com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse
Class SparseVector

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Vector>, BanachSpace<Vector,Real>, HilbertSpace<Vector,Real>, VectorSpace<Vector,Real>, SparseStructure, Vector, java.lang.Iterable<SparseVector.Entry>

Direct Known Subclasses:

Basis

public class SparseVector
extends java.lang.Object
implements Vector, SparseStructure, java.lang.Iterable<SparseVector.Entry>

A sparse vector stores only non-zero values.

Nested Class Summary

static class	SparseVector.Entry This is an entry in a SparseVector.
static class	SparseVector.Iterator This wrapper class overrides the Iterator.remove() method to throw an exception when called.

Constructor Summary

SparseVector(int size)
Construct a sparse vector.

SparseVector(int size, int[] indices, double[] values)
Construct a sparse vector.

SparseVector(SparseVector that)
Copy constructor.

Method Summary

Vector	add(double c) Add a constant to all entries in this vector.
SparseVector	add(SparseVector that)
Vector	add(Vector that) \(this + that\)
double	angle(Vector that) Measure the angle, \(\theta\), between this and that.
SparseVector	deepCopy() The implementation returns an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.
Vector	divide(Vector that) Divide this by that, entry-by-entry.
double	get(int index) Get the value at position i.
double	innerProduct(SparseVector that)
double	innerProduct(Vector that) Inner product in the Euclidean space is the dot product.
java.util.Iterator<SparseVector.Entry>	iterator()
Vector	minus(double c) Subtract a constant from all entries in this vector.
SparseVector	minus(SparseVector that)
Vector	minus(Vector that) \(this - that\)
SparseVector	multiply(SparseVector that)
SparseVector	multiply(Vector that) Multiply this by that, entry-by-entry.
int	nNonZeros() Get the number of non-zero entries in the structure.
double	norm() Compute the length or magnitude or Euclidean norm of a vector, namely, \(\|v\|\).
double	norm(int p) Get the norm of a vector.
SparseVector	opposite() Get the opposite of this vector.
Vector	pow(double c) Take the exponentiation of all entries in this vector, entry-by-entry.
SparseVector	scaled(double c) Scale this vector by a constant, entry-by-entry.
SparseVector	scaled(Real c) Scale this vector by a constant, entry-by-entry.
void	set(int index, double value) Change the value of an entry in this vector.
int	size() Get the length of this vector.
double[]	toArray() Cast this vector into a 1D double[].
java.lang.String	toString()
SparseVector	ZERO() Get a 0-vector that has the same length as this vector.

Methods inherited from class java.lang.Object

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

Constructor Detail

SparseVector

public SparseVector(int size)

Construct a sparse vector.

Parameters:

size - the size of the vector

SparseVector

public SparseVector(int size,
                    int[] indices,
                    double[] values)

Construct a sparse vector.

Parameters:

size - the size of the vector

indices - the indices of the non-zero values

values - the non-zero values

SparseVector

public SparseVector(SparseVector that)

Copy constructor.

Parameters:

that - the vector to be copied

Method Detail

size

public int size()

Description copied from interface: Vector

Get the length of this vector.

Specified by:

size in interface Vector

Returns:

the vector length

get

public double get(int index)

Description copied from interface: Vector

Get the value at position i.

Specified by:

get in interface Vector

Parameters:

index - the position of a vector entry

Returns:

v[i]

set

public void set(int index,
                double value)

Description copied from interface: Vector

Change the value of an entry in this vector. This is the only method that may change the entries of a vector.

Specified by:

set in interface Vector

Parameters:

index - the index of the entry to change. The indices are counting from 1, NOT 0.

value - the value to change to

iterator

public java.util.Iterator<SparseVector.Entry> iterator()

Specified by:

iterator in interface java.lang.Iterable<SparseVector.Entry>

add

public Vector add(Vector that)

Description copied from interface: Vector

\(this + that\)

Specified by:

add in interface AbelianGroup<Vector>

Specified by:

add in interface Vector

Parameters:

that - a vector

Returns:

\(this + that\)

add

public SparseVector add(SparseVector that)

minus

public Vector minus(Vector that)

Description copied from interface: Vector

\(this - that\)

Specified by:

minus in interface AbelianGroup<Vector>

Specified by:

minus in interface Vector

Parameters:

that - a vector

Returns:

\(this - that\)

minus

public SparseVector minus(SparseVector that)

multiply

public SparseVector multiply(Vector that)

Description copied from interface: Vector

Multiply this by that, entry-by-entry.

