MOAB: Mesh Oriented datABase  (version 5.4.1)
MsqHessian.hpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2004 Sandia Corporation and Argonne National
00005     Laboratory.  Under the terms of Contract DE-AC04-94AL85000
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00007     rights in this software.
00008 
00009     This library is free software; you can redistribute it and/or
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00014     This library is distributed in the hope that it will be useful,
00015     but WITHOUT ANY WARRANTY; without even the implied warranty of
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00017     Lesser General Public License for more details.
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00019     You should have received a copy of the GNU Lesser General Public License
00020     (lgpl.txt) along with this library; if not, write to the Free Software
00021     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
00022 
00023     [email protected], [email protected], [email protected],
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00025 
00026   ***************************************************************** */
00027 // -*- Mode : c++; tab-width: 3; c-tab-always-indent: t; indent-tabs-mode: nil; c-basic-offset: 3
00028 // -*-
00029 //
00030 //    AUTHOR: Todd Munson <[email protected]>
00031 //       ORG: Argonne National Laboratory
00032 //    E-MAIL: [email protected]
00033 //
00034 // ORIG-DATE:  2-Jan-03 at 11:02:19 bu Thomas Leurent
00035 //  LAST-MOD:  5-Oct-04 by Jason Kraftcheck
00036 //
00037 // DESCRIPTION:
00038 // ============
00039 /*! \file MsqHessian.hpp
00040 
00041  The MsqHessian class stores a sparse hessian for a given objective
00042  function. The objective function must be C2 and such that its hessian
00043  has non-zero entries only for the duplet of derivatives corresponding
00044  to nodes of a same element.
00045 
00046  \author Thomas Leurent
00047 */
00048 
00049 #ifndef MsqHessian_hpp
00050 #define MsqHessian_hpp
00051 
00052 #include "Mesquite.hpp"
00053 #include "Matrix3D.hpp"
00054 #include "PatchData.hpp"
00055 #include "MsqTimer.hpp"
00056 
00057 #include <iosfwd>
00058 
00059 namespace MBMesquite
00060 {
00061 class ObjectiveFunction;
00062 
00063 /*!
00064   \class MsqHessian
00065   \brief Vector3D is the object that effeciently stores the objective function
00066   Hessian each entry is a Matrix3D object (i.e. a vertex Hessian).
00067 */
00068 class MESQUITE_EXPORT MsqHessian
00069 {
00070   protected:             // data accessed directly in tests.
00071     Matrix3D* mEntries;  //!< CSR block entries. size: nb of nonzero blocks, i.e. mRowStart[mSize] .
00072     size_t* mRowStart;   //!< start of each row in mEntries. size: nb of vertices (mSize).
00073     size_t* mColIndex;   //!< CSR block structure: column indexes of the row entries.
00074 
00075     size_t mSize;  //!< number of rows (or number of columns, this is a square matrix).
00076 
00077     Matrix3D* mPreconditioner;
00078     size_t precondArraySize;
00079 
00080     Vector3D* mR;         //!< array used in the CG solver
00081     Vector3D* mZ;         //!< array used in the CG solver
00082     Vector3D* mP;         //!< array used in the CG solver
00083     Vector3D* mW;         //!< array used in the CG solver
00084     size_t cgArraySizes;  //!< size of arrays allocated in the CG solver.
00085     size_t maxCGiter;     //!< max nb of iterations of the CG solver.
00086 
00087   public:
00088     MsqHessian();
00089     ~MsqHessian();
00090 
00091     void initialize( PatchData& pd, MsqError& err );
00092     void initialize( const MsqHessian& other );
00093 
00094     inline void zero_out();
00095 
00096     size_t size() const
00097     {
00098         return mSize;
00099     }
00100 
00101     //! returns the diagonal blocks, memory must be allocated before call.
00102     void get_diagonal_blocks( std::vector< Matrix3D >& diag, MsqError& err ) const;
00103 
00104     Matrix3D* get_block( size_t i, size_t j );
00105     const Matrix3D* get_block( size_t i, size_t j ) const;
00106 
00107     // inline void accumulate_entries(PatchData &pd, const size_t &elem_index,
00108     //                               Matrix3D* const &mat3d_array, MsqError &err);
00109 
00110     void compute_preconditioner( MsqError& err );
00111     void apply_preconditioner( Vector3D zloc[], Vector3D rloc[], MsqError& err );
00112 
00113     void cg_solver( Vector3D x[], Vector3D b[], MsqError& err );
00114     //! Hessian - vector product, summed with a second vector (optional).
00115     friend void axpy( Vector3D res[],
00116                       size_t size_r,
00117                       const MsqHessian& H,
00118                       const Vector3D x[],
00119                       size_t size_x,
00120                       const Vector3D y[],
00121                       size_t size_y,
00122                       MsqError& err );
00123 
00124     //! r = this * x, where r and x are arrays of length size().
