library: libMatrix
#include "TMatrixFBase.h" |
TMatrixFBase
class description - source file - inheritance tree (.pdf)
This is an abstract class, constructors will not be documented.
Look at the header to check for available constructors.
private:
Float_t* GetElements()
protected:
virtual void Allocate(Int_t nrows, Int_t ncols, Int_t row_lwb = 0, Int_t col_lwb = 0, Int_t init = 0, Int_t nr_nonzero = -1)
public:
virtual ~TMatrixFBase()
virtual TMatrixFBase& Abs()
virtual TMatrixFBase& Apply(const TElementActionF& action)
virtual TMatrixFBase& Apply(const TElementPosActionF& action)
static TClass* Class()
virtual void Clear(Option_t* option = "")
virtual Float_t ColNorm() const
virtual Double_t Determinant() const
virtual void Determinant(Double_t& d1, Double_t& d2) const
virtual void Draw(Option_t* option = "")
virtual Float_t E2Norm() const
virtual void ExtractRow(Int_t row, Int_t col, Float_t* v, Int_t n = -1) const
virtual const Int_t* GetColIndexArray() const
virtual Int_t* GetColIndexArray()
Int_t GetColLwb() const
Int_t GetColUpb() const
virtual void GetMatrix2Array(Float_t* data, Option_t* option = "") const
virtual const Float_t* GetMatrixArray() const
virtual Float_t* GetMatrixArray()
Int_t GetNcols() const
Int_t GetNoElements() const
Int_t GetNrows() const
virtual const Int_t* GetRowIndexArray() const
virtual Int_t* GetRowIndexArray()
Int_t GetRowLwb() const
Int_t GetRowUpb() const
virtual TMatrixFBase& GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixFBase& target, Option_t* option = "S") const
Float_t GetTol() const
virtual TMatrixFBase& InsertRow(Int_t row, Int_t col, const Float_t* v, Int_t n = -1)
void Invalidate()
virtual TClass* IsA() const
Bool_t IsOwner() const
Bool_t IsSymmetric() const
Bool_t IsValid() const
void MakeValid()
virtual Float_t Max() const
virtual Float_t Min() const
virtual Int_t NonZeros() const
Float_t Norm1() const
virtual TMatrixFBase& NormByDiag(const TVectorF& v, Option_t* option = "D")
Float_t NormInf() const
Bool_t operator!=(Float_t val) const
virtual Float_t operator()(Int_t rown, Int_t coln) const
virtual Float_t& operator()(Int_t rown, Int_t coln)
Bool_t operator<(Float_t val) const
Bool_t operator<=(Float_t val) const
TMatrixFBase& operator=(const TMatrixFBase&)
Bool_t operator==(Float_t val) const
Bool_t operator>(Float_t val) const
Bool_t operator>=(Float_t val) const
virtual void Print(Option_t* name = "") const
virtual TMatrixFBase& Randomize(Float_t alpha, Float_t beta, Double_t& seed)
virtual TMatrixFBase& ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
virtual TMatrixFBase& ResizeTo(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros = -1)
virtual Float_t RowNorm() const
virtual TMatrixFBase& SetColIndexArray(Int_t* data)
virtual TMatrixFBase& SetMatrixArray(const Float_t* data, Option_t* option = "")
virtual TMatrixFBase& SetRowIndexArray(Int_t* data)
virtual TMatrixFBase& SetSub(Int_t row_lwb, Int_t col_lwb, const TMatrixFBase& source)
Float_t SetTol(Float_t tol)
virtual TMatrixFBase& Shift(Int_t row_shift, Int_t col_shift)
virtual void ShowMembers(TMemberInspector& insp, char* parent)
virtual TMatrixFBase& Sqr()
virtual TMatrixFBase& Sqrt()
virtual void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)
virtual Float_t Sum() const
virtual TMatrixFBase& UnitMatrix()
virtual TMatrixFBase& Zero()
protected:
Int_t fNrows number of rows
Int_t fNcols number of columns
Int_t fRowLwb lower bound of the row index
Int_t fColLwb lower bound of the col index
Int_t fNelems number of elements in matrix
Int_t fNrowIndex length of row index array (= fNrows+1) wich is only used for sparse matrices
Float_t fTol sqrt(epsilon); epsilon is smallest number number so that 1+epsilon > 1
Bool_t fIsOwner !default kTRUE, when Use array kFALSE
public:
static const enum TMatrixFBase:: kSizeMax
static const enum TMatrixFBase:: kWorkMax
static const TMatrixFBase::EMatrixStatusBits kStatus
static const TMatrixFBase::EMatrixCreatorsOp1 kZero
static const TMatrixFBase::EMatrixCreatorsOp1 kUnit
static const TMatrixFBase::EMatrixCreatorsOp1 kTransposed
static const TMatrixFBase::EMatrixCreatorsOp1 kInverted
static const TMatrixFBase::EMatrixCreatorsOp1 kAtA
static const TMatrixFBase::EMatrixCreatorsOp2 kMult
static const TMatrixFBase::EMatrixCreatorsOp2 kTransposeMult
static const TMatrixFBase::EMatrixCreatorsOp2 kInvMult
static const TMatrixFBase::EMatrixCreatorsOp2 kMultTranspose
static const TMatrixFBase::EMatrixCreatorsOp2 kPlus
static const TMatrixFBase::EMatrixCreatorsOp2 kMinus
Linear Algebra Package
----------------------
The present package implements all the basic algorithms dealing
with vectors, matrices, matrix columns, rows, diagonals, etc.
