void StaticPlaneSphereConstraint::computeGeneralizedFrictionGivenTangentSample( const VectorXs& q, const VectorXs& t, const unsigned column, SparseMatrixsc& D ) const { assert( t.size() == 3 ); assert( column < unsigned( D.cols() ) ); assert( q.size() % 12 == 0 ); assert( fabs( t.norm() - 1.0 ) <= 1.0e-6 ); assert( fabs( m_plane.n().dot( t ) ) <= 1.0e-6 ); // Effect on center of mass D.insert( 3 * m_sphere_idx + 0, column ) = t.x(); D.insert( 3 * m_sphere_idx + 1, column ) = t.y(); D.insert( 3 * m_sphere_idx + 2, column ) = t.z(); // Effect on orientation { const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; // Compute the displacement from the center of mass to the point of contact assert( fabs( m_plane.n().norm() - 1.0 ) <= 1.0e-10 ); assert( m_r >= 0.0 ); const Vector3s r_world{ - m_r * m_plane.n() }; const Vector3s ntilde{ r_world.cross( Eigen::Map<const Vector3s>( t.data() ) ) }; D.insert( 3 * ( nbodies + m_sphere_idx ) + 0, column ) = ntilde.x(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 1, column ) = ntilde.y(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 2, column ) = ntilde.z(); } }
scalar HertzianPenaltyForce::computePotential( const VectorXs& q, const SparseMatrixsc& M, const VectorXs& r ) const { assert( q.size() % 2 == 0 ); assert( q.size() == M.rows() ); assert( q.size() == M.cols() ); assert( r.size() == q.size() / 2 ); scalar U{ 0.0 }; // For each ball for( unsigned ball0 = 0; ball0 < r.size(); ++ball0 ) { // For each subsequent ball for( unsigned ball1 = ball0 + 1; ball1 < r.size(); ++ball1 ) { // Compute the total radius const scalar total_radius{ r(ball0) + r(ball1) }; // Compute a vector pointing from ball0 to ball1 const Vector2s n{ q.segment<2>( 2 * ball1 ) - q.segment<2>( 2 * ball0 ) }; // If the squared distance is greater or equal to the sum of the radii squared, no force if( n.squaredNorm() > total_radius * total_radius ) { continue; } // Compute the penetration depth const scalar delta{ n.norm() - total_radius }; assert( delta < 0.0 ); // U = 0.5 * k * pen_depth^(5/2) U += 0.5 * m_k * std::pow( -delta, scalar( 2.5 ) ); } } return U; }
void Ball2DState::setMass( const VectorXs& m ) { m_M = createM( m ); m_Minv = createMinv( m ); #ifndef NDEBUG const SparseMatrixsc should_be_id{ m_M * m_Minv }; const Eigen::Map<const ArrayXs> should_be_id_data{ should_be_id.valuePtr(), should_be_id.nonZeros() }; assert( ( ( should_be_id_data - 1.0 ).abs() <= 1.0e-6 ).all() ); #endif }
void BodyBodyConstraint::computeGeneralizedFrictionGivenTangentSample( const VectorXs& q, const VectorXs& t, const unsigned column, SparseMatrixsc& D ) const { assert( column < unsigned( D.cols() ) ); assert( q.size() % 12 == 0 ); assert( t.size() == 3 ); assert( fabs( t.norm() - 1.0 ) <= 1.0e-6 ); assert( fabs( m_n.dot( t ) ) <= 1.0e-6 ); assert( m_idx0 < m_idx1 ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; // Effect on center of mass of body i D.insert( 3 * m_idx0 + 0, column ) = t.x(); D.insert( 3 * m_idx0 + 1, column ) = t.y(); D.insert( 3 * m_idx0 + 2, column ) = t.z(); // Effect on orientation of body i { const Vector3s ntilde0{ m_r0.cross( Eigen::Map<const Vector3s>{ t.data() } ) }; D.insert( 3 * ( m_idx0 + nbodies ) + 0, column ) = ntilde0.x(); D.insert( 3 * ( m_idx0 + nbodies ) + 1, column ) = ntilde0.y(); D.insert( 3 * ( m_idx0 + nbodies ) + 2, column ) = ntilde0.z(); } // Effect on center of mass of body j D.insert( 3 * m_idx1 + 0, column ) = - t.x(); D.insert( 3 * m_idx1 + 1, column ) = - t.y(); D.insert( 3 * m_idx1 + 2, column ) = - t.z(); // Effect on orientation of body j { const Vector3s ntilde1{ m_r1.cross( Eigen::Map<const Vector3s>{ t.data() } ) }; D.insert( 3 * ( m_idx1 + nbodies ) + 0, column ) = - ntilde1.x(); D.insert( 3 * ( m_idx1 + nbodies ) + 1, column ) = - ntilde1.y(); D.insert( 3 * ( m_idx1 + nbodies ) + 2, column ) = - ntilde1.z(); } }
void TeleportedCircleCircleConstraint::evalgradg( const VectorXs& q, const int col, SparseMatrixsc& G, const FlowableSystem& fsys ) const { assert( col >= 0 ); assert( col < G.cols() ); // MUST BE ADDED GOING DOWN THE COLUMN. DO NOT TOUCH ANOTHER COLUMN. assert( m_idx0 < m_idx1 ); assert( 3 * m_idx0 + 1 < unsigned( G.rows() ) ); G.insert( 3 * m_idx0 + 0, col ) = m_n.x(); G.insert( 3 * m_idx0 + 1, col ) = m_n.y(); assert( 3 * m_idx1 + 1 < unsigned( G.rows() ) ); G.insert( 3 * m_idx1 + 0, col ) = - m_n.x(); G.insert( 3 * m_idx1 + 1, col ) = - m_n.y(); }
void StaticPlaneSphereConstraint::evalgradg( const VectorXs& q, const int col, SparseMatrixsc& G, const FlowableSystem& fsys ) const { assert( col >= 0 ); assert( col < G.cols() ); assert( 3 * m_sphere_idx + 2 < unsigned( G.rows() ) ); const Vector3s n{ m_plane.n() }; assert( fabs( n.norm() - 1.0 ) <= 1.0e-6 ); // MUST BE ADDED GOING DOWN THE COLUMN. DO NOT TOUCH ANOTHER COLUMN. G.insert( 3 * m_sphere_idx + 0, col ) = n.x(); G.insert( 3 * m_sphere_idx + 1, col ) = n.y(); G.insert( 3 * m_sphere_idx + 2, col ) = n.z(); }
void FrictionOperatorUtilities::formGeneralizedFrictionBasis( const VectorXs& q0, const VectorXs& v0, const std::vector<std::unique_ptr<Constraint>>& K, const int num_samples, SparseMatrixsc& D, VectorXs& drel ) { assert( num_samples > 0 ); assert( D.rows() == v0.size() ); assert( num_samples * int( K.size() ) == D.cols() ); // Reserve space for entries reserveSpaceInBasisMatrix( num_samples, K, D ); // Build the matrix buildLinearFrictionBasis( q0, v0, num_samples, K, D, drel ); D.makeCompressed(); }
static void buildLinearFrictionBasis( const VectorXs& q, const VectorXs& v, const int nsamples, const std::vector<std::unique_ptr<Constraint>>& K, SparseMatrixsc& D, VectorXs& drel ) { assert( D.cols() % nsamples == 0 ); const unsigned ncons{ static_cast<unsigned>( D.cols() ) / nsamples }; std::vector<std::unique_ptr<Constraint>>::const_iterator itr{ K.begin() }; for( unsigned con_idx = 0; con_idx < ncons; ++con_idx ) { (*itr)->computeGeneralizedFrictionDisk( q, v, con_idx * nsamples, nsamples, D, drel ); ++itr; } assert( itr == K.end() ); }
void MathUtilities::extractLowerTriangularMatrix( const SparseMatrixsc& A, SparseMatrixsr& B ) { std::vector< Eigen::Triplet<scalar> > triplets; for( int col = 0; col < A.outerSize(); ++col ) { for( SparseMatrixsc::InnerIterator it( A, col ); it; ++it ) { if( col > it.row() ) { continue; } triplets.push_back( Eigen::Triplet<scalar>( it.row(), col, it.value() ) ); } } B.resize( A.rows(), A.cols() ); B.setFromTriplets( triplets.begin(), triplets.end() ); B.makeCompressed(); }
