MFEM
v4.0
Finite element discretization library
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Data type sparse matrix. More...
#include <sparsemat.hpp>
Public Member Functions | |
SparseMatrix () | |
Create an empty SparseMatrix. More... | |
SparseMatrix (int nrows, int ncols=-1) | |
Create a sparse matrix with flexible sparsity structure using a row-wise linked list (LIL) format. More... | |
SparseMatrix (int *i, int *j, double *data, int m, int n) | |
Create a sparse matrix in CSR format. Ownership of i, j, and data is transferred to the SparseMatrix. More... | |
SparseMatrix (int *i, int *j, double *data, int m, int n, bool ownij, bool owna, bool issorted) | |
Create a sparse matrix in CSR format. Ownership of i, j, and data is optionally transferred to the SparseMatrix. More... | |
SparseMatrix (int nrows, int ncols, int rowsize) | |
Create a sparse matrix in CSR format where each row has space allocated for exactly rowsize entries. More... | |
SparseMatrix (const SparseMatrix &mat, bool copy_graph=true) | |
Copy constructor (deep copy). More... | |
SparseMatrix (const Vector &v) | |
Create a SparseMatrix with diagonal v, i.e. A = Diag(v) More... | |
SparseMatrix & | operator= (const SparseMatrix &rhs) |
Assignment operator: deep copy. More... | |
void | MakeRef (const SparseMatrix &master) |
Clear the contents of the SparseMatrix and make it a reference to master. More... | |
int | Size () const |
For backward compatibility, define Size() to be synonym of Height(). More... | |
void | Clear () |
Clear the contents of the SparseMatrix. More... | |
bool | Empty () const |
Check if the SparseMatrix is empty. More... | |
int * | GetI () |
Return the array I. More... | |
const int * | GetI () const |
Return the array I, const version. More... | |
int * | GetJ () |
Return the array J. More... | |
const int * | GetJ () const |
Return the array J, const version. More... | |
double * | GetData () |
Return the element data, i.e. the array A. More... | |
const double * | GetData () const |
Return the element data, i.e. the array A, const version. More... | |
int | RowSize (const int i) const |
Returns the number of elements in row i. More... | |
int | MaxRowSize () const |
Returns the maximum number of elements among all rows. More... | |
int * | GetRowColumns (const int row) |
Return a pointer to the column indices in a row. More... | |
const int * | GetRowColumns (const int row) const |
Return a pointer to the column indices in a row, const version. More... | |
double * | GetRowEntries (const int row) |
Return a pointer to the entries in a row. More... | |
const double * | GetRowEntries (const int row) const |
Return a pointer to the entries in a row, const version. More... | |
void | SetWidth (int width_=-1) |
Change the width of a SparseMatrix. More... | |
int | ActualWidth () const |
Returns the actual Width of the matrix. More... | |
void | SortColumnIndices () |
Sort the column indices corresponding to each row. More... | |
void | MoveDiagonalFirst () |
Move the diagonal entry to the first position in each row, preserving the order of the rest of the columns. More... | |
virtual double & | Elem (int i, int j) |
Returns reference to a_{ij}. More... | |
virtual const double & | Elem (int i, int j) const |
Returns constant reference to a_{ij}. More... | |
double & | operator() (int i, int j) |
Returns reference to A[i][j]. More... | |
const double & | operator() (int i, int j) const |
Returns reference to A[i][j]. More... | |
void | GetDiag (Vector &d) const |
Returns the Diagonal of A. More... | |
DenseMatrix * | ToDenseMatrix () const |
Produces a DenseMatrix from a SparseMatrix. More... | |
void | ToDenseMatrix (DenseMatrix &B) const |
Produces a DenseMatrix from a SparseMatrix. More... | |
virtual MemoryClass | GetMemoryClass () const |
Return the MemoryClass preferred by the Operator. More... | |
virtual void | Mult (const Vector &x, Vector &y) const |
Matrix vector multiplication. More... | |
void | AddMult (const Vector &x, Vector &y, const double a=1.0) const |
y += A * x (default) or y += a * A * x More... | |
void | MultTranspose (const Vector &x, Vector &y) const |
Multiply a vector with the transposed matrix. y = At * x. More... | |
void | AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const |
y += At * x (default) or y += a * At * x More... | |
void | BuildTranspose () const |
Build and store internally the transpose of this matrix which will be used in the methods AddMultTranspose() and MultTranspose(). More... | |
void | ResetTranspose () const |
void | PartMult (const Array< int > &rows, const Vector &x, Vector &y) const |
void | PartAddMult (const Array< int > &rows, const Vector &x, Vector &y, const double a=1.0) const |
void | BooleanMult (const Array< int > &x, Array< int > &y) const |
y = A * x, treating all entries as booleans (zero=false, nonzero=true). More... | |
void | BooleanMultTranspose (const Array< int > &x, Array< int > &y) const |
y = At * x, treating all entries as booleans (zero=false, nonzero=true). More... | |
double | InnerProduct (const Vector &x, const Vector &y) const |
Compute y^t A x. More... | |
void | GetRowSums (Vector &x) const |
For all i compute \( x_i = \sum_j A_{ij} \). More... | |
double | GetRowNorml1 (int irow) const |
For i = irow compute \( x_i = \sum_j | A_{i, j} | \). More... | |
virtual MatrixInverse * | Inverse () const |
This virtual method is not supported: it always returns NULL. More... | |
void | EliminateRow (int row, const double sol, Vector &rhs) |
