コード例 #1
0
ファイル: rev_jac_sweep.hpp プロジェクト: GodinA/adcomp
void RevJacSweep(
	bool                  nz_compare,
	size_t                n,
	size_t                numvar,
	player<Base>         *play,
	Vector_set&           var_sparsity
)
{
	OpCode           op;
	size_t         i_op;
	size_t        i_var;

	const addr_t*   arg = CPPAD_NULL;

	size_t            i, j, k;

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = play->num_par_rec();

	// check numvar argument
	CPPAD_ASSERT_UNKNOWN( numvar > 0 );
	CPPAD_ASSERT_UNKNOWN( play->num_var_rec()   == numvar );
	CPPAD_ASSERT_UNKNOWN( var_sparsity.n_set() == numvar );

	// upper limit (exclusive) for elements in the set
	size_t limit = var_sparsity.end();

	// vecad_sparsity contains a sparsity pattern for each VecAD object.
	// vecad_ind maps a VecAD index (beginning of the VecAD object)
	// to the index of the corresponding set in vecad_sparsity.
	size_t num_vecad_ind   = play->num_vec_ind_rec();
	size_t num_vecad_vec   = play->num_vecad_vec_rec();
	Vector_set  vecad_sparsity;
	vecad_sparsity.resize(num_vecad_vec, limit);
	pod_vector<size_t> vecad_ind;
	if( num_vecad_vec > 0 )
	{	size_t length;
		vecad_ind.extend(num_vecad_ind);
		j             = 0;
		for(i = 0; i < num_vecad_vec; i++)
		{	// length of this VecAD
			length   = play->GetVecInd(j);
			// set to proper index for this VecAD
			vecad_ind[j] = i;
			for(k = 1; k <= length; k++)
				vecad_ind[j+k] = num_vecad_vec; // invalid index
			// start of next VecAD
			j       += length + 1;
		}
		CPPAD_ASSERT_UNKNOWN( j == play->num_vec_ind_rec() );
	}

	// work space used by UserOp.
	typedef std::set<size_t> size_set;
	size_set::iterator set_itr;  // iterator for a standard set
	size_set::iterator set_end;  // end of iterator sequence
	vector< size_set > set_r;   // set sparsity pattern for the argument x
	vector< size_set > set_s;   // set sparisty pattern for the result y
	//
	vector<bool>       bool_r;   // bool sparsity pattern for the argument x
	vector<bool>       bool_s;   // bool sparisty pattern for the result y
	//
	const size_t user_q = limit; // maximum element plus one
	size_t user_index = 0;       // indentifier for this atomic operation
	size_t user_id    = 0;       // user identifier for this call to operator
	size_t user_i     = 0;       // index in result vector
	size_t user_j     = 0;       // index in argument vector
	size_t user_m     = 0;       // size of result vector
	size_t user_n     = 0;       // size of arugment vector
	//
	atomic_base<Base>* user_atom = CPPAD_NULL; // user's atomic op calculator
	bool               user_bool = false;      // use bool or set sparsity ?
# ifndef NDEBUG
	bool               user_ok   = false;      // atomic op return value
# endif
	// next expected operator in a UserOp sequence
	enum { user_start, user_arg, user_ret, user_end } user_state = user_end;

	// Initialize
	play->reverse_start(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == EndOp );
# if CPPAD_REV_JAC_SWEEP_TRACE
	std::cout << std::endl;
	CppAD::vectorBool z_value(limit);
# endif
	bool more_operators = true;
	while(more_operators)
	{
		// next op
		play->reverse_next(op, arg, i_op, i_var);
# ifndef NDEBUG
		if( i_op <= n )
		{	CPPAD_ASSERT_UNKNOWN((op == InvOp) | (op == BeginOp));
		}
		else	CPPAD_ASSERT_UNKNOWN((op != InvOp) & (op != BeginOp));
# endif

