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Oussama
@@ -19,64 +19,60 @@ subject to the following restrictions:
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//Math library was replaced from fmatvec to a the file src/LinearMath/btMatrixX.h
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//STL/std::vector replaced by btAlignedObjectArray
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#include "btLemkeAlgorithm.h"
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#undef BT_DEBUG_OSTREAM
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#ifdef BT_DEBUG_OSTREAM
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using namespace std;
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#endif //BT_DEBUG_OSTREAM
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#endif //BT_DEBUG_OSTREAM
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btScalar btMachEps()
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{
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static bool calculated=false;
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static bool calculated = false;
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static btScalar machEps = btScalar(1.);
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if (!calculated)
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{
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do {
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do
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{
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machEps /= btScalar(2.0);
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// If next epsilon yields 1, then break, because current
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// epsilon is the machine epsilon.
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}
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while ((btScalar)(1.0 + (machEps/btScalar(2.0))) != btScalar(1.0));
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// printf( "\nCalculated Machine epsilon: %G\n", machEps );
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calculated=true;
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} while ((btScalar)(1.0 + (machEps / btScalar(2.0))) != btScalar(1.0));
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// printf( "\nCalculated Machine epsilon: %G\n", machEps );
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calculated = true;
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}
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return machEps;
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}
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btScalar btEpsRoot() {
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btScalar btEpsRoot()
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{
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static btScalar epsroot = 0.;
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static bool alreadyCalculated = false;
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if (!alreadyCalculated) {
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if (!alreadyCalculated)
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{
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epsroot = btSqrt(btMachEps());
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alreadyCalculated = true;
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}
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return epsroot;
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}
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btVectorXu btLemkeAlgorithm::solve(unsigned int maxloops /* = 0*/)
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btVectorXu btLemkeAlgorithm::solve(unsigned int maxloops /* = 0*/)
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{
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steps = 0;
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steps = 0;
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int dim = m_q.size();
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int dim = m_q.size();
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#ifdef BT_DEBUG_OSTREAM
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if(DEBUGLEVEL >= 1) {
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cout << "Dimension = " << dim << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 1)
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{
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cout << "Dimension = " << dim << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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btVectorXu solutionVector(2 * dim);
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solutionVector.setZero();
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//, INIT, 0.);
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//, INIT, 0.);
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btMatrixXu ident(dim, dim);
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ident.setIdentity();
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@@ -85,287 +81,289 @@ btScalar btEpsRoot() {
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#endif
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btMatrixXu mNeg = m_M.negative();
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btMatrixXu A(dim, 2 * dim + 2);
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btMatrixXu A(dim, 2 * dim + 2);
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//
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A.setSubMatrix(0, 0, dim - 1, dim - 1,ident);
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A.setSubMatrix(0, dim, dim - 1, 2 * dim - 1,mNeg);
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A.setSubMatrix(0, 0, dim - 1, dim - 1, ident);
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A.setSubMatrix(0, dim, dim - 1, 2 * dim - 1, mNeg);
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A.setSubMatrix(0, 2 * dim, dim - 1, 2 * dim, -1.f);
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A.setSubMatrix(0, 2 * dim + 1, dim - 1, 2 * dim + 1,m_q);
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A.setSubMatrix(0, 2 * dim + 1, dim - 1, 2 * dim + 1, m_q);
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#ifdef BT_DEBUG_OSTREAM
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cout << A << std::endl;
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#endif //BT_DEBUG_OSTREAM
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#endif //BT_DEBUG_OSTREAM
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// btVectorXu q_;
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// q_ >> A(0, 2 * dim + 1, dim - 1, 2 * dim + 1);
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// btVectorXu q_;
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// q_ >> A(0, 2 * dim + 1, dim - 1, 2 * dim + 1);
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btAlignedObjectArray<int> basis;
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//At first, all w-values are in the basis
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for (int i = 0; i < dim; i++)
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basis.push_back(i);
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btAlignedObjectArray<int> basis;
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//At first, all w-values are in the basis
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for (int i = 0; i < dim; i++)
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basis.push_back(i);
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int pivotRowIndex = -1;
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btScalar minValue = 1e30f;
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bool greaterZero = true;
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for (int i=0;i<dim;i++)
