Class SparseMatrix

Class defining a sparse matrix.

Inheritance

SparseMatrix

Implements

IGroupAction<Matrix, Double>

IGroupAction<SparseMatrix, Double>

Inherited Members

Matrix.RowCount

Matrix.ColumnCount

Matrix.Transpose(Matrix)

Matrix.Add(Matrix, Matrix)

Matrix.Subtract(Matrix, Matrix)

Matrix.Opposite(Matrix)

Matrix.Multiply(Matrix, Matrix)

Matrix.TransposeMultiplySelf(Matrix)

Matrix.Multiply(Double, Matrix)

Matrix.Multiply(Matrix, Double)

Matrix.Divide(Matrix, Double)

Matrix.Multiply(Matrix, Vector)

Matrix.Multiply(Matrix, DenseVector)

Matrix.Multiply(Matrix, SparseVector)

Matrix.TransposeMultiply(Matrix, Vector)

Matrix.TransposeMultiply(Matrix, DenseVector)

Matrix.TransposeMultiply(Matrix, SparseVector)

Matrix.At(Int32, Int32)

Matrix.IGroupAction<Matrix, Double>.Multiply(Double)

Matrix.IGroupAction<Matrix, Double>.Divide(Double)

Namespace: BRIDGES.LinearAlgebra.Matrices

Assembly: BRIDGES.dll

Syntax

public abstract class SparseMatrix : Matrix, IGroupAction<Matrix, double>, IGroupAction<SparseMatrix, double>

Constructors

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SparseMatrix(Int32, Int32)

Initialises a new instance of the SparseMatrix class.

Declaration

protected SparseMatrix(int rowCount, int columnCount)

Parameters

Type	Name	Description
Int32	rowCount	Number of rows of the SparseMatrix.
Int32	columnCount	Number of columns of the SparseMatrix.

Properties

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Item[Int32]

Gets or sets the non-zero value of this sparse matrix at a given index.

Declaration

public abstract double this[int index] { get; set; }

Parameters

Type	Name	Description
Int32	index	Index of the non-zero value to get.

Property Value

Type	Description
Double	The non-zero value of this sparse matrix at the given index.

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NonZerosCount

Gets the number of non-zero values in this sparse matrix.

Declaration

public abstract int NonZerosCount { get; }

Property Value

Type	Description
Int32

Methods

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Add(SparseMatrix, SparseMatrix)

Computes the addition of two SparseMatrix.

Declaration

public static SparseMatrix Add(SparseMatrix left, SparseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the addition.
SparseMatrix	right	Right SparseMatrix for the addition.

Returns

Type	Description
SparseMatrix	The SparseMatrix resulting from the addition.

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Divide(SparseMatrix, Double)

Computes the scalar division of a SparseMatrix with a number.

Declaration

public static SparseMatrix Divide(SparseMatrix operand, double divisor)

Parameters

Type	Name	Description
SparseMatrix	operand	SparseMatrix to divide.
Double	divisor	number to divide with.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the scalar division.

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Multiply(SparseMatrix, SparseMatrix)

Computes the multiplication of two SparseMatrix.

Declaration

public static SparseMatrix Multiply(SparseMatrix left, SparseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the multiplication.
SparseMatrix	right	Right SparseMatrix for the multiplication.

Returns

Type	Description
SparseMatrix	The SparseMatrix resulting from the multiplication.

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Multiply(SparseMatrix, DenseVector)

Computes the right multiplication of a SparseMatrix with a DenseVector : A·V.

Declaration

public static DenseVector Multiply(SparseMatrix matrix, DenseVector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
DenseVector	vector	DenseVector to multiply with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the multiplication.

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Multiply(SparseMatrix, SparseVector)

Computes the right multiplication of a SparseMatrix with a SparseVector : A·V.

Declaration

public static SparseVector Multiply(SparseMatrix matrix, SparseVector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
SparseVector	vector	SparseVector to multiply with.

Returns

Type	Description
SparseVector	The new SparseVector resulting from the multiplication.

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Multiply(SparseMatrix, Vector)

Computes the right multiplication of a SparseMatrix with a Vector : A·V.

Declaration

public static Vector Multiply(SparseMatrix matrix, Vector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
Vector	vector	Vector to multiply with.

Returns

Type	Description
Vector	The new Vector resulting from the multiplication.

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Multiply(SparseMatrix, Double)

Computes the right scalar multiplication of a SparseMatrix with a number.

Declaration

public static SparseMatrix Multiply(SparseMatrix operand, double factor)

Parameters

Type	Name	Description
SparseMatrix	operand	SparseMatrix to multiply on the right.
Double	factor	number to multiply with.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the right scalar multiplication.

