mathtools.java

改进的多目标遗传算法聚类

	**/
	public static final double frac( double x ) {
		x = x - (long) x;
		if ( x < 0. )
			++x;
		
		return x;
	}

	/**
	*  Straight linear 1D interpolation between two points.
	*
	*  @param   x1,y1  Coordinates of the 1st point (the high point).
	*  @param   x2,y2  Coordinates of the 2nd point (the low point).
	*  @param   x      The X coordinate of the point for which we want to
	*                  interpolate to determine a Y coordinate.  Will
	*                  extrapolate if X is outside of the bounds of the 
	*                  point arguments.
	*  @return  The interpolated Y value corresponding to the input X
	*           value is returned.
	**/
	public static final double lineInterp( double x1, double y1, double x2,
						  double y2, double x ) {
		return ((y2 - y1) / (x2 - x1) * (x - x1) + y1);
	}

	/**
	*  Converts a positive decimal number to it's binary
	*  equivelant.
	*
	*  @param  decimal  The positive decimal number to be encoded in
	*                   binary.
	*  @param  bits     The bitset to encode the number in.
	**/
	public static final void dec2bin( int decimal, BitSet bits ) {
		if ( decimal < 0 )
			throw new IllegalArgumentException( "Cannot convert a negative number to binary." );
		
		int i = 0;
		int value = decimal;
		while ( value > 0 ) {
			if ( value % 2 > 0 )
				bits.set( i );
			
			else
				bits.clear( i );
			
			value /= 2;
			++i;
		}

		for ( i = i; i < bits.size(); ++i ) {
			bits.clear( i );
		}
	}

	/**
	*  Converts binary number to it's base 10 decimal equivelant.
	*
	*  @param   bits  The bitset that encodes the number to be converted.
	*  @return  Returns the decimal equivelent of the given binary number.
	**/
	public static final long bin2dec( BitSet bits ) {
		long value = 0;
		int length = bits.size();

		for ( int i = 0; i < length; ++i ) {
			if ( bits.get( i ) )
				value += pow2( i );
		}
		return value;
	}

    /**
    *  Return the hyperbolic cosine of the specified argument
    *  in the range MIN_LOG to MAX_LOG.
    *  The hyperbolic cosine is defined as:
    *      cosh(x) = (exp(x) + exp(-x))/2
    *
    *  @param  x  Value to determine hyperbolic cosine of.
    **/
    public static final double cosh(double x) {
        if (Double.isNaN(x))	return Double.NaN;
        if (x < 0)	x = -x;
        if (x > (MAX_LOG + LOG2))	return Double.POSITIVE_INFINITY;
        
        double y=0;
        if (x >= (MAX_LOG - LOG2)) {
            y = Math.exp(0.5*x);
            y = (0.5*y)*y;
            
        } else {
            y = Math.exp(x);
            y = 0.5*y + 0.5/y;
        }
        
        return y;
    }
    
    /**
    *  Return the hyperbolic sine of the specified argument
    *  in the range MIN_LOG to MAX_LOG.
    *  The hyperbolic sine is defined as:
    *      sinh(x) = (exp(x) - exp(-x))/2
    *
    *  @param  x  Value to determine hyperbolic sine of.
    **/
    public static final double sinh(double x) {
        if (Double.isNaN(x))	return Double.NaN;
        if (x == 0)	return 0;
        if ( (x > (MAX_LOG + LOG2)) || (x > -(MIN_LOG - LOG2)) ) {
            if (x > 0)
                return Double.POSITIVE_INFINITY;
            else
                return Double.NEGATIVE_INFINITY;
        }
        
        double a = Math.abs(x);
        if ( a >= (MAX_LOG - LOG2) ) {
            a = Math.exp(0.5*a);
            a = (0.5*a)*a;
            
        } else {
            a = Math.exp(a);
            a = 0.5*a + 0.5/a;
        }
        if (x < 0)
            a = -a;
       
        return a;
    }
    
    /**
    *  Returns the hyperbolic tangent of the specified argument
    *  in the range MIN_LOG to MAX_LOG.
    *  The hyperbolic tangent is defined as:
    *      tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2*x) + 1)
    *
    *  @param  x  Value to determine the hyperbolic tangent of.
    **/
    public static final double tanh(double x) {
        if (Double.isNaN(x))	return Double.NaN;
        if (x == 0)	return 0;
        double z = Math.abs(x);
        if (z > 0.5*MAX_LOG) {
            if (x > 0)
                return 1.0;
            else
                return -1.0;
        }
        
        double s = Math.exp(2*z);
        z = 1.0 - 2.0/(s + 1.0);
        if (x < 0)
            z = -z;
        
        return z;
	}
    
    /**
    *  Returns the inverse hyperbolic cosine of the specified argument.
    *  The inverse hyperbolic cosine is defined as:
    *      acosh(x) = log(x + sqrt( (x-1)(x+1) )
    *
    *  @param x  Value to return inverse hyperbolic cosine of.
    *  @throws IllegalArgumentException if x is less than 1.0. 
    **/
    public static final double acosh(double x) {
        if (Double.isNaN(x))		return Double.NaN;
        if (Double.isInfinite(x))	return x;
        if (x < 1.0)
            throw new IllegalArgumentException("x less than 1.0");
        
        double y = 0;
        if (x > 1.0E8) {
            y = Math.log(x) + LOG2;
            