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for (int i = 0; i < dim; i++)
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{
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btScalar v =A(i,2*dim+1);
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if (v<minValue)
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btScalar v = A(i, 2 * dim + 1);
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if (v < minValue)
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{
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minValue=v;
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minValue = v;
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pivotRowIndex = i;
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}
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if (v<0)
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if (v < 0)
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greaterZero = false;
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}
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// int pivotRowIndex = q_.minIndex();//minIndex(q_); // first row is that with lowest q-value
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int z0Row = pivotRowIndex; // remember the col of z0 for ending algorithm afterwards
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int pivotColIndex = 2 * dim; // first col is that of z0
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// int pivotRowIndex = q_.minIndex();//minIndex(q_); // first row is that with lowest q-value
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int z0Row = pivotRowIndex; // remember the col of z0 for ending algorithm afterwards
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int pivotColIndex = 2 * dim; // first col is that of z0
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#ifdef BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 3)
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if (DEBUGLEVEL >= 3)
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{
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// cout << "A: " << A << endl;
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cout << "pivotRowIndex " << pivotRowIndex << endl;
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cout << "pivotColIndex " << pivotColIndex << endl;
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cout << "Basis: ";
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for (int i = 0; i < basis.size(); i++)
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cout << basis[i] << " ";
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cout << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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// cout << "A: " << A << endl;
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cout << "pivotRowIndex " << pivotRowIndex << endl;
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cout << "pivotColIndex " << pivotColIndex << endl;
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cout << "Basis: ";
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for (int i = 0; i < basis.size(); i++)
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cout << basis[i] << " ";
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cout << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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if (!greaterZero)
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{
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if (maxloops == 0)
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{
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maxloops = 100;
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// maxloops = UINT_MAX; //TODO: not a really nice way, problem is: maxloops should be 2^dim (=1<<dim), but this could exceed UINT_MAX and thus the result would be 0 and therefore the lemke algorithm wouldn't start but probably would find a solution within less then UINT_MAX steps. Therefore this constant is used as a upper border right now...
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}
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if (maxloops == 0) {
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maxloops = 100;
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// maxloops = UINT_MAX; //TODO: not a really nice way, problem is: maxloops should be 2^dim (=1<<dim), but this could exceed UINT_MAX and thus the result would be 0 and therefore the lemke algorithm wouldn't start but probably would find a solution within less then UINT_MAX steps. Therefore this constant is used as a upper border right now...
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}
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/*start looping*/
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for(steps = 0; steps < maxloops; steps++) {
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GaussJordanEliminationStep(A, pivotRowIndex, pivotColIndex, basis);
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/*start looping*/
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for (steps = 0; steps < maxloops; steps++)
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{
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GaussJordanEliminationStep(A, pivotRowIndex, pivotColIndex, basis);
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#ifdef BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 3) {
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// cout << "A: " << A << endl;
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cout << "pivotRowIndex " << pivotRowIndex << endl;
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cout << "pivotColIndex " << pivotColIndex << endl;
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cout << "Basis: ";
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for (int i = 0; i < basis.size(); i++)
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cout << basis[i] << " ";
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cout << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 3)
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{
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// cout << "A: " << A << endl;
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cout << "pivotRowIndex " << pivotRowIndex << endl;
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cout << "pivotColIndex " << pivotColIndex << endl;
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cout << "Basis: ";
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for (int i = 0; i < basis.size(); i++)
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cout << basis[i] << " ";
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cout << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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int pivotColIndexOld = pivotColIndex;
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int pivotColIndexOld = pivotColIndex;
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/*find new column index */
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if (basis[pivotRowIndex] < dim) //if a w-value left the basis get in the correspondent z-value
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pivotColIndex = basis[pivotRowIndex] + dim;
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else
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//else do it the other way round and get in the corresponding w-value
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pivotColIndex = basis[pivotRowIndex] - dim;
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/*find new column index */
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if (basis[pivotRowIndex] < dim) //if a w-value left the basis get in the correspondent z-value
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pivotColIndex = basis[pivotRowIndex] + dim;
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else
