code: /*
   Written by Xuchen Han <xuchenhan2015@u.northwestern.edu>
   
   Bullet Continuous Collision Detection and Physics Library
   Copyright (c) 2019 Google Inc. 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.
   */
  
  #include "btDeformableContactProjection.h"
  #include "btDeformableMultiBodyDynamicsWorld.h"
  #include <algorithm>
  #include <cmath>
  btScalar btDeformableContactProjection::update(btCollisionObject** deformableBodies, int numDeformableBodies, const btContactSolverInfo& infoGlobal)
  {
  	btScalar residualSquare = 0;
  	for (int i = 0; i < numDeformableBodies; ++i)
  	{
  		for (int j = 0; j < m_softBodies.size(); ++j)
  		{
  			btCollisionObject* psb = m_softBodies[j];
  			if (psb != deformableBodies[i])
  			{
  				continue;
  			}
  			for (int k = 0; k < m_nodeRigidConstraints[j].size(); ++k)
  			{
  				btDeformableNodeRigidContactConstraint& constraint = m_nodeRigidConstraints[j][k];
  				btScalar localResidualSquare = constraint.solveConstraint(infoGlobal);
  				residualSquare = btMax(residualSquare, localResidualSquare);
  			}
  			for (int k = 0; k < m_nodeAnchorConstraints[j].size(); ++k)
  			{
  				btDeformableNodeAnchorConstraint& constraint = m_nodeAnchorConstraints[j][k];
  				btScalar localResidualSquare = constraint.solveConstraint(infoGlobal);
  				residualSquare = btMax(residualSquare, localResidualSquare);
  			}
  			for (int k = 0; k < m_faceRigidConstraints[j].size(); ++k)
  			{
  				btDeformableFaceRigidContactConstraint& constraint = m_faceRigidConstraints[j][k];
  				btScalar localResidualSquare = constraint.solveConstraint(infoGlobal);
  				residualSquare = btMax(residualSquare, localResidualSquare);
  			}
  			for (int k = 0; k < m_deformableConstraints[j].size(); ++k)
  			{
  				btDeformableFaceNodeContactConstraint& constraint = m_deformableConstraints[j][k];
  				btScalar localResidualSquare = constraint.solveConstraint(infoGlobal);
  				residualSquare = btMax(residualSquare, localResidualSquare);
  			}
  		}
  	}
  	return residualSquare;
  }
  
  btScalar btDeformableContactProjection::solveSplitImpulse(btCollisionObject** deformableBodies, int numDeformableBodies, const btContactSolverInfo& infoGlobal)
  {
  	btScalar residualSquare = 0;
  	for (int i = 0; i < numDeformableBodies; ++i)
  	{
  		for (int j = 0; j < m_softBodies.size(); ++j)
  		{
  			btCollisionObject* psb = m_softBodies[j];
  			if (psb != deformableBodies[i])
  			{
  				continue;
  			}
  			for (int k = 0; k < m_nodeRigidConstraints[j].size(); ++k)
  			{
  				btDeformableNodeRigidContactConstraint& constraint = m_nodeRigidConstraints[j][k];
  				btScalar localResidualSquare = constraint.solveSplitImpulse(infoGlobal);
  				residualSquare = btMax(residualSquare, localResidualSquare);
  			}
  			for (int k = 0; k < m_faceRigidConstraints[j].size(); ++k)
  			{
  				btDeformableFaceRigidContactConstraint& constraint = m_faceRigidConstraints[j][k];
  				btScalar localResidualSquare = constraint.solveSplitImpulse(infoGlobal);
  				residualSquare = btMax(residualSquare, localResidualSquare);
  			}
  		}
  	}
  	return residualSquare;
  }
  
  void btDeformableContactProjection::setConstraints(const btContactSolverInfo& infoGlobal)
  {
  	BT_PROFILE("setConstraints");
  	for (int i = 0; i < m_softBodies.size(); ++i)
  	{
  		btSoftBody* psb = m_softBodies[i];
  		if (!psb->isActive())
  		{
  			continue;
  		}
  
