# ifndef CPPAD_TEST_MORE_DEPRECATED_OLD_MAT_MUL_HPP
# define CPPAD_TEST_MORE_DEPRECATED_OLD_MAT_MUL_HPP
// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------

/*
@begin old_mat_mul.hpp@@
$spell
   old_mat_mul.hpp
   cppad
   CppAD
   namespace
   struct
   nr
   nc
   bool
   vx
   const
   im
   mj
   ij
   px
   py
   std
   tx
   ty
   resize
   nz
   var
   jac
   Jacobian
   hes
   vy
$$


$section Define Matrix Multiply as a User Atomic Operation$$


$head Syntax$$
This file is located in the $code example$$ directory.
It can be copied to the current working directory and included
with the syntax
$codei%
   # include "old_mat_mul.hpp"
%$$

$head Example$$
The file old_mat_mul.cpp contains an example use of
$code old_mat_mul.hpp$$.

$head Begin Source$$
$srccode%cpp% */
# include <cppad/cppad.hpp>      // Include CppAD definitions
namespace {                      // Begin empty namespace
   using CppAD::vector;        // Let vector denote CppAD::vector
/* %$$

$head Extra Call Information$$
$srccode%cpp% */
   // Information we will attach to each mat_mul call
   struct call_info {
      size_t nr_result;
      size_t n_middle;
      size_t nc_result;
      vector<bool>  vx;
   };
   vector<call_info> info_; // vector of call information

   // number of orders for this operation (k + 1)
   size_t n_order_ = 0;
   // number of rows in the result matrix
   size_t nr_result_ = 0;
   // number of columns in left matrix and number of rows in right matrix
   size_t n_middle_ = 0;
   // number of columns in the result matrix
   size_t nc_result_ = 0;
   // which components of x are variables
   vector<bool>* vx_ = nullptr;

   // get the information corresponding to this call
   void get_info(size_t id, size_t k, size_t n, size_t m)
   {  n_order_   = k + 1;
      nr_result_ = info_[id].nr_result;
      n_middle_  = info_[id].n_middle;
      nc_result_ = info_[id].nc_result;
      vx_        = &(info_[id].vx);

      assert(n == nr_result_ * n_middle_ + n_middle_ * nc_result_);
      assert(m ==  nr_result_ * nc_result_);
   }

/* %$$
$head Matrix Indexing$$
$srccode%cpp% */
   // Convert left matrix index pair and order to a single argument index
   size_t left(size_t i, size_t j, size_t ell)
   {  assert( i < nr_result_ );
      assert( j < n_middle_ );
      return (i * n_middle_ + j) * n_order_ + ell;
   }
   // Convert right matrix index pair and order to a single argument index
   size_t right(size_t i, size_t j, size_t ell)
   {  assert( i < n_middle_ );
      assert( j < nc_result_ );
      size_t offset = nr_result_ * n_middle_;
      return (offset + i * nc_result_ + j) * n_order_ + ell;
   }
   // Convert result matrix index pair and order to a single result index
   size_t result(size_t i, size_t j, size_t ell)
   {  assert( i < nr_result_ );
      assert( j < nc_result_ );
      return (i * nc_result_ + j) * n_order_ + ell;
   }
/* %$$

$head One Matrix Multiply$$
Forward mode matrix multiply left times right and sum into result:
$srccode%cpp% */
   void multiply_and_sum(
      size_t                order_left ,
      size_t                order_right,
      const vector<double>&         tx ,
      vector<double>&               ty )
   {  size_t i, j;
      size_t order_result = order_left + order_right;
      for(i = 0; i < nr_result_; i++)
      {  for(j = 0; j < nc_result_; j++)
         {  double sum = 0.;
            size_t middle, im_left, mj_right, ij_result;
            for(middle = 0; middle < n_middle_; middle++)
            {  im_left  = left(i, middle, order_left);
               mj_right = right(middle, j, order_right);
               sum     += tx[im_left] * tx[mj_right];
            }
            ij_result = result(i, j, order_result);
            ty[ ij_result ] += sum;
         }
      }
      return;
   }
/* %$$

