/**
* Compute the Kramer-Mesner matrix.
*
* Precondition: t < k
*/
KramerMesnerMatrix computeKMMatrix(const Group& G, unsigned int t, unsigned int k) {
std::vector<KMBuilderOutput> builderOutputs; // stores the relevant data for k = 2 onwards
Matrix A;
for (int i = 2; i <= k; i++) {
boost::scoped_ptr<KMBuilder> builder;
// Get orbit representatives of (i - 1)-subsets
std::vector<Subset> orbitReps;
if (i == 2) {
// As it is the first time, we have to compute the orbit representatives of singleton subsets...
Subset pointsRemaining = generateX(G.getNumPoints());
while (!pointsRemaining.empty()) {
typedef OrbitSet<Permutation, unsigned long>::const_iterator OrbitSetIterator;
unsigned long point = *(pointsRemaining.begin()); // A new representative...
Subset singletonSet = makeSingletonSet(point); // ...as a set
orbitReps.push_back(singletonSet);
// Compute the orbit of the point, and remove it from the remaining points
OrbitSet<Permutation, unsigned long> orbit = G.orbit(point, Transversal::TrivialAction());
for (OrbitSetIterator it = orbit.begin(); it != orbit.end(); it++) {
pointsRemaining.erase(pointsRemaining.find(*it));
}
}
builder.reset(new KMBuilder(G, i, orbitReps));
} else {
// We get them from what we computed earlier
KMBuilderOutput& input = builderOutputs[i - 3];
orbitReps = input.getNewReps();
builder.reset(new KMBuilder(G, i, orbitReps, input.getPrunerData()));
}
KMBuilderOutput builderOutput = builder->build();
builderOutputs.push_back(builderOutput);
// From the identity that A[t][k] = A[t][s] * A[s][k] / combinat(k - t, k - s) for any s
// between t and k, we get the following:
if (i == t + 1) {
assignMatrix(A, builderOutput.getNewMatrix());
} else if (i > t + 1) {
assignMatrix(A, matrixMultiply(A, builderOutput.getNewMatrix()));
scalarDivide(i - t, A);
}
}
return KramerMesnerMatrix(G, builderOutputs[t - 2].getNewReps(), builderOutputs[k - 2].getNewReps(), A);
}
struct sparsematrix partition_to_matrix(struct sparsematrix* A){
struct sparsematrix A1 = assignMatrix(A,1);
struct sparsematrix A2 = assignMatrix(A,2);
struct sparsematrix B;
MMSparseMatrixInit(&B);
B.m = A->m;
B.n = A->n;
B.NrNzElts = A->NrNzElts;
B.i = vecallocl(B.NrNzElts);
B.j = vecallocl(B.NrNzElts);
B.ReValue = vecallocd(B.NrNzElts);
int index_B = 0, i;
for(i=0;i<A1.NrNzElts;i++){
B.i[index_B] = A1.i[i];
B.j[index_B] = A1.j[i];
B.ReValue[index_B++] = 1.0;
}
for(i=0;i<A2.NrNzElts;i++){
B.i[index_B] = A2.i[i];
B.j[index_B] = A2.j[i];
B.ReValue[index_B++] = 2.0;
}
MMDeleteSparseMatrix(&A1);
MMDeleteSparseMatrix(&A2);
struct sparsematrixplus plus = reorder_row_incr(&B);
MMDeleteSparseMatrix(&B);
vecfreel(plus.perm);
return plus.matrix;
}