		// rest of information depends on the case
		switch( op )
		{
			case AbsOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AddvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case BeginOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			more_operators = false;
			break;
			// -------------------------------------------------

			case CSkipOp:
			// CSkipOp has a variable number of arguments and
			// reverse_next thinks it one has one argument.
			// We must inform reverse_next of this special case.
			play->reverse_cskip(op, arg, i_op, i_var);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// reverse_next thinks it one has one argument.
			// We must inform reverse_next of this special case.
			play->reverse_csum(op, arg, i_op, i_var);
			reverse_sparse_jacobian_csum_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case CExpOp:
			reverse_sparse_jacobian_cond_op(
				nz_compare, i_var, arg, num_par, var_sparsity
			);
			break;
			// ---------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DisOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			// derivative is identically zero
			break;
			// -------------------------------------------------

			case DivvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ErfOp:
			// arg[1] is always the parameter 0
			// arg[0] is always the parameter 2 / sqrt(pi)
			CPPAD_ASSERT_NARG_NRES(op, 3, 5);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ExpOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 1);
			break;
			// -------------------------------------------------

			case LdpOp:
			reverse_sparse_jacobian_load_op(
				op,
				i_var,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case LdvOp:
			reverse_sparse_jacobian_load_op(
				op,
				i_var,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case EqpvOp:
			case EqvvOp:
			case LtpvOp:
			case LtvpOp:
			case LtvvOp:
			case LepvOp:
			case LevpOp:
			case LevvOp:
			case NepvOp:
			case NevvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 0);
			break;
			// -------------------------------------------------

			case LogOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case MulvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ParOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);

			break;
			// -------------------------------------------------

			case PowvpOp:
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case PowvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case PriOp:
 			CPPAD_ASSERT_NARG_NRES(op, 5, 0);
			break;
			// -------------------------------------------------

			case SignOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			// derivative is identically zero
			break;
			// -------------------------------------------------

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SqrtOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case StppOp:
			// sparsity cannot proagate through a parameter
			CPPAD_ASSERT_NARG_NRES(op, 3, 0);
			break;
			// -------------------------------------------------

			case StpvOp:
			reverse_sparse_jacobian_store_op(
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case StvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 3, 0);
			break;
			// -------------------------------------------------

			case StvvOp:
			reverse_sparse_jacobian_store_op(
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case SubvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case UserOp:
			// start or end atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( NumRes( UserOp ) == 0 );
			CPPAD_ASSERT_UNKNOWN( NumArg( UserOp ) == 4 );
			if( user_state == user_end )
			{	user_index = arg[0];
				user_id    = arg[1];
				user_n     = arg[2];
				user_m     = arg[3];
				user_atom  = atomic_base<Base>::class_object(user_index);
# ifndef NDEBUG
				if( user_atom == CPPAD_NULL )
				{	std::string msg =
						atomic_base<Base>::class_name(user_index)
						+ ": atomic_base function has been deleted";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
				user_bool  = user_atom->sparsity() ==
							atomic_base<Base>::bool_sparsity_enum;
				if( user_bool )
				{	if( bool_r.size() != user_m * user_q )
						bool_r.resize( user_m * user_q );
					if( bool_s.size() != user_n * user_q )
						bool_s.resize( user_n * user_q );
					for(i = 0; i < user_m; i++)
						for(j = 0; j < user_q; j++)
							bool_r[ i * user_q + j] = false;
				}
				else
				{	if(set_r.size() != user_m )
						set_r.resize(user_m);
					if(set_s.size() != user_n )
						set_s.resize(user_n);
					for(i = 0; i < user_m; i++)
						set_r[i].clear();
				}
				user_j     = user_n;
				user_i     = user_m;
				user_state = user_ret;
			}
			else
			{	CPPAD_ASSERT_UNKNOWN( user_state == user_start );
				CPPAD_ASSERT_UNKNOWN( user_index == size_t(arg[0]) );
				CPPAD_ASSERT_UNKNOWN( user_id    == size_t(arg[1]) );
				CPPAD_ASSERT_UNKNOWN( user_n     == size_t(arg[2]) );
				CPPAD_ASSERT_UNKNOWN( user_m     == size_t(arg[3]) );
# ifndef NDEBUG
				if( ! user_ok )
				{	std::string msg =
						atomic_base<Base>::class_name(user_index)
						+ ": atomic_base.rev_sparse_jac: returned false";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
				user_state = user_end;
               }
			break;