$head Reverse Partials One Order$$
Compute reverse mode partials for one order and sum into px:
$srccode%cpp% */
   void reverse_multiply(
      size_t                order_left ,
      size_t                order_right,
      const vector<double>&         tx ,
      const vector<double>&         ty ,
      vector<double>&               px ,
      const vector<double>&         py )
   {  size_t i, j;
      size_t order_result = order_left + order_right;
      for(i = 0; i < nr_result_; i++)
      {  for(j = 0; j < nc_result_; j++)
         {  size_t middle, im_left, mj_right, ij_result;
            for(middle = 0; middle < n_middle_; middle++)
            {  ij_result = result(i, j, order_result);
               im_left   = left(i, middle, order_left);
               mj_right  = right(middle, j, order_right);
               // sum       += tx[im_left]  * tx[mj_right];
               px[im_left]  += tx[mj_right] * py[ij_result];
               px[mj_right] += tx[im_left]  * py[ij_result];
            }
         }
      }
      return;
   }
/* %$$
$head Set Union$$
$srccode%cpp% */
   using CppAD::set_union;
/* %$$

$head CppAD User Atomic Callback Functions$$
$srccode%cpp% */
   // ----------------------------------------------------------------------
   // forward mode routine called by CppAD
   bool mat_mul_forward(
      size_t                   id ,
      size_t                    k ,
      size_t                    n ,
      size_t                    m ,
      const vector<bool>&      vx ,
      vector<bool>&            vy ,
      const vector<double>&    tx ,
      vector<double>&          ty
   )
   {  size_t i, j, ell;
      get_info(id, k, n, m);

      // check if this is during the call to mat_mul(id, ax, ay)
      if( vx.size() > 0 )
      {  assert( k == 0 && vx.size() > 0 );

         // store the vx information in info_
         assert( vx_->size() == 0 );
         info_[id].vx.resize(n);
         for(j = 0; j < n; j++)
            info_[id].vx[j] = vx[j];
         assert( vx_->size() == n );

         // now compute vy
         for(i = 0; i < nr_result_; i++)
         {  for(j = 0; j < nc_result_; j++)
            {  // compute vy[ result(i, j, 0) ]
               bool   var = false;
               bool   nz_left, nz_right;
               size_t middle, im_left, mj_right, ij_result;
               for(middle = 0; middle < n_middle_; middle++)
               {  im_left  = left(i, middle, k);
                  mj_right = right(middle, j, k);
                  nz_left  = vx[im_left] || (tx[im_left] != 0.);
                  nz_right = vx[mj_right] || (tx[mj_right]!= 0.);
                  // if not multiplying by the constant zero
                  if( nz_left & nz_right )
                     var |= (vx[im_left] || vx[mj_right]);
               }
               ij_result     = result(i, j, k);
               vy[ij_result] = var;
            }
         }
      }

      // initialize result as zero
      for(i = 0; i < nr_result_; i++)
      {  for(j = 0; j < nc_result_; j++)
            ty[ result(i, j, k) ] = 0.;
      }
      // sum the product of proper orders
      for(ell = 0; ell <=k; ell++)
         multiply_and_sum(ell, k-ell, tx, ty);

      // All orders are implemented and there are no possible error
      // conditions, so always return true.
      return true;
   }
   // ----------------------------------------------------------------------
   // reverse mode routine called by CppAD
   bool mat_mul_reverse(
      size_t                   id ,
      size_t                    k ,
      size_t                    n ,
      size_t                    m ,
      const vector<double>&    tx ,
      const vector<double>&    ty ,
      vector<double>&          px ,
      const vector<double>&    py
   )
   {  get_info(id, k, n, m);

      size_t ell = n * n_order_;
      while(ell--)
         px[ell] = 0.;

      size_t order = n_order_;
      while(order--)
      {  // reverse sum the products for specified order
         for(ell = 0; ell <=order; ell++)
            reverse_multiply(ell, order-ell, tx, ty, px, py);
      }

      // All orders are implemented and there are no possible error
      // conditions, so always return true.
      return true;
   }

   // ----------------------------------------------------------------------
   // forward Jacobian sparsity routine called by CppAD
   bool mat_mul_for_jac_sparse(
      size_t                               id ,
      size_t                                n ,
      size_t                                m ,
      size_t                                p ,
      const vector< std::set<size_t> >&     r ,
      vector< std::set<size_t> >&           s )
   {  size_t i, j, k, im_left, middle, mj_right, ij_result;
      k = 0;
      get_info(id, k, n, m);

      for(i = 0; i < nr_result_; i++)
      {  for(j = 0; j < nc_result_; j++)
         {  ij_result = result(i, j, k);
            s[ij_result].clear();
            for(middle = 0; middle < n_middle_; middle++)
            {  im_left   = left(i, middle, k);
               mj_right  = right(middle, j, k);

