/* $Id: hes_fg_map.cpp 2625 2012-12-23 14:34:12Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the 
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */
# include "cppad_ipopt_nlp.hpp"
# include "hes_fg_map.hpp"

// ---------------------------------------------------------------------------
namespace cppad_ipopt {
// ---------------------------------------------------------------------------
/*!
\defgroup hes_fg_map_cpp hes_fg_map.cpp
\{
\file hes_fg_map.cpp
\brief Creates a mapping between two representations for Hessian of fg. 
*/


/*!
Create mapping from CppAD to Ipopt sparse representations of Hessian of F(x).

The functions 
\f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and
\f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ are defined by the 
\ref Users_Representation.
We define the function 
\f$ F : {\bf R}^n \rightarrow {\bf R} \f$ by
\f[
	F(x) = \sum_{i=0}^m fg(x)_i
\f]

\param fg_info
For <tt>k = 0 , ... , K-1</tt>,
for <tt>ell = 0 , ... , L[k]</tt>,
the function call 
\verbatim
	fg_info->index(k, ell, I, J);	
\endverbatim
is made by \c hes_fg_map. 
The values \c k and \c ell are inputs.
The input size of \c I ( \c J ) 
is greater than or equal <tt>p[k] ( q[k] )</tt>
and this size is not changed.
The input values of the elements of \c I and \c J are not specified.
The output value of the elements of \c I define
\f[
I_{k, \ell} = ( {\rm I[0]} , \cdots , {\rm I[p[k]-1]} )
\f]
The output value of the elements of \c J define
\f[
J_{k, \ell} = ( {\rm J[0]} , \cdots , {\rm J[q[k]-1]} )
\f]

\param m
is the dimension of the range space for \f$ g(x) \f$; i.e.,
\f$ g(x) \in {\bf R}^m \f$.

\param n
is the dimension of the domain space for \f$ f(x) \f$ and \f$ g(x) \f$;
i.e., \f$ x \in {\bf R}^n \f$.

\param K
is the number of functions \f$ r_k ( u ) \f$ used for the representation of 
\f$ f(x) \f$ and \f$ g(x) \f$.

\param L
is a vector with size \c K.
For <tt>k = 0 , ... , K-1, L[k]</tt>
is the number of terms that use \f$ r_k (u) \f$
in the representation of \f$ f(x) \f$ and \f$ g(x) \f$.

\param p
is a vector with size \c K.
For <tt>k = 0 , ... , K-1, p[k]</tt>
is dimension of the range space for \f$ r_k (u) \f$; i.e.,
\f$ r_k (u) \in {\bf R}^{p(k)} \f$.

\param q
is a vector with size \c K.
For <tt>k = 0 , ... , K-1, q[k]</tt>
is dimension of the domain space for \f$ r_k (u) \f$; i.e.,
\f$ u \in {\bf R}^{q(k)} \f$.

\param pattern_hes_r
is a vector with size \c K.
For <tt>k = 0 , ... , K-1, pattern_jac_r[k]</tt>
is a CppAD sparsity pattern for the Hessian of the function 
\f[
	R(u) = \sum_{i=0}^{p[k]-1} r_k (u)_i
\f]
As such, <tt>pattern_hes_r[k].size() == q[k] * q[k]</tt>.

\param I
is a work vector of length greater than or equal <tt>p[k]</tt> for all \c k.
The input and output value of its elements are unspecified.
The size of \c I is not changed.

\param J
is a work vector of length greater than or equal <tt>q[k]</tt> for all \c k.
The input and output value of its elements are unspecified.
The size of \c J is not changed.

\param index_hes_fg:
On input, this is empty; i.e., <tt>index_jac_g.size() == 0</tt>.
On output, it is the index mapping from \f$ (i, j) \f$ in the Jacobian of 
\f$ g(x) \f$ to the corresponding index value used by Ipopt to represent
the Jacobian.
Furthermore, if <tt>index_jac_g[i].find(j) == index_jac_g[i].end()</tt>,
then the \f$ (i, j)\f$ entry in the Jacobian of \f$ g(x) \f$ is always zero.
*/
void hes_fg_map(
	cppad_ipopt_fg_info*  fg_info                                  , 
	size_t                                          m              ,
	size_t                                          n              ,
	size_t                                          K              ,
	const CppAD::vector<size_t>&                    L              ,
	const CppAD::vector<size_t>&                    p              ,
	const CppAD::vector<size_t>&                    q              ,
	const CppAD::vector<CppAD::vectorBool>&         pattern_hes_r  ,
	CppAD::vector<size_t>&                          I              ,
	CppAD::vector<size_t>&                          J              ,
	CppAD::vector< std::map<size_t,size_t> >&       index_hes_fg   )
{
	using CppAD::vectorBool;
	size_t i, j, ij, k, ell;

	CPPAD_ASSERT_UNKNOWN( K == L.size() );
	CPPAD_ASSERT_UNKNOWN( K == p.size() );
	CPPAD_ASSERT_UNKNOWN( K == q.size() );
	CPPAD_ASSERT_UNKNOWN( K == pattern_hes_r.size() );
# ifndef NDEBUG
	for(k = 0; k < K; k++)
	{	 CPPAD_ASSERT_UNKNOWN( p[k] <= I.size() );
		 CPPAD_ASSERT_UNKNOWN( q[k] <= J.size() );
		 CPPAD_ASSERT_UNKNOWN( q[k]*q[k] == pattern_hes_r[k].size() );
	}
# endif
	
	// Now compute pattern for fg
	// (use standard set representation because can be huge).
	CppAD::vector< std::set<size_t> > pattern_hes_fg(n);
	for(k = 0; k < K; k++) for(ell = 0; ell < L[k]; ell++)
	{	fg_info->index(k, ell, I, J);	
		for(i = 0; i < q[k]; i++) 
		{	for(j = 0; j < q[k]; j++)
			{	ij  = i * q[k] + j;
				if( pattern_hes_r[k][ij] )
					pattern_hes_fg[J[i]].insert(J[j]);
			}
		}
	}

	// Now compute the mapping from (i, j) in the Hessian of fg to the 
	// corresponding index value used by Ipopt to represent the Hessian.
	CPPAD_ASSERT_UNKNOWN( index_hes_fg.size() == 0 );
	index_hes_fg.resize(n);
	std::set<size_t>::const_iterator itr;
	ell = 0;
	for(i = 0; i < n; i++)
	{	for(	itr = pattern_hes_fg[i].begin(); 
			itr != pattern_hes_fg[i].end(); itr++)
		{
			index_hes_fg[i][*itr] = ell++;
		}
	}
	return;
}

// ---------------------------------------------------------------------------
/*! \} */
} // end namespace cppad_ipopt
// ---------------------------------------------------------------------------
