public static GaPoTNumVector TermsArrayToVector(int rowsCount, int columnsCount, int[] rowIndicesArray, int[] columnIndicesArray, double[] valuesArray)
{
var matrixData = GaNumMatlabSparseMatrixData.CreateMatrix(rowsCount, columnsCount, rowIndicesArray, columnIndicesArray, valuesArray);
var mv = new GaPoTNumVector();
mv.AddTerms(matrixData);
return(mv);
}
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($"Is simple rotor? {rotor.IsSimpleRotor()}");
Console.WriteLine();
Console.WriteLine();
return(rotor);
}
public static void DisplayFrame(GaPoTNumFrame frame)
{
var n = frame.Count;
Console.WriteLine("Frame Matrix:");
Console.WriteLine(frame.GetMatrix().GetLaTeXArray());
Console.WriteLine();
Console.WriteLine("Frame Inner Products Matrix:");
Console.WriteLine(frame.GetInnerProductsMatrix().GetLaTeXArray());
Console.WriteLine();
Console.WriteLine("Frame Inner Angles Matrix:");
Console.WriteLine(frame.GetInnerAnglesMatrix().GetLaTeXArray());
Console.WriteLine();
Console.WriteLine("Auto Vector Projection on Frame:");
Console.WriteLine("$" + GaPoTNumVector.CreateAutoVector(n).GetProjectionOnFrame(frame).TermsToLaTeX() + "$");
Console.WriteLine();
}
public static void DisplayFrame(GaPoTNumFrame sourceFrame, GaPoTNumFrame targetFrame)
{
var n = targetFrame.Count;
var matrixExpr = targetFrame.GetMatrix(n);
var orthoFrameEquation = targetFrame.ToLaTeXEquationsArray(
"c",
@"\mu"
);
Console.WriteLine(orthoFrameEquation);
Console.WriteLine();
Console.WriteLine("Rotation Matrix:");
Console.WriteLine();
Console.WriteLine($@"\[{matrixExpr.GetLaTeXArray()}\]");
Console.WriteLine();
var anglesTextList = sourceFrame
.GetAnglesToFrame(targetFrame)
.Select(a => a.GetLaTeXAngleInDegrees())
.ToArray();
Console.WriteLine("Angles between frames vectors:");
foreach (var angleText in anglesTextList)
{
Console.WriteLine($@"\[{angleText}\]");
Console.WriteLine();
}
var autoVectorProjection = GaPoTNumVector
.CreateAutoVector(n)
.GetProjectionOnFrame(targetFrame);
Console.WriteLine("Projection of auto-vector:");
Console.WriteLine($@"\[{autoVectorProjection.TermsToLaTeX()}\]");
Console.WriteLine();
var rotorsSequence =
GaPoTNumRotorsSequence.Create(
sourceFrame.GetRotorsToFrame(targetFrame)
);
//if (!rotorsSequence.ValidateRotation(sourceFrame, targetFrame))
// throw new InvalidOperationException("Error in rotation sequence");
//for (var i = 0; i < sourceFrame.Count - 1; i++)
//{
// var f1 = sourceFrame.GetSubFrame(0, i + 1);
// var f2 = targetFrame.GetSubFrame(0, i + 1);
// var rs = rotorsSequence.GetSubSequence(0, i + 1);
// if (!rs.ValidateRotation(f1, f2))
// throw new InvalidOperationException("Error in rotation sequence");
//}
Console.WriteLine("Rotors Sequence:");
Console.WriteLine();
for (var i = 0; i < rotorsSequence.Count; i++)
{
var rotorEquation = rotorsSequence[i].ToLaTeXEquationsArray(
$"R_{i + 1}",
@"\mu"
);
Console.WriteLine(rotorEquation);
Console.WriteLine();
}
if (n > 4)
{
return;
}