  		// set Dirichlet constraint
  		for (int j = 0; j < psb->m_nodes.size(); ++j)
  		{
  			if (psb->m_nodes[j].m_im == 0)
  			{
  				btDeformableStaticConstraint static_constraint(&psb->m_nodes[j], infoGlobal);
  				m_staticConstraints[i].push_back(static_constraint);
  			}
  		}
  
  		// set up deformable anchors
  		for (int j = 0; j < psb->m_deformableAnchors.size(); ++j)
  		{
  			btSoftBody::DeformableNodeRigidAnchor& anchor = psb->m_deformableAnchors[j];
  			// skip fixed points
  			if (anchor.m_node->m_im == 0)
  			{
  				continue;
  			}
  			anchor.m_c1 = anchor.m_cti.m_colObj->getWorldTransform().getBasis() * anchor.m_local;
  			btDeformableNodeAnchorConstraint constraint(anchor, infoGlobal);
  			m_nodeAnchorConstraints[i].push_back(constraint);
  		}
  
  		// set Deformable Node vs. Rigid constraint
  		for (int j = 0; j < psb->m_nodeRigidContacts.size(); ++j)
  		{
  			const btSoftBody::DeformableNodeRigidContact& contact = psb->m_nodeRigidContacts[j];
  			// skip fixed points
  			if (contact.m_node->m_im == 0)
  			{
  				continue;
  			}
  			btDeformableNodeRigidContactConstraint constraint(contact, infoGlobal);
  			m_nodeRigidConstraints[i].push_back(constraint);
  		}
  
  		// set Deformable Face vs. Rigid constraint
  		for (int j = 0; j < psb->m_faceRigidContacts.size(); ++j)
  		{
  			const btSoftBody::DeformableFaceRigidContact& contact = psb->m_faceRigidContacts[j];
  			// skip fixed faces
  			if (contact.m_c2 == 0)
  			{
  				continue;
  			}
  			btDeformableFaceRigidContactConstraint constraint(contact, infoGlobal, m_useStrainLimiting);
  			m_faceRigidConstraints[i].push_back(constraint);
  		}
  	}
  }
  
  void btDeformableContactProjection::project(TVStack& x)
  {
  #ifndef USE_MGS
  	const int dim = 3;
  	for (int index = 0; index < m_projectionsDict.size(); ++index)
  	{
  		btAlignedObjectArray<btVector3>& projectionDirs = *m_projectionsDict.getAtIndex(index);
  		size_t i = m_projectionsDict.getKeyAtIndex(index).getUid1();
  		if (projectionDirs.size() >= dim)
  		{
  			// static node
  			x[i].setZero();
  			continue;
  		}
  		else if (projectionDirs.size() == 2)
  		{
  			btVector3 dir0 = projectionDirs[0];
  			btVector3 dir1 = projectionDirs[1];
  			btVector3 free_dir = btCross(dir0, dir1);
  			if (free_dir.safeNorm() < SIMD_EPSILON)
  			{
  				x[i] -= x[i].dot(dir0) * dir0;
  			}
  			else
  			{
  				free_dir.normalize();
  				x[i] = x[i].dot(free_dir) * free_dir;
  			}
  		}
  		else
  		{
  			btAssert(projectionDirs.size() == 1);
  			btVector3 dir0 = projectionDirs[0];
  			x[i] -= x[i].dot(dir0) * dir0;
  		}
  	}
  #else
  	btReducedVector p(x.size());
  	for (int i = 0; i < m_projections.size(); ++i)
  	{
  		p += (m_projections[i].dot(x) * m_projections[i]);
  	}
  	for (int i = 0; i < p.m_indices.size(); ++i)
  	{
  		x[p.m_indices[i]] -= p.m_vecs[i];
  	}
  #endif
  }
  
