NumberAlgebra.html

NumberAlgebra.java

// FILE. . . . . d:/hak/hlt/src/hlt/math/matrix/sources/NumberAlgebra.java
// EDIT BY . . . Hassan Ait-Kaci
// ON MACHINE. . Hak-Laptop
// STARTED ON. . Tue Dec  3 17:40:58 2019

package hlt.math.matrix;

package hlt.math.matrix documentation listing


import java.util.HashMap;
import java.util.Iterator;

This is an abstract class that can be subclassed by any class defining two dual operations sum and product on a pair of double values, as well as two nullary zero() and one() operations, a unary operation negation, and a binary difference operation, all returning a double.

It provides default implementations for all six as the six standard Java built-in floating-point arithmetic operations + and *, the double constants 0.0 and 1.0, and unary and binary -; i.e., sum(x,y) = x+y, product(x,y) = x*y, zero() = 0.0, one() = 1.0, negation(x) = -x, and difference(x,y) = x-y. These default methods are not final. So, unless redefined to other methods in a subclass, they are inherited.

To understand how the algebra classes are organized in this package and could be used by other packages, see this detailed description.

See also: MatrixPackageDescription, StandardAlgebra, MaxMinAlgebra, Matrix

Copyy: © by the author

Author: Hassan Aït-Kaci

Version: Last modified on Wed Dec 18 07:39:41 2019 by hak

abstract public class NumberAlgebra
{
  /* ************************************************************************ */

Constructors

Constructs a new NumberAlgebra with the default operations. It is not public.

  protected NumberAlgebra ()
  {
  }

This defines the default zero() of this NumberAlgebra as 0.0. It can be redefined in a subclass. It should always verify sum(x,zero()) = sum(zero(),x) = x, for any double x.

  public double zero ()
  {
    return 0.0;
  }

This defines the default one() of this NumberAlgebra as 1.0. It can be redefined in a subclass. It should always verify product(x,one()) = product(one(),x) = x, for any double.

  public double one ()
  {
    return 1.0;
  }

This defines the default sum of this NumberAlgebra. It can be redefined in a subclass. It should always verify sum(x,zero()) = sum(zero(),x) = x, for any double x.

  public double sum (double x, double y)
  {
    return x + y;	
  }

This defines the default product of this NumberAlgebra as *. It can be redefined in a subclass. It should always verify product(x,one()) = product(one(),x) = x, for any double.

  public double product (double x, double y)
  {
    return x * y;	
  }

This defines the default difference of this NumberAlgebra as binary -. It can be redefined in a subclass. It should always verify difference(zero(),x) = negation(x), for any double.

  public double difference (double x, double y)
  {
    return x - y;	
  }

This defines the default negation of this NumberAlgebra as binary -. It can be redefined in a subclass. It should always verify difference(zero(),x) = negation(x), for any double.

  public double negation (double x)
  {
    return -x;
  }

Return the default String form for this NumberAlgebra. It must redefined in any subclass.

  public String toString ()
  {
    return "Number Algebra";
  }

  /* ************************************************************************ */

Static Class Components and Algebra Manipulation Methods

This gathers all the paraphernalia necessary and/or useful for the control of parameterization of matrix operations with respect to redefinable arithmetic operations on a matrix double entries.

A private holder for the canonical StandardAlgebra object.

  static private StandardAlgebra standardAlgebra;

Return the canonical StandardAlgebra.

  static final public StandardAlgebra standardAlgebra ()
  {
    if (standardAlgebra == null)
      standardAlgebra = (StandardAlgebra)registeredAlgebra(new StandardAlgebra());

    return standardAlgebra;
  }

A private holder for the canonical MaxMinAlgebra object.

  static private MaxMinAlgebra maxMinAlgebra;

Return the canonical MaxMinAlgebra.

  static final public MaxMinAlgebra maxMinAlgebra ()
  {
    if (maxMinAlgebra == null)
      maxMinAlgebra = (MaxMinAlgebra)registeredAlgebra(new MaxMinAlgebra());

    return maxMinAlgebra;
  }

  /* ************************************************************************ */

This is the current NumberAlgebra in effect for all matrix operations. It is set by default to the canonical StandardAlgebra.

  static private NumberAlgebra currentAlgebra;

Return

  static final public NumberAlgebra currentAlgebra ()
  {
    if (currentAlgebra == null)
      currentAlgebra = standardAlgebra();

    return currentAlgebra;
  }

Set the current canonical NumberAlgebra on double matrix entries in effect for all matrix operations to the (canonical representative algebra of the) given NumberAlgebra.

  static final public void setCurrentAlgebra (NumberAlgebra algebra)
  {
    currentAlgebra = registeredAlgebra(algebra);
  }

Return the current number algebra on double matrix entries in effect for all matrix operations.

  static final public NumberAlgebra getCurrentAlgebra ()
  {
    if (currentAlgebra == null)
      throw new RuntimeException
	("There is no NumberAlgebra currently set.");

    return currentAlgebra;
  }

Set the current number algebra in effect for all matrix operations to the canonical StandardAlgebra.

  static final public void setStandardAlgebra ()
  {
    currentAlgebra = standardAlgebra();
  }

Set the current number algebra in effect for all matrix operations to the canonical MaxMinAlgebra.

  static final public void setMaxMinAlgebra ()
  {
    currentAlgebra = maxMinAlgebra();
  }

  /* ************************************************************************ */

This is the repository of all registered concrete NumberAlgebras. It is used to provide a unique canonical algebra object for a given algebra name. Thus, it associates a String (the algebra name) to the unique NumberAlgebra it denotes.

  static final private HashMap algebras = new HashMap();

Retrieve and return the unique canonical NumberAlgebra object representative sharing the given algebra's name. If none exists, register this algebra under its name (its toString() form), and return it.

  static final public NumberAlgebra registeredAlgebra (NumberAlgebra algebra)
  {
    String name = algebra.toString().intern();

    NumberAlgebra alg = (NumberAlgebra)algebras.get(name);

    if (alg != null)
      return alg;

    algebras.put(name,algebra);
    System.err.println("*** Registering new algebra: "+name);    

    return algebra;
  }

  static final public void showRegisteredAlgebras ()
  {
    System.out.println("\tCurrently registered number algebras:\n");    

    for (Iterator it = algebras.keySet().iterator(); it.hasNext();)
      System.out.println("\t"+it.next());

  System.out.println();
  }

}

This file was generated on Wed Dec 18 03:37:41 PST 2019 from file NumberAlgebra.java
by the hlt.language.tools.Hilite Java tool written by Hassan Aït-Kaci