Template Class CSRGeneralMatrix¶

Class Documentation¶

template<class ValueType>
class CSRGeneralMatrix¶

The CSRGeneralMatrix class represents a sparse matrix stored in CSR-Format (i.e. compressed sparse row). If speed is important, use this CSRGeneralMatrix instead of the Matrix class.

Public Functions

inline CSRGeneralMatrix()¶

Default constructor

inline CSRGeneralMatrix(count dimension, ValueType zero = 0)¶

Constructs the CSRGeneralMatrix with size dimension x dimension.

Parameters:

• dimension – Defines how many rows and columns this matrix has.

• zero – The zero element (default = 0).

inline CSRGeneralMatrix(count nRows, count nCols, ValueType zero = 0)¶

Constructs the CSRGeneralMatrix with size nRows x nCols.

Parameters:

• nRows – Number of rows.

• nCols – Number of columns.

• zero – The zero element (default = 0).

inline CSRGeneralMatrix(count dimension, const std::vector<Triplet> &triplets, ValueType zero = 0, bool isSorted = false)¶

Constructs the dimension x dimension Matrix from the elements at position positions with values @values.

Parameters:

• dimension – Defines how many rows and columns this matrix has.

• triplets – The nonzero elements.

• zero – The zero element (default is 0).

• isSorted – True, if the triplets are sorted per row. Default is false.

inline CSRGeneralMatrix(count nRows, count nCols, const std::vector<Triplet> &triplets, ValueType zero = 0, bool isSorted = false)¶

Constructs the nRows x nCols Matrix from the elements at position positions with values @values.

Parameters:

• nRows – Defines how many rows this matrix has.

• nCols – Defines how many columns this matrix has.

• triplets – The nonzero elements.

• zero – The zero element (default is 0).

• isSorted – True, if the triplets are sorted per row. Default is false.

inline CSRGeneralMatrix(count nRows, count nCols, const std::vector<std::vector<index>> &columnIdx, const std::vector<std::vector<ValueType>> &values, ValueType zero = 0, bool isSorted = false)¶

Constructs the nRows x nCols Matrix from the elements stored in columnIdx and values. columnIdx and values store the colums and values by row.

Parameters:

• nRows –

• nCols –

• columnIdx –

• values –

• zero – The zero element (default is 0).

• isSorted – True if the column indices in columnIdx are sorted in every row.

inline CSRGeneralMatrix(count nRows, count nCols, const std::vector<index> &rowIdx, const std::vector<index> &columnIdx, const std::vector<ValueType> &nonZeros, ValueType zero = 0, bool isSorted = false)¶

Constructs the nRows x nCols Matrix from the elements at position positions with values @values.

Parameters:

• nRows – Defines how many rows this matrix has.

• nCols – Defines how many columns this matrix has.

• rowIdx – The rowIdx vector of the CSR format.

• columnIdx – The columnIdx vector of the CSR format.

• nonZeros – The nonZero vector of the CSR format. Should be as long as the columnIdx vector.

• zero – The zero element (default is 0).

• isSorted – True, if the triplets are sorted per row. Default is false.

CSRGeneralMatrix(const CSRGeneralMatrix &other) = default¶

Default copy constructor

CSRGeneralMatrix(CSRGeneralMatrix &&other) noexcept = default¶

Default move constructor

~CSRGeneralMatrix() = default¶

Default destructor

CSRGeneralMatrix &operator=(CSRGeneralMatrix &&other) noexcept = default¶

Default move assignment operator

CSRGeneralMatrix &operator=(const CSRGeneralMatrix &other) = default¶

Default copy assignment operator

inline bool operator==(const CSRGeneralMatrix &other) const¶

Compares this matrix to other and returns true if the shape and zero element are the same as well as all entries, otherwise returns false.

Parameters:

other –

inline bool operator!=(const CSRGeneralMatrix &other) const¶

Compares this matrix to other and returns false if the shape and zero element are the same as well as all entries, otherwise returns true.

