Class DenseMatrix¶

Class Documentation¶

class DenseMatrix¶

Represents a dense matrix. Use this matrix to run LU decompositions and LU solves. Note that most matrices are rather sparse s.t. CSRMatrix might be a better representation.

Public Functions

DenseMatrix()¶

Default constructor

DenseMatrix(count dimension, double zero = 0.0)¶

Constructs the DenseMatrix with size dimension x dimension.

Parameters:

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

• zero – The zero element (default is 0.0).

DenseMatrix(count nRows, count nCols, double zero = 0.0)¶

Constructs the DenseMatrix with size nRows x nCols.

Parameters:

• nRows – Number of rows.

• nCols – Number of columns.

• zero – The zero element (default is 0.0).

DenseMatrix(count dimension, const std::vector<Triplet> &triplets, double zero = 0.0)¶

Constructs the dimension x dimension DenseMatrix 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 0.0).

DenseMatrix(count nRows, count nCols, const std::vector<Triplet> &triplets, double zero = 0.0)¶

Constructs the nRows x nCols DenseMatrix 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 0.0).

DenseMatrix(count nRows, count nCols, const std::vector<double> &entries, double zero = 0.0)¶

Constructs an instance of DenseMatrix given the number of rows (nRows) and the number of columns (nCols) and its values (entries).

Note

The size of the entries vector should be equal to nRows * nCols.

Parameters:

• nRows – Number of rows.

• nCols – Number of columns.

• entries – Entries of the matrix.

• zero – The zero element (default is 0.0).

~DenseMatrix() = default¶

Default destructor

DenseMatrix(const DenseMatrix &other) = default¶

Default copy constructor

DenseMatrix(DenseMatrix &&other) = default¶

Default move constructor

DenseMatrix &operator=(DenseMatrix &&other) = default¶

Default copy assignment operator

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

Default move assignment operator

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

Compares this matrix to other and returns true if the shapes and entries are the same, otherwise returns false.

Parameters:

other –

inline bool isApprox(const DenseMatrix &other, const double eps = 0.01) const¶

Compares this matrix to other and returns true if the shape and zero element are the same as well as all entries are the same (within the absolute error range of eps), otherwise returns false.

Parameters:

• other –

• eps –

inline count numberOfRows() const¶

Returns:

Number of rows.

inline count numberOfColumns() const¶

Returns:

Number of columns.

inline double getZero() const¶

Returns the zero element of the matrix.

count nnzInRow(index i) const¶

Note

This function is linear in the number of columns of the matrix.

Parameters:

i – The row index.

Returns:

Number of non-zeros in row i.

count nnz() const¶

Note

This function takes nRows * nCols operations.

Returns:

Number of non-zeros in this matrix.

double operator()(index i, index j) const¶

Returns:

Value at matrix position (i,j).

double &operator()(index i, index j)¶

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

void setValue(index i, index j, double value)¶

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

Vector row(index i) const¶

Returns:

Row i of this matrix as vector.

Vector column(index j) const¶

Returns:

Column j of this matrix as vector.

Vector diagonal() const¶

Returns:

The main diagonal of this matrix.

DenseMatrix operator+(const DenseMatrix &other) const¶

Adds this matrix to other and returns the result.

Returns:

The sum of this matrix and other.

DenseMatrix &operator+=(const DenseMatrix &other)¶

Adds other to this matrix.

Returns:

Reference to this matrix.

DenseMatrix operator-(const DenseMatrix &other) const¶

Subtracts other from this matrix and returns the result.

Returns:

The difference of this matrix and other.

DenseMatrix &operator-=(const DenseMatrix &other)¶

Subtracts other from this matrix.

Returns:

Reference to this matrix.

DenseMatrix operator*(double scalar) const¶

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

Returns:

The result of multiplying this matrix with scalar.

DenseMatrix &operator*=(double scalar)¶

Multiplies this matrix with a scalar specified in scalar.

Returns:

Reference to this matrix.

Vector operator*(const Vector &vector) const¶

Multiplies this matrix with vector and returns the result.

Returns:

The result of multiplying this matrix with vector.

DenseMatrix operator*(const DenseMatrix &other) const¶

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

Returns:

The result of multiplying this matrix with other.

DenseMatrix operator/(double 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.

DenseMatrix &operator/=(double divisor)¶

Divides this matrix by a divisor specified in divisor.

Returns:

Reference to this matrix.

DenseMatrix transpose() const¶

Transposes this matrix and returns it.

DenseMatrix 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 –

void assign(const std::vector<index> &rowIndices, const std::vector<index> &columnIndices, const DenseMatrix &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 forElementsInRow(index row, L handle) const¶

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

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

Iterate in parallel over all elements 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 forNonZeroElementsInRow(index row, L handle) const¶

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

Note

This is a DenseMatrix! Therefore this operation needs O(numberOfRows()) time regardless of the number of non-zeros actually present.

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, double value)

Note

This is a DenseMatrix! Therefore this operation needs O(numberOfRows()) sequential time regardless of the number of non-zeros actually present.

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).

Note

This is a DenseMatrix! Therefore this operation needs O(numberOfRows() * numberOfColumns()) time regardless of the number of non-zeros actually present.

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.

Note

This is a DenseMatrix! Therefore this operation needs O(numberOfRows() * numberOfColumns()) sequential time regardless of the number of non-zeros actually present.

Public Static Functions

static DenseMatrix adjacencyMatrix(const Graph &graph, double zero = 0.0)¶

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

Parameters:

graph –

static DenseMatrix diagonalMatrix(const Vector &diagonalElements, double zero = 0.0)¶

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 DenseMatrix incidenceMatrix(const Graph &graph, double zero = 0.0)¶

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

Parameters:

graph –

static DenseMatrix laplacianMatrix(const Graph &graph, double zero = 0.0)¶

Returns the (weighted) Laplacian matrix of the (weighteD) Graph graph.

Parameters:

graph –

static void LUDecomposition(DenseMatrix &matrix)¶

Decomposes the given matrix into lower L and upper U matrix (in-place).

Parameters:

matrix – The matrix to decompose into LU.

static Vector LUSolve(const DenseMatrix &LU, const Vector &b)¶

Computes the solution vector x to the system LU * x = b where LU is a matrix decomposed into L and U.

Parameters:

• LU – Matrix decomposed into lower L and upper U matrix.

• b – Right-hand side.

Returns:

Solution vector x to the linear equation system LU * x = b.

template<typename L>
static inline DenseMatrix binaryOperator(const DenseMatrix &A, const DenseMatrix &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.

Parameters:

• A –

• B –

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

Returns:

A binaryOp B.