Functions for Matrices
In that page, we detail functions that are not related to Lapack
| Transpose | replaces a matrix by its transpose |
| TransposeConj | replaces a matrix by its conjugate transpose |
| SetRow | modifies a row of the matrix |
| GetRow | extracts a row from the matrix |
| SetCol | modifies a column of the matrix |
| GetCol | extracts a column from the matrix |
| MaxAbs | returns highest absolute value of A |
| Norm1 | returns 1-norm of A |
| NormInf | returns infinity-norm of A |
| ApplyInversePermutation | permutes row and column numbers of a matrix |
| ScaleMatrix | multiplies rows and columns of a matrix by coefficients |
| ScaleLeftMatrix | multiplies rows of a matrix by coefficients |
| Copy | copies a sparse matrix into another one (conversion of format if needed) |
| ConvertMatrix_to_Coordinates | conversion of a sparse matrix into coordinates format |
| ConvertMatrix_from_Coordinates | conversion of a matrix given as a triplet (i, j, val) to a sparse matrix |
| ConvertToCSC | converts a sparse matrix to CSC (Compressed Sparse Column) format |
| ConvertToCSR | converts a sparse matrix to CSR (Compressed Sparse Row) format |
| ConvertToSparse | converts dense matrices to sparse matrices by specifying a threshold. |
| SOR | applies successive over-relaxations to matrix |
| Cg, Gmres, BiCgSTAB, etc | solves iteratively a linear system |
| IsComplexMatrix | returns true if the matrix is complex |
| IsSparseMatrix | returns true if the matrix is sparse |
| IsSymmetricMatrix | returns true if the matrix is symmetric |
Transpose, TransposeConj
Syntax :
void Transpose(Matrix&); void TransposeConj(Matrix&);
Transpose overwrites a matrix by its transpose, while TransposeConj overwrites a matrix by its conjugate transpose. These functions are only available for dense matrices.
Example :
Matrix<double> A(5, 5); A.Fill(); Transpose(A); Matrix<complex<double> > B(5, 5); // you fill B as you want, then overwrites it by conj(transpose(B)) TransposeConj(B);
Location :
SetRow
Syntax :
void SetRow(const Vector&, int, Matrix&);
This function modifies a row in the provided matrix. This function is available only for dense matrices.
Example :
Matrix<double> A(5, 5); A.Fill(); // now you construct a row Vector<double> row(5); row.FillRand(); // and you put it in A int irow = 1; SetRow(row, irow, A);
Location :
GetRow
Syntax :
void GetRow(const Matrix&, int, Vector&);
This function extracts a row from the provided matrix. This function is available only for dense matrices.
Example :
Matrix<double> A(5, 5); A.Fill(); // now you extract the first row Vector<double> row; GetRow(A, 0, row);
Location :
SetCol
Syntax :
void SetCol(const Vector&, int, Matrix&);
This function modifies a column in the provided matrix. This function is available only for dense matrices.
Example :
Matrix<double> A(5, 5); A.Fill(); // now you construct a column Vector<double> col(5); col.FillRand(); // and you put it in A int icol = 1; SetCol(col, icol, A);
Location :
GetCol
Syntax :
void GetCol(const Matrix&, int, Vector&);
This function extracts a column from the provided matrix. This function is available only for dense matrices.
Example :
Matrix<double> A(5, 5); A.Fill(); // now you extract the first column Vector<double> col; GetCol(A, 0, col);
Location :
MaxAbs
Syntax :
T MaxAbs(const Matrix<T>&);
This function returns the highest absolute value of a matrix.
Example :
Matrix<complex<double> > A(5, 5); A.Fill(); double module_max = MaxAbs(A);
Location :
Norm1
Syntax :
T Norm1(const Matrix<T>&);
This function returns the 1-norm of a matrix.
Example :
Matrix<complex<double> > A(5, 5); A.Fill(); double anorm_one = Norm1(A);
Location :
NormInf
Syntax :
T NormInf(const Matrix<T>&);
This function returns the infinite norm of a matrix.
Example :
Matrix<complex<double> > A(5, 5); A.Fill(); double anorm_inf = NormInf(A);
Location :
ApplyInversePermutation
Syntax :
void ApplyInversePermutation(Matrix&, const Vector<int>&, const Vector<int>&);
This function permutes a given matrix with the provided new row numbers and column numbers. ApplyInversePermutation(A, row, col) does the same operation as A(row, col) = A in Matlab. This function is only available for RowMajor, ColMajor, ArrayRowSparse, ArrayRowSymSparse, ArrayRowComplexSparse and ArrayRowSymComplexSparse.
