Class DenseMatrix

Class defining a dense matrix.

Inheritance

Object

Matrix

DenseMatrix

Implements

IGroupAction<Matrix, Double>

IGroupAction<DenseMatrix, Double>

Inherited Members

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

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

Namespace: BRIDGES.LinearAlgebra.Matrices

Assembly: BRIDGES.dll

Syntax

public sealed class DenseMatrix : Matrix, IGroupAction<Matrix, double>, IGroupAction<DenseMatrix, double>

Constructors

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DenseMatrix(DenseMatrix)

Initialises a new instance of the DenseMatrix class from another DenseMatrix.

Declaration

public DenseMatrix(DenseMatrix matrix)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix to deep copy.

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DenseMatrix(Double[,])

Initialises a new instance of the DenseMatrix class by defining its values.

Declaration

public DenseMatrix(double[, ] components)

Parameters

Type	Name	Description
Double[,]	components	Values of the matrix.

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DenseMatrix(Int32, Int32, Double[])

Initialises a new instance of the DenseMatrix class by defining its size and values row by row.

Declaration

public DenseMatrix(int rowCount, int columnCount, double[] components)

Parameters

Type	Name	Description
Int32	rowCount	Number of rows of the DenseMatrix.
Int32	columnCount	Number of columns of the DenseMatrix.
Double[]	components	Component values given row by row.

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DenseMatrix(Int32, Int32)

Initialises a new instance of the DenseMatrix class by defining its number of row and column.

Declaration

public DenseMatrix(int rowCount, int columnCount)

Parameters

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

Properties

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ColumnCount

Gets the number of columns in this matrix.

Declaration

public override int ColumnCount { get; }

Property Value

Type	Description
Int32

Overrides

Matrix.ColumnCount

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Item[Int32, Int32]

Gets the value of this matrix at the given row and column.

Declaration

public double this[int row, int column] { get; set; }

Parameters

Type	Name	Description
Int32	row	Row index of the value to get.
Int32	column	Column index of the value to get.

Property Value

Type	Description
Double	The value at the given row and column index.

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RowCount

Gets the number of rows in this matrix.

Declaration

public override int RowCount { get; }

Property Value

Type	Description
Int32

Overrides

Matrix.RowCount

Methods

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Add(DenseMatrix, DenseMatrix)

Computes the addition of two DenseMatrix.

Declaration

public static DenseMatrix Add(DenseMatrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix resulting from the addition.

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Add(DenseMatrix, Matrix)

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

Declaration

public static DenseMatrix Add(DenseMatrix left, Matrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Add(DenseMatrix, CompressedColumn)

Computes the right addition of a DenseMatrix with a CompressedColumn.

Declaration

public static DenseMatrix Add(DenseMatrix left, CompressedColumn right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Add(DenseMatrix, CompressedRow)

Computes the right addition of a DenseMatrix with a CompressedRow.

Declaration

public static DenseMatrix Add(DenseMatrix left, CompressedRow right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Add(DenseMatrix, SparseMatrix)

Computes the right addition of a DenseMatrix with a SparseMatrix.

Declaration

public static DenseMatrix Add(DenseMatrix left, SparseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Add(Matrix, DenseMatrix)

Computes the left addition of a DenseMatrix with a Matrix on the right.

Declaration

public static DenseMatrix Add(Matrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Add(CompressedColumn, DenseMatrix)

Computes the left addition of a DenseMatrix with a CompressedColumn.

Declaration

public static DenseMatrix Add(CompressedColumn left, DenseMatrix right)

Parameters

Type	Name	Description
CompressedColumn	left	Left CompressedColumn 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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Add(CompressedRow, DenseMatrix)

Computes the right addition of a DenseMatrix with a CompressedRow.

Declaration

public static DenseMatrix Add(CompressedRow left, DenseMatrix right)

Parameters

Type	Name	Description
CompressedRow	left	Left CompressedRow 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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Add(SparseMatrix, DenseMatrix)

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

Declaration

public static DenseMatrix Add(SparseMatrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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At(Int32, Int32)

Get the value of the matrix at the given row and column index.

Declaration

public override double At(int row, int column)

Parameters

Type	Name	Description
Int32	row	Row index of the value to get.
Int32	column	Column index of the value to get.

Returns

Type	Description
Double	The value at the given row and column index.

Overrides

Matrix.At(Int32, Int32)

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Divide(DenseMatrix, Double)

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

Declaration

public static DenseMatrix Divide(DenseMatrix operand, double divisor)

Parameters

Type	Name	Description
DenseMatrix	operand	DenseMatrix to multiply on the right.
Double	divisor

Returns

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

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Identity(Int32)

Returns the neutral Matrix for the multiplication.

Declaration

public static DenseMatrix Identity(int size)

Parameters

Type	Name	Description
Int32	size	Number of rows and columns of the Matrix.

