DenseVector (SuanShuExtension API)

java.lang.Object
- com.numericalmethod.suanshu.vector.doubles.dense.DenseVector

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Vector>, BanachSpace<Vector,Real>, HilbertSpace<Vector,Real>, VectorSpace<Vector,Real>, Vector, java.io.Serializable

Direct Known Subclasses:

Gradient, SVEC
```
public class DenseVector
extends java.lang.Object
implements Vector
```
This class implements the standard, dense, double based vector representation.

See Also:

Wikipedia: Euclidean vector, Serialized Form

Constructor Summary

Constructors
Constructor and Description
`DenseVector(DenseVector vector)` Copy constructor.
`DenseVector(double... data)` Construct a vector, initialized by a `double[]`.
`DenseVector(int length)` Construct a vector.
`DenseVector(int[] data)` Construct a vector, initialized by a `int[]`.
`DenseVector(int length, double value)` Construct a vector, initialized by repeating a value.
`DenseVector(Matrix A)` Construct a vector from a column or row matrix.
`DenseVector(Vector v)` Cast any vector to a `DenseVector`.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`DenseVector`	`add(double scalar)` 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`.
`DenseVector`	`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.
`boolean`	`equals(java.lang.Object obj)`
`double`	`get(int i)` Get the value at position i.
`int`	`hashCode()`
`double`	`innerProduct(Vector that)` Inner product in the Euclidean space is the dot product.
`DenseVector`	`minus(double scalar)` 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(int p)` Get the norm of a vector.
`Vector`	`opposite()` Get the opposite of this vector.
`DenseVector`	`pow(double scalar)` Take the exponentiation of all entries in this vector, entry-by-entry.
`DenseVector`	`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 from, DenseVector replacement)` Replace a sub-vector `v[from : replacement.length]` by a replacement starting at position `from`.
`void`	`set(int i, 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()`
`DenseVector`	`ZERO()` Get a 0-vector that has the same length as this vector.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - DenseVector
```
public DenseVector(int length)
```
    Construct a vector.
    
    Parameters:
    
    length - the length of this vector
  - DenseVector
```
public DenseVector(int length,
                   double value)
```
    Construct a vector, initialized by repeating a value.
    
    Parameters:
    
    length - the length of this vector
    
    value - the initial value
  - DenseVector
```
public DenseVector(double... data)
```
    Construct a vector, initialized by a double[].
    
    Parameters:
    
    data - an 1D array
  - DenseVector
```
public DenseVector(int[] data)
```
    Construct a vector, initialized by a int[].
    
    Parameters:
    
    data - an 1D array
  - DenseVector
```
public DenseVector(Matrix A)
```
    Construct a vector from a column or row matrix.
    
    Parameters:
    
    A - a column or row matrix
  - DenseVector
```
public DenseVector(Vector v)
```
    Cast any vector to a DenseVector.
    
    Parameters:
    
    v - a vector
  - DenseVector
```
public DenseVector(DenseVector vector)
```
    Copy constructor.
    
    Parameters:
    
    vector - a vector
- 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
  - set
```
public void set(int i,
                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:
    
    i - the index of the entry to change. The indices are counting from 1, NOT 0.
    
    value - the value to change to
  - set
```
public void set(int from,
                DenseVector replacement)
```
    Replace a sub-vector v[from : replacement.length] by a replacement starting at position from.
    
    Parameters:
    
    from - the starting position of the replacement
    
    replacement - a vector for substitution
    
    Throws:
    
    java.lang.IllegalArgumentException - if the replacement length exceeds the end of this vector
  - get
```
public double get(int i)
```
    Description copied from interface: Vector
    
    Get the value at position i.
    
    Specified by:
    
    get in interface Vector
    
    Parameters:
    
    i - the position of a vector entry
    
    Returns:
    
    v[i]
  - 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:
    
    \(this - that\)
  - scaled
```
public DenseVector 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 VectorSpace<Vector,Real>
    
    Specified by:
    
    scaled in interface Vector
    
    Parameters:
    
    c - a constant
    
    Returns:
    
    \(c \times this\)
    
    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
  - 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:
    
    \(this / that\)
  - add
```
public DenseVector add(double scalar)
```
    Description copied from interface: Vector
    
    Add a constant to all entries in this vector.
    
    Specified by:
    
    add in interface Vector
    
    Parameters:
    
    scalar - a constant
    
    Returns:
    
    \(v + c\)
  - minus
```
public DenseVector minus(double scalar)
```
    Description copied from interface: Vector
    
    Subtract a constant from all entries in this vector.
    
    Specified by:
    
    minus in interface Vector
    
    Parameters:
    
    scalar - a constant
    
    Returns:
    
    \(v - c\)
  - pow
```
public DenseVector pow(double scalar)
```
    Description copied from interface: Vector
    
    Take the exponentiation of all entries in this vector, entry-by-entry.
    
    Specified by:
    
    pow in interface Vector
    
    Parameters:
    
    scalar - a constant
    
    Returns:
    
    \(v ^ s\)
  - 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:
    
    \(\|v\|_p\)
  - 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)
  - 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
  - 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
  - ZERO
```
public DenseVector 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 DenseVector 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
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object

Class DenseVector

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

DenseVector

DenseVector

DenseVector

DenseVector

DenseVector

DenseVector

DenseVector

Method Detail

size

set

set

get

add

minus

scaled

scaled

opposite

multiply

divide

add

minus

pow

norm

norm

angle

innerProduct

ZERO

toArray

deepCopy

toString

equals

hashCode