			case UsrapOp:
			// parameter argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( 0 < user_j && user_j <= user_n );
			CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			--user_j;
			if( user_j == 0 )
				user_state = user_start;
			break;

			case UsravOp:
			// variable argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( 0 < user_j && user_j <= user_n );
			CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			CPPAD_ASSERT_UNKNOWN( 0 < arg[0] );
			--user_j;
			// It might be faster if we add set union to var_sparsity
			// where one of the sets is not in var_sparsity.
			if( user_bool )
			{	for(j = 0; j < user_q; j++)
					if( bool_s[ user_j * user_q + j ] )	
						var_sparsity.add_element(arg[0], j);	
			}
			else
			{	set_itr = set_s[user_j].begin();
				set_end = set_s[user_j].end();
				while( set_itr != set_end )
					var_sparsity.add_element(arg[0], *set_itr++);	
			}
			if( user_j == 0 )
				user_state = user_start;
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( 0 < user_i && user_i <= user_m );
			CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			--user_i;
			if( user_i == 0 )
			{	// call users function for this operation
				user_atom->set_id(user_id);
				if( user_bool)
					CPPAD_ATOMIC_CALL(
						user_q, bool_r, bool_s
				);
				else
					CPPAD_ATOMIC_CALL(
						user_q, set_r, set_s
				);
				user_state = user_arg;
			}
			break;

			case UsrrvOp:
			// variable result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( 0 < user_i && user_i <= user_m );
			--user_i;
			var_sparsity.begin(i_var);
			i = var_sparsity.next_element();
			while( i < user_q )
			{	if( user_bool )
					bool_r[ user_i * user_q + i ] = true;
					else
						set_r[user_i].insert(i);
				i = var_sparsity.next_element();
			}
			if( user_i == 0 )
			{	// call users function for this operation
				user_atom->set_id(user_id);
				if( user_bool)
					CPPAD_ATOMIC_CALL(
						user_q, bool_r, bool_s
				);
				else
					CPPAD_ATOMIC_CALL(
						user_q, set_r, set_s
				);
				user_state = user_arg;
			}
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_REV_JAC_SWEEP_TRACE
		for(j = 0; j < limit; j++)
			z_value[j] = false;
		var_sparsity.begin(i_var);
		j = var_sparsity.next_element();
		while( j < limit )
		{	z_value[j] = true;
			j          = var_sparsity.next_element();
		}
		printOp(
			std::cout,
			play,
			i_op,
			i_var,
			op,
			arg
		);
		if( NumRes(op) > 0 && op != BeginOp ) printOpResult(
			std::cout,
			0,
			(CppAD::vectorBool *) CPPAD_NULL,
			1,
			&z_value
		);
		std::cout << std::endl;
	}
	std::cout << std::endl;
# else
	}
コード例 #2
0
void ForJacSweep(
	size_t                n            ,
	size_t                numvar       ,
	player<Base>*         play         ,
	Vector_set&           var_sparsity )
{
	OpCode           op;
	size_t         i_op;
	size_t        i_var;

	const addr_t*   arg = 0;

	size_t            i, j, k;

	// check numvar argument
	CPPAD_ASSERT_UNKNOWN( play->num_rec_var()  == numvar );
	CPPAD_ASSERT_UNKNOWN( var_sparsity.n_set() == numvar );

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = play->num_rec_par();

	// cum_sparsity accumulates sparsity pattern a cummulative sum
	size_t limit = var_sparsity.end();