  void btDeformableContactProjection::setProjection()
  {
  #ifndef USE_MGS
  	BT_PROFILE("btDeformableContactProjection::setProjection");
  	btAlignedObjectArray<btVector3> units;
  	units.push_back(btVector3(1, 0, 0));
  	units.push_back(btVector3(0, 1, 0));
  	units.push_back(btVector3(0, 0, 1));
  	for (int i = 0; i < m_softBodies.size(); ++i)
  	{
  		btSoftBody* psb = m_softBodies[i];
  		if (!psb->isActive())
  		{
  			continue;
  		}
  		for (int j = 0; j < m_staticConstraints[i].size(); ++j)
  		{
  			int index = m_staticConstraints[i][j].m_node->index;
  			m_staticConstraints[i][j].m_node->m_constrained = true;
  			if (m_projectionsDict.find(index) == NULL)
  			{
  				m_projectionsDict.insert(index, units);
  			}
  			else
  			{
  				btAlignedObjectArray<btVector3>& projections = *m_projectionsDict[index];
  				for (int k = 0; k < 3; ++k)
  				{
  					projections.push_back(units[k]);
  				}
  			}
  		}
  		for (int j = 0; j < m_nodeAnchorConstraints[i].size(); ++j)
  		{
  			int index = m_nodeAnchorConstraints[i][j].m_anchor->m_node->index;
  			m_nodeAnchorConstraints[i][j].m_anchor->m_node->m_constrained = true;
  			if (m_projectionsDict.find(index) == NULL)
  			{
  				m_projectionsDict.insert(index, units);
  			}
  			else
  			{
  				btAlignedObjectArray<btVector3>& projections = *m_projectionsDict[index];
  				for (int k = 0; k < 3; ++k)
  				{
  					projections.push_back(units[k]);
  				}
  			}
  		}
  		for (int j = 0; j < m_nodeRigidConstraints[i].size(); ++j)
  		{
  			int index = m_nodeRigidConstraints[i][j].m_node->index;
  			m_nodeRigidConstraints[i][j].m_node->m_constrained = true;
  			if (m_nodeRigidConstraints[i][j].m_binding)
  			{
  				if (m_nodeRigidConstraints[i][j].m_static)
  				{
  					if (m_projectionsDict.find(index) == NULL)
  					{
  						m_projectionsDict.insert(index, units);
  					}
  					else
  					{
  						btAlignedObjectArray<btVector3>& projections = *m_projectionsDict[index];
  						for (int k = 0; k < 3; ++k)
  						{
  							projections.push_back(units[k]);
  						}
  					}
  				}
  				else
  				{
  					if (m_projectionsDict.find(index) == NULL)
  					{
  						btAlignedObjectArray<btVector3> projections;
  						projections.push_back(m_nodeRigidConstraints[i][j].m_normal);
  						m_projectionsDict.insert(index, projections);
  					}
  					else
  					{
  						btAlignedObjectArray<btVector3>& projections = *m_projectionsDict[index];
  						projections.push_back(m_nodeRigidConstraints[i][j].m_normal);
  					}
  				}
  			}
  		}
  		for (int j = 0; j < m_faceRigidConstraints[i].size(); ++j)
  		{
  			const btSoftBody::Face* face = m_faceRigidConstraints[i][j].m_face;
  			if (m_faceRigidConstraints[i][j].m_binding)
  			{
  				for (int k = 0; k < 3; ++k)
  				{
  					face->m_n[k]->m_constrained = true;
  				}
  			}
  			for (int k = 0; k < 3; ++k)
  			{
  				btSoftBody::Node* node = face->m_n[k];
  				int index = node->index;
  				if (m_faceRigidConstraints[i][j].m_static)
  				{
  					if (m_projectionsDict.find(index) == NULL)
  					{
  						m_projectionsDict.insert(index, units);
  					}
  					else
  					{
  						btAlignedObjectArray<btVector3>& projections = *m_projectionsDict[index];
  						for (int l = 0; l < 3; ++l)
  						{
  							projections.push_back(units[l]);
  						}
  					}
  				}
  				else
  				{
  					if (m_projectionsDict.find(index) == NULL)
  					{
  						btAlignedObjectArray<btVector3> projections;
  						projections.push_back(m_faceRigidConstraints[i][j].m_normal);
  						m_projectionsDict.insert(index, projections);
  					}
  					else
  					{
  						btAlignedObjectArray<btVector3>& projections = *m_projectionsDict[index];
  						projections.push_back(m_faceRigidConstraints[i][j].m_normal);
  					}
  				}
  			}
  		}
  	}
  #else
  	int dof = 0;
  	for (int i = 0; i < m_softBodies.size(); ++i)
  	{
  		dof += m_softBodies[i]->m_nodes.size();
  	}
  	for (int i = 0; i < m_softBodies.size(); ++i)
  	{
  		btSoftBody* psb = m_softBodies[i];
  		if (!psb->isActive())
  		{
  			continue;
  		}
  		for (int j = 0; j < m_staticConstraints[i].size(); ++j)
  		{
  			int index = m_staticConstraints[i][j].m_node->index;
  			m_staticConstraints[i][j].m_node->m_penetration = SIMD_INFINITY;
  			btAlignedObjectArray<int> indices;
  			btAlignedObjectArray<btVector3> vecs1, vecs2, vecs3;
  			indices.push_back(index);
  			vecs1.push_back(btVector3(1, 0, 0));
  			vecs2.push_back(btVector3(0, 1, 0));
  			vecs3.push_back(btVector3(0, 0, 1));
  			m_projections.push_back(btReducedVector(dof, indices, vecs1));
  			m_projections.push_back(btReducedVector(dof, indices, vecs2));
  			m_projections.push_back(btReducedVector(dof, indices, vecs3));
  		}
  
