. | |
| void * | operator new (size_t sz) |
| void * | operator new (size_t sz, void *vp) |
| void * | operator new[] (size_t sz) |
| void * | operator new[] (size_t sz, void *vp) |
| virtual void | P2X (const Double_t *p, Double_t *x, Int_t nTest) |
| Calculate x as a function of nTest of the most significant principal components p, and return it in x. | |
| virtual void | Paint (Option_t *option="") |
| This method must be overridden if a class wants to paint itself. | |
| virtual void | Pop () |
| Pop on object drawn in a pad to the top of the display list. | |
| void | Print (Option_t *opt="MSE") const override |
| Print the statistics Options are. | |
| virtual Int_t | Read (const char *name) |
| Read contents of object with specified name from the current directory. | |
| virtual void | RecursiveRemove (TObject *obj) |
| Recursively remove this object from a list. | |
| void | ResetBit (UInt_t f) |
| virtual void | SaveAs (const char *filename="", Option_t *option="") const |
| Save this object in the file specified by filename. | |
| virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
| Save a primitive as a C++ statement(s) on output stream "out". | |
| void | SetBit (UInt_t f) |
| void | SetBit (UInt_t f, Bool_t set) |
| Set or unset the user status bits as specified in f. | |
| virtual void | SetDrawOption (Option_t *option="") |
| Set drawing option for object. | |
| virtual void | SetName (const char *name) |
| Set the name of the TNamed. | |
| virtual void | SetNameTitle (const char *name, const char *title) |
| Set all the TNamed parameters (name and title). | |
| virtual void | SetTitle (const char *title="") |
| Set the title of the TNamed. | |
| virtual void | SetUniqueID (UInt_t uid) |
| Set the unique object id. | |
| virtual Int_t | Sizeof () const |
| Return size of the TNamed part of the TObject. | |
| void | Streamer (TBuffer &) override |
| Stream an object of class TObject. | |
| void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
| virtual void | SumOfSquareResiduals (const Double_t *x, Double_t *s) |
| Calculates the sum of the square residuals, that is. | |
| virtual void | SysError (const char *method, const char *msgfmt,...) const |
| Issue system error message. | |
| void | Test (Option_t *option="") |
| Test the PCA, bye calculating the sum square of residuals (see method SumOfSquareResiduals), and display the histogram. | |
| R__ALWAYS_INLINE Bool_t | TestBit (UInt_t f) const |
| Int_t | TestBits (UInt_t f) const |
| virtual void | UseCurrentStyle () |
| Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. | |
| virtual void | Warning (const char *method, const char *msgfmt,...) const |
| Issue warning message. | |
| virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) |
| Write this object to the current directory. | |
| virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const |
| Write this object to the current directory. | |
| virtual void | X2P (const Double_t *x, Double_t *p) |
| Calculate the principal components from the original data vector x, and return it in p. | |
Static Public Member Functions | |
| static TClass * | Class () |
| static const char * | Class_Name () |
| static constexpr Version_t | Class_Version () |
| static const char * | DeclFileName () |
| static Longptr_t | GetDtorOnly () |
| Return destructor only flag. | |
| static Bool_t | GetObjectStat () |
| Get status of object stat flag. | |
| static void | SetDtorOnly (void *obj) |
| Set destructor only flag. | |
| static void | SetObjectStat (Bool_t stat) |
| Turn on/off tracking of objects in the TObjectTable. | |
Protected Types | |
| enum | { kOnlyPrepStep = (1ULL << ( 3 )) } |
Protected Member Functions | |
| TPrincipal (const TPrincipal &) | |
| Copy constructor. | |
| virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
| Interface to ErrorHandler (protected). | |
| void | MakeNormalised () |
| Normalize the covariance matrix. | |
| void | MakeRealCode (const char *filename, const char *prefix, Option_t *option="") |
| This is the method that actually generates the code for the transformations to and from feature space and pattern space It's called by TPrincipal::MakeCode and TPrincipal::MakeMethods. | |
| void | MakeZombie () |
| TPrincipal & | operator= (const TPrincipal &) |
| Assignment operator. | |
| void | SavePrimitiveNameTitle (std::ostream &out, const char *variable_name) |
| Save object name and title into the output stream "out". | |
Static Protected Member Functions | |
| static void | SavePrimitiveConstructor (std::ostream &out, TClass *cl, const char *variable_name, const char *constructor_agrs="", Bool_t empty_line=kTRUE) |
| Save object constructor in the output stream "out". | |
| static void | SavePrimitiveDraw (std::ostream &out, const char *variable_name, Option_t *option=nullptr) |
| Save invocation of primitive Draw() method Skipped if option contains "nodraw" string. | |
| static TString | SavePrimitiveVector (std::ostream &out, const char *prefix, Int_t len, Double_t *arr, Int_t flag=0) |
| Save array in the output stream "out" as vector. | |
Protected Attributes | |
| TMatrixD | fCovarianceMatrix |
| Covariance matrix. | |
| TVectorD | fEigenValues |
| Eigenvalue vector of trans. | |
| TMatrixD | fEigenVectors |
| Eigenvector matrix of trans. | |
| TList * | fHistograms |
| List of histograms. | |
| Bool_t | fIsNormalised |
| Normalize matrix? | |
| TVectorD | fMeanValues |
| Mean value over all data points. | |
| TString | fName |
| Int_t | fNumberOfDataPoints |
| Number of data points. | |
| Int_t | fNumberOfVariables |
| Number of variables. | |
| TVectorD | fOffDiagonal |
| Elements of the tridiagonal. | |
| TVectorD | fSigmas |
| vector of sigmas | |
| Bool_t | fStoreData |
| Should we store input data? | |
| TString | fTitle |
| Double_t | fTrace |
| Trace of covarience matrix. | |
| TVectorD | fUserData |
| Vector of original data points. | |
Static Private Member Functions | |
| static void | AddToTObjectTable (TObject *) |
| Private helper function which will dispatch to TObjectTable::AddObj. | |
Private Attributes | |
| UInt_t | fBits |
| bit field status word | |
| UInt_t | fUniqueID |
| object unique identifier | |
Static Private Attributes | |
| static Longptr_t | fgDtorOnly = 0 |
| object for which to call dtor only (i.e. no delete) | |
| static Bool_t | fgObjectStat = kTRUE |
| if true keep track of objects in TObjectTable | |
#include <TPrincipal.h>
| Enumerator | |
|---|---|
| kOnlyPrepStep | Used to request that the class specific implementation of This is just for example by TBufferMerger to request that the TTree inside the file calls |
|
inherited |
|
inherited |
| Enumerator | |
|---|---|
| kCanDelete | if object in a list can be deleted |
| kMustCleanup | if object destructor must call RecursiveRemove() |
| kIsReferenced | |
| kHasUUID | if object has a TUUID (its fUniqueID=UUIDNumber) |
| kCannotPick | if object in a pad cannot be picked |
| kNoContextMenu | if object does not want context menu |
| kInvalidObject | if object ctor succeeded but object should not be used |
|
protected |
Copy constructor.