	// vecad_sparsity contains a sparsity pattern from each VecAD object
	// to all the other variables.
	// vecad_ind maps a VecAD index (the beginning of the
	// VecAD object) to its from index in vecad_sparsity
	size_t num_vecad_ind   = play->num_rec_vecad_ind();
	size_t num_vecad_vec   = play->num_rec_vecad_vec();
	Vector_set  vecad_sparsity;
	vecad_sparsity.resize(num_vecad_vec, limit);
	pod_vector<size_t> vecad_ind;
	if( num_vecad_vec > 0 )
	{	size_t length;
		vecad_ind.extend(num_vecad_ind);
		j             = 0;
		for(i = 0; i < num_vecad_vec; i++)
		{	// length of this VecAD
			length   = play->GetVecInd(j);
			// set to proper index for this VecAD
			vecad_ind[j] = i; 
			for(k = 1; k <= length; k++)
				vecad_ind[j+k] = num_vecad_vec; // invalid index
			// start of next VecAD
			j       += length + 1;
		}
		CPPAD_ASSERT_UNKNOWN( j == play->num_rec_vecad_ind() );
	}

	// work space used by UserOp.
	typedef std::set<size_t> size_set;
	const size_t user_q = limit; // maximum element plus one
	size_set::iterator set_itr;  // iterator for a standard set
	size_set::iterator set_end;  // end of iterator sequence
	vector< size_set > user_r;   // sparsity pattern for the argument x
	vector< size_set > user_s;   // sparisty pattern for the result y
	size_t user_index = 0;       // indentifier for this user_atomic operation
	size_t user_id    = 0;       // user identifier for this call to operator
	size_t user_i     = 0;       // index in result vector
	size_t user_j     = 0;       // index in argument vector
	size_t user_m     = 0;       // size of result vector
	size_t user_n     = 0;       // size of arugment vector
	// next expected operator in a UserOp sequence
	enum { user_start, user_arg, user_ret, user_end } user_state = user_start;

# if CPPAD_FOR_JAC_SWEEP_TRACE
	std::cout << std::endl;
	CppAD::vector<bool> z_value(limit);
# endif

	// skip the BeginOp at the beginning of the recording
	play->start_forward(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == BeginOp );
	while(op != EndOp)
	{
		// this op
		play->next_forward(op, arg, i_op, i_var);
		CPPAD_ASSERT_UNKNOWN( (i_op > n)  | (op == InvOp) );  
		CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );  

		// rest of information depends on the case
		switch( op )
		{
			case AbsOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AddvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// next_forward thinks it one has one argument.
			// we must inform next_forward of this special case.
			play->forward_csum(op, arg, i_op, i_var);
			forward_sparse_jacobian_csum_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case CExpOp:
			forward_sparse_jacobian_cond_op(
				i_var, arg, num_par, var_sparsity
			);
			break;
			// ---------------------------------------------------

			case ComOp:
			CPPAD_ASSERT_NARG_NRES(op, 4, 0);
			CPPAD_ASSERT_UNKNOWN( arg[1] > 1 );
			break;
			// --------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DisOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			var_sparsity.clear(i_var);
			break;
			// -------------------------------------------------

			case DivvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case EndOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 0);
			break;
			// -------------------------------------------------

			case ExpOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 1);
			// sparsity pattern is already defined
			break;
			// -------------------------------------------------

			case LdpOp:
			forward_sparse_load_op(
				op,
				i_var,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case LdvOp:
			forward_sparse_load_op(
				op,
				i_var,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case LogOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case MulvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ParOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			var_sparsity.clear(i_var);
			break;
			// -------------------------------------------------

			case PowvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			forward_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case PowvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			forward_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case PriOp:
			CPPAD_ASSERT_NARG_NRES(op, 5, 0);
			break;
			// -------------------------------------------------

			case SignOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SqrtOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case StppOp:
			CPPAD_ASSERT_NARG_NRES(op, 3, 0);
			// storing a parameter does not affect vector sparsity
			break;
			// -------------------------------------------------

			case StpvOp:
			forward_sparse_store_op(
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case StvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 3, 0);
			// storing a parameter does not affect vector sparsity
			break;
			// -------------------------------------------------