bool MathUtilities::isIdentity( const SparseMatrixsc& A, const scalar& tol ) { if( !isSquare( A ) ) { return false; } for( int outer_idx = 0; outer_idx < A.outerSize(); ++outer_idx ) { for( SparseMatrixsc::InnerIterator it( A, outer_idx ); it; ++it ) { if( it.row() == it.col() ) { if( fabs( it.value() - 1.0 ) > tol ) { return false; } } else { if( fabs( it.value() ) > tol ) { return false; } } } } return true; }
void MathUtilities::extractTripletData( const SparseMatrixsc& matrix, VectorXi& rows, VectorXi& cols, VectorXs& vals ) { rows.resize( matrix.nonZeros() ); cols.resize( matrix.nonZeros() ); vals.resize( matrix.nonZeros() ); int flat_index{ 0 }; for( int outer_index = 0; outer_index < matrix.outerSize(); ++outer_index ) { for( Eigen::SparseMatrix<double>::InnerIterator it( matrix, outer_index ); it; ++it ) { rows( flat_index ) = it.row(); cols( flat_index ) = it.col(); vals( flat_index++ ) = it.value(); } } assert( flat_index == matrix.nonZeros() ); }
int MathUtilities::values( const SparseMatrixsc& A, scalar* vals ) { assert( vals != nullptr ); int curel{ 0 }; for( int col = 0; col < A.outerSize(); ++col ) { for( SparseMatrixsc::InnerIterator it( A, col ); it; ++it ) { vals[curel] = it.value(); ++curel; } } assert( curel == A.nonZeros() ); return curel; }
void MathUtilities::convertDenseToSparse( const bool filter_zeros, const MatrixXXsc& dense_matrix, SparseMatrixsc& sparse_matrix ) { std::vector<Eigen::Triplet<scalar>> triplets; for( int row = 0; row < dense_matrix.rows(); ++row ) { for( int col = 0; col < dense_matrix.cols(); ++col ) { if( dense_matrix( row, col ) != 0.0 || !filter_zeros ) { triplets.emplace_back( Eigen::Triplet<scalar>{ row, col, dense_matrix( row, col ) } ); } } } sparse_matrix.resize( dense_matrix.rows(), dense_matrix.cols() ); sparse_matrix.setFromTriplets( std::begin( triplets ), std::end( triplets ) ); sparse_matrix.makeCompressed(); }
void MathUtilities::printSparseMathematicaMatrix( const SparseMatrixsc& A, const scalar& eps ) { std::cout << "{"; int entry_num = 0; for( int k = 0; k < A.outerSize(); ++k ) { for( typename SparseMatrixsc::InnerIterator it(A,k); it; ++it ) { std::cout << "{" << (it.row()+1) << "," << (it.col()+1) << "}->"; if( fabs(it.value()) < eps ) { std::cout << 0.0; } else { std::cout << it.value(); } entry_num++; if( entry_num != A.nonZeros() ) { std::cout << ","; } } } std::cout << "}" << std::endl; }
// TODO: Use utility class here void MathUtilities::deserialize( SparseMatrixsc& A, std::istream& stm ) { assert( stm.good() ); VectorXi col_ptr; VectorXi row_ind; VectorXs val; // Read the number of rows in the matrix int rows{ -1 }; stm.read((char*)&rows,sizeof(int)); assert( rows >= 0 ); // Read the number of columns in the matrix int cols{ -1 }; stm.read((char*)&cols,sizeof(int)); assert( cols >= 0 ); // Read the column pointer array col_ptr.resize(cols+1); stm.read((char*)col_ptr.data(),col_ptr.size()*sizeof(int)); // Read the number of nonzeros in the array int nnz{ -1 }; stm.read((char*)&nnz,sizeof(int)); assert( nnz >= 0 ); // Read the row-index array row_ind.resize(nnz); stm.read((char*)row_ind.data(),row_ind.size()*sizeof(int)); // Read the value array val.resize(nnz); stm.read((char*)val.data(),val.size()*sizeof(scalar)); A.resize(rows,cols); A.reserve(nnz); for( int col = 0; col < cols; ++col ) { A.startVec(col); for( int curel = col_ptr(col); curel < col_ptr(col+1); ++curel ) { int row = row_ind(curel); scalar curval = val(curel); A.insertBack(row,col) = curval; } } A.finalize(); }
