Sparse Matrices
First, methods and functions related to sparse matrices stored as a vector of sparse rows are detailed. This type of matrix is interesting because it allows fast insertion of elements in the matrix. Then the matrices using Harwell-Boeing format are detailed. Functions related to sparse matrices are explained. We advise the user to use always storage of matrix by rows, since this last storage is more efficient for the matrix-vector product. Row and column indices start at 0, as for dense matrices.
Basic declaration of easily modifiable sparse matrices:
These matrices are available only after SeldonSolver.hxx has been included.
Classes :
Matrix<T, Prop, ArrayRowSparse>
Matrix<T, Prop, ArrayColSparse>
Matrix<T, Prop, ArrayRowSymSparse>
Matrix<T, Prop, ArrayColSymSparse>
Example :
// sparse matrix of doubles Matrix<double, General, ArrayRowSparse> A; // sparse symmetric matrix Matrix<float, Symmetric, ArrayRowSymSparse> B; // changing size of the matrix A.Reallocate(m, n); // a_13 = a_13 + 1.5 A.AddInteraction(1, 3, 1.5);
Methods for easily modifiable sparse matrices :
| Matrix constructors | |
| Matrix operators | |
| GetM | returns the number of rows in the matrix |
| GetN | returns the number of columns in the matrix |
| GetDataSize | returns the number of elements effectively stored |
| GetNonZeros | returns the number of elements effectively stored |
| GetData | returns a pointer to the array containing the values |
| GetIndex | returns a pointer to the array containing column numbers |
| SetData | sets the pointer to the arrays containing values and column numbers |
| Nullify | removes elements of the matrix without releasing memory |
| 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) |
| Value | direct access to a value |
| Index | direct access to a column number |
| 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 |
| ReallocateRow / ReallocateColumn | changes the size of a row |
| ResizeRow / ResizeColumn | changes the size of a row and keeps previous values |
| ClearRow / ClearColumn | clears a row |
| SwapRow / SwapColumn | exchanges two rows |
| ReplaceIndexRow / ReplaceIndexColumn | changes column numbers |
| GetRowSize / GetColumnSize | returns the number of elements in the row |
| PrintRow / PrintColumn | prints a row |
| AssembleRow / AssembleColumn | assembles a row |
| AddInteraction | adds/inserts an element in the matrix |
| AddInteractionRow | adds/inserts an element in a matrix row |
| AddInteractionColumn | adds/inserts elements in a matrix column |
| displays the matrix | |
| Write | writes the vector in binary format |
| Read | reads the vector in binary format |
| WriteText | writes the vector in text format |
| ReadText | reads the vector in text format |
Another class of storage of sparse matrices is available, the so-called Harwell-Boeing format. The values are stored in a single array, preventing from a fast insertion of elements. Nevertheless, this type of storage requires slightly less memory and the associated matrix-vector product is more efficient.
Basic declaration of Harwell-Boeing sparse matrices:
Classes :
Matrix<T, Prop, RowSparse>
Matrix<T, Prop, ColSparse>
Matrix<T, Prop, RowSymSparse>
Matrix<T, Prop, ColSymSparse>
Example :
// sparse matrix of doubles Matrix<double, General, RowSparse> A; // sparse symmetric matrix Matrix<float, Symmetric, RowSymSparse> B;
Methods for Harwell-Boeing sparse matrices :
| Matrix constructors | |
| Matrix operators | |
| GetM | returns the number of rows in the matrix |
| GetN | returns the number of columns in the matrix |
| GetDataSize | returns the number of elements effectively stored |
| GetNonZeros | returns the number of elements effectively stored |
| GetData | returns a pointer to the array containing the values |
| GetInd | returns a pointer to the array containing column numbers |
| GetPtr | returns a pointer to the array containing row numbers |
| GetPtrSize | returns size of array Ptr |
| GetIndSize | returns size of array Ind |
| Clear | removes all elements of the matrix |
| SetData | sets the pointer to the array containing the values |
| Nullify | clears the matrix without releasing memory |
| displays the matrix | |
| Write | writes the vector in binary format |
| Read | reads the vector in binary format |
| WriteText | writes the vector in text format |
| ReadText | reads the vector in text format |
Functions :
| Mlt | multiplication by a scalar or matrix-vector product |
| MltAdd | performs a matrix-vector product |
| Add | adds two matrices |
