/// <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");
}
}
static void Main(string[] args)
{
System.Console.WriteLine("Hello world");
{
ArrayList AL = new ArrayList();
AL.Add(new BasisBlade(1, 1.0, "a1"));
AL.Add(new BasisBlade(2, 1.0, "a2"));
Multivector A = new Multivector(AL);
System.Console.WriteLine("A = " + A.ToString());
ArrayList BL = new ArrayList();
BL.Add(new BasisBlade(2, 1.0, "b1"));
BL.Add(new BasisBlade(3, 1.0, "b2"));
Multivector B = new Multivector(BL);
System.Console.WriteLine("B = " + B.ToString());
Multivector AB = Multivector.gp(A, B);
System.Console.WriteLine("AB = " + AB.ToString());
Symbolic.HashtableSymbolicEvaluator HSE = new Symbolic.HashtableSymbolicEvaluator();
HSE.Add("a1", 3.0);
HSE.Add("a2", -2.0);
HSE.Add("b1", 4.0);
HSE.Add("b2", 1.0);
Multivector ABeval = AB.SymbolicEval(HSE);
System.Console.WriteLine("ABeval = " + ABeval.ToString());
return;
}
Metric M;
try
{
// Conformal metric (no, e1, e2, e3, ni)
/* int N = 5;
* double[] EVM = new double[]{
* -0.707107, -0.707107, 0, 0, 0,
* 0, 0, 0, 0, 1,
* 0, 0, 1, 0, 0,
* 0, 0, 0, -1, 0,
* -0.707107, 0.707107, 0, 0, 0};
*
* double[] EV = new double[] { -1.0, 1.0, 1.0, 1.0, 1.0 };*/
/*// Euclidean metric (e1, e2, e3)
* double[] m = new double[]{
* 1.0, 0.0, 0.0,
* 0.0, 1.0, 0.0,
* 0.0, 0.0, 1.0};*/
// Conformal metric (no, e1, e2, e3, ni)
double[] m = new double[] {
0.0, 0.0, 0.0, 0.0, -1.0,
0.0, 1.0, 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 0.0, 1.0, 0.0,
-1.0, 0.0, 0.0, 0.0, 0.0
};
M = new Metric(m);
}
catch (Exception E)
{
System.Console.WriteLine(E.ToString());
return;
}
/*{
* ArrayList AL = new ArrayList();
* AL.Add(new BasisBlade(1 << 3)); // e1
* Multivector A = new Multivector(AL);
*
* ArrayList BL = new ArrayList();
* BL.Add(new BasisBlade(1 << 3)); // e1
* Multivector B = new Multivector(BL);
*
* Multivector V = Multivector.InnerProduct(A, B, M, BasisBlade.InnerProductType.LEFT_CONTRACTION);
*
* System.Console.WriteLine("A = " + A.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("B = " + B.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("A . B = " + V.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* }*/
/* ArrayList AL = new ArrayList();
* // AL.Add(new BasisBlade(2 + 16, 1.0, "a_e1ni"));
* // AL.Add(new BasisBlade(4 + 16, 1.0, "a_e2ni"));
* // AL.Add(new BasisBlade(8 + 16, 1.0, "a_e3ni"));
* // AL.Add(new BasisBlade(2 + 4, 1.0, "a_e1e2"));
* // AL.Add(new BasisBlade(4 + 8, 1.0, "a_e2e3"));
* // AL.Add(new BasisBlade(8 + 2, 1.0, "a_e1e3"));
* // AL.Add(new BasisBlade(1 + 16, 1.0, "a_noni"));
* AL.Add(new BasisBlade(2 + 16, 1.0));
* AL.Add(new BasisBlade(4 + 16, 2.0));
* AL.Add(new BasisBlade(8 + 16, 3.0));
* AL.Add(new BasisBlade(2 + 4, 4.0));
* AL.Add(new BasisBlade(4 + 8, 5.0));
* AL.Add(new BasisBlade(8 + 2, 6.0));
* Multivector A = new Multivector(AL);
*
* Multivector Aexp = A.Exp(M, false, 0.0);
*
* System.Console.WriteLine("A = " + A.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }) + ",");
* System.Console.WriteLine("expA = " + Aexp.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }) + ",");*/
// Symbolic.HashtableSymbolicEvaluator HSE = new Symbolic.HashtableSymbolicEvaluator();
// HSE.Add("a_e1ni", 1.0);
// HSE.Add("a_e2ni", 2.0);
// HSE.Add("a_e3ni", 3.0);
// HSE.Add("a_e1e2", 4.0);
// HSE.Add("a_e2e3", 5.0);
// HSE.Add("a_e1e3", 6.0);
// HSE.Add("a_noni", 6.0);
// System.Console.WriteLine("A = " + A.SymbolicEval(HSE).ToString(new string[] { "no", "e1", "e2", "e3", "ni" }) + ",");
