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>

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

This class represents sparse vector which stores the non-zero values only.

Nested Class Summary

static class	SparseVector.Entry This class represents an entry in a SparseVector.
static class	SparseVector.Iterator This wrapper class overrides the Iterator.remove() method for throwing exception when it is called.

Constructor Summary

SparseVector(int size)
Create an instance of sparse vector of the specified size.

SparseVector(int size, int[] indices, double[] values)
Create an instance of sparse vector with non-zero values.

SparseVector(SparseVector that)
Copy constructor.

Method Summary

Vector	add(double scalar) v + s Add a scalar to all entries in the vector v.
Vector	add(Vector that) this + that
double	angle(Vector that) Measure the angle between this and that.
SparseVector	deepCopy() The implementation can return 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) this / that Divide this by that, entry-by-entry.
int	dropTolerance(double tolerance) Remove non-zero entries x whose magnitude is less than or equal to the tolerance, i.e., (|x| <= tolerance).
double	get(int index) Get the value at position index.
double	innerProduct(Vector that) Inner product in the Euclidean space is the dot product.
java.util.Iterator<SparseVector.Entry>	iterator()
Vector	minus(double scalar) v - s Subtract a scalar from all entries in the vector v.
Vector	minus(Vector that) this - that
Vector	multiply(Vector v) this * that Multiply this by that, entry-by-entry.
int	nnz() Get the number of non-zero entries in the matrix.
double	norm() Compute the length or magnitude or Euclidean norm of a vector, namely, ||v||.
double	norm(int p) Compute the norm of a vector.
Vector	opposite() Get the opposite of this vector.
Vector	pow(double scalar) v ^ s Take the exponentiation of all entries in the vector v by a scalar.
Vector	scaled(double scalar) scalar * this Here is a way to get a unit version of the vector: vector.scaled(1. / vector.norm())
Vector	scaled(Real scalar) scalar * that If scalar is 1, it simply returns itself.
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() Get a copy of all vector entries in the form of a 1D double[] array.
java.lang.String	toString()
Vector	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)

Create an instance of sparse vector of the specified size.

Parameters:

size - the size of the vector

SparseVector

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

Create an instance of sparse vector with non-zero values.

Parameters:

size - the size of the vector

indices - the indices of the input 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 length of this vector

get

public double get(int index)

Description copied from interface: Vector

Get the value at position index.

Specified by:

get in interface Vector

Parameters:

index - position of a vector entry

Returns:

v[index]

set

public void set(int index,
                double value)

Description copied from interface: Vector

Change the value of an entry in this vector.

The indices are, for example,: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ......

Note that we count from 1, NOT 0.

This is the only method that may change the entries of a vector.

Specified by:

set in interface Vector

Parameters:

index - the entry to change

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:

a vector which is the sum of this and 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:

a vector which is the difference between this and that

multiply

public Vector multiply(Vector v)

Description copied from interface: Vector

this * that

Multiply this by that, entry-by-entry.

Specified by:

multiply in interface Vector

Parameters:

v - a vector

Returns:

this * that, entry-by-entry

divide

public Vector divide(Vector that)

Description copied from interface: Vector

this / that

Divide this by that, entry-by-entry.

Specified by:

divide in interface Vector

Parameters:

that - a vector

Returns:

this / that, entry-by-entry

add

public Vector add(double scalar)

Description copied from interface: Vector

v + s

Add a scalar to all entries in the vector v.

Specified by:

add in interface Vector

Parameters:

scalar - s

Returns:

v + s

minus

public Vector minus(double scalar)

Description copied from interface: Vector

v - s

Subtract a scalar from all entries in the vector v.

Specified by:

minus in interface Vector

Parameters:

scalar - s

Returns:

v - s

innerProduct

public double innerProduct(Vector that)

Description copied from interface: Vector

Inner product in the Euclidean space is the dot product.

Dot product is an operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity.

Specified by:

innerProduct in interface HilbertSpace<Vector,Real>

Specified by:

innerProduct in interface Vector

Parameters:

that - a vector

Returns:

dot product of two vectors, this and that, i.e.,

this ∙ that

See Also:

Wikipedia: Dot product

pow

public Vector pow(double scalar)

Description copied from interface: Vector

v ^ s

Take the exponentiation of all entries in the vector v by a scalar.

Specified by:

pow in interface Vector

Parameters:

scalar - s

Returns:

v ^ s

scaled

public Vector scaled(double scalar)

Description copied from interface: Vector

scalar * this

Here is a way to get a unit version of the vector:

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

Specified by:

scaled in interface Vector

Parameters:

scalar - a double scalar

Returns:

a vector which is scaled by scalar

scaled

public Vector scaled(Real scalar)

Description copied from interface: Vector

scalar * that

If scalar is 1, it simply returns itself. So, 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:

scalar - a Real number scalar

Returns:

a vector which is scaled by scalar

See Also:

Wikipedia: Scalar multiplication

opposite

public Vector 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

Compute the norm of a vector. When p is finite,

 |v|p = ∑ [(abs(vi)^p)]^(1/p)
 

When p is +∞ (Integer.MAX_VALUE),

 |v|p = max(abs(vi))
 

When p is -∞ (Integer.MIN_VALUE),

 |v|p = min(abs(vi))
 

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 between this and that.

That is,

this ∙ that = ||this|| * ||that|| cos(angle)

Specified by:

angle in interface HilbertSpace<Vector,Real>

Specified by:

angle in interface Vector

Parameters:

that - a vector

Returns:

the angle between this and that

ZERO

public Vector 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:

a 0-vector, which has the same length as this vector

toArray

public double[] toArray()

Description copied from interface: Vector

Get a copy of all vector entries in the form of a 1D double[] array.

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 can return 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

nnz

public int nnz()

Description copied from interface: SparseStructure

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

Specified by:

nnz in interface SparseStructure

Returns:

the number of non-zero entries in the matrix

dropTolerance

public int dropTolerance(double tolerance)

Description copied from interface: SparseStructure

Remove non-zero entries x whose magnitude is less than or equal to the tolerance, i.e., (|x| <= tolerance).

Specified by:

dropTolerance in interface SparseStructure

Parameters:

tolerance - the tolerance for non-zeros

Returns:

the number of non-zeros removed

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object