| Copy | copies/converts one matrix into another one |
| PermuteMatrix | applies permutation to matrix |
| ScaleMatrix | applies a scaling both for columns and rows |
| ScaleLeftMatrix | applies a left scaling (on rows) |
| 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 | solves linear system by using LU factorization |
| SOR | applies successive over-relaxations to matrix |
| Cg, Gmres, BiCgSTAB, etc | solves iteratively a linear system |
Matrix constructors for ArrayRowSparse, ArrayRowSymSparse
Syntax :
Matrix(); Matrix(int m, int n);
Example :
// default constructor -> empty matrix Matrix<double, General, ArrayRowSparse> V; cout << "Number of elements "<< V.GetDataSize() << endl; // should return 0 // then you can use Reallocate to set the number of rows and columns V.Reallocate(3, 2); // the last command doesn't create any non-zero element // you can create one with AddInteraction for example V.AddInteraction(0, 1, 1.5); // we construct symmetric matrix with 4 rows Matrix<double, Symmetric, ArrayRowSymSparse> W(4, 4);
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Matrix constructors for RowSparse, RowSymSparse
Syntax :
Matrix(); Matrix(int m, int n); Matrix(int m, int n, int nnz); Matrix(m, n, values, ptr, ind);
Example :
// default constructor -> empty matrix Matrix<double, General, RowSparse> V; cout << "Number of elements "<< V.GetDataSize() << endl; // should return 0 // the two other constructors are useless Matrix<double, Symmetric, ArrayRowSymSparse> W(4, 4); Matrix<double, General, RowSparse> A(3, 4, 10); // in the last constructor you provide int m = 5; // number of rows int n = 6; // number of columns int nnz = 12; // number of non-zero entries Vector<double> values(nnz); // values values.FillRand(); // you have to initialize values Vector<int> columns(nnz); // for each value column number // for each row, column numbers are sorted // first row columns(0) = 0; columns(1) = 2; columns(2) = 4; // second row columns(3) = 1; // third row columns(4) = 0; columns(5) = 1; columns(6) = 3; // fourth row columns(7) = 4; columns(8) = 5; // last row columns(9) = 2; columns(10) = 3; columns(11) = 5; // for each row, index of first value Vector<int> ptr(m+1); ptr(0) = 0; ptr(1) = 3; ptr(2) = 4; ptr(3) = 7; ptr(4) = 9; ptr(5) = 12; // values on the row are to be seeked between ptr(i) and ptr(i+1) // Now the constructor: Matrix<double, General, RowSparse> M(m, n, values, ptr, columns); // Note that 'values', 'ptr' and 'columns' are nullified (that is, emptied): // the arrays to which they pointed have been transferred to M.
Related topics :
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
Matrix operators for ArrayRowSparse, ArrayRowSymSparse
Syntax :
const T& operator (int i, int j) const; T& operator (int i, int j); Matrix& operator =(const T0& alpha)
The operator () can be used to insert or modify elements of matrix. However, this operator will create a non-zero entry (if it does not exist) except if the matrix is declared as const.
Example :
Matrix<double, General, ArrayRowSparse> V(3, 3); // use of operator () to modify matrix V(0, 0) = 2.0; V(1, 0) = V(0, 0) + 1.0; // this command will add a non-zero entry v_20 cout << V(2, 0) << endl; // set all elements to a given value V = 1;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Matrix operators for RowSparse, RowSymSparse
Syntax :
T operator (int i, int j) const;
The operator () cannot be used to insert or modify elements of matrix.
Example :
Matrix<double, General, RowSparse> V(3, 3); // use of operator () to read elements of matrix cout << "V(0,0) = " << V(0, 0) << endl;
Related topics :
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
GetM
Syntax :
int GetM() const;
This method returns the number of rows.
Example :
Matrix<float, General, ArrayRowSparse> V(3, 2); // V.GetM() should return 3 cout << "Number of rows of V " << V.GetM() << endl;
Location :
Class Matrix_Base
Class Matrix_ArraySparse
Matrix_Base.hxx Matrix_Base.cxx
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
GetN
Syntax :
int GetN() const;
This method returns the number of columns
Example :
Matrix<float, Symmetric, ArrayRowSymSparse> V(3, 2); // V.GetN() should return 2 cout << "Number of rows of V " << V.GetN() << endl;
Location :
Class Matrix_Base
Class Matrix_ArraySparse
Matrix_Base.hxx Matrix_Base.cxx
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
GetDataSize, GetNonZeros
Syntax :
int GetDataSize() const; int GetNonZeros() const;
These methods returns the number of elements effectively stored in the matrix.