// System.Console.WriteLine("expA = " + Aexp.SymbolicEval(HSE).ToString(new string[] { "no", "e1", "e2", "e3", "ni" }) + ",");
/* // compute square
* Multivector A2 = Multivector.gp(A, A, M);
* System.Console.WriteLine("A2 = " + A2.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
*
*
* // evaluate with random coords
* Symbolic.RandomSymbolicEvaluator RSE = new Symbolic.RandomSymbolicEvaluator(-100.0, 100.0);
* int pos = 0, neg = 0, zero = 0;
* for (int i = 0; i < 1; i++)
* {
* Multivector MV = A2.SymbolicEval(RSE);
* double val = MV.RealScalarPart();
* System.Console.WriteLine("MV = " + MV);
* System.Console.WriteLine("val = " + val);
* if (val > 1e-7) pos++;
* else if (val < -1e-7) neg++;
* else zero++;
* RSE.reset();
* }
* System.Console.WriteLine("pos = " + pos);
* System.Console.WriteLine("neg = " + neg);
* System.Console.WriteLine("zero = " + zero);*/
/*
* ArrayList AL = new ArrayList();
* AL.Add(new BasisBlade(1 << 0, 1.0, "a_e1"));
* AL.Add(new BasisBlade(1 << 1, 1.0, "a_e2"));
* AL.Add(new BasisBlade(1 << 2, 1.0, "a_e3"));
* Multivector A = new Multivector(AL);
*
* ArrayList BL = new ArrayList();
* BL.Add(new BasisBlade(1 << 0, 1.0, "b_e1"));
* BL.Add(new BasisBlade(1 << 1, 1.0, "b_e2"));
* BL.Add(new BasisBlade(1 << 2, 1.0, "b_e3"));
* Multivector B = new Multivector(BL);
*
* System.Console.WriteLine("A = " + A.ToString());
* System.Console.WriteLine("B = " + B.ToString());
* System.Console.WriteLine("A B = " + Multivector.gp(A, B).ToString());
*/
/*
* BasisBlade Z = new BasisBlade(1 << 0, 1.0, new Object[][] {
* new Object[] { "blah", "aaaarg", 3.0, 2.0, 1 },
* new Object[] { "bloooey", 'x', "crap", true, false},
* new Object[] { "blah", "aaaarg", -10.0, 1 }
* });
*
* System.Console.WriteLine("Z = " + Z.ToString());
* return;*/
// OK: now check for harder objects . . .
/*
* Symbolic.HashtableSymbolicEvaluator HSE = new Symbolic.HashtableSymbolicEvaluator();
* HSE.Add("a_e1", 1.0);
* HSE.Add("a_e2", 2.0);
* HSE.Add("a_e3", 3.0);
* //Symbolic.RandomSymbolicEvaluator HSE = new Symbolic.RandomSymbolicEvaluator(-100.0, 100.0);
*
*
* ArrayList AL = new ArrayList();
* //AL.Add(new BasisBlade(1 << 0, 1.0, "a_no"));
* AL.Add(new BasisBlade(1 << 1, 1.0, "a_e1"));
* AL.Add(new BasisBlade(1 << 2, 1.0, "a_e2"));
* AL.Add(new BasisBlade(1 << 3, 1.0, "a_e3"));
* AL.Add(new BasisBlade(1 << 4, 1.0, "a_e1"));
* Multivector A = new Multivector(AL);
* A = Multivector.gp(A, Symbolic.ScalarOp.Exp(new Multivector(new BasisBlade(0, 1.0, "a_e2"))));
* System.Console.WriteLine("A = " + A.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* // todo: check if exp, etc is working, then check why not collapse (by Multivector simplify, basis blade simplify) to single scalar value . .
* Multivector Ae = A.SymbolicEval(HSE);
* System.Console.WriteLine("Ae = " + Ae.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* return;
*
* ArrayList BL = new ArrayList();
* // BL.Add(new BasisBlade(1 << 0, 1.0));//, "b_no"));
* BL.Add(new BasisBlade(1 << 1, -2.0));//, "b_e1"));
* BL.Add(new BasisBlade(1 << 2, 3.0));//, "b_e2"));
* BL.Add(new BasisBlade(1 << 3, -4.0));//, "b_e3"));
* // BL.Add(new BasisBlade(1 << 4, 1.0));//, "b_ni"));
* Multivector B = new Multivector(BL);
*
*
* A = Multivector.op(A, B);
*
* B = Multivector.gp(A, A);
*
* System.Console.WriteLine("A = " + A.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("B = " + B.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
*
* // how to know whether outcome of symbolic computation is positive, negative or zero???