Eliminates a column from the transpose matrix. More... | |
void | EliminateRow (int row, DiagonalPolicy dpolicy=DIAG_ZERO) |
Eliminates a row from the matrix. More... | |
void | EliminateCol (int col, DiagonalPolicy dpolicy=DIAG_ZERO) |
Eliminates the column col from the matrix. More... | |
void | EliminateCols (const Array< int > &cols, const Vector *x=NULL, Vector *b=NULL) |
Eliminate all columns i for which cols[i] != 0. More... | |
void | EliminateRowCol (int rc, const double sol, Vector &rhs, DiagonalPolicy dpolicy=DIAG_ONE) |
Eliminate row rc and column rc and modify the rhs using sol. More... | |
void | EliminateRowColMultipleRHS (int rc, const Vector &sol, DenseMatrix &rhs, DiagonalPolicy dpolicy=DIAG_ONE) |
Similar to EliminateRowCol(int, const double, Vector &, DiagonalPolicy), but multiple values for eliminated unknowns are accepted, and accordingly multiple right-hand-sides are used. More... | |
void | EliminateRowColDiag (int rc, double value) |
Perform elimination and set the diagonal entry to the given value. More... | |
void | EliminateRowCol (int rc, DiagonalPolicy dpolicy=DIAG_ONE) |
Eliminate row rc and column rc. More... | |
void | EliminateRowCol (int rc, SparseMatrix &Ae, DiagonalPolicy dpolicy=DIAG_ONE) |
Similar to EliminateRowCol(int, DiagonalPolicy) + save the eliminated entries into Ae so that (*this) + Ae is equal to the original matrix. More... | |
void | SetDiagIdentity () |
If a row contains only one diag entry of zero, set it to 1. More... | |
virtual void | EliminateZeroRows (const double threshold=1e-12) |
If a row contains only zeros, set its diagonal to 1. More... | |
void | Gauss_Seidel_forw (const Vector &x, Vector &y) const |
Gauss-Seidel forward and backward iterations over a vector x. More... | |
void | Gauss_Seidel_back (const Vector &x, Vector &y) const |
double | GetJacobiScaling () const |
Determine appropriate scaling for Jacobi iteration. More... | |
void | Jacobi (const Vector &b, const Vector &x0, Vector &x1, double sc) const |
void | DiagScale (const Vector &b, Vector &x, double sc=1.0) const |
void | Jacobi2 (const Vector &b, const Vector &x0, Vector &x1, double sc=1.0) const |
void | Jacobi3 (const Vector &b, const Vector &x0, Vector &x1, double sc=1.0) const |
virtual void | Finalize (int skip_zeros=1) |
Finalize the matrix initialization, switching the storage format from LIL to CSR. More... | |
void | Finalize (int skip_zeros, bool fix_empty_rows) |
A slightly more general version of the Finalize(int) method. More... | |
bool | Finalized () const |
bool | areColumnsSorted () const |
void | Threshold (double tol, bool fix_empty_rows=false) |
Remove entries smaller in absolute value than a given tolerance tol. If fix_empty_rows is true, a zero value is inserted in the diagonal entry (for square matrices only) More... | |
void | GetBlocks (Array2D< SparseMatrix * > &blocks) const |
void | GetSubMatrix (const Array< int > &rows, const Array< int > &cols, DenseMatrix &subm) const |
void | SetColPtr (const int row) const |
Initialize the SparseMatrix for fast access to the entries of the given row which becomes the "current row". More... | |
void | ClearColPtr () const |
Reset the "current row" set by calling SetColPtr(). This method must be called between any two calls to SetColPtr(). More... | |
double & | SearchRow (const int col) |
Perform a fast search for an entry in the "current row". See SetColPtr(). More... | |
void | _Add_ (const int col, const double a) |
Add a value to an entry in the "current row". See SetColPtr(). More... | |
void | _Set_ (const int col, const double a) |
Set an entry in the "current row". See SetColPtr(). More... | |
double | _Get_ (const int col) const |
Read the value of an entry in the "current row". See SetColPtr(). More... | |
double & | SearchRow (const int row, const int col) |
void | _Add_ (const int row, const int col, const double a) |
void | _Set_ (const int row, const int col, const double a) |
void | Set (const int i, const int j, const double a) |
void | Add (const int i, const int j, const double a) |
void | SetSubMatrix (const Array< int > &rows, const Array< int > &cols, const DenseMatrix &subm, int skip_zeros=1) |
void | SetSubMatrixTranspose (const Array< int > &rows, const Array< int > &cols, const DenseMatrix &subm, int skip_zeros=1) |
void | AddSubMatrix (const Array< int > &rows, const Array< int > &cols, const DenseMatrix &subm, int skip_zeros=1) |
bool | RowIsEmpty (const int row) const |
virtual int | GetRow (const int row, Array< int > &cols, Vector &srow) const |
Extract all column indices and values from a given row. More... | |
void | SetRow (const int row, const Array< int > &cols, const Vector &srow) |
void | AddRow (const int row, const Array< int > &cols, const Vector &srow) |
void | ScaleRow (const int row, const double scale) |
void | ScaleRows (const Vector &sl) |
this = diag(sl) * this; More... | |
void | ScaleColumns (const Vector &sr) |
this = this * diag(sr); More... | |
SparseMatrix & | operator+= (const SparseMatrix &B) |
Add the sparse matrix 'B' to '*this'. This operation will cause an error if '*this' is finalized and 'B' has larger sparsity pattern. More... | |
void | Add (const double a, const SparseMatrix &B) |
Add the sparse matrix 'B' scaled by the scalar 'a' into '*this'. Only entries in the sparsity pattern of '*this' are added. More... | |
SparseMatrix & | operator= (double a) |
SparseMatrix & | operator*= (double a) |