//var rotor21 = rotorsSequence[1].Gp(rotorsSequence[0]);
//var rotor21Equation = rotor21.ToLaTeXEquationsArray(
// $"R_{{21}}=R_2 R_1",
// @"\mu"
//);
//Console.WriteLine(rotor21Equation);
//Console.WriteLine();
//var rotor32 = rotorsSequence[2].Gp(rotorsSequence[1]);
//var rotor32Equation = rotor32.ToLaTeXEquationsArray(
// $"R_{{32}}=R_3 R_2",
// @"\mu"
//);
//Console.WriteLine(rotor32Equation);
//Console.WriteLine();
Console.WriteLine("Final Rotor $R = R_3 R_{21} = R_{32} R_1$:");
Console.WriteLine();
var finalRotor = rotorsSequence.GetFinalRotor();
var finalRotorEquation = finalRotor.ToLaTeXEquationsArray(
"R",
@"\mu"
);
Console.WriteLine(finalRotorEquation);
Console.WriteLine();
//Console.WriteLine($"m{n} = {matrixExpr};");
//Console.WriteLine($"MatrixForm[FullSimplify[m{n}]]");
//Console.WriteLine($"MatrixForm[FullSimplify[Dot[m{n}, Transpose[m{n}]]]]");
//Console.WriteLine($"Pseudo-Scalar = {frame.GetPseudoScalar()}");
//Console.WriteLine();
}
public static void Execute()
{
var n = 4;
var uFrame = GaPoTNumFrame.CreateBasisFrame(n);
var cFrame = GaPoTNumFrame.CreateGramSchmidtFrame(n, n - 1, out var eFrame);
var eFrameEquation = eFrame.ToLaTeXEquationsArray(
"e",
@"\mu"
);
Console.WriteLine("e-frame:");
Console.WriteLine(eFrameEquation);
Console.WriteLine();
var cFrameEquation =
cFrame.ToLaTeXEquationsArray(
"c",
@"\mu"
);
Console.WriteLine("c-frame:");
Console.WriteLine(cFrameEquation);
Console.WriteLine();
var cFrameMatrix =
cFrame.GetMatrix().GetLaTeXArray();
Console.WriteLine("c-frame matrix:");
Console.WriteLine(cFrameMatrix);
Console.WriteLine();
var rotorsSequence =
GaPoTNumRotorsSequence.Create(
cFrame.GetRotorsToFrame(uFrame)
);
var finalRotor =
rotorsSequence.GetFinalRotor();
var R1 = rotorsSequence[1].Gp(rotorsSequence[0]);
var R2 = rotorsSequence[2];
var autoVector = GaPoTNumVector.CreateAutoVector(n);
var rotatedAutoVector =
rotorsSequence.Rotate(autoVector);
var v1 = Math.Sqrt(2) * Math.Cos(0);
var v2 = Math.Sqrt(2) * Math.Cos(0 - 1 * 2 * Math.PI / 4);
var v3 = Math.Sqrt(2) * Math.Cos(0 - 2 * 2 * Math.PI / 4);
var v4 = -(v1 + v2 + v3);
var inputVector = new GaPoTNumVector()
.AddTerm(1, v1)
.AddTerm(2, v2)
.AddTerm(3, v3)
.AddTerm(4, v4);
Console.WriteLine("Final Rotor:");
Console.WriteLine($"{finalRotor.TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine($"{finalRotor.TermsToText()}");
Console.WriteLine();
Console.WriteLine("R1:");
Console.WriteLine($"{R1.TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("R2:");
Console.WriteLine($"{R2.TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("R2 R1 - R:");
Console.WriteLine($"{(R2.Gp(R1) - finalRotor).TermsToText()}");
Console.WriteLine($"{(R1.Gp(R2) - finalRotor).TermsToText()}");
Console.WriteLine();
Console.WriteLine("Rotated Auto Vector:");
Console.WriteLine($"{rotatedAutoVector.TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("Input Vector:");
Console.WriteLine($"{inputVector.TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