Example :
Matrix<float, Symmetric, ArrayRowSymSparse> V(3, 3); V.AddInteraction(0, 1, 1.0); // V.GetDataSize() should return 1 cout << "Number of elements of V " << V.GetSize() << endl;
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Class Matrix_ArraySparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
GetData for ArrayRowSparse, ArrayRowSymSparse
Syntax :
T* GetData(int i) const; Vector<T, Vect_Sparse, Allocator>* GetData() const;
These methods are useful to retrieve the pointer to the values, but they need to be used with caution.
Example :
Matrix<double, General, ArrayRowSparse> V(3, 4); V.Fill(); // values of second row are retrieved int irow = 1; double* data = V.GetData(irow); // you can use data as a normal C array // here the sum of elements of the row is computed double sum = 0; for (int i = 0; i < V.GetRowSize(irow); i++) sum += data[i]; // you can also retrieve all the rows Vector<double, Vect_Sparse>* all_rows = V.GetData();
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Clear
Syntax :
void Clear();
This method removes all the elements of the matrix.
Example :
Matrix<double, General, ArrayRowSparse> A(3, 3); A.AddInteraction(0, 2, 2.8); // clears matrix A A.Clear();
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Class Matrix_ArraySparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Reallocate
Syntax :
void Reallocate(int, int);
This method changes the size of the matrix, but removes previous elements.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 4); A.AddInteraction(0, 2, 2.8); // resizes matrix A A.Reallocate(4, 3); // previous elements are removed : A is empty cout << "number of non-zero entries " << A.GetDataSize() << endl;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Resize
Syntax :
void Resize(int, int);
This method changes the size of the matrix, and keeps previous elements.
Example :
Matrix<double, Symmetric, ArrayRowSymSparse> A(4,4); A(1,3) = 2.0; A(0,2) = -1.0; // resizes matrix A and keeps previous added interactions A.Resize(5,5); // GetDataSize() should return 2 cout << "number of non-zero entries of A " << A.GetDataSize() << endl;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
SetData for ArrayRowSparse, ArrayRowSymSparse
Syntax :
void SetData(int, int, T*, int*); void SetData(int, int, Vector<T, Vect_Sparse>*);
This method changes a row of the matrix or all the rows by directly changing pointers. This is a low-level method and should be used very cautiously. It is better to use other methods to modify the matrix.
Example :
// first use, you construct all the rows int m = 10, n = 9; Vector<Vector<double, Vect_Sparse> > rows(m); rows(0).AddInteraction(1, 2.4); rows(1).AddInteraction(3, -1.2); // ... // then you can feed a sparse matrix with rows Matrix<double, General, ArrayRowSparse> A; A.SetData(m, n, rows.GetData()); // you nullify rows to avoid segmentation fault rows.Nullify(); // second use, you specify one row Vector<double, Vect_Sparse> one_row; one_row.AddInteraction(4, 2.3); one_row.AddInteraction(0, -0.7); // and you put it in the matrix int irow = 2; A.SetData(irow, one_row.GetM(), one_row.GetData(), one_row.GetIndex()); one_row.Nullify();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Nullify for ArrayRowSparse, ArrayRowSymSparse
Syntax :
void Nullify(); void Nullify(int);
This method clears the matrix without releasing memory. You can also clear one single row. This method should be used carefully, and generally in conjunction with method SetData.
Example :
Matrix<double, General, ArrayRowSparse> A; // you retrieve one row of A int irow = 2; Vector<double, Vect_Sparse> one_row; one_row.SetData(A.GetRowSize(irow), A.GetData(irow), A.GetIndex(irow)); // you need to call Nullify to avoid segmentation fault A.Nullify(irow); // you can retrieve all the rows Vector<Vector<double, Vect_Sparse> > rows; rows.SetData(m, A.GetData()); // again Nullify is necessary A.Nullify();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
GetIndex for ArrayRowSparse, ArrayRowSymSparse
Syntax :
void GetIndex(int);
This method returns the pointer to the array containing column numbers of the specified row.
Example :
Matrix<double, General, ArrayRowSparse> A; // you retrieve column numbers of row 1 IVect col; int irow = 1; col.SetData(A.GetRowSize(irow), A.GetIndex(irow)); // after use of col, don't forget to call Nullify col.Nullify();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
SetData for RowSparse, RowSymSparse
Syntax :
void SetData(int, int, int, T*, int*, int*); void SetData(int, int, Vector<T>, Vector<int>, Vector<int>);
This method initializes the matrix and is equivalent to a call to the constructor.