void | Print (std::ostream &out=mfem::out, int width_=4) const |
Prints matrix to stream out. More... | |
void | PrintMatlab (std::ostream &out=mfem::out) const |
Prints matrix in matlab format. More... | |
void | PrintMM (std::ostream &out=mfem::out) const |
Prints matrix in Matrix Market sparse format. More... | |
void | PrintCSR (std::ostream &out) const |
Prints matrix to stream out in hypre_CSRMatrix format. More... | |
void | PrintCSR2 (std::ostream &out) const |
Prints a sparse matrix to stream out in CSR format. More... | |
void | PrintInfo (std::ostream &out) const |
Print various sparse matrix staticstics. More... | |
double | IsSymmetric () const |
Returns max_{i,j} |(i,j)-(j,i)| for a finalized matrix. More... | |
void | Symmetrize () |
(*this) = 1/2 ((*this) + (*this)^t) More... | |
virtual int | NumNonZeroElems () const |
Returns the number of the nonzero elements in the matrix. More... | |
double | MaxNorm () const |
int | CountSmallElems (double tol) const |
Count the number of entries with |a_ij| <= tol. More... | |
int | CheckFinite () const |
Count the number of entries that are NOT finite, i.e. Inf or Nan. More... | |
void | SetGraphOwner (bool ownij) |
Set the graph ownership flag (I and J arrays). More... | |
void | SetDataOwner (bool owna) |
Set the data ownership flag (A array). More... | |
bool | OwnsGraph () const |
Get the graph ownership flag (I and J arrays). More... | |
bool | OwnsData () const |
Get the data ownership flag (A array). More... | |
void | LoseData () |
Lose the ownership of the graph (I, J) and data (A) arrays. More... | |
void | Swap (SparseMatrix &other) |
virtual | ~SparseMatrix () |
Destroys sparse matrix. More... | |
Type | GetType () const |
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AbstractSparseMatrix (int s=0) | |
Creates a square matrix of the given size. More... | |
AbstractSparseMatrix (int h, int w) | |
Creates a matrix of the given height and width. More... | |
virtual | ~AbstractSparseMatrix () |
Destroys AbstractSparseMatrix. More... | |
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Matrix (int s) | |
Creates a square matrix of size s. More... | |
Matrix (int h, int w) | |
Creates a matrix of the given height and width. More... | |
virtual | ~Matrix () |
Destroys matrix. More... | |
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Operator (int s=0) | |
Construct a square Operator with given size s (default 0). More... | |
Operator (int h, int w) | |
Construct an Operator with the given height (output size) and width (input size). More... | |
int | Height () const |
Get the height (size of output) of the Operator. Synonym with NumRows(). More... | |
int | NumRows () const |
Get the number of rows (size of output) of the Operator. Synonym with Height(). More... | |
int | Width () const |
Get the width (size of input) of the Operator. Synonym with NumCols(). More... | |
int | NumCols () const |
Get the number of columns (size of input) of the Operator. Synonym with Width(). More... | |
virtual Operator & | GetGradient (const Vector &x) const |
Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error. More... | |
virtual const Operator * | GetProlongation () const |
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More... | |
virtual const Operator * | GetRestriction () const |
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity. More... | |
void | FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0) |
Form a constrained linear system using a matrix-free approach. More... | |
virtual void | RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x) |
Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem(). More... | |
void | PrintMatlab (std::ostream &out, int n=0, int m=0) const |
Prints operator with input size n and output size m in Matlab format. More... | |
virtual | ~Operator () |
Virtual destructor. More... | |
Type | GetType () const |
Return the type ID of the Operator class. More... | |
Protected Types | |
typedef MemAlloc< RowNode, 1024 > | RowNodeAlloc |
Protected Member Functions | |
void | Destroy () |
void | SetEmpty () |
Protected Attributes | |
RowNode ** | Rows |
Array of linked lists, one for every row. This array represents the linked list (LIL) storage format. More... | |
int | current_row |
int * | ColPtrJ |
RowNode ** | ColPtrNode |
SparseMatrix * | At |
Transpose of A. Owned. Used to perform MultTranspose() on devices. More... | |
RowNodeAlloc * | NodesMem |
bool | isSorted |
Are the columns sorted already. More... | |
Arrays used by the CSR storage format. | |
Memory< int > | I |
Array with size (height+1) containing the row offsets. More... | |
Memory< int > | J |
Array with size I[height], containing the column indices for all matrix entries, as indexed by the I array. More... | |
Memory< double > | A |
Array with size I[height], containing the actual entries of the sparse matrix, as indexed by the I array. More... | |
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int | height |
Dimension of the output / number of rows in the matrix. More... | |
int | width |
Dimension of the input / number of columns in the matrix. More... | |
Additional Inherited Members | |
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enum | DiagonalPolicy { DIAG_ZERO, DIAG_ONE, DIAG_KEEP } |
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enum | Type { ANY_TYPE, MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC } |
Enumeration defining IDs for some classes derived from Operator. More... | |
Data type sparse matrix.
