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- Dense Matrices
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Dense matrices

In that page, methods and functions related to dense matrices are detailed.

Basic declaration :

Classes :

Matrix<T,Prop,RowMajor>
Matrix<T,Prop,RowSymPacked>
Matrix<T,Prop,RowHermPacked>
Matrix<T,Prop,RowUpTriangPacked>
Matrix<T,Prop,RowLoTriangPacked>

Example :

// dense matrix of doubles
Matrix<double> A;

// dense symmetric matrix
Matrix<float, Symmetric, RowSymPacked> B;

// dense hermitian matrix
Matrix<double, General, RowHermPacked> > C;

// dense lower triangular matrix
Matrix<double, General, RowLoTriangPacked> > D;

// dense upper triangular matrix
Matrix<double, General, RowUpTriangPacked> > E;

Methods :

Matrix constructors
Matrix operators
GetM	returns the number of rows in the matrix
GetN	returns the number of columns in the matrix
GetSize	returns the number of elements in the matrix
GetDataSize	returns the number of elements effectively stored
GetData	returns a pointer to the array containing the values
GetDataConst	returns a pointer to the array containing the values
GetDataVoid	returns a pointer to the array containing the values
GetDataConstVoid	returns a pointer to the array containing the values
Clear	removes all elements of the matrix
Reallocate	changes the size of matrix (does not keep previous elements)
Resize	changes the size of matrix (keeps previous elements)
SetData	sets the pointer to the array containing the values
Nullify	clears the matrix without releasing memory
Val	access to a matrix element
Copy	copies a matrix
Zero	sets all elements to zero
SetIdentity	sets matrix to identity matrix
Fill	sets all elements to a given value
FillRand	fills randomly the matrix
Print	displays the matrix
Write	writes the matrix in binary format
Read	reads the matrix in binary format
WriteText	writes the matrix in text format
ReadText	reads the matrix in text format

Functions :

Mlt	multiplication by a scalar or matrix-vector product
MltAdd	performs a matrix-vector or matrix-matrix product
Add	adds two matrices
Copy	copies a matrix into another one
Rank1Update	Adds a contribution X.Y' to a matrix
Rank2Update	Adds a contribution X.Y' + Y.X' to a symmetric matrix
Solve	solves a triangular system
Transpose	replaces a matrix by its transpose
TransposeConj	replaces a matrix by its conjugate transpose
MaxAbs	returns highest absolute value of A
Norm1	returns 1-norm of A
NormInf	returns infinity-norm of A
GetRow	returns a matrix row
SetRow	changes a matrix row
GetCol	returns a matrix column
SetCol	changes a matrix column
GetLU	performs a LU (or LDL^t) factorization
SolveLU	solve linear system by using LU factorization
RefineSolutionLU	improves solution computed by SolveLU
ReciprocalConditionNumber	computes the inverse of matrix condition number
GetScalingFactors	computes row and column scalings to equilibrate a matrix
GetInverse	computes the matrix inverse
GetQR	QR factorization of matrix
GetLQ	LQ factorization of matrix
GetQ_FromQR	Forms explicitely Q from QR factorization
MltQ_FromQR	multiplies vector by Q
SolveQR	solves least-square problems by using QR factorization
SolveLQ	solves least-square problems by using LQ factorization
GetEigenvalues	computes eigenvalues
GetEigenvaluesEigenvectors	computes eigenvalues and eigenvectors
GetSVD	performs singular value decomposition (SVD)

Matrix constructors

Syntax :

  Matrix();
  Matrix(int, int );

Example :

// default constructor -> empty matrix
Matrix<int> V;
cout << "Number of elements "<< V.GetSize() << endl; // should return 0 
// then you can use Reallocate to set the number of rows and columns
V.Reallocate(3, 2);
V.Fill();

// we construct matrix with 4 rows and 3 columns
Matrix<double> W(4, 3);
// W is not initialized, you have to fill it
W.Fill(1.0);

Location :

Class Matrix_Pointers
Class Matrix_Symmetric
Class Matrix_SymPacked
Class Matrix_Hermitian
Class Matrix_HermPacked
Class Matrix_Triangular
Class Matrix_TriangPacked
Matrix_Pointers.hxx Matrix_Pointers.cxx
Matrix_Symmetric.hxx Matrix_Symmetric.cxx
Matrix_SymPacked.hxx Matrix_SymPacked.cxx
Matrix_Hermitian.hxx Matrix_Hermitian.cxx
Matrix_HermPacked.hxx Matrix_HermPacked.cxx
Matrix_Triangular.hxx Matrix_Triangular.cxx
Matrix_TriangPacked.hxx Matrix_TriangPacked.cxx

Matrix operators

Syntax :

  const T& operator (int i, int j) const;
  T& operator (int i, int j);
  T& operator [int i];
  const T& operator [int i] const;
  Matrix& operator =(const Matrix& )
  Vector& operator =(const T0& alpha)
  Vector& operator *=(const T0& alpha)

The operator [] should not be used in normal use. The operator () can't be used to modify values of matrix for specific storages, e.g. RowSym, RowHerm, RowUpTriang.

