// 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
// ----------------------------------------------------------------------------


# include <cppad/cppad.hpp>
# include <vector>
# include <valarray>

# define CheckOp(Op)                   \
   Y[index] = X[0] Op 2.;         \
   Check[index * n + 0] = true;   \
   Check[index * n + 1] = false;  \
   Check[index * n + 2] = false;  \
   index++;                       \
   Y[index] = X[0] Op X[1];       \
   Check[index * n + 0] = true;   \
   Check[index * n + 1] = true;   \
   Check[index * n + 2] = false;  \
   index++;                       \
   Y[index] = 3.   Op X[1];       \
   Check[index * n + 0] = false;  \
   Check[index * n + 1] = true;   \
   Check[index * n + 2] = false;  \
   index++;

# define CheckUnaryFun(Fun)            \
   Y[index] = Fun(X[0]);          \
   Check[index * n + 0] = true;   \
   Check[index * n + 1] = false;  \
   Check[index * n + 2] = false;  \
   index++;                       \
   Y[index] = Fun(X[0] + X[1]);   \
   Check[index * n + 0] = true;   \
   Check[index * n + 1] = true;   \
   Check[index * n + 2] = false;  \
   index++;                       \
   Y[index] = Fun(X[1]);          \
   Check[index * n + 0] = false;  \
   Check[index * n + 1] = true;   \
   Check[index * n + 2] = false;  \
   index++;


# define CheckBinaryFun(Fun)           \
   Y[index] = Fun( X[0] , 2.);    \
   Check[index * n + 0] = true;   \
   Check[index * n + 1] = false;  \
   Check[index * n + 2] = false;  \
   index++;                       \
   Y[index] = Fun( X[0] , X[1]);  \
   Check[index * n + 0] = true;   \
   Check[index * n + 1] = true;   \
   Check[index * n + 2] = false;  \
   index++;                       \
   Y[index] = Fun( 3.   , X[1]);  \
   Check[index * n + 0] = false;  \
   Check[index * n + 1] = true;   \
   Check[index * n + 2] = false;  \
   index++;


namespace { // Begin empty namespace

bool case_one()
{  bool ok = true;
   using namespace CppAD;

   // dimension of the domain space
   size_t n = 3;

   // dimension of the range space
   size_t m = (4 + 11 + 1) * 3 + 4;

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) X(n);
   X[0] = .1;
   X[1] = .2;
   X[2] = .3;
   Independent(X);

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) Y(m);

   // check results vector
   CPPAD_TESTVECTOR( bool )       Check(m * n);

   // initialize index into Y
   size_t index = 0;

   // 4 binary operators
   CheckOp(+);
   CheckOp(-);
   CheckOp(*);
   CheckOp(/);

   // 11 unary functions
   CheckUnaryFun(abs);
   CheckUnaryFun(acos);
   CheckUnaryFun(asin);
   CheckUnaryFun(atan);
   CheckUnaryFun(cos);
   CheckUnaryFun(cosh);
   CheckUnaryFun(exp);
   CheckUnaryFun(log);
   CheckUnaryFun(sin);
   CheckUnaryFun(sinh);
   CheckUnaryFun(sqrt);

   // 1 binary function
   CheckBinaryFun(pow);

   // conditional expression (value of comparison does not matter)
   Y[index] = CondExpLt(X[0], X[1], X[0], AD<double>(2.));
   Check[index * n + 0] = true;
   Check[index * n + 1] = false;
   Check[index * n + 2] = false;
   index++;
   Y[index] = CondExpLt(X[0], X[1], X[0], X[1]);
   Check[index * n + 0] = true;
   Check[index * n + 1] = true;
   Check[index * n + 2] = false;
   index++;
   Y[index] = CondExpLt(X[0], X[1], AD<double>(3.), X[1]);
   Check[index * n + 0] = false;
   Check[index * n + 1] = true;
   Check[index * n + 2] = false;
   index++;

   // non-trivial composition
   Y[index] = X[0] * X[1] + X[1] * X[2];
   Check[index * n + 0] = true;
   Check[index * n + 1] = true;
   Check[index * n + 2] = true;
   index++;

   // check final index
   assert( index == m );

   // create function object F : X -> Y
   ADFun<double> F(X, Y);

