} // end of ComputeOmInitFromVectorsSigns()
/// <summary>
/// Returns info about <c>bitmap</c>.
///
/// If bitmap is not in the domain of <c>om</c>, the basis blade in the returned value will be null,
/// and the domainIdx will be -1.
///
/// If the grade of the bitmap is 1, the domainIdx will be -1 because it is
/// assumed to be an input vector.
/// </summary>
/// <param name="S"></param>
/// <param name="om"></param>
/// <param name="bitmap"></param>
/// <returns><c>BasisBlade, grade, domainIdx</c> for <c>bitmap</c></returns>
public static G25.Tuple <RefGA.BasisBlade, int, int> GetDomainBladeInfo(Specification S, OM om, uint bitmap)
{
int grade = (int)RefGA.Bits.BitCount(bitmap);
if (grade == 1) // basis vector
{
return(new G25.Tuple <RefGA.BasisBlade, int, int>(new RefGA.BasisBlade(bitmap), grade, -1));
}
// find the bitmap in the domain
RefGA.BasisBlade B = null;
int domainIdx = -1;
for (int i = 0; i < om.DomainForGrade(grade).Length; i++)
{
if (bitmap == om.DomainForGrade(grade)[i].bitmap)
{
domainIdx = i;
B = om.DomainForGrade(grade)[i];
break;
}
}
return(new G25.Tuple <RefGA.BasisBlade, int, int>(B, grade, domainIdx));
} // end of GetDomainBladeInfo()
} // end of ComputeOmInitFromVectorsPlan()
/// <summary>
/// Computes the signs for the plan as computed by GetOmInitFromVectorsPlan().
///
/// Because the basis blades in the domain of 'om' do not have to be in canonical order,
/// there may be some signs required to correctly executed the plan
/// </summary>
/// <param name="S"></param>
/// <param name="om"></param>
/// <param name="plan"></param>
/// <returns>signs for the plan</returns>
public static double[][] ComputeOmInitFromVectorsSigns(Specification S, OM om, uint[][][] plan)
{
double[][] result = new double[S.m_dimension + 1][];
for (int g = 1; g <= S.m_dimension; g++)
{
result[g] = new double[om.DomainForGrade(g).Length];
for (int d = 0; d < om.DomainForGrade(g).Length; d++)
{
// get domain blade we have to construct
RefGA.BasisBlade D = om.DomainForGrade(g)[d];
// follow the plan to construct the blade
RefGA.BasisBlade P = RefGA.BasisBlade.ONE;
for (int p = 0; p < plan[g][d].Length; p++)
{
G25.Tuple <RefGA.BasisBlade, int, int> info = GetDomainBladeInfo(S, om, plan[g][d][p]);
P = RefGA.BasisBlade.op(P, info.Value1);
}
// compute sign difference & store
double s = D.scale / P.scale;
result[g][d] = s;
}
}
return(result);
} // end of ComputeOmInitFromVectorsSigns()
/// <summary>
/// 'Plans' how to initialize an outermorphism from vector images.
///
/// The plan is returned in the form of nested array <c>uint[grade][domain][plan steps]</c>.
/// The <c>plan steps</c> are the bitmaps of the basis blades that should be wedged together
/// to form the basis blade for <c>grade,domain</c>.
/// </summary>
/// <param name="S"></param>
/// <param name="om"></param>
/// <returns>plan for initialization of <c>om</c> from vector images.</returns>
public static uint[][][] ComputeOmInitFromVectorsPlan(Specification S, OM om)
{
// keep track of which basis blades are available (domain vectors are the input, so they are always available)
bool[] availableBasisBlades = new bool[1 << S.m_dimension];
for (int i = 0; i < om.DomainVectors.Length; i++)
{
availableBasisBlades[om.DomainVectors[i].bitmap] = true;
}
// for each grade, figure out how to construct the basis blades of that grade from basis blades which are already available
uint[][][] result = new uint[S.m_dimension + 1][][];
for (int g = 1; g <= S.m_dimension; g++)
{
result[g] = new uint[om.DomainForGrade(g).Length][];
for (int d = 0; d < om.DomainForGrade(g).Length; d++)
{
RefGA.BasisBlade D = om.DomainForGrade(g)[d];
// find the largest part of D which is already known
List <uint> plan = new List <uint>();
uint bitmap = D.bitmap;
while (bitmap != 0)
{
// find first bit, plan it, see if the rest is available
uint lowestBitIdx = (uint)RefGA.Bits.LowestOneBit(bitmap);
uint lowestBitmap = (uint)(1 << (int)lowestBitIdx);
plan.Add(lowestBitmap);
bitmap ^= lowestBitmap;
if (availableBasisBlades[bitmap]) // if remaining bitmap has already been computed, use that
{
plan.Add(bitmap);
bitmap ^= bitmap;
}
}
// plan for this basis blade is done:
result[g][d] = plan.ToArray();
availableBasisBlades[D.bitmap] = true;
}
}
return(result);
} // end of ComputeOmInitFromVectorsPlan()
/// <summary>
/// 'Plans' how to initialize an outermorphism from vector images.
