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ROOT 6.08/07 Reference Guide |
LU Decomposition class.
Decompose a general n x n matrix A into P A = L U
where P is a permutation matrix, L is unit lower triangular and U is upper triangular. L is stored in the strict lower triangular part of the matrix fLU. The diagonal elements of L are unity and are not stored. U is stored in the diagonal and upper triangular part of the matrix fU. P is stored in the index array fIndex : j = fIndex[i] indicates that row j and row i should be swapped .
fSign gives the sign of the permutation, (-1)^n, where n is the number of interchanges in the permutation.
fLU has the same indexing range as matrix A .
The decomposition fails if a diagonal element of abs(fLU) is == 0, The matrix fUL is made invalid .
Definition at line 25 of file TDecompLU.h.
Public Member Functions | |
TDecompLU () | |
Default constructor. More... | |
TDecompLU (Int_t nrows) | |
Constructor for (nrows x nrows) matrix. More... | |
TDecompLU (Int_t row_lwb, Int_t row_upb) | |
Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) matrix. More... | |
TDecompLU (const TMatrixD &m, Double_t tol=0.0, Int_t implicit=1) | |
Constructor for matrix a. More... | |
TDecompLU (const TDecompLU &another) | |
Copy constructor. More... | |
virtual | ~TDecompLU () |
virtual Bool_t | Decompose () |
Matrix A is decomposed in components U and L so that P * A = U * L If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular. More... | |
virtual void | Det (Double_t &d1, Double_t &d2) |
Calculate determinant det = d1*TMath::Power(2.,d2) More... | |
const TMatrixD & | GetLU () |
const TMatrixD | GetMatrix () |
Reconstruct the original matrix using the decomposition parts. More... | |
virtual Int_t | GetNcols () const |
virtual Int_t | GetNrows () const |
Bool_t | Invert (TMatrixD &inv) |
For a matrix A(m,m), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (m x m) Ainv is returned . More... | |
TMatrixD | Invert (Bool_t &status) |
For a matrix A(m,n), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (n x m) Ainv is returned . More... | |
TMatrixD | Invert () |
TDecompLU & | operator= (const TDecompLU &source) |
assignment operator More... | |
void | Print (Option_t *opt="") const |
Print internals of this object. More... | |
virtual void | SetMatrix (const TMatrixD &a) |
Set matrix to be decomposed. More... | |
virtual Bool_t | Solve (TVectorD &b) |
Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed. More... | |
virtual TVectorD | Solve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | Solve (TMatrixDColumn &b) |
Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed. More... | |
virtual Bool_t | TransSolve (TVectorD &b) |
Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed. More... | |
virtual TVectorD | TransSolve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | TransSolve (TMatrixDColumn &b) |
Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed. More... | |
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TDecompBase () | |
Default constructor. More... | |
TDecompBase (const TDecompBase &another) | |
Copy constructor. More... | |
virtual | ~TDecompBase () |
virtual Double_t | Condition () |
Matrix condition number. More... | |
Int_t | GetColLwb () const |
Double_t | GetCondition () const |
Double_t | GetDet1 () const |
Double_t | GetDet2 () const |
Int_t | GetRowLwb () const |
Double_t | GetTol () const |
virtual Bool_t | MultiSolve (TMatrixD &B) |
Solve set of equations with RHS in columns of B. More... | |
TDecompBase & | operator= (const TDecompBase &source) |
Assignment operator. More... | |
Double_t | SetTol (Double_t tol) |
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TObject () | |
TObject constructor. More... | |
TObject (const TObject &object) | |
TObject copy ctor. More... | |
virtual | ~TObject () |
TObject destructor. More... | |
void | AbstractMethod (const char *method) const |
Use this method to implement an "abstract" method that you don't want to leave purely abstract. More... | |
virtual void | AppendPad (Option_t *option="") |
Append graphics object to current pad. More... | |
virtual void | Browse (TBrowser *b) |
Browse object. May be overridden for another default action. More... | |
virtual const char * | ClassName () const |
Returns name of class to which the object belongs. More... | |
virtual void | Clear (Option_t *="") |
virtual TObject * | Clone (const char *newname="") const |
Make a clone of an object using the Streamer facility. More... | |
virtual Int_t | Compare (const TObject *obj) const |
Compare abstract method. More... | |
virtual void | Copy (TObject &object) const |
Copy this to obj. More... | |
virtual void | Delete (Option_t *option="") |
Delete this object. More... | |
virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
Computes distance from point (px,py) to the object. More... | |
virtual void | Draw (Option_t *option="") |
Default Draw method for all objects. More... | |
virtual void | DrawClass () const |
Draw class inheritance tree of the class to which this object belongs. More... | |
virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current pad. More... | |
virtual void | Dump () const |
Dump contents of object on stdout. More... | |
virtual void | Error (const char *method, const char *msgfmt,...) const |
Issue error message. More... | |
virtual void | Execute (const char *method, const char *params, Int_t *error=0) |
Execute method on this object with the given parameter string, e.g. More... | |
virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=0) |
Execute method on this object with parameters stored in the TObjArray. More... | |
virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
Execute action corresponding to an event at (px,py). More... | |
virtual void | Fatal (const char *method, const char *msgfmt,...) const |
Issue fatal error message. More... | |
virtual TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. More... | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. More... | |
virtual Option_t * | GetDrawOption () const |
Get option used by the graphics system to draw this object. More... | |
virtual const char * | GetIconName () const |
Returns mime type name of object. More... | |
