/// <returns>true if the basis blade scales of A and B match. Blades which are not present in both A and B are ignored</returns>
public static bool BasisBladeScalesMatch(MV A, MV B)
{
if (A == null)
{
Console.WriteLine("Arrr!");
}
if (B == null)
{
Console.WriteLine("Arrr!");
}
Dictionary <Tuple <int, int>, Tuple <int, int> > D = GetCoordMap(A, B);
foreach (KeyValuePair <Tuple <int, int>, Tuple <int, int> > kvp in D)
{
BasisBlade a = A.Group(kvp.Key.Value1)[kvp.Key.Value2];
BasisBlade b = B.Group(kvp.Value.Value1)[kvp.Value.Value2];
if (a.scale != b.scale)
{
return(false);
}
}
return(true);
}
/// <summary>
/// Transforms <paramref name="A"/> to the metric basis (<paramref name="A"/> must be on eigenbasis).
/// </summary>
/// <param name="A">The list of BasisBlades (must be on the orthogonal 'eigen' basis).</param>
/// <returns><paramref name="A"/> on the new basis.</returns>
public ArrayList ToMetricBasis(ArrayList A)
{
ArrayList result = new ArrayList();
for (int i = 0; i < A.Count; i++)
{
ArrayList tmp = ToMetricBasis((BasisBlade)A[i]);
result.AddRange(tmp);
}
return(BasisBlade.Simplify(result));
}
public BasisBlade AbsoluteLargestConstantBasisBlade()
{
double maxValue = -1.0;
BasisBlade B = null;
for (int c = 0; c < NbConstBasisBlade; c++)
{
if (Math.Abs(ConstBasisBlade(c).scale) > maxValue)
{
maxValue = Math.Abs(ConstBasisBlade(c).scale);
B = ConstBasisBlade(c);
}
}
return(B);
}
/// <summary>
/// Transforms a basis blade to another basis which is represented by the columns of M.
/// </summary>
/// <param name="a">The basis blade to transform according to <paramref name="M"/>.</param>
/// <param name="M">The matrix to use to transform <paramref name="a"/>.</param>
/// <returns>a list of BasisBlade whose sum represents <paramref name="a"/> on the new basis.</returns>
public static ArrayList Transform(BasisBlade a, DotNetMatrix.GeneralMatrix M)
{
ArrayList A = new ArrayList();
A.Add(new BasisBlade(0, a.scale, a.symScale)); // start with just the scalar part;
int dim = M.RowDimension;
// for each 1 bit: convert to list of blades
int i = 0;
uint b = a.bitmap;
while (b != 0)
{
if ((b & 1) != 0)
{
// take column 'i' out of the matrix, wedge it to 'A'
ArrayList tmp = new ArrayList();
for (int j = 0; j < dim; j++)
{
double m = M.GetElement(j, i);
if (m != 0.0)
{
for (int k = 0; k < A.Count; k++)
{
BasisBlade o = BasisBlade.op((BasisBlade)A[k], new BasisBlade((uint)(1 << j), m));
if (o.scale != 0.0)
{
tmp.Add(o);
}
}
}
}
A = tmp;
}
b >>= 1;
i++;
}
return(A);
}
public Metric RoundEigenMetric(double roundingEpsilon)
{
double[] newEigenMetric = (double[])m_eigenMetric.Clone();
bool changed = false;
for (int i = 0; i < newEigenMetric.Length; i++)
{
double r = BasisBlade.Round(roundingEpsilon, newEigenMetric[i]);
if (r != newEigenMetric[i])
{
newEigenMetric[i] = r;
changed = true;
}
}
if (changed)
{
return(new Metric(m_matrix, m_eig, newEigenMetric, m_invEigMatrix, m_isDiagonal, m_isEuclidean, m_isAntiEuclidean));
}
else
{
return(this);
}
}
private void sum(BasisBlade bb)
{
int idx = c3ga.BasisElementIndexByBitmap[bb.getBitmap()];
coord[idx] += bb.getScale() / (float)c3ga.BasisElementSignByIndex[idx];
}
private mv Parse()
{
int token;
bool firstLoop = true;
// get the first token
token = getNextToken();
while (true) {
// reset for next basis blade
BasisBlade bb = new BasisBlade();
bool beDone = false; // basis element done
if (token == T_END_OF_STRING) break;
int cnt = 0;
while ((token == T_PLUS) || (token == T_MINUS)) { // accept all +-
cnt++;
startIdx = endIdx+1;
if (token == T_MINUS) bb.multiply(-1.0f); // -
token = getNextToken();
}
// require at least one +- if this is not the first term:
if ((!firstLoop) && (cnt == 0)) {
throw GetException("Expected '+' or '-'");
}
if ((token == T_NUMBER) ||
((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))) // must be number or basis vector
{
if (token == T_NUMBER) {
{ // multiply scale with value of number
try {
bb.multiply((float)Double.Parse(substring(startIdx, endIdx)));
} catch (Exception ) {
throw GetException("Cannot parse number");
}
}
startIdx = endIdx+1;
// * or ^ ?
