public static GaPoTNumMultivector ComplexEigenPairToBivector(Complex eigenValue, Vector eigenVector)
{
var realValue = eigenValue.Real;
var imagValue = eigenValue.Imaginary;
var realVector = new GaPoTNumVector(eigenVector.Select(c => c.Real));
var imagVector = new GaPoTNumVector(eigenVector.Select(c => c.Imaginary));
var scalar = realValue * realValue + imagValue * imagValue;
var angle = Math.Atan2(imagValue, realValue);
Console.WriteLine($"Eigen value real part: {realValue.ToString("G").GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine($"Eigen value imag part: {imagValue.ToString("G").GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine($"Eigen value length: {scalar.ToString("G").GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine($"Eigen value angle: {angle.RadiansToDegrees().ToString("G").GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("Eigen vector real part:");
Console.WriteLine(realVector.TermsToLaTeX().GetLaTeXDisplayEquation());
Console.WriteLine();
Console.WriteLine("Eigen vector imag part:");
Console.WriteLine(imagVector.TermsToLaTeX().GetLaTeXDisplayEquation());
Console.WriteLine();
var blade = realVector.Op(imagVector);
Console.WriteLine("Blade:");
Console.WriteLine(blade.ToLaTeXEquationsArray("B", @"\mu"));
Console.WriteLine();
var rotor = GaPoTNumMultivector.CreateSimpleRotor(angle, blade);
Console.WriteLine("Final rotor:");
Console.WriteLine(rotor.ToLaTeXEquationsArray("R", @"\mu"));
Console.WriteLine();
Console.WriteLine($"Is simple rotor? {rotor.IsSimpleRotor()}");
Console.WriteLine();
Console.WriteLine();
return(rotor);
}
public static void Execute3()
{
var bitsCount = 4;
//var mv = GaPoTNumMultivector.CreateZero().AddTerms(
// Enumerable.Range(0, 1 << bitsCount).Select(id => new GaPoTNumMultivectorTerm(id, 1))
//);
var mv = GaPoTNumMultivector
.CreateZero()
.AddTerm(3, 1)
.AddTerm(5, 2)
.AddTerm(0, -2);
Console.WriteLine(mv.ToText());
}
public static void Execute()
{
var n = 3;
var fbdFrame = GaPoTNumFrame.CreateFbdFrame(n);
var m1 = fbdFrame.GetMatrix(n - 1).GetLaTeXArray();
var m2 = fbdFrame.GetInnerProductsMatrix().GetLaTeXArray();
var m3 = fbdFrame.GetInnerAnglesInDegreesMatrix().GetLaTeXArray();
Console.WriteLine("FBD Frame Matrix:");
Console.WriteLine(m1);
Console.WriteLine();
Console.WriteLine("FBD Frame Inner Products Matrix:");
Console.WriteLine(m2);
Console.WriteLine();
Console.WriteLine("FBD Frame Inner Angles Matrix:");
Console.WriteLine(m3);
Console.WriteLine();
//return;
var sourceFrame = GaPoTNumFrame.CreateBasisFrame(n);
var uPseudoScalar = GaPoTNumMultivector
.CreateZero()
.SetTerm((1 << n) - 1, 1.0d);
for (var refVectorIndex = 0; refVectorIndex < n; refVectorIndex++)
{
Console.Write(@"\section{Reference vector: $\mu_" + (refVectorIndex + 1) + "$}");
Console.WriteLine();
var kirchhoffFrameBase = GaPoTNumFrame.CreateEmptyFrame();
var refVector = sourceFrame[refVectorIndex];
for (var i = 0; i < n; i++)
{
if (i == refVectorIndex)
{
continue;
}
kirchhoffFrameBase.AppendVector(sourceFrame[i] - refVector);
}
var kirchhoffFramesList =
kirchhoffFrameBase.GetFramePermutations();
var j = 1;
foreach (var kirchhoffFrame in kirchhoffFramesList)
{
Console.Write(@"\subsection{Kirchhoff Frame Permutation " + j + "}");
Console.WriteLine();
var targetFrame = kirchhoffFrame.GetOrthogonalFrame(true);
targetFrame.AppendVector(
-GaPoTNumUtils
.OuterProduct(targetFrame)
.Gp(uPseudoScalar.CliffordConjugate())
.GetVectorPart()
);
Debug.Assert(
targetFrame.IsOrthonormal()
);
Debug.Assert(
sourceFrame.HasSameHandedness(targetFrame)
);
DisplayFrames(
sourceFrame,
kirchhoffFrame,
targetFrame
);
j++;
}
}
}
public static GaPoTNumMultivector CreateBasisBlade(int idsPattern)
{
return(GaPoTNumMultivector.CreateZero().AddTerm(idsPattern, 1.0d));
}
public static void Execute()
{
var refVectorIndex = 0;
for (var n = 3; n <= 8; n++)
{
var uFrame =
GaPoTNumFrame.CreateBasisFrame(n);
var uPseudoScalar =