Definition at line 315 of file TPrincipal.cxx.
| TPrincipal::TPrincipal | ( | ) |
Empty constructor. Do not use.
Definition at line 228 of file TPrincipal.cxx.
|
override |
Destructor.
Definition at line 360 of file TPrincipal.cxx.
Constructor.
Argument is number of variables in the sample of data Options are:
The created object is named "principal" by default.
Definition at line 252 of file TPrincipal.cxx.
|
inherited |
Call this function within a function that you don't want to define as purely virtual, in order not to force all users deriving from that class to implement that maybe (on their side) unused function; but at the same time, emit a run-time warning if they try to call it, telling that it is not implemented in the derived class: action must thus be taken on the user side to override it.
In other word, this method acts as a "runtime purely virtual" warning instead of a "compiler purely virtual" error.
Definition at line 1149 of file TObject.cxx.
Add a data point and update the covariance matrix.
The input array must be fNumberOfVariables long.
The Covariance matrix and mean values of the input data is calculated on the fly by the following equations:
\[ \left<x_i\right>^{(0)} = x_{i0} \]
\[ \left<x_i\right>^{(n)} = \left<x_i\right>^{(n-1)} + \frac1n \left(x_{in} - \left<x_i\right>^{(n-1)}\right) \]
\[ C_{ij}^{(0)} = 0 \]
\[ C_{ij}^{(n)} = C_{ij}^{(n-1)} + \frac1{n-1}\left[\left(x_{in} - \left<x_i\right>^{(n)}\right) \left(x_{jn} - \left<x_j\right>^{(n)}\right)\right] - \frac1n C_{ij}^{(n-1)} \]
since this is a really fast method, with no rounding errors (please refer to CERN 72-21 pp. 54-106).
The data is stored internally in a TVectorD, in the following way:
\[ \mathbf{x} = \left[\left(x_{0_0},\ldots,x_{{P-1}_0}\right),\ldots, \left(x_{0_i},\ldots,x_{{P-1}_i}\right), \ldots\right] \]
With \(P\) as defined in the class description.
Definition at line 413 of file TPrincipal.cxx.
|
staticprivateinherited |
Private helper function which will dispatch to TObjectTable::AddObj.
Included here to avoid circular dependency between header files.
Definition at line 195 of file TObject.cxx.
|
virtualinherited |
Append graphics object to current pad.
In case no current pad is set yet, create a default canvas with the name "c1".
Definition at line 204 of file TObject.cxx.
|
overridevirtual |
Browse the TPrincipal object in the TBrowser.
Reimplemented from TObject.
Definition at line 470 of file TPrincipal.cxx.
|
inlineinherited |
Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.
The intent is for this routine to be called instead of directly calling the function Hash during "insert" operations. See TObject::HasInconsistenTObjectHash();
(*) The setup is consistent when all classes in the class hierarchy that overload TObject::Hash do call ROOT::CallRecursiveRemoveIfNeeded in their destructor. i.e. it is safe to call the Hash virtual function during the RecursiveRemove operation.
Definition at line 79 of file TPrincipal.h.
|
virtualinherited |
Returns name of class to which the object belongs.
Definition at line 227 of file TObject.cxx.
|
overridevirtual |
Clear the data in Object.
Notice, that's not possible to change the dimension of the original data.
Reimplemented from TNamed.
Definition at line 493 of file TPrincipal.cxx.
Make a clone of an object using the Streamer facility.
If newname is specified, this will be the name of the new object.
Reimplemented from TObject.
Reimplemented in TStreamerInfo, and TTreeIndex.
Definition at line 73 of file TNamed.cxx.
Compare two TNamed objects.
Returns 0 when equal, -1 when this is smaller and +1 when bigger (like strcmp).
Reimplemented from TObject.
Reimplemented in TStructNodeProperty.
Definition at line 84 of file TNamed.cxx.
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overridevirtualinherited |
Copy this to obj.
Reimplemented from TObject.
Reimplemented in TSystemDirectory, TSystemFile, TProfile, TProfile2D, TProfile3D, TPieSlice, TStyle, TText, and TXTRU.
Definition at line 93 of file TNamed.cxx.
Definition at line 79 of file TPrincipal.h.
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virtualinherited |
Delete this object.
Typically called as a command via the interpreter. Normally use "delete" operator when object has been allocated on the heap.
Reimplemented in TDirectory, TDirectoryFile, TFile, TSystemDirectory, TSystemFile, TTreeViewer, TGItemContext, TCanvas, TGFrame, TGTextEdit, TAxis, RooLinkedList, TExMap, TObjectTable, TProtoClass, TKeySQL, TKeyXML, TQCommand, TBtree, TClonesArray, THashList, THashTable, TList, TMap, TObjArray, TOrdCollection, TRefArray, TListOfDataMembers, TListOfEnums, TListOfEnumsWithLock, TListOfFunctions, TListOfFunctionTemplates, TViewPubDataMembers, TViewPubFunctions, TThread, TKey, TMVA::Results, TTree, and TCollection.
Definition at line 268 of file TObject.cxx.
Computes distance from point (px,py) to the object.
This member function must be implemented for each graphics primitive. This default function returns a big number (999999).
