public override void Calculate(CalculationItemStack calculationStack, bool isToAdd = true)
{
if (null == Value)
{
if (null == Numbers)
{
if (null != Symbolic)
{
List <SymbolValuePair> symbolValueList = calculationStack.GetAsSymbolValueList();
Numbers = Symbolic.Clone(symbolValueList);
}
else
{
if (null != Symbol)
{
List <SymbolValuePair> symbolValueList = calculationStack.GetAsSymbolValueList();
Value = (ValueItem)Symbol.Clone(symbolValueList);
return;
}
}
}
double value = Numbers.GetValue();
Value = new ValueItem();
Value.Value = value;
}
if (isToAdd)
{
calculationStack.Items.Add(this);
}
}
internal override Symbolic PreEval(Symbolic x)
{
Complex z = x.ToComplex();
if (z.Re < 0 || z.Im != 0.0)
{
return(new Complex(JMath.log(z.Re * z.Re + z.Im * z.Im) / 2, JMath.atan2(z.Im, z.Re)));
}
return(new Complex(JMath.log(z.Re)));
}
internal override Symbolic PreEval(Symbolic x)
{
Complex z = x.ToComplex();
if (z.Im == 0.0)
{
return(new Complex(Math.Tan(z.Re)));
}
return(( Symbolic )evalx(trigrule, z));
}
public virtual Algebraic rat_reverse(Algebraic expr)
{
if (gcd.Equals(Symbolic.ZERO))
{
return(expr);
}
Symbolic gc = gcd;
Algebraic s = new Exponential(Symbolic.ONE, Symbolic.ZERO, @var, Symbolic.ONE * gc);
return(expr.Value(t, s));
}
public SubstExp(Variable @var, Algebraic expr)
{
this.@var = @var;
ArrayList v = new ArrayList();
(new GetExpVars2(v)).SymEval(expr);
this.gcd = Exponential.exp_gcd(v, @var);
if (gcd.Equals(Symbolic.ZERO))
{
t = @var;
}
}
public override bool Smaller(Symbolic x)
{
var xu = x.ToComplex();
if (Re == xu.Re)
{
return(Im < xu.Im);
}
else
{
return(Re < xu.Re);
}
}
internal override Symbolic PreEval(Symbolic x)
{
Complex z = x.ToComplex();
double r = JMath.exp(z.Re);
if (z.Im != 0.0)
{
return(new Complex(r * Math.Cos(z.Im), r * Math.Sin(z.Im)));
}
return(new Complex(r));
}
internal override Symbolic PreEval(Symbolic x)
{
if (!x.IsInteger() || x.Smaller(Symbolic.ZERO))
{
throw new JasymcaException("Argument to factorial must be a positive integer, is " + x);
}
Algebraic r = Symbolic.ONE;
while (Symbolic.ONE.Smaller(x))
{
r = r * x;
x = ( Symbolic )(x - Symbolic.ONE);
}
return(( Symbolic )r);
}
internal override Symbolic PreEval(Symbolic x)
{
return(Equals(x, Symbolic.ZERO) ? Symbolic.ONE : Symbolic.ZERO);
}
internal override Algebraic SymEval(Symbolic x, Symbolic y)
{
return(x < y ? Symbolic.ONE : Symbolic.ZERO);
}
internal override Algebraic SymEval(Symbolic x, Symbolic y)
{
return(y < x ? Symbolic.ZERO : Symbolic.ONE);
}
internal override Symbolic PreEval(Symbolic x)
{
return(( Symbolic )SymEval(x));
}
public abstract bool Smaller(Symbolic a);
internal override Symbolic PreEval(Symbolic x)
{
return(null);
}
internal virtual Algebraic fzexakt(Symbolic x)
{
if (x < Symbolic.ZERO)
{
var r = fzexakt(( Symbolic )(-x));
if (r != null)
{
return(r.Conj());
}
return(r);
}
if (x.IsInteger())
{
if (x.ToInt() % 2 == 0)
{
return(Symbolic.ONE);
}
else
{
return(Symbolic.MINUS);
}
}
var qs = x + new Complex(0.5);
if (((Symbolic)qs).IsInteger())
{
if (((Symbolic)qs).ToInt() % 2 == 0)
{
return(Symbolic.IMINUS);
}
else
{
return(Symbolic.IONE);
}
}
qs = x * new Complex(4);
if (((Symbolic)qs).IsInteger())
{
