[suitesparse] Create wrapper for SPQR solver

Signed-off-by: Christoph Grüninger <gruenich@dune-project.org>

dune/istl/spqr.hh

+// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
+// vi: set et ts=4 sw=2 sts=2:
+#ifndef DUNE_ISTL_SPQR_HH
+#define DUNE_ISTL_SPQR_HH
+
+#if HAVE_SPQR || defined DOXYGEN
+
+#include<complex>
+#include<type_traits>
+
+#include<SuiteSparseQR.hpp>
+#include<dune/common/exceptions.hh>
+#include<dune/common/unused.hh>
+
+#include<dune/istl/solvers.hh>
+#include<dune/istl/solvertype.hh>
+#include<dune/istl/colcompmatrix.hh>
+
+namespace Dune {
+  /**
+   * @addtogroup ISTL
+   *
+   * @{
+   */
+  /**
+   * @file
+   * @author Marco Agnese, Andrea Sacconi
+   * @brief Class for using SPQR with ISTL matrices.
+   */
+
+  // forward declarations
+  template<class M, class T, class TM, class TD, class TA>
+  class SeqOverlappingSchwarz;
+
+  template<class T, bool tag>
+  struct SeqOverlappingSchwarzAssemblerHelper;
+
+  /** @brief Use the %SPQR package to directly solve linear systems -- empty default class
+   * @tparam Matrix the matrix type defining the system
+   * Details on SPQR can be found on
+   * http://www.cise.ufl.edu/research/sparse/spqr/
+   */
+  template<class Matrix>
+  class SPQR
+  {};
+
+  /** @brief The %SPQR direct sparse solver for matrices of type BCRSMatrix
+   *
+   * Specialization for the Dune::BCRSMatrix. %SPQR will always go double
+   * precision and supports complex numbers
+   * too (use std::complex<double> for that).
+   *
+   * \tparam T Number type.  Only double and std::complex<double> is supported
+   * \tparam A STL-compatible allocator type
+   * \tparam n Number of rows in a matrix block
+   * \tparam m Number of columns in a matrix block
+   *
+   * \note This will only work if dune-istl has been configured to use SPQR
+   */
+  template<typename T, typename A, int n, int m>
+  class SPQR<BCRSMatrix<FieldMatrix<T,n,m>,A > >
+    : public InverseOperator<BlockVector<FieldVector<T,m>, typename A::template rebind<FieldVector<T,m> >::other>,
+                             BlockVector<FieldVector<T,n>, typename A::template rebind<FieldVector<T,n> >::other> >
+  {
+    public:
+    /** @brief The matrix type. */
+    typedef Dune::BCRSMatrix<FieldMatrix<T,n,m>,A> Matrix;
+    typedef Dune::BCRSMatrix<FieldMatrix<T,n,m>,A> matrix_type;
+    /** @brief The corresponding SuperLU Matrix type.*/
+    typedef Dune::ColCompMatrix<Matrix> SPQRMatrix;
+    /** @brief Type of an associated initializer class. */
+    typedef ColCompMatrixInitializer<BCRSMatrix<FieldMatrix<T,n,m>,A> > MatrixInitializer;
+    /** @brief The type of the domain of the solver. */
+    typedef Dune::BlockVector<FieldVector<T,m>, typename A::template rebind<FieldVector<T,m> >::other> domain_type;
+    /** @brief The type of the range of the solver. */
+    typedef Dune::BlockVector<FieldVector<T,n>, typename A::template rebind<FieldVector<T,n> >::other> range_type;
+
+    /** @brief Construct a solver object from a BCRSMatrix
+     *
+     * This computes the matrix decomposition, and may take a long time
+     * (and use a lot of memory).
+     *
+     *  @param matrix the matrix to solve for
+     *  @param verbose, 0 or 1, set the verbosity level, defaults to 0
+     */
+    SPQR(const Matrix& matrix, int verbose=0) : matrixIsLoaded_(false), verbose_(verbose)
+    {
+      //check whether T is a supported type
+      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
+                    "Unsupported Type in SPQR (only double and std::complex<double> supported)");
+      cc_ = new cholmod_common();
+      cholmod_l_start(cc_);
+      setMatrix(matrix);
+    }
+
+     /** @brief Constructor for compatibility with SuperLU standard constructor
+     *
+     * This computes the matrix decomposition, and may take a long time
+     * (and use a lot of memory).