Example :
// you fill A as you wish Matrix<double, Symmetric, ArrayRowSymSparse> A(5, 5); // then new row and column numbers IVect row(5); // for symmetric matrix, row and column permutation must be the same // if you want to keep symmetry ApplyInversePermutation(A, row, row); // for unsymmetric matrices, you can specify different permutations IVect col(5); Matrix<double, General, ArrayRowSparse> B(5, 5); ApplyInversePermutation(B, row, col);
Location :
ScaleMatrix
Syntax :
void ScaleMatrix(Matrix&, const Vector&, const Vector&);
This function multiplies each row and column with a coefficient, i.e. A is replaced by L*A*R where L and R are diagonal matrices and you provide the diagonal when you call ScaleMatrix. This function is only available for ArrayRowSparse, ArrayRowSymSparse, ArrayRowComplexSparse and ArrayRowSymComplexSparse.
Example :
// you fill A as you wish Matrix<double, Symmetric, ArrayRowSymSparse> A(5, 5); // then scaling vectors Vector<double> scale(5); // for symmetric matrix, row and column scaling must be the same // if you want to keep symmetry ScaleMatrix(A, scale, scale); // for unsymmetric matrices, you can specify different scalings IVect scale_right(5); Matrix<double, General, ArrayRowSparse> B(5, 5); ApplyInversePermutation(B, scale, scale_right);
Location :
ScaleLeftMatrix
Syntax :
void ScaleLeftMatrix(Matrix&, const Vector&);
This function multiplies each row with a coefficient, i.e. A is replaced by L*A where L is diagonal and you provide the diagonal when you call ScaleLeftMatrix. This function is only available for ArrayRowSparse, and ArrayRowComplexSparse.
Example :
// you fill A as you wish Matrix<double, General, ArrayRowSparse> A(5, 5); // then scaling vector Vector<double> scale(5); ScaleLeftMatrix(A, scale);
Location :
Copy
Syntax :
void Copy(const Matrix&, Matrix2&);
This function copies a sparse matrix into another one. If the types of the matrices differ, a conversion is performed. However, not all the conversion have been implemented, so you may have a compilation error when copying some matrices.
Example :
// you fill A as you wish Matrix<double, General, ArrayRowSparse> A(5, 5); // then you can copy it to another form Matrix<double, General, RowSparse> B; // B does not need to be allocated Copy(A, B); // For other types that don't compile // you can use ConvertMatrix_to_Coordinates : Matrix<double, Symmetric, ColSymSparse> C; // conversion to triplet form (i, j, value) IVect IndRow, IndCol; Vector<double> Val; ConvertMatrix_to_Coordinates(A, IndRow, IndCol, Val, 0, true); // then C is filled ConvertMatrix_from_Coordinates(IndRow, IndCol, Val, C, 0);
Location :
ConvertMatrix_to_Coordinates
Syntax :
void ConvertMatrix_to_Coordinates(const Matrix& A, Vector& IndRow, Vector& IndCol, Vector& Val, int index, bool sym);
This function converts a sparse matrix to the triplet form (i, j, val) (coordinate format). The row and column numbers will start at index, therefore you can switch between 1-based indices and 0-based indices.
Example :
// you fill A as you wish Matrix<double, General, ArrayRowSparse> A(5, 5); // conversion to triplet form (i, j, value) IVect IndRow, IndCol; Vector<double> Val; ConvertMatrix_to_Coordinates(A, IndRow, IndCol, Val, 0, true); // number of non-zero entries : int nnz = IndRow.GetM(); for (int i = 0; i < nnz; i++) { cout << "Row index : " << IndRow(i) << endl; cout << "Column index : " << IndCol(i) << endl; cout << "value : " << Val(i) << endl; }
Location :
ConvertMatrix_from_Coordinates
Syntax :
void ConvertMatrix_from_Coordinates(Vector& IndRow, Vector& IndCol, Vector& Val, Matrix& A, int index);
This function converts a triplet form (i, j, val) (coordinate format) to a sparse matrix. The row and column numbers are assumed to start at index, therefore you can switch between 1-based indices and 0-based indices.