Example :
// first you construct the matrix by using arrays ptr, values, columns int m = 5; // number of rows int n = 6; // number of columns int nnz = 12; // number of non-zero entries Vector<double> values(nnz); // values values.FillRand(); // you have to initialize values Vector<int> columns(nnz); // for each value column number // for each row, column numbers are sorted // first row columns(0) = 0; columns(1) = 2; columns(2) = 4; // second row columns(3) = 1; // third row columns(4) = 0; columns(5) = 1; columns(6) = 3; // fourth row columns(7) = 4; columns(8) = 5; // last row columns(9) = 2; columns(10) = 3; columns(11) = 5; // for each row, index of first value Vector<int> ptr(m+1); ptr(0) = 0; ptr(1) = 3; ptr(2) = 4; ptr(3) = 7; ptr(4) = 9; ptr(5) = 12; // then you call SetData Matrix<double, General, RowSparse> A; A.SetData(m, n, values, ptr, columns);
Related topics :
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
Nullify
Syntax :
void Nullify();
This method clears the matrix without releasing memory. This method should be used carefully, and generally in conjunction with method SetData. You can look at the example shown in the explanation of method SetData.
Related topics :
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
GetData for RowSparse, RowSymSparse
Syntax :
T* GetData() const;
This method retrieves the pointer to the values.
Example :
// construction of a sparse matrix Matrix<double, General, RowSparse> V(m, n, nnz, values, ptr, columns); // values of non-zero entries are retrieved 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];
Related topics :
Location :
Class Matrix_Base
Matrix_Base.hxx Matrix_Base.cxx
GetPtr, GetPtrSize for RowSparse, RowSymSparse
Syntax :
int* GetPtr() const; int GetPtrSize() const;
This method retrieves the pointer to the indices of the first element of each row.
Example :
// construction of a sparse matrix (m = number of rows) Matrix<double, General, RowSparse> V(m, n, nnz, values, ptr, columns); // we get indices of the first element of each row int* ptr = V.GetPtr(); // and also the size of this array (should be number of rows + 1) int size = V.GetPtrSize(); // you can use data as a normal C array // here the number of elements of each row is computed Vector<int> size_row(m); for (int i = 0; i < m; i++) size_row(i) = ptr[i+1] - ptr[i];
Related topics :
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
GetInd, GetIndSize for RowSparse, RowSymSparse
Syntax :
int* GetInd() const; int GetIndSize() const;
This method retrieves the pointer to the column numbers of each row.
Example :
// construction of a sparse matrix (m = number of rows) Matrix<double, General, RowSparse> V(m, n, nnz, values, ptr, columns); // we get column numbers int* ind = V.GetInd(); // and also the size of this array (should be nnz) int size = V.GetIndSize(); // you can use data as a normal C array // here the number of elements of each column is computed Vector<int> size_col(n); size_col.Zero(); for (int i = 0; i < nnz; i++) size_col(ind[i])++;
Related topics :
Location :
Class Matrix_Sparse
Class Matrix_SymSparse
Matrix_Sparse.hxx Matrix_Sparse.cxx
Matrix_SymSparse.hxx Matrix_SymSparse.cxx
Index
Syntax :
int Index(int, int) const; int& Index(int, int);
This method allows the user to modify directly the column numbers. The drawback of this method is that the user has to take care that the column numbers are sorted and unique (no duplicate).
Example :
// declaration of a sparse matrix int m = 5; int n = 4; Matrix<double, General, ArrayRowSparse> V(m, n); // we set the number of non-zero entries of first row V.ReallocateRow(0, 2); // you initialize column numbers with Index, and values with Value V.Index(0, 0) = 1; V.Value(0, 0) = 0.5; V.Index(0, 1) = 3; V.Value(0, 1) = -0.5; // now matrix should be equal to [0 1 -0.5; 0 3 -0.5] cout << " V = " << V << endl; // if you add a new value on the first row V.ResizeRow(0, 3); V.Index(0, 2) = 0; V.Value(0, 2) = 1.1; // you better be careful because the new entry is not at the correct position // one way to fix that problem is to call Assemble V.AssembleRow(0);
Related topics :
ReallocateRow
ResizeRow
AssembleRow
AddInteractionRow
Value
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Value
Syntax :
const T& Value(int, int) const; T& Value(int, int);
This method allows the user to modify directly the values.