+     *
+     * @param matrix the matrix to solve for
+     * @param verbose, 0 or 1, set the verbosity level, defaults to 0
+     */
+    SPQR(const Matrix& matrix, int verbose, bool) : matrixIsLoaded_(false), verbose_(verbose)
+    {
+      //check whether T is a supported type
+      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
+                    "Unsupported Type in SPQR (only double and std::complex<double> supported)");
+      cc_ = new cholmod_common();
+      cholmod_l_start(cc_);
+      setMatrix(matrix);
+    }
+
+    /** @brief Default constructor. */
+    SPQR() : matrixIsLoaded_(false), verbose_(0)
+    {
+      //check whether T is a supported type
+      static_assert((std::is_same<T,double>::value) || (std::is_same<T,std::complex<double> >::value),
+                    "Unsupported Type in SPQR (only double and std::complex<double> supported)");
+      cc_ = new cholmod_common();
+      cholmod_l_start(cc_);
+    }
+
+    /** @brief Destructor. */
+    virtual ~SPQR()
+    {
+      if ((spqrMatrix_.N() + spqrMatrix_.M() > 0) || matrixIsLoaded_)
+        free();
+      cholmod_l_finish(cc_);
+    }
+
+    /** \copydoc InverseOperator::apply(X&, Y&, InverseOperatorResult&) */
+    virtual void apply(domain_type& x, range_type& b, InverseOperatorResult& res)
+    {
+      const std::size_t dimMat(spqrMatrix_.N());
+      // fill B
+      for(std::size_t k = 0; k != dimMat; ++k)
+        (static_cast<T*>(B_->x))[k] = b[k];
+      cholmod_dense* BTemp = B_;
+      B_ = SuiteSparseQR_qmult<T>(0, spqrfactorization_, B_, cc_);
+      X_ = SuiteSparseQR_solve<T>(1, spqrfactorization_, B_, cc_);
+      cholmod_l_free_dense(&BTemp, cc_);
+      // fill x
+      for(std::size_t k = 0; k != dimMat; ++k)
+        x [k] = (static_cast<T*>(X_->x))[k];
+      // this is a direct solver
+      res.iterations = 1;
+      res.converged = true;
+      if(verbose_ > 0)
+      {
+        std::cout<<std::endl<<"Solving with SuiteSparseQR"<<std::endl;
+        std::cout<<"Flops Taken: "<<cc_->SPQR_flopcount<<std::endl;
+        std::cout<<"Analysis Time: "<<cc_->SPQR_analyze_time<<" s"<<std::endl;
+        std::cout<<"Factorize Time: "<<cc_->SPQR_factorize_time<<" s"<<std::endl;
+        std::cout<<"Backsolve Time: "<<cc_->SPQR_solve_time<<" s"<<std::endl;
+        std::cout<<"Peak Memory Usage: "<<cc_->memory_usage<<" bytes"<<std::endl;
+        std::cout<<"Rank Estimate: "<<cc_->SPQR_istat[4]<<std::endl<<std::endl;
+      }
+    }
+
+    /** \copydoc InverseOperator::apply(X&,Y&,double,InverseOperatorResult&) */
+    virtual void apply (domain_type& x, range_type& b, double reduction, InverseOperatorResult& res)
+    {
+      DUNE_UNUSED_PARAMETER(reduction);
+      apply(x, b, res);
+    }
+
+    /**
+     * @brief Additional apply method with c-arrays in analogy to superlu.
