CppAD: A C++ Algorithmic Differentiation Package
20130918
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00001 /* $Id$ */ 00002 /* -------------------------------------------------------------------------- 00003 CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 Bradley M. Bell 00004 00005 CppAD is distributed under multiple licenses. This distribution is under 00006 the terms of the 00007 Eclipse Public License Version 1.0. 00008 00009 A copy of this license is included in the COPYING file of this distribution. 00010 Please visit http://www.coin-or.org/CppAD/ for information on other licenses. 00011 -------------------------------------------------------------------------- */ 00012 # include "cppad_ipopt_nlp.hpp" 00013 # include "hes_fg_map.hpp" 00014 00015 // --------------------------------------------------------------------------- 00016 namespace cppad_ipopt { 00017 // --------------------------------------------------------------------------- 00018 /*! 00019 \{ 00020 \file hes_fg_map.cpp 00021 \brief Creates a mapping between two representations for Hessian of fg. 00022 */ 00023 00024 00025 /*! 00026 Create mapping from CppAD to Ipopt sparse representations of Hessian of F(x). 00027 00028 The functions 00029 \f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and 00030 \f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ are defined by the 00031 \ref Users_Representation. 00032 We define the function 00033 \f$ F : {\bf R}^n \rightarrow {\bf R} \f$ by 00034 \f[ 00035 F(x) = \sum_{i=0}^m fg(x)_i 00036 \f] 00037 00038 \param fg_info 00039 For <tt>k = 0 , ... , K-1</tt>, 00040 for <tt>ell = 0 , ... , L[k]</tt>, 00041 the function call 00042 \verbatim 00043 fg_info->index(k, ell, I, J); 00044 \endverbatim 00045 is made by \c hes_fg_map. 00046 The values \c k and \c ell are inputs. 00047 The input size of \c I ( \c J ) 00048 is greater than or equal <tt>p[k] ( q[k] )</tt> 00049 and this size is not changed. 00050 The input values of the elements of \c I and \c J are not specified. 00051 The output value of the elements of \c I define 00052 \f[ 00053 I_{k, \ell} = ( {\rm I[0]} , \cdots , {\rm I[p[k]-1]} ) 00054 \f] 00055 The output value of the elements of \c J define 00056 \f[ 00057 J_{k, \ell} = ( {\rm J[0]} , \cdots , {\rm J[q[k]-1]} ) 00058 \f] 00059 00060 \param m 00061 is the dimension of the range space for \f$ g(x) \f$; i.e., 00062 \f$ g(x) \in {\bf R}^m \f$. 00063 00064 \param n 00065 is the dimension of the domain space for \f$ f(x) \f$ and \f$ g(x) \f$; 00066 i.e., \f$ x \in {\bf R}^n \f$. 00067 00068 \param K 00069 is the number of functions \f$ r_k ( u ) \f$ used for the representation of 00070 \f$ f(x) \f$ and \f$ g(x) \f$. 00071 00072 \param L 00073 is a vector with size \c K. 00074 For <tt>k = 0 , ... , K-1, L[k]</tt> 00075 is the number of terms that use \f$ r_k (u) \f$ 00076 in the representation of \f$ f(x) \f$ and \f$ g(x) \f$. 00077 00078 \param p 00079 is a vector with size \c K. 00080 For <tt>k = 0 , ... , K-1, p[k]</tt> 00081 is dimension of the range space for \f$ r_k (u) \f$; i.e., 00082 \f$ r_k (u) \in {\bf R}^{p(k)} \f$. 00083 00084 \param q 00085 is a vector with size \c K. 00086 For <tt>k = 0 , ... , K-1, q[k]</tt> 00087 is dimension of the domain space for \f$ r_k (u) \f$; i.e., 00088 \f$ u \in {\bf R}^{q(k)} \f$. 