/// <summary>
/// Normalize according to folowing rules
/// a) if there is a minus sign it will remain only in numerator
/// b) if there is common divisor, both numerator and denominator are divided by this common divisor
/// </summary>
/// <returns></returns>
public Rational <T, TPolicy> Normalize()
{
if (Policy.IsOne(Denominator))
{
return(this);
}
if (Policy.IsZero(Numerator))
{
return(new Rational <T, TPolicy>(Policy.Zero(), Policy.One()));
}
var n = Numerator;
var d = Denominator;
if ((Policy.IsBelowZero(n) && Policy.IsBelowZero(d)) || Policy.IsBelowZero(d))
{
n = Policy.Negate(n);
d = Policy.Negate(d);
}
var gcd = Policy.Gcd(Policy.Abs(n), d);
if (!Policy.IsOne(gcd))
{
n = Policy.Div(n, gcd);
d = Policy.Div(d, gcd);
}
return(new Rational <T, TPolicy>(n, d));
}
/// <summary>
/// Returns the column with the most negative coefficient in the objective function row.
/// </summary>
/// <param name="tableau"></param>
/// <returns></returns>
private int?GetPivotColumn(SimplexTableau <T, TPolicy> tableau)
{
T minValue = Policy.Zero();
int?minPos = null;
for (int i = tableau.NumObjectiveFunctions; i < tableau.Width - 1; i++)
{
T entry = tableau.GetEntry(0, i);
// check if the entry is strictly smaller than the current minimum
// do not use a ulp/epsilon check
if (Policy.IsBelowZero(Policy.Sub(entry, minValue)))
{
minValue = entry;
minPos = i;
// Bland's rule: chose the entering column with the lowest index
if (pivotSelection == PivotSelectionRule.BLAND && IsValidPivotColumn(tableau, i))
{
break;
}
}
}
return(minPos);
}
/// <summary>
/// True if |x - y| <= eps
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="eps"></param>
/// <returns></returns>
public static bool Equals(T x, T y, T eps)
{
return(Policy.IsBelowZero(Policy.Sub(Policy.Abs(Policy.Sub(y, x)), eps)));
}