+     * @param x solution array
+     * @param b rhs array
+     */
+    void apply(T* x, T* b)
+    {
+      b = SuiteSparseQR_qmult<T>(0, spqrfactorization_, b, cc_);
+      x = SuiteSparseQR_solve<T>(1, spqrfactorization_, b, cc_);
+      if(verbose_ > 0)
+      {
+        std::cout<<std::endl<<"Solving with SuiteSparseQR"<<std::endl;
+        std::cout<<"Flops Taken: "<<cc_->SPQR_flopcount<<std::endl;
+        std::cout<<"Analysis Time: "<<cc_->SPQR_analyze_time<<" s"<<std::endl;
+        std::cout<<"Factorize Time: "<<cc_->SPQR_factorize_time<<" s"<<std::endl;
+        std::cout<<"Backsolve Time: "<<cc_->SPQR_solve_time<<" s"<<std::endl;
+        std::cout<<"Peak Memory Usage: "<<cc_->memory_usage<<" bytes"<<std::endl;
+        std::cout<<"Rank Estimate: "<<cc_->SPQR_istat[4]<<std::endl<<std::endl;
+      }
+    }
+
+    /** @brief Initialize data from given matrix. */
+    void setMatrix(const Matrix& matrix)
+    {
+      if ((spqrMatrix_.N() + spqrMatrix_.M() > 0) || matrixIsLoaded_)
+        free();
+      spqrMatrix_ = matrix;
+      decompose();
+    }
+
+    /**
+     * @brief Sets the verbosity level for the solver.
+     * @param v verbosity level: 0 only error messages, 1 a bit of statistics.
+     */
+    inline void setVerbosity(int v)
+    {
+      verbose_=v;
+    }
+
+    /**
+     * @brief Free allocated space.
+     * @warning Later calling apply will result in an error.
+     */
+    void free()
+    {
+      cholmod_l_free_sparse(&A_, cc_);
+      cholmod_l_free_dense(&B_, cc_);
+      cholmod_l_free_dense(&X_, cc_);
+      SuiteSparseQR_free<double>(&spqrfactorization_, cc_);
+      spqrMatrix_.free();
+      matrixIsLoaded_ = false;
+    }
+
+    /** @brief Get method name. */
+    inline const char* name()
+    {
+      return "SPQR";
+    }
+
+    /**
+     * @brief Get QR factorization.
+     * @warning It is up to the user to preserve consistency when modifyng it.
+     */
+    SuiteSparseQR_factorization<double>* getFactorization()
+    {
+      return spqrfactorization_;
+    }
+
+    private:
+    template<class M,class X, class TM, class TD, class T1>
+    friend class SeqOverlappingSchwarz;
+
+    friend struct SeqOverlappingSchwarzAssemblerHelper<SPQR<Matrix>,true>;
+
+    /** @brief Computes the SPQR decomposition. */
+    void decompose()
+    {
+      const std::size_t dimMat(spqrMatrix_.N());
+      const std::size_t nnz(spqrMatrix_.getColStart()[dimMat]);
+      // initialise the matrix A (sorted, packed, unsymmetric, real entries)
+      A_ = cholmod_l_allocate_sparse(dimMat, dimMat, nnz, 1, 1, 0, 1, cc_);
+      // copy all the entries of Ap, Ai, Ax
+      for(std::size_t k = 0; k != (dimMat+1); ++k)
+        (static_cast<long int *>(A_->p))[k] = spqrMatrix_.getColStart()[k];
+      for(std::size_t k = 0; k != nnz; ++k)
+      {
+        (static_cast<long int*>(A_->i))[k] = spqrMatrix_.getRowIndex()[k];
+        (static_cast<T*>(A_->x))[k] = spqrMatrix_.getValues()[k];
+      }
+      // initialise the vector B
+      B_ = cholmod_l_allocate_dense(dimMat, 1, dimMat, A_->xtype, cc_);
+      // compute factorization of A
+      spqrfactorization_=SuiteSparseQR_factorize<T>(SPQR_ORDERING_DEFAULT,SPQR_DEFAULT_TOL,A_,cc_);
+    }
+
+    SPQRMatrix spqrMatrix_;
+    bool matrixIsLoaded_;
+    int verbose_;
+    cholmod_common* cc_;
+    cholmod_sparse* A_;
+    cholmod_dense* X_;
+    cholmod_dense* B_;
+    SuiteSparseQR_factorization<T>* spqrfactorization_;
+  };
+
+  template<typename T, typename A, int n, int m>
+  struct IsDirectSolver<SPQR<BCRSMatrix<FieldMatrix<T,n,m>,A> > >
+  {
+    enum {value = true};
+  };
+
+  template<typename T, typename A, int n, int m>
+  struct StoresColumnCompressed<SPQR<BCRSMatrix<FieldMatrix<T,n,m>,A> > >
+  {
+    enum {value = true};
+  };
+
+}
+
+#endif //HAVE_SPQR
+#endif //DUNE_ISTL_SPQR_HH