Skyline matrices
An implementation of skyline matrices (general or symmetric) is proposed in Montjoie. Symmetric skyline matrices are not easily modifiable (as RowSparse), you have to provide directly the pattern and values of the non-zero entries. General skyline matrices are easily modifiable (as ArrayRowSparse), with methods AddInteraction/AddInteractionRow. Unitary tests of these classes are present in file src/Program/Unit/skyline_matrix_test.cc.
Basic use
// General skyline matrices Matrix<double, General, RowSkyLine> A; int n = 2000; A.Reallocate(n, n); // then you can add non-zero entries with AddInteraction(i, j, value) A.AddInteraction(0, 3, 1.5); // and AddInteractionRow(i, nb_val, col_number, values); IVect col_num(3); Vector<double> values(3); col_num(0) = 2; col_num(1) = 4; col_num(2) = 5; values.FillRand(); int nb_val = 3; A.AddInteractionRow(3, nb_val, col_num, values); // or with ReallocateRow(i, size_row, first_col_number) and Value A.ReallocateRow(1, 2, 4); // adding a_14, a_15 terms A.Value(1, 0) = 2.3; // setting a_14 A.Value(1, 1) = -3.5; // setting a_15 // once the matrix is constructed, you can perform LU factorisation // (performed without pivoting) GetLU(A); // and solves linear systems SolveLU(A, x, b);
Methods for unsymmetric skyline matrices :
| Clear | clears the matrix |
| Reallocate | changes the size of the matrix |
| ReallocateRow | changes the size of a row of the matrix |
| AddInteraction | adds a value to entry A(i, j) |
| AddInteractionRow | adds severals value on a row of the matrix |
| GetRowSize | returns the number of non-zero entries contained in a row |
| GetFirstColNumber | returns the column number of the first non-zero entry in the row i |
| GetMemorySize | returns size of the memory used by the object in bytes |
| Value | access to the j-th non-zero entry of the row i |
| GetM | returns the number of rows |
| GetN | returns the number of columns |
| GetDataSize | returns the number of elements effectively stored in the matrix |
| Fill | sets all non-zero entries to a given value |
| FillRand | sets randomly values of all non-zero entries |
| Zero | sets all non-zero entries to zero |
| WriteText | writes the matrix on the disk |
Methods for symmetric skyline matrices :
| Clear | clears the matrix |
| Reallocate | changes the size of the matrix |
| GetM | returns the number of rows |
| GetN | returns the number of columns |
| GetData | returns the pointer to the array containing non-zero entries |
| GetInd | returns the pointer to the array containing beginning indexes for each row |
| SetData | sets directly the two arrays representing the structure |
| GetMemorySize | returns the memory used by the object in bytes |
| GetDataSize | returns the number of elements effectively stored in the matrix |
| Fill | sets all non-zero entries to a given value |
| FillRand | sets randomly values of all non-zero entries |
| Zero | sets all non-zero entries to zero |
| WriteText | writes the matrix on the disk |
Functions for skyline matrices :
| Copy | Basic conversion from any matrix to skyline matrix |
| MltAdd | performs matrix vector products |
| GetLU | LU factorisation without pivoting |
| SolveLU | LU resolution without pivoting |
| GetCholesky | computes the cholesky factorisation of a symmetric skyline matrix |
| SolveCholesky | solves linear system L x = b or LT x = b, once GetCholesky has been called |
| MltCholesky | computes y = L x or t = LT x, once GetCholesky has been called |
Diagonal matrices
An implementation of diagonal matrices is proposed in Montjoie. They implement standard methods available for other matrices, and Mlt/MltAdd functions. Here an example how to use these matrices:
Basic use
int n = 10;
// you can use the constructor with the number of rows and columns
Matrix<double, Symmetric, DiagonalRow> A(n, n);
// or the Reallocate method
A.Reallocate(2*n, 2*n);
// non-zero entries are modified with AddInteraction
A.AddInteraction(0, 0, 2.5);
// which is equivalent to Get(i, j) +=
A.Get(1, 1) += 0.7;
// access operator is used in read-only mode
cout << A(0, 3) << endl;
// the matrix can be written on a file
A.WriteText("A.dat");
Methods for diagonal matrices :
| GetMemorySize | returns the memory used by the object in bytes |
| Reallocate | reallocates the matrix with m rows |
| Resize | resizes the matrix with m rows |
| Get | returns access to element i, j of the matrix |
| AddInteraction | adds a value to the element i, j of the matrix |
| Clear | clears the matrix |
| ClearRow | clears a row of the matrix |
| SetData | sets the pointer storing the diagonal |
| Nullify | nullifies the pointer storing the diagonal |
| WriteText | writes the matrix in a file or a stream |
Clear
Syntax
void Clear();