var rotatedVector =
rotorsSequence.Rotate(inputVector);
Console.WriteLine("Rotated Vector:");
Console.WriteLine($"{rotatedVector.TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("Rotated Vector . Rotated Auto Vector:");
Console.WriteLine($"{rotatedVector.DotProduct(rotatedAutoVector):G}");
Console.WriteLine();
var eI = eFrame.GetPseudoScalar();
Console.WriteLine("Input Vector inside e-frame: ");
Console.WriteLine($"{inputVector.Op(eI).TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("Rotated Vector inside e-frame: ");
Console.WriteLine($"{rotatedVector.Op(eI).TermsToLaTeX().GetLaTeXDisplayEquation()}");
Console.WriteLine();
Console.WriteLine("Input Vector squared norm: ");
Console.WriteLine($"{inputVector.Norm2()}");
Console.WriteLine();
Console.WriteLine("Rotated Vector squared norm: ");
Console.WriteLine($"{rotatedVector.Norm2()}");
Console.WriteLine();
}
public static void Execute()
{
var n = 3;
var uFrame = GaPoTNumFrame.CreateBasisFrame(n);
var cFrame = GaPoTNumFrame.CreateGramSchmidtFrame(n, n - 1, out var eFrame);
var rotorsSequence =
GaPoTNumRotorsSequence.Create(
uFrame.GetRotorsToFrame(cFrame)
).Reverse();
var finalRotor =
rotorsSequence.GetFinalRotor();
var autoVector = GaPoTNumVector.CreateAutoVector(n);
var rotatedAutoVector =
rotorsSequence.Rotate(autoVector);
//var v1 = Math.Sqrt(2);
//var v2 = Math.Sqrt(2) * Math.Cos(-Math.PI / 3);
//var v3 = Math.Sqrt(2) * Math.Cos(Math.PI / 3);
var v1 = 1.0d;
var v2 = Math.Cos(-2 * Math.PI / 3);
var v3 = Math.Cos(2 * Math.PI / 3);
var inputVector = new GaPoTNumVector()
.AddTerm(1, v1)
.AddTerm(2, v2)
.AddTerm(3, v3);
Console.WriteLine("Final Rotor:");
Console.WriteLine($"{finalRotor.TermsToLaTeX()}");
Console.WriteLine();
Console.WriteLine("Rotated Auto Vector:");
Console.WriteLine($"{rotatedAutoVector.TermsToLaTeX()}");
Console.WriteLine();
Console.WriteLine("Input Vector:");
Console.WriteLine($"{inputVector.TermsToLaTeX()}");
Console.WriteLine();
var rotatedVector =
rotorsSequence.Rotate(inputVector);
Console.WriteLine("Rotated Vector:");
Console.WriteLine($"{rotatedVector.TermsToLaTeX()}");
Console.WriteLine();
Console.WriteLine("Rotated Vector . Rotated Auto Vector:");
Console.WriteLine($"{rotatedVector.DotProduct(rotatedAutoVector):G}");
Console.WriteLine();
var eI = eFrame.GetPseudoScalar();
Console.WriteLine("Input Vector inside e-frame: ");
Console.WriteLine($"{inputVector.Op(eI).TermsToLaTeX()}");
Console.WriteLine();
Console.WriteLine("Rotated Vector inside e-frame: ");
Console.WriteLine($"{rotatedVector.Op(eI).TermsToLaTeX()}");
Console.WriteLine();
Console.WriteLine("Input Vector squared norm: ");
Console.WriteLine($"{inputVector.Norm2()}");
Console.WriteLine();
Console.WriteLine("Rotated Vector squared norm: ");
Console.WriteLine($"{rotatedVector.Norm2()}");
Console.WriteLine();
}
public static GaPoTNumVector CreateBasisVector(int id)
{
return(GaPoTNumVector.CreateZero().AddTerm(id, 1.0d));
}