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Multiply(Double, SparseMatrix)

Computes the left scalar multiplication of a SparseMatrix with a number.

Declaration

public static SparseMatrix Multiply(double factor, SparseMatrix operand)

Parameters

Type	Name	Description
Double	factor	number to multiply with.
SparseMatrix	operand	SparseMatrix to multiply on the left.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the left scalar multiplication.

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NonZeros()

Provides an enumerable collection to iterate on the non-zero entries of the SparseMatrix non-zero entries.

Declaration

public abstract IEnumerable<(int rowIndex, int columnIndex, double value)> NonZeros()

Returns

Type	Description
IEnumerable<(, , )<Int32, Int32, Double>>	The enumerable collection containing row index, the column index and the value of the SparseMatrix non-zero entries.

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Subtract(SparseMatrix, SparseMatrix)

Computes the subtraction of two SparseMatrix.

Declaration

public static SparseMatrix Subtract(SparseMatrix left, SparseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix to subtract.
SparseMatrix	right	Right SparseMatrix to subtract with.

Returns

Type	Description
SparseMatrix	The SparseMatrix resulting from the subtraction.

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ToArray()

Translates this matrix into its bi-dimensional array representation.

Declaration

public override double[, ] ToArray()

Returns

Type	Description
Double[,]	The bi-dimensional array representing the matrix.

Overrides

Matrix.ToArray()

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Transpose(SparseMatrix)

Transposes the SparseMatrix

Declaration

public static SparseMatrix Transpose(SparseMatrix matrix)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to tranpose.

Returns

Type	Description
SparseMatrix	The new SparseMatrix, transposed of the initial one.

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TransposeMultiply(SparseMatrix, DenseVector)

Computes the right multiplication of a SparseMatrix with a DenseVector : A·V.

Declaration

public static DenseVector TransposeMultiply(SparseMatrix matrix, DenseVector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
DenseVector	vector	DenseVector to multiply with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the multiplication.

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TransposeMultiply(SparseMatrix, SparseVector)

Computes the right multiplication of a SparseMatrix with a SparseVector : A·V.

Declaration

public static SparseVector TransposeMultiply(SparseMatrix matrix, SparseVector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
SparseVector	vector	SparseVector to multiply with.

Returns

Type	Description
SparseVector	The new SparseVector resulting from the multiplication.

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TransposeMultiply(SparseMatrix, Vector)

Computes the right multiplication of a transposed SparseMatrix with a Vector : A^t·V.

Declaration

public static Vector TransposeMultiply(SparseMatrix matrix, Vector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to transpose then multiply on the right.
Vector	vector	Vector to multiply with.

Returns

Type	Description
Vector	The new Vector resulting from the multiplication.

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TransposeMultiplySelf(SparseMatrix)

Computes the left multiplication of a SparseMatrix with its transposition : A^t·A.

Declaration

public static SparseMatrix TransposeMultiplySelf(SparseMatrix operand)

Parameters

Type	Name	Description
SparseMatrix	operand	SparseMatrix for the operation.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the operation.

Operators

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Addition(SparseMatrix, DenseMatrix)

Computes the right addition of a SparseMatrix with a DenseMatrix on the right.

Declaration

public static DenseMatrix operator +(SparseMatrix left, DenseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the addition.
DenseMatrix	right	Right DenseMatrix for the addition.

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Addition(SparseMatrix, Matrix)

Computes the right addition of a SparseMatrix with a Matrix on the right.

Declaration

public static Matrix operator +(SparseMatrix left, Matrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the addition.
Matrix	right	Right Matrix for the addition.

Returns

Type	Description
Matrix	The new Matrix resulting from the addition.

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Addition(SparseMatrix, SparseMatrix)

Computes the addition of two SparseMatrix.

Declaration

public static SparseMatrix operator +(SparseMatrix left, SparseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the addition.
SparseMatrix	right	Right SparseMatrix for the addition.

Returns

Type	Description
SparseMatrix	The SparseMatrix resulting from the addition.

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Division(SparseMatrix, Double)

Computes the scalar division of a SparseMatrix with a number.

Declaration

public static SparseMatrix operator /(SparseMatrix operand, double divisor)

Parameters

Type	Name	Description
SparseMatrix	operand	SparseMatrix to divide.
Double	divisor	number to divide with.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the scalar division.

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Multiply(SparseMatrix, DenseMatrix)

Computes the right multiplication of a SparseMatrix with a DenseMatrix.

Declaration

public static DenseMatrix operator *(SparseMatrix left, DenseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the multiplication.
DenseMatrix	right	Right DenseMatrix for the multiplication.

