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-/*
-Bullet Continuous Collision Detection and Physics Library
-Copyright (c) 2003-2013 Erwin Coumans http://bulletphysics.org
-
-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.
-*/
-///original version written by Erwin Coumans, October 2013
-
-#ifndef BT_LEMKE_SOLVER_H
-#define BT_LEMKE_SOLVER_H
-
-#include "btMLCPSolverInterface.h"
-#include "btLemkeAlgorithm.h"
-
-///The btLemkeSolver is based on "Fast Implementation of Lemkeā€™s Algorithm for Rigid Body Contact Simulation (John E. Lloyd) "
-///It is a slower but more accurate solver. Increase the m_maxLoops for better convergence, at the cost of more CPU time.
-///The original implementation of the btLemkeAlgorithm was done by Kilian Grundl from the MBSim team
-class btLemkeSolver : public btMLCPSolverInterface
-{
-protected:
-public:
- btScalar m_maxValue;
- int m_debugLevel;
- int m_maxLoops;
- bool m_useLoHighBounds;
-
- btLemkeSolver()
- : m_maxValue(100000),
- m_debugLevel(0),
- m_maxLoops(1000),
- m_useLoHighBounds(true)
- {
- }
- virtual bool solveMLCP(const btMatrixXu& A, const btVectorXu& b, btVectorXu& x, const btVectorXu& lo, const btVectorXu& hi, const btAlignedObjectArray<int>& limitDependency, int numIterations, bool useSparsity = true)
- {
- if (m_useLoHighBounds)
- {
- BT_PROFILE("btLemkeSolver::solveMLCP");
- int n = A.rows();
- if (0 == n)
- return true;
-
- bool fail = false;
-
- btVectorXu solution(n);
- btVectorXu q1;
- q1.resize(n);
- for (int row = 0; row < n; row++)
- {
- q1[row] = -b[row];
- }
-
- // cout << "A" << endl;
- // cout << A << endl;
-
- /////////////////////////////////////
-
- //slow matrix inversion, replace with LU decomposition
- btMatrixXu A1;
- btMatrixXu B(n, n);
- {
- //BT_PROFILE("inverse(slow)");
- A1.resize(A.rows(), A.cols());
- for (int row = 0; row < A.rows(); row++)
- {
- for (int col = 0; col < A.cols(); col++)
- {
- A1.setElem(row, col, A(row, col));
- }
- }
-
- btMatrixXu matrix;
- matrix.resize(n, 2 * n);
- for (int row = 0; row < n; row++)
- {
- for (int col = 0; col < n; col++)
- {
- matrix.setElem(row, col, A1(row, col));
- }
- }
-
- btScalar ratio, a;
- int i, j, k;
- for (i = 0; i < n; i++)
- {
- for (j = n; j < 2 * n; j++)
- {
- if (i == (j - n))
- matrix.setElem(i, j, 1.0);
- else
- matrix.setElem(i, j, 0.0);
- }
- }
- for (i = 0; i < n; i++)
- {
- for (j = 0; j < n; j++)
- {
- if (i != j)
- {
- btScalar v = matrix(i, i);
- if (btFuzzyZero(v))
- {
- a = 0.000001f;
- }
- ratio = matrix(j, i) / matrix(i, i);
- for (k = 0; k < 2 * n; k++)
- {
- matrix.addElem(j, k, -ratio * matrix(i, k));
- }
- }
- }
- }
- for (i = 0; i < n; i++)
- {
- a = matrix(i, i);
- if (btFuzzyZero(a))
- {
- a = 0.000001f;
- }
- btScalar invA = 1.f / a;
- for (j = 0; j < 2 * n; j++)
- {
- matrix.mulElem(i, j, invA);
- }
- }
-
- for (int row = 0; row < n; row++)
- {
- for (int col = 0; col < n; col++)
- {
- B.setElem(row, col, matrix(row, n + col));
- }
- }
- }
-
- btMatrixXu b1(n, 1);
-
- btMatrixXu M(n * 2, n * 2);
- for (int row = 0; row < n; row++)
- {
- b1.setElem(row, 0, -b[row]);
- for (int col = 0; col < n; col++)
- {
- btScalar v = B(row, col);
- M.setElem(row, col, v);
- M.setElem(n + row, n + col, v);
- M.setElem(n + row, col, -v);
- M.setElem(row, n + col, -v);
- }
- }
-
- btMatrixXu Bb1 = B * b1;
- // q = [ (-B*b1 - lo)' (hi + B*b1)' ]'
-
- btVectorXu qq;
- qq.resize(n * 2);
- for (int row = 0; row < n; row++)
- {