///
/// The plan is returned in the form of nested array <c>uint[grade][domain][plan steps]</c>.
/// The <c>plan steps</c> are the bitmaps of the basis blades that should be wedged together
/// to form the basis blade for <c>grade,domain</c>.
/// </summary>
/// <param name="S"></param>
/// <param name="om"></param>
/// <returns>plan for initialization of <c>om</c> from vector images.</returns>
public static uint[][][] ComputeOmInitFromVectorsPlan(Specification S, OM om)
{
// keep track of which basis blades are available (domain vectors are the input, so they are always available)
bool[] availableBasisBlades = new bool[1 << S.m_dimension];
for (int i = 0; i < om.DomainVectors.Length; i++)
availableBasisBlades[om.DomainVectors[i].bitmap] = true;
// for each grade, figure out how to construct the basis blades of that grade from basis blades which are already available
uint[][][] result = new uint[S.m_dimension + 1][][];
for (int g = 1; g <= S.m_dimension; g++)
{
result[g] = new uint[om.DomainForGrade(g).Length][];
for (int d = 0; d < om.DomainForGrade(g).Length; d++)
{
RefGA.BasisBlade D = om.DomainForGrade(g)[d];
// find the largest part of D which is already known
List<uint> plan = new List<uint>();
uint bitmap = D.bitmap;
while (bitmap != 0)
{
// find first bit, plan it, see if the rest is available
uint lowestBitIdx = (uint)RefGA.Bits.LowestOneBit(bitmap);
uint lowestBitmap = (uint)(1 << (int)lowestBitIdx);
plan.Add(lowestBitmap);
bitmap ^= lowestBitmap;
if (availableBasisBlades[bitmap]) // if remaining bitmap has already been computed, use that
{
plan.Add(bitmap);
bitmap ^= bitmap;
}
}
// plan for this basis blade is done:
result[g][d] = plan.ToArray();
availableBasisBlades[D.bitmap] = true;
}
}
return result;
}
/// <summary>
/// Computes the signs for the plan as computed by GetOmInitFromVectorsPlan().
///
/// Because the basis blades in the domain of 'om' do not have to be in canonical order,
/// there may be some signs required to correctly executed the plan
/// </summary>
/// <param name="S"></param>
/// <param name="om"></param>
/// <param name="plan"></param>
/// <returns>signs for the plan</returns>
public static double[][] ComputeOmInitFromVectorsSigns(Specification S, OM om, uint[][][] plan)
{
double[][] result = new double[S.m_dimension + 1][];
for (int g = 1; g <= S.m_dimension; g++)
{
result[g] = new double[om.DomainForGrade(g).Length];
for (int d = 0; d < om.DomainForGrade(g).Length; d++)
{
// get domain blade we have to construct
RefGA.BasisBlade D = om.DomainForGrade(g)[d];
// follow the plan to construct the blade
RefGA.BasisBlade P = RefGA.BasisBlade.ONE;
for (int p = 0; p < plan[g][d].Length; p++)
{
G25.Tuple<RefGA.BasisBlade, int, int> info = GetDomainBladeInfo(S, om, plan[g][d][p]);
P = RefGA.BasisBlade.op(P, info.Value1);
}
// compute sign difference & store
double s = D.scale / P.scale;
result[g][d] = s;
}
}
return result;
}
/// <summary>
/// Returns info about <c>bitmap</c>.
///
/// If bitmap is not in the domain of <c>om</c>, the basis blade in the returned value will be null,
/// and the domainIdx will be -1.
///
/// If the grade of the bitmap is 1, the domainIdx will be -1 because it is
/// assumed to be an input vector.
/// </summary>
/// <param name="S"></param>
/// <param name="om"></param>
/// <param name="bitmap"></param>
/// <returns><c>BasisBlade, grade, domainIdx</c> for <c>bitmap</c></returns>
public static G25.Tuple<RefGA.BasisBlade, int, int> GetDomainBladeInfo(Specification S, OM om, uint bitmap)
{
int grade = (int)RefGA.Bits.BitCount(bitmap);
if (grade == 1) // basis vector
return new G25.Tuple<RefGA.BasisBlade, int, int>(new RefGA.BasisBlade(bitmap), grade, -1);
// find the bitmap in the domain
RefGA.BasisBlade B = null;
int domainIdx = -1;
for (int i = 0; i < om.DomainForGrade(grade).Length; i++)
{
if (bitmap == om.DomainForGrade(grade)[i].bitmap)
{
domainIdx = i;
B = om.DomainForGrade(grade)[i];
break;
}
}
return new G25.Tuple<RefGA.BasisBlade, int, int>(B, grade, domainIdx);
}