               // s[ij_result] = union( s[ij_result], r[im_left] )
               s[ij_result] = set_union(s[ij_result], r[im_left]);

               // s[ij_result] = union( s[ij_result], r[mj_right] )
               s[ij_result] = set_union(s[ij_result], r[mj_right]);
            }
         }
      }
      return true;
   }
   // ----------------------------------------------------------------------
   // reverse Jacobian sparsity routine called by CppAD
   bool mat_mul_rev_jac_sparse(
      size_t                               id ,
      size_t                                n ,
      size_t                                m ,
      size_t                                p ,
      vector< std::set<size_t> >&           r ,
      const vector< std::set<size_t> >&     s )
   {  size_t i, j, k, im_left, middle, mj_right, ij_result;
      k = 0;
      get_info(id, k, n, m);

      for(j = 0; j < n; j++)
         r[j].clear();

      for(i = 0; i < nr_result_; i++)
      {  for(j = 0; j < nc_result_; j++)
         {  ij_result = result(i, j, k);
            for(middle = 0; middle < n_middle_; middle++)
            {  im_left   = left(i, middle, k);
               mj_right  = right(middle, j, k);

               // r[im_left] = union( r[im_left], s[ij_result] )
               r[im_left] = set_union(r[im_left], s[ij_result]);

               // r[mj_right] = union( r[mj_right], s[ij_result] )
               r[mj_right] = set_union(r[mj_right], s[ij_result]);
            }
         }
      }
      return true;
   }
   // ----------------------------------------------------------------------
   // reverse Hessian sparsity routine called by CppAD
   bool mat_mul_rev_hes_sparse(
      size_t                               id ,
      size_t                                n ,
      size_t                                m ,
      size_t                                p ,
      const vector< std::set<size_t> >&     r ,
      const vector<bool>&                   s ,
      vector<bool>&                         t ,
      const vector< std::set<size_t> >&     u ,
      vector< std::set<size_t> >&           v )
   {  size_t i, j, k, im_left, middle, mj_right, ij_result;
      k = 0;
      get_info(id, k, n, m);

      for(j = 0; j < n; j++)
      {  t[j] = false;
         v[j].clear();
      }

      assert( vx_->size() == n );
      for(i = 0; i < nr_result_; i++)
      {  for(j = 0; j < nc_result_; j++)
         {  ij_result = result(i, j, k);
            for(middle = 0; middle < n_middle_; middle++)
            {  im_left   = left(i, middle, k);
               mj_right  = right(middle, j, k);

               // back propagate Jacobian sparsity
               t[im_left]   = (t[im_left] || s[ij_result]);
               t[mj_right]  = (t[mj_right] || s[ij_result]);
               // Visual Studio C++ 2008 warns unsafe mix of int and
               // bool if we use the following code directly above:
               // t[im_left]  |= s[ij_result];
               // t[mj_right] |= s[ij_result];

               // back propagate Hessian sparsity
               // v[im_left]  = union( v[im_left],  u[ij_result] )
               // v[mj_right] = union( v[mj_right], u[ij_result] )
               v[im_left] = set_union(v[im_left],  u[ij_result] );
               v[mj_right] = set_union(v[mj_right], u[ij_result] );

               // Check for case where the (i,j) result element
               // is in reverse Jacobian and both left and right
               // operands in multiplication are variables
               if(s[ij_result] && (*vx_)[im_left] && (*vx_)[mj_right])
               {  // v[im_left] = union( v[im_left], r[mj_right] )
                  v[im_left] = set_union(v[im_left], r[mj_right] );
                  // v[mj_right] = union( v[mj_right], r[im_left] )
                  v[mj_right] = set_union(v[mj_right], r[im_left] );
               }
            }
         }
      }
      return true;
   }
/* %$$

$head Declare mat_mul Function$$
Declare the $code AD<double>$$ routine $codei%mat_mul(%id%, %ax%, %ay%)%$$
and end empty namespace
(we could use any $cref/simple vector template class/SimpleVector/$$
instead of $code CppAD::vector$$):
$srccode%cpp% */
   CPPAD_USER_ATOMIC(
      mat_mul                 ,
      CppAD::vector           ,
      double                  ,
      mat_mul_forward         ,
      mat_mul_reverse         ,
      mat_mul_for_jac_sparse  ,
      mat_mul_rev_jac_sparse  ,
      mat_mul_rev_hes_sparse
   )
} // End empty namespace
/* %$$
$end
*/

# endif