        } else {
            double a = Math.sqrt( (x - 1.0)*(x + 1.0) );
            y = Math.log(x + a);
        }
        
        return y;
    }
    
    /**
    *  Returns the inverse hyperbolic sine of the specified argument.
    *  The inverse hyperbolic sine is defined as:
    *      asinh(x) = log( x + sqrt(1 + x*x) )
    *
    *  @param xx  Value to return inverse hyperbolic cosine of.
    **/
    public static final double asinh(double xx) {
        if (Double.isNaN(xx))	return Double.NaN;
        if (Double.isInfinite(xx))	return xx;
        if (xx == 0)	return 0;
        
        int sign = 1;
        double x = xx;
        if (xx < 0) {
            sign = -1;
            x = -xx;
        }
        
        double y = 0;
        if (x > 1.0E8) {
            y = sign*(Math.log(x) + LOG2);
            
        } else {
            double a = Math.sqrt(x*x + 1.0);
            y = sign*Math.log(x + a);
        }
    
        return y;
    }
    
    /**
    *  Returns the inverse hyperbolic tangent of the specified argument.
    *  The inverse hyperbolic tangent is defined as:
    *      atanh(x) = 0.5 * log( (1 + x)/(1 - x) )
    *
    *  @param x  Value to return inverse hyperbolic cosine of.
    *  @throws IllegalArgumentException if x is outside the range -1, to +1.
    **/
    public static final double atanh(double x) {
        if (Double.isNaN(x))	return Double.NaN;
        if (x == 0)	return 0;
        
        double z = Math.abs(x);
        if (z >= 1.0) {
            if (x == 1.0)
                return Double.POSITIVE_INFINITY;
            if (x == -1.0)
                return Double.NEGATIVE_INFINITY;
            
            throw new IllegalArgumentException("x outside of range -1 to +1");
        }
        
        if (z < 1.0E-7)	return x;
        
        double y = 0.5*Math.log((1.0 + x)/(1.0 - x));
        
        return y;
    }
    
    
	/**
	*  Returns the absolute value of "a" times the sign of "b".
	**/
	public static final double sign(double a, double b) {
		return Math.abs(a)*(b < 0 ? -1 : 1);
	}
	

	/**
	*  Returns the absolute value of "a" times the sign of "b".
	**/
	public static final float sign(float a, double b) {
		return Math.abs(a)*(b < 0 ? -1 : 1);
	}
	

	/**
	*  Returns the absolute value of "a" times the sign of "b".
	**/
	public static final long sign(long a, double b) {
		return Math.abs(a)*(b < 0 ? -1 : 1);
	}
	

	/**
	*  Returns the absolute value of "a" times the sign of "b".
	**/
	public static final int sign(int a, double b) {
		return Math.abs(a)*(b < 0 ? -1 : 1);
	}
	

	/**
	*  Used to test out the methods in this class.
	**/
	public static void main(String args[]) {
	
		System.out.println();
		System.out.println("Testing MathTools...");
		
		System.out.println("  2 is an " + (even(2) ? "even" : "odd") + " number.");
		System.out.println("  3 is an " + (odd(3) ? "odd" : "even") + " number.");
		System.out.println("  The square of 3.8 is " + sqr(3.8) + ".");
		System.out.println("  The cube root of 125 is " + cubeRoot(125) + ".");
		System.out.println("  The integer 3^7 is " + pow(3,7) + ".");
		System.out.println("  The integer 2^8 is " + pow2(8) + ".");
		System.out.println("  The double 10^-3 is " + pow10(-3) + ".");
		System.out.println("  The base 10 logarithm of 8 is " + log10(8) + ".");
		System.out.println("  The base 2 logarithm of 8 is " + log2(8) + ".");
		System.out.println("  1346.4667 rounded to the nearest 100 is " +
									roundToPlace(1346.4667, 2) + ".");
		System.out.println("  1346.4667 rounded up to the nearest 100 is " +
									roundUpToPlace(1346.4667, 2) + ".");
		System.out.println("  1346.4667 rounded down to the nearest 10 is " +
									roundDownToPlace(1346.4667, 1) + ".");
		System.out.println("  The GCD of 125 and 45 is " + greatestCommonDivisor(125,45) + ".");
		System.out.println("  The fractional part of 3.141593 is " + frac(3.141593) + ".");
        double x = 5;
        System.out.println("  The hyperbolic sine of " + (float)x + " = " + (float)sinh(x) + ".");
        System.out.println("  The hyperbolic cosine of " + (float)x + " = " + (float)cosh(x) + ".");
        x = -.25;
        System.out.println("  The hyperbolic tangent of " + (float)x + " = " + (float)tanh(x) + ".");
        x = cosh(5);
        System.out.println("  The inv. hyperbolic cosine of " + (float)x + " = " + (float)acosh(x) + ".");
        System.out.println("  The inv. hyperbolic sine of " + (float)x + " = " + (float)asinh(x) + ".");
        x = tanh(-0.25);
        System.out.println("  The inv. hyperbolic tangent of " + (float)x + " = " + (float)atanh(x) + ".");
		
		System.out.println("  4.56 with the sign of -6.33 is " + sign(4.56F, -6.33));

	}

}