Squashed 'third_party/eigen/' changes from 61d72f6..cf794d3
Change-Id: I9b814151b01f49af6337a8605d0c42a3a1ed4c72
git-subtree-dir: third_party/eigen
git-subtree-split: cf794d3b741a6278df169e58461f8529f43bce5d
diff --git a/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h b/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h
new file mode 100644
index 0000000..0aea0e0
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h
@@ -0,0 +1,216 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H
+#define EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Low-level conjugate gradient algorithm for least-square problems
+ * \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 A'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 Preconditioner>
+EIGEN_DONT_INLINE
+void least_square_conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, Index& 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;
+ Index maxIters = iters;
+
+ Index m = mat.rows(), n = mat.cols();
+
+ VectorType residual = rhs - mat * x;
+ VectorType normal_residual = mat.adjoint() * residual;
+
+ RealScalar rhsNorm2 = (mat.adjoint()*rhs).squaredNorm();
+ if(rhsNorm2 == 0)
+ {
+ x.setZero();
+ iters = 0;
+ tol_error = 0;
+ return;
+ }
+ RealScalar threshold = tol*tol*rhsNorm2;
+ RealScalar residualNorm2 = normal_residual.squaredNorm();
+ if (residualNorm2 < threshold)
+ {
+ iters = 0;
+ tol_error = sqrt(residualNorm2 / rhsNorm2);
+ return;
+ }
+
+ VectorType p(n);
+ p = precond.solve(normal_residual); // initial search direction
+
+ VectorType z(n), tmp(m);
+ RealScalar absNew = numext::real(normal_residual.dot(p)); // the square of the absolute value of r scaled by invM
+ Index i = 0;
+ while(i < maxIters)
+ {
+ tmp.noalias() = mat * p;
+
+ Scalar alpha = absNew / tmp.squaredNorm(); // the amount we travel on dir
+ x += alpha * p; // update solution
+ residual -= alpha * tmp; // update residual
+ normal_residual = mat.adjoint() * residual; // update residual of the normal equation
+
+ residualNorm2 = normal_residual.squaredNorm();
+ if(residualNorm2 < threshold)
+ break;
+
+ z = precond.solve(normal_residual); // approximately solve for "A'A z = normal_residual"
+
+ RealScalar absOld = absNew;
+ absNew = numext::real(normal_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 = z + beta * p; // update search direction
+ i++;
+ }
+ tol_error = sqrt(residualNorm2 / rhsNorm2);
+ iters = i;
+}
+
+}
+
+template< typename _MatrixType,
+ typename _Preconditioner = LeastSquareDiagonalPreconditioner<typename _MatrixType::Scalar> >
+class LeastSquaresConjugateGradient;
+
+namespace internal {
+
+template< typename _MatrixType, typename _Preconditioner>
+struct traits<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> >
+{
+ typedef _MatrixType MatrixType;
+ typedef _Preconditioner Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A conjugate gradient solver for sparse (or dense) least-square problems
+ *
+ * This class allows to solve for A x = b linear problems using an iterative conjugate gradient algorithm.
+ * The matrix A can be non symmetric and rectangular, but the matrix A' A should be positive-definite to guaranty stability.
+ * Otherwise, the SparseLU or SparseQR classes might be preferable.
+ * The matrix A and the vectors x and b can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix.
+ * \tparam _Preconditioner the type of the preconditioner. Default is LeastSquareDiagonalPreconditioner
+ *
+ * \implsparsesolverconcept
+ *
+ * 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 m=1000000, n = 10000;
+ VectorXd x(n), b(m);
+ SparseMatrix<double> A(m,n);
+ // fill A and b
+ LeastSquaresConjugateGradient<SparseMatrix<double> > lscg;
+ lscg.compute(A);
+ x = lscg.solve(b);
+ std::cout << "#iterations: " << lscg.iterations() << std::endl;
+ std::cout << "estimated error: " << lscg.error() << std::endl;
+ // update b, and solve again
+ x = lscg.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.
+ *
+ * \sa class ConjugateGradient, SparseLU, SparseQR
+ */
+template< typename _MatrixType, typename _Preconditioner>
+class LeastSquaresConjugateGradient : public IterativeSolverBase<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> >
+{
+ typedef IterativeSolverBase<LeastSquaresConjugateGradient> Base;
+ using Base::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::RealScalar RealScalar;
+ typedef _Preconditioner Preconditioner;
+
+public:
+
+ /** Default constructor. */
+ LeastSquaresConjugateGradient() : 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.
+ */
+ template<typename MatrixDerived>
+ explicit LeastSquaresConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
+
+ ~LeastSquaresConjugateGradient() {}
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ for(Index j=0; j<b.cols(); ++j)
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ typename Dest::ColXpr xj(x,j);
+ internal::least_square_conjugate_gradient(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
+ }
+
+ m_isInitialized = true;
+ m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+ /** \internal */
+ using Base::_solve_impl;
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const
+ {
+ x.setZero();
+ _solve_with_guess_impl(b.derived(),x);
+ }
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H