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//else do it the other way round and get in the corresponding w-value
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pivotColIndex = basis[pivotRowIndex] - dim;
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/*the column becomes part of the basis*/
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basis[pivotRowIndex] = pivotColIndexOld;
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/*the column becomes part of the basis*/
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basis[pivotRowIndex] = pivotColIndexOld;
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pivotRowIndex = findLexicographicMinimum(A, pivotColIndex);
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pivotRowIndex = findLexicographicMinimum(A, pivotColIndex);
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if(z0Row == pivotRowIndex) { //if z0 leaves the basis the solution is found --> one last elimination step is necessary
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GaussJordanEliminationStep(A, pivotRowIndex, pivotColIndex, basis);
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basis[pivotRowIndex] = pivotColIndex; //update basis
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break;
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}
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}
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if (z0Row == pivotRowIndex)
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{ //if z0 leaves the basis the solution is found --> one last elimination step is necessary
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GaussJordanEliminationStep(A, pivotRowIndex, pivotColIndex, basis);
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basis[pivotRowIndex] = pivotColIndex; //update basis
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break;
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}
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}
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#ifdef BT_DEBUG_OSTREAM
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if(DEBUGLEVEL >= 1) {
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cout << "Number of loops: " << steps << endl;
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cout << "Number of maximal loops: " << maxloops << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 1)
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{
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cout << "Number of loops: " << steps << endl;
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cout << "Number of maximal loops: " << maxloops << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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if(!validBasis(basis)) {
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info = -1;
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if (!validBasis(basis))
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{
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info = -1;
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#ifdef BT_DEBUG_OSTREAM
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if(DEBUGLEVEL >= 1)
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cerr << "Lemke-Algorithm ended with Ray-Termination (no valid solution)." << endl;
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#endif //BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 1)
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cerr << "Lemke-Algorithm ended with Ray-Termination (no valid solution)." << endl;
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#endif //BT_DEBUG_OSTREAM
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return solutionVector;
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}
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}
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return solutionVector;
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}
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}
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#ifdef BT_DEBUG_OSTREAM
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if (DEBUGLEVEL >= 2) {
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// cout << "A: " << A << endl;
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cout << "pivotRowIndex " << pivotRowIndex << endl;
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cout << "pivotColIndex " << pivotColIndex << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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for (int i = 0; i < basis.size(); i++)
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if (DEBUGLEVEL >= 2)
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{
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solutionVector[basis[i]] = A(i,2*dim+1);//q_[i];
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// cout << "A: " << A << endl;
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cout << "pivotRowIndex " << pivotRowIndex << endl;
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cout << "pivotColIndex " << pivotColIndex << endl;
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}
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#endif //BT_DEBUG_OSTREAM
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for (int i = 0; i < basis.size(); i++)
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{
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solutionVector[basis[i]] = A(i, 2 * dim + 1); //q_[i];
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}
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info = 0;
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info = 0;
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return solutionVector;
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}
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return solutionVector;
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}
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int btLemkeAlgorithm::findLexicographicMinimum(const btMatrixXu& A, const int & pivotColIndex) {
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int RowIndex = 0;
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int dim = A.rows();
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btAlignedObjectArray<btVectorXu> Rows;
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for (int row = 0; row < dim; row++)
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{
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btVectorXu vec(dim + 1);
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vec.setZero();//, INIT, 0.)
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Rows.push_back(vec);
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btScalar a = A(row, pivotColIndex);
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if (a > 0) {
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Rows[row][0] = A(row, 2 * dim + 1) / a;
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Rows[row][1] = A(row, 2 * dim) / a;
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for (int j = 2; j < dim + 1; j++)
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Rows[row][j] = A(row, j - 1) / a;
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int btLemkeAlgorithm::findLexicographicMinimum(const btMatrixXu& A, const int& pivotColIndex)
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{
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int RowIndex = 0;
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int dim = A.rows();
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btAlignedObjectArray<btVectorXu> Rows;
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for (int row = 0; row < dim; row++)
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{
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btVectorXu vec(dim + 1);
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vec.setZero(); //, INIT, 0.)