			case StvvOp:
			forward_sparse_store_op(
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case SubvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			forward_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case UserOp:
			// start or end an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( NumRes( UserOp ) == 0 );
			CPPAD_ASSERT_UNKNOWN( NumArg( UserOp ) == 4 );
			if( user_state == user_start )
			{	user_index = arg[0];
				user_id    = arg[1];
				user_n     = arg[2];
				user_m     = arg[3];
				if(user_r.size() < user_n )
					user_r.resize(user_n);
				if(user_s.size() < user_m )
					user_s.resize(user_m);
				user_j     = 0;
				user_i     = 0;
				user_state = user_arg;
			}
			else
			{	CPPAD_ASSERT_UNKNOWN( user_state == user_end );
				CPPAD_ASSERT_UNKNOWN( user_index == size_t(arg[0]) );
				CPPAD_ASSERT_UNKNOWN( user_id    == size_t(arg[1]) );
				CPPAD_ASSERT_UNKNOWN( user_n     == size_t(arg[2]) );
				CPPAD_ASSERT_UNKNOWN( user_m     == size_t(arg[3]) );
				user_state = user_start;
			}
			break;

			case UsrapOp:
			// parameter argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			// parameters have an empty sparsity pattern
			user_r[user_j].clear();
			++user_j;
			if( user_j == user_n )
			{	// call users function for this operation
				user_atomic<Base>::for_jac_sparse(user_index, user_id,
					user_n, user_m, user_q, user_r, user_s
				);
				user_state = user_ret;
			}
			break;

			case UsravOp:
			// variable argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			// set user_r[user_j] to sparsity pattern for variable arg[0]
			user_r[user_j].clear();
			var_sparsity.begin(arg[0]);
			i = var_sparsity.next_element();
			while( i < user_q )
			{	user_r[user_j].insert(i);
				i = var_sparsity.next_element();
			}
			++user_j;
			if( user_j == user_n )
			{	// call users function for this operation
				user_atomic<Base>::for_jac_sparse(user_index, user_id,
					user_n, user_m, user_q, user_r, user_s
				);
				user_state = user_ret;
			}
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;

			case UsrrvOp:
			// variable result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			// It might be faster if we add set union to var_sparsity
			// where one of the sets is not in var_sparsity
			set_itr = user_s[user_i].begin();
			set_end = user_s[user_i].end();
			while( set_itr != set_end )
				var_sparsity.add_element(i_var, *set_itr++);
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_FOR_JAC_SWEEP_TRACE
		// value for this variable
		for(j = 0; j < limit; j++)
			z_value[j] = false;
		var_sparsity.begin(i_var);
		j = var_sparsity.next_element();
		while( j < limit )
		{	z_value[j] = true;
			j = var_sparsity.next_element();
		}
		printOp(
			std::cout,
			play,
			i_var,
			op,
			arg,
			1,
			&z_value,
			0,
			(CppAD::vector<bool> *) CPPAD_NULL
		);
	}
	std::cout << std::endl;
# else
	}
コード例 #3
0
ファイル: rev_jac_sweep.hpp プロジェクト: kaskr/CppAD
void RevJacSweep(
	bool                  dependency,
	size_t                n,
	size_t                numvar,
	local::player<Base>*  play,
	Vector_set&           var_sparsity
)
{
	OpCode           op;
	size_t         i_op;
	size_t        i_var;

	const addr_t*   arg = CPPAD_NULL;

	size_t            i, j, k;

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = play->num_par_rec();

	// check numvar argument
	CPPAD_ASSERT_UNKNOWN( numvar > 0 );
	CPPAD_ASSERT_UNKNOWN( play->num_var_rec()   == numvar );
	CPPAD_ASSERT_UNKNOWN( var_sparsity.n_set() == numvar );

	// upper limit (exclusive) for elements in the set
	size_t limit = var_sparsity.end();

