gov.sandia.cognition.math.matrix

Interface VectorSpace<VectorType extends VectorSpace<VectorType,?>,EntryType extends VectorSpace.Entry>

Type Parameters:

VectorType - Type of VectorSpace

EntryType - Type of entry for the iteration

All Superinterfaces:

java.lang.Cloneable, CloneableSerializable, java.lang.Iterable<EntryType>, Ring<VectorType>, java.io.Serializable

All Known Subinterfaces:

InfiniteVector<KeyType>, Vector, Vector1D, Vector2D, Vector3D

All Known Implementing Classes:

AbstractMTJVector, AbstractVector, AbstractVectorSpace, DefaultInfiniteVector, DenseVector, DenseVector, SparseVector, SparseVector, Vector1, Vector2, Vector3

@PublicationReference(author="Wikipedia",
                      title="Vector space",
                      type=WebPage,
                      year=2011,
                      url="http://en.wikipedia.org/wiki/Vector_space")
public interface VectorSpace<VectorType extends VectorSpace<VectorType,?>,EntryType extends VectorSpace.Entry>
extends Ring<VectorType>, java.lang.Iterable<EntryType>

In the Foundry, a VectorSpace is a type of Ring that we can perform Vector-like operations on: norm, distances between Vectors, etc.

Since:

3.3.1

Author:

Kevin R. Dixon

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	VectorSpace.Entry Entry into the VectorSpace

Method Summary

Modifier and Type	Method and Description
double	angle(VectorType other) Computes the angle between two Vectors.
double	cosine(VectorType other) Computes the cosine between two Vectors
double	dot(VectorType other) The inner product of this vector with the given vector.
double	dotProduct(VectorType other) The inner product of this vector with the given vector.
double	euclideanDistance(VectorType other) Euclidean distance between this and other, which is the 2-norm between the difference of the Vectors
double	euclideanDistanceSquared(VectorType other) Squared Euclidean distance between this and other, which is the 2-norm between the difference of the Vectors
double	getMaxValue() The maximum value associated with any key in the vector.
double	getMinValue() The minimum value associated with any key in the vector.
boolean	isUnitVector() Determines if this vector is a unit vector (norm2 = 1.0).
boolean	isUnitVector(double tolerance) Determines if this vector is a unit vector within some tolerance for the 2-norm.
double	norm(double power) Returns the p-norm of the Vector with the given power.
double	norm1() 1-norm of the vector (sum of absolute values in the vector)
double	norm2() 2-norm of the vector (aka Euclidean distance of the vector)
double	norm2Squared() Squared 2-norm of the vector (aka squared Euclidean distance of the vector)
double	normInfinity() Returns the infinity norm of the Vector, which is the maximum absolute value of an element in the Vector.
double	sum() Computes the sum of the elements in the vector.
VectorType	unitVector() Returns the unit vector of this vector.
void	unitVectorEquals() Modifies this vector to be a the unit vector.

Methods inherited from interface gov.sandia.cognition.math.Ring

clone, dotTimes, dotTimesEquals, equals, equals, isZero, isZero, minus, minusEquals, negative, negativeEquals, plus, plusEquals, scale, scaledMinus, scaledMinusEquals, scaledPlus, scaledPlusEquals, scaleEquals, zero

Methods inherited from interface java.lang.Iterable

forEach, iterator, spliterator

Method Detail

sum

double sum()

Computes the sum of the elements in the vector.

Returns:

The sum of the elements in the vector.

Since:

3.0

getMaxValue

double getMaxValue()

The maximum value associated with any key in the vector.

Returns:

The maximum value associated with any key in the vector. If the vector is empty, then Double.NEGATIVE_INFINITY is returned.

getMinValue

double getMinValue()

The minimum value associated with any key in the vector.

Returns:

The minimum value associated with any key in the vector. If the vector is empty, then Double.POSITIVE_INFINITY is returned.

norm1

double norm1()

1-norm of the vector (sum of absolute values in the vector)

Returns:

1-norm of the vector, [0,\infty)

norm2

double norm2()

2-norm of the vector (aka Euclidean distance of the vector)

Returns:

2-norm of the vector, [0,\infty)

norm2Squared

double norm2Squared()

Squared 2-norm of the vector (aka squared Euclidean distance of the vector)

Returns:

Squared 2-norm of the vector, [0,\infty)

normInfinity

double normInfinity()

Returns the infinity norm of the Vector, which is the maximum absolute value of an element in the Vector.

Returns:

Maximum absolute value of any element in the Vector.

norm

@PublicationReference(author="Wikipedia",
                      title="Vector norm, p-norm",
                      type=WebPage,
                      year=2011,
                      url="http://en.wikipedia.org/wiki/Vector_norm#p-norm")
double norm(double power)

Returns the p-norm of the Vector with the given power.

Parameters:

power - Power to exponentiate each entry, must be greater than 0.0, Double.POSITIVE_INFINITY

Returns:

p-norm with the given power.

dot

double dot(VectorType other)

The inner product of this vector with the given vector. That is, the sum of each element of this vector times the corresponding element in the other vector. The same as dotProduct.

Parameters:

other - The Vector with which to compute the dot product with this. Must have the same dimensionality as this.

Returns:

The dot product. The value is between 0 and Infinity.

dotProduct

double dotProduct(VectorType other)

The inner product of this vector with the given vector. That is, the sum of each element of this vector times the corresponding element in the other vector. The same as dot.

Parameters:

other - The Vector with which to compute the dot product with this. Must have the same dimensionality as this.

Returns:

The dot product. The value is between 0 and Infinity.

angle

double angle(VectorType other)

Computes the angle between two Vectors.

Parameters:

other - Another vector with which to compute the angle. Must be the same dimensionality.

Returns:

The angle between the two vectors in [0, PI].

cosine

double cosine(VectorType other)

Computes the cosine between two Vectors

Parameters:

other - another vector with which to compute the cosine, must be the same dimension as this

Returns:

cosine between the vectors, [0,1]

euclideanDistance

double euclideanDistance(VectorType other)

Euclidean distance between this and other, which is the 2-norm between the difference of the Vectors

Parameters:

other - Vector to which to compute the distance, must be the same dimension as this

Returns:

this.minus( other ).norm2(), which is [0,\infty)

euclideanDistanceSquared

double euclideanDistanceSquared(VectorType other)

Squared Euclidean distance between this and other, which is the 2-norm between the difference of the Vectors

Parameters:

other - Vector to which to compute the squared distance, must be the same dimension as this

Returns:

this.minus( other ).norm2Squared(), which is [0,\infty)

unitVector

VectorType unitVector()

Returns the unit vector of this vector. That is, a vector in the same "direction" where the length (norm2) is 1.0. This is computed by dividing each element buy the length (norm2). If this vector is all zeros, then the vector returned will be all zeros.

Returns:

The unit vector of this vector.

unitVectorEquals

void unitVectorEquals()

Modifies this vector to be a the unit vector. That is, a vector in the same "direction" where the length (norm2) is 1.0. This is computed by dividing each element buy the length (norm2). If this vector is all zeros, then this vector will all zeros.

isUnitVector

boolean isUnitVector()

Determines if this vector is a unit vector (norm2 = 1.0).

Returns:

True if this vector is a unit vector; otherwise, false.

isUnitVector

boolean isUnitVector(double tolerance)

Determines if this vector is a unit vector within some tolerance for the 2-norm.

Parameters:

tolerance - The tolerance around 1.0 to allow the length.

Returns:

True if this is a unit vector within the given tolerance; otherwise, false.