00125     void product( Vector3D* r, const Vector3D* x ) const;
00126 
00127     friend std::ostream& operator<<( std::ostream&, const MsqHessian& );
00128 
00129     inline void add( size_t row, size_t col, const Matrix3D& m, MsqError& err );
00130 
00131     inline void scale( double value );
00132 
00133     void add( const MsqHessian& other );
00134 
00135     // Release all storage.  Object is invalid until next call
00136     // to initialize(..).
00137     void clear();
00138 
00139     inline double norm() const;  //!< Frobenius norm
00140 
00141   private:
00142     MsqHessian& operator=( const MsqHessian& h );
00143     MsqHessian( const MsqHessian& copy );
00144 };
00145 
00146 inline double MsqHessian::norm() const
00147 {
00148     double sum = 0.0;
00149     for( size_t i = 0; i < mRowStart[mSize]; ++i )
00150         sum += Frobenius_2( mEntries[i] );
00151     return sqrt( sum );
00152 }
00153 
00154 /*! Sets all Hessian entries to zero. This is usually used before
00155   starting to accumulate elements hessian in the objective function
00156   hessian. */
00157 inline void MsqHessian::zero_out()
00158 {
00159     if( mSize == 0 ) return;  // empty hessian.
00160 
00161     size_t i;
00162     for( i = 0; i < mRowStart[mSize]; ++i )
00163     {
00164         mEntries[i].zero();
00165     }
00166 }
00167 
00168 inline void MsqHessian::scale( double value )
00169 {
00170     for( size_t i = 0; i < mRowStart[mSize]; ++i )
00171         mEntries[i] *= value;
00172 }
00173 
00174 /*! Accumulates entries of an element hessian into an objective function
00175   hessian. Make sure to use zero_out() before starting the accumulation
00176   process.
00177 
00178   \param pd: PatchData in that contains the element which Hessian
00179   we are accumulating in the Hessian matrix. This must be the same
00180   PatchData that was used in MsqHessian::initialize().
00181   \param elem_index: index of the element in the PatchData.
00182   \param mat3d_array: This is the upper triangular part of the element Hessian
00183   for all nodes, including fixed nodes, for which the entries must be null Matrix3Ds.
00184   \param nb_mat3d. The size of the mat3d_array: (n+1)n/2, where n is
00185   the number of nodes in the element.
00186 */
00187 //  inline void MsqHessian::accumulate_entries(PatchData &pd, const size_t &elem_index,
00188 //                                             Matrix3D* const &mat3d_array, MsqError &err)
00189 //    {
00190 //      if (&pd != origin_pd) {
00191 //        MSQ_SETERR(err)(
00192 //                    "Cannot accumulate elements from a different patch. "
00193 //                    "Use MsqHessian::initialize first.",
00194 //                    MsqError::INVALID_ARG );
00195 //        return;
00196 //      }
00197 //
00198 //      size_t nve = pd.get_element_array(err)[elem_index].vertex_count();
00199 //      size_t* ve = pd.get_element_array(err)[elem_index].get_vertex_index_array();
00200 //      size_t e = mAccumElemStart[elem_index];
00201 //      size_t i, j, c = 0;
00202 //      for (i = 0; i < nve; ++i)
00203 //      {
00204 //        for (j = i; j < nve; ++j)
00205 //        {
00206 //          if (ve[i] < mSize && ve[j] < mSize)
00207 //          {
00208 //            int k = mAccumulation[e++];
00209 //            if (k >= 0)
00210 //              mEntries[k] += mat3d_array[c];
00211 //            else
00212 //              mEntries[-k].plus_transpose_equal( mat3d_array[c] );
00213 //          }
00214 //          ++c;
00215 //        }
00216 //      }
00217 //    }
00218 
00219 inline void MsqHessian::add( size_t row, size_t col, const Matrix3D& m, MsqError& err )
00220 {
00221     if( row <= col )
00222     {
00223         for( size_t i = mRowStart[row]; i != mRowStart[row + 1]; ++i )
00224             if( mColIndex[i] == col )
00225             {
00226                 mEntries[i] += m;
00227                 return;
00228             }
00229     }
00230     else
00231     {
00232         for( size_t i = mRowStart[col]; i != mRowStart[col + 1]; ++i )
00233             if( mColIndex[i] == row )
00234             {
00235                 mEntries[i].plus_transpose_equal( m );
00236                 return;
00237             }
00238     }
00239 
00240     MSQ_SETERR( err )
00241     ( MsqError::INVALID_ARG, "Hessian entry (%lu,%lu) does not exist.", (unsigned long)row, (unsigned long)col );
00242 }
00243 
00244 /*!
00245   \param res: array of Vector3D in which the result is stored.
00246   \param size_r: size of the res array.
00247   \param x: vector multiplied by the Hessian.
00248   \param size_x: size of the x array.
00249   \param y: vector added to the Hessian vector product. Set to 0 (NULL) if not needed.
00250   \param size_y: size of the y array. Set to 0 if not needed.