   // ---------------------------------------------------------
   // dependency matrix for the identity function W(x) = x
   CPPAD_TESTVECTOR( bool ) Px(n * n);
   size_t i, j;
   for(i = 0; i < n; i++)
   {  for(j = 0; j < n; j++)
         Px[ i * n + j ] = false;
      Px[ i * n + i ] = true;
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR( bool ) Py(m * n);
   Py = F.ForSparseJac(n, Px);

   // check values
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
         ok &= (Py[i * n + j] == Check[i * n + j]);
   }

   // ---------------------------------------------------------
   // dependency matrix for the identity function W(x) = x
   CPPAD_TESTVECTOR(std::set<size_t>) Sx(n);
   for(i = 0; i < n; i++)
   {  assert( Sx[i].empty() );
      Sx[i].insert(i);
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR(std::set<size_t>) Sy(m);
   Sy = F.ForSparseJac(n, Sx);

   // check values
   bool found;
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
      {  found = Sy[i].find(j) != Sy[i].end();
         ok &= (found == Check[i * n + j]);
      }
   }

   return ok;
}

bool case_two()
{  bool ok = true;
   using namespace CppAD;

   // dimension of the domain space
   size_t n = 3;

   // dimension of the range space
   size_t m = 3;

   // initialize the vector as zero
   CppAD::VecAD<double> Z(n - 1);
   size_t k;
   for(k = 0; k < n-1; k++)
      Z[k] = 0.;

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) X(n);
   X[0] = 0.;
   X[1] = 1.;
   X[2] = 2.;
   Independent(X);

   // VecAD vector is going to depend on X[1] and X[2]
   Z[ X[0] ] = X[1];
   Z[ X[1] ] = X[2];

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) Y(m);

   // check results vector
   CPPAD_TESTVECTOR( bool )       Check(m * n);

   // initialize index into Y
   size_t index = 0;

   // First component only depends on X[0];
   Y[index]             = X[0];
   Check[index * n + 0] = true;
   Check[index * n + 1] = false;
   Check[index * n + 2] = false;
   index++;

   // Second component depends on the vector Z
   AD<double> zero(0);
   Y[index]             = Z[zero]; // Load by a parameter
   Check[index * n + 0] = false;
   Check[index * n + 1] = true;
   Check[index * n + 2] = true;
   index++;

   // Third component depends on the vector Z
   Y[index]             = Z[ X[0] ]; // Load by a variable
   Check[index * n + 0] = false;
   Check[index * n + 1] = true;
   Check[index * n + 2] = true;
   index++;

   // check final index
   assert( index == m );

   // create function object F : X -> Y
   ADFun<double> F(X, Y);

   // -----------------------------------------------------------------
   // dependency matrix for the identity function W(x) = x
   CPPAD_TESTVECTOR( bool ) Px(n * n);
   size_t i, j;
   for(i = 0; i < n; i++)
   {  for(j = 0; j < n; j++)
         Px[ i * n + j ] = false;
      Px[ i * n + i ] = true;
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR( bool ) Py(m * n);
   Py = F.ForSparseJac(n, Px);

   // check values
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
         ok &= (Py[i * n + j] == Check[i * n + j]);
   }

   // ---------------------------------------------------------
   // dependency matrix for the identity function W(x) = x
   CPPAD_TESTVECTOR(std::set<size_t>) Sx(n);
   for(i = 0; i < n; i++)
   {  assert( Sx[i].empty() );
      Sx[i].insert(i);
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR(std::set<size_t>) Sy(m);
   Sy = F.ForSparseJac(n, Sx);

   // check values
   bool found;
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
      {  found = Sy[i].find(j) != Sy[i].end();
         ok &= (found == Check[i * n + j]);
      }
   }

   return ok;
}

bool case_three()
{  bool ok = true;
   using namespace CppAD;

   // dimension of the domain space
   size_t n = 2;

   // dimension of the range space
   size_t m = 3;

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) X(n);
   X[0] = 2.;
   X[1] = 3.;
   Independent(X);

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) Y(m);

   // check results vector
   CPPAD_TESTVECTOR( bool )       Check(m * n);

   // initialize index into Y
   size_t index = 0;

   // Y[0] only depends on X[0];
   Y[index]             = pow(X[0], 2.);
   Check[index * n + 0] = true;
   Check[index * n + 1] = false;
   index++;