Parameters:

other –

inline count numberOfRows() const noexcept¶

Returns:

Number of rows.

inline count numberOfColumns() const noexcept¶

Returns:

Number of columns.

inline ValueType getZero() const noexcept¶

Returns the zero element of the matrix.

inline count nnzInRow(const index i) const¶

Parameters:

i – The row index.

Returns:

Number of non-zeros in row i.

inline count nnz() const noexcept¶

Returns:

Number of non-zeros in this matrix.

inline ValueType operator()(index i, index j) const¶

Returns:

Value at matrix position (i,j).

inline void setValue(index i, index j, ValueType value)¶

Set the matrix at position (i, j) to value.

Note

This operation can be linear in the number of non-zeros due to vector element movements

inline void sort()¶

Sorts the column indices in each row for faster access.

inline bool sorted() const noexcept¶

Returns:

True if the matrix is sorted, otherwise false.

inline Vector row(index i) const¶

Returns:

Row i of this matrix as vector.

inline Vector column(index j) const¶

Returns:

Column j of this matrix as vector.

inline Vector diagonal() const¶

Returns:

The main diagonal of this matrix.

inline CSRGeneralMatrix operator+(const CSRGeneralMatrix &other) const¶

Adds this matrix to other and returns the result.

Returns:

The sum of this matrix and other.

inline CSRGeneralMatrix &operator+=(const CSRGeneralMatrix &other)¶

Adds other to this matrix.

Returns:

Reference to this matrix.

inline CSRGeneralMatrix operator-(const CSRGeneralMatrix &other) const¶

Subtracts other from this matrix and returns the result.

Returns:

The difference of this matrix and other.

inline CSRGeneralMatrix &operator-=(const CSRGeneralMatrix &other)¶

Subtracts other from this matrix.

Returns:

Reference to this matrix.

inline CSRGeneralMatrix operator*(const ValueType &scalar) const¶

Multiplies this matrix with a scalar specified in scalar and returns the result.

Returns:

The result of multiplying this matrix with scalar.

inline CSRGeneralMatrix &operator*=(const ValueType &scalar)¶

Multiplies this matrix with a scalar specified in scalar.

Returns:

Reference to this matrix.

inline Vector operator*(const Vector &vector) const¶

Multiplies this matrix with vector and returns the result.

Returns:

The result of multiplying this matrix with vector.

inline CSRGeneralMatrix operator*(const CSRGeneralMatrix &other) const¶

Multiplies this matrix with other and returns the result in a new matrix.

Returns:

The result of multiplying this matrix with other.

inline CSRGeneralMatrix operator/(const ValueType &divisor) const¶

Divides this matrix by a divisor specified in divisor and returns the result in a new matrix.

Returns:

The result of dividing this matrix by divisor.

inline CSRGeneralMatrix &operator/=(const ValueType &divisor)¶

Divides this matrix by a divisor specified in divisor.

Returns:

Reference to this matrix.

inline CSRGeneralMatrix transpose() const¶

Transposes this matrix and returns it.

inline CSRGeneralMatrix extract(const std::vector<index> &rowIndices, const std::vector<index> &columnIndices) const¶

Extracts a matrix with rows and columns specified by rowIndices and columnIndices from this matrix. The order of rows and columns is equal to the order in rowIndices and columnIndices. It is also possible to specify a row or column more than once to get duplicates.

Parameters:

• rowIndices –

• columnIndices –

inline void assign(const std::vector<index> &rowIndices, const std::vector<index> &columnIndices, const CSRGeneralMatrix &source)¶

Assign the contents of the matrix source to this matrix at rows and columns specified by rowIndices and columnIndices. That is, entry (i,j) of source is assigned to entry (rowIndices[i], columnIndices[j]) of this matrix. Note that the dimensions of @rowIndices and columnIndices must coincide with the number of rows and columns of source.

Parameters:

• rowIndices –

• columnIndices –

• source –

template<typename F>
void apply(F unaryElementFunction)¶

Applies the unary function unaryElementFunction to each value in the matrix. Note that it must hold that the function applied to the zero element of this matrix returns the zero element.