// This method and the smooth version share the second half of code. Abstract that out. void StaticPlaneSphereConstraint::computeGeneralizedFrictionDisk( const VectorXs& q, const VectorXs& v, const int start_column, const int num_samples, SparseMatrixsc& D, VectorXs& drel ) const { assert( start_column >= 0 ); assert( start_column < D.cols() ); assert( num_samples > 0 ); assert( start_column + num_samples - 1 < D.cols() ); assert( q.size() % 12 == 0 ); assert( q.size() == 2 * v.size() ); const Vector3s n{ m_plane.n() }; assert( fabs( n.norm() - 1.0 ) <= 1.0e-6 ); std::vector<Vector3s> friction_disk( static_cast<std::vector<Vector3s>::size_type>( num_samples ) ); assert( friction_disk.size() == std::vector<Vector3s>::size_type( num_samples ) ); { // Compute the relative velocity Vector3s tangent_suggestion{ computeRelativeVelocity( q, v ) }; if( tangent_suggestion.cross( n ).squaredNorm() < 1.0e-9 ) { tangent_suggestion = FrictionUtilities::orthogonalVector( n ); } tangent_suggestion *= -1.0; // Sample the friction disk FrictionUtilities::generateOrthogonalVectors( n, friction_disk, tangent_suggestion ); } assert( unsigned( num_samples ) == friction_disk.size() ); // Compute the displacement from the center of mass to the point of contact assert( fabs( n.norm() - 1.0 ) <= 1.0e-10 ); assert( m_r >= 0.0 ); const Vector3s r_world{ - m_r * n }; // Cache the velocity of the collision point on the plane const Vector3s plane_collision_point_vel{ computePlaneCollisionPointVelocity( q ) }; // For each sample of the friction disk const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; for( unsigned friction_sample = 0; friction_sample < unsigned( num_samples ); ++friction_sample ) { const unsigned cur_col{ start_column + friction_sample }; assert( cur_col < unsigned( D.cols() ) ); // Effect on center of mass D.insert( 3 * m_sphere_idx + 0, cur_col ) = friction_disk[friction_sample].x(); D.insert( 3 * m_sphere_idx + 1, cur_col ) = friction_disk[friction_sample].y(); D.insert( 3 * m_sphere_idx + 2, cur_col ) = friction_disk[friction_sample].z(); // Effect on orientation { const Vector3s ntilde{ r_world.cross( friction_disk[friction_sample] ) }; D.insert( 3 * ( nbodies + m_sphere_idx ) + 0, cur_col ) = ntilde.x(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 1, cur_col ) = ntilde.y(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 2, cur_col ) = ntilde.z(); } // Relative velocity contribution from kinematic scripting assert( cur_col < drel.size() ); drel( cur_col ) = - friction_disk[friction_sample].dot( plane_collision_point_vel ); } }
void MathUtilities::createDiagonalMatrix( const scalar& c, SparseMatrixsc& D ) { assert( D.rows() == D.cols() ); D.reserve( VectorXi::Constant( D.cols(), 1 ) ); for( int i = 0; i < D.cols(); ++i ) { D.insert(i,i) = c; } D.makeCompressed(); }
