// FILE. . . . . d:/hak/hlt/src/hlt/math/matrix/sources/MaxMinAlgebra.java
// EDIT BY . . . Hassan Ait-Kaci
// ON MACHINE. . Hak-Laptop
// STARTED ON. . Thu Dec 5 12:40:13 2019
package hlt.math.matrix;
/**
* package hlt.math.matrix
* documentation listing
*/
/**
* This is a concrete subclass of NumberAlgebra defining its
* operations as the algebra defining sum as Math.max,
* product as Math.min, zero() as
* NEGATIVE_INFINITY, and one() as
* POSITIVE_INFINITY. The negation and
* difference operations are undefined.
*
* @see NumberAlgebra
* @see Matrix
*
* @version Last modified on Fri Dec 13 13:12:50 2019 by hak
* @author Hassan Aït-Kaci
* @copyy © by the author
*/
public class MaxMinAlgebra extends NumberAlgebra
{
/**
* Return the zero of this MaxMinAlgebra as
* NEGATIVE_INFINITY. It verifies sum(x,zero()) =
* sum(zero(),x) = x, for any double
* x.
*/
public double zero ()
{
return Double.NEGATIVE_INFINITY;
}
/**
* Return the one of this algebra as
* POSITIVE_INFINITY. It verifies product(x,one())
* = product(one(),x) = x, for any double
* x.
*/
public double one ()
{
return Double.POSITIVE_INFINITY;
}
/**
* Return the sum of the arguments as Math.max.
* Verifies sum(x,zero()) = sum(zero(),x) =
* x, for any double x:
* max(x,NEGATIVE_INFINITY) =
* max(NEGATIVE_INFINITY,x) = x for any
* double x.
*/
public final double sum (double x, double y)
{
return Math.max(x,y);
}
/**
* Return the product of the arguments as Math.min.
* Verifies product(x,one()) = product(one(),x) =
* x, for any double x:
* min(x,POSITIVE_INFINITY) =
* min(POSITIVE_INFINITY,x) = x for any
* double x.
*/
public final double product (double x, double y)
{
return Math.min(x,y);
}
/**
* Throws a runtime exception to indicate that the negation
* operation is undefined for a this MaxMinAlgebra. It can be
* redefined to a well-defined operation in a subclass.
*/
public double negation (double x)
{
throw new RuntimeException
("The negation operation is undefined for a "+this);
}
/**
* Throws a runtime exception to indicate that the difference
* operation is undefined for a this MaxMinAlgebra. It can be
* redefined to a well-defined operation in a subclass.
*/
public double difference (double x, double y)
{
throw new RuntimeException
("The difference operation is undefined for a "+this);
}
/**
* Define a String form for this MaxMinAlgebra. It
* must be redefined in any subclass.
*/
public String toString ()
{
return "Max/Min Algebra";
}
}