Returns

Type	Description
DenseMatrix	The DenseMatrix of the given size, with ones on the diagonal and zeros elsewhere.

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Multiply(DenseMatrix, DenseMatrix)

Computes the multiplication of two DenseMatrix.

Declaration

public static DenseMatrix Multiply(DenseMatrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, Matrix)

Computes the right multiplication of a DenseMatrix with a Matrix.

Declaration

public static DenseMatrix Multiply(DenseMatrix left, Matrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, CompressedColumn)

Computes the right multiplication of a DenseMatrix with a CompressedColumn.

Declaration

public static DenseMatrix Multiply(DenseMatrix left, CompressedColumn right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, CompressedRow)

Computes the right multiplication of a DenseMatrix with a CompressedRow.

Declaration

public static DenseMatrix Multiply(DenseMatrix left, CompressedRow right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, SparseMatrix)

Computes the right multiplication of a DenseMatrix with a SparseMatrix.

Declaration

public static DenseMatrix Multiply(DenseMatrix left, SparseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, DenseVector)

Computes the right multiplication of a DenseMatrix with a DenseVector : A*V.

Declaration

public static DenseVector Multiply(DenseMatrix matrix, DenseVector vector)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix 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(DenseMatrix, SparseVector)

Computes the right multiplication of a DenseMatrix with a SparseVector : A*V.

Declaration

public static DenseVector Multiply(DenseMatrix matrix, SparseVector vector)

Parameters

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

Returns

Type	Description
DenseVector	The new DenseVector resulting from the multiplication.

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Multiply(DenseMatrix, Vector)

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

Declaration

public static Vector Multiply(DenseMatrix matrix, Vector vector)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix 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(DenseMatrix, Double)

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

Declaration

public static DenseMatrix Multiply(DenseMatrix operand, double factor)

Parameters

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

Returns

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

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Multiply(Matrix, DenseMatrix)

Computes the left multiplication of a DenseMatrix with a Matrix on the right.

Declaration

public static DenseMatrix Multiply(Matrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(CompressedColumn, DenseMatrix)

Computes the left multiplication of a DenseMatrix with a CompressedColumn.

Declaration

public static DenseMatrix Multiply(CompressedColumn left, DenseMatrix right)

Parameters

Type	Name	Description
CompressedColumn	left	Left CompressedColumn 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(CompressedRow, DenseMatrix)

Computes the right multiplication of a DenseMatrix with a CompressedRow.

Declaration

public static DenseMatrix Multiply(CompressedRow left, DenseMatrix right)

Parameters

Type	Name	Description
CompressedRow	left	Left CompressedRow 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, DenseMatrix)

Computes the left multiplication of a DenseMatrix with a SparseMatrix on the right.

Declaration

public static DenseMatrix Multiply(SparseMatrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(Double, DenseMatrix)

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

Declaration

public static DenseMatrix Multiply(double factor, DenseMatrix operand)

Parameters

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

Returns

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

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Opposite(DenseMatrix)

Computes the opposite of the DenseMatrix.

Declaration

public static DenseMatrix Opposite(DenseMatrix operand)

Parameters

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

Returns

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

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Subtract(DenseMatrix, DenseMatrix)

Computes the subtraction of two DenseMatrix.

Declaration

public static DenseMatrix Subtract(DenseMatrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix resulting from the subtraction.

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Subtract(DenseMatrix, Matrix)

Computes the subtraction of a DenseMatrix with a Matrix.

Declaration

public static DenseMatrix Subtract(DenseMatrix left, Matrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(DenseMatrix, CompressedColumn)

Computes the subtraction of a DenseMatrix with a CompressedColumn.

Declaration

public static DenseMatrix Subtract(DenseMatrix left, CompressedColumn right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(DenseMatrix, CompressedRow)

Computes the subtraction of a DenseMatrix with a CompressedRow.

Declaration

public static DenseMatrix Subtract(DenseMatrix left, CompressedRow right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(DenseMatrix, SparseMatrix)

Computes the subtraction of a DenseMatrix with a SparseMatrix.

Declaration

public static DenseMatrix Subtract(DenseMatrix left, SparseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(Matrix, DenseMatrix)

Computes the left subtraction of a DenseMatrix with a Matrix on the right.

Declaration

public static DenseMatrix Subtract(Matrix left, DenseMatrix right)

Parameters

Type	Name	Description
Matrix	left	Right DenseMatrix to subtract on the left.
DenseMatrix	right	Left Matrix to subtract with from the left.

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(CompressedColumn, DenseMatrix)

Computes the left subtraction of a DenseMatrix with a CompressedColumn.

Declaration

public static DenseMatrix Subtract(CompressedColumn left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(CompressedRow, DenseMatrix)

Computes the right subtraction of a DenseMatrix with a CompressedRow.

Declaration

public static DenseMatrix Subtract(CompressedRow left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtract(SparseMatrix, DenseMatrix)

Computes the left subtraction of a DenseMatrix with a SparseMatrix on the right.