void NearEarthGravityForce::computeForce( const VectorXs& q, const VectorXs& v, const SparseMatrixsc& M, VectorXs& result ) const { assert( q.size() % 12 == 0 ); assert( v.size() == q.size() / 2 ); assert( M.rows() == M.cols() ); assert( M.nonZeros() == q.size() ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; const Eigen::Map<const VectorXs> masses{ M.valuePtr(), 3 * nbodies }; for( unsigned i = 0; i < nbodies; ++i ) { assert( masses( 3 * i + 0 ) == masses( 3 * i + 1 ) ); assert( masses( 3 * i + 1 ) == masses( 3 * i + 2 ) ); result.segment<3>( 3 * i ) += masses( 3 * i ) * m_g; } }
void MathUtilities::serialize( const SparseMatrixsc& A, std::ostream& stm ) { assert( stm.good() ); VectorXi col_ptr; VectorXi row_ind; VectorXs val; MathUtilities::extractDataCCS( A, col_ptr, row_ind, val ); assert( col_ptr.size() == A.cols() + 1 ); assert( row_ind.size() == A.nonZeros() ); assert( val.size() == A.nonZeros() ); // Size of col_ptr == A.cols() + 1 Utilities::serializeBuiltInType( A.rows(), stm ); Utilities::serializeBuiltInType( A.cols(), stm ); stm.write( reinterpret_cast<char*>( col_ptr.data() ), col_ptr.size() * sizeof(int) ); // Size of row_ind == size of val == A.nonZeros() Utilities::serializeBuiltInType( A.nonZeros(), stm ); stm.write( reinterpret_cast<char*>( row_ind.data() ), row_ind.size() * sizeof(int) ); stm.write( reinterpret_cast<char*>( val.data() ), val.size() * sizeof(scalar) ); }
// Determine which elements are non-zero int MathUtilities::sparsityPattern( const SparseMatrixsc& A, int* rows, int* cols ) { assert( rows != nullptr ); assert( cols != nullptr ); int curel{ 0 }; for( int col = 0; col < A.outerSize(); ++col ) { for( SparseMatrixsc::InnerIterator it( A, col ); it; ++it ) { rows[curel] = it.row(); cols[curel] = col; ++curel; } } assert( curel == A.nonZeros() ); return curel; }
static void reserveSpaceInBasisMatrix( const int nsamples, const std::vector<std::unique_ptr<Constraint>>& K, SparseMatrixsc& D ) { assert( D.cols() % nsamples == 0 ); const int ncons{ D.cols() / nsamples }; VectorXi column_nonzeros{ D.cols() }; std::vector<std::unique_ptr<Constraint>>::const_iterator itr{ K.begin() }; for( int con_idx = 0; con_idx < ncons; ++con_idx ) { for( int smpl_num = 0; smpl_num < nsamples; ++smpl_num ) { column_nonzeros( con_idx * nsamples + smpl_num ) = (*itr)->frictionStencilSize(); } ++itr; } assert( itr == K.end() ); D.reserve( column_nonzeros ); }
scalar NearEarthGravityForce::computePotential( const VectorXs& q, const SparseMatrixsc& M ) const { assert( q.size() % 12 == 0 ); assert( M.rows() == M.cols() ); assert( M.nonZeros() == q.size() ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; const Eigen::Map<const VectorXs> masses{ M.valuePtr(), 3 * nbodies }; scalar U = 0.0; for( unsigned i = 0; i < nbodies; ++i ) { assert( masses( 3 * i + 0 ) == masses( 3 * i + 1 ) ); assert( masses( 3 * i + 1 ) == masses( 3 * i + 2 ) ); U += - masses( 3 * i ) * m_g.dot( q.segment<3>( 3 * i ) ); } return U; }