This function clears the matrix.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // for general matrices, you can allocate each row separately for (int i = 0; i < n; i++) A.ReallocateRow(i, 4, max(0, i-2)); // the matrix is erased A.Clear();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
Reallocate
Syntax
void Reallocate(int m, int n);
This function initializes the matrix with m rows and n columns.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // for general matrices, you can reallocate each row separately for (int i = 0; i < n; i++) A.ReallocateRow(i, 4, max(0, i-2)); // the matrix is erased A.Clear();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
ReallocateRow
Syntax
void ReallocateRow(int irow, int size_row, int first_index);
This function sets the row irow with size_row elements, the column number of the first element being equal to first_index.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
AddInteraction
Syntax
void AddInteraction(int i, int j, const T& val);
This function adds the value val to the non-zero entry located at row i and column j. If the non-zero entry does not exist at this place, the profile is increased in order to contain this non-zero entry.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // once the pattern has been defined, you can set non-zero entries to zero A.Zero(); // and use AddInteraction to add values A.AddInteraction(0, 1, 2.4); A.AddInteraction(2, 2, 0.8);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
AddInteractionRow
Syntax
void AddInteractionRow(int i, int n, const IVect& col_num, const Vector<T>& val);
This function adds n values val to the non-zero entries located at row i and columns col_num. If a non-zero entry does not exist, the profile is increased in order to contain this non-zero entry.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // once the pattern has been defined, you can set non-zero entries to zero A.Zero(); // and use AddInteraction to add values A.AddInteraction(0, 1, 2.4); A.AddInteraction(2, 2, 0.8); // AddInteractionRow to add several values at the same time IVect col_num(3); Vector<double> val(3); col_num(0) = 0; val(0) = 0.9; col_num(1) = 1; val(1) = -2.4; col_num(2) = 3; val(2) = 1.7; A.AddInteractionRow(1, 3, col_num, val);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetRowSize
Syntax
int GetRowSize(int i) const;
This function returns the number of non-zero entries contained in the row i.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // at any moment, you can know the number of non-zero entries of a row (e.g. row 4) int nnz_row = A.GetRowSize(4);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
GetFirstColNumber
Syntax
int GetFirstColNumber(int i) const;
This function returns the column number of the first non-zero entry contained in the row i.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // at any moment, you can know the first column number on row i int first_pos = A.GetFirstColNumber(i);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
Value
Syntax
T Value(int i, int j) const; T& Value(int i, int j);
This function returns the j-th non-zero entry of the row i. This function can be used to modify the non-zero entry.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // you can set the values with Value A.Value(0, 0) = 2.3; A.Value(0, 1) = 2.7; A.Value(1, 0) = 3.8; A.Value(1, 1) = -2.4; A.Value(1, 2) = 1.9; A.Value(1, 3) = -0.6; A.Value(2, 0) = 4.4; A.Value(2, 1) = -3.7; A.Value(3, 0) = 0.9; A.Value(3, 1) = 2.5; A.Value(4, 0) = -3.5; A.Value(4, 1) = 1.2;
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
GetM
Syntax
int GetM() const;
This function returns the number of rows in the matrix
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // at any moment you can retrieve the number of rows int n = A.GetM();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetN
Syntax
int GetN() const;
This function returns the number of columns in the matrix
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // at any moment you can retrieve the number of columns int n = A.GetN();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetMemorySize
Syntax
size_t GetMemorySize() const;
This function returns the memory used by the object in bytes.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // at any moment you can retrieve the memory effectively used to store the matrix size_t num_bytes = A.GetMemorySize();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetDataSize
Syntax
int GetDataSize() const;
This function returns the number of non-zero entries stored in the matrix.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // at any moment you can retrieve the number of elements stored int nnz = A.GetDataSize();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
Fill
Syntax
void Fill(const T& val);
This function sets all non-zero entries to a same value (val).
