sparse module: add preliminary support for direct sparse LU solver

using SuperLU. Calling SuperLU was very painful, but it was worth it, it seems to be damn fast !
2026-04-10 11:34:33 +08:00 · 2008-10-19 15:26:28 +00:00
parent 6be0131774
commit ecc6c43dba
5 changed files with 562 additions and 6 deletions
--- a/Eigen/src/Sparse/SparseLU.h
+++ b/Eigen/src/Sparse/SparseLU.h
@@ -0,0 +1,148 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SPARSELU_H
+#define EIGEN_SPARSELU_H
+
+/** \ingroup Sparse_Module
+  *
+  * \class SparseLU
+  *
+  * \brief LU decomposition of a sparse matrix and associated features
+  *
+  * \param MatrixType the type of the matrix of which we are computing the LU factorization
+  *
+  * \sa class LU, class SparseLLT
+  */
+template<typename MatrixType, int Backend = DefaultBackend>
+class SparseLU
+{
+  protected:
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    typedef SparseMatrix<Scalar,Lower> LUMatrixType;
+
+    enum {
+      MatrixLUIsDirty             = 0x10000
+    };
+
+  public:
+
+    /** Creates a dummy LU factorization object with flags \a flags. */
+    SparseLU(int flags = 0)
+      : m_flags(flags), m_status(0)
+    {
+      m_precision = RealScalar(0.1) * Eigen::precision<RealScalar>();
+    }
+
+    /** Creates a LU object and compute the respective factorization of \a matrix using
+      * flags \a flags. */
+    SparseLU(const MatrixType& matrix, int flags = 0)
+      : /*m_matrix(matrix.rows(), matrix.cols()),*/ m_flags(flags), m_status(0)
+    {
+      m_precision = RealScalar(0.1) * Eigen::precision<RealScalar>();
+      compute(matrix);
+    }
+
+    /** Sets the relative threshold value used to prune zero coefficients during the decomposition.
+      *
+      * Setting a value greater than zero speeds up computation, and yields to an imcomplete
+      * factorization with fewer non zero coefficients. Such approximate factors are especially
+      * useful to initialize an iterative solver.
+      *
+      * Note that the exact meaning of this parameter might depends on the actual
+      * backend. Moreover, not all backends support this feature.
+      *
+      * \sa precision() */
+    void setPrecision(RealScalar v) { m_precision = v; }
+
+    /** \returns the current precision.
+      *
+      * \sa setPrecision() */
+    RealScalar precision() const { return m_precision; }
+
+    /** Sets the flags. Possible values are:
+      *  - CompleteFactorization
+      *  - IncompleteFactorization
+      *  - MemoryEfficient
+      *  - one of the ordering methods
+      *  - etc...
+      *
+      * \sa flags() */
+    void setFlags(int f) { m_flags = f; }
+    /** \returns the current flags */
+    int flags() const { return m_flags; }
+
+    void setOrderingMethod(int m)
+    {
+      ei_assert(m&~OrderingMask == 0 && m!=0 && "invalid ordering method");
+      m_flags = m_flags&~OrderingMask | m&OrderingMask;
+    }
+
+    int orderingMethod() const
+    {
+      return m_flags&OrderingMask;
+    }
+
+    /** Computes/re-computes the LU factorization */
+    void compute(const MatrixType& matrix);
+
+    /** \returns the lower triangular matrix L */
+    //inline const MatrixType& matrixL() const { return m_matrixL; }
+
+    /** \returns the upper triangular matrix U */
+    //inline const MatrixType& matrixU() const { return m_matrixU; }
+
+    template<typename BDerived, typename XDerived>
+    bool solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x) const;
+
+    /** \returns true if the factorization succeeded */
+    inline bool succeeded(void) const { return m_succeeded; }
+
+  protected:
+    RealScalar m_precision;
+    int m_flags;
+    mutable int m_status;
+    bool m_succeeded;
+};
+
+/** Computes / recomputes the LU decomposition of matrix \a a
+  * using the default algorithm.
+  */
+template<typename MatrixType, int Backend>
+void SparseLU<MatrixType,Backend>::compute(const MatrixType& a)
+{
+  ei_assert(false && "not implemented yet");
+}
+
+/** Computes *x = U^-1 L^-1 b */
+template<typename MatrixType, int Backend>
+template<typename BDerived, typename XDerived>
+bool SparseLU<MatrixType,Backend>::solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x) const
+{
+  ei_assert(false && "not implemented yet");
+  return false;
+}
+
+#endif // EIGEN_SPARSELU_H