Example :
// creating a sparse matrix // A = | 1 0 0 2| // | -1 2 3 0| // | 0 1.2 0 2.5| int nnz = 7; IVect IndRow(nnz), IndCol(nnz); Vector<double> Val(nnz); IndRow(0) = 0; IndCol(0) = 0; Val(0) = 1.0; IndRow(1) = 0; IndCol(1) = 3; Val(1) = 2.0; IndRow(2) = 1; IndCol(2) = 0; Val(2) = -1.0; IndRow(3) = 1; IndCol(3) = 1; Val(3) = 2.0; IndRow(4) = 1; IndCol(4) = 2; Val(4) = 3.0; IndRow(5) = 2; IndCol(5) = 1; Val(5) = 1.2; IndRow(6) = 2; IndCol(6) = 3; Val(6) = 2.5; // conversion to a Seldon structure Matrix<double, General, RowSparse> ConvertMatrix_from_Coordinates(IndRow, IndCol, Val, A, 0);
Location :
ConvertToCSC
Syntax :
void ConvertToCSC(const Matrix& A, Property& sym, Vector& Ptr, Vector& Ind, Vector& Val, bool sym_pat);
This function converts a matrix to Compressed Sparse Column (CSC) format. Val stores the values of non-zero entries, Ind the row indexes of the non-zero entries, and Ptr the locations in Val of non-zero entries starting a column. This is the storage represented by ColSparse in Seldon. If Property is Symmetric, only upper part of the matrix will be converted (ColSymSparse storage). If sym_pat is true, the sparsity pattern is symmetrized, that is to say that if a(i, j) exists, then a(j, i) also exists. Default value of sym_pat is false. This feature is used for exemple in the interface of Pastix solver, since this solver requires that the sparsity pattern is symmetric (values may be not symmetric).
Example :
// you fill A as you wish Matrix<double, General, ArrayRowSparse> A(5, 5); // then you can retrieve Ptr, Ind, Val arrays of CSC format General prop; ConvertToCSC(A, prop, Ptr, Ind, Val);
ConvertToCSR
Syntax :
void ConvertToCSR(const Matrix& A, Property& sym, Vector& Ptr, Vector& Ind, Vector& Val);
This function converts a matrix to Compressed Sparse Row (CSR) format. Val stores the values of non-zero entries, Ind the column indexes of the non-zero entries, and Ptr the locations in Val of non-zero entries starting a row. This is the storage represented by RowSparse in Seldon. If Property is Symmetric, only upper part of the matrix will be converted (RowSymSparse storage).
Example :
// you fill A as you wish Matrix<double, General, ArrayColSparse> A(5, 5); // then you can retrieve Ptr, Ind, Val arrays of CSR format General prop; ConvertToCSR(A, prop, Ptr, Ind, Val);
Location :
ConvertToSparse
Syntax :
void ConvertToSparse(const Matrix& A, Matrix& B, const T& threshold);
This function converts a dense matrix to a sparse matrix. All values whose modulus is below or equal to threshold are skipped.
Example :
// you fill A as you wish Matrix<double, General, RowMajor> A(5, 5); // then you can convert it to a sparse matrix Matrix<double, General, RowSparse> B; ConvertToSparse(A, B, 1e-12); // and retrieve the number of non-zero entries int nnz = B.GetDataSize();
Location :
IsComplexMatrix
Syntax :
void IsComplexMatrix(const Matrix&)
This function returns true if the matrix is complex. It does not check if all the values are real, but merely returns true if the value type is complex (e.g. T = complex<double>).
Example :
// complex matrix Matrix<complex<double>, General, RowMajor> A; // IsComplexMatrix should return true if (IsComplexMatrix(A)) { cout << "A is complex" << endl; }
Location :
IsSymmetricMatrix
Syntax :
void IsSymmetricMatrix(const Matrix&)
This function returns true if the matrix is symmetric. It does not check if a(i,j) = a(j,i) for all i and j, but merely returns true if the property of the matrix is set to symmetric.
Example :
// complex matrix Matrix<complex<double>, Symmetric, RowSymPacked> A; // IsSymmetricMatrix should return true if (IsSymmetricMatrix(A)) { cout << "A is symmetric" << endl; }
Location :
IsSparseMatrix
Syntax :
void IsSparseMatrix(const Matrix&)
This function returns true if the matrix is sparse. It does not check if all the values are different from 0, but merely returns true if the storage associated with the matrix is a sparse storage.
Example :
// complex matrix Matrix<complex<double>, General, ArrayRowSparse> A; // IsSparseMatrix should return true if (IsSparseMatrix(A)) { cout << "A is sparse" << endl; }