In addition eigen-Vector analysis and several matrix decomposition
have been added (LU,QRH,Cholesky and SVD) . The decompositions are
used in matrix inversion, equation solving.
Matrix elements are arranged in memory in a ROW-wise fashion
fashion . For (n x m) matrices where n*m < kSizeMax (=25 currently)
storage space is avaialble on the stack, thus avoiding expensive
allocation/deallocation of heap space . However, this introduces of
course kSizeMax overhead for each matrix object . If this is an
issue recompile with a new appropriate value (>=0) for kSizeMax
Another way to assign and store matrix data is through Use
see for instance stressLinear.cxx file .
Unless otherwise specified, matrix and vector indices always start
with 0, spanning up to the specified limit-1. However, there are
constructors to which one can specify aribtrary lower and upper
bounds, e.g. TMatrixF m(1,10,1,5) defines a matrix that ranges,
nad that can be addresses, from 1..10, 1..5 (a(1,1)..a(10,5)).
The present package provides all facilities to completely AVOID
returning matrices. Use "TMatrixF A(TMatrixF::kTransposed,B);"
and other fancy constructors as much as possible. If one really needs
to return a matrix, return a TMatLazy object instead. The
conversion is completely transparent to the end user, e.g.
"TMatrixF m = THaarMatrixF(5);" and _is_ efficient.
Since TMatrixF et al. are fully integrated in ROOT they of course
can be stored in a ROOT database.
For usage examples see $ROOTSYS/test/stressLinear.cxx
Acknowledgements
----------------
1. Oleg E. Kiselyov
First implementations were based on the his code . We have diverged
quite a bit since then but the ideas/code for lazy matrix and
"nested function" are 100% his .
You can see him and his code in action at http://okmij.org/ftp
2. Chris R. Birchenhall,
We adapted his idea of the implementation for the decomposition
classes instead of our messy installation of matrix inversion
His installation of matrix condition number, using an iterative
scheme using the Hage algorithm is worth looking at !
Chris has a nice writeup (matdoc.ps) on his matrix classes at
ftp://ftp.mcc.ac.uk/pub/matclass/
3. Mark Fischler and Steven Haywood of CLHEP
They did the slave labor of spelling out all sub-determinants
for Cramer inversion of (4x4),(5x5) and (6x6) matrices
The stack storage for small matrices was also taken from them
4. Roldan Pozo of TNT (http://math.nist.gov/tnt/)
He converted the EISPACK routines for the eigen-vector analysis to
C++ . We started with his implementation
5. Siegmund Brandt (http://siux00.physik.uni-siegen.de/~brandt/datan
We adapted his (very-well) documented SVD routines
How to efficiently use this package
-----------------------------------
1. Never return complex objects (matrices or vectors)
Danger: For example, when the following snippet:
TMatrixF foo(int n)
{
TMatrixF foom(n,n); fill_in(foom); return foom;
}
TMatrixF m = foo(5);
runs, it constructs matrix foo:foom, copies it onto stack as a
return value and destroys foo:foom. Return value (a matrix)
from foo() is then copied over to m (via a copy constructor),
and the return value is destroyed. So, the matrix constructor is
called 3 times and the destructor 2 times. For big matrices,
the cost of multiple constructing/copying/destroying of objects
may be very large. *Some* optimized compilers can cut down on 1
copying/destroying, but still it leaves at least two calls to
the constructor. Note, TMatLazy (see below) can construct
TMatrixF m "inplace", with only a _single_ call to the
constructor.