Definition at line 40 of file sparsemat.hpp.
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protected |
Definition at line 73 of file sparsemat.hpp.
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Create an empty SparseMatrix.
Definition at line 85 of file sparsemat.hpp.
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Create a sparse matrix with flexible sparsity structure using a row-wise linked list (LIL) format.
New entries are added as needed by methods like AddSubMatrix(), SetSubMatrix(), etc. Calling Finalize() will convert the SparseMatrix to the more compact compressed sparse row (CSR) format.
Definition at line 31 of file sparsemat.cpp.
mfem::SparseMatrix::SparseMatrix | ( | int * | i, |
int * | j, | ||
double * | data, | ||
int | m, | ||
int | n | ||
) |
Create a sparse matrix in CSR format. Ownership of i, j, and data is transferred to the SparseMatrix.
Definition at line 55 of file sparsemat.cpp.
mfem::SparseMatrix::SparseMatrix | ( | int * | i, |
int * | j, | ||
double * | data, | ||
int | m, | ||
int | n, | ||
bool | ownij, | ||
bool | owna, | ||
bool | issorted | ||
) |
Create a sparse matrix in CSR format. Ownership of i, j, and data is optionally transferred to the SparseMatrix.
If the parameter data is NULL, then the internal A array is allocated by this constructor (initializing it with zeros and taking ownership, regardless of the parameter owna).
Definition at line 72 of file sparsemat.cpp.
mfem::SparseMatrix::SparseMatrix | ( | int | nrows, |
int | ncols, | ||
int | rowsize | ||
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mfem::SparseMatrix::SparseMatrix | ( | const SparseMatrix & | mat, |
bool | copy_graph = true |
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Copy constructor (deep copy).
If mat is finalized and copy_graph is false, the I and J arrays will use a shallow copy (copy the pointers only) without transferring ownership.
Definition at line 121 of file sparsemat.cpp.
mfem::SparseMatrix::SparseMatrix | ( | const Vector & | v | ) |
Create a SparseMatrix with diagonal v, i.e. A = Diag(v)
Definition at line 186 of file sparsemat.cpp.
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Destroys sparse matrix.
Definition at line 519 of file sparsemat.hpp.
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Add a value to an entry in the "current row". See SetColPtr().
Definition at line 404 of file sparsemat.hpp.
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Definition at line 413 of file sparsemat.hpp.
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Read the value of an entry in the "current row". See SetColPtr().
Definition at line 680 of file sparsemat.hpp.
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Set an entry in the "current row". See SetColPtr().
Definition at line 407 of file sparsemat.hpp.
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inline |
Definition at line 415 of file sparsemat.hpp.
int mfem::SparseMatrix::ActualWidth | ( | ) | const |
Returns the actual Width of the matrix.
This method can be called for matrices finalized or not.
Definition at line 2904 of file sparsemat.cpp.
void mfem::SparseMatrix::Add | ( | const int | i, |
const int | j, | ||
const double | a | ||
) |
Definition at line 2244 of file sparsemat.cpp.
void mfem::SparseMatrix::Add | ( | const double | a, |
const SparseMatrix & | B | ||
) |
Add the sparse matrix 'B' scaled by the scalar 'a' into '*this'. Only entries in the sparsity pattern of '*this' are added.
Definition at line 2616 of file sparsemat.cpp.
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y += A * x (default) or y += a * A * x
Implements mfem::AbstractSparseMatrix.
Definition at line 552 of file sparsemat.cpp.
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y += At * x (default) or y += a * At * x
Implements mfem::AbstractSparseMatrix.
Definition at line 623 of file sparsemat.cpp.
Definition at line 2467 of file sparsemat.cpp.
void mfem::SparseMatrix::AddSubMatrix | ( | const Array< int > & | rows, |
const Array< int > & | cols, | ||
const DenseMatrix & | subm, | ||
int | skip_zeros = 1 |
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) |
Definition at line 2187 of file sparsemat.cpp.
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inline |
Definition at line 373 of file sparsemat.hpp.
y = A * x, treating all entries as booleans (zero=false, nonzero=true).
The actual values stored in the data array, A, are not used - this means and that all entries in the sparsity pattern are considered to be true by this method.
Definition at line 726 of file sparsemat.cpp.
y = At * x, treating all entries as booleans (zero=false, nonzero=true).
The actual values stored in the data array, A, are not used - this means and that all entries in the sparsity pattern are considered to be true by this method.
