CppAD: A C++ Algorithmic Differentiation Package 20110419
|
00001 /* $Id$ */ 00002 /* -------------------------------------------------------------------------- 00003 CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-10 Bradley M. Bell 00004 00005 CppAD is distributed under multiple licenses. This distribution is under 00006 the terms of the 00007 Common 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 CPPAD_BEGIN_NAMESPACE 00016 /*! 00017 \file hes_fg_map.cpp 00018 \brief Creates a mapping between two representations for Hessian of fg. 00019 */ 00020 00021 /*! 00022 Create mapping from CppAD to Ipopt sparse representations of Hessian of F(x). 00023 00024 The functions 00025 \f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and 00026 \f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ are defined by the 00027 \ref Users_Representation. 00028 We define the function 00029 \f$ F : {\bf R}^n \rightarrow {\bf R} \f$ by 00030 \f[ 00031 F(x) = \sum_{i=0}^m fg(x)_i 00032 \f] 00033 00034 \param fg_info 00035 For <tt>k = 0 , ... , K-1</tt>, 00036 for <tt>ell = 0 , ... , L[k]</tt>, 00037 the function call 00038 \verbatim 00039 fg_info->index(k, ell, I, J); 00040 \endverbatim 00041 is made by \c hes_fg_map. 00042 The values \c k and \c ell are inputs. 00043 The input size of \c I ( \c J ) 00044 is greater than or equal <tt>p[k] ( q[k] )</tt> 00045 and this size is not changed. 00046 The input values of the elements of \c I and \c J are not specified. 00047 The output value of the elements of \c I define 00048 \f[ 00049 I_{k, \ell} = ( {\rm I[0]} , \cdots , {\rm I[p[k]-1]} ) 00050 \f] 00051 The output value of the elements of \c J define 00052 \f[ 00053 J_{k, \ell} = ( {\rm J[0]} , \cdots , {\rm J[q[k]-1]} ) 00054 \f] 00055 00056 \param m 00057 is the dimension of the range space for \f$ g(x) \f$; i.e., 00058 \f$ g(x) \in {\bf R}^m \f$. 00059 00060 \param n 00061 is the dimension of the domain space for \f$ f(x) \f$ and \f$ g(x) \f$; 00062 i.e., \f$ x \in {\bf R}^n \f$. 00063 00064 \param K 00065 is the number of functions \f$ r_k ( u ) \f$ used for the representation of 00066 \f$ f(x) \f$ and \f$ g(x) \f$. 00067 00068 \param L 00069 is a vector with size \c K. 00070 For <tt>k = 0 , ... , K-1, L[k]</tt> 00071 is the number of terms that use \f$ r_k (u) \f$ 00072 in the representation of \f$ f(x) \f$ and \f$ g(x) \f$. 00073 00074 \param p 00075 is a vector with size \c K. 00076 For <tt>k = 0 , ... , K-1, p[k]</tt> 00077 is dimension of the range space for \f$ r_k (u) \f$; i.e., 00078 \f$ r_k (u) \in {\bf R}^{p(k)} \f$. 00079 00080 \param q 00081 is a vector with size \c K. 00082 For <tt>k = 0 , ... , K-1, q[k]</tt> 00083 is dimension of the domain space for \f$ r_k (u) \f$; i.e., 00084 \f$ u \in {\bf R}^{q(k)} \f$. 00085 00086 \param pattern_hes_r 00087 is a vector with size \c K. 00088 For <tt>k = 0 , ... , K-1, pattern_jac_r[k]</tt> 00089 is a CppAD sparsity pattern for the Hessian of the function 00090 \f[ 00091 R(u) = \sum_{i=0}^{p[k]-1} r_k (u)_i 00092 \f] 00093 As such, <tt>pattern_hes_r[k].size() == q[k] * q[k]</tt>. 00094 00095 \param I 00096 is a work vector of length greater than or equal <tt>p[k]</tt> for all \c k. 00097 The input and output value of its elements are unspecified. 00098 The size of \c I is not changed. 00099 00100 \param J 00101 is a work vector of length greater than or equal <tt>q[k]</tt> for all \c k. 00102 The input and output value of its elements are unspecified. 00103 The size of \c J is not changed. 00104 00105 \param index_hes_fg: 00106 On input, this is empty; i.e., <tt>index_jac_g.size() == 0</tt>. 00107 On output, it is the index mapping from \f$ (i, j) \f$ in the Jacobian of 00108 \f$ g(x) \f$ to the corresponding index value used by Ipopt to represent 00109 the Jacobian. 00110 Furthermore, if <tt>index_jac_g[i].find(j) == index_jac_g[i].end()</tt>, 00111 then the \f$ (i, j)\f$ entry in the Jacobian of \f$ g(x) \f$ is always zero. 00112 */ 00113 void hes_fg_map( 00114 cppad_ipopt_fg_info* fg_info , 00115 size_t m , 00116 size_t n , 00117 size_t K , 00118 const CppAD::vector<size_t>& L , 00119 const CppAD::vector<size_t>& p , 00120 const CppAD::vector<size_t>& q , 00121 const CppAD::vector<CppAD::vectorBool>& pattern_hes_r , 00122 CppAD::vector<size_t>& I , 00123 CppAD::vector<size_t>& J , 00124 CppAD::vector< std::map<size_t,size_t> >& index_hes_fg ) 00125 { 00126 using CppAD::vectorBool; 00127 size_t i, j, ij, k, ell; 00128 00129 CPPAD_ASSERT_UNKNOWN( K == L.size() ); 00130 CPPAD_ASSERT_UNKNOWN( K == p.size() ); 00131 CPPAD_ASSERT_UNKNOWN( K == q.size() ); 00132 CPPAD_ASSERT_UNKNOWN( K == pattern_hes_r.size() ); 00133 # ifndef NDEBUG 00134 for(k = 0; k < K; k++) 00135 { CPPAD_ASSERT_UNKNOWN( p[k] <= I.size() ); 00136 CPPAD_ASSERT_UNKNOWN( q[k] <= J.size() ); 00137 CPPAD_ASSERT_UNKNOWN( q[k]*q[k] == pattern_hes_r[k].size() ); 00138 } 00139 # endif 00140 00141 // Now compute pattern for fg 00142 // (use standard set representation because can be huge). 00143 CppAD::vector< std::set<size_t> > pattern_hes_fg(n); 00144 for(k = 0; k < K; k++) for(ell = 0; ell < L[k]; ell++) 00145 { fg_info->index(k, ell, I, J); 00146 for(i = 0; i < q[k]; i++) 00147 { for(j = 0; j < q[k]; j++) 00148 { ij = i * q[k] + j; 00149 if( pattern_hes_r[k][ij] ) 00150 pattern_hes_fg[J[i]].insert(J[j]); 00151 } 00152 } 00153 } 00154 00155 // Now compute the mapping from (i, j) in the Hessian of fg to the 00156 // corresponding index value used by Ipopt to represent the Hessian. 00157 CPPAD_ASSERT_UNKNOWN( index_hes_fg.size() == 0 ); 00158 index_hes_fg.resize(n); 00159 std::set<size_t>::const_iterator itr; 00160 ell = 0; 00161 for(i = 0; i < n; i++) 00162 { for( itr = pattern_hes_fg[i].begin(); 00163 itr != pattern_hes_fg[i].end(); itr++) 00164 { 00165 index_hes_fg[i][*itr] = ell++; 00166 } 00167 } 00168 return; 00169 } 00170 00171 CPPAD_END_NAMESPACE