public override Operand EvaluationStep(Context context)
{
Operand operand = base.EvaluationStep(context);
if (operand != null)
{
return(operand);
}
// To avoid infinite evaluation looping, we must apply...
// 1) vB = v.B + v^B, and
// 2) v^B = vB - v.B,
// ...according to rules that dictate when and where they're appropriate.
// Also to avoid infinite looping, the distributive property must take
// precedence over anything we do here.
// All reduction cases must be eliminated before it is safe to handle the expansion cases.
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA != null && bladeB != null && bladeA.Grade > 1 && bladeB.Grade > 1)
{
GeometricProduct geometricProduct;
if (context.useOperandCache)
{
geometricProduct = new GeometricProduct(new List <Operand>()
{
new Blade(new NumericScalar(1.0), bladeA.vectorList.ToList()), new Blade(new NumericScalar(1.0), bladeB.vectorList.ToList())
});
string key = geometricProduct.Print(Format.PARSEABLE, context);
Operand cachedResult = null;
if (!context.operandCache.GetStorage(key, ref cachedResult))
{
context.useOperandCache = false;
cachedResult = Operand.ExhaustEvaluation(geometricProduct, context);
context.useOperandCache = true;
context.operandCache.SetStorage(key, cachedResult);
}
return(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, cachedResult
}));
}
// Here our choice of which blade to reduce is arbitrary from a stand-point of correctness.
// However, we might converge faster by choosing the blade with smaller grade.
// Note there is also something arbitrary about how we're reducing the blades.
int j = bladeA.Grade <= bladeB.Grade ? i : i + 1;
Blade blade = operandList[j] as Blade;
Blade subBlade = blade.MakeSubBlade(0);
Blade vector = new Blade(blade.vectorList[0]);
geometricProduct = new GeometricProduct(new List <Operand>()
{
vector, subBlade
});
InnerProduct innerProduct = new InnerProduct(new List <Operand>()
{
vector.Copy(), subBlade.Copy()
});
operandList[j] = new Sum(new List <Operand>()
{
geometricProduct, new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), innerProduct
})
});
return(this);
}
}
// All reduction cases eliminated, it is now safe to handle some expansion cases.
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA == null || bladeB == null)
{
continue;
}
if ((bladeA.Grade == 1 && bladeB.Grade > 1) || (bladeA.Grade > 1 && bladeB.Grade == 1))
{
InnerProduct innerProduct = new InnerProduct(new List <Operand>()
{
bladeA, bladeB
});
OuterProduct outerProduct = new OuterProduct(new List <Operand>()
{
bladeA.Copy(), bladeB.Copy()
});
operandList[i] = new Sum(new List <Operand>()
{
innerProduct, outerProduct
});
operandList.RemoveAt(i + 1);
return(this);
}
}
// It is now safe to handle the remaining expansion cases.
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA == null || bladeB == null)
{
continue;
}
if (bladeA.Grade == 1 && bladeB.Grade == 1)
{
operandList.RemoveAt(i + 1);
GeometricProduct innerProduct = new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, context.BilinearForm(bladeA.vectorList[0], bladeB.vectorList[0])
});
Blade outerProduct = new Blade(new GeometricProduct(new List <Operand>()
{
bladeA.scalar.Copy(), bladeB.scalar.Copy()
}));
outerProduct.vectorList.Add(bladeA.vectorList[0]);
outerProduct.vectorList.Add(bladeB.vectorList[0]);
operandList[i] = new Sum(new List <Operand>()
{
innerProduct, outerProduct
});
return(this);
}
}
return(null);
}
public override Operand EvaluationStep(Context context)
{
Operand operand = base.EvaluationStep(context);
if (operand != null)
{
return(operand);
}
if (operandList.Count == 2)
{
Blade bladeA = operandList[0] as Blade;
Blade bladeB = operandList[1] as Blade;
if (bladeA != null && bladeB != null)
{
if (bladeA.Grade == 1 && bladeB.Grade == 1)
{
return(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, context.BilinearForm(bladeA.vectorList[0], bladeB.vectorList[0])
}));
}
else if (bladeA.Grade == 1 && bladeB.Grade > 1)
{
Sum sum = new Sum();
for (int i = 0; i < bladeB.vectorList.Count; i++)
{
Blade subBlade = bladeB.MakeSubBlade(i);
subBlade.scalar = new GeometricProduct(new List <Operand>()
{
new NumericScalar(i % 2 == 1 ? -1.0 : 1.0), bladeA.scalar, bladeB.scalar, context.BilinearForm(bladeA.vectorList[0], bladeB.vectorList[i])
});
sum.operandList.Add(subBlade);
}
return(sum);
}
else if (bladeA.Grade > 1 && bladeB.Grade == 1)
{
operandList[0] = bladeB;
operandList[1] = bladeA;
if (bladeA.Grade % 2 == 0)
{
operandList.Add(new NumericScalar(-1.0));
}
return(this);
}
else if (bladeA.Grade > 1 && bladeB.Grade > 1)
{
if (context.useOperandCache)
{
InnerProduct innerProduct = new InnerProduct(new List <Operand>()
{
new Blade(new NumericScalar(1.0), bladeA.vectorList.ToList()), new Blade(new NumericScalar(1.0), bladeB.vectorList.ToList())
});
string key = innerProduct.Print(Format.PARSEABLE, context);
Operand cachedResult = null;
if (!context.operandCache.GetStorage(key, ref cachedResult))
{
context.useOperandCache = false;
cachedResult = Operand.ExhaustEvaluation(innerProduct, context);
context.useOperandCache = true;
context.operandCache.SetStorage(key, cachedResult);
}
return(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, cachedResult
}));
}
if (bladeA.Grade <= bladeB.Grade)
{
return(new InnerProduct(new List <Operand>()
{
bladeA.MakeSubBlade(bladeA.Grade - 1), new InnerProduct(new List <Operand>()
{
new Blade(bladeA.vectorList[bladeA.Grade - 1]), bladeB
})
}));
}
else
{
return(new InnerProduct(new List <Operand>()
{
new InnerProduct(new List <Operand>()
{
bladeA, new Blade(bladeB.vectorList[0])
}), bladeB.MakeSubBlade(0)
}));
}
}
}
}
return(null);
}