372 lines
9.6 KiB
C++
372 lines
9.6 KiB
C++
/* Copyright (C) 2004-2013 MBSim Development Team
|
|
|
|
Code was converted for the Bullet Continuous Collision Detection and Physics Library
|
|
|
|
This software is provided 'as-is', without any express or implied warranty.
|
|
In no event will the authors be held liable for any damages arising from the use of this software.
|
|
Permission is granted to anyone to use this software for any purpose,
|
|
including commercial applications, and to alter it and redistribute it freely,
|
|
subject to the following restrictions:
|
|
|
|
1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
|
|
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
|
|
3. This notice may not be removed or altered from any source distribution.
|
|
*/
|
|
|
|
//The original version is here
|
|
//https://code.google.com/p/mbsim-env/source/browse/trunk/kernel/mbsim/numerics/linear_complementarity_problem/lemke_algorithm.cc
|
|
//This file is re-distributed under the ZLib license, with permission of the original author
|
|
//Math library was replaced from fmatvec to a the file src/LinearMath/btMatrixX.h
|
|
//STL/std::vector replaced by btAlignedObjectArray
|
|
|
|
|
|
|
|
#include "btLemkeAlgorithm.h"
|
|
|
|
#undef BT_DEBUG_OSTREAM
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
using namespace std;
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
btScalar btMachEps()
|
|
{
|
|
static bool calculated=false;
|
|
static btScalar machEps = btScalar(1.);
|
|
if (!calculated)
|
|
{
|
|
do {
|
|
machEps /= btScalar(2.0);
|
|
// If next epsilon yields 1, then break, because current
|
|
// epsilon is the machine epsilon.
|
|
}
|
|
while ((btScalar)(1.0 + (machEps/btScalar(2.0))) != btScalar(1.0));
|
|
// printf( "\nCalculated Machine epsilon: %G\n", machEps );
|
|
calculated=true;
|
|
}
|
|
return machEps;
|
|
}
|
|
|
|
btScalar btEpsRoot() {
|
|
|
|
static btScalar epsroot = 0.;
|
|
static bool alreadyCalculated = false;
|
|
|
|
if (!alreadyCalculated) {
|
|
epsroot = btSqrt(btMachEps());
|
|
alreadyCalculated = true;
|
|
}
|
|
return epsroot;
|
|
}
|
|
|
|
|
|
|
|
btVectorXu btLemkeAlgorithm::solve(unsigned int maxloops /* = 0*/)
|
|
{
|
|
|
|
|
|
steps = 0;
|
|
|
|
int dim = m_q.size();
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
if(DEBUGLEVEL >= 1) {
|
|
cout << "Dimension = " << dim << endl;
|
|
}
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
btVectorXu solutionVector(2 * dim);
|
|
solutionVector.setZero();
|
|
|
|
//, INIT, 0.);
|
|
|
|
btMatrixXu ident(dim, dim);
|
|
ident.setIdentity();
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
cout << m_M << std::endl;
|
|
#endif
|
|
|
|
btMatrixXu mNeg = m_M.negative();
|
|
|
|
btMatrixXu A(dim, 2 * dim + 2);
|
|
//
|
|
A.setSubMatrix(0, 0, dim - 1, dim - 1,ident);
|
|
A.setSubMatrix(0, dim, dim - 1, 2 * dim - 1,mNeg);
|
|
A.setSubMatrix(0, 2 * dim, dim - 1, 2 * dim, -1.f);
|
|
A.setSubMatrix(0, 2 * dim + 1, dim - 1, 2 * dim + 1,m_q);
|
|
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
cout << A << std::endl;
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
|
|
// btVectorXu q_;
|
|
// q_ >> A(0, 2 * dim + 1, dim - 1, 2 * dim + 1);
|
|
|
|
btAlignedObjectArray<int> basis;
|
|
//At first, all w-values are in the basis
|
|
for (int i = 0; i < dim; i++)
|
|
basis.push_back(i);
|
|
|
|
int pivotRowIndex = -1;
|
|
btScalar minValue = 1e30f;
|
|
bool greaterZero = true;
|
|
for (int i=0;i<dim;i++)
|
|
{
|
|
btScalar v =A(i,2*dim+1);
|
|
if (v<minValue)
|
|
{
|
|
minValue=v;
|
|
pivotRowIndex = i;
|
|
}
|
|
if (v<0)
|
|
greaterZero = false;
|
|
}
|
|
|
|
|
|
|
|
// int pivotRowIndex = q_.minIndex();//minIndex(q_); // first row is that with lowest q-value
|
|
int z0Row = pivotRowIndex; // remember the col of z0 for ending algorithm afterwards
|
|
int pivotColIndex = 2 * dim; // first col is that of z0
|
|
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
if (DEBUGLEVEL >= 3)
|
|
{
|
|
// cout << "A: " << A << endl;
|
|
cout << "pivotRowIndex " << pivotRowIndex << endl;
|
|
cout << "pivotColIndex " << pivotColIndex << endl;
|
|
cout << "Basis: ";
|
|
for (int i = 0; i < basis.size(); i++)
|
|
cout << basis[i] << " ";
|
|
cout << endl;
|
|
}
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
if (!greaterZero)
|
|
{
|
|
|
|
if (maxloops == 0) {
|
|
maxloops = 100;
|
|
// 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...