Definition at line 756 of file sparsemat.cpp.
void mfem::SparseMatrix::BuildTranspose | ( | ) | const |
Build and store internally the transpose of this matrix which will be used in the methods AddMultTranspose() and MultTranspose().
If this method has been called, the internal transpose matrix will be used to perform the action of the transpose matrix in AddMultTranspose(), and MultTranspose().
Warning: any changes in this matrix will invalidate the internal transpose. To rebuild the transpose, call ResetTranspose() followed by a call to this method. If the internal transpose is already built, this method has no effect.
When any non-default backend is enabled, i.e. Device::IsEnabled() is true, the methods AddMultTranspose(), and MultTranspose(), require the internal transpose to be built. If that is not the case (i.e. the internal transpose is not built), these methods will raise an error with an appropriate message pointing to this method. When using the default backend, calling this method is optional.
This method can only be used when the sparse matrix is finalized.
Definition at line 668 of file sparsemat.cpp.
int mfem::SparseMatrix::CheckFinite | ( | ) | const |
Count the number of entries that are NOT finite, i.e. Inf or Nan.
Definition at line 1234 of file sparsemat.cpp.
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Clear the contents of the SparseMatrix.
Definition at line 135 of file sparsemat.hpp.
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Reset the "current row" set by calling SetColPtr(). This method must be called between any two calls to SetColPtr().
Definition at line 634 of file sparsemat.hpp.
int mfem::SparseMatrix::CountSmallElems | ( | double | tol | ) | const |
Count the number of entries with |a_ij| <= tol.
Definition at line 1206 of file sparsemat.cpp.
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protected |
Definition at line 2873 of file sparsemat.cpp.
Definition at line 2107 of file sparsemat.cpp.
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virtual |
Returns constant reference to a_{ij}.
Implements mfem::Matrix.
Definition at line 423 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateCol | ( | int | col, |
DiagonalPolicy | dpolicy = DIAG_ZERO |
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Eliminates the column col from the matrix.
Definition at line 1311 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateCols | ( | const Array< int > & | cols, |
const Vector * | x = NULL , |
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Vector * | b = NULL |
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Eliminate all columns i for which cols[i] != 0.
Elimination of a column means that all entries in the column are set to zero. In addition, if the pointers x and b are not NULL, the eliminated matrix entries are multiplied by the corresponding solution value in *x and subtracted from the r.h.s. vector, *b.
Definition at line 1351 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRow | ( | int | row, |
const double | sol, | ||
Vector & | rhs | ||
) |
Eliminates a column from the transpose matrix.
Definition at line 1263 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRow | ( | int | row, |
DiagonalPolicy | dpolicy = DIAG_ZERO |
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) |
Eliminates a row from the matrix.
Definition at line 1279 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRowCol | ( | int | rc, |
const double | sol, | ||
Vector & | rhs, | ||
DiagonalPolicy | dpolicy = DIAG_ONE |
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) |
Eliminate row rc and column rc and modify the rhs using sol.
Eliminates the column rc to the rhs, deletes the row rc and replaces the element (rc,rc) with 1.0; assumes that element (i,rc) is assembled if and only if the element (rc,i) is assembled. By default, elements (rc,rc) are set to 1.0, although this behavior can be adjusted by changing the dpolicy parameter.
Definition at line 1390 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRowCol | ( | int | rc, |
DiagonalPolicy | dpolicy = DIAG_ONE |
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) |
Eliminate row rc and column rc.
Definition at line 1610 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRowCol | ( | int | rc, |
SparseMatrix & | Ae, | ||
DiagonalPolicy | dpolicy = DIAG_ONE |
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) |
Similar to EliminateRowCol(int, DiagonalPolicy) + save the eliminated entries into Ae so that (*this) + Ae is equal to the original matrix.
Definition at line 1752 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRowColDiag | ( | int | rc, |
double | value | ||
) |
Perform elimination and set the diagonal entry to the given value.
Definition at line 1689 of file sparsemat.cpp.
void mfem::SparseMatrix::EliminateRowColMultipleRHS | ( | int | rc, |
const Vector & | sol, | ||
DenseMatrix & | rhs, | ||
DiagonalPolicy | dpolicy = DIAG_ONE |
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) |
Similar to EliminateRowCol(int, const double, Vector &, DiagonalPolicy), but multiple values for eliminated unknowns are accepted, and accordingly multiple right-hand-sides are used.
Definition at line 1486 of file sparsemat.cpp.
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If a row contains only zeros, set its diagonal to 1.
Implements mfem::AbstractSparseMatrix.
Definition at line 1857 of file sparsemat.cpp.
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inline |
Check if the SparseMatrix is empty.
Definition at line 138 of file sparsemat.hpp.
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Finalize the matrix initialization, switching the storage format from LIL to CSR.
This method should be called once, after the matrix has been initialized. Internally, this method converts the matrix from row-wise linked list (LIL) format into CSR (compressed sparse row) format.
Reimplemented from mfem::Matrix.
Definition at line 367 of file sparsemat.hpp.
void mfem::SparseMatrix::Finalize | ( | int | skip_zeros, |
bool | fix_empty_rows | ||
) |
A slightly more general version of the Finalize(int) method.
Definition at line 928 of file sparsemat.cpp.