Algebraic sq2 = FunctionVariable.Create("sqrt", new Complex(0.5));
switch (((Symbolic)qs).ToInt() % 8)
{
case 1:
return((Symbolic.ONE + Symbolic.IONE) / Symbolic.SQRT2);
case 3:
return((Symbolic.MINUS + Symbolic.IONE) / Symbolic.SQRT2);
case 5:
return((Symbolic.MINUS + Symbolic.IMINUS) / Symbolic.SQRT2);
case 7:
return((Symbolic.ONE + Symbolic.IMINUS) / Symbolic.SQRT2);
}
}
qs = x * new Complex(6);
if (((Symbolic)qs).IsInteger())
{
switch (((Symbolic)qs).ToInt() % 12)
{
case 1:
return((Symbolic.SQRT3 + Symbolic.IONE) / Symbolic.TWO);
case 2:
return((Symbolic.ONE + Symbolic.SQRT3) * Symbolic.IONE / Symbolic.TWO);
case 4:
return((Symbolic.SQRT3 * Symbolic.IONE + Symbolic.MINUS) / Symbolic.TWO);
case 5:
return((Symbolic.IONE - Symbolic.SQRT3) / Symbolic.TWO);
case 7:
return((Symbolic.IMINUS - Symbolic.SQRT3) / Symbolic.TWO);
case 8:
return((Symbolic.SQRT3 * Symbolic.IMINUS - Symbolic.ONE) / Symbolic.TWO);
case 10:
return((Symbolic.SQRT3 * Symbolic.IMINUS + Symbolic.ONE) / Symbolic.TWO);
case 11:
return((Symbolic.IMINUS + Symbolic.SQRT3) / Symbolic.TWO);
}
}
return(null);
}
public override bool Smaller(Symbolic x)
{
return(ToComplex().Smaller(x));
}
internal override Algebraic SymEval(Symbolic x, Symbolic y)
{
return(Equals(x, Symbolic.ONE) && Equals(y, Symbolic.ONE) ? Symbolic.ONE : Symbolic.ZERO);
}
public virtual Symbolic gcd(Symbolic x)
{
return(ToNumber().gcd(x.ToNumber()));
}
public SubstExp(Symbolic gcd, Variable @var)
{
this.gcd = gcd;
this.@var = @var;
}
internal override Symbolic PreEval(Symbolic x)
{
return(new Complex(Sfun.logGamma(x.ToComplex().Re)));
}
/// <summary>
/// If this FunctionGenerator can implement 'F', then this function should complete the (possible)
/// blanks in 'F'. This means:
/// - Fill in F.m_returnTypeName if it is empty
/// - Fill in F.m_argumentTypeNames (and m_argumentVariableNames) if it is empty.
///
/// As the return type is required, many functions will also compute the return value and other info
/// needed for generating the code inside this function. These intermediate values are then
/// stored in class variables so they can be reused in WriteFunction()
/// </summary>
public override void CompleteFGS()
{
NB_ARGS = m_fgs.NbArguments; // all arguments must be explicitly listed
// init argument pointers from the completed typenames (language sensitive);
m_fgs.InitArgumentPtrFromTypeNames(m_specification);
// get all function info
FloatType FT = m_specification.GetFloatType(m_fgs.FloatNames[0]);
bool computeMultivectorValue = true;
G25.CG.Shared.FuncArgInfo[] tmpFAI = G25.CG.Shared.FuncArgInfo.GetAllFuncArgInfo(m_specification, m_fgs, NB_ARGS, FT, m_specification.m_GMV.Name, computeMultivectorValue);
{ // compute return value
RefGA.Multivector no = GetOrigin(m_specification, m_fgs);
RefGA.Multivector ni = GetInfinity(m_specification, m_fgs);
// compose a vector value (the Euclidean part)
RefGA.Multivector vectorValue = RefGA.Multivector.ZERO;
if ((IsRandom(m_specification, m_fgs)) || (IsCoordBased(m_specification, m_fgs, FT)))
{
m_returnValue = no;
for (int i = 0; i < m_specification.m_dimension - 2; i++)
{
string bvName = "e" + (i + 1).ToString(); // todo: this assumes a fixed name for the basis vectors. Make these names options?