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // you can set all non-zero entries to a given value A.Fill(-0.5);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
FillRand
Syntax
void FillRand();
This function sets all non-zero entries to random values.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // you can set all non-zero entries to a random values A.FillRand();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
Zero
Syntax
void Zero();
This function sets all non-zero entries to 0.
Example :
// default constructor Matrix<double, General, RowSkyLine> A; // for example, if you want to construct the following pattern : // A = | x x 0 0 0 | // | x x x x 0 | // | 0 x x 0 0 | // | 0 0 0 x x | // | 0 x x x 0 | A.Reallocate(5, 5); A.ReallocateRow(0, 2, 0); A.ReallocateRow(1, 4, 0); A.ReallocateRow(2, 2, 1); A.ReallocateRow(3, 2, 3); A.ReallocateRow(4, 3, 1); // you can set all non-zero entries to 0 A.Zero();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
WriteText
Syntax
void WriteText(const string&); void WriteText(ostream&);
This function writes the matrix in a file or an output stream. As usual, the file contains the matrix in the triplet form (i j val) with indexes beginning at 1 (instead of 0).
Example :
// default constructor
Matrix<double, General, RowSkyLine> A;
// for example, if you want to construct the following pattern :
// A = | x x 0 0 0 |
// | x x x x 0 |
// | 0 x x 0 0 |
// | 0 0 0 x x |
// | 0 x x x 0 |
A.Reallocate(5, 5);
A.ReallocateRow(0, 2, 0);
A.ReallocateRow(1, 4, 0);
A.ReallocateRow(2, 2, 1);
A.ReallocateRow(3, 2, 3);
A.ReallocateRow(4, 3, 1);
// you can set all non-zero entries to 0
A.Zero();
// and write the matrix on the disk
A.WriteText("matrix.dat");
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetData
Syntax
T* GetData() const
This method returns the pointer storing the values of non-zero entries stored in a symmetric skyline matrix
Example :
// default constructor Matrix<double, Symmetric, SymColSkyLine> A; // a basic way to construct a symmetric skyline matrix is // to construct a sparse matrix, then convert it Matrix<double, Symmetric, ArrayRowSymSparse> B(n, n); B.AddInteraction(0, 0, -5.2); B.AddInteraction(0, 2, 3.4); Copy(B, A); // pointer to non-zero entries stored in A : double* data = A.GetData(); // number of non-zero entries int nnz = A.GetDataSize(); // if you want to modify directly the values, you can use the pointer data for (int i = 0; i < nnz; i++) data[i] += 2.3;
Location :
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetInd
Syntax
int* GetInd() const
This method returns the pointer storing the first index for each row of a symmetric skyline matrix
Example :
// default constructor
Matrix<double, Symmetric, SymColSkyLine> A;
// a basic way to construct a symmetric skyline matrix is
// to construct a sparse matrix, then convert it
Matrix<double, Symmetric, ArrayRowSymSparse> B(n, n);
B.AddInteraction(0, 0, -5.2);
B.AddInteraction(0, 2, 3.4);
Copy(B, A);
// pointer to non-zero entries stored in A :
double* data = A.GetData();
// pointer to first indexes (for each row)
int* ind = A.GetInd();
// number of non-zero entries
int nnz = A.GetDataSize();
// if you want to modify directly the values, you can use the pointer data
// ind is used to access to the wished row
// in this example, only even rows are modified
for (int i = 0; i < A.GetM(); i++)
if (i%2 == 0)
{
for (int j = ind[i]; j < ind[i+1]; j++)
data[j] += 2.3;
}
Location :
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
SetData
Syntax
void SetData(IVect& ind, Vector<T>& val)
This method fills directly the structure with the arrays ind and val. The first array stores the first index for each row, the second array stores the non-zero entries. On output, the arrays ind and val are empty (they are nullified).
