public GaPoTNumBiversor[] GetPartsImpedance(GaPoTNumVector current, params int[] partLengthsArray)
{
var mvU = GetParts(partLengthsArray);
var mvI = current.GetParts(partLengthsArray).Inverse();
return(mvU.Gp(mvI));
}
public static GaPoTNumRotorsSequence CreateFromOrthonormalFrames(GaPoTNumFrame sourceFrame, GaPoTNumFrame targetFrame)
{
Debug.Assert(targetFrame.Count == sourceFrame.Count);
Debug.Assert(sourceFrame.IsOrthonormal() && targetFrame.IsOrthonormal());
Debug.Assert(sourceFrame.HasSameHandedness(targetFrame));
var rotorsSequence = new GaPoTNumRotorsSequence();
var sourceFrameVectors = new GaPoTNumVector[sourceFrame.Count];
for (var i = 0; i < sourceFrame.Count; i++)
{
sourceFrameVectors[i] = sourceFrame[i];
}
for (var i = 0; i < sourceFrame.Count - 1; i++)
{
var sourceVector = sourceFrameVectors[i];
var targetVector = targetFrame[i];
var rotor =
sourceVector.GetRotorToVector(targetVector);
rotorsSequence.AppendRotor(rotor);
for (var j = i + 1; j < sourceFrame.Count; j++)
{
sourceFrameVectors[j] = sourceFrameVectors[j].ApplyRotor(rotor);
}
}
return(rotorsSequence);
}
public static GaPoTNumMultivector CreateSimpleRotor(GaPoTNumVector sourceVector, GaPoTNumVector targetVector)
{
var invNorm1 = 1.0d / sourceVector.Norm();
var invNorm2 = 1.0d / targetVector.Norm();
var cosAngle = sourceVector.DotProduct(targetVector) * invNorm1 * invNorm2;
if (cosAngle == 1.0d)
{
return(new GaPoTNumMultivector().SetTerm(0, 1.0d));
}
//TODO: Handle the case for cosAngle == -1
var cosHalfAngle = Math.Sqrt(0.5d * (1.0d + cosAngle));
var sinHalfAngle = Math.Sqrt(0.5d * (1.0d - cosAngle));
var rotationBlade = sourceVector.Op(targetVector);
var rotationBladeScalar =
sinHalfAngle /
Math.Sqrt(Math.Abs(rotationBlade.Gp(rotationBlade).GetTermValue(0)));
var rotor = cosHalfAngle - rotationBladeScalar * rotationBlade;
//var rotationAngle = Math.Acos(DotProduct(v2) * invNorm1 * invNorm2) / 2;
//var unitBlade = rotationBlade.ScaleBy(rotationBladeInvNorm);
//var unitBladeNorm = unitBlade.Gp(unitBlade).TermsToText();
//var rotor= Math.Cos(rotationAngle) - (rotationBladeInvNorm * Math.Sin(rotationAngle)) * rotationBlade;
//Normalize rotor
//var invRotorNorm = 1.0d / Math.Sqrt(rotor.Gp(rotor.Reverse()).GetTermValue(0));
//rotor.IsSimpleRotor();
return(rotor);
}
public static GaPoTNumVector operator -(GaPoTNumVector v)
{
var result = new GaPoTNumVector();
foreach (var term in v._termsDictionary.Values)
{
result.AddTerm(term.TermId, -term.Value);
}
return(result);
}
public double DotProduct(GaPoTNumVector v)
{
var result = 0.0d;
foreach (var term1 in _termsDictionary.Values)
{
if (v._termsDictionary.TryGetValue(term1.TermId, out var term2))
{
result += term1.Value * term2.Value;
}
}
return(result);
}
public GaPoTNumVector GetProjectionOnFrame(GaPoTNumFrame frame)
{
var vector = new GaPoTNumVector();
foreach (var term in _termsDictionary.Values)
{
var i = term.TermId - 1;
var v = term.Value;
vector += v * frame[i];
}
return(vector);
}
public static GaPoTNumVector operator /(GaPoTNumVector v, double s)
{
s = 1.0d / s;
var result = new GaPoTNumVector();
foreach (var term in v._termsDictionary.Values)
{
result.AddTerm(
term.TermId,
term.Value * s
);
}
return(result);
}
public static GaPoTNumVector[] Subtract(this GaPoTNumVector[] vectorsList1, GaPoTNumVector[] vectorsList2)
{
if (vectorsList1.Length != vectorsList2.Length)
{
throw new InvalidOperationException();
}
var results = new GaPoTNumVector[vectorsList1.Length];
for (var i = 0; i < vectorsList1.Length; i++)
{
results[i] = vectorsList1[i].Subtract(vectorsList2[i]);
}
return(results);
}
public static GaPoTNumRotorsSequence CreateFromFrames(int baseSpaceDimensions, GaPoTNumFrame sourceFrame, GaPoTNumFrame targetFrame)
{
Debug.Assert(targetFrame.Count == sourceFrame.Count);
//Debug.Assert(IsOrthonormal() && targetFrame.IsOrthonormal());
Debug.Assert(sourceFrame.HasSameHandedness(targetFrame));
var rotorsSequence = new GaPoTNumRotorsSequence();
var pseudoScalar =
GaPoTNumMultivector
.CreateZero()
.SetTerm((1 << baseSpaceDimensions) - 1, 1.0d);
var sourceFrameVectors = new GaPoTNumVector[sourceFrame.Count];
var targetFrameVectors = new GaPoTNumVector[targetFrame.Count];
for (var i = 0; i < sourceFrame.Count; i++)
{