Reimplemented in TGeoTessellated, TStyle, TGeoBBox, TGeoCompositeShape, TGeoCone, TGeoConeSeg, TGeoEltu, TGeoHalfSpace, TGeoHype, TGeoNode, TGeoParaboloid, TGeoPcon, TGeoPgon, TGeoScaledShape, TGeoShapeAssembly, TGeoSphere, TGeoTorus, TGeoTube, TGeoTubeSeg, TGeoVolume, TGeoXtru, TGeoOverlap, TGeoTrack, TGeoVGShape, TASImage, TColorWheel, TPad, TBox, TCrown, TCurlyArc, TCurlyLine, TDiamond, TEllipse, TGraphPolargram, TLine, TMarker, TPave, TPie, TPolyLine, TText, TGraphEdge, TGraphNode, TAxis3D, TBRIK, TMarker3DBox, TNode, TPCON, TPolyLine3D, TPolyMarker3D, TSPHE, TTUBE, TTUBS, TXTRU, TGL5DDataSet, TGLHistPainter, TGLParametricEquation, TGLTH3Composition, TGLViewer, TAxis, TEfficiency, TF1, TF2, TF3, TGraph, TGraph2D, TH1, THStack, TMultiGraph, TPolyMarker, TScatter, TScatter2D, TSpline, THistPainter, TPaletteAxis, TGenerator, TParticle, TPrimary, TFileDrawMap, TTreePerfStats, TParallelCoord, TParallelCoordRange, TParallelCoordVar, TSpider, TGeoShape, TPoints3DABC, TVirtualHistPainter, TPieSlice, and TGLScenePad.
Definition at line 284 of file TObject.cxx.
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protectedvirtualinherited |
Interface to ErrorHandler (protected).
Reimplemented in TTreeViewer, and TThread.
Definition at line 1059 of file TObject.cxx.
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virtualinherited |
Default Draw method for all objects.
Reimplemented in TClassTree, ROOT::RGeoPainter, TGListTree, TGPicture, TMultiDimFit, TRatioPlot, TGraph, TGraphTime, THStack, TMultiGraph, TChain, TTree, TFITSHDU, TEfficiency, RooStats::HypoTestInverterPlot, ROOT::Experimental::XRooFit::xRooNLLVar::xRooHypoPoint, ROOT::Experimental::XRooFit::xRooNLLVar::xRooHypoSpace, ROOT::Experimental::XRooFit::xRooNode, TGeoParallelWorld, TDirectory, TCollection, TBrowser, TClass, TGeoBatemanSol, TGeoNode, TGeoPhysicalNode, TGeoPolygon, TGeoShape, TGeoVolume, TGeoOverlap, TGeoPainter, TGeoTrack, TGeoVGShape, TASImage, TButton, TCanvas, TColorWheel, TPad, TArrow, TBox, TDiamond, TEllipse, TFrame, TLegend, TMarker, TPave, TPaveLabel, TPavesText, TPaveText, TPolyLine, TWbox, TGraphStruct, TEveGeoNode, TEveGeoTopNode, TGeometry, THelix, TNode, TNodeDiv, TPolyLine3D, TPolyMarker3D, TStructViewer, TStructViewerGUI, TF1, TF2, TF3, TH1, TPolyMarker, TSpline, TFile, TMatrixTBase< Element >, TMatrixTBase< AReal >, TMatrixTBase< Double_t >, TVectorT< Element >, TVectorT< Double_t >, TMultiLayerPerceptron, TGenerator, RooAbsData, TTreePerfStats, TParallelCoordVar, TGItemContext, TVirtualPad, TPie, TGraph2D, TGraphPolar, TGraphPolargram, TParallelCoord, TParallelCoordRange, TSpider, RooPlot, and RooStats::SamplingDistPlot.
Definition at line 293 of file TObject.cxx.
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virtualinherited |
Draw class inheritance tree of the class to which this object belongs.
If a class B inherits from a class A, description of B is drawn on the right side of description of A. Member functions overridden by B are shown in class A with a blue line crossing-out the corresponding member function. The following picture is the class inheritance tree of class TPaveLabel:
Reimplemented in TSystemDirectory, TSystemFile, and TGFrame.
Definition at line 308 of file TObject.cxx.
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1).
If pad was not selected - gPad will be used.
Reimplemented in TSystemDirectory, TSystemFile, TGFrame, TAxis, and TCanvas.
Definition at line 319 of file TObject.cxx.
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virtualinherited |
Dump contents of object on stdout.
Using the information in the object dictionary (class TClass) each data member is interpreted. If a data member is a pointer, the pointer value is printed
The following output is the Dump of a TArrow object:
Reimplemented in TSystemFile, TCollection, TClass, TGFrame, and TGPack.
Definition at line 367 of file TObject.cxx.
Issue error message.
Use "location" to specify the method where the error occurred. Accepts standard printf formatting arguments.
Reimplemented in TFitResult.
Definition at line 1098 of file TObject.cxx.
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virtualinherited |
Execute method on this object with the given parameter string, e.g.
"3.14,1,\"text\"".
Reimplemented in TMethodCall, TCling, TInterpreter, ROOT::R::TRInterface, and TContextMenu.
Definition at line 378 of file TObject.cxx.
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virtualinherited |
Execute method on this object with parameters stored in the TObjArray.
The TObjArray should contain an argv vector like:
Reimplemented in TCling, TMethodCall, TInterpreter, ROOT::R::TRInterface, and TContextMenu.
Definition at line 398 of file TObject.cxx.
Execute action corresponding to an event at (px,py).
This method must be overridden if an object can react to graphics events.