Example :
// default constructor Matrix<double, Symmetric, SymColSkyLine> A; // a way to construct a symmetric sky-line matrix // is to construct the arrays ind and val // for example, if we consider the following matrix // A = | 2.3 2.2 -1.4 0 0 | // | 2.2 4.2 0 2.8 0 | // |-1.4 0 3.1 5.2 0 | // | 0 2.8 5.2 7.5 1.0 | // | 0 0 0 1.0 4.6 | // ind = (0, 3, 6, 8, 10, 11) // val = (2.3, 2.2, -1.4, 4.2, 0, 2.8, 3.1, 5.2, 7.5, 1.0, 4.6) IVect ind(6); Vector<double> val(11); ind(0) = 0; ind(1) = 3; ind(2) = 6; ind(3) = 8; ind(4) = 10; ind(5) = 11; val(0) = 2.3; val(1) = 2.2; val(2) = -1.4; val(3) = 4.2; val(4) = 0; val(5) = 2.8; val(6) = 3.1; val(7) = 5.2; val(8) = 7.5; val(9) = 1.0; val(10) = 4.6; A.SetData(ind, val); // then you can use the matrix // for example compute the Cholesky factorization GetCholesky(A);
Location :
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
Copy
Syntax
void Copy(const Matrix1&, Matrix2&);
This function converts a sparse matrix into a skyline matrix.
Example :
// you can construct a sparse matrix Matrix<double, General, ArrayRowSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, General, RowSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear();
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
MltAdd
Syntax
void MltAdd(const T& alpha, const Matrix& A, const Vector& X, const T& beta, Vector& Y);
This function performs a matrix vector product with a skyline matrix.
Example :
// you can construct a sparse matrix Matrix<double, General, ArrayRowSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, General, RowSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear(); Vector<double> X(n), Y(n); Y.FillRand(); X.FillRand(); // computes Y = beta Y + alpha A X MltAdd(alpha, A, X, beta, Y);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetLU
Syntax
void GetLU(Matrix& A);
This function replaces a skyline matrix A by its LU factorisation.
Example :
// you can construct a sparse matrix Matrix<double, General, ArrayRowSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, General, RowSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear(); // and compute its LU factorisation GetLU(A); // then you can compute the solution of A X = B Vector<double> X(n), B(n); B.FillRand(); X = B; SolveLU(A, X);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
SolveLU
Syntax
void SolveLU(Matrix& A, Vector& X); void SolveLU(SeldonTrans, Matrix& A, Vector& X);
This function computes the solution of A X = B or AT X = B, assuming that A has been replaced by its L and U factors by calling GetLU before.
Example :
// you can construct a sparse matrix Matrix<double, General, ArrayRowSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, General, RowSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear(); // and compute its LU factorisation GetLU(A); // then you can compute the solution of A X = B Vector<double> X(n), B(n); B.FillRand(); X = B; SolveLU(A, X);
Location :
GeneralSkyLineMatrix.hxx
GeneralSkyLineMatrix.cxx
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetCholesky
Syntax
void GetCholesky(Matrix& A);
This function replaces a skyline matrix A by its Cholesky factorisation. It is available only for symmetric skyline matrices.
Example :
// you can construct a sparse matrix Matrix<double, Symmetric, ArrayRowSymSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, Symmetric, SymColSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear(); // and compute its Cholesky factorisation GetCholesky(A); // then you can compute the solution of L^T X = B for example Vector<double> X(n), B(n); B.FillRand(); X = B; SolveCholesky(SeldonTrans, A, X); // or perform the matrix vector product B = L X B = X; MltCholesky(SeldonNoTrans, A, B);
Location :
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
SolveCholesky
Syntax
void SolveCholesky(Matrix& A, Vector& X);
This function solves the linear system L X = B or LT X = B where A has been replaced by its Cholesky factor L (A = L LT), by calling GetCholesky.
Example :
// you can construct a sparse matrix Matrix<double, Symmetric, ArrayRowSymSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, Symmetric, SymColSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear(); // and compute its Cholesky factorisation GetCholesky(A); // then you can compute the solution of L^T X = B for example Vector<double> X(n), B(n); B.FillRand(); X = B; SolveCholesky(SeldonTrans, A, X); // or perform the matrix vector product B = L X B = X; MltCholesky(SeldonNoTrans, A, B);
Location :
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
MltCholesky
Syntax
void MltCholesky(Matrix& A, Vector& X);
This function performs the matrix vector product Y = L X or Y = LT X where A has been replaced by its Cholesky factor L (A = L LT), by calling GetCholesky.