   // Y[1] depends on X[1]
   Y[index]             = pow(2., X[1]);
   Check[index * n + 0] = false;
   Check[index * n + 1] = true;
   index++;

   // Y[2] depends on X[0] and X[1]
   Y[index]             = pow(X[0], X[1]);
   Check[index * n + 0] = true;
   Check[index * n + 1] = true;
   index++;

   // check final index
   assert( index == m );

   // create function object F : X -> Y
   ADFun<double> F(X, Y);

   // -----------------------------------------------------------------
   // dependency matrix for the identity function
   CPPAD_TESTVECTOR( bool ) Px(n * n);
   size_t i, j;
   for(i = 0; i < n; i++)
   {  for(j = 0; j < n; j++)
         Px[ i * n + j ] = false;
      Px[ i * n + i ] = true;
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR( bool ) Py(m * n);
   Py = F.ForSparseJac(n, Px);

   // check values
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
         ok &= (Py[i * n + j] == Check[i * n + j]);
   }

   // ---------------------------------------------------------
   // dependency matrix for the identity function
   CPPAD_TESTVECTOR(std::set<size_t>) Sx(n);
   for(i = 0; i < n; i++)
   {  assert( Sx[i].empty() );
      Sx[i].insert(i);
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR(std::set<size_t>) Sy(m);
   Sy = F.ForSparseJac(n, Sx);

   // check values
   bool found;
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
      {  found = Sy[i].find(j) != Sy[i].end();
         ok &= (found == Check[i * n + j]);
      }
   }

   return ok;
}

bool case_four()
{  bool ok = true;
   using namespace CppAD;

   // dimension of the domain space
   size_t n = 2;

   // dimension of the range space
   size_t m = 3;

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) X(n);
   X[0] = 2.;
   X[1] = 3.;
   Independent(X);

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) Y(m);

   // check results vector
   CPPAD_TESTVECTOR( bool )       Check(m * n);

   // initialize index into Y
   size_t index = 0;

   // Y[0] only depends on X[0];
   Y[index]             = pow(X[0], 2.);
   Check[index * n + 0] = true;
   Check[index * n + 1] = false;
   index++;

   // Y[1] depends on X[1]
   Y[index]             = pow(2., X[1]);
   Check[index * n + 0] = false;
   Check[index * n + 1] = true;
   index++;

   // Y[2] depends on X[0] and X[1]
   Y[index]             = pow(X[0], X[1]);
   Check[index * n + 0] = true;
   Check[index * n + 1] = true;
   index++;

   // check final index
   assert( index == m );

   // create function object F : X -> Y
   ADFun<double> F(X, Y);

   // -----------------------------------------------------------------
   // dependency matrix for the identity function
   CPPAD_TESTVECTOR( bool ) Px(n * n);
   size_t i, j;
   for(i = 0; i < n; i++)
   {  for(j = 0; j < n; j++)
         Px[ i * n + j ] = false;
      Px[ i * n + i ] = true;
   }

   // evaluate the dependency matrix for F(X(x))
   bool transpose = true;
   CPPAD_TESTVECTOR( bool ) Py(n * m);
   Py = F.ForSparseJac(n, Px, transpose);

   // check values
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
         ok &= (Py[j * m + i] == Check[i * n + j]);
   }

   // ---------------------------------------------------------
   // dependency matrix for the identity function
   CPPAD_TESTVECTOR(std::set<size_t>) Sx(n);
   for(i = 0; i < n; i++)
   {  assert( Sx[i].empty() );
      Sx[i].insert(i);
   }

   // evaluate the dependency matrix for F(X(x))
   CPPAD_TESTVECTOR(std::set<size_t>) Sy(n);
   Sy = F.ForSparseJac(n, Sx, transpose);

   // check values
   bool found;
   for(i = 0; i < m; i++)
   {  for(j = 0; j < n; j++)
      {  found = Sy[j].find(i) != Sy[j].end();
         ok &= (found == Check[i * n + j]);
      }
   }

   return ok;
}

} // End empty namespace

bool for_jac_sparsity(void)
{  bool ok = true;

   ok &= case_one();
   ok &= case_two();
   ok &= case_three();
   ok &= case_four();

   return ok;
}