  		for (int j = 0; j < m_nodeAnchorConstraints[i].size(); ++j)
  		{
  			int index = m_nodeAnchorConstraints[i][j].m_anchor->m_node->index;
  			m_nodeAnchorConstraints[i][j].m_anchor->m_node->m_penetration = SIMD_INFINITY;
  			btAlignedObjectArray<int> indices;
  			btAlignedObjectArray<btVector3> vecs1, vecs2, vecs3;
  			indices.push_back(index);
  			vecs1.push_back(btVector3(1, 0, 0));
  			vecs2.push_back(btVector3(0, 1, 0));
  			vecs3.push_back(btVector3(0, 0, 1));
  			m_projections.push_back(btReducedVector(dof, indices, vecs1));
  			m_projections.push_back(btReducedVector(dof, indices, vecs2));
  			m_projections.push_back(btReducedVector(dof, indices, vecs3));
  		}
  		for (int j = 0; j < m_nodeRigidConstraints[i].size(); ++j)
  		{
  			int index = m_nodeRigidConstraints[i][j].m_node->index;
  			m_nodeRigidConstraints[i][j].m_node->m_penetration = -m_nodeRigidConstraints[i][j].getContact()->m_cti.m_offset;
  			btAlignedObjectArray<int> indices;
  			indices.push_back(index);
  			btAlignedObjectArray<btVector3> vecs1, vecs2, vecs3;
  			if (m_nodeRigidConstraints[i][j].m_static)
  			{
  				vecs1.push_back(btVector3(1, 0, 0));
  				vecs2.push_back(btVector3(0, 1, 0));
  				vecs3.push_back(btVector3(0, 0, 1));
  				m_projections.push_back(btReducedVector(dof, indices, vecs1));
  				m_projections.push_back(btReducedVector(dof, indices, vecs2));
  				m_projections.push_back(btReducedVector(dof, indices, vecs3));
  			}
  			else
  			{
  				vecs1.push_back(m_nodeRigidConstraints[i][j].m_normal);
  				m_projections.push_back(btReducedVector(dof, indices, vecs1));
  			}
  		}
  		for (int j = 0; j < m_faceRigidConstraints[i].size(); ++j)
  		{
  			const btSoftBody::Face* face = m_faceRigidConstraints[i][j].m_face;
  			btVector3 bary = m_faceRigidConstraints[i][j].getContact()->m_bary;
  			btScalar penetration = -m_faceRigidConstraints[i][j].getContact()->m_cti.m_offset;
  			for (int k = 0; k < 3; ++k)
  			{
  				face->m_n[k]->m_penetration = btMax(face->m_n[k]->m_penetration, penetration);
  			}
  			if (m_faceRigidConstraints[i][j].m_static)
  			{
  				for (int l = 0; l < 3; ++l)
  				{
  					btReducedVector rv(dof);
  					for (int k = 0; k < 3; ++k)
  					{
  						rv.m_indices.push_back(face->m_n[k]->index);
  						btVector3 v(0, 0, 0);
  						v[l] = bary[k];
  						rv.m_vecs.push_back(v);
  						rv.sort();
  					}
  					m_projections.push_back(rv);
  				}
  			}
  			else
  			{
  				btReducedVector rv(dof);
  				for (int k = 0; k < 3; ++k)
  				{
  					rv.m_indices.push_back(face->m_n[k]->index);
  					rv.m_vecs.push_back(bary[k] * m_faceRigidConstraints[i][j].m_normal);
  					rv.sort();
  				}
  				m_projections.push_back(rv);
  			}
  		}
  	}
  	btModifiedGramSchmidt<btReducedVector> mgs(m_projections);
  	mgs.solve();
  	m_projections = mgs.m_out;
  #endif
  }
  