Reimplemented in TParallelCoord, TParallelCoordRange, TParallelCoordVar, TGeoManager, TGeoNode, TGeoShape, TGeoVolume, TGeoOverlap, TGeoTrack, TASImage, TASPaletteEditor::LimitLine, TButton, TCanvas, TGroupButton, TPad, TSliderBox, TBox, TCrown, TCurlyArc, TCurlyLine, TDiamond, TEllipse, TFrame, TGraphPolargram, TLine, TLink, TMarker, TPave, TPolyLine, TText, TWbox, TGraphEdge, TGraphNode, TAxis3D, TMarker3DBox, TNode, TPolyLine3D, TPolyMarker3D, TView3D, TGL5DDataSet, TGLEventHandler, TGLHistPainter, TGLParametricEquation, TGLTH3Composition, TGLViewer, TAxis, TEfficiency, TF1, TF2, TF3, TGraph, TGraph2D, TH1, TPolyMarker, TScatter, TScatter2D, TSpline, THistPainter, TPaletteAxis, TGenerator, TParticle, TPrimary, TTreePerfStats, TSpider, TView, TVirtualHistPainter, TPie, and TGLScenePad.
Definition at line 415 of file TObject.cxx.
Issue fatal error message.
Use "location" to specify the method where the fatal error occurred. Accepts standard printf formatting arguments.
Definition at line 1126 of file TObject.cxx.
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virtualinherited |
Encode TNamed into output buffer.
Reimplemented in TKeySQL, TSQLFile, TKeyXML, TXMLFile, TDirectoryFile, TFile, and TKey.
Definition at line 103 of file TNamed.cxx.
Must be redefined in derived classes.
This function is typically used with TCollections, but can also be used to find an object by name inside this object.
Reimplemented in TListOfEnums, TMap, TDirectory, TFolder, TROOT, TListOfTypes, TListOfTypes, TBtree, TCollection, THashList, THashTable, TList, TObjArray, TListOfDataMembers, TListOfDataMembers, TListOfEnums, TListOfEnumsWithLock, TListOfFunctions, TListOfFunctionTemplates, TListOfFunctionTemplates, TViewPubDataMembers, TViewPubFunctions, TPad, TGeometry, THbookFile, TGraph, TGraph2D, TH1, RooAbsCollection, and RooLinkedList.
Definition at line 425 of file TObject.cxx.
Must be redefined in derived classes.
This function is typically used with TCollections, but can also be used to find an object inside this object.
Reimplemented in TMap, TDirectory, TFolder, TROOT, TListOfTypes, TBtree, TCollection, THashList, THashTable, TList, TObjArray, TListOfDataMembers, TListOfEnums, TListOfEnumsWithLock, TListOfFunctions, TListOfFunctionTemplates, TViewPubDataMembers, TViewPubFunctions, TPad, TGeometry, THbookFile, TGraph, TGraph2D, TH1, RooAbsCollection, and RooLinkedList.
Definition at line 435 of file TObject.cxx.
Return the covariance matrix.
Definition at line 60 of file TPrincipal.h.
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virtualinherited |
Get option used by the graphics system to draw this object.
Note that before calling object.GetDrawOption(), you must have called object.Draw(..) before in the current pad.
Reimplemented in TBrowser, TFitEditor, TGedFrame, TGFileBrowser, TRootBrowser, and TRootBrowserLite.
Definition at line 445 of file TObject.cxx.
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staticinherited |
Return destructor only flag.
Definition at line 1196 of file TObject.cxx.
Definition at line 61 of file TPrincipal.h.
Definition at line 62 of file TPrincipal.h.
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inline |
Definition at line 63 of file TPrincipal.h.
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virtualinherited |
Returns mime type name of object.
Used by the TBrowser (via TGMimeTypes class). Override for class of which you would like to have different icons for objects of the same class.
Reimplemented in TSystemFile, TGeoVolume, TASImage, TGMainFrame, TKey, ROOT::Experimental::XRooFit::xRooNode, TBranch, TVirtualBranchBrowsable, TMethodBrowsable, and TBranchElement.
Definition at line 472 of file TObject.cxx.
Definition at line 64 of file TPrincipal.h.
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inlineoverridevirtualinherited |
Returns string containing info about the object at position (px,py).
This method is typically overridden by classes of which the objects can report peculiarities for different positions. Returned string will be re-used (lock in MT environment).
Reimplemented in TGeoNode, TGeoVolume, TGeoTrack, TASImage, TColorWheel, TAxis3D, TNode, TGL5DDataSet, TGLHistPainter, TGLParametricEquation, TGLTH3Composition, TF1, TF2, TGraph, TH1, THistPainter, TPaletteAxis, TFileDrawMap, TParallelCoordVar, and TVirtualHistPainter.
Definition at line 491 of file TObject.cxx.
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staticinherited |
Get status of object stat flag.
Definition at line 1181 of file TObject.cxx.
Reimplemented in TGeoVolume, TArrow, TGaxis, TLegendEntry, TPave, TPolyLine, TAxis3D, THelix, TNode, TPolyLine3D, TPolyMarker3D, TH1, TPolyMarker, TFile, TMapFile, TPSocket, TSocket, TUDPSocket, TSelector, and TPoints3DABC.
Return a row of the user supplied data.
If row is out of bounds, 0 is returned. It's up to the user to delete the returned array. Row 0 is the first row;
Definition at line 520 of file TPrincipal.cxx.
Definition at line 66 of file TPrincipal.h.
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inlineoverridevirtualinherited |
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virtualinherited |
Return the unique object id.
Definition at line 480 of file TObject.cxx.
Definition at line 67 of file TPrincipal.h.
Execute action in response of a timer timing out.
This method must be overridden if an object has to react to timers.
Reimplemented in TGWindow, TGuiBldDragManager, TGraphTime, TGLEventHandler, TGCommandPlugin, TGDNDManager, TGFileContainer, TGPopupMenu, TGScrollBar, TGShutter, TGTextEdit, TGTextEditor, TGTextEntry, TGTextView, TGToolTip, TGHtml, and TTreeViewer.
Definition at line 516 of file TObject.cxx.
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inlineoverridevirtualinherited |
Return hash value for this object.
Note: If this routine is overloaded in a derived class, this derived class should also add
Otherwise, when RecursiveRemove is called (by ~TObject or example) for this type of object, the transversal of THashList and THashTable containers will will have to be done without call Hash (and hence be linear rather than logarithmic complexity). You will also see warnings like
Reimplemented from TObject.
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inlineinherited |
Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.
missing call to RecursiveRemove in destructor).