// TODO: Despecialize from smooth void FrictionOperator::formGeneralizedSmoothFrictionBasis( const unsigned ndofs, const unsigned ncons, const VectorXs& q, const std::vector<std::unique_ptr<Constraint>>& K, const MatrixXXsc& bases, SparseMatrixsc& D ) { assert( ncons == K.size() ); const unsigned nambientdims{ static_cast<unsigned>( bases.rows() ) }; const unsigned nsamples{ nambientdims - 1 }; D.resize( ndofs, nsamples * ncons ); auto itr = K.cbegin(); { VectorXi column_nonzeros( D.cols() ); for( unsigned collision_number = 0; collision_number < ncons; ++collision_number ) { for( unsigned sample_number = 0; sample_number < nsamples; ++sample_number ) { assert( nsamples * collision_number + sample_number < column_nonzeros.size() ); column_nonzeros( nsamples * collision_number + sample_number ) = (*itr)->frictionStencilSize(); } ++itr; } assert( ( column_nonzeros.array() > 0 ).all() ); assert( itr == K.cend() ); D.reserve( column_nonzeros ); } itr = K.cbegin(); for( unsigned collision_number = 0; collision_number < ncons; ++collision_number ) { for( unsigned sample_number = 0; sample_number < nsamples; ++sample_number ) { const unsigned current_column{ nsamples * collision_number + sample_number }; const VectorXs current_sample{ bases.col( nambientdims * collision_number + sample_number + 1 ) }; assert( fabs( current_sample.dot( bases.col( nambientdims * collision_number ) ) ) <= 1.0e-6 ); (*itr)->computeGeneralizedFrictionGivenTangentSample( q, current_sample, current_column, D ); } ++itr; } assert( itr == K.cend() ); D.prune( []( const Eigen::Index& row, const Eigen::Index& col, const scalar& value ) { return value != 0.0; } ); assert( D.innerNonZeroPtr() == nullptr ); }
void StaticPlaneSphereConstraint::resolveImpact( const scalar& CoR, const SparseMatrixsc& M, const scalar& ndotv, VectorXs& vout, scalar& alpha ) const { assert( CoR >= 0.0 ); assert( CoR <= 1.0 ); assert( ndotv < 0.0 ); assert( vout.size() % 3 == 0 ); assert( M.rows() == M.cols() ); assert( M.nonZeros() == 2 * vout.size() ); assert( 3 * m_sphere_idx + 2 < vout.size() ); const Eigen::Map<const VectorXs> m{ M.valuePtr(), vout.size() }; assert( m( 3 * m_sphere_idx ) == m( 3 * m_sphere_idx + 1 ) ); assert( m( 3 * m_sphere_idx ) == m( 3 * m_sphere_idx + 2 ) ); const scalar msphere{ m( 3 * m_sphere_idx ) }; // Compute the impulse alpha = - ( 1.0 + CoR ) * ndotv * msphere; assert( alpha >= 0.0 ); vout.segment<3>( 3 * m_sphere_idx ) += - ( 1.0 + CoR ) * ndotv * m_plane.n(); }
void MathUtilities::extractDataCCS( const SparseMatrixsc& A, VectorXi& col_ptr, VectorXi& row_ind, VectorXs& val ) { col_ptr.resize( A.cols() + 1 ); row_ind.resize( A.nonZeros() ); val.resize( A.nonZeros() ); col_ptr(0) = 0; for( int col = 0; col < A.outerSize(); ++col ) { col_ptr(col+1) = col_ptr(col); for( SparseMatrixsc::InnerIterator it(A,col); it; ++it ) { const int row{ it.row() }; val(col_ptr(col+1)) = it.value(); row_ind(col_ptr(col+1)) = row; ++col_ptr(col+1); } } assert( col_ptr( col_ptr.size() - 1 ) == row_ind.size() ); }