  void btDeformableContactProjection::checkConstraints(const TVStack& x)
  {
  	for (int i = 0; i < m_lagrangeMultipliers.size(); ++i)
  	{
  		btVector3 d(0, 0, 0);
  		const LagrangeMultiplier& lm = m_lagrangeMultipliers[i];
  		for (int j = 0; j < lm.m_num_constraints; ++j)
  		{
  			for (int k = 0; k < lm.m_num_nodes; ++k)
  			{
  				d[j] += lm.m_weights[k] * x[lm.m_indices[k]].dot(lm.m_dirs[j]);
  			}
  		}
  		//		printf("d = %f, %f, %f\n", d[0], d[1], d[2]);
  		//        printf("val = %f, %f, %f\n", lm.m_vals[0], lm.m_vals[1], lm.m_vals[2]);
  	}
  }
  
  void btDeformableContactProjection::setLagrangeMultiplier()
  {
  	for (int i = 0; i < m_softBodies.size(); ++i)
  	{
  		btSoftBody* psb = m_softBodies[i];
  		if (!psb->isActive())
  		{
  			continue;
  		}
  		for (int j = 0; j < m_staticConstraints[i].size(); ++j)
  		{
  			int index = m_staticConstraints[i][j].m_node->index;
  			m_staticConstraints[i][j].m_node->m_constrained = true;
  			LagrangeMultiplier lm;
  			lm.m_num_nodes = 1;
  			lm.m_indices[0] = index;
  			lm.m_weights[0] = 1.0;
  			lm.m_num_constraints = 3;
  			lm.m_dirs[0] = btVector3(1, 0, 0);
  			lm.m_dirs[1] = btVector3(0, 1, 0);
  			lm.m_dirs[2] = btVector3(0, 0, 1);
  			m_lagrangeMultipliers.push_back(lm);
  		}
  		for (int j = 0; j < m_nodeAnchorConstraints[i].size(); ++j)
  		{
  			int index = m_nodeAnchorConstraints[i][j].m_anchor->m_node->index;
  			m_nodeAnchorConstraints[i][j].m_anchor->m_node->m_constrained = true;
  			LagrangeMultiplier lm;
  			lm.m_num_nodes = 1;
  			lm.m_indices[0] = index;
  			lm.m_weights[0] = 1.0;
  			lm.m_num_constraints = 3;
  			lm.m_dirs[0] = btVector3(1, 0, 0);
  			lm.m_dirs[1] = btVector3(0, 1, 0);
  			lm.m_dirs[2] = btVector3(0, 0, 1);
  			m_lagrangeMultipliers.push_back(lm);
  		}
  
  		for (int j = 0; j < m_nodeRigidConstraints[i].size(); ++j)
  		{
  			if (!m_nodeRigidConstraints[i][j].m_binding)
  			{
  				continue;
  			}
  			int index = m_nodeRigidConstraints[i][j].m_node->index;
  			m_nodeRigidConstraints[i][j].m_node->m_constrained = true;
  			LagrangeMultiplier lm;
  			lm.m_num_nodes = 1;
  			lm.m_indices[0] = index;
  			lm.m_weights[0] = 1.0;
  			if (m_nodeRigidConstraints[i][j].m_static)
  			{
  				lm.m_num_constraints = 3;
  				lm.m_dirs[0] = btVector3(1, 0, 0);
  				lm.m_dirs[1] = btVector3(0, 1, 0);
  				lm.m_dirs[2] = btVector3(0, 0, 1);
  			}
  			else
  			{
  				lm.m_num_constraints = 1;
  				lm.m_dirs[0] = m_nodeRigidConstraints[i][j].m_normal;
  			}
  			m_lagrangeMultipliers.push_back(lm);
  		}
  