Note: Since the consistency is only tested for during inserts, this routine will return true for object that have never been inserted whether or not they have a consistent setup. This has no negative side-effect as searching for the object with the right or wrong Hash will always yield a not-found answer (Since anyway no hash can be guaranteed unique, there is always a check)
Issue info message.
Use "location" to specify the method where the warning occurred. Accepts standard printf formatting arguments.
Definition at line 1072 of file TObject.cxx.
Returns kTRUE if object inherits from class "classname".
Reimplemented in TClass.
Definition at line 549 of file TObject.cxx.
Returns kTRUE if object inherits from TClass cl.
Reimplemented in TClass.
Definition at line 557 of file TObject.cxx.
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virtualinherited |
Dump contents of this object in a graphics canvas.
Same action as Dump but in a graphical form. In addition pointers to other objects can be followed.
The following picture is the Inspect of a histogram object:
Reimplemented in TSystemFile, TInspectorObject, TGFrame, and ROOT::Experimental::XRooFit::xRooNode.
Definition at line 570 of file TObject.cxx.
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inlineoverridevirtual |
Reimplemented from TNamed.
Definition at line 79 of file TPrincipal.h.
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inlineinherited |
IsDestructed.
Default equal comparison (objects are equal if they have the same address in memory).
More complicated classes might want to override this function.
Reimplemented in TObjString, TQCommand, TPair, and TGObject.
Definition at line 589 of file TObject.cxx.
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inlineoverridevirtual |
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).
Reimplemented from TObject.
Definition at line 68 of file TPrincipal.h.
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inlineinherited |
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inlineoverridevirtualinherited |
Reimplemented from TObject.
Reimplemented in TStructNodeProperty.
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inlineinherited |
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overridevirtualinherited |
List TNamed name and title.
Reimplemented from TObject.
Reimplemented in ROOT::Experimental::XRooFit::xRooBrowser, TVirtualStreamerInfo, TROOT, TStreamerElement, TStreamerBase, TStreamerSTL, TText, TStreamerInfo, TTask, and TNode.
Definition at line 112 of file TNamed.cxx.
Generates the file <filename>, with .C appended if it does argument doesn't end in .cxx or .C.
The file contains the implementation of two functions
which does the same as TPrincipal::X2P and TPrincipal::P2X respectively. Please refer to these methods.
Further, the static variables:
are initialized. The only ROOT header file needed is Rtypes.h
See TPrincipal::MakeRealCode for a list of options
Definition at line 561 of file TPrincipal.cxx.
Make histograms of the result of the analysis.
The option string say which histograms to create
TPrincipal::SumOfSquareResiduals) The histograms will be named <name>_<type><number>, where <name> is the first argument, <type> is one of X,P,D,E,S, and <number> is the variable. Definition at line 586 of file TPrincipal.cxx.
Generate the file <classname>PCA.cxx which contains the implementation of two methods:
which does the same as TPrincipal::X2P and TPrincipal::P2X respectively. Please refer to these methods.
Further, the public static members:
are initialized, and assumed to exist. The class declaration is assumed to be in <classname>.h and assumed to be provided by the user.
See TPrincipal::MakeRealCode for a list of options
The minimal class definition is:
Whether the methods <classname>::X2P and <classname>::P2X should be static or not, is up to the user.
Definition at line 870 of file TPrincipal.cxx.
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protected |
Normalize the covariance matrix.
Definition at line 808 of file TPrincipal.cxx.
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virtual |
Perform the principal components analysis.
This is done in several stages in the TMatrix::EigenVectors method:
Definition at line 883 of file TPrincipal.cxx.
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protected |
This is the method that actually generates the code for the transformations to and from feature space and pattern space It's called by TPrincipal::MakeCode and TPrincipal::MakeMethods.
The options are: NONE so far
Definition at line 905 of file TPrincipal.cxx.
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inherited |
Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary).
Definition at line 1160 of file TObject.cxx.
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virtualinherited |
This method must be overridden to handle object notification (the base implementation is no-op).
Different objects in ROOT use the Notify method for different purposes, in coordination with other objects that call this method at the appropriate time.
For example, TLeaf uses it to load class information; TBranchRef to load contents of referenced branches TBranchRef; most notably, based on Notify, TChain implements a callback mechanism to inform interested parties when it switches to a new sub-tree.
Reimplemented in TMessageHandler, TNotifyLink< Type >, TNotifyLink< RNoCleanupNotifierHelper >, TNotifyLink< ROOT::Detail::TBranchProxy >, TNotifyLink< TTreeReader >, TFileHandler, TSignalHandler, TStdExceptionHandler, TProcessEventTimer, TTimer, TIdleTimer, TSingleShotCleaner, TCollection, TRefTable, TBrowserTimer, TInterruptHandler, TTermInputHandler, TThreadTimer, TGLRedrawTimer, TViewTimer, TGContainerKeyboardTimer, TGContainerScrollTimer, TGInputHandler, TViewUpdateTimer, TPopupDelayTimer, TRepeatTimer, TSBRepeatTimer, TGTextEditHist, TInsCharCom, TDelCharCom, TBreakLineCom, TInsTextCom, TDelTextCom, TBlinkTimer, TTipDelayTimer, TGuiBldDragManagerRepeatTimer, TARInterruptHandler, TASLogHandler, TASInterruptHandler, TASSigPipeHandler, TASInputHandler, TSocketHandler, TTimeOutTimer, TBranchElement, TBranchRef, TLeafObject, TSelector, TTree, TSelectorDraw, TSelectorEntries, TTreeFormula, TTreeFormulaManager, TTreeReader, h1analysis, h1analysisTreeReader, and TSysEvtHandler.
Definition at line 618 of file TObject.cxx.
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inherited |
Use this method to declare a method obsolete.
Specify as of which version the method is obsolete and as from which version it will be removed.
Definition at line 1169 of file TObject.cxx.
|
inherited |
Operator delete for sized deallocation.
Definition at line 1234 of file TObject.cxx.
|
inherited |
Operator delete.
Definition at line 1212 of file TObject.cxx.
|
inherited |
Only called by placement new when throwing an exception.