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(SparseMatrix, Matrix)

Computes the right multiplication of a SparseMatrix with a Matrix.

Declaration

public static Matrix operator *(SparseMatrix left, Matrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the multiplication.
Matrix	right	Right Matrix for the multiplication.

Returns

Type	Description
Matrix	The new Matrix resulting from the multiplication.

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Multiply(SparseMatrix, SparseMatrix)

Computes the multiplication of two SparseMatrix.

Declaration

public static SparseMatrix operator *(SparseMatrix left, SparseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix for the multiplication.
SparseMatrix	right	Right SparseMatrix for the multiplication.

Returns

Type	Description
SparseMatrix	The SparseMatrix resulting from the multiplication.

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Multiply(SparseMatrix, DenseVector)

Computes the right multiplication of a SparseMatrix with a DenseVector : A·V.

Declaration

public static DenseVector operator *(SparseMatrix matrix, DenseVector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
DenseVector	vector	DenseVector to multiply with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the multiplication.

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Multiply(SparseMatrix, SparseVector)

Computes the right multiplication of a SparseMatrix with a SparseVector : A·V.

Declaration

public static SparseVector operator *(SparseMatrix matrix, SparseVector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
SparseVector	vector	SparseVector to multiply with.

Returns

Type	Description
SparseVector	The new SparseVector resulting from the multiplication.

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Multiply(SparseMatrix, Vector)

Computes the right multiplication of a SparseMatrix with a Vector : A·V.

Declaration

public static Vector operator *(SparseMatrix matrix, Vector vector)

Parameters

Type	Name	Description
SparseMatrix	matrix	SparseMatrix to multiply on the right.
Vector	vector	Vector to multiply with.

Returns

Type	Description
Vector	The new Vector resulting from the multiplication.

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Multiply(SparseMatrix, Double)

Computes the right scalar multiplication of a SparseMatrix with a number.

Declaration

public static SparseMatrix operator *(SparseMatrix operand, double factor)

Parameters

Type	Name	Description
SparseMatrix	operand	SparseMatrix to multiply on the right.
Double	factor	number to multiply with.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the right scalar multiplication.

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Multiply(Double, SparseMatrix)

Computes the left scalar multiplication of a SparseMatrix with a number.

Declaration

public static SparseMatrix operator *(double factor, SparseMatrix operand)

Parameters

Type	Name	Description
Double	factor	number to multiply with.
SparseMatrix	operand	SparseMatrix to multiply on the left.

Returns

Type	Description
SparseMatrix	The new SparseMatrix resulting from the left scalar multiplication.

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Subtraction(SparseMatrix, DenseMatrix)

Computes the subtraction of a SparseMatrix with a DenseMatrix.

Declaration

public static DenseMatrix operator -(SparseMatrix left, DenseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix to subtract.
DenseMatrix	right	Right DenseMatrix to subtract with.

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtraction(SparseMatrix, Matrix)

Computes the subtraction of a SparseMatrix with a Matrix.

Declaration

public static Matrix operator -(SparseMatrix left, Matrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix to subtract.
Matrix	right	Right Matrix to subtract with.

Returns

Type	Description
Matrix	The new Matrix resulting from the subtraction.

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Subtraction(SparseMatrix, SparseMatrix)

Computes the subtraction of two SparseMatrix.

Declaration

public static SparseMatrix operator -(SparseMatrix left, SparseMatrix right)

Parameters

Type	Name	Description
SparseMatrix	left	Left SparseMatrix to subtract.
SparseMatrix	right	Right SparseMatrix to subtract with.

Returns

Type	Description
SparseMatrix	The SparseMatrix resulting from the subtraction.

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UnaryNegation(SparseMatrix)

Computes the opposite of the SparseMatrix.

Declaration

public static SparseMatrix operator -(SparseMatrix operand)

Parameters

Type	Name	Description
SparseMatrix	operand	SparseMatrix whose opposite is to be computed.

Returns

Type	Description
SparseMatrix	The SparseMatrix, opposite of the initial one.

Explicit Interface Implementations

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IGroupAction<SparseMatrix, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

SparseMatrix IGroupAction<SparseMatrix, double>.Divide(double divisor)

Parameters

Type	Name	Description
Double	divisor

Returns

Type	Description
SparseMatrix	The new element resulting from the scalar dividion.

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IGroupAction<SparseMatrix, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

SparseMatrix IGroupAction<SparseMatrix, double>.Multiply(double factor)

Parameters

Type	Name	Description
Double	factor

Returns

Type	Description
SparseMatrix	The new element resulting from the scalar multiplication.

Implements

IGroupAction<TSelf, TValue>