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diff --git a/source/blender/physics/intern/ConstrainedConjugateGradient.h b/source/blender/physics/intern/ConstrainedConjugateGradient.h new file mode 100644 index 00000000000..2d4389f6766 --- /dev/null +++ b/source/blender/physics/intern/ConstrainedConjugateGradient.h @@ -0,0 +1,294 @@ + +#ifndef EIGEN_CONSTRAINEDCG_H +#define EIGEN_CONSTRAINEDCG_H + +#include <Eigen/Core> + +namespace Eigen { + +namespace internal { + +/** \internal Low-level conjugate gradient algorithm + * \param mat The matrix A + * \param rhs The right hand side vector b + * \param x On input and initial solution, on output the computed solution. + * \param precond A preconditioner being able to efficiently solve for an + * approximation of Ax=b (regardless of b) + * \param iters On input the max number of iteration, on output the number of performed iterations. + * \param tol_error On input the tolerance error, on output an estimation of the relative error. + */ +template<typename MatrixType, typename Rhs, typename Dest, typename FilterMatrixType, typename Preconditioner> +EIGEN_DONT_INLINE +void constrained_conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x, + const FilterMatrixType &filter, + const Preconditioner& precond, int& iters, + typename Dest::RealScalar& tol_error) +{ + using std::sqrt; + using std::abs; + typedef typename Dest::RealScalar RealScalar; + typedef typename Dest::Scalar Scalar; + typedef Matrix<Scalar,Dynamic,1> VectorType; + + RealScalar tol = tol_error; + int maxIters = iters; + + int n = mat.cols(); + + VectorType residual = filter * (rhs - mat * x); //initial residual + + RealScalar rhsNorm2 = (filter * rhs).squaredNorm(); + if(rhsNorm2 == 0) + { + /* XXX TODO set constrained result here */ + x.setZero(); + iters = 0; + tol_error = 0; + return; + } + RealScalar threshold = tol*tol*rhsNorm2; + RealScalar residualNorm2 = residual.squaredNorm(); + if (residualNorm2 < threshold) + { + iters = 0; + tol_error = sqrt(residualNorm2 / rhsNorm2); + return; + } + + VectorType p(n); + p = filter * precond.solve(residual); //initial search direction + + VectorType z(n), tmp(n); + RealScalar absNew = numext::real(residual.dot(p)); // the square of the absolute value of r scaled by invM + int i = 0; + while(i < maxIters) + { + tmp.noalias() = filter * (mat * p); // the bottleneck of the algorithm + + Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir + x += alpha * p; // update solution + residual -= alpha * tmp; // update residue + + residualNorm2 = residual.squaredNorm(); + if(residualNorm2 < threshold) + break; + + z = precond.solve(residual); // approximately solve for "A z = residual" + + RealScalar absOld = absNew; + absNew = numext::real(residual.dot(z)); // update the absolute value of r + RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction + p = filter * (z + beta * p); // update search direction + i++; + } + tol_error = sqrt(residualNorm2 / rhsNorm2); + iters = i; +} + +} + +#if 0 /* unused */ +template<typename MatrixType> +struct MatrixFilter +{ + MatrixFilter() : + m_cmat(NULL) + { + } + + MatrixFilter(const MatrixType &cmat) : + m_cmat(&cmat) + { + } + + void setMatrix(const MatrixType &cmat) { m_cmat = &cmat; } + + template <typename VectorType> + void apply(VectorType v) const + { + v = (*m_cmat) * v; + } + +protected: + const MatrixType *m_cmat; +}; +#endif + +template< typename _MatrixType, int _UpLo=Lower, + typename _FilterMatrixType = _MatrixType, + typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> > +class ConstrainedConjugateGradient; + +namespace internal { + +template< typename _MatrixType, int _UpLo, typename _FilterMatrixType, typename _Preconditioner> +struct traits<ConstrainedConjugateGradient<_MatrixType,_UpLo,_FilterMatrixType,_Preconditioner> > +{ + typedef _MatrixType MatrixType; + typedef _FilterMatrixType FilterMatrixType; + typedef _Preconditioner Preconditioner; +}; + +} + +/** \ingroup IterativeLinearSolvers_Module + * \brief A conjugate gradient solver for sparse self-adjoint problems with additional constraints + * + * This class allows to solve for A.x = b sparse linear problems using a conjugate gradient algorithm. + * The sparse matrix A must be selfadjoint. The vectors x and b can be either dense or sparse. + * + * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix. + * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower + * or Upper. Default is Lower. + * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner + * + * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() + * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations + * and NumTraits<Scalar>::epsilon() for the tolerance. + * + * This class can be used as the direct solver classes. Here is a typical usage example: + * \code + * int n = 10000; + * VectorXd x(n), b(n); + * SparseMatrix<double> A(n,n); + * // fill A and b + * ConjugateGradient<SparseMatrix<double> > cg; + * cg.compute(A); + * x = cg.solve(b); + * std::cout << "#iterations: " << cg.iterations() << std::endl; + * std::cout << "estimated error: " << cg.error() << std::endl; + * // update b, and solve again + * x = cg.solve(b); + * \endcode + * + * By default the iterations start with x=0 as an initial guess of the solution. + * One can control the start using the solveWithGuess() method. Here is a step by + * step execution example starting with a random guess and printing the evolution + * of the estimated error: + * * \code + * x = VectorXd::Random(n); + * cg.setMaxIterations(1); + * int i = 0; + * do { + * x = cg.solveWithGuess(b,x); + * std::cout << i << " : " << cg.error() << std::endl; + * ++i; + * } while (cg.info()!=Success && i<100); + * \endcode + * Note that such a step by step excution is slightly slower. + * + * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner + */ +template< typename _MatrixType, int _UpLo, typename _FilterMatrixType, typename _Preconditioner> +class ConstrainedConjugateGradient : public IterativeSolverBase<ConstrainedConjugateGradient<_MatrixType,_UpLo,_FilterMatrixType,_Preconditioner> > +{ + typedef IterativeSolverBase<ConstrainedConjugateGradient> Base; + using Base::mp_matrix; + using Base::m_error; + using Base::m_iterations; + using Base::m_info; + using Base::m_isInitialized; +public: + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + typedef typename MatrixType::RealScalar RealScalar; + typedef _FilterMatrixType FilterMatrixType; + typedef _Preconditioner Preconditioner; + + enum { + UpLo = _UpLo + }; + +public: + + /** Default constructor. */ + ConstrainedConjugateGradient() : Base() {} + + /** Initialize the solver with matrix \a A for further \c Ax=b solving. + * + * This constructor is a shortcut for the default constructor followed + * by a call to compute(). + * + * \warning this class stores a reference to the matrix A as well as some + * precomputed values that depend on it. Therefore, if \a A is changed + * this class becomes invalid. Call compute() to update it with the new + * matrix A, or modify a copy of A. + */ + ConstrainedConjugateGradient(const MatrixType& A) : Base(A) {} + + ~ConstrainedConjugateGradient() {} + + FilterMatrixType &filter() { return m_filter; } + const FilterMatrixType &filter() const { return m_filter; } + + /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A + * \a x0 as an initial solution. + * + * \sa compute() + */ + template<typename Rhs,typename Guess> + inline const internal::solve_retval_with_guess<ConstrainedConjugateGradient, Rhs, Guess> + solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const + { + eigen_assert(m_isInitialized && "ConjugateGradient is not initialized."); + eigen_assert(Base::rows()==b.rows() + && "ConjugateGradient::solve(): invalid number of rows of the right hand side matrix b"); + return internal::solve_retval_with_guess + <ConstrainedConjugateGradient, Rhs, Guess>(*this, b.derived(), x0); + } + + /** \internal */ + template<typename Rhs,typename Dest> + void _solveWithGuess(const Rhs& b, Dest& x) const + { + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + for(int j=0; j<b.cols(); ++j) + { + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + typename Dest::ColXpr xj(x,j); + internal::constrained_conjugate_gradient(mp_matrix->template selfadjointView<UpLo>(), b.col(j), xj, m_filter, + Base::m_preconditioner, m_iterations, m_error); + } + + m_isInitialized = true; + m_info = m_error <= Base::m_tolerance ? Success : NoConvergence; + } + + /** \internal */ + template<typename Rhs,typename Dest> + void _solve(const Rhs& b, Dest& x) const + { + x.setOnes(); + _solveWithGuess(b,x); + } + +protected: + FilterMatrixType m_filter; +}; + + +namespace internal { + +template<typename _MatrixType, int _UpLo, typename _Filter, typename _Preconditioner, typename Rhs> +struct solve_retval<ConstrainedConjugateGradient<_MatrixType,_UpLo,_Filter,_Preconditioner>, Rhs> + : solve_retval_base<ConstrainedConjugateGradient<_MatrixType,_UpLo,_Filter,_Preconditioner>, Rhs> +{ + typedef ConstrainedConjugateGradient<_MatrixType,_UpLo,_Filter,_Preconditioner> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template<typename Dest> void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_CONSTRAINEDCG_H |