  		for (int j = 0; j < m_faceRigidConstraints[i].size(); ++j)
  		{
  			if (!m_faceRigidConstraints[i][j].m_binding)
  			{
  				continue;
  			}
  			btSoftBody::Face* face = m_faceRigidConstraints[i][j].m_face;
  
  			btVector3 bary = m_faceRigidConstraints[i][j].getContact()->m_bary;
  			LagrangeMultiplier lm;
  			lm.m_num_nodes = 3;
  
  			for (int k = 0; k < 3; ++k)
  			{
  				face->m_n[k]->m_constrained = true;
  				lm.m_indices[k] = face->m_n[k]->index;
  				lm.m_weights[k] = bary[k];
  			}
  			if (m_faceRigidConstraints[i][j].m_static)
  			{
  				face->m_pcontact[3] = 1;
  				lm.m_num_constraints = 3;
  				lm.m_dirs[0] = btVector3(1, 0, 0);
  				lm.m_dirs[1] = btVector3(0, 1, 0);
  				lm.m_dirs[2] = btVector3(0, 0, 1);
  			}
  			else
  			{
  				face->m_pcontact[3] = 0;
  				lm.m_num_constraints = 1;
  				lm.m_dirs[0] = m_faceRigidConstraints[i][j].m_normal;
  			}
  			m_lagrangeMultipliers.push_back(lm);
  		}
  	}
  }
  
  //
  void btDeformableContactProjection::applyDynamicFriction(TVStack& f)
  {
  	for (int i = 0; i < m_softBodies.size(); ++i)
  	{
  		for (int j = 0; j < m_nodeRigidConstraints[i].size(); ++j)
  		{
  			const btDeformableNodeRigidContactConstraint& constraint = m_nodeRigidConstraints[i][j];
  			const btSoftBody::Node* node = constraint.m_node;
  			if (node->m_im != 0)
  			{
  				int index = node->index;
  				f[index] += constraint.getDv(node) * (1. / node->m_im);
  			}
  		}
  		for (int j = 0; j < m_faceRigidConstraints[i].size(); ++j)
  		{
  			const btDeformableFaceRigidContactConstraint& constraint = m_faceRigidConstraints[i][j];
  			const btSoftBody::Face* face = constraint.getContact()->m_face;
  			for (int k = 0; k < 3; ++k)
  			{
  				const btSoftBody::Node* node = face->m_n[k];
  				if (node->m_im != 0)
  				{
  					int index = node->index;
  					f[index] += constraint.getDv(node) * (1. / node->m_im);
  				}
  			}
  		}
  		for (int j = 0; j < m_deformableConstraints[i].size(); ++j)
  		{
  			const btDeformableFaceNodeContactConstraint& constraint = m_deformableConstraints[i][j];
  			const btSoftBody::Face* face = constraint.getContact()->m_face;
  			const btSoftBody::Node* node = constraint.getContact()->m_node;
  			if (node->m_im != 0)
  			{
  				int index = node->index;
  				f[index] += constraint.getDv(node) * (1. / node->m_im);
  			}
  			for (int k = 0; k < 3; ++k)
  			{
  				const btSoftBody::Node* node = face->m_n[k];
  				if (node->m_im != 0)
  				{
  					int index = node->index;
  					f[index] += constraint.getDv(node) * (1. / node->m_im);
  				}
  			}
  		}
  	}
  }
  
  void btDeformableContactProjection::reinitialize(bool nodeUpdated)
  {
  	int N = m_softBodies.size();
  	if (nodeUpdated)
  	{
  		m_staticConstraints.resize(N);
  		m_nodeAnchorConstraints.resize(N);
  		m_nodeRigidConstraints.resize(N);
  		m_faceRigidConstraints.resize(N);
  		m_deformableConstraints.resize(N);
  	}
  	for (int i = 0; i < N; ++i)
  	{
  		m_staticConstraints[i].clear();
  		m_nodeAnchorConstraints[i].clear();
  		m_nodeRigidConstraints[i].clear();
  		m_faceRigidConstraints[i].clear();
  		m_deformableConstraints[i].clear();
  	}
  #ifndef USE_MGS
  	m_projectionsDict.clear();
  #else
  	m_projections.clear();
  #endif
  	m_lagrangeMultipliers.clear();
  }
  