token = getNextToken();
if ((token == T_WEDGE) || (token == T_MUL)) {
startIdx = endIdx+1;
// must find basis vector
token = getNextToken();
}
else { // just a single scalar is OK
startIdx = endIdx+1;
beDone = true;
}
}
if (!beDone) {
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR)) {
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx+1;
}
else {
throw GetException("Expected basis vector");
}
}
if (!beDone) {
// accept ^ basis vector as many times as it takes
while (true) {
// ^
token = getNextToken();
if (token != T_WEDGE) break;
startIdx = endIdx+1;
// basis vector
token = getNextToken();
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR)) {
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx+1;
}
else {
throw GetException("Expected basis vector");
}
}
}
} // end of 'if number or bv'
else if (token == T_BAD_CHARACTER) {
throw GetException("Bad character");
}
else if (token == T_BAD_NUMBER) {
throw GetException("Bad number");
}
else if (token == T_BAD_IDENTIFIER) {
throw GetException("Bad identifier");
}
else {
throw GetException("Unexpected token");
}
// add
sum(bb);
// remember that the first loop is done
firstLoop = false;
}
mv result = new mv(GroupBitmap.GRADE_0 | GroupBitmap.GRADE_1 | GroupBitmap.GRADE_2 | GroupBitmap.GRADE_3 | GroupBitmap.GRADE_4 | GroupBitmap.GRADE_5 | 0, coord);
result.Compress(0.0f);
return result;
}
/// <summary>
/// Transforms BasisBlade <paramref name="a"/> to the regular basis of this metric.
/// </summary>
/// <param name="a">The BasisBlade (must be on the orthogonal 'eigen' basis).</param>
/// <returns><paramref name="a"/> on the new basis.</returns>
public ArrayList ToMetricBasis(BasisBlade a)
{
return(Transform(a, m_eig.GetV()));
}
/// <summary>
/// Transforms BasisBlade <paramref name="a"/> to the orthogonal basis of this metric.
/// </summary>
/// <param name="a">The BasisBlade (must be on the regular basis).</param>
/// <returns><paramref name="a"/> on the new basis.</returns>
public ArrayList ToEigenbasis(BasisBlade a)
{
return(Transform(a, m_invEigMatrix));
}
private mv Parse()
{
int token;
bool firstLoop = true;
// get the first token
token = getNextToken();
while (true)
{
// reset for next basis blade
BasisBlade bb = new BasisBlade();
bool beDone = false; // basis element done
if (token == T_END_OF_STRING)
{
break;
}
int cnt = 0;
while ((token == T_PLUS) || (token == T_MINUS)) // accept all +-
{
cnt++;
startIdx = endIdx + 1;
if (token == T_MINUS)
{
bb.multiply(-1.0f); // -
}
token = getNextToken();
}
// require at least one +- if this is not the first term:
if ((!firstLoop) && (cnt == 0))
{
throw GetException("Expected '+' or '-'");
}
if ((token == T_NUMBER) ||
((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))) // must be number or basis vector
{
if (token == T_NUMBER)
{
{ // multiply scale with value of number
try {
bb.multiply((float)Double.Parse(substring(startIdx, endIdx)));
} catch (Exception) {
throw GetException("Cannot parse number");
}
}
startIdx = endIdx + 1;
// * or ^ ?
token = getNextToken();
if ((token == T_WEDGE) || (token == T_MUL))
{
startIdx = endIdx + 1;
// must find basis vector
token = getNextToken();
}
else // just a single scalar is OK
{
startIdx = endIdx + 1;
beDone = true;
}
}
if (!beDone)
{
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))
{
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx + 1;
}
else
{
throw GetException("Expected basis vector");
}
}
if (!beDone)
{
// accept ^ basis vector as many times as it takes
while (true)
{
// ^
token = getNextToken();
if (token != T_WEDGE)
{
break;
}
startIdx = endIdx + 1;
// basis vector
token = getNextToken();
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))
{
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx + 1;
}
else
{
throw GetException("Expected basis vector");
}
}
}
} // end of 'if number or bv'
else if (token == T_BAD_CHARACTER)
{
throw GetException("Bad character");
}
else if (token == T_BAD_NUMBER)
{
throw GetException("Bad number");
}
else if (token == T_BAD_IDENTIFIER)
{
throw GetException("Bad identifier");
}
else
{
throw GetException("Unexpected token");
}
// add
sum(bb);
// remember that the first loop is done
firstLoop = false;
}
mv result = new mv(GroupBitmap.GRADE_0 | GroupBitmap.GRADE_1 | GroupBitmap.GRADE_2 | GroupBitmap.GRADE_3 | GroupBitmap.GRADE_4 | GroupBitmap.GRADE_5 | 0, coord);
result.Compress(0.0f);
return(result);
} // end of Parse()
private void sum(BasisBlade bb)
{
int idx = c3ga.BasisElementIndexByBitmap[bb.getBitmap()];
coord[idx] += bb.getScale() / (float)c3ga.BasisElementSignByIndex[idx];
}