Class Vector

Class defining a vector in a real vector space.

Inheritance

Object

Vector

DenseVector

SparseVector

Implements

IEnumerable<Double>

IDotProduct<Vector, Double>

INorm<Vector>

IMetric<Vector>

IGroupAction<Vector, Double>

Namespace: BRIDGES.LinearAlgebra.Vectors

Assembly: BRIDGES.dll

Syntax

public abstract class Vector : IEquatable<Vector>, IDotProduct<Vector, double>, INorm<Vector>, IMetric<Vector>, IGroupAction<Vector, double>

Constructors

| Improve this Doc View Source

Vector(Int32)

Initialises a new instance of the Vector class.

Declaration

protected Vector(int size)

Parameters

Type	Name	Description
Int32	size	Number of compoenent of the new Vector.

Properties

| Improve this Doc View Source

Item[Int32]

Gets or sets the component at a given index.

Declaration

public abstract 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.

| Improve this Doc View Source

Size

Number of component of this vector.

Declaration

public abstract int Size { get; }

Property Value

Type	Description
Int32

Methods

| Improve this Doc View Source

Add(Vector, Vector)

Computes the addition of two Vector.

Declaration

public static Vector Add(Vector left, Vector right)

Parameters

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

Returns

Type	Description
Vector	The Vector resulting from the addition.

| Improve this Doc View Source

Divide(Vector, Double)

Computes the scalar division of a Vector with a number.

Declaration

public static Vector Divide(Vector operand, double divisor)

Parameters

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

Returns

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

| Improve this Doc View Source

Equals(Vector)

Class defining a vector in a real vector space.

Declaration

public virtual bool Equals(Vector other)

Parameters

Type	Name	Description
Vector	other

Returns

Type	Description
Boolean

| Improve this Doc View Source

Equals(Object)

Class defining a vector in a real vector space.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj

Returns

Type	Description
Boolean

| Improve this Doc View Source

GetEnumerator()

Class defining a vector in a real vector space.

Declaration

public abstract IEnumerator<double> GetEnumerator()

Returns

Type	Description
IEnumerator<Double>

| Improve this Doc View Source

GetHashCode()

Class defining a vector in a real vector space.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32

| Improve this Doc View Source

GramSchmidt(IEnumerable<Vector>)

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

Declaration

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

Parameters

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

Returns

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

Remarks

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

| Improve this Doc View Source

Multiply(Vector, Double)

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

Declaration

public static Vector Multiply(Vector operand, double factor)

Parameters

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

Returns

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

| Improve this Doc View Source

Multiply(Double, Vector)

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

Declaration

public static Vector Multiply(double factor, Vector operand)

Parameters

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

Returns

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

| Improve this Doc View Source

Norm()

Computes the length of this vector.

Declaration

public virtual double Norm()

Returns

Type	Description
Double	The value of the vector length.

| Improve this Doc View Source

Opposite(Vector)

Computes the opposite of the Vector.

Declaration

public static Vector Opposite(Vector operand)

Parameters

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

Returns

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

| Improve this Doc View Source

SquaredNorm()

Computes the squared norm of this vector.

Declaration

public virtual double SquaredNorm()

Returns

Type	Description
Double	The value of the vector squared norm.

| Improve this Doc View Source

Subtract(Vector, Vector)

Computes the subtraction of two Vector.

Declaration

public static Vector Subtract(Vector left, Vector right)

Parameters

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

Returns

Type	Description
Vector	The Vector resulting from the subtraction.

| Improve this Doc View Source

ToArray()

Translates this vector into its array representation.

Declaration

public abstract double[] ToArray()

Returns

Type	Description
Double[]	The array representing the vector.

| Improve this Doc View Source

ToString()

Class defining a vector in a real vector space.

Declaration

public override string ToString()

Returns

Type	Description
String

| Improve this Doc View Source

TransposeMultiply(Vector, Vector)

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

Declaration

public static double TransposeMultiply(Vector left, Vector right)

Parameters

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

Returns

Type	Description
Double	The scalar value resulting from the operation.

Operators

| Improve this Doc View Source

Addition(Vector, Vector)

Computes the addition of two Vector.

Declaration

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

Parameters

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

Returns

Type	Description
Vector	The Vector resulting from the addition.

| Improve this Doc View Source

Division(Vector, Double)

Computes the scalar division of a Vector with a number.

Declaration

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

Parameters

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

Returns

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

| Improve this Doc View Source

Equality(Vector, Vector)

Evaluates whether two Vector are equal or not.

Declaration

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

Parameters

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

Returns

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

| Improve this Doc View Source

Inequality(Vector, Vector)

Evaluates whether two Vector are different.

Declaration

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

Parameters

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

Returns

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

| Improve this Doc View Source

Multiply(Vector, Double)

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

Declaration

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

Parameters

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

Returns

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

| Improve this Doc View Source

Multiply(Double, Vector)

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

Declaration

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

Parameters

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

Returns

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

| Improve this Doc View Source

Subtraction(Vector, Vector)

Computes the subtraction of two Vector.

Declaration

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

Parameters

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

Returns

Type	Description
Vector	The Vector resulting from the subtraction.

| Improve this Doc View Source

UnaryNegation(Vector)

Computes the opposite of the Vector.

Declaration

public static Vector operator -(Vector operand)

Parameters

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

Returns

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

Explicit Interface Implementations

| Improve this Doc View Source

IDotProduct<Vector, Double>.DotProduct(Vector)

Computes the dot product of this element with another element.

Declaration

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

Parameters

Type	Name	Description
Vector	other

Returns

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

| Improve this Doc View Source

IMetric<Vector>.DistanceTo(Vector)

Computes the distance of this element to another element.

Declaration

double IMetric<Vector>.DistanceTo(Vector other)

Parameters

Type	Name	Description
Vector	other

Returns

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

| Improve this Doc View Source

IGroupAction<Vector, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

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

Parameters

Type	Name	Description
Double	divisor

Returns

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

| Improve this Doc View Source

IGroupAction<Vector, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

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

Parameters

Type	Name	Description
Double	factor

Returns

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

Implements

IEnumerable<>

IDotProduct<TSelf, TValue>

INorm<TSelf>

IMetric<TSelf>

IGroupAction<TSelf, TValue>