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inline |
Definition at line 372 of file sparsemat.hpp.
Definition at line 1960 of file sparsemat.cpp.
Gauss-Seidel forward and backward iterations over a vector x.
Definition at line 1876 of file sparsemat.cpp.
void mfem::SparseMatrix::GetBlocks | ( | Array2D< SparseMatrix * > & | blocks | ) | const |
Split the matrix into M x N blocks of sparse matrices in CSR format. The 'blocks' array is M x N (i.e. M and N are determined by its dimensions) and its entries are overwritten by the new blocks.
Definition at line 1008 of file sparsemat.cpp.
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Return the element data, i.e. the array A.
Definition at line 151 of file sparsemat.hpp.
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Return the element data, i.e. the array A, const version.
Definition at line 153 of file sparsemat.hpp.
void mfem::SparseMatrix::GetDiag | ( | Vector & | d | ) | const |
Returns the Diagonal of A.
Definition at line 486 of file sparsemat.cpp.
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Return the array I.
Definition at line 141 of file sparsemat.hpp.
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Return the array I, const version.
Definition at line 143 of file sparsemat.hpp.
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Return the array J.
Definition at line 146 of file sparsemat.hpp.
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Return the array J, const version.
Definition at line 148 of file sparsemat.hpp.
double mfem::SparseMatrix::GetJacobiScaling | ( | ) | const |
Determine appropriate scaling for Jacobi iteration.
Definition at line 2043 of file sparsemat.cpp.
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inlinevirtual |
Return the MemoryClass preferred by the Operator.
This is the MemoryClass that will be used to access the input and output vectors in the Mult() and MultTranspose() methods.
For example, classes using the MFEM_FORALL macro for implementation can return the value returned by Device::GetMemoryClass().
The default implementation of this method in class Operator returns MemoryClass::HOST.
Reimplemented from mfem::Operator.
Definition at line 213 of file sparsemat.hpp.
Extract all column indices and values from a given row.
If the matrix is finalized (i.e. in CSR format), cols and srow will simply be references to the specific portion of the J and A arrays. As required by the AbstractSparseMatrix interface this method returns:
Implements mfem::AbstractSparseMatrix.
Definition at line 2380 of file sparsemat.cpp.
int * mfem::SparseMatrix::GetRowColumns | ( | const int | row | ) |
Return a pointer to the column indices in a row.
Definition at line 299 of file sparsemat.cpp.
const int * mfem::SparseMatrix::GetRowColumns | ( | const int | row | ) | const |
Return a pointer to the column indices in a row, const version.
Definition at line 306 of file sparsemat.cpp.
double * mfem::SparseMatrix::GetRowEntries | ( | const int | row | ) |
Return a pointer to the entries in a row.
Definition at line 313 of file sparsemat.cpp.
const double * mfem::SparseMatrix::GetRowEntries | ( | const int | row | ) | const |
Return a pointer to the entries in a row, const version.
Definition at line 320 of file sparsemat.cpp.
double mfem::SparseMatrix::GetRowNorml1 | ( | int | irow | ) | const |
For i = irow compute \( x_i = \sum_j | A_{i, j} | \).
Definition at line 843 of file sparsemat.cpp.
void mfem::SparseMatrix::GetRowSums | ( | Vector & | x | ) | const |
For all i compute \( x_i = \sum_j A_{ij} \).
Definition at line 820 of file sparsemat.cpp.
void mfem::SparseMatrix::GetSubMatrix | ( | const Array< int > & | rows, |
const Array< int > & | cols, | ||
DenseMatrix & | subm | ||
) | const |
Definition at line 2331 of file sparsemat.cpp.
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inline |
Definition at line 521 of file sparsemat.hpp.
Compute y^t A x.
Definition at line 779 of file sparsemat.cpp.
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virtual |
This virtual method is not supported: it always returns NULL.
Implements mfem::Matrix.
Definition at line 1258 of file sparsemat.cpp.
double mfem::SparseMatrix::IsSymmetric | ( | ) | const |
Returns max_{i,j} |(i,j)-(j,i)| for a finalized matrix.
Definition at line 1098 of file sparsemat.cpp.
void mfem::SparseMatrix::Jacobi | ( | const Vector & | b, |
const Vector & | x0, | ||
Vector & | x1, | ||
double | sc | ||
) | const |
One scaled Jacobi iteration for the system A x = b. x1 = x0 + sc D^{-1} (b - A x0) where D is the diag of A.
Definition at line 2076 of file sparsemat.cpp.
void mfem::SparseMatrix::Jacobi2 | ( | const Vector & | b, |
const Vector & | x0, | ||
Vector & | x1, | ||
double | sc = 1.0 |
||
) | const |
x1 = x0 + sc D^{-1} (b - A x0) where \( D_{ii} = \sum_j |A_{ij}| \).
Definition at line 2139 of file sparsemat.cpp.
void mfem::SparseMatrix::Jacobi3 | ( | const Vector & | b, |
const Vector & | x0, | ||
Vector & | x1, | ||
double | sc = 1.0 |
||
) | const |
x1 = x0 + sc D^{-1} (b - A x0) where \( D_{ii} = \sum_j A_{ij} \).
