public sealed class DenseVector : Vector, IDotProduct<Vector, double>, INorm<Vector>, IMetric<Vector>, IGroupAction<Vector, double>, IDotProduct<DenseVector, double>, INorm<DenseVector>, IMetric<DenseVector>, IGroupAction<DenseVector, double>

Constructors

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DenseVector(DenseVector)

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

Declaration

public DenseVector(DenseVector vector)

Parameters

Type	Name	Description
DenseVector	vector	DenseVector to deep copy.

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DenseVector(SparseVector)

Initialises a new instance of the DenseVector class from a SparseVector.

Declaration

public DenseVector(SparseVector vector)

Parameters

Type	Name	Description
SparseVector	vector	SparseVector to copy.

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DenseVector(IList<Double>)

Initialises a new instance of the DenseVector class from its components.

Declaration

public DenseVector(IList<double> components)

Parameters

Type	Name	Description
IList<Double>	components	Components of the DenseVector.

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DenseVector(Int32)

Initialises a new instance of the DenseVector class of given size, containing only zeros.

Declaration

public DenseVector(int size)

Parameters

Type	Name	Description
Int32	size	Number of component of the DenseVector.

Properties

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Item[Int32]

Gets or sets the component at a given index.

Declaration

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

Parameters

Type	Name	Description
Int32	index	Index of the component to get or set.

Property Value

Type	Description
Double	The value of the component.

Overrides

Vector.Item[Int32]

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Size

Number of component of this vector.

Declaration

public override int Size { get; }

Property Value

Type	Description
Int32

Overrides

Vector.Size

Methods

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Add(DenseVector, DenseVector)

Computes the addition of two DenseVector.

Declaration

public static DenseVector Add(DenseVector left, DenseVector right)

Parameters

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

Returns

Type	Description
DenseVector	The new DenseVector resulting from the addition.

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Add(DenseVector, SparseVector)

Computes the right addition of a DenseVector with a SparseVector.

Declaration

public static DenseVector Add(DenseVector left, SparseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector for the addition.
SparseVector	right	Right SparseVector for the addition.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the addition.

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Add(DenseVector, Vector)

Computes the right addition of a DenseVector with a Vector.

Declaration

public static DenseVector Add(DenseVector left, Vector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector for the addition.
Vector	right	Right Vector for the addition.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the addition.

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Divide(DenseVector, Double)

Computes the scalar division of a DenseVector with a number.

Declaration

public static DenseVector Divide(DenseVector operand, double divisor)

Parameters

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

Returns

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

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Equals(DenseVector)

Class defining a dense vector.

Declaration

public bool Equals(DenseVector other)

Parameters

Type	Name	Description
DenseVector	other

Returns

Type	Description
Boolean

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Equals(Vector)

Class defining a dense vector.

Declaration

public override bool Equals(Vector other)

Parameters

Type	Name	Description
Vector	other

Returns

Type	Description
Boolean

Overrides

Vector.Equals(Vector)

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Equals(Object)

Class defining a dense vector.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj

Returns

Type	Description
Boolean

Overrides

Vector.Equals(Object)

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GetEnumerator()

Class defining a dense vector.

Declaration

public override IEnumerator<double> GetEnumerator()

Returns

Type	Description
IEnumerator<Double>

Overrides

Vector.GetEnumerator()

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GetHashCode()

Class defining a dense vector.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32

Overrides

Vector.GetHashCode()

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GramSchmidt(IEnumerable<DenseVector>)

Ortho-normalise the set of DenseVector using a Gram-Schimdt process.

Declaration

public static DenseVector[] GramSchmidt(IEnumerable<DenseVector> vectors)

Parameters

Type	Name	Description
IEnumerable<DenseVector>	vectors	Set of DenseVector to operate on.

Returns

Type	Description
DenseVector[]	The ortho-normal set of DenseVector.

Remarks

If the vectors are not linearly independent the number of vectors will change.

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Multiply(DenseVector, Double)

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

Declaration

public static DenseVector Multiply(DenseVector operand, double factor)

Parameters

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

Returns

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

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Multiply(Double, DenseVector)

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

Declaration

public static DenseVector Multiply(double factor, DenseVector operand)

Parameters

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

Returns

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

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Opposite(DenseVector)

Computes the opposite of the DenseVector.

Declaration

public static DenseVector Opposite(DenseVector operand)

Parameters

Type	Name	Description
DenseVector	operand	DenseVector from which the opposite is computed.

Returns

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

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StandardVector(Int32, Int32)

Returns the unit DenseVector of a given size, with one at the given row index and zeros elsewhere.

Declaration

public static DenseVector StandardVector(int size, int index)

Parameters

Type	Name	Description
Int32	size	Size of the DenseVector.
Int32	index	Index of the standard vector, i.e of the component equal to one.

Returns

Type	Description
DenseVector	The new DenseVector representing the standard vector.

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Subtract(DenseVector, DenseVector)

Computes the subtraction of two DenseVector.

Declaration

public static DenseVector Subtract(DenseVector left, DenseVector right)

Parameters

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

Returns

Type	Description
DenseVector	The new DenseVector resulting from the subtraction.

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Subtract(DenseVector, SparseVector)

Computes the right subtraction of a DenseVector with a SparseVector.

Declaration

public static DenseVector Subtract(DenseVector left, SparseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to subtract.
SparseVector	right	Right SparseVector to subtract with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the subtraction.

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Subtract(DenseVector, Vector)

Computes the right subtraction of a DenseVector with a Vector.

Declaration

public static DenseVector Subtract(DenseVector left, Vector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to subtract.
Vector	right	Right Vector to subtract with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the subtraction.

