Package dev.nm.algebra.linear.vector.doubles

Class SubVectorRef

java.lang.Object

dev.nm.algebra.linear.vector.doubles.SubVectorRef

All Implemented Interfaces:

Vector, AbelianGroup<Vector>, BanachSpace<Vector,Real>, HilbertSpace<Vector,Real>, VectorSpace<Vector,Real>, DeepCopyable

public class SubVectorRef
extends Object

Represents a sub-vector backed by the referenced vector, without data copying. Note that changes to the referenced vector will also be reflected in the sub-vector instance.

Constructor Summary

Constructors

Constructor	Description
SubVectorRef(Vector v, int from, int to)

Method Summary

Modifier and Type	Method	Description
Vector	add(double c)	Add a constant to all entries in this vector.
Vector	add(Vector that)	\(this + that\)
double	angle(Vector that)	Measure the angle, \(\theta\), between this and that.
Vector	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 i)	Get the value at position i.
double	innerProduct(Vector that)	Inner product in the Euclidean space is the dot product.
Vector	minus(double c)	Subtract a constant from all entries in this vector.
Vector	minus(Vector that)	\(this - that\)
Vector	multiply(Vector that)	Multiply this by that, entry-by-entry.
double	norm()	Compute the length or magnitude or Euclidean norm of a vector, namely, \(\|v\|\).
double	norm(double p)	Gets the \(L^p\)-norm \(\|v\|_p\) of this vector.
Vector	opposite()	Get the opposite of this vector.
Vector	pow(double c)	Take the exponentiation of all entries in this vector, entry-by-entry.
Vector	scaled(double c)	Scale this vector by a constant, entry-by-entry.
Vector	scaled(Real c)	Scale this vector by a constant, entry-by-entry.
void	set(int i, double value)	Deprecated.
int	size()	Get the length of this vector.
double[]	toArray()	Cast this vector into a 1D double[].
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

SubVectorRef

public SubVectorRef(Vector v,
                    int from,
                    int to)

Method Detail

size

public int size()

Description copied from interface: Vector

Get the length of this vector.

Returns:

the vector length

get

public double get(int i)

Description copied from interface: Vector

Get the value at position i.

Parameters:

i - the position of a vector entry

Returns:

v[i]

set

@Deprecated
public void set(int i,
                double value)

Deprecated.

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.

Parameters:

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

value - the value to change to

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

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:

\(v ^ c\)

scaled

public Vector 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 Vector 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 Vector

Specified by:

scaled in interface VectorSpace<Vector,Real>

Parameters:

c - a constant

Returns:

\(c \times this\)

See Also:

Wikipedia: Scalar multiplication

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)

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

toArray

public double[] toArray()

Description copied from interface: Vector

Cast this vector into a 1D double[].

Returns:

a copy of all vector entries as a double[]

deepCopy

public Vector 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.

Returns:

an independent (deep) copy of the instance

toString

public String toString()

Overrides:

toString in class Object

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:

\(this + that\)

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:

\(this - that\)

multiply

public Vector 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:

\(this \cdot that\)

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:

\(this / that\)

norm

public double norm(double p)

Description copied from interface: Vector

Gets the \(L^p\)-norm \(\|v\|_p\) of this vector.

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

Specified by:

norm in interface Vector

Parameters:

p - p ≥ 1, or Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY

Returns:

\(\|v\|_p\)

See Also:

Wikipedia: Norm (mathematics)

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 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:

the 0-vector