virtual const char * | GetName () const |
Returns name of object. More... | |
virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
Returns string containing info about the object at position (px,py). More... | |
virtual Option_t * | GetOption () const |
virtual const char * | GetTitle () const |
Returns title of object. More... | |
virtual UInt_t | GetUniqueID () const |
Return the unique object id. More... | |
virtual Bool_t | HandleTimer (TTimer *timer) |
Execute action in response of a timer timing out. More... | |
virtual ULong_t | Hash () const |
Return hash value for this object. More... | |
virtual void | Info (const char *method, const char *msgfmt,...) const |
Issue info message. More... | |
virtual Bool_t | InheritsFrom (const char *classname) const |
Returns kTRUE if object inherits from class "classname". More... | |
virtual Bool_t | InheritsFrom (const TClass *cl) const |
Returns kTRUE if object inherits from TClass cl. More... | |
virtual void | Inspect () const |
Dump contents of this object in a graphics canvas. More... | |
void | InvertBit (UInt_t f) |
virtual Bool_t | IsEqual (const TObject *obj) const |
Default equal comparison (objects are equal if they have the same address in memory). More... | |
virtual Bool_t | IsFolder () const |
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More... | |
Bool_t | IsOnHeap () const |
virtual Bool_t | IsSortable () const |
Bool_t | IsZombie () const |
virtual void | ls (Option_t *option="") const |
The ls function lists the contents of a class on stdout. More... | |
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). More... | |
virtual Bool_t | Notify () |
This method must be overridden to handle object notification. More... | |
void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
Use this method to declare a method obsolete. More... | |
void | operator delete (void *ptr) |
Operator delete. More... | |
void | operator delete[] (void *ptr) |
Operator delete []. More... | |
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) |
TObject & | operator= (const TObject &rhs) |
TObject assignment operator. More... | |
virtual void | Paint (Option_t *option="") |
This method must be overridden if a class wants to paint itself. More... | |
virtual void | Pop () |
Pop on object drawn in a pad to the top of the display list. More... | |
virtual Int_t | Read (const char *name) |
Read contents of object with specified name from the current directory. More... | |
virtual void | RecursiveRemove (TObject *obj) |
Recursively remove this object from a list. More... | |
void | ResetBit (UInt_t f) |
virtual void | SaveAs (const char *filename="", Option_t *option="") const |
Save this object in the file specified by filename. More... | |
virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
Save a primitive as a C++ statement(s) on output stream "out". More... | |
void | SetBit (UInt_t f, Bool_t set) |
Set or unset the user status bits as specified in f. More... | |
void | SetBit (UInt_t f) |
virtual void | SetDrawOption (Option_t *option="") |
Set drawing option for object. More... | |
virtual void | SetUniqueID (UInt_t uid) |
Set the unique object id. More... | |
virtual void | SysError (const char *method, const char *msgfmt,...) const |
Issue system error message. More... | |
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. More... | |
virtual void | Warning (const char *method, const char *msgfmt,...) const |
Issue warning message. More... | |
virtual Int_t | Write (const char *name=0, Int_t option=0, Int_t bufsize=0) |
Write this object to the current directory. More... | |
virtual Int_t | Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const |
Write this object to the current directory. More... | |
Static Public Member Functions | |
static Bool_t | InvertLU (TMatrixD &a, Double_t tol, Double_t *det=0) |
Calculate matrix inversion through in place forward/backward substitution. More... | |
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static Long_t | GetDtorOnly () |
Return destructor only flag. More... | |
static Bool_t | GetObjectStat () |
Get status of object stat flag. More... | |
static void | SetDtorOnly (void *obj) |
Set destructor only flag. More... | |
static void | SetObjectStat (Bool_t stat) |
Turn on/off tracking of objects in the TObjectTable. More... | |
Protected Member Functions | |
virtual const TMatrixDBase & | GetDecompMatrix () const |
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Int_t | Hager (Double_t &est, Int_t iter=5) |
void | ResetStatus () |
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virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). More... | |
void | MakeZombie () |
Static Protected Member Functions | |
static Bool_t | DecomposeLUCrout (TMatrixD &lu, Int_t *index, Double_t &sign, Double_t tol, Int_t &nrZeros) |
Crout/Doolittle algorithm of LU decomposing a square matrix, with implicit partial pivoting. More... | |
static Bool_t | DecomposeLUGauss (TMatrixD &lu, Int_t *index, Double_t &sign, Double_t tol, Int_t &nrZeros) |
LU decomposition using Gaussian Elimination with partial pivoting (See Golub & Van Loan, Matrix Computations, Algorithm 3.4.1) of a square matrix . More... | |
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static void | DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2) |
Protected Attributes | |
Int_t | fImplicitPivot |
Int_t * | fIndex |
TMatrixD | fLU |
Int_t | fNIndex |
Double_t | fSign |
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Int_t | fColLwb |
Double_t | fCondition |
Double_t | fDet1 |
Double_t | fDet2 |
Int_t | fRowLwb |
Double_t | fTol |
Additional Inherited Members | |
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enum | { kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff } |
enum | { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) } |
enum | EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) } |
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enum | { kWorkMax = 100 } |
enum | EMatrixDecompStat { kInit = BIT(14), kPatternSet = BIT(15), kValuesSet = BIT(16), kMatrixSet = BIT(17), kDecomposed = BIT(18), kDetermined = BIT(19), kCondition = BIT(20), kSingular = BIT(21) } |
#include <TDecompLU.h>
TDecompLU::TDecompLU | ( | ) |
Default constructor.
