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include/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h

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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2014 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_BASIC_PRECONDITIONERS_H
+#define EIGEN_BASIC_PRECONDITIONERS_H
+
+// IWYU pragma: private
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup IterativeLinearSolvers_Module
+  * \brief A preconditioner based on the digonal entries
+  *
+  * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
+  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
+    \code
+    A.diagonal().asDiagonal() . x = b
+    \endcode
+  *
+  * \tparam Scalar_ the type of the scalar.
+  *
+  * \implsparsesolverconcept
+  *
+  * This preconditioner is suitable for both selfadjoint and general problems.
+  * The diagonal entries are pre-inverted and stored into a dense vector.
+  *
+  * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
+  *
+  * \sa class LeastSquareDiagonalPreconditioner, class ConjugateGradient
+  */
+template <typename Scalar_>
+class DiagonalPreconditioner {
+  typedef Scalar_ Scalar;
+  typedef Matrix<Scalar, Dynamic, 1> Vector;
+
+ public:
+  typedef typename Vector::StorageIndex StorageIndex;
+  enum { ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic };
+
+  DiagonalPreconditioner() : m_isInitialized(false) {}
+
+  template <typename MatType>
+  explicit DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols()) {
+    compute(mat);
+  }
+
+  EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_invdiag.size(); }
+  EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_invdiag.size(); }
+
+  template <typename MatType>
+  DiagonalPreconditioner& analyzePattern(const MatType&) {
+    return *this;
+  }
+
+  template <typename MatType>
+  DiagonalPreconditioner& factorize(const MatType& mat) {
+    m_invdiag.resize(mat.cols());
+    for (int j = 0; j < mat.outerSize(); ++j) {
+      typename MatType::InnerIterator it(mat, j);
+      while (it && it.index() != j) ++it;
+      if (it && it.index() == j && it.value() != Scalar(0))
+        m_invdiag(j) = Scalar(1) / it.value();
+      else
+        m_invdiag(j) = Scalar(1);
+    }
+    m_isInitialized = true;
+    return *this;
+  }
+
+  template <typename MatType>
+  DiagonalPreconditioner& compute(const MatType& mat) {
+    return factorize(mat);
+  }
+
+  /** \internal */
+  template <typename Rhs, typename Dest>
+  void _solve_impl(const Rhs& b, Dest& x) const {
+    x = m_invdiag.array() * b.array();
+  }
+
+  template <typename Rhs>
+  inline const Solve<DiagonalPreconditioner, Rhs> solve(const MatrixBase<Rhs>& b) const {
+    eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
+    eigen_assert(m_invdiag.size() == b.rows() &&
+                 "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
+    return Solve<DiagonalPreconditioner, Rhs>(*this, b.derived());
+  }
+
+  ComputationInfo info() { return Success; }
+
+ protected:
+  Vector m_invdiag;
+  bool m_isInitialized;
+};
+
+/** \ingroup IterativeLinearSolvers_Module
+  * \brief Jacobi preconditioner for LeastSquaresConjugateGradient
+  *
+  * This class allows to approximately solve for A' A x  = A' b problems assuming A' A is a diagonal matrix.
+  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
+    \code
+    (A.adjoint() * A).diagonal().asDiagonal() * x = b
+    \endcode
+  *
+  * \tparam Scalar_ the type of the scalar.
+  *
+  * \implsparsesolverconcept
+  *
+  * The diagonal entries are pre-inverted and stored into a dense vector.
+  *
+  * \sa class LeastSquaresConjugateGradient, class DiagonalPreconditioner
+  */
+template <typename Scalar_>
+class LeastSquareDiagonalPreconditioner : public DiagonalPreconditioner<Scalar_> {
+  typedef Scalar_ Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef DiagonalPreconditioner<Scalar_> Base;
+  using Base::m_invdiag;
+
+ public:
+  LeastSquareDiagonalPreconditioner() : Base() {}
+
+  template <typename MatType>
+  explicit LeastSquareDiagonalPreconditioner(const MatType& mat) : Base() {
+    compute(mat);
+  }
+
+  template <typename MatType>
+  LeastSquareDiagonalPreconditioner& analyzePattern(const MatType&) {
+    return *this;
+  }
+
+  template <typename MatType>
+  LeastSquareDiagonalPreconditioner& factorize(const MatType& mat) {
+    // Compute the inverse squared-norm of each column of mat
+    m_invdiag.resize(mat.cols());
+    if (MatType::IsRowMajor) {
+      m_invdiag.setZero();
+      for (Index j = 0; j < mat.outerSize(); ++j) {
+        for (typename MatType::InnerIterator it(mat, j); it; ++it) m_invdiag(it.index()) += numext::abs2(it.value());
+      }
+      for (Index j = 0; j < mat.cols(); ++j)
+        if (numext::real(m_invdiag(j)) > RealScalar(0)) m_invdiag(j) = RealScalar(1) / numext::real(m_invdiag(j));
+    } else {
+      for (Index j = 0; j < mat.outerSize(); ++j) {
+        RealScalar sum = mat.col(j).squaredNorm();
+        if (sum > RealScalar(0))
+          m_invdiag(j) = RealScalar(1) / sum;
+        else
+          m_invdiag(j) = RealScalar(1);
+      }
+    }
+    Base::m_isInitialized = true;
+    return *this;
+  }
+
+  template <typename MatType>
+  LeastSquareDiagonalPreconditioner& compute(const MatType& mat) {
+    return factorize(mat);
+  }
+
+  ComputationInfo info() { return Success; }
+
+ protected:
+};
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A naive preconditioner which approximates any matrix as the identity matrix
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa class DiagonalPreconditioner
+ */
+class IdentityPreconditioner {
+ public:
+  IdentityPreconditioner() {}
+
+  template <typename MatrixType>
+  explicit IdentityPreconditioner(const MatrixType&) {}
+
+  template <typename MatrixType>
+  IdentityPreconditioner& analyzePattern(const MatrixType&) {
+    return *this;
+  }
+
+  template <typename MatrixType>
+  IdentityPreconditioner& factorize(const MatrixType&) {
+    return *this;
+  }
+
+  template <typename MatrixType>
+  IdentityPreconditioner& compute(const MatrixType&) {
+    return *this;
+  }
+
+  template <typename Rhs>
+  inline const Rhs& solve(const Rhs& b) const {
+    return b;
+  }
+
+  ComputationInfo info() { return Success; }
+};
+
+}  // end namespace Eigen
+
+#endif  // EIGEN_BASIC_PRECONDITIONERS_H