/// <summary>
/// Create a derived frame system using a change of basis matrix for the basis vectors
/// </summary>
/// <param name="baseFrame">The base frame. It may be any kind of frame</param>
/// <param name="cbm">The 'Change Of Basis Vectors' matrix. It must be invertable</param>
/// <returns></returns>
public static GaSymMetricNonOrthogonal CreateDerivedCbmFrameSystem(GaSymFrame baseFrame, MathematicaMatrix cbm)
{
var baseIpm = baseFrame.Ipm.ToMathematicaMatrix();
var cbmTrans = (MathematicaMatrix)cbm.Transpose();
var cbmInverseTrans = (MathematicaMatrix)cbmTrans.Inverse();
var ipm = cbm * baseIpm * cbmTrans;
var baseToDerivedCba = cbmInverseTrans.ToOutermorphismTree();
var derivedToBaseCba = cbmTrans.ToOutermorphismTree();
if (ipm.IsDiagonal())
{
var derivedFrame = CreateOrthogonal(ipm.GetDiagonal());
return(new GaSymMetricNonOrthogonal(baseFrame, derivedFrame, derivedToBaseCba, baseToDerivedCba));
}
if (baseFrame.IsOrthogonal)
{
var derivedFrame = new GaSymFrameNonOrthogonal(baseFrame, ipm, derivedToBaseCba, baseToDerivedCba);
return(derivedFrame.NonOrthogonalMetric);
}
var gaFrame =
//new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
CreateNonOrthogonalFromIpm(ipm.ToMathematicaMatrix());
return(gaFrame.NonOrthogonalMetric);
//return new DerivedFrameSystem(baseFrame, gaFrame, derivedToBaseOm, baseToDerivedOm);
}
/// <summary>
/// Create a derived frame system using a change of basis matrix for the basis vectors
/// </summary>
/// <param name="baseFrame">The base frame. It may be any kind of frame</param>
/// <param name="cbm">The 'Change Of Basis Vectors' matrix. It must be invertable</param>
/// <returns></returns>
public static DerivedFrameSystem CreateDerivedCbmFrameSystem(GaFrame baseFrame, MathematicaMatrix cbm)
{
var baseIpm = baseFrame.Ipm.ToMathematicaMatrix();
var cbmTrans = (MathematicaMatrix)cbm.Transpose();
var cbmInverseTrans = (MathematicaMatrix)cbmTrans.Inverse();
var ipm = cbm * baseIpm * cbmTrans;
var baseToDerivedOm = GaOuterMorphismFull.Create(cbmInverseTrans);
var derivedToBaseOm = GaOuterMorphismFull.Create(cbmTrans);
if (ipm.IsDiagonal())
{
var derivedFrame = CreateOrthogonal(ipm.GetDiagonal());
return(new DerivedFrameSystem(baseFrame, derivedFrame, derivedToBaseOm, baseToDerivedOm));
}
if (baseFrame.IsOrthogonal)
{
var derivedFrame = new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
return(derivedFrame.Dfs);
}
var gaFrame =
//new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
CreateNonOrthogonalFromIpm(ipm.ToMathematicaMatrix());
return(gaFrame.Dfs);
//return new DerivedFrameSystem(baseFrame, gaFrame, derivedToBaseOm, baseToDerivedOm);
}