Example :

Matrix<double> V(3, 3);
// use of operator () to modify matrix
V(0, 0) = 2.0;
V(1, 0) = V(0, 0) + 1.0;

// operator [] should be used with caution
V[3] = V[0] + 1.4;

Matrix<double> W;
// use of operator = to copy contents of vector V
W = V;

// set all elements to a given value
W = 1;

// multiplication by a scalar
Matrix<double> A(3, 2);
A.Fill();
A *= 1.5;

Location :

GetM

Syntax :

  int GetM() const;

This method returns the number of rows

Example :

Matrix<float> V(3, 2);
// V.GetM() should return 3 
cout << "Number of rows of V " << V.GetM() << endl;

Location :

Class Matrix_Base
Matrix_Base.hxx
Matrix_Base.cxx

GetN

Syntax :

  int GetN() const;

This method returns the number of columns.

Example :

Matrix<float> V(3, 2);
// V.GetN() should return 2 
cout << "Number of rows of V " << V.GetM() << endl;

Location :

Class Matrix_Base
Matrix_Base.hxx
Matrix_Base.cxx

GetSize

Syntax :

  int GetSize() const;

This method returns the number of elements in the matrix

Example :

Matrix<float, Symmetric, RowSymPacked> V(3, 3);
// V.GetSize() should return 9
cout << "Number of elements of V " << V.GetSize() << endl;

Location :

Class Matrix_Base
Matrix_Base.hxx
Matrix_Base.cxx

GetDataSize

Syntax :

  int GetDataSize() const;

This method returns the number of elements effectively stored in the matrix. This is different from GetSize for some storages, e.g. RowSymPacked, RowHermPacked, RowUpTriangPacked.

Example :

Matrix<float, Symmetric, RowSymPacked> V(3, 3);
// V.GetDataSize() should return 6
cout << "Number of elements of V " << V.GetDataSize() << endl;

Location :

GetData, GetDataConst, GetDataVoid, GetDataConstVoid

Syntax :

  T* GetData() const;
  const T* GetDataConst() const;
  void* GetDataVoid() const;
  const void* GetDataConstVoid() const;

These methods are useful to retrieve the pointer to the values. In practice, you can use those methods in order to interface with C/fortran subroutines or to perform some low level operations. But in this last case, you have to be careful, because debugging operations will be more tedious.

Example :

Matrix<double> V(3, 4); V.Fill();
double* data = V.GetData();
// you can use data as a normal C array
// here the sum of elements is computed
double sum = 0;
for (int i = 0; i < V.GetDataSize(); i++)
  sum += data[i];

// if you want to call a fortran subroutine daxpy
Matrix<double> X(3, 3); 
double coef = 2.0;
int m = X.GetM();
int n = X.GetN();
daxpy_(&coef, &m, &n, X.GetData(),);

// for complex numbers, conversion to void* is needed :
Matrix<complex<double> > Xc(4, 4);
complex<double> beta(1,1);
zaxpy(reinterpret_cast<const void*>(beta), Xc.GetDataVoid());

Location :

Class Matrix_Base
Matrix_Base.hxx
Matrix_Base.cxx

Clear

Syntax :

  void Clear();

This method removes all the elements of the matrix.

Example :

Matrix<double> A(3, 2);
A.Fill();
// clears matrix A
A.Clear();

Location :

Reallocate

Syntax :

  void Reallocate(int, int);

This method changes the size of the matrix, but removes previous elements.

Example :

Matrix<long int> A(5, 4);
V.Fill();
// resizes matrix A
A.Reallocate(4, 3);
// you need to initialize all elements of A
A.Zero();

Location :

Resize

Syntax :

  void Resize(int, int);

This method changes the size of the matrix, and keeps previous elements.

Example :

Matrix<long double> A(3,3);
A.Fill();
// resizes matrix A
A.Resize(4,4);
// you need to initialize new elements if there are new
for (int i = 0; i < 4; i++)
  A(4,i) = A(i,4) = 0;

Location :

SetData

Syntax :

  void SetData(int, int, T*);

This method sets the pointer to the array containing elements. This method should be used carefully, and generally in conjunction with method Nullify.

Example :

// for example, you can define a function with a pointer as argument
void f(int m, int n, double* data)
{
  // and sets this array into a Matrix instance
  Matrix<double> A;
  // m : number of rows, n : number of columns
  A.SetData(m, n, data);
  // then you use a C++ method
  double coef = Norm1(A);
  // you don't release memory, because data is used after the function
  A.Nullify();
}

Location :

Nullify

Syntax :

  void Nullify();

This method clears the matrix without releasing memory. This method should be used carefully, and generally in conjunction with method Nullify. You can look at the example shown in the explanation of method SetData.

Location :

Copy

Syntax :

  void Copy(const Matrix&);

This method copies a matrix into the current matrix.