00089 00090 \param pattern_hes_r 00091 is a vector with size \c K. 00092 For <tt>k = 0 , ... , K-1, pattern_jac_r[k]</tt> 00093 is a CppAD sparsity pattern for the Hessian of the function 00094 \f[ 00095 R(u) = \sum_{i=0}^{p[k]-1} r_k (u)_i 00096 \f] 00097 As such, <tt>pattern_hes_r[k].size() == q[k] * q[k]</tt>. 00098 00099 \param I 00100 is a work vector of length greater than or equal <tt>p[k]</tt> for all \c k. 00101 The input and output value of its elements are unspecified. 00102 The size of \c I is not changed. 00103 00104 \param J 00105 is a work vector of length greater than or equal <tt>q[k]</tt> for all \c k. 00106 The input and output value of its elements are unspecified. 00107 The size of \c J is not changed. 00108 00109 \param index_hes_fg: 00110 On input, this is empty; i.e., <tt>index_jac_g.size() == 0</tt>. 00111 On output, it is the index mapping from \f$ (i, j) \f$ in the Jacobian of 00112 \f$ g(x) \f$ to the corresponding index value used by Ipopt to represent 00113 the Jacobian. 00114 Furthermore, if <tt>index_jac_g[i].find(j) == index_jac_g[i].end()</tt>, 00115 then the \f$ (i, j)\f$ entry in the Jacobian of \f$ g(x) \f$ is always zero. 00116 */ 00117 void hes_fg_map( 00118 cppad_ipopt_fg_info* fg_info , 00119 size_t m , 00120 size_t n , 00121 size_t K , 00122 const CppAD::vector<size_t>& L , 00123 const CppAD::vector<size_t>& p , 00124 const CppAD::vector<size_t>& q , 00125 const CppAD::vector<CppAD::vectorBool>& pattern_hes_r , 00126 CppAD::vector<size_t>& I , 00127 CppAD::vector<size_t>& J , 00128 CppAD::vector< std::map<size_t,size_t> >& index_hes_fg ) 00129 { 00130 using CppAD::vectorBool; 00131 size_t i, j, ij, k, ell; 00132 00133 CPPAD_ASSERT_UNKNOWN( K == L.size() ); 00134 CPPAD_ASSERT_UNKNOWN( K == p.size() ); 00135 CPPAD_ASSERT_UNKNOWN( K == q.size() ); 00136 CPPAD_ASSERT_UNKNOWN( K == pattern_hes_r.size() ); 00137 # ifndef NDEBUG 00138 for(k = 0; k < K; k++) 00139 { CPPAD_ASSERT_UNKNOWN( p[k] <= I.size() ); 00140 CPPAD_ASSERT_UNKNOWN( q[k] <= J.size() ); 00141 CPPAD_ASSERT_UNKNOWN( q[k]*q[k] == pattern_hes_r[k].size() ); 00142 } 00143 # endif 00144 00145 // Now compute pattern for fg 00146 // (use standard set representation because can be huge). 00147 CppAD::vector< std::set<size_t> > pattern_hes_fg(n); 00148 for(k = 0; k < K; k++) for(ell = 0; ell < L[k]; ell++) 00149 { fg_info->index(k, ell, I, J); 00150 for(i = 0; i < q[k]; i++) 00151 { for(j = 0; j < q[k]; j++) 00152 { ij = i * q[k] + j; 00153 if( pattern_hes_r[k][ij] ) 00154 pattern_hes_fg[J[i]].insert(J[j]); 00155 } 00156 } 00157 } 00158 00159 // Now compute the mapping from (i, j) in the Hessian of fg to the 00160 // corresponding index value used by Ipopt to represent the Hessian. 00161 CPPAD_ASSERT_UNKNOWN( index_hes_fg.size() == 0 ); 00162 index_hes_fg.resize(n); 00163 std::set<size_t>::const_iterator itr; 00164 ell = 0; 00165 for(i = 0; i < n; i++) 00166 { for( itr = pattern_hes_fg[i].begin(); 00167 itr != pattern_hes_fg[i].end(); itr++) 00168 { 00169 index_hes_fg[i][*itr] = ell++; 00170 } 00171 } 00172 return; 00173 } 00174 00175 // --------------------------------------------------------------------------- 00176 } // end namespace cppad_ipopt 00177 // ---------------------------------------------------------------------------