Example :
// declaration of a sparse matrix int m = 5; int n = 4; Matrix<double, General, ArrayRowSparse> V(m, n); // we set the number of non-zero entries of first row V.ReallocateRow(0, 2); // you initialize column numbers with Index, and values with Value V.Index(0, 0) = 1; V.Value(0, 0) = 0.5; V.Index(0, 1) = 3; V.Value(0, 1) = -0.5; // now matrix should be equal to [0 1 -0.5; 0 3 -0.5] cout << " V = " << V << endl;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Zero
Syntax :
void Zero();
This method sets to 0 all values contained in non-zero entries. This is useful when you want to keep the pattern of the sparse matrix, but initialize values to 0.
Example :
Matrix<double, General, ArrayRowSparse> V(5, 3); // creation of pattern V.AddInteraction(0, 3, 1.0); V.AddInteraction(2, 4, -1.0); // values are set to 0 V.Zero(); // then you can increment values of the pattern V(0, 3) += 1.5;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
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, Symmetric, ArrayRowSymSparse> V(5, 5); // initialization V.SetIdentity();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Fill
Syntax :
void Fill(); void Fill(const T0& );
This method fills matrix with 0, 1, 2, etc or with a given value.
Example :
Matrix<double, General, ArrayRowSparse> A(5,5); A(1,2) = 3; A(2,4) = 5; A(3,0) = 6; A.Fill(); // A should contain [1 2 0.0, 2 4 1.0, 3 0 2.0] A.Fill(2); // A should contain [1 2 2.0, 2 4 2.0, 3 0 2.0]
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
FillRand
Syntax :
void FillRand();
This method sets values of non-zero entries randomly.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 3); A(1,2) = 0.1; A(2,4) = 0.1; A.FillRand(); // A should contain 2 non-zero entries with random values
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
ReallocateRow / ReallocateColumn
Syntax :
void ReallocateRow(int, int );
ReallocateColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method creates n non-zero entries in specified row.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); // for second row, we create 3 non-zero entries int irow = 1; int n = 3; A.ReallocateRow(irow, n); // you need to initialize elements of the row A.Index(irow, 0) = 0; A.Value(irow, 0) = 0.5; A.Index(irow, 1) = 2; A.Value(irow, 1) = -0.4; A.Index(irow, 2) = 3; A.Value(irow, 2) = 0.6;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
ResizeRow / ResizeColumn
Syntax :
void ResizeRow(int, int );
ResizeColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method creates n non-zero entries in specified row, and keeps previous elements.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); // for second row, we create 3 non-zero entries int irow = 1; int n = 3; A.ReallocateRow(irow, n); // you need to initialize elements of the row A.Index(irow, 0) = 0; A.Value(irow, 0) = 0.5; A.Index(irow, 1) = 2; A.Value(irow, 1) = -0.4; A.Index(irow, 2) = 3; A.Value(irow, 2) = 0.6; // you can change the size of the row A.ResizeRow(irow, n+1); // you need to initialize only the new entry A.Index(irow, 3) = 5; A.Index(irow, 3) = 3.5;
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
ClearRow / ClearColumn
Syntax :
void ClearRow(int,);
ClearColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method removes non-zero entries in specified row.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); A(1, 3) = 4.0; // one non-zero entry in second row // we clear second row A.ClearRow(1);
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
SwapRow / SwapColumn
Syntax :
void ClearRow(int);
SwapColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method swaps two rows. This method should be used very cautiously for symmetric matrices, since in that case only upper part of the matrix is stored.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); A(1, 3) = 4.0; // one non-zero entry in second row A(2, 4) = -1.0; // we swap third and second row A.SwapRow(1, 2);
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
ReplaceIndexRow / ReplaceIndexColumn
Syntax :
void ReplaceIndexRow(int, Vector<int>&);
ReplaceIndexColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method changes column numbers of the specified row.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); A(1, 3) = 4.0; A(1, 4) = -1.0; // we change column numbers of second row IVect new_number(2); new_number(0) = 0; new_number(1) = 2; A.ReplaceIndexRow(1, new_number);
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
GetRowSize / GetColumnSize
Syntax :
void GetRowSize(int) const;
GetColumnSize is the name used for storages ArrayColSparse and ArrayColSymSparse. This method returns the number of non-zero entries in the specified row.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); A(1, 3) = 4.0; A(1, 4) = -1.0; // two non-zero entries in second row cout << "Number of elements in second row " << A.GetRowSize(1) << endl;
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
PrintRow / PrintColumn
Syntax :
void PrintRow(int) const;
PrintColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method returns the number of non-zero entries in the specified row.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 6); A(1, 3) = 4.0; A(1, 4) = -1.0; // we print second row cout << "Second row of A " << A.PrintRow(1) << endl;
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
AssembleRow / AssembleColumn
Syntax :
void AssembleRow(int) const;
AssembleColumn is the name used for storages ArrayColSparse and ArrayColSymSparse. This method sorts and merges non-zero entries of a row. You don't need to call this method if you are using methods AddInteraction, AddInteractionRow or the access operator ().