Definition at line 2163 of file sparsemat.cpp.
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Lose the ownership of the graph (I, J) and data (A) arrays.
Definition at line 514 of file sparsemat.hpp.
void mfem::SparseMatrix::MakeRef | ( | const SparseMatrix & | master | ) |
Clear the contents of the SparseMatrix and make it a reference to master.
After this call, the matrix will point to the same data as master but it will not own its data. The master must be finalized.
Definition at line 223 of file sparsemat.cpp.
double mfem::SparseMatrix::MaxNorm | ( | ) | const |
Definition at line 1181 of file sparsemat.cpp.
int mfem::SparseMatrix::MaxRowSize | ( | ) | const |
Returns the maximum number of elements among all rows.
Definition at line 275 of file sparsemat.cpp.
void mfem::SparseMatrix::MoveDiagonalFirst | ( | ) |
Move the diagonal entry to the first position in each row, preserving the order of the rest of the columns.
Definition at line 394 of file sparsemat.cpp.
Matrix vector multiplication.
Implements mfem::AbstractSparseMatrix.
Definition at line 545 of file sparsemat.cpp.
Multiply a vector with the transposed matrix. y = At * x.
Implements mfem::AbstractSparseMatrix.
Definition at line 616 of file sparsemat.cpp.
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virtual |
Returns the number of the nonzero elements in the matrix.
Implements mfem::AbstractSparseMatrix.
Definition at line 1159 of file sparsemat.cpp.
double & mfem::SparseMatrix::operator() | ( | int | i, |
int | j | ||
) |
Returns reference to A[i][j].
Definition at line 428 of file sparsemat.cpp.
const double & mfem::SparseMatrix::operator() | ( | int | i, |
int | j | ||
) | const |
Returns reference to A[i][j].
Definition at line 451 of file sparsemat.cpp.
SparseMatrix & mfem::SparseMatrix::operator*= | ( | double | a | ) |
Definition at line 2663 of file sparsemat.cpp.
SparseMatrix & mfem::SparseMatrix::operator+= | ( | const SparseMatrix & | B | ) |
Add the sparse matrix 'B' to '*this'. This operation will cause an error if '*this' is finalized and 'B' has larger sparsity pattern.
Definition at line 2586 of file sparsemat.cpp.
SparseMatrix & mfem::SparseMatrix::operator= | ( | const SparseMatrix & | rhs | ) |
Assignment operator: deep copy.
Definition at line 213 of file sparsemat.cpp.
SparseMatrix & mfem::SparseMatrix::operator= | ( | double | a | ) |
Definition at line 2639 of file sparsemat.cpp.
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Get the data ownership flag (A array).
Definition at line 511 of file sparsemat.hpp.
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Get the graph ownership flag (I and J arrays).
Definition at line 508 of file sparsemat.hpp.
void mfem::SparseMatrix::PartAddMult | ( | const Array< int > & | rows, |
const Vector & | x, | ||
Vector & | y, | ||
const double | a = 1.0 |
||
) | const |
Definition at line 708 of file sparsemat.cpp.
Definition at line 682 of file sparsemat.cpp.
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virtual |
Prints matrix to stream out.
Reimplemented from mfem::Matrix.
Definition at line 2687 of file sparsemat.cpp.
void mfem::SparseMatrix::PrintCSR | ( | std::ostream & | out | ) | const |
Prints matrix to stream out in hypre_CSRMatrix format.
Definition at line 2773 of file sparsemat.cpp.
void mfem::SparseMatrix::PrintCSR2 | ( | std::ostream & | out | ) | const |
Prints a sparse matrix to stream out in CSR format.
Definition at line 2797 of file sparsemat.cpp.
void mfem::SparseMatrix::PrintInfo | ( | std::ostream & | out | ) | const |
Print various sparse matrix staticstics.
Definition at line 2822 of file sparsemat.cpp.
void mfem::SparseMatrix::PrintMatlab | ( | std::ostream & | out = mfem::out | ) | const |
Prints matrix in matlab format.
Definition at line 2731 of file sparsemat.cpp.
void mfem::SparseMatrix::PrintMM | ( | std::ostream & | out = mfem::out | ) | const |
Prints matrix in Matrix Market sparse format.
Definition at line 2751 of file sparsemat.cpp.
void mfem::SparseMatrix::ResetTranspose | ( | ) | const |
Reset (destroy) the internal transpose matrix. See BuildTranspose() for more details.
Definition at line 676 of file sparsemat.cpp.
bool mfem::SparseMatrix::RowIsEmpty | ( | const int | row | ) | const |
Definition at line 2359 of file sparsemat.cpp.
int mfem::SparseMatrix::RowSize | ( | const int | i | ) | const |
Returns the number of elements in row i.
Definition at line 252 of file sparsemat.cpp.
void mfem::SparseMatrix::ScaleColumns | ( | const Vector & | sr | ) |
this = this * diag(sr);
Definition at line 2558 of file sparsemat.cpp.
void mfem::SparseMatrix::ScaleRow | ( | const int | row, |
const double | scale | ||
) |
Definition at line 2499 of file sparsemat.cpp.
void mfem::SparseMatrix::ScaleRows | ( | const Vector & | sl | ) |
this = diag(sl) * this;
Definition at line 2527 of file sparsemat.cpp.