- qq[row] = -Bb1(row, 0) - lo[row];
- qq[n + row] = Bb1(row, 0) + hi[row];
- }
-
- btVectorXu z1;
-
- btMatrixXu y1;
- y1.resize(n, 1);
- btLemkeAlgorithm lemke(M, qq, m_debugLevel);
- {
- //BT_PROFILE("lemke.solve");
- lemke.setSystem(M, qq);
- z1 = lemke.solve(m_maxLoops);
- }
- for (int row = 0; row < n; row++)
- {
- y1.setElem(row, 0, z1[2 * n + row] - z1[3 * n + row]);
- }
- btMatrixXu y1_b1(n, 1);
- for (int i = 0; i < n; i++)
- {
- y1_b1.setElem(i, 0, y1(i, 0) - b1(i, 0));
- }
-
- btMatrixXu x1;
-
- x1 = B * (y1_b1);
-
- for (int row = 0; row < n; row++)
- {
- solution[row] = x1(row, 0); //n];
- }
-
- int errorIndexMax = -1;
- int errorIndexMin = -1;
- float errorValueMax = -1e30;
- float errorValueMin = 1e30;
-
- for (int i = 0; i < n; i++)
- {
- x[i] = solution[i];
- volatile btScalar check = x[i];
- if (x[i] != check)
- {
- //printf("Lemke result is #NAN\n");
- x.setZero();
- return false;
- }
-
- //this is some hack/safety mechanism, to discard invalid solutions from the Lemke solver
- //we need to figure out why it happens, and fix it, or detect it properly)
- if (x[i] > m_maxValue)
- {
- if (x[i] > errorValueMax)
- {
- fail = true;
- errorIndexMax = i;
- errorValueMax = x[i];
- }
- ////printf("x[i] = %f,",x[i]);
- }
- if (x[i] < -m_maxValue)
- {
- if (x[i] < errorValueMin)
- {
- errorIndexMin = i;
- errorValueMin = x[i];
- fail = true;
- //printf("x[i] = %f,",x[i]);
- }
- }
- }
- if (fail)
- {
- int m_errorCountTimes = 0;
- if (errorIndexMin < 0)
- errorValueMin = 0.f;
- if (errorIndexMax < 0)
- errorValueMax = 0.f;
- m_errorCountTimes++;
- // printf("Error (x[%d] = %f, x[%d] = %f), resetting %d times\n", errorIndexMin,errorValueMin, errorIndexMax, errorValueMax, errorCountTimes++);
- for (int i = 0; i < n; i++)
- {
- x[i] = 0.f;
- }
- }
- return !fail;
- }
- else
-
- {
- int dimension = A.rows();
- if (0 == dimension)
- return true;
-
- // printf("================ solving using Lemke/Newton/Fixpoint\n");
-
- btVectorXu q;
- q.resize(dimension);
- for (int row = 0; row < dimension; row++)
- {
- q[row] = -b[row];
- }
-
- btLemkeAlgorithm lemke(A, q, m_debugLevel);
-
- lemke.setSystem(A, q);
-
- btVectorXu solution = lemke.solve(m_maxLoops);
-
- //check solution
-
- bool fail = false;
- int errorIndexMax = -1;
- int errorIndexMin = -1;
- float errorValueMax = -1e30;
- float errorValueMin = 1e30;
-
- for (int i = 0; i < dimension; i++)
- {
- x[i] = solution[i + dimension];
- volatile btScalar check = x[i];
- if (x[i] != check)
- {
- x.setZero();
- return false;
- }
-
- //this is some hack/safety mechanism, to discard invalid solutions from the Lemke solver
- //we need to figure out why it happens, and fix it, or detect it properly)
- if (x[i] > m_maxValue)
- {
- if (x[i] > errorValueMax)
- {
- fail = true;
- errorIndexMax = i;
- errorValueMax = x[i];
- }
- ////printf("x[i] = %f,",x[i]);
- }
- if (x[i] < -m_maxValue)
- {
- if (x[i] < errorValueMin)
- {
- errorIndexMin = i;
- errorValueMin = x[i];
- fail = true;
- //printf("x[i] = %f,",x[i]);
- }
- }
- }
- if (fail)
- {
- static int errorCountTimes = 0;
- if (errorIndexMin < 0)
- errorValueMin = 0.f;
- if (errorIndexMax < 0)
- errorValueMax = 0.f;
- printf("Error (x[%d] = %f, x[%d] = %f), resetting %d times\n", errorIndexMin, errorValueMin, errorIndexMax, errorValueMax, errorCountTimes++);
- for (int i = 0; i < dimension; i++)
- {
- x[i] = 0.f;
- }
- }
-
- return !fail;
- }
- return true;
- }
-};
-
-#endif //BT_LEMKE_SOLVER_H