int bvIdx = m_specification.GetBasisVectorIndex(bvName);
if (bvIdx < 0)
{
throw new G25.UserException("Cannot find basis vector " + bvName, XML.FunctionToXmlString(m_specification, m_fgs));
}
RefGA.Multivector basisVector = RefGA.Multivector.GetBasisVector(bvIdx);
if (IsRandom(m_specification, m_fgs))
{
vectorValue = RefGA.Multivector.Add(vectorValue, RefGA.Multivector.gp(new RefGA.Multivector("ce" + (i + 1).ToString()), basisVector));
}
else
{
vectorValue = RefGA.Multivector.Add(vectorValue, RefGA.Multivector.gp(tmpFAI[i].MultivectorValue[0], basisVector));
}
}
}
else if (IsVectorBased(m_specification, m_fgs, FT))
{
vectorValue = tmpFAI[0].MultivectorValue[0];
m_vectorType = tmpFAI[0].Type;
}
else if (IsFlatPointBased(m_specification, m_fgs, FT))
{
m_flatPointType = tmpFAI[0].Type as G25.SMV;
RefGA.BasisBlade.InnerProductType lc = RefGA.BasisBlade.InnerProductType.LEFT_CONTRACTION;
RefGA.Multivector noni = RefGA.Multivector.OuterProduct(no, ni);
// scale = no^ni . pointPair
RefGA.Multivector scale =
RefGA.Multivector.InnerProduct(noni, tmpFAI[0].MultivectorValue[0], m_M, lc).ScalarPart();
if (m_G25M.m_round)
{
scale = scale.Round(1e-14);
}
// sphere = no . pointPair
RefGA.Multivector sphere = RefGA.Multivector.InnerProduct(no, tmpFAI[0].MultivectorValue[0], m_M, lc);
// normalizedSphere = sphere / scale
bool needToNormalize = (scale.HasSymbolicScalars() || (scale.RealScalarPart() != 1.0));
RefGA.Multivector normalizedSphere = (needToNormalize) ? RefGA.Multivector.gp(sphere, RefGA.Symbolic.UnaryScalarOp.Inverse(scale)) : sphere;
// keep only euclidean vectors
RefGA.Multivector euclMultivector = getSumOfUnitEuclideanBasisVectors();
// vector = sphere-noni
m_pointPairVectorValue = RefGA.Multivector.hp(normalizedSphere, euclMultivector);
// round vector
if (m_G25M.m_round)
{
m_pointPairVectorValue = m_pointPairVectorValue.Round(1e-14);
}
// get type
m_vectorType = (G25.SMV)G25.CG.Shared.SpecializedReturnType.FindTightestMatch(m_specification, m_pointPairVectorValue, FT);
if (m_vectorType == null)
{
throw new G25.UserException("Missing Euclidean vector type; cannot construct conformal point from " + m_fgs.ArgumentTypeNames[0], XML.FunctionToXmlString(m_specification, m_fgs));
}
// get 'value' (just a reference to the name of the variable where m_pointPairVectorValue will be stored.
bool pointer = false;
vectorValue = Symbolic.SMVtoSymbolicMultivector(m_specification, (G25.SMV)m_vectorType, VECTOR_NAME, pointer);
}
else
{
throw new G25.UserException("Invalid arguments specified.", XML.FunctionToXmlString(m_specification, m_fgs));
}
{ // add no and 0.5 vectorValue^2 ni
RefGA.Multivector vectorValueSquared = RefGA.Multivector.scp(vectorValue, vectorValue);
RefGA.Multivector niPart = RefGA.Multivector.gp(
RefGA.Multivector.gp(vectorValueSquared, ni), 0.5);
m_returnValue = RefGA.Multivector.Add(RefGA.Multivector.Add(no, vectorValue), niPart);
}
} // end of compute return value
// get name of return type
if (m_fgs.m_returnTypeName.Length == 0)
{
m_fgs.m_returnTypeName = G25.CG.Shared.SpecializedReturnType.GetReturnType(m_specification, m_cgd, m_fgs, FT, m_returnValue).GetName();
}
} // end of CompleteFGS()