Parameters:

unaryElementFunction –

template<typename L>
inline void forNonZeroElementsInRow(index row, L handle) const¶

Iterate over all non-zero elements of row row in the matrix and call handler(index column, ValueType value)

template<typename L>
inline void parallelForNonZeroElementsInRow(index row, L handle) const¶

Iterate in parallel over all non-zero elements of row row in the matrix and call handler(index column, ValueType value)

template<typename L>
inline void forElementsInRow(index i, L handle) const¶

Iterate over all elements in row i in the matrix and call handle(index column, ValueType value)

template<typename L>
inline void parallelForElementsInRow(index row, L handle) const¶

Iterate in parallel over all elements (including zeros) of row row in the matrix and call handler(index column, double value)

template<typename L>
inline void forElementsInRowOrder(L handle) const¶

Iterate over all elements of the matrix in row order and call handler (lambda closure).

template<typename L>
inline void parallelForElementsInRowOrder(L handle) const¶

Iterate in parallel over all rows and call handler (lambda closure) on elements of the matrix.

template<typename L>
inline void forNonZeroElementsInRowOrder(L handle) const¶

Iterate over all non-zero elements of the matrix in row order and call handler (lambda closure).

template<typename L>
inline void parallelForNonZeroElementsInRowOrder(L handle) const¶

Iterate in parallel over all rows and call handler (lambda closure) on non-zero elements of the matrix.

template<typename L>
inline CSRGeneralMatrix<ValueType> binaryOperator(const CSRGeneralMatrix<ValueType> &A, const CSRGeneralMatrix<ValueType> &B, L binaryOp)¶

Public Static Functions

template<typename L>
static CSRGeneralMatrix binaryOperator(const CSRGeneralMatrix &A, const CSRGeneralMatrix &B, L binaryOp)¶

Computes A binaryOp B on the elements of matrix A and matrix B.

Note

A and B must have the same dimensions and must be sorted.

Parameters:

• A – Sorted CSRGeneralMatrix.

• B – Sorted CSRGeneralMatrix.

• binaryOp – Function handling (ValueType, ValueType) -> ValueType

Returns:

A binaryOp B.

static inline CSRGeneralMatrix mTmMultiply(const CSRGeneralMatrix &A, const CSRGeneralMatrix &B)¶

Computes A^T * B.

Note

The number of rows of A must be equal to the number of rows of B.

Parameters:

• A –

• B –

Returns:

A^T * B.

static inline CSRGeneralMatrix mmTMultiply(const CSRGeneralMatrix &A, const CSRGeneralMatrix &B)¶

Computes A * B^T.

Note

The number of columns of A must be equal to the number of columns of B.

Parameters:

• A –

• B –

Returns:

A * B^T.

static inline Vector mTvMultiply(const CSRGeneralMatrix &matrix, const Vector &vector)¶

Computes matrix^T * vector.

Note

The number of rows of matrix must be equal to the dimension of vector.

Parameters:

• matrix –

• vector –

Returns:

matrix^T * vector.

static inline CSRGeneralMatrix adjacencyMatrix(const Graph &graph, ValueType zero = 0)¶

Compute the (weighted) adjacency matrix of the (weighted) Graph graph.

Parameters:

graph –

static inline CSRGeneralMatrix diagonalMatrix(const Vector &diagonalElements, ValueType zero = 0)¶

Creates a diagonal matrix with dimension equal to the dimension of the Vector diagonalElements. The values on the diagonal are the ones stored in diagonalElements (i.e. D(i,i) = diagonalElements[i]).

Parameters:

diagonalElements –

static inline CSRGeneralMatrix incidenceMatrix(const Graph &graph, ValueType zero = 0)¶

Returns the (weighted) incidence matrix of the (weighted) Graph graph.

Parameters:

graph –

static inline CSRGeneralMatrix laplacianMatrix(const Graph &graph, ValueType zero = 0)¶

Compute the (weighted) Laplacian of the (weighted) Graph graph.

Parameters:

graph –

static inline CSRGeneralMatrix normalizedLaplacianMatrix(const Graph &graph, ValueType zero = 0)¶

Returns the (weighted) normalized Laplacian matrix of the (weighted) Graph graph

Parameters:

graph –