/// <summary>
/// Evaluates a Multivector to a summary of its expected value (-1, 0, 1).
/// The function uses a Symbolic.RandomSymbolicEvaluator to randomly evaluate
/// <paramref name="A"/>. If the results are consistently negative, zero or
/// positive then -1, 0 or 1 is returned. Otherwise an exception is thrown.
/// </summary>
/// <param name="A">The multivector to evaluate</param>
/// <returns>-1, 0 or 1</returns>
/// <remarks>
/// Used by Multivector.Exp(), Multivector.Cos() and Multivector.Sin() to see
/// if the input bivector has a scalar square.
/// </remarks>
public static double EvaluateRandomSymbolicToScalar(Multivector A)
{
double EPS = 1e-4;
int NB_ITER = 100;
int REQ = 98;
Symbolic.RandomSymbolicEvaluator RSE = new Symbolic.RandomSymbolicEvaluator(-100.0, 100.0);
int pos = 0, neg = 0, zero = 0;
for (int i = 0; i < NB_ITER; i++)
{
Multivector E = A.SymbolicEval(RSE);
double scalarPart = E.RealScalarPart();
Multivector theRest = Multivector.Subtract(E, scalarPart);
if (Math.Abs(theRest.Norm_e().RealScalarPart()) > Math.Abs(scalarPart) * EPS)
{
throw new Exception("Multivector did not evaluate to scalar");
}
if (scalarPart > EPS)
{
pos++;
}
else if (scalarPart < -EPS)
{
neg++;
}
else
{
zero++;
}
}
if (pos >= REQ)
{
return(1.0);
}
else if (zero >= REQ)
{
return(0.0);
}
else if (neg >= REQ)
{
return(-1.0);
}
else
{
throw new Exception("Multivector did not evaluate to a consistent value");
}
}
/// <summary>
/// Evaluates a Multivector to a summary of its expected value (-1, 0, 1).
/// The function uses a Symbolic.RandomSymbolicEvaluator to randomly evaluate
/// <paramref name="A"/>. If the results are consistently negative, zero or
/// positive then -1, 0 or 1 is returned. Otherwise an exception is thrown.
/// </summary>
/// <param name="A">The multivector to evaluate</param>
/// <returns>-1, 0 or 1</returns>
/// <remarks>
/// Used by Multivector.Exp(), Multivector.Cos() and Multivector.Sin() to see
/// if the input bivector has a scalar square.
/// </remarks>
public static double EvaluateRandomSymbolicToScalar(Multivector A)
{
double EPS = 1e-4;
int NB_ITER = 100;
int REQ = 98;
Symbolic.RandomSymbolicEvaluator RSE = new Symbolic.RandomSymbolicEvaluator(-100.0, 100.0);
int pos = 0, neg = 0, zero = 0;
for (int i = 0; i < NB_ITER; i++)
{
Multivector E = A.SymbolicEval(RSE);
double scalarPart = E.RealScalarPart();
Multivector theRest = Multivector.Subtract(E, scalarPart);
if (Math.Abs(theRest.Norm_e().RealScalarPart()) > Math.Abs(scalarPart) * EPS)
throw new Exception("Multivector did not evaluate to scalar");
if (scalarPart > EPS) pos++;
else if (scalarPart < -EPS) neg++;
else zero++;
}
if (pos >= REQ) return 1.0;
else if (zero >= REQ) return 0.0;
else if (neg >= REQ) return -1.0;
else throw new Exception("Multivector did not evaluate to a consistent value");
}
