org.moeaframework.util
Class Vector

java.lang.Object
  org.moeaframework.util.Vector

public class Vector
extends Object

Mathematical operators for manipulating vectors (double arrays).

Method Summary

static double[]	add(double[] u, double[] v) Returns the sum of the two specified vectors, u + v.
static double[]	divide(double[] u, double a) Returns the scalar division of the specified vector, u / a.
static double	dot(double[] u, double[] v) Returns the dot (inner) product of the two specified vectors.
static boolean	isZero(double[] u) Returns true if the specified vector contains all zeros; false otherwise.
static double	magnitude(double[] u) Returns the magnitude (Euclidean norm) of the specified vector.
static double[]	mean(double[][] vs) Returns the mean vector of the specified vectors.
static double[]	multiply(double a, double[] u) Returns the scalar multiple of the specified vector, a * u.
static double[]	negate(double[] u) Returns the negation of the specified vector, -u.
static double[]	normalize(double[] u) Returns the specified vector normalized to have a magnitude of 1.
static double[][]	orthogonalize(double[][] vs) Returns the orthogonal basis for the specified vectors using the Gram-Schmidt process.
static double[]	orthogonalize(double[] u, Iterable<double[]> vs) Returns the vector u orthogonal to the already orthogonalized vectors vs.
static double[]	project(double[] u, double[] v) Returns the projection of u onto v.
static double[]	subtract(double[] u, double[] v) Returns the difference between the two specified vectors, u - v.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

subtract

public static double[] subtract(double[] u,
                                double[] v)

Returns the difference between the two specified vectors, u - v. The two vectors must be of the same length.

Parameters:

u - the first vector

v - the second vector

Returns:

the difference between the two specified vectors, u - v

Throws:

IllegalArgumentException - if the two vectors are not the same length

add

public static double[] add(double[] u,
                           double[] v)

Returns the sum of the two specified vectors, u + v. The two vectors must be of the same length.

Parameters:

u - the first vector

v - the second vector

Returns:

the sum of the two specified vectors, u + v

Throws:

IllegalArgumentException - if the two vectors are not the same length

multiply

public static double[] multiply(double a,
                                double[] u)

Returns the scalar multiple of the specified vector, a * u.

Parameters:

a - the scalar value

u - the vector

Returns:

the scalar multiple of the specified vector, a * u

negate

public static double[] negate(double[] u)

Returns the negation of the specified vector, -u. This is equivalent to calling multiply(-1, u).

Parameters:

u - the vector

Returns:

the negation of the specified vector, -u

divide

public static double[] divide(double[] u,
                              double a)

Returns the scalar division of the specified vector, u / a.

Parameters:

u - the vector

a - the scalar value (the denominator)

Returns:

the scalar division of the specified vector, u / a

dot

public static double dot(double[] u,
                         double[] v)

Returns the dot (inner) product of the two specified vectors. The two vectors must be the same length.

Parameters:

u - the first vector

v - the second vector

Returns:

the dot (inner) product of the two specified vectors

Throws:

IllegalArgumentException - if the two vectors are not the same length

magnitude

public static double magnitude(double[] u)

Returns the magnitude (Euclidean norm) of the specified vector.

Parameters:

u - the vector

Returns:

the magnitude (Euclidean norm) of the specified vector

normalize

public static double[] normalize(double[] u)

Returns the specified vector normalized to have a magnitude of 1. The specified vector must contain at least one non-zero component; otherwise an exception is thrown.

Parameters:

u - the vector

Returns:

the specified vector normalized to have a magnitude of 1

Throws:

IllegalArgumentException - if the specified vector contains all zeros

project

public static double[] project(double[] u,
                               double[] v)

Returns the projection of u onto v. The two vectors must be the same length.

Parameters:

u - the vector being projected

v - the vector onto which u is being projected

Returns:

the projection of u onto v

Throws:

IllegalArgumentException - if the two vectors are not the same length

orthogonalize

public static double[][] orthogonalize(double[][] vs)

Returns the orthogonal basis for the specified vectors using the Gram-Schmidt process.

Parameters:

vs - the vectors to be orthogonalized

Returns:

the orthogonal basis

orthogonalize

public static double[] orthogonalize(double[] u,
                                     Iterable<double[]> vs)

Returns the vector u orthogonal to the already orthogonalized vectors vs. This method is provided to allow incremental construction of the orthogonal basis:

 List<double[]> basis = new ArrayList<double[]>();
 for (double[] v : vectors) {
        double[] e = orthogonalize(v, basis);
        basis.add(e);
 }
 

Parameters:

u - the vector

vs - the already orthogonalized vectors

Returns:

the vector u orthogonal to the already orthogonalized vectors vs

mean

public static double[] mean(double[][] vs)

Returns the mean vector of the specified vectors.

Parameters:

vs - the vectors

Returns:

the mean vector of the specified vectors

Throws:

IllegalArgumentException - if the specified vectors is empty

isZero

public static boolean isZero(double[] u)

Returns true if the specified vector contains all zeros; false otherwise.

Parameters:

u - the vector

Returns:

true if the specified vector contains all zeros; false otherwise