Definition at line 45 of file TDecompLU.cxx.
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explicit |
Constructor for (nrows x nrows) matrix.
Definition at line 56 of file TDecompLU.cxx.
Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) matrix.
Definition at line 69 of file TDecompLU.cxx.
Constructor for matrix a.
Definition at line 85 of file TDecompLU.cxx.
TDecompLU::TDecompLU | ( | const TDecompLU & | another | ) |
Copy constructor.
Definition at line 115 of file TDecompLU.cxx.
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inlinevirtual |
Definition at line 49 of file TDecompLU.h.
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virtual |
Matrix A is decomposed in components U and L so that P * A = U * L If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.
Implements TDecompBase.
Definition at line 126 of file TDecompLU.cxx.
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staticprotected |
Crout/Doolittle algorithm of LU decomposing a square matrix, with implicit partial pivoting.
The decomposition is stored in fLU: U is explicit in the upper triag and L is in multiplier form in the subdiagionals . Row permutations are mapped out in fIndex. fSign, used for calculating the determinant, is +/- 1 for even/odd row permutations. .
Definition at line 599 of file TDecompLU.cxx.
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staticprotected |
LU decomposition using Gaussian Elimination with partial pivoting (See Golub & Van Loan, Matrix Computations, Algorithm 3.4.1) of a square matrix .
The decomposition is stored in fLU: U is explicit in the upper triag and L is in multiplier form in the subdiagionals . Row permutations are mapped out in fIndex. fSign, used for calculating the determinant, is +/- 1 for even/odd row permutations. Since this algorithm uses partial pivoting without scaling like in Crout/Doolitle. it is somewhat faster but less precise .
Definition at line 708 of file TDecompLU.cxx.
Calculate determinant det = d1*TMath::Power(2.,d2)
Reimplemented from TDecompBase.
Definition at line 509 of file TDecompLU.cxx.
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inlineprotectedvirtual |
Implements TDecompBase.
Definition at line 40 of file TDecompLU.h.
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inline |
Definition at line 54 of file TDecompLU.h.
const TMatrixD TDecompLU::GetMatrix | ( | ) |
Reconstruct the original matrix using the decomposition parts.
Definition at line 151 of file TDecompLU.cxx.
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inlinevirtual |
Implements TDecompBase.
Definition at line 53 of file TDecompLU.h.
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inlinevirtual |
Implements TDecompBase.
Definition at line 52 of file TDecompLU.h.
For a matrix A(m,m), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (m x m) Ainv is returned .
Definition at line 526 of file TDecompLU.cxx.
For a matrix A(m,n), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (n x m) Ainv is returned .
Definition at line 544 of file TDecompLU.cxx.
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inline |
Definition at line 71 of file TDecompLU.h.
Calculate matrix inversion through in place forward/backward substitution.
Definition at line 775 of file TDecompLU.cxx.
assignment operator
Definition at line 573 of file TDecompLU.cxx.
Print internals of this object.
Reimplemented from TDecompBase.
Definition at line 559 of file TDecompLU.cxx.
Set matrix to be decomposed.
Definition at line 202 of file TDecompLU.cxx.
Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 233 of file TDecompLU.cxx.
Implements TDecompBase.
Definition at line 61 of file TDecompLU.h.
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virtual |
Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 299 of file TDecompLU.cxx.
Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 371 of file TDecompLU.cxx.
Implements TDecompBase.
Definition at line 64 of file TDecompLU.h.
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virtual |
Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 440 of file TDecompLU.cxx.
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protected |
Definition at line 29 of file TDecompLU.h.
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protected |
Definition at line 32 of file TDecompLU.h.
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protected |
Definition at line 34 of file TDecompLU.h.
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protected |
Definition at line 31 of file TDecompLU.h.
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protected |
Definition at line 33 of file TDecompLU.h.