|
|
}
|
|
|
|
/*start looping*/
|
|
for(steps = 0; steps < maxloops; steps++) {
|
|
|
|
GaussJordanEliminationStep(A, pivotRowIndex, pivotColIndex, basis);
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
if (DEBUGLEVEL >= 3) {
|
|
// cout << "A: " << A << endl;
|
|
cout << "pivotRowIndex " << pivotRowIndex << endl;
|
|
cout << "pivotColIndex " << pivotColIndex << endl;
|
|
cout << "Basis: ";
|
|
for (int i = 0; i < basis.size(); i++)
|
|
cout << basis[i] << " ";
|
|
cout << endl;
|
|
}
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
int pivotColIndexOld = pivotColIndex;
|
|
|
|
/*find new column index */
|
|
if (basis[pivotRowIndex] < dim) //if a w-value left the basis get in the correspondent z-value
|
|
pivotColIndex = basis[pivotRowIndex] + dim;
|
|
else
|
|
//else do it the other way round and get in the corresponding w-value
|
|
pivotColIndex = basis[pivotRowIndex] - dim;
|
|
|
|
/*the column becomes part of the basis*/
|
|
basis[pivotRowIndex] = pivotColIndexOld;
|
|
|
|
pivotRowIndex = findLexicographicMinimum(A, pivotColIndex);
|
|
|
|
if(z0Row == pivotRowIndex) { //if z0 leaves the basis the solution is found --> one last elimination step is necessary
|
|
GaussJordanEliminationStep(A, pivotRowIndex, pivotColIndex, basis);
|
|
basis[pivotRowIndex] = pivotColIndex; //update basis
|
|
break;
|
|
}
|
|
|
|
}
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
if(DEBUGLEVEL >= 1) {
|
|
cout << "Number of loops: " << steps << endl;
|
|
cout << "Number of maximal loops: " << maxloops << endl;
|
|
}
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
if(!validBasis(basis)) {
|
|
info = -1;
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
if(DEBUGLEVEL >= 1)
|
|
cerr << "Lemke-Algorithm ended with Ray-Termination (no valid solution)." << endl;
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
return solutionVector;
|
|
}
|
|
|
|
}
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
if (DEBUGLEVEL >= 2) {
|
|
// cout << "A: " << A << endl;
|
|
cout << "pivotRowIndex " << pivotRowIndex << endl;
|
|
cout << "pivotColIndex " << pivotColIndex << endl;
|
|
}
|
|
#endif //BT_DEBUG_OSTREAM
|
|
|
|
for (int i = 0; i < basis.size(); i++)
|
|
{
|
|
solutionVector[basis[i]] = A(i,2*dim+1);//q_[i];
|
|
}
|
|
|
|
info = 0;
|
|
|
|
return solutionVector;
|
|
}
|
|
|
|
int btLemkeAlgorithm::findLexicographicMinimum(const btMatrixXu& A, const int & pivotColIndex) {
|
|
int RowIndex = 0;
|
|
int dim = A.rows();
|
|
btAlignedObjectArray<btVectorXu> Rows;
|
|
for (int row = 0; row < dim; row++)
|
|
{
|
|
|
|
btVectorXu vec(dim + 1);
|
|
vec.setZero();//, INIT, 0.)
|
|
Rows.push_back(vec);
|
|
btScalar a = A(row, pivotColIndex);
|
|
if (a > 0) {
|
|
Rows[row][0] = A(row, 2 * dim + 1) / a;
|
|
Rows[row][1] = A(row, 2 * dim) / a;
|
|
for (int j = 2; j < dim + 1; j++)
|
|
Rows[row][j] = A(row, j - 1) / a;
|
|
|
|
#ifdef BT_DEBUG_OSTREAM
|
|
// if (DEBUGLEVEL) {
|
|
// cout << "Rows(" << row << ") = " << Rows[row] << endl;
|
|
// }
|
|
#endif
|
|
}
|
|
}
|
|
|
|
for (int i = 0; i < Rows.size(); i++)
|
|
{
|
|
if (Rows[i].nrm2() > 0.) {
|
|
|
|
int j = 0;
|
|
for (; j < Rows.size(); j++)
|
|
{
|
|
if(i != j)
|
|
{
|
|
if(Rows[j].nrm2() > 0.)
|
|
{
|
|
btVectorXu test(dim + 1);
|
|
for (int ii=0;ii<dim+1;ii++)
|
|
{
|
|
test[ii] = Rows[j][ii] - Rows[i][ii];
|
|
}
|
|
|
|
//=Rows[j] - Rows[i]
|
|
if (! LexicographicPositive(test))
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (j == Rows.size())
|
|
{
|
|
RowIndex += i;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
return RowIndex;
|
|
}
|
|
|
|
bool btLemkeAlgorithm::LexicographicPositive(const btVectorXu & v)
|
|
{
|
|
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;
|
|
|
|
return false;
|
|
}
|
|
|
|
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++)
|
|
{
|
|
if (i != pivotRowIndex)
|
|
{
|
|
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++)
|
|
{
|
|
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);
|
|
}
|
|
}
|
|
#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;
|
|
}
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
|