/// <summary>
/// This method can be used to test if the construction of the linear affine flux
/// was correct
/// </summary>
/// <returns>if the given nonlinear flux is representable as an affine linear function,
/// this should return 0 or a very small value</returns>
public double Test()
{
Vector2D X;
Vector2D n;
int L = m_Flux.ArgumentOrdering.Length;
int I = 20 * L;
Random rand = new Random();
double[] Uin = new double[L];
double[] Uout = new double[L];
Vector2D o;
Vector2D[] m1 = new Vector2D[L];
Vector2D[] m2 = new Vector2D[L];
double oSc;
double[] m1Sc = new double[L];
double[] m2Sc = new double[L];
double errsum = 0.0;
for (int i = 0; i < I; i++)
{
// populate Arguments with random values
// -------------------------------------
X.x = rand.NextDouble() * 10.0 - 5.0;
X.y = rand.NextDouble() * 10.0 - 5.0;
for (int l = L - 1; l >= 0; l--)
{
Uin[l] = rand.NextDouble() * 2.0 - 1.0;
Uout[l] = rand.NextDouble() * 2.0 - 1.0;
}
n.x = rand.NextDouble() * 2.0 - 1.0;
n.y = rand.NextDouble() * 2.0 - 1.0;
n.Normalize();
// test "BorderEdgeFlux"
// ---------------------
{
// "nonlinear" version
double nbe = m_Flux.BorderEdgeFlux(0.0, X, n, Uin);
// linear version
this.BorderEdgeFlux(0.0, X, n, m1Sc, out oSc);
double lbe = 0.0;
lbe += oSc;
for (int l = L - 1; l >= 0; l--)
{
lbe += m1Sc[l] * Uin[l];
}
nbe -= lbe; // now, "nbe" should be equal to "lbe"
errsum += Math.Abs(nbe);
}
// test "Flux"
// -----------
{
// "nonlinear" version
Vector2D nf = m_Flux.Flux(0.0, X, Uin);
// linear version
this.Flux(0.0, X, m1, out o);
Vector2D lf = new Vector2D();
lf.Acc(o);
for (int l = L - 1; l >= 0; l--)
{
lf.Acc(m1[l], Uin[l]);
}
nf.Sub(lf); // now, "nf" should be equal to "lf"
errsum += nf.Abs();
}
// test "Flux"
// -----------
{
// "nonlinear" version
double nif = m_Flux.InnerEdgeFlux(0.0, X, n, Uin, Uout);
// linear version
this.InnerEdgeFlux(0.0, X, n, m1Sc, m2Sc, out oSc);
double lif = 0.0;
lif += oSc;
for (int l = L - 1; l >= 0; l--)
{
lif += m1Sc[l] * Uin[l];
}
for (int l = L - 1; l >= 0; l--)
{
lif += m2Sc[l] * Uout[l];
}
nif -= lif; // now, "nif" should be equal to "lif"
errsum += Math.Abs(nif);
}
}
return(errsum);
}