2. Use "two-address instructions"
"void TMatrixF::operator += (const TMatrixF &B);"
as much as possible.
That is, to add two matrices, it's much more efficient to write
A += B;
than
TMatrixF C = A + B;
(if both operand should be preserved,
TMatrixF C = A; C += B;
is still better).
3. Use glorified constructors when returning of an object seems
inevitable:
"TMatrixF A(TMatrixF::kTransposed,B);"
"TMatrixF C(A,TMatrixF::kTransposeMult,B);"
like in the following snippet (from $ROOTSYS/test/vmatrix.cxx)
that verifies that for an orthogonal matrix T, T'T = TT' = E.
TMatrixF haar = THaarMatrixF(5);
TMatrixF unit(TMatrixF::kUnit,haar);
TMatrixF haar_t(TMatrixF::kTransposed,haar);
TMatrixF hth(haar,TMatrixF::kTransposeMult,haar);
TMatrixF hht(haar,TMatrixF::kMult,haar_t);
TMatrixF hht1 = haar; hht1 *= haar_t;
VerifyMatrixIdentity(unit,hth);
VerifyMatrixIdentity(unit,hht);
VerifyMatrixIdentity(unit,hht1);
4. Accessing row/col/diagonal of a matrix without much fuss
(and without moving a lot of stuff around):
TMatrixF m(n,n); TVectorF v(n); TMatrixFDiag(m) += 4;
v = TMatrixFRow(m,0);
TMatrixColumn m1(m,1); m1(2) = 3; // the same as m(2,1)=3;
Note, constructing of, say, TMatrixFDiag does *not* involve any
copying of any elements of the source matrix.
5. It's possible (and encouraged) to use "nested" functions
For example, creating of a Hilbert matrix can be done as follows:
void foo(const TMatrixF &m)
{
TMatrixF m1(TMatrixF::kZero,m);
struct MakeHilbert : public TElementPosActionF {
void Operation(Float_t &element) { element = 1./(fI+fJ-1); }
};
m1.Apply(MakeHilbert());
}
of course, using a special method THilbertMatrixF() is
still more optimal, but not by a whole lot. And that's right,
class MakeHilbert is declared *within* a function and local to
that function. It means one can define another MakeHilbert class
(within another function or outside of any function, that is, in
the global scope), and it still will be OK. Note, this currently
is not yet supported by the interpreter CINT.
Another example is applying of a simple function to each matrix
element:
void foo(TMatrixF &m,TMatrixF &m1)
{
typedef double (*dfunc_t)(double);
class ApplyFunction : public TElementActionF {
dfunc_t fFunc;
void Operation(Float_t &element) { element=fFunc(element); }
public:
ApplyFunction(dfunc_t func):fFunc(func) {}
};
ApplyFunction x(TMath::Sin);
m.Apply(x);
}
Validation code $ROOTSYS/test/vmatrix.cxx and vvector.cxx contain
a few more examples of that kind.
6. Lazy matrices: instead of returning an object return a "recipe"
how to make it. The full matrix would be rolled out only when
and where it's needed:
TMatrixF haar = THaarMatrixF(5);
THaarMatrixF() is a *class*, not a simple function. However
similar this looks to a returning of an object (see note #1
above), it's dramatically different. THaarMatrixF() constructs a
TMatLazy, an object of just a few bytes long. A
"TMatrixF(const TMatLazy &recipe)" constructor follows the
recipe and makes the matrix haar() right in place. No matrix
element is moved whatsoever!
TMatrixFBase& SetMatrixArray(const Float_t *data,Option_t *option)
Copy array data to matrix . It is assumed that array is of size >= fNelems
(=)))) fNrows*fNcols
option indicates how the data is stored in the array:
option =
'F' : column major (Fortran) m[i][j] = array[i+j*fNrows]
else : row major (C) m[i][j] = array[i*fNcols+j] (default)
Bool_t IsSymmetric() const
void GetMatrix2Array(Float_t *data,Option_t *option) const
Copy matrix data to array . It is assumed that array is of size >= fNelems
(=)))) fNrows*fNcols
option indicates how the data is stored in the array:
option =
'F' : column major (Fortran) array[i+j*fNrows] = m[i][j]
else : row major (C) array[i*fNcols+j] = m[i][j] (default)
TMatrixFBase& InsertRow(Int_t rown,Int_t coln,const Float_t *v,Int_t n)
void ExtractRow(Int_t rown,Int_t coln,Float_t *v,Int_t n) const
Store in array v, n matrix elements of row rown starting at column coln
TMatrixFBase& Shift(Int_t row_shift,Int_t col_shift)
Shift the row index by adding row_shift and the column index by adding
col_shift, respectively. So [rowLwb..rowUpb][colLwb..colUpb] becomes
[rowLwb+row_shift..rowUpb+row_shift][colLwb+col_shift..colUpb+col_shift]
TMatrixFBase& Zero()
TMatrixFBase& Abs()
Take an absolute value of a matrix, i.e. apply Abs() to each element.