	// vecad_sparsity contains a sparsity pattern for each VecAD object.
	// vecad_ind maps a VecAD index (beginning of the VecAD object)
	// to the index of the corresponding set in vecad_sparsity.
	size_t num_vecad_ind   = play->num_vec_ind_rec();
	size_t num_vecad_vec   = play->num_vecad_vec_rec();
	Vector_set  vecad_sparsity;
	vecad_sparsity.resize(num_vecad_vec, limit);
	pod_vector<size_t> vecad_ind;
	if( num_vecad_vec > 0 )
	{	size_t length;
		vecad_ind.extend(num_vecad_ind);
		j             = 0;
		for(i = 0; i < num_vecad_vec; i++)
		{	// length of this VecAD
			length   = play->GetVecInd(j);
			// set to proper index for this VecAD
			vecad_ind[j] = i;
			for(k = 1; k <= length; k++)
				vecad_ind[j+k] = num_vecad_vec; // invalid index
			// start of next VecAD
			j       += length + 1;
		}
		CPPAD_ASSERT_UNKNOWN( j == play->num_vec_ind_rec() );
	}

	// ----------------------------------------------------------------------
	// user's atomic op calculator
	atomic_base<Base>* user_atom = CPPAD_NULL; // user's atomic op calculator
	//
	// work space used by UserOp.
	vector<Base>       user_x;   // parameters in x as integers
	vector<size_t>     user_ix;  // variable indices for argument vector
	vector<size_t>     user_iy;  // variable indices for result vector
	//
	// information set by forward_user (initialization to avoid warnings)
	size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0;
	// information set by forward_user (necessary initialization)
	enum_user_state user_state = end_user; // proper initialization
	// ----------------------------------------------------------------------
	//
	// pointer to the beginning of the parameter vector
	// (used by atomic functions
	const Base* parameter = CPPAD_NULL;
	if( num_par > 0 )
		parameter = play->GetPar();
	//
	// Initialize
	play->reverse_start(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == EndOp );
# if CPPAD_REV_JAC_SWEEP_TRACE
	std::cout << std::endl;
	CppAD::vectorBool z_value(limit);
# endif
	bool more_operators = true;
	while(more_operators)
	{	bool flag; // temporary for use in switch cases
		//
		// next op
		play->reverse_next(op, arg, i_op, i_var);
# ifndef NDEBUG
		if( i_op <= n )
		{	CPPAD_ASSERT_UNKNOWN((op == InvOp) | (op == BeginOp));
		}
		else	CPPAD_ASSERT_UNKNOWN((op != InvOp) & (op != BeginOp));
# endif

		// rest of information depends on the case
		switch( op )
		{
			case AbsOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AddvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AcoshOp:
			// sqrt(x * x - 1), acosh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
# endif
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AsinhOp:
			// sqrt(1 + x * x), asinh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
# endif
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AtanhOp:
			// 1 - x * x, atanh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
# endif
			// -------------------------------------------------

			case BeginOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			more_operators = false;
			break;
			// -------------------------------------------------

			case CSkipOp:
			// CSkipOp has a variable number of arguments and
			// reverse_next thinks it one has one argument.
			// We must inform reverse_next of this special case.
			play->reverse_cskip(op, arg, i_op, i_var);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// reverse_next thinks it one has one argument.
			// We must inform reverse_next of this special case.
			play->reverse_csum(op, arg, i_op, i_var);
			reverse_sparse_jacobian_csum_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case CExpOp:
			reverse_sparse_jacobian_cond_op(
				dependency, i_var, arg, num_par, var_sparsity
			);
			break;
			// ---------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DisOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			// derivative is identically zero but dependency is not
			if( dependency ) reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ErfOp:
			// arg[1] is always the parameter 0
			// arg[0] is always the parameter 2 / sqrt(pi)
			CPPAD_ASSERT_NARG_NRES(op, 3, 5);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ExpOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case Expm1Op:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
# endif
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 1);
			break;
			// -------------------------------------------------

