org.apache.commons.math3.geometry
Interface Vector<S extends Space>

Type Parameters:

S - Type of the space.

All Superinterfaces:

Serializable

All Known Implementing Classes:

Vector1D, Vector2D, Vector3D

public interface Vector<S extends Space>
extends Serializable

This interface represents a generic vector in a vectorial space or a point in an affine space.

Since:

3.0

Version:

$Id: Vector.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Space, Vector

Method Summary

Vector<S>	add(double factor, Vector<S> v) Add a scaled vector to the instance.
Vector<S>	add(Vector<S> v) Add a vector to the instance.
double	distance(Vector<S> v) Compute the distance between the instance and another vector according to the L2 norm.
double	distance1(Vector<S> v) Compute the distance between the instance and another vector according to the L1 norm.
double	distanceInf(Vector<S> v) Compute the distance between the instance and another vector according to the L∞ norm.
double	distanceSq(Vector<S> v) Compute the square of the distance between the instance and another vector.
double	dotProduct(Vector<S> v) Compute the dot-product of the instance and another vector.
double	getNorm() Get the L2 norm for the vector.
double	getNorm1() Get the L1 norm for the vector.
double	getNormInf() Get the L∞ norm for the vector.
double	getNormSq() Get the square of the norm for the vector.
Space	getSpace() Get the space to which the vector belongs.
Vector<S>	getZero() Get the null vector of the vectorial space or origin point of the affine space.
boolean	isInfinite() Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
boolean	isNaN() Returns true if any coordinate of this vector is NaN; false otherwise
Vector<S>	negate() Get the opposite of the instance.
Vector<S>	normalize() Get a normalized vector aligned with the instance.
Vector<S>	scalarMultiply(double a) Multiply the instance by a scalar.
Vector<S>	subtract(double factor, Vector<S> v) Subtract a scaled vector from the instance.
Vector<S>	subtract(Vector<S> v) Subtract a vector from the instance.
String	toString(NumberFormat format) Get a string representation of this vector.

Method Detail

getSpace

Space getSpace()

Get the space to which the vector belongs.

Returns:

containing space

getZero

Vector<S> getZero()

Get the null vector of the vectorial space or origin point of the affine space.

Returns:

null vector of the vectorial space or origin point of the affine space

getNorm1

double getNorm1()

Get the L₁ norm for the vector.

Returns:

L₁ norm for the vector

getNorm

double getNorm()

Get the L₂ norm for the vector.

Returns:

Euclidean norm for the vector

getNormSq

double getNormSq()

Get the square of the norm for the vector.

Returns:

square of the Euclidean norm for the vector

getNormInf

double getNormInf()

Get the L_∞ norm for the vector.

Returns:

L_∞ norm for the vector

add

Vector<S> add(Vector<S> v)

Add a vector to the instance.

Parameters:

v - vector to add

Returns:

a new vector

add

Vector<S> add(double factor,
              Vector<S> v)

Add a scaled vector to the instance.

Parameters:

factor - scale factor to apply to v before adding it

v - vector to add

Returns:

a new vector

subtract

Vector<S> subtract(Vector<S> v)

Subtract a vector from the instance.

Parameters:

v - vector to subtract

Returns:

a new vector

subtract

Vector<S> subtract(double factor,
                   Vector<S> v)

Subtract a scaled vector from the instance.

Parameters:

factor - scale factor to apply to v before subtracting it

v - vector to subtract

Returns:

a new vector

negate

Vector<S> negate()

Get the opposite of the instance.

Returns:

a new vector which is opposite to the instance

normalize

Vector<S> normalize()
                                  throws MathArithmeticException

Get a normalized vector aligned with the instance.

Returns:

a new normalized vector

Throws:

MathArithmeticException - if the norm is zero

scalarMultiply

Vector<S> scalarMultiply(double a)

Multiply the instance by a scalar.

Parameters:

a - scalar

Returns:

a new vector

isNaN

boolean isNaN()

Returns true if any coordinate of this vector is NaN; false otherwise

Returns:

true if any coordinate of this vector is NaN; false otherwise

isInfinite

boolean isInfinite()

Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise

Returns:

true if any coordinate of this vector is infinite and none are NaN; false otherwise

distance1

double distance1(Vector<S> v)

Compute the distance between the instance and another vector according to the L₁ norm.

Calling this method is equivalent to calling: q.subtract(p).getNorm1() except that no intermediate vector is built

Parameters:

v - second vector

Returns:

the distance between the instance and p according to the L₁ norm

distance

double distance(Vector<S> v)

Compute the distance between the instance and another vector according to the L₂ norm.

Calling this method is equivalent to calling: q.subtract(p).getNorm() except that no intermediate vector is built

Parameters:

v - second vector

Returns:

the distance between the instance and p according to the L₂ norm

distanceInf

double distanceInf(Vector<S> v)

Compute the distance between the instance and another vector according to the L_∞ norm.

Calling this method is equivalent to calling: q.subtract(p).getNormInf() except that no intermediate vector is built

Parameters:

v - second vector

Returns:

the distance between the instance and p according to the L_∞ norm

distanceSq

double distanceSq(Vector<S> v)

Compute the square of the distance between the instance and another vector.

Calling this method is equivalent to calling: q.subtract(p).getNormSq() except that no intermediate vector is built

Parameters:

v - second vector

Returns:

the square of the distance between the instance and p

dotProduct

double dotProduct(Vector<S> v)

Compute the dot-product of the instance and another vector.

Parameters:

v - second vector

Returns:

the dot product this.v

toString

String toString(NumberFormat format)

Get a string representation of this vector.

Parameters:

format - the custom format for components

Returns:

a string representation of this vector