sourceFrameVectors[i] = sourceFrame[i];
targetFrameVectors[i] = targetFrame[i];
}
for (var i = 0; i < sourceFrame.Count - 1; i++)
{
var sourceVector = sourceFrameVectors[i];
var targetVector = targetFrameVectors[i];
var rotor =
sourceVector.GetRotorToVector(targetVector);
rotorsSequence.AppendRotor(rotor);
pseudoScalar = targetVector.ToMultivector().Lcp(pseudoScalar.Inverse());
for (var j = i + 1; j < sourceFrame.Count; j++)
{
sourceFrameVectors[j] =
sourceFrameVectors[j].ApplyRotor(rotor).GetProjectionOnBlade(pseudoScalar);
targetFrameVectors[j] =
targetFrameVectors[j].GetProjectionOnBlade(pseudoScalar);
}
}
return(rotorsSequence);
}
public GaPoTNumVector[] GetOffsetParts(params int[] partLengthsArray)
{
var results = new GaPoTNumVector[partLengthsArray.Length];
var termId1 = 1;
for (var i = 0; i < partLengthsArray.Length; i++)
{
var termId2 = termId1 + partLengthsArray[i] - 1;
results[i] = GetOffsetPartByTermIDsRange(termId1, termId2);
termId1 = termId2 + 1;
}
return(results);
}
public static GaPoTNumVector operator *(GaPoTNumVector v1, GaPoTNumBiversor bv2)
{
var vector = new GaPoTNumVector();
foreach (var term1 in v1.GetTerms())
{
foreach (var term2 in bv2.GetTerms())
{
var scalarValue = term1.Value * term2.Value;
if (term2.IsScalar)
{
vector.AddTerm(
term1.TermId,
scalarValue
);
continue;
}
if (term1.TermId == term2.TermId1)
{
vector.AddTerm(
term2.TermId2,
scalarValue
);
continue;
}
if (term1.TermId == term2.TermId2)
{
vector.AddTerm(
term2.TermId1,
-scalarValue
);
}
}
}
return(vector);
}
public GaPoTNumVector Inverse()
{
var norm2 = Norm2();
var result = new GaPoTNumVector();
if (norm2 == 0)
{
throw new DivideByZeroException();
}
var invNorm2 = 1.0d / norm2;
foreach (var term in _termsDictionary.Values)
{
result.SetTerm(
term.TermId,
term.Value * invNorm2
);
}
return(result);
}
public GaPoTNumVector Subtract(GaPoTNumVector v)
{
return(this - v);
}
public double GetAngle(GaPoTNumVector v)
{
return(Math.Acos(DotProduct(v) / Math.Sqrt(Norm2() * v.Norm2())));
}
private static GaPoTNumVector GaPoTNumParseVector(IronyParsingResults parsingResults, ParseTreeNode rootNode)
{
if (rootNode.ToString() != "spVector")
{
throw new SyntaxErrorException(parsingResults.ToString());
}
var vector = new GaPoTNumVector();
var vectorNode = rootNode;
foreach (var vectorElementNode in vectorNode.ChildNodes)
{
if (vectorElementNode.ToString() == "spTerm")
{
//Term Form
var value = double.Parse(vectorElementNode.ChildNodes[0].FindTokenAndGetText());
var id = int.Parse(vectorElementNode.ChildNodes[1].FindTokenAndGetText());
if (id < 0)
{
throw new SyntaxErrorException(parsingResults.ToString());
}
vector.AddTerm(id, value);
}
else if (vectorElementNode.ToString() == "spPolarPhasor")
{
//Polar Phasor Form
var magnitude = double.Parse(vectorElementNode.ChildNodes[1].FindTokenAndGetText());
var phase = double.Parse(vectorElementNode.ChildNodes[2].FindTokenAndGetText());
var id1 = int.Parse(vectorElementNode.ChildNodes[3].FindTokenAndGetText());
var id2 = int.Parse(vectorElementNode.ChildNodes[4].FindTokenAndGetText());
if (id1 < 0 || id2 != id1 + 1)
{
throw new SyntaxErrorException(parsingResults.ToString());
}
//Convert phase from degrees to radians
phase = phase.DegreesToRadians();
vector.AddPolarPhasor(id1, magnitude, phase);
}
else if (vectorElementNode.ToString() == "spRectPhasor")
{
//Rectangular Phasor Form
var xValue = double.Parse(vectorElementNode.ChildNodes[1].FindTokenAndGetText());
var yValue = double.Parse(vectorElementNode.ChildNodes[2].FindTokenAndGetText());
var id1 = int.Parse(vectorElementNode.ChildNodes[3].FindTokenAndGetText());
var id2 = int.Parse(vectorElementNode.ChildNodes[4].FindTokenAndGetText());
if (id1 < 0 || id2 != id1 + 1)
{
throw new SyntaxErrorException(parsingResults.ToString());
}
vector.AddRectPhasor(id1, xValue, yValue);
}
else
{
throw new SyntaxErrorException(parsingResults.ToString());
}
}
return(vector);
}
public GaPoTNumVector Add(GaPoTNumVector v)
{
return(this + v);
}
public GaPoTNumMultivector Op(GaPoTNumVector v)
{
return(Op(v.ToMultivector()));
}
public GaPoTNumVector Gp(GaPoTNumVector v)
{
return(this * v);
}
public GaPoTNumMultivector GetRotorToVector(GaPoTNumVector v2)
{
return(GaPoTNumMultivector.CreateSimpleRotor(this, v2));
}