Example :

// copy of a matrix M
Matrix<double> M(3, 3), A;
M.FillRand();
A.Copy(M);
// this is equivalent to use operator =
A = M;

Location :

Val

Syntax :

  T& Val(int, int);
  const T& Val(int, int) const;

This method is similar to operator (), except that it always works, especially for storages like RowSym, RowHerm, RowUpTriang.

Example :

Matrix<double, General, RowUpTriang> A(3,3);
// operator () does not work to change the value
// A(0,0) = 1;  => Error during compilation
A.Val(0,0) = 2.0;  // Okay it works

Location :

Zero

Syntax :

  void Zero();

This method fills memory of 0, is convenient for matrices made of doubles, integers, floats, but not for more complicated types. In that case, it is better to use the method Fill.

Example :

Matrix<double> V(5, 3);
// initialization
V.Fill();

Matrix<IVect> W(10, 2);
// W.Zero() is incorrect and would generate an error at the execution
// a good initialization is to use Fill
IVect zero(5); zero.Zero();
W.Fill(zero);

Location :

SetIdentity

Syntax :

  void SetIdentity();

This method sets all elements to 0, except on the diagonal set to 1. This forms the so-called identity matrix.

Example :

Matrix<double> V(5, 5);
// initialization
V.SetIdentity();

Location :

Fill

Syntax :

  void Fill();
  template<class T0>
  void Fill(const T0& );

This method fills matrix with 0, 1, 2, etc or with a given value.

Example :

Matrix<int> A(2,2);
A.Fill();
// A should contain [0 1; 2 3]

A.Fill(2);
// A should contain [2 2; 2 2]

Location :

FillRand

Syntax :

  void FillRand();

This method fills the matrix with random values.

Example :

Matrix<double> A(5, 3);
A.FillRand();
// A should contain 15 random values

Location :

Print

Syntax :

  void Print() const;
  void Print(int) const;
  void Print(int, int, int, int) const;

This method displays the matrix.

Example :

Matrix<string> A(2, 2);
A(0,0) = string("hello");
A(0,1) = string("world");
A(1,0) = string("you");
A(1,1) = string("welcome");
A.Print(); 
// should display :
// hello world
// you welcome

// you can also display a sub-matrix
A.Print(0, 0, 0, 1); 
// should display "hello world"

// A.Print(2); is equivalent to A.Print(0, 0, 2, 2);

Location :

Write

Syntax :

  void Write(string) const;
  void Write(ofstream&) const;

This method writes the matrix on a file/stream in binary format. The file will contain the number of rows, columns, then the list of elements.

Example :

Matrix<double> A(2, 2); 
// you can write directly in a file
A.Fill();
A.Write("matrix.dat");

// or open a stream with other datas
ofstream file_out("matrix.dat");
int my_info = 3;
file_out.write(reinterpret_cast<char*>(&my_info), sizeof(int));
A.Write(file_out);
file_out.close();

Location :

Read

Syntax :

  void Read(string);
  void Read(ifstream&);

This method sets the matrix from a file/stream in binary format. The file contains the number of rows, columns, then the list of elements.

Example :

Matrix<double> V(3, 4); 
// you can read directly on a file
V.Read("matrix.dat");

// or read from a stream
ifstream file_in("matrix.dat");
int my_info;
file_in.read(reinterpret_cast<char*<(&my_info), sizeof(int));
V.Read(file_in);
file_in.close();

Location :

WriteText

Syntax :

  void WriteText(string) const;
  void WriteText(ofstream&) const;

This method writes the matrix on a file/stream in text format. The file will contain the list of elements.

Example :

Matrix<double> V(2); 
// you can write directly in a file
V.Fill();
V.WriteText("matrix.dat");

// or open a stream with other datas
ofstream file_out("matrix.dat");
int my_info = 3;
file_out << my_info << '\n';
V.WriteText(file_out);
file_out.close();

Location :

ReadText

Syntax :

  void ReadText(string);
  void ReadText(ifstream&);

This method sets the matrix from a file/stream in text format. The file contains the list of elements.

Example :

Matrix<double> V; 
// you can read directly on a file
V.ReadText("matrix.dat");

// or read from a stream
ifstream file_in("matrix.dat");
int my_info;
file_in >> my_info;
V.ReadText(file_in);
file_in.close();

Dense matrices

Basic declaration :

Classes :

Example :

Methods :

Functions :

Matrix constructors

Syntax :

Example :

Related topics :

Location :

Matrix operators

Syntax :

Example :

Related topics :

Location :

GetM

Syntax :

Example :

Location :

GetN

Syntax :

Example :

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GetSize

Syntax :

Example :

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GetDataSize

Syntax :

Example :

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GetData, GetDataConst, GetDataVoid, GetDataConstVoid

Syntax :

Example :

Related topics :

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Clear

Syntax :

Example :

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Reallocate

Syntax :

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Resize

Syntax :

Example :

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SetData

Syntax :

Example :

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Nullify

Syntax :

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Copy

Syntax :

Example :

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Val

Syntax :

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Zero

Syntax :

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SetIdentity

Syntax :

Example :

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