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Rows.push_back(vec);
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btScalar a = A(row, pivotColIndex);
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if (a > 0)
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{
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Rows[row][0] = A(row, 2 * dim + 1) / a;
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Rows[row][1] = A(row, 2 * dim) / a;
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for (int j = 2; j < dim + 1; j++)
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Rows[row][j] = A(row, j - 1) / a;
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#ifdef BT_DEBUG_OSTREAM
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// if (DEBUGLEVEL) {
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// cout << "Rows(" << row << ") = " << Rows[row] << endl;
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// if (DEBUGLEVEL) {
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// cout << "Rows(" << row << ") = " << Rows[row] << endl;
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// }
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#endif
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}
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}
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#endif
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}
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}
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for (int i = 0; i < Rows.size(); i++)
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{
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if (Rows[i].nrm2() > 0.) {
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for (int i = 0; i < Rows.size(); i++)
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{
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if (Rows[i].nrm2() > 0.)
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{
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int j = 0;
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for (; j < Rows.size(); j++)
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{
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if (i != j)
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{
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if (Rows[j].nrm2() > 0.)
|
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{
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btVectorXu test(dim + 1);
|
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for (int ii = 0; ii < dim + 1; ii++)
|
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{
|
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test[ii] = Rows[j][ii] - Rows[i][ii];
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}
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||||
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int j = 0;
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for (; j < Rows.size(); j++)
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{
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||||
if(i != j)
|
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{
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if(Rows[j].nrm2() > 0.)
|
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{
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btVectorXu test(dim + 1);
|
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for (int ii=0;ii<dim+1;ii++)
|
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{
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test[ii] = Rows[j][ii] - Rows[i][ii];
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}
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//=Rows[j] - Rows[i]
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if (!LexicographicPositive(test))
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break;
|
||||
}
|
||||
}
|
||||
}
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||||
|
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//=Rows[j] - Rows[i]
|
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if (! LexicographicPositive(test))
|
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break;
|
||||
}
|
||||
}
|
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}
|
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if (j == Rows.size())
|
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{