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inline |
Perform a fast search for an entry in the "current row". See SetColPtr().
If the matrix is not finalized and the entry is not found in the SparseMatrix, it will be added to the sparsity pattern initialized with zero. If the matrix is finalized and the entry is not found, an error will be generated.
Definition at line 653 of file sparsemat.hpp.
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inline |
Definition at line 694 of file sparsemat.hpp.
void mfem::SparseMatrix::Set | ( | const int | i, |
const int | j, | ||
const double | a | ||
) |
Definition at line 2225 of file sparsemat.cpp.
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inline |
Initialize the SparseMatrix for fast access to the entries of the given row which becomes the "current row".
Fast access to the entries of the "current row" can be performed using the methods: SearchRow(const int), Add(const int, const double), Set(const int, const double), and Get(const int).
Definition at line 599 of file sparsemat.hpp.
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inline |
Set the data ownership flag (A array).
Definition at line 505 of file sparsemat.hpp.
void mfem::SparseMatrix::SetDiagIdentity | ( | ) |
If a row contains only one diag entry of zero, set it to 1.
Definition at line 1846 of file sparsemat.cpp.
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protected |
Definition at line 235 of file sparsemat.cpp.
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inline |
Set the graph ownership flag (I and J arrays).
Definition at line 501 of file sparsemat.hpp.
Definition at line 2420 of file sparsemat.cpp.
void mfem::SparseMatrix::SetSubMatrix | ( | const Array< int > & | rows, |
const Array< int > & | cols, | ||
const DenseMatrix & | subm, | ||
int | skip_zeros = 1 |
||
) |
Definition at line 2263 of file sparsemat.cpp.
void mfem::SparseMatrix::SetSubMatrixTranspose | ( | const Array< int > & | rows, |
const Array< int > & | cols, | ||
const DenseMatrix & | subm, | ||
int | skip_zeros = 1 |
||
) |
Definition at line 2296 of file sparsemat.cpp.
void mfem::SparseMatrix::SetWidth | ( | int | width_ = -1 | ) |
Change the width of a SparseMatrix.
If width_ = -1 (DEFAULT), this routine will set the new width to the actual Width of the matrix awidth = max(J) + 1. Values 0 <= width_ < awidth are not allowed (error check in Debug Mode only)
This method can be called for matrices finalized or not.
Definition at line 327 of file sparsemat.cpp.
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inline |
For backward compatibility, define Size() to be synonym of Height().
Definition at line 132 of file sparsemat.hpp.
void mfem::SparseMatrix::SortColumnIndices | ( | ) |
Sort the column indices corresponding to each row.
Definition at line 365 of file sparsemat.cpp.
void mfem::SparseMatrix::Swap | ( | SparseMatrix & | other | ) |
Definition at line 3617 of file sparsemat.cpp.
void mfem::SparseMatrix::Symmetrize | ( | ) |
(*this) = 1/2 ((*this) + (*this)^t)
Definition at line 1140 of file sparsemat.cpp.
void mfem::SparseMatrix::Threshold | ( | double | tol, |
bool | fix_empty_rows = false |
||
) |
Remove entries smaller in absolute value than a given tolerance tol. If fix_empty_rows is true, a zero value is inserted in the diagonal entry (for square matrices only)
Definition at line 867 of file sparsemat.cpp.
DenseMatrix * mfem::SparseMatrix::ToDenseMatrix | ( | ) | const |
Produces a DenseMatrix from a SparseMatrix.
Definition at line 515 of file sparsemat.cpp.
void mfem::SparseMatrix::ToDenseMatrix | ( | DenseMatrix & | B | ) | const |
Produces a DenseMatrix from a SparseMatrix.
Definition at line 528 of file sparsemat.cpp.
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protected |
Array with size I[height], containing the actual entries of the sparse matrix, as indexed by the I array.
Definition at line 58 of file sparsemat.hpp.
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mutableprotected |
Transpose of A. Owned. Used to perform MultTranspose() on devices.
Definition at line 70 of file sparsemat.hpp.
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mutableprotected |
Definition at line 66 of file sparsemat.hpp.
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mutableprotected |
Definition at line 67 of file sparsemat.hpp.
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mutableprotected |
Definition at line 65 of file sparsemat.hpp.
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protected |
Array with size (height+1) containing the row offsets.
The data for row r, 0 <= r < height, is at offsets j, I[r] <= j < I[r+1]. The offsets, j, are indices in the J and A arrays. The first entry in this array is always zero, I[0] = 0, and the last entry, I[height], gives the total number of entries stored (at a minimum, all nonzeros must be represented) in the sparse matrix.
Definition at line 52 of file sparsemat.hpp.
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Are the columns sorted already.
Definition at line 78 of file sparsemat.hpp.
|
protected |
Array with size I[height], containing the column indices for all matrix entries, as indexed by the I array.
Definition at line 55 of file sparsemat.hpp.
|
protected |
Definition at line 74 of file sparsemat.hpp.
|
protected |
Array of linked lists, one for every row. This array represents the linked list (LIL) storage format.
Definition at line 63 of file sparsemat.hpp.