GaPoTNumMultivector
.CreateZero()
.SetTerm((1 << n) - 1, 1.0d);
var eFrame =
GaPoTNumFrame.CreateKirchhoffFrame(n, refVectorIndex);
var pFrame =
uFrame.GetProjectionOnFrame(eFrame);
var fbdFrame = GaPoTNumFrame.CreateFbdFrame(n);
var rotorsSequence = GaPoTNumRotorsSequence.CreateFromFrames(
n,
pFrame,
fbdFrame
);
//var pFrame1 = pFrame
// .GetSubFrame(0, n - 1)
// .PrependVector(GaPoTNumVector.CreateAutoVector(n))
// .GetOrthogonalFrame(true);
//var fbdFrame1 = fbdFrame
// .GetSubFrame(0, n - 1)
// .PrependVector(GaPoTNumVector.CreateAutoVector(n))
// .GetOrthogonalFrame(true);
//var rs = GaPoTNumRotorsSequence.Create(
// pFrame1.GetRotorsToFrame(fbdFrame1)
//);
var pFrame2 = rotorsSequence.Rotate(pFrame);
Console.Write(@"\section{Dimensions: " + n + "}");
Console.WriteLine();
Console.Write(@"\subsection{FBD Frame:}");
Console.WriteLine();
DisplayFrame(fbdFrame);
Console.Write(@"\subsection{Projected Frame:}");
Console.WriteLine();
DisplayFrame(pFrame);
Console.Write(@"\subsection{Rotated Projected Frame:}");
Console.WriteLine();
DisplayFrame(pFrame2);
Console.WriteLine("Rotors Sequence:");
for (var i = 0; i < rotorsSequence.Count; i++)
{
var rotorEquation =
rotorsSequence[i].ToLaTeXEquationsArray(
$"R_{{{i + 1}}}",
@"\mu"
);
Console.WriteLine(rotorEquation);
Console.WriteLine();
}
}
}
public static void Execute(int n)
{
var uFrame =
GaPoTNumFrame.CreateBasisFrame(n);
var cFrame =
GaPoTNumFrame.CreateGramSchmidtFrame(n, 0);
var rs1 =
GaPoTNumRotorsSequence.CreateFromOrthonormalFrames(cFrame, uFrame);
var rotationMatrix = (Matrix)Matrix.Build.DenseOfArray(
rs1.GetFinalMatrix(n).ToComplexArray()
);
var cFrameMatrix = (Matrix)Matrix.Build.DenseOfArray(
cFrame.GetMatrix().ToComplexArray()
);
//Make sure the rotation matrix is correct
var m = rotationMatrix.Multiply(cFrameMatrix);
var finalRotor = rs1.GetFinalRotor();
Console.WriteLine("Rotation matrix:");
Console.WriteLine(rotationMatrix);
Console.WriteLine();
Console.WriteLine("Final rotor:");
Console.WriteLine(finalRotor.ToLaTeXEquationsArray("R", @"\mu"));
Console.WriteLine();
Console.WriteLine("Rotated cFrame using matrix:");
Console.WriteLine("MatrixForm[" + m + "]");
Console.WriteLine();
rotationMatrix.EigenDecomposition(out var eigenValuesExpr, out var eigenVectorsExpr);
Console.WriteLine("Eigen values:");
foreach (var value in eigenValuesExpr)
{
Console.WriteLine(value);
}
Console.WriteLine();
Console.WriteLine("Eigen vectors:");
foreach (var vector in eigenVectorsExpr)
{
Console.WriteLine(vector);
}
Console.WriteLine();
var eigenRotorsArray = new GaPoTNumMultivector[n];
for (var i = 0; i < n; i++)
{
eigenRotorsArray[i] = ComplexEigenPairToBivector(
eigenValuesExpr[i],
eigenVectorsExpr[i]
);
}
//Make sure the blades of these rotors are eigen blades of the rotation matrix
for (var i = 0; i < n; i++)
{
var(angleExpr, blade) =
eigenRotorsArray[i].GetSimpleRotorAngleBlade();
var bladeDiff = (rs1.Rotate(blade) - blade).Round(7);
Console.WriteLine("Angle:");
Console.WriteLine(angleExpr.ToString("G").GetLaTeXDisplayEquation());
Console.WriteLine();
Console.WriteLine("Blade:");
Console.WriteLine(blade.ToLaTeXEquationsArray("b_1", @"\mu"));
Console.WriteLine();
Console.WriteLine("Rotated Blade - Blade:");
Console.WriteLine(bladeDiff.ToLaTeXEquationsArray("b_1", @"\mu"));
Console.WriteLine();
}
var diff =
(eigenRotorsArray[0].Gp(eigenRotorsArray[1]) -
eigenRotorsArray[1].Gp(eigenRotorsArray[0]))
.Round(7);
Console.WriteLine("Difference:");
Console.WriteLine(diff.TermsToLaTeX().GetLaTeXDisplayEquation());
Console.WriteLine();
var rs = GaPoTNumRotorsSequence.Create(
eigenRotorsArray[0],
eigenRotorsArray[1]
);
//var rs = GaPoTNumRotorsSequence.Create(
// eigenRotorsArray[0]
//);
var uFrame1 = rs.Rotate(cFrame);
Console.WriteLine("Rotated cFrame:");
for (var i = 0; i < n; i++)
{
Console.WriteLine(uFrame1[i].Round(7).TermsToLaTeX().GetLaTeXDisplayEquation());
Console.WriteLine();
}
}