* // simply fill in values for random variables?
*
*
* //Multivector unitA = A.Unit_r(M);
* //System.Console.WriteLine("unitA = " + unitA.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
*/
/* Multivector ApAgB = Multivector.Add(Multivector.Add(A, Multivector.gp(A, B, M)), Multivector.gp(Multivector.GetPseudoscalar(4), 0.01));
*
* // still testing . . .
* System.Console.WriteLine("ApAgB = " + ApAgB.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* int g = ApAgB.LargestGradePartIndex();
*
* System.Console.WriteLine("Largest grade part = " + g);
* System.Console.WriteLine("Largest grade part = " + ApAgB.ExtractGrade(g).ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
*
* System.Console.WriteLine("Top grade part = " + ApAgB.TopGradePartIndex(0.02));*/
/*
* BasisBlade se1 = new BasisBlade(1 << 1, 1.0, "ae1");
* BasisBlade se2 = new BasisBlade(1 << 2, 1.0, "ae2");
* BasisBlade X = BasisBlade.op(se1, se2);
* System.Console.WriteLine("se1 = " + se1);
* System.Console.WriteLine("se2 = " + se2);
* System.Console.WriteLine("X = " + X);
*/
/*
* Multivector no = new Multivector(new BasisBlade(1, 1.0));
* Multivector ni = new Multivector(new BasisBlade(1 << 4, 1.0));
* Multivector noni = Multivector.GeometricProduct(no, ni, M);
*
* System.Console.WriteLine("no = " + no.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("ni = " + ni.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("noni = " + noni.ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("noni2 = " + noni.ExtractGrade(2).ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
* System.Console.WriteLine("dual(noni) = " + noni.Dual(M).ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
*
* System.Console.WriteLine("dual(I) = " + Multivector.GetPseudoscalar(5).Dual(M).ToString(new string[] { "no", "e1", "e2", "e3", "ni" }));
*/
/*BasisBlade no = new BasisBlade(1);
* BasisBlade ni = new BasisBlade(1 << 4);
*
* System.Console.WriteLine("no = " + no);
* System.Console.WriteLine("ni = " + ni);
*
* System.Collections.ArrayList L = BasisBlade.GeometricProduct(ni, no, M);
* System.Console.WriteLine("L = " + BasisBlade.ToString(L, new string[] {"no", "e1", "e2", "e3", "ni"}));
*/
/*
* BasisBlade A = new BasisBlade(1 | 4, 2.0);
* BasisBlade B = new BasisBlade(2, 2.0);
* BasisBlade C = new BasisBlade(1 | 4, 3.0);
* BasisBlade D =new BasisBlade(1, 1.0);
* System.Collections.ArrayList L = new System.Collections.ArrayList();
* L.Add(A); L.Add(B); L.Add(C); L.Add(D); L.Add(new BasisBlade(2 | 4, 2.0));
*
* System.Console.WriteLine("Before: ");
* foreach (BasisBlade BB in L)
* {
* System.Console.WriteLine(BB.ToString());
* }
* L = BasisBlade.Simplify(L);
* System.Console.WriteLine("After: ");
* foreach (BasisBlade BB in L)
* {
* System.Console.WriteLine(BB.ToString());
* }
*/
// System.Console.WriteLine("A = " + A);
// System.Console.WriteLine("B = " + B); // .ToString(new string[] { "no", "e1", "ni" })
// System.Console.WriteLine("A ^ B = " + (A ^ B));
/* try
* {
* double[][] MA = new double[][]{
* new double[]{0.0, 0.0, 0.0, 0.0, -1.0},
* new double[]{0.0, 1.0, 0.0, 0.0, 0.0},
* new double[]{0.0, 0.0, 1.0, 0.0, 0.0},
* new double[]{0.0, 0.0, 0.0, 1.0, 0.0},
* new double[]{-1.0, 0.0, 0.0, 0.0, 0.0}};
* new Metric(MA);
* }
* catch (Exception E)
* {
* System.Console.WriteLine(E.ToString());
* }*/
/*
*
* double[] A = new double[]{
* 1.0, 0.0, 0.0,
* 0.0, 1.0, 0.0,
* 0.0, 0.0, 1.0};
* int nbRows = 3;
* int nbColumns = 3;
* bool columnWise = false;
* dnAnalytics.LinearAlgebra.Matrix M = dnAnalytics.LinearAlgebra.MatrixBuilder.CreateMatrix(A, nbRows, nbColumns, columnWise);
*
* System.Console.WriteLine("Hi hoi!" + M);
*
*/
}
/// <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");
}