TMatrixFBase& Sqr()
Square each element of the matrix.
TMatrixFBase& Sqrt()
Take square root of all elements.
TMatrixFBase& UnitMatrix()
Make a unit matrix (matrix need not be a square one).
TMatrixFBase& NormByDiag(const TVectorF &v,Option_t *option)
option:
"D" : b(i,j) = a(i,j)/sqrt(abs*(v(i)*v(j))) (default)
else : b(i,j) = a(i,j)*sqrt(abs*(v(i)*v(j))) (default)
Float_t RowNorm() const
Row matrix norm, MAX{ SUM{ |M(i,j)|, over j}, over i}.
The norm is induced by the infinity vector norm.
Float_t ColNorm() const
Column matrix norm, MAX{ SUM{ |M(i,j)|, over i}, over j}.
The norm is induced by the 1 vector norm.
Float_t E2Norm() const
Square of the Euclidian norm, SUM{ m(i,j)^2 }.
Int_t NonZeros() const
Compute the number of elements != 0.0
Float_t Sum() const
Compute sum of elements
Float_t Min() const
return minimum matrix element value
Float_t Max() const
return maximum vector element value
void Draw(Option_t *option)
Draw this matrix using an intermediate histogram
The histogram is named "TMatrixF" by default and no title
void Print(Option_t *name) const
Print the matrix as a table of elements .
TMatrixFBase& Apply(const TElementActionF &action)
TMatrixFBase& Apply(const TElementPosActionF &action)
Apply action to each element of the matrix. To action the location
of the current element is passed.
TMatrixFBase& Randomize(Float_t alpha,Float_t beta,Double_t &seed)
randomize matrix element values
void Streamer(TBuffer &R__b)
Stream an object of class TMatrixFBase.
Inline Functions
void ~TMatrixFBase()
Float_t* GetElements()
void Allocate(Int_t nrows, Int_t ncols, Int_t row_lwb = 0, Int_t col_lwb = 0, Int_t init = 0, Int_t nr_nonzero = -1)
Int_t GetRowLwb() const
Int_t GetRowUpb() const
Int_t GetNrows() const
Int_t GetColLwb() const
Int_t GetColUpb() const
Int_t GetNcols() const
Int_t GetNoElements() const
Float_t GetTol() const
const Float_t* GetMatrixArray() const
Float_t* GetMatrixArray()
const Int_t* GetRowIndexArray() const
Int_t* GetRowIndexArray()
const Int_t* GetColIndexArray() const
Int_t* GetColIndexArray()
TMatrixFBase& SetRowIndexArray(Int_t* data)
TMatrixFBase& SetColIndexArray(Int_t* data)
Float_t SetTol(Float_t tol)
void Clear(Option_t* option = "")
void Invalidate()
void MakeValid()
Bool_t IsValid() const
Bool_t IsOwner() const
TMatrixFBase& GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixFBase& target, Option_t* option = "S") const
TMatrixFBase& SetSub(Int_t row_lwb, Int_t col_lwb, const TMatrixFBase& source)
TMatrixFBase& ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
TMatrixFBase& ResizeTo(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros = -1)
Double_t Determinant() const
void Determinant(Double_t& d1, Double_t& d2) const
Float_t NormInf() const
Float_t Norm1() const
Float_t operator()(Int_t rown, Int_t coln) const
Float_t& operator()(Int_t rown, Int_t coln)
Bool_t operator==(Float_t val) const
Bool_t operator!=(Float_t val) const
Bool_t operator<(Float_t val) const
Bool_t operator<=(Float_t val) const
Bool_t operator>(Float_t val) const
Bool_t operator>=(Float_t val) const
TClass* Class()
TClass* IsA() const
void ShowMembers(TMemberInspector& insp, char* parent)
void StreamerNVirtual(TBuffer& b)
TMatrixFBase& operator=(const TMatrixFBase&)
Last update: root/matrix:$Name: $:$Id: TMatrixFBase.cxx,v 1.17 2004/10/23 20:19:05 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
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