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ToArray()

Translates this vector into its array representation.

Declaration

public override double[] ToArray()

Returns

Type	Description
Double[]	The array representing the vector.

Overrides

Vector.ToArray()

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ToString()

Class defining a dense vector.

Declaration

public override string ToString()

Returns

Type	Description
String

Overrides

Vector.ToString()

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TransposeMultiply(DenseVector, DenseVector)

Computes the multiplication between the transposed left DenseVector and the right DenseVector.

Declaration

public static double TransposeMultiply(DenseVector left, DenseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to transpose, then multiply.
DenseVector	right	Right DenseVector to multiply.

Returns

Type	Description
Double	The scalar value resulting from the operation.

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TransposeMultiply(DenseVector, SparseVector)

Computes the multiplication between the transposed left DenseVector and the right SparseVector.

Declaration

public static double TransposeMultiply(DenseVector left, SparseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to transpose, then multiply.
SparseVector	right	Right SparseVector to multiply.

Returns

Type	Description
Double	The scalar value resulting from the operation.

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TransposeMultiply(DenseVector, Vector)

Computes the multiplication between the transposed left DenseVector and the right Vector.

Declaration

public static double TransposeMultiply(DenseVector left, Vector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to transpose, then multiply.
Vector	right	Right Vector to multiply.

Returns

Type	Description
Double	The scalar value resulting from the operation.

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Zero(Int32)

Returns the neutral DenseVector for the addition.

Declaration

public static DenseVector Zero(int size)

Parameters

Type	Name	Description
Int32	size	Number of component of the DenseVector.

Returns

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

Operators

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Addition(DenseVector, DenseVector)

Computes the addition of two DenseVector.

Declaration

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

Parameters

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

Returns

Type	Description
DenseVector	The new DenseVector resulting from the addition.

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Addition(DenseVector, SparseVector)

Computes the right addition of a DenseVector with a SparseVector.

Declaration

public static DenseVector operator +(DenseVector left, SparseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector for the addition.
SparseVector	right	Right SparseVector for the addition.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the addition.

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Addition(DenseVector, Vector)

Computes the right addition of a DenseVector with a Vector.

Declaration

public static DenseVector operator +(DenseVector left, Vector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector for the addition.
Vector	right	Right Vector for the addition.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the addition.

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Division(DenseVector, Double)

Computes the scalar division of a DenseVector with a number.

Declaration

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

Parameters

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

Returns

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

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Equality(DenseVector, DenseVector)

Evaluates whether two DenseVector are equal or not.

Declaration

public static bool operator ==(DenseVector left, DenseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector for the comparison.
DenseVector	right	Right DenseVector for the comparison.

Returns

Type	Description
Boolean	true if the two DenseVector are equal, false otherwise.

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Inequality(DenseVector, DenseVector)

Evaluates whether two DenseVector are different.

Declaration

public static bool operator !=(DenseVector left, DenseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector for the comparison.
DenseVector	right	Right DenseVector for the comparison.

Returns

Type	Description
Boolean	true if the two DenseVector are different, false otherwise.

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Multiply(DenseVector, Double)

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

Declaration

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

Parameters

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

Returns

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

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Multiply(Double, DenseVector)

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

Declaration

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

Parameters

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

Returns

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

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Subtraction(DenseVector, DenseVector)

Computes the subtraction of two DenseVector.

Declaration

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

Parameters

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

Returns

Type	Description
DenseVector	The new DenseVector resulting from the subtraction.

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Subtraction(DenseVector, SparseVector)

Computes the right subtraction of a DenseVector with a SparseVector.

Declaration

public static DenseVector operator -(DenseVector left, SparseVector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to subtract.
SparseVector	right	Right SparseVector to subtract with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the subtraction.

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Subtraction(DenseVector, Vector)

Computes the right subtraction of a DenseVector with a Vector.

Declaration

public static DenseVector operator -(DenseVector left, Vector right)

Parameters

Type	Name	Description
DenseVector	left	Left DenseVector to subtract.
Vector	right	Right Vector to subtract with.

Returns

Type	Description
DenseVector	The new DenseVector resulting from the subtraction.

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UnaryNegation(DenseVector)

Computes the opposite of the DenseVector.

Declaration

public static DenseVector operator -(DenseVector operand)

Parameters

Type	Name	Description
DenseVector	operand	DenseVector from which the opposite is computed.

Returns

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

Explicit Interface Implementations

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IDotProduct<DenseVector, Double>.DotProduct(DenseVector)

Computes the dot product of this element with another element.

Declaration

double IDotProduct<DenseVector, double>.DotProduct(DenseVector other)

Parameters

Type	Name	Description
DenseVector	other

Returns

Type	Description
Double	The value of the dot product of the two elements.

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IMetric<DenseVector>.DistanceTo(DenseVector)

Computes the distance of this element to another element.

Declaration

double IMetric<DenseVector>.DistanceTo(DenseVector other)

Parameters

Type	Name	Description
DenseVector	other

Returns

Type	Description
Double	The value of the distance between the two elements.

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IGroupAction<DenseVector, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

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

Parameters

Type	Name	Description
Double	divisor

Returns

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

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IGroupAction<DenseVector, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

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

Parameters

Type	Name	Description
Double	factor

Returns

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

Implements

IDotProduct<TSelf, TValue>

INorm<TSelf>

IMetric<TSelf>

IGroupAction<TSelf, TValue>

IEquatable<>

IEnumerable<>

IDotProduct<TSelf, TValue>

INorm<TSelf>

IMetric<TSelf>

IGroupAction<TSelf, TValue>