Definition at line 1266 of file TObject.cxx.
|
inherited |
Operator delete [] for sized deallocation.
Definition at line 1245 of file TObject.cxx.
|
inherited |
Operator delete [].
Definition at line 1223 of file TObject.cxx.
|
inherited |
Only called by placement new[] when throwing an exception.
Definition at line 1274 of file TObject.cxx.
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inlineinherited |
|
inlineinherited |
|
inlineinherited |
|
protected |
Assignment operator.
Definition at line 336 of file TPrincipal.cxx.
Calculate x as a function of nTest of the most significant principal components p, and return it in x.
It's the users responsibility to make sure that both x and p are of the right size (i.e., memory must be allocated for x).
Definition at line 1073 of file TPrincipal.cxx.
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virtualinherited |
This method must be overridden if a class wants to paint itself.
The difference between Paint() and Draw() is that when a object draws itself it is added to the display list of the pad in which it is drawn (and automatically redrawn whenever the pad is redrawn). While paint just draws the object without adding it to the pad display list.
Reimplemented in TPie, TSQLFile, TXMLFile, ROOT::RGeoPainter, TGaxis, TGraph, TGraphTime, THStack, TMultiGraph, TScatter, TScatter2D, TTreePerfStats, ROOT::Experimental::RTreeMapPainter, TEfficiency, TRatioPlot, TGeoBoolNode, TGeoUnion, TGeoIntersection, TGeoSubtraction, TMarker3DBox, TGL5DDataSet, TGLHistPainter, TGLParametricEquation, TGLTH3Composition, TGraph2DPainter, TSpectrum2Painter, TFileDrawMap, TDirectory, TExec, TMacro, TStyle, TBits, TCollection, TGeoNode, TGeoPhysicalNode, TGeoShape, TGeoVolume, TGeoOverlap, TGeoPainter, TGeoTrack, TGeoVGShape, TASImage, TASPaletteEditor::PaintPalette, TASPaletteEditor::LimitLine, TAnnotation, TButton, TCanvas, TClassTree, TColorWheel, TPad, TArrow, TBox, TCrown, TDiamond, TEllipse, TFrame, TLatex, TLegend, TLine, TMarker, TMathText, TPave, TPaveLabel, TPaveStats, TPavesText, TPaveText, TPolyLine, TText, TWbox, TGraphEdge, TGraphNode, TEveArrow, TEveCaloViz, TEveDigitSet, TEveGeoTopNode, TEveGeoShape, TEvePlot3D, TEvePointSet, TEveProjectionAxes, TEveScene, TEveShape, TEveStraightLineSet, TEveText, TEveTriangleSet, TAxis3D, TNode, TNodeDiv, TPolyLine3D, TPolyMarker3D, TShape, TF1, TF2, TF3, TGraph2D, TH1, TPolyMarker, TSpline, THistPainter, TPaletteAxis, TFile, TGenerator, TParticle, TPrimary, TParallelCoordVar, TVirtualPad, TVirtualGeoPainter, TVirtualGeoTrack, TVirtualHistPainter, TParallelCoordRange, TSpider, TGraphPolargram, and TParallelCoord.
Definition at line 631 of file TObject.cxx.
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virtualinherited |
Pop on object drawn in a pad to the top of the display list.
I.e. it will be drawn last and on top of all other primitives.
Reimplemented in TPad, TFrame, and TVirtualPad.
Definition at line 640 of file TObject.cxx.
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overridevirtual |
Print the statistics Options are.
Reimplemented from TNamed.
Definition at line 1093 of file TPrincipal.cxx.
Read contents of object with specified name from the current directory.
First the key with the given name is searched in the current directory, next the key buffer is deserialized into the object. The object must have been created before via the default constructor. See TObject::Write().
Reimplemented in TKeyXML, TBuffer, TKey, and TKeySQL.
Definition at line 673 of file TObject.cxx.
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virtualinherited |
Recursively remove this object from a list.
Typically implemented by classes that can contain multiple references to a same object.
Reimplemented in THistPainter, TCling, TDirectory, TFolder, TProcessID, TROOT, TCollection, THashList, TList, TObjArray, TBrowser, TObjectSpy, TObjectRefSpy, TListOfDataMembers, TListOfEnums, TListOfEnumsWithLock, TListOfFunctions, TListOfFunctionTemplates, ROOT::Internal::TCheckHashRecursiveRemoveConsistency, TViewPubDataMembers, TViewPubFunctions, TDialogCanvas, TInspectCanvas, TPad, TLegend, TGeometry, TNode, ROOT::RBrowserDataCleanup, TFitEditor, TGedEditor, TH1Editor, TH2Editor, TGFileBrowser, TRootBrowser, TRootBrowserLite, TRootContextMenu, TRootBrowserHistory, TEfficiency, TGraph, TGraph2D, TH1, THStack, TMultiGraph, TFileMerger, RooAbsCollection, RooAbsData, RooLinkedList, RooMCStudy, RooWorkspace, TChain, TFriendElement, TTree, TTreePlayer, and TVirtualPad.
Definition at line 684 of file TObject.cxx.
Save this object in the file specified by filename.
otherwise the object is written to filename as a CINT/C++ script. The C++ code to rebuild this object is generated via SavePrimitive(). The "option" parameter is passed to SavePrimitive. By default it is an empty string. It can be used to specify the Draw option in the code generated by SavePrimitive.
The function is available via the object context menu.
Reimplemented in TSpline, TFolder, TGeoVolume, TClassTree, TPad, TPaveClass, TGObject, TSpline3, TSpline5, ROOT::Experimental::XRooFit::xRooNode, TTreePerfStats, TVirtualPad, TGraph, and TH1.
Definition at line 708 of file TObject.cxx.
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virtualinherited |
Save a primitive as a C++ statement(s) on output stream "out".