Example :
Matrix<double, General, ArrayRowSparse> A(5, 5); A.ReallocateRow(1, 3); // we initialize non-zero entries but non-sorted and with duplicates A.Index(1, 0) = 4; A.Value(1, 0) = 1.2; A.Index(1, 1) = 2; A.Value(1, 1) = -0.7; A.Index(1, 2) = 4; A.Value(1, 2) = 2.5; // we sort column numbers of row 1 A.AssembleRow(1); // now A should be equal to [1 2 -0.7, 1 4 3.7]
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
AddInteraction
Syntax :
void AddInteraction(int, int, T);
This methods adds/inserts a value in the matrix. This is equivalent to use the access operator () in conjunction with operator +=.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 5); // insertion A.AddInteraction(1, 3, 2.6); // we add A.AddInteraction(1, 3, -1.0); // now A should be equal to [1 3 1.6]
Related topics :
AddInteractionRow
AddInteractionColumn
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
AddInteractionRow
Syntax :
void AddInteractionRow(int, int, Vector<int>, Vector<T>);
This methods adds/inserts several values in a row of the matrix. This is more efficient to use that method rather than calling AddInteraction several times.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 5); // insertion, you don't need to sort column numbers int irow = 2; int nb_values = 3; IVect col(nb_values); Vector<double> values(nb_values); col(0) = 0; values(0) = 0.1; col(1) = 3; values(1) = 0.6; col(2) = 2; values(2) = -1.4; A.AddInteractionRow(irow, nb_values, col, values);
Related topics :
AddInteraction
AddInteractionColumn
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
AddInteractionColumn
Syntax :
void AddInteractionColumns(int, int, Vector<int>, Vector<T>);
This methods adds/inserts several values in a column of the matrix.
Example :
Matrix<double, General, ArrayRowSparse> A(5, 5); // insertion, you don't need to sort row numbers int icol = 2; int nb_values = 3; IVect row(nb_values); Vector<double> values(nb_values); row(0) = 0; values(0) = 0.1; row(1) = 3; values(1) = 0.6; row(2) = 2; values(2) = -1.4; A.AddInteractionColumn(icol, nb_values, row, values);
Related topics :
AddInteraction
AddInteractionRow
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
Syntax :
void Print() const;
This method displays the matrix.
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
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, non-zero entries, then the array of values, indices of first elements of rows, and finals the array of column numbers.
Example :
// construction of a sparse matrix Matrix<double, General, RowSparse> A(m, n, nnz, values, ptr, columns); // you can write directly in a file 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();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
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, non-zero entries, then the array of values, indices of first elements of each row, column numbers.
Example :
Matrix<double, General RowSparse> A; // you can read directly on a file A.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)); A.Read(file_in); file_in.close();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
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 on each line a non-zero entry, i.e. :
row_number col_number value
The row numbers and columns numbers used 1-index convention, i.e. the first row has its row number equal to 1. An exemple of output file is
1 1 0.123
1 3 0.254
1 4 -0.928
2 1 -0.2
2 5 -0.3
Example :
Matrix<double, General, ArrayRowSparse> A(4,4); A(1,3) = -1.0; A(2,2) = 2.5; // you can write directly in a file A.WriteText("matrix.dat"); // or open a stream with other datas ofstream file_out("matrix.dat"); int my_info = 3; file_out << my_info << '\n'; A.WriteText(file_out); file_out.close();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
ReadText
Syntax :
void ReadText(string); void ReadText(ifstream&);
This method sets the matrix from a file/stream in text format. The format is detailed in method WriteText.
Example :
Matrix<double, Symmetric, ArrayRowSymSparse> 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();
Related topics :
Location :
Class Matrix_ArraySparse
Matrix_ArraySparse.hxx Matrix_ArraySparse.cxx