			case LdpOp:
			reverse_sparse_jacobian_load_op(
				dependency,
				op,
				i_var,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case LdvOp:
			reverse_sparse_jacobian_load_op(
				dependency,
				op,
				i_var,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case EqpvOp:
			case EqvvOp:
			case LtpvOp:
			case LtvpOp:
			case LtvvOp:
			case LepvOp:
			case LevpOp:
			case LevvOp:
			case NepvOp:
			case NevvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 0);
			break;
			// -------------------------------------------------

			case LogOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case Log1pOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
# endif
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case MulvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case ParOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);

			break;
			// -------------------------------------------------

			case PowvpOp:
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case PowvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 3);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case PriOp:
			CPPAD_ASSERT_NARG_NRES(op, 5, 0);
			break;
			// -------------------------------------------------

			case SignOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			// derivative is identically zero but dependency is not
			if( dependency ) reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SqrtOp:
			CPPAD_ASSERT_NARG_NRES(op, 1, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case StppOp:
			// does not affect sparsity or dependency when both are parameters
			CPPAD_ASSERT_NARG_NRES(op, 3, 0);
			break;
			// -------------------------------------------------

			case StpvOp:
			reverse_sparse_jacobian_store_op(
				dependency,
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case StvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 3, 0);
			// storing a parameter only affects dependency
			reverse_sparse_jacobian_store_op(
				dependency,
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case StvvOp:
			reverse_sparse_jacobian_store_op(
				dependency,
				op,
				arg,
				num_vecad_ind,
				vecad_ind.data(),
				var_sparsity,
				vecad_sparsity
			);
			break;
			// -------------------------------------------------

			case SubvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_NARG_NRES(op, 1, 2);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case UserOp:
			CPPAD_ASSERT_UNKNOWN(
				user_state == start_user || user_state == end_user
			);
			flag = user_state == end_user;
			user_atom = play->reverse_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			if( flag )
			{	// start of user atomic operation sequence
				user_x.resize( user_n );
				user_ix.resize( user_n );
				user_iy.resize( user_m );
			}
			else
			{	// end of users atomic operation sequence
				user_atom->set_old(user_old);
				user_atom->rev_sparse_jac(
					user_x, user_ix, user_iy, var_sparsity
				);
			}
			break;

			case UsrapOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			play->reverse_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			// argument parameter value
			user_x[user_j] = parameter[arg[0]];
			// special variable index used for parameters
			user_ix[user_j] = 0;
			//
			break;

			case UsravOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			CPPAD_ASSERT_UNKNOWN( 0 < arg[0] );
			play->reverse_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			// argument variables not available during sparsity calculations
			user_x[user_j] = CppAD::numeric_limits<Base>::quiet_NaN();
			// variable index for this argument
			user_ix[user_j] = arg[0];
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			play->reverse_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			// special variable index used for parameters
			user_iy[user_i] = 0;
			break;

			case UsrrvOp:
			play->reverse_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			// variable index for this result
			user_iy[user_i] = i_var;
			break;
			// -------------------------------------------------

			case ZmulpvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[1], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ZmulvpOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_unary_op(
				i_var, arg[0], var_sparsity
			);
			break;
			// -------------------------------------------------

			case ZmulvvOp:
			CPPAD_ASSERT_NARG_NRES(op, 2, 1);
			reverse_sparse_jacobian_binary_op(
				i_var, arg, var_sparsity
			);
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_REV_JAC_SWEEP_TRACE
		for(j = 0; j < limit; j++)
			z_value[j] = false;
		typename Vector_set::const_iterator itr(var_sparsity, i_var);
		j = *itr;
		while( j < limit )
		{	z_value[j] = true;
			j          = *(++itr);
		}
		printOp(
			std::cout,
			play,
			i_op,
			i_var,
			op,
			arg
		);
		// Note that sparsity for UsrrvOp are computed before call to
		// atomic function so no need to delay printing (as in forward mode)
		if( NumRes(op) > 0 && op != BeginOp ) printOpResult(
			std::cout,
			0,
			(CppAD::vectorBool *) CPPAD_NULL,
			1,
			&z_value
		);
		std::cout << std::endl;
	}
	std::cout << std::endl;
# else
	}