Reimplemented in TGeoTessellated, TGraphEdge, TGraphNode, TGeoIdentity, TStyle, TCurlyArc, TCurlyLine, TGedMarkerSelect, TGedPatternSelect, TGColorSelect, TGFont, TGVerticalLayout, TGHorizontalLayout, TGRowLayout, TGColumnLayout, TGMatrixLayout, TGTileLayout, TGListLayout, TGListDetailsLayout, TGTextLBEntry, TGNumberEntryField, TGNumberEntry, TGTableLayoutHints, TGTableLayout, TGTextEdit, TGTextView, TGXYLayoutHints, TGXYLayout, TRootContainer, TGHtml, TEfficiency, TExec, TMacro, TGeoArb8, TGeoTrap, TGeoGtra, TGeoBBox, TGeoBoolNode, TGeoUnion, TGeoIntersection, TGeoSubtraction, TGeoCompositeShape, TGeoCone, TGeoConeSeg, TGeoElementRN, TGeoDecayChannel, TGeoEltu, TGeoHalfSpace, TGeoHype, TGeoMaterial, TGeoMixture, TGeoTranslation, TGeoRotation, TGeoCombiTrans, TGeoHMatrix, TGeoMedium, TGeoPara, TGeoParaboloid, TGeoPatternX, TGeoPatternY, TGeoPatternZ, TGeoPatternParaX, TGeoPatternParaY, TGeoPatternParaZ, TGeoPatternTrapZ, TGeoPatternCylR, TGeoPatternCylPhi, TGeoPatternSphR, TGeoPatternSphTheta, TGeoPatternSphPhi, TGeoPcon, TGeoPgon, TGeoScaledShape, TGeoShapeAssembly, TGeoSphere, TGeoTorus, TGeoTrd1, TGeoTrd2, TGeoTube, TGeoTubeSeg, TGeoCtub, TGeoVolume, TGeoXtru, TASImage, TAnnotation, TButton, TCanvas, TGroupButton, TPad, TPaveClass, TSlider, TSliderBox, TArc, TArrow, TBox, TCrown, TCutG, TDiamond, TEllipse, TFrame, TGaxis, TGraphPolar, TGraphPolargram, TLatex, TLegend, TLine, TMarker, TMathText, TPave, TPaveLabel, TPaveStats, TPavesText, TPaveText, TPolyLine, TText, TWbox, TGraphStruct, TAxis3D, THelix, TMarker3DBox, TPolyLine3D, TPolyMarker3D, TGHorizontal3DLine, TGVertical3DLine, TGButton, TGTextButton, TGPictureButton, TGCheckButton, TGRadioButton, TGButtonGroup, TGVButtonGroup, TGHButtonGroup, TGContainer, TGCanvas, TGComboBox, TGLineStyleComboBox, TGLineWidthComboBox, TGDockableFrame, TGDoubleVSlider, TGDoubleHSlider, TGFrame, TGCompositeFrame, TGVerticalFrame, TGHorizontalFrame, TGMainFrame, TGTransientFrame, TGGroupFrame, TGFSComboBox, TGFileContainer, TGGC, TGIcon, TGLabel, TGLayoutHints, TGListBox, TGListTree, TGListView, TGLVContainer, TGMdiFrame, TGMdiMainFrame, TGMdiMenuBar, TGPopupMenu, TGMenuTitle, TGMenuBar, TGProgressBar, TGHProgressBar, TGVProgressBar, TGHScrollBar, TGVScrollBar, TGShapedFrame, TGShutterItem, TGShutter, TGVSlider, TGHSlider, TGSplitFrame, TGVSplitter, TGHSplitter, TGVFileSplitter, TGStatusBar, TGTabLayout, TGTab, TGTextEntry, TGToolBar, TGTripleVSlider, TGTripleHSlider, TRootEmbeddedCanvas, TF1, TF12, TF2, TF3, TGraph, TGraph2D, TGraph2DAsymmErrors, TGraph2DErrors, TGraphAsymmErrors, TGraphBentErrors, TGraphErrors, TGraphMultiErrors, TH1, TH2Poly, THStack, TMultiGraph, TPolyMarker, TProfile, TProfile2D, TProfile3D, TScatter, TScatter2D, TSpline3, TSpline5, TPaletteAxis, TChain, TTreePerfStats, TParallelCoord, TParallelCoordVar, TPie, and TPieSlice.
Definition at line 858 of file TObject.cxx.
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staticprotectedinherited |
Save object constructor in the output stream "out".
Can be used as first statement when implementing SavePrimitive() method for the object
Definition at line 777 of file TObject.cxx.
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staticprotectedinherited |
Save invocation of primitive Draw() method Skipped if option contains "nodraw" string.
Definition at line 845 of file TObject.cxx.
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protectedinherited |
Save object name and title into the output stream "out".
Definition at line 135 of file TNamed.cxx.
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staticprotectedinherited |
Save array in the output stream "out" as vector.
Create unique variable name based on prefix value Returns name of vector which can be used in constructor or in other places of C++ code If flag === kTRUE, just add empty line If flag === 111, check if array is empty and return nullptr or <vectorname>.data()
Definition at line 796 of file TObject.cxx.
Set or unset the user status bits as specified in f.
Definition at line 888 of file TObject.cxx.
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virtualinherited |
Set drawing option for object.
This option only affects the drawing style and is stored in the option field of the TObjOptLink supporting a TPad's primitive list (TList). Note that it does not make sense to call object.SetDrawOption(option) before having called object.Draw().
Reimplemented in TSystemDirectory, TSystemFile, TPad, TGFrame, TAxis, TBrowser, TPaveStats, TGedFrame, TRootBrowserLite, and RooPlot.
Definition at line 871 of file TObject.cxx.
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staticinherited |
Set destructor only flag.
Definition at line 1204 of file TObject.cxx.
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virtualinherited |
Set the name of the TNamed.
WARNING: if the object is a member of a THashTable or THashList container the container must be Rehash()'ed after SetName(). For example the list of objects in the current directory is a THashList.
Reimplemented in TEveScene, TColor, TSystemDirectory, TSystemFile, TNode, TRotMatrix, TShape, TEfficiency, TFormula, TGraph2D, TH1, RooAbsArg, RooAbsData, RooDataHist, RooDataSet, RooFitResult, RooPlot, ROOT::Experimental::XRooFit::xRooNode, TChain, TEventList, TTree, TGraph, and TDirectory.
Definition at line 149 of file TNamed.cxx.