Declaration

public static DenseMatrix Subtract(SparseMatrix left, DenseMatrix right)

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix 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(DenseMatrix)

Transposes the DenseMatrix

Declaration

public static DenseMatrix Transpose(DenseMatrix matrix)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix to tranpose.

Returns

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

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TransposeMultiply(DenseMatrix, DenseVector)

Computes the right multiplication of a transposed DenseMatrix with a DenseVector : A^t·V.

Declaration

public static DenseVector TransposeMultiply(DenseMatrix matrix, DenseVector vector)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix to transpose then 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(DenseMatrix, SparseVector)

Computes the right multiplication of a transposed DenseMatrix with a SparseVector : A^t·V.

Declaration

public static DenseVector TransposeMultiply(DenseMatrix matrix, SparseVector vector)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix to transpose then multiply on the right.
SparseVector	vector	SparseVector to multiply with.

Returns

Type	Description
DenseVector	The new SparseVector resulting from the multiplication.

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TransposeMultiply(DenseMatrix, Vector)

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

Declaration

public static Vector TransposeMultiply(DenseMatrix matrix, Vector vector)

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix 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(DenseMatrix)

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

Declaration

public static DenseMatrix TransposeMultiplySelf(DenseMatrix operand)

Parameters

Type	Name	Description
DenseMatrix	operand	DenseMatrix for the operation.

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the operation.

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Zero(Int32, Int32)

Returns the neutral DenseMatrix for the addition.

Declaration

public static DenseMatrix Zero(int rowCount, int columnCount)

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix of the given size, with zeros on every coordinates.

Operators

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Addition(DenseMatrix, DenseMatrix)

Computes the addition of two DenseMatrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix resulting from the addition.

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Addition(DenseMatrix, Matrix)

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

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Addition(DenseMatrix, CompressedColumn)

Computes the right addition of a DenseMatrix with a CompressedColumn.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Addition(DenseMatrix, CompressedRow)

Computes the right addition of a DenseMatrix with a CompressedRow.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Addition(DenseMatrix, SparseMatrix)

Computes the right addition of a DenseMatrix with a SparseMatrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the addition.

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Division(DenseMatrix, Double)

Computes the scalar division of a DenseMatrix with a number.

Declaration

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

Parameters

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

Returns

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

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Multiply(DenseMatrix, DenseMatrix)

Computes the multiplication of two DenseMatrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, Matrix)

Computes the right multiplication of a DenseMatrix with a Matrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, CompressedColumn)

Computes the right multiplication of a DenseMatrix with a CompressedColumn.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, CompressedRow)

Computes the right multiplication of a DenseMatrix with a CompressedRow.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, SparseMatrix)

Computes the right multiplication of a DenseMatrix with a SparseMatrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the multiplication.

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Multiply(DenseMatrix, DenseVector)

Computes the right multiplication of a DenseMatrix with a DenseVector : A*V.

Declaration

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

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix 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(DenseMatrix, SparseVector)

Computes the right multiplication of a DenseMatrix with a SparseVector : A*V.

Declaration

public static DenseVector operator *(DenseMatrix matrix, SparseVector vector)

Parameters

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

Returns

Type	Description
DenseVector	The new DenseVector resulting from the multiplication.

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Multiply(DenseMatrix, Vector)

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

Declaration

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

Parameters

Type	Name	Description
DenseMatrix	matrix	DenseMatrix 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(DenseMatrix, Double)

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

Declaration

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

Parameters

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

Returns

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

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Multiply(Double, DenseMatrix)

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

Declaration

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

Parameters

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

Returns

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

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Subtraction(DenseMatrix, DenseMatrix)

Computes the subtraction of two DenseMatrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The DenseMatrix resulting from the subtraction.

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Subtraction(DenseMatrix, Matrix)

Computes the subtraction of a DenseMatrix with a Matrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtraction(DenseMatrix, CompressedColumn)

Computes the subtraction of a DenseMatrix with a CompressedColumn.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtraction(DenseMatrix, CompressedRow)

Computes the subtraction of a DenseMatrix with a CompressedRow.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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Subtraction(DenseMatrix, SparseMatrix)

Computes the subtraction of a DenseMatrix with a SparseMatrix.

Declaration

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

Parameters

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

Returns

Type	Description
DenseMatrix	The new DenseMatrix resulting from the subtraction.

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UnaryNegation(DenseMatrix)

Computes the opposite of the DenseMatrix.

Declaration

public static DenseMatrix operator -(DenseMatrix operand)

Parameters

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

Returns

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

Explicit Interface Implementations

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IGroupAction<DenseMatrix, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

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

Parameters

Type	Name	Description
Double	divisor

Returns

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

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IGroupAction<DenseMatrix, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

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

Parameters

Type	Name	Description
Double	factor

Returns

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

Implements

IGroupAction<TSelf, TValue>