00251 */
00252 inline void axpy( Vector3D res[],
00253                   size_t size_r,
00254                   const MsqHessian& H,
00255                   const Vector3D x[],
00256                   size_t size_x,
00257                   const Vector3D y[],
00258                   size_t size_y,
00259                   MsqError& /*err*/ )
00260 {
00261     if( ( size_r != H.mSize ) || ( size_x != H.mSize ) || ( size_y != H.mSize && size_y != 0 ) )
00262     {
00263         // throw an error
00264     }
00265 
00266     Vector3D tmpx, tmpm;  // for cache opt.
00267     size_t* col     = H.mColIndex;
00268     const size_t nn = H.mSize;
00269     size_t rl;  // row length
00270     size_t el;  // entries index
00271     size_t lo;
00272     size_t c;  // column index
00273     size_t i, j;
00274 
00275     if( y != 0 )
00276     {
00277         for( i = 0; i < nn; ++i )
00278         {
00279             res[i] = y[i];
00280         }
00281     }
00282     else
00283     {  // y == 0
00284         for( i = 0; i < nn; ++i )
00285         {
00286             res[i] = 0.;
00287         }
00288     }
00289 
00290     el = 0;
00291     for( i = 0; i < nn; ++i )
00292     {
00293         rl = H.mRowStart[i + 1] - H.mRowStart[i];
00294         lo = *col++;
00295 
00296         // Diagonal entry
00297         tmpx = x[i];
00298         eqAx( tmpm, H.mEntries[el], tmpx );
00299         ++el;
00300 
00301         // Non-diagonal entries
00302         for( j = 1; j < rl; ++j )
00303         {
00304             c = *col++;
00305             //          res[i] += H.mEntries[e] * x[c];
00306             plusEqAx( tmpm, H.mEntries[el], x[c] );
00307             //          res[c] += transpose(H.mEntries[e]) * tmpxi;
00308             plusEqTransAx( res[c], H.mEntries[el], tmpx );
00309             ++el;
00310         }
00311         res[lo] += tmpm;
00312     }
00313 }
00314 
00315 /*! Computes \f$ z=M^{-1}r \f$ . */
00316 inline void MsqHessian::apply_preconditioner( Vector3D zloc[], Vector3D rloc[], MsqError& /*err*/ )
00317 {
00318     size_t m;
00319 
00320     for( m = 0; m < mSize; ++m )
00321     {
00322 #ifdef DIAGONAL_PRECONDITIONER
00323         // preconditioner is identity matrix for now.
00324         zloc[m][0] = mPreconditioner[m][0][0] * rloc[m][0];
00325         zloc[m][1] = mPreconditioner[m][1][1] * rloc[m][1];
00326         zloc[m][2] = mPreconditioner[m][2][2] * rloc[m][2];
00327 #else
00328         // z = inv(L^T) * r
00329         zloc[m][0] = rloc[m][0];
00330         zloc[m][1] = rloc[m][1] - mPreconditioner[m][0][1] * zloc[m][0];
00331         zloc[m][2] = rloc[m][2] - mPreconditioner[m][0][2] * zloc[m][0] - mPreconditioner[m][1][2] * zloc[m][1];
00332 
00333         // z = inv(D) * z
00334         zloc[m][0] *= mPreconditioner[m][0][0];
00335         zloc[m][1] *= mPreconditioner[m][1][1];
00336         zloc[m][2] *= mPreconditioner[m][2][2];
00337 
00338         // z = inv(L) * z
00339         zloc[m][2] = zloc[m][2];
00340         zloc[m][1] = zloc[m][1] - mPreconditioner[m][1][2] * zloc[m][2];
00341         zloc[m][0] = zloc[m][0] - mPreconditioner[m][0][1] * zloc[m][1] - mPreconditioner[m][0][2] * zloc[m][2];
00342 #endif
00343     }
00344 }
00345 
00346 /*! Returns a pointer to the Matrix3D block at position i,j if it exist.
00347   Returns the NULL pointer if position i,j (0-based) is a NULL entry.
00348   Note that block i,j must be in the upper triangular part of the
00349   (symetric) hessian. */
00350 inline Matrix3D* MsqHessian::get_block( size_t i, size_t j )
00351 {
00352     size_t c;
00353 
00354     if( i >= mSize || j >= mSize || j < i ) return NULL;
00355 
00356     for( c = mRowStart[i]; c < mRowStart[i + 1]; ++c )
00357     {
00358         if( mColIndex[c] == j ) return ( mEntries + c );
00359     }
00360 
00361     // if there is no block at position i,j (zero entry).
00362     return NULL;
00363 }
00364 inline const Matrix3D* MsqHessian::get_block( size_t i, size_t j ) const
00365 {
00366     return const_cast< MsqHessian* >( this )->get_block( i, j );
00367 }
00368 
00369 /* ------------------ I/O ----------------- */
00370 
00371 std::ostream& operator<<( std::ostream& s, const MsqHessian& h );
00372 
00373 }  // namespace MBMesquite
00374 
00375 #endif  // MsqHessian_hpp
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