Example :
// you can construct a sparse matrix Matrix<double, Symmetric, ArrayRowSymSparse> Asp; Asp.Reallocate(5, 5); Asp.AddInteraction(0, 1, 2.8); Asp.AddInteraction(1, 3, 0.8); // ... // then you can convert this sparse matrix into a skyline matrix A Matrix<double, Symmetric, SymColSkyLine> A; Copy(Asp, A); // you can release the memory of Asp if you want Asp.Clear(); // and compute its Cholesky factorisation GetCholesky(A); // then you can compute the solution of L^T X = B for example Vector<double> X(n), B(n); B.FillRand(); X = B; SolveCholesky(SeldonTrans, A, X); // or perform the matrix vector product B = L X B = X; MltCholesky(SeldonNoTrans, A, B);
Location :
SymmetricSkyLineMatrix.hxx
SymmetricSkyLineMatrix.cxx
GetMemorySize
Syntax
size_t GetMemorySize();
This function returns the memory used by the matrix in bytes.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // size used to store A : cout << A.GetMemorySize() << endl;
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
Reallocate
Syntax
void Reallocate(int, int);
This function modifies the size of the matrix. Previous elements may be lost.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // you can enforce deallocation with Clear A.Clear();
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
Resize
Syntax
void Resize(int, int);
This function modifies the size of the matrix. Previous elements are kept.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // matrix can be modified with Get A.Get(0, 0) = 3.0; A.Get(1, 1) = -1.0; A.Get(2, 2) = -2.5; // Resize keeps previous elements A.Resize(n+1, n+1);
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
Get
Syntax
T& Get(int, int);
This function returns an access to element i, j of the matrix.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // matrix can be modified with Get A.Get(0, 0) = 3.0; A.Get(1, 1) = -1.0; A.Get(2, 2) = -2.5;
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
AddInteraction
Syntax
void AddInteraction(int, int, const T&);
This function adds a value to the element i, j of the matrix. If j is different from i, the element is not added since the matrix is diagonal.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // matrix can be modified with Get or AddInteraction A.Get(0, 0) = 3.0; A.Get(1, 1) = -1.0; A.Get(2, 2) = -2.5; A.AddInteraction(1, 1, 2.3); // element 1, 1 should contain now -1+2.3 = 1.3
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
Clear
Syntax
void Clear();
This function clears the matrix.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); // the matrix is erased A.Clear();
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
ClearRow
Syntax
void ClearRow(int);
This function clears a row of the matrix. For a diagonal matrix, it consists of setting the diagonal element to zero.
Example :
// default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can allocate the matrix with Reallocate A.Reallocate(n, n); A.AddInteraction(2, 2, 2.4); A.AddInteraction(2, 2, -0.6); // you can clear row 2 (the value returns to 0) A.ClearRow(2);
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
SetData
Syntax
void SetData(int, T*);
This function is a low-level function and should be used carefully, it sets the pointer storing the diagonal.
Example :
Vector<double> diagA(10); // default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can use a pointer stored in another vector A.SetData(diagA.GetM(), diagA.GetData()); // to avoid a duplicate delete, Nullify should be called before calling the destructor of A: A.Nullify();
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
Nullify
Syntax
void Nullify();
This function is a low-level function and should be used carefully, it nullifies the pointer storing the diagonal.
Example :
Vector<double> diagA(10); // default constructor Matrix<double, Symmetric, DiagonalRow> A; // then you can use a pointer stored in another vector A.SetData(diagA.GetM(), diagA.GetData()); // to avoid a duplicate delete, Nullify should be called before calling the destructor of A: A.Nullify();
Location :
DiagonalMatrix.hxx
DiagonalMatrixInline.cxx
WriteText
Syntax
void WriteText(const string&); void WriteText(ostream&);
This function writes the matrix to a file or an output stream.
Example :
// a diagonal matrix is constructed
Matrix<double, Symmetric, DiagonalRow> A(n, n);
// and filled
A.Get(2, 2) = 3.0;
// finally, the matrix can be written in a file
A.WriteText("A.dat");