Set all the TNamed parameters (name and title).
WARNING: if the name is changed and the object is a member of a THashTable or THashList container the container must be Rehash()'ed after SetName(). For example the list of objects in the current directory is a THashList.
Reimplemented in TContextMenu, TNode, TGraph2D, TH1, RooAbsArg, RooAbsData, RooDataHist, RooDataSet, RooFitResult, RooPlot, and TGraph.
Definition at line 163 of file TNamed.cxx.
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staticinherited |
Turn on/off tracking of objects in the TObjectTable.
Definition at line 1188 of file TObject.cxx.
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virtualinherited |
Set the title of the TNamed.
Reimplemented in ROOT::TSchemaRule::TSources, TParallelCoordVar, RooPlot, TSystemDirectory, TSystemFile, TEfficiency, TH1, THnBase, ROOT::Experimental::XRooFit::xRooNode, Axis2, TASImage, TF1, TGraph, and TGraph2D.
Definition at line 173 of file TNamed.cxx.
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virtualinherited |
Set the unique object id.
Definition at line 899 of file TObject.cxx.
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virtualinherited |
Return size of the TNamed part of the TObject.
Reimplemented in TSQLFile, TXMLFile, TDirectory, TDirectoryFile, TFile, and TKey.
Definition at line 182 of file TNamed.cxx.
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overridevirtual |
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inline |
Definition at line 79 of file TPrincipal.h.
Calculates the sum of the square residuals, that is.
\[ E_N = \sum_{i=0}^{P-1} \left(x_i - x^\prime_i\right)^2 \]
where \(x^\prime_i = \sum_{j=i}^N p_i e_{n_j}\) is the \(i^{\mbox{th}}\) component of the principal vector, corresponding to \(x_i\), the original data; I.e., the square distance to the space spanned by \(N\) eigenvectors.
Definition at line 1182 of file TPrincipal.cxx.
Issue system error message.
Use "location" to specify the method where the system error occurred. Accepts standard printf formatting arguments.
Definition at line 1112 of file TObject.cxx.
| void TPrincipal::Test | ( | Option_t * | option = "" | ) |
Test the PCA, bye calculating the sum square of residuals (see method SumOfSquareResiduals), and display the histogram.
Definition at line 1204 of file TPrincipal.cxx.
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inlineinherited |
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virtualinherited |
Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.
Reimplemented in TCanvas, TPad, TFrame, TPaveStats, TPaveText, TAxis3D, TGraph, TH1, and TTree.
Definition at line 909 of file TObject.cxx.
Issue warning message.
Use "location" to specify the method where the warning occurred. Accepts standard printf formatting arguments.
Definition at line 1084 of file TObject.cxx.
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virtualinherited |
Write this object to the current directory.
For more see the const version of this method.
Reimplemented in TSQLFile, TXMLFile, TDirectory, TBuffer, ROOT::TBufferMergerFile, TDirectoryFile, TFile, TParallelMergingFile, TCollection, TMap, and TTree.
Definition at line 989 of file TObject.cxx.
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virtualinherited |
Write this object to the current directory.
The data structure corresponding to this object is serialized. The corresponding buffer is written to the current directory with an associated key with name "name".
Writing an object to a file involves the following steps:
Bufsize can be given to force a given buffer size to write this object. By default, the buffersize will be taken from the average buffer size of all objects written to the current file so far.
If a name is specified, it will be the name of the key. If name is not given, the name of the key will be the name as returned by GetName().
The option can be a combination of: kSingleKey, kOverwrite or kWriteDelete Using the kOverwrite option a previous key with the same name is overwritten. The previous key is deleted before writing the new object. Using the kWriteDelete option a previous key with the same name is deleted only after the new object has been written. This option is safer than kOverwrite but it is slower. NOTE: Neither kOverwrite nor kWriteDelete reduces the size of a TFile– the space is simply freed up to be overwritten; in the case of a TTree, it is more complicated. If one opens a TTree, appends some entries, then writes it out, the behaviour is effectively the same. If, however, one creates a new TTree and writes it out in this way, only the metadata is replaced, effectively making the old data invisible without deleting it. TTree::Delete() can be used to mark all disk space occupied by a TTree as free before overwriting its metadata this way. The kSingleKey option is only used by TCollection::Write() to write a container with a single key instead of each object in the container with its own key.
An object is read from the file into memory via TKey::Read() or via TObject::Read().
The function returns the total number of bytes written to the file. It returns 0 if the object cannot be written.
Reimplemented in TSQLFile, TXMLFile, TDirectory, TBuffer, TDirectoryFile, TFile, TParallelMergingFile, TCollection, TMap, and TTree.
Definition at line 964 of file TObject.cxx.
Calculate the principal components from the original data vector x, and return it in p.
It's the users responsibility to make sure that both x and p are of the right size (i.e., memory must be allocated for p).
Definition at line 1228 of file TPrincipal.cxx.
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privateinherited |
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protected |
Covariance matrix.
Definition at line 29 of file TPrincipal.h.
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protected |
Eigenvalue vector of trans.
Definition at line 32 of file TPrincipal.h.
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protected |
Eigenvector matrix of trans.
Definition at line 31 of file TPrincipal.h.
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staticprivateinherited |
if true keep track of objects in TObjectTable
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protected |
List of histograms.
Definition at line 40 of file TPrincipal.h.
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protected |
Normalize matrix?
Definition at line 42 of file TPrincipal.h.
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protected |
Mean value over all data points.
Definition at line 27 of file TPrincipal.h.
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protected |
Number of data points.
Definition at line 24 of file TPrincipal.h.
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protected |
Number of variables.
Definition at line 25 of file TPrincipal.h.
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protected |
Elements of the tridiagonal.
Definition at line 34 of file TPrincipal.h.
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protected |
vector of sigmas
Definition at line 28 of file TPrincipal.h.
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protected |
Should we store input data?
Definition at line 43 of file TPrincipal.h.
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protected |
Trace of covarience matrix.
Definition at line 38 of file TPrincipal.h.
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privateinherited |
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protected |
Vector of original data points.
Definition at line 36 of file TPrincipal.h.