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RowIndex += i;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if (j == Rows.size())
|
||||
{
|
||||
RowIndex += i;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
return RowIndex;
|
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}
|
||||
|
||||
return RowIndex;
|
||||
}
|
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|
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bool btLemkeAlgorithm::LexicographicPositive(const btVectorXu & v)
|
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bool btLemkeAlgorithm::LexicographicPositive(const btVectorXu& v)
|
||||
{
|
||||
int i = 0;
|
||||
// if (DEBUGLEVEL)
|
||||
// cout << "v " << v << endl;
|
||||
int i = 0;
|
||||
// if (DEBUGLEVEL)
|
||||
// cout << "v " << v << endl;
|
||||
|
||||
while(i < v.size()-1 && fabs(v[i]) < btMachEps())
|
||||
i++;
|
||||
if (v[i] > 0)
|
||||
return true;
|
||||
while (i < v.size() - 1 && fabs(v[i]) < btMachEps())
|
||||
i++;
|
||||
if (v[i] > 0)
|
||||
return true;
|
||||
|
||||
return false;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
void btLemkeAlgorithm::GaussJordanEliminationStep(btMatrixXu& A, int pivotRowIndex, int pivotColumnIndex, const btAlignedObjectArray<int>& basis)
|
||||
void btLemkeAlgorithm::GaussJordanEliminationStep(btMatrixXu& A, int pivotRowIndex, int pivotColumnIndex, const btAlignedObjectArray<int>& basis)
|
||||
{
|
||||
|
||||
btScalar a = -1 / A(pivotRowIndex, pivotColumnIndex);
|
||||
#ifdef BT_DEBUG_OSTREAM
|
||||
cout << A << std::endl;
|
||||
#endif
|
||||
|
||||
for (int i = 0; i < A.rows(); i++)
|
||||
for (int i = 0; i < A.rows(); i++)
|
||||
{
|
||||
if (i != pivotRowIndex)
|
||||
{
|
||||
for (int j = 0; j < A.cols(); j++)
|
||||
if (i != pivotRowIndex)
|
||||
{
|
||||
if (j != pivotColumnIndex)
|
||||
{
|
||||
btScalar v = A(i, j);
|
||||
v += A(pivotRowIndex, j) * A(i, pivotColumnIndex) * a;
|
||||
A.setElem(i, j, v);
|
||||
}
|
||||
for (int j = 0; j < A.cols(); j++)
|
||||
{
|
||||
if (j != pivotColumnIndex)
|
||||
{
|
||||
btScalar v = A(i, j);
|
||||
v += A(pivotRowIndex, j) * A(i, pivotColumnIndex) * a;
|
||||
A.setElem(i, j, v);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#ifdef BT_DEBUG_OSTREAM
|
||||
cout << A << std::endl;
|
||||
#endif //BT_DEBUG_OSTREAM
|
||||
for (int i = 0; i < A.cols(); i++)
|
||||
#endif //BT_DEBUG_OSTREAM
|
||||
for (int i = 0; i < A.cols(); i++)
|
||||
{
|
||||
A.mulElem(pivotRowIndex, i,-a);
|
||||
}
|
||||
#ifdef BT_DEBUG_OSTREAM
|
||||
cout << A << std::endl;
|
||||
#endif //#ifdef BT_DEBUG_OSTREAM
|
||||
|
||||
for (int i = 0; i < A.rows(); i++)
|
||||
{
|
||||
if (i != pivotRowIndex)
|
||||
{
|
||||
A.setElem(i, pivotColumnIndex,0);
|
||||
}
|
||||
A.mulElem(pivotRowIndex, i, -a);
|
||||
}
|
||||
#ifdef BT_DEBUG_OSTREAM
|
||||
cout << A << std::endl;
|
||||
#endif //#ifdef BT_DEBUG_OSTREAM
|
||||
}
|
||||
#endif //#ifdef BT_DEBUG_OSTREAM
|
||||
|
||||
bool btLemkeAlgorithm::greaterZero(const btVectorXu & vector)
|
||||
for (int i = 0; i < A.rows(); i++)
|
||||
{
|
||||
if (i != pivotRowIndex)
|
||||
{
|
||||
A.setElem(i, pivotColumnIndex, 0);
|
||||
}
|
||||
}
|
||||
#ifdef BT_DEBUG_OSTREAM
|
||||
cout << A << std::endl;
|
||||
#endif //#ifdef BT_DEBUG_OSTREAM
|
||||
}
|
||||
|
||||
bool btLemkeAlgorithm::greaterZero(const btVectorXu& vector)
|
||||
{
|
||||
bool isGreater = true;
|
||||
for (int i = 0; i < vector.size(); i++) {
|
||||
if (vector[i] < 0) {
|
||||
isGreater = false;
|
||||
break;
|
||||
}
|
||||
}
|
||||
bool isGreater = true;
|
||||
for (int i = 0; i < vector.size(); i++)
|
||||
{
|
||||
if (vector[i] < 0)
|
||||
{
|
||||
isGreater = false;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
return isGreater;
|
||||
}
|
||||
|
||||
bool btLemkeAlgorithm::validBasis(const btAlignedObjectArray<int>& basis)
|
||||
{
|
||||
bool isValid = true;
|
||||
for (int i = 0; i < basis.size(); i++) {
|
||||
if (basis[i] >= basis.size() * 2) { //then z0 is in the base
|
||||
isValid = false;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
return isValid;
|
||||
}
|
||||
return isGreater;
|
||||
}
|
||||
|
||||
bool btLemkeAlgorithm::validBasis(const btAlignedObjectArray<int>& basis)
|
||||
{
|
||||
bool isValid = true;
|
||||
for (int i = 0; i < basis.size(); i++)
|
||||
{
|
||||
if (basis[i] >= basis.size() * 2)
|
||||
{ //then z0 is in the base
|
||||
isValid = false;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
return isValid;
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user