void LCPOperatorQL::flow( const std::vector<std::unique_ptr<Constraint>>& cons, const SparseMatrixsc& M, const SparseMatrixsc& Minv, const VectorXs& q0, const VectorXs& v0, const VectorXs& v0F, const SparseMatrixsc& N, const SparseMatrixsc& Q, const VectorXs& nrel, const VectorXs& CoR, VectorXs& alpha ) { // Q in 1/2 \alpha^T Q \alpha assert( Q.rows() == Q.cols() ); MatrixXXsc Qdense = Q; // Linear term in the objective VectorXs Adense; ImpactOperatorUtilities::computeLCPQPLinearTerm( N, nrel, CoR, v0, v0F, Adense ); // Solve the QP assert( Qdense.rows() == Adense.size() ); assert( Adense.size() == alpha.size() ); const int status = solveQP( m_tol, Qdense, Adense, alpha ); // Check for problems if( 0 != status ) { std::cerr << "Warning, failed to solve QP in LCPOperatorQL::flow: " << QLUtilities::QLReturnStatusToString(status) << std::endl; } // TODO: Sanity check the solution here }
void FrictionOperatorUtilities::formLinearFrictionDiskConstraint( const int num_samples, SparseMatrixsc& E ) { { const VectorXi column_nonzeros{ VectorXi::Constant( E.cols(), num_samples ) }; E.reserve( column_nonzeros ); } // For each column for( int col = 0; col < E.cols(); ++col ) { for( int samplenum = 0; samplenum < num_samples; ++samplenum ) { // Note the negative for QL E.insert( num_samples * col + samplenum, col ) = 1.0; } } E.makeCompressed(); assert( E.nonZeros() == E.cols() * num_samples ); assert( E.sum() == E.nonZeros() ); }
int MathUtilities::nzLowerTriangular( const SparseMatrixsc& A ) { int num{ 0 }; for( int col = 0; col < A.outerSize(); ++col ) { for( SparseMatrixsc::InnerIterator it( A, col ); it; ++it ) { // Skip entries above the diagonal if( col > it.row() ) { continue; } ++num; } } return num; }
void HertzianPenaltyForce::computeForce( const VectorXs& q, const VectorXs& v, const SparseMatrixsc& M, const VectorXs& r, VectorXs& result ) const { assert( q.size() % 2 == 0 ); assert( q.size() == v.size() ); assert( q.size() == M.rows() ); assert( q.size() == M.cols() ); assert( r.size() == q.size() / 2 ); assert( q.size() == result.size() ); // For each ball for( unsigned ball0 = 0; ball0 < r.size(); ++ball0 ) { // For each subsequent ball for( unsigned ball1 = ball0 + 1; ball1 < r.size(); ++ball1 ) { // Compute the total radius const scalar total_radius{ r(ball0) + r(ball1) }; // Compute a vector pointing from ball0 to ball1 Vector2s n{ q.segment<2>( 2 * ball1 ) - q.segment<2>( 2 * ball0 ) }; // Compute the squared length of the vector scalar d{ n.squaredNorm() }; // If the squared distance is greater or equal to the sum of the radii squared, no force if( d > total_radius * total_radius ) { continue; } // Normalize the vector between the balls d = sqrt( d ); assert( d != 0.0 ); n /= d; assert( fabs( n.norm() - 1.0 ) <= 1.0e-6 ); // Compute the penetration depth d -= total_radius; assert( d < 0.0 ); // F = 5 * k * pen_depth^(3/2) * n const Vector2s F{ ( 5.0 / 4.0 ) * m_k * std::pow( -d, scalar( 1.5 ) ) * n }; result.segment<2>( 2 * ball1 ) += F; result.segment<2>( 2 * ball0 ) -= F; } } }
void Ball2DGravityForce::computeForce( const VectorXs& q, const VectorXs& v, const SparseMatrixsc& M, const VectorXs& r, VectorXs& result ) const { assert( q.size() % 2 == 0 ); assert( q.size() == v.size() ); assert( q.size() == M.rows() ); assert( q.size() == M.cols() ); assert( q.size() == result.size() ); for( int i = 0; i < q.size(); i += 2 ) { assert( M.valuePtr()[ i ] == M.valuePtr()[ i + 1 ] ); assert( M.valuePtr()[ i ] > 0.0 ); result.segment<2>( i ) += M.valuePtr()[ i ] * m_g; } }