Specified by:

multiply in interface Vector

Parameters:

that - a vector

Returns:

\(this \cdot that\)

multiply

public SparseVector multiply(SparseVector that)

divide

public Vector divide(Vector that)

Description copied from interface: Vector

Divide this by that, entry-by-entry.

Specified by:

divide in interface Vector

Parameters:

that - a vector

Returns:

\(this / that\)

add

public Vector add(double c)

Description copied from interface: Vector

Add a constant to all entries in this vector.

Specified by:

add in interface Vector

Parameters:

c - a constant

Returns:

\(v + c\)

minus

public Vector minus(double c)

Description copied from interface: Vector

Subtract a constant from all entries in this vector.

Specified by:

minus in interface Vector

Parameters:

c - a constant

Returns:

\(v - c\)

innerProduct

public double innerProduct(Vector that)

Description copied from interface: Vector

Inner product in the Euclidean space is the dot product.

Specified by:

innerProduct in interface HilbertSpace<Vector,Real>

Specified by:

innerProduct in interface Vector

Parameters:

that - a vector

Returns:

\(this \cdot that\)

See Also:

Wikipedia: Dot product

innerProduct

public double innerProduct(SparseVector that)

pow

public Vector pow(double c)

Description copied from interface: Vector

Take the exponentiation of all entries in this vector, entry-by-entry.

Specified by:

pow in interface Vector

Parameters:

c - a constant

Returns:

\(v ^ s\)

scaled

public SparseVector scaled(double c)

Description copied from interface: Vector

Scale this vector by a constant, entry-by-entry. Here is a way to get a unit version of the vector:

vector.scaled(1. / vector.norm())

Specified by:

scaled in interface Vector

Parameters:

c - a constant

Returns:

\(c \times this\)

scaled

public SparseVector scaled(Real c)

Description copied from interface: Vector

Scale this vector by a constant, entry-by-entry. Here is a way to get a unit version of the vector:

vector.scaled(1. / vector.norm())

Specified by:

scaled in interface VectorSpace<Vector,Real>

Specified by:

scaled in interface Vector

Parameters:

c - a constant

Returns:

\(c \times this\)

See Also:

Wikipedia: Scalar multiplication

opposite

public SparseVector opposite()

Description copied from interface: Vector

Get the opposite of this vector.

Specified by:

opposite in interface AbelianGroup<Vector>

Specified by:

opposite in interface Vector

Returns:

-v

See Also:

Wikipedia: Additive inverse

norm

public double norm()

Description copied from interface: Vector

Compute the length or magnitude or Euclidean norm of a vector, namely, \(\|v\|\).

Specified by:

norm in interface BanachSpace<Vector,Real>

Specified by:

norm in interface Vector

Returns:

the Euclidean norm

See Also:

Wikipedia: Norm (mathematics)

norm

public double norm(int p)

Description copied from interface: Vector

Get the norm of a vector.

• When p is finite, \(\|v\|_p = \sum_{i}|v_i^p|^\frac{1}{p}\).
• When p is \(+\infty\) (Integer.MAX_VALUE), \|v\|_p = \max|v_i|.
• When p is \(-\infty\) (Integer.MIN_VALUE),\|v\|_p = \min|v_i|.

Specified by:

norm in interface Vector

Parameters:

p - an integer, Integer.MAX_VALUE, or Integer.MIN_VALUE

Returns:

\(\|v\|_p\)

angle

public double angle(Vector that)

Description copied from interface: Vector

Measure the angle, \(\theta\), between this and that. That is, \[ this \cdot that = \|this\| \times \|that\| \times \cos \theta \]

Specified by:

angle in interface HilbertSpace<Vector,Real>

Specified by:

angle in interface Vector

Parameters:

that - a vector

Returns:

the angle, \(\theta\), between this and that

ZERO

public SparseVector ZERO()

Description copied from interface: Vector

Get a 0-vector that has the same length as this vector.

Specified by:

ZERO in interface AbelianGroup<Vector>

Specified by:

ZERO in interface Vector

Returns:

the 0-vector

toArray

public double[] toArray()

Description copied from interface: Vector

Cast this vector into a 1D double[].

Specified by:

toArray in interface Vector

Returns:

a copy of all vector entries as a double[]

deepCopy

public SparseVector deepCopy()

Description copied from interface: DeepCopyable

The implementation returns an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.

Specified by:

deepCopy in interface DeepCopyable

Specified by:

deepCopy in interface Vector

Returns:

an independent (deep) copy of the instance

nNonZeros

public int nNonZeros()

Description copied from interface: SparseStructure

Get the number of non-zero entries in the structure.

Specified by:

nNonZeros in interface SparseStructure

Returns:

the number of non-zero entries in the structure

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object