size_t forward2sweep(
const size_t q,
const size_t r,
const size_t n,
const size_t numvar,
player<Base>* play,
const size_t J,
Base* taylor,
const bool* cskip_op,
const pod_vector<addr_t>& var_by_load_op
)
{
CPPAD_ASSERT_UNKNOWN( q > 0 );
CPPAD_ASSERT_UNKNOWN( J >= q + 1 );
CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar );
// used to avoid compiler errors until all operators are implemented
size_t p = q;
// op code for current instruction
OpCode op;
// index for current instruction
size_t i_op;
// next variables
size_t i_var;
// operation argument indices
const addr_t* arg = CPPAD_NULL;
// initialize the comparision operator (ComOp) counter
const size_t compareCount = 0;
// work space used by UserOp.
vector<bool> user_vx; // empty vecotor
vector<bool> user_vy; // empty vecotor
vector<Base> user_tx_one; // argument vector Taylor coefficients
vector<Base> user_tx_all;
vector<Base> user_ty_one; // result vector Taylor coefficients
vector<Base> user_ty_all;
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
# 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_trace }
user_state = user_start;
// length of the parameter vector (used by CppAD assert macros)
const size_t num_par = play->num_par_rec();
// pointer to the beginning of the parameter vector
const Base* parameter = CPPAD_NULL;
if( num_par > 0 )
parameter = play->GetPar();
// temporary indices
size_t i, j, k, ell;
// number of orders for this user calculation
// (not needed for order zero)
const size_t user_q1 = q+1;
// variable indices for results vector
// (done differently for order zero).
vector<size_t> user_iy;
// skip the BeginOp at the beginning of the recording
play->forward_start(op, arg, i_op, i_var);
CPPAD_ASSERT_UNKNOWN( op == BeginOp );
# if CPPAD_FORWARD2SWEEP_TRACE
std::cout << std::endl;
CppAD::vector<Base> Z_vec(q+1);
# endif
bool more_operators = true;
while(more_operators)
{
// this op
play->forward_next(op, arg, i_op, i_var);
CPPAD_ASSERT_UNKNOWN( (i_op > n) | (op == InvOp) );
CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );
CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
// check if we are skipping this operation
while( cskip_op[i_op] )
{ if( op == CSumOp )
{ // CSumOp has a variable number of arguments
play->forward_csum(op, arg, i_op, i_var);
}
play->forward_next(op, arg, i_op, i_var);
CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
}
// action depends on the operator
switch( op )
{
case AbsOp:
forward_abs_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case AddvvOp:
forward_addvv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case AddpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
forward_addpv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case AcosOp:
// sqrt(1 - x * x), acos(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_acos_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case AsinOp:
// sqrt(1 - x * x), asin(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_asin_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case AtanOp:
// 1 + x * x, atan(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_atan_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case CExpOp:
forward_cond_op_dir(
q, r, i_var, arg, num_par, parameter, J, taylor
);
break;
// ---------------------------------------------------
case ComOp:
CPPAD_ASSERT_UNKNOWN(q > 0 );
break;
// ---------------------------------------------------
case CosOp:
// sin(x), cos(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_cos_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// ---------------------------------------------------
case CoshOp:
// sinh(x), cosh(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_cosh_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case CSkipOp:
// CSkipOp has a variable number of arguments and
// forward_next thinks it has no arguments.
// we must inform forward_next of this special case.
play->forward_cskip(op, arg, i_op, i_var);
break;
// -------------------------------------------------
case CSumOp:
// CSumOp has a variable number of arguments and
// forward_next thinks it has no arguments.
// we must inform forward_next of this special case.
forward_csum_op_dir(
q, r, i_var, arg, num_par, parameter, J, taylor
);
play->forward_csum(op, arg, i_op, i_var);
break;
// -------------------------------------------------
case DisOp:
forward_dis_op(p, q, r, i_var, arg, J, taylor);
break;
// -------------------------------------------------
case DivvvOp:
forward_divvv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case DivpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
forward_divpv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case DivvpOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
forward_divvp_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case EndOp:
// needed for sparse_jacobian test
CPPAD_ASSERT_NARG_NRES(op, 0, 0);
more_operators = false;
break;
// -------------------------------------------------
case ExpOp:
forward_exp_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case InvOp:
CPPAD_ASSERT_NARG_NRES(op, 0, 1);
break;
// -------------------------------------------------
case LdpOp:
case LdvOp:
forward_load_op(
play,
op,
p,
q,
r,
J,
i_var,
arg,
var_by_load_op.data(),
taylor
);
break;
// -------------------------------------------------
case LogOp:
forward_log_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case MulvvOp:
forward_mulvv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case MulpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
forward_mulpv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case ParOp:
k = i_var*(J-1)*r + i_var + (q-1)*r;
for(ell = 0; ell < r; ell++)
taylor[k + ell] = Base(0);
break;
// -------------------------------------------------
case PowpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
forward_powpv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case PowvpOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
forward_powvp_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case PowvvOp:
forward_powvv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case PriOp:
CPPAD_ASSERT_UNKNOWN(q > 0);
break;
// -------------------------------------------------
case SignOp:
// sign(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_sign_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case SinOp:
// cos(x), sin(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_sin_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case SinhOp:
// cosh(x), sinh(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_sinh_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case SqrtOp:
forward_sqrt_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case StppOp:
case StpvOp:
case StvpOp:
case StvvOp:
CPPAD_ASSERT_UNKNOWN(q > 0 );
break;
// -------------------------------------------------
case SubvvOp:
forward_subvv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case SubpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
forward_subpv_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case SubvpOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
forward_subvp_op_dir(q, r, i_var, arg, parameter, J, taylor);
break;
// -------------------------------------------------
case TanOp:
// tan(x)^2, tan(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_tan_op_dir(q, r, i_var, arg[0], J, taylor);
break;
// -------------------------------------------------
case TanhOp:
// tanh(x)^2, tanh(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
forward_tanh_op_dir(q, r, i_var, arg[0], J, taylor);
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];
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
if(user_tx_one.size() != user_n * user_q1)
user_tx_one.resize(user_n * user_q1);
if( user_tx_all.size() != user_n * (q * r + 1) )
user_tx_all.resize(user_n * (q * r + 1));
//
if(user_ty_one.size() != user_m * user_q1)
user_ty_one.resize(user_m * user_q1);
if( user_ty_all.size() != user_m * (q * r + 1) )
user_ty_all.resize(user_m * (q * r + 1));
//
if(user_iy.size() != user_m)
user_iy.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]) );
// call users function for this operation
user_atom->set_id(user_id);
for(ell = 0; ell < r; ell++)
{ // set user_tx
for(j = 0; j < user_n; j++)
{ size_t j_all = j * (q * r + 1);
size_t j_one = j * user_q1;
user_tx_one[j_one+0] = user_tx_all[j_all+0];
for(k = 1; k < user_q1; k++)
{ size_t k_all = j_all + (k-1)*r+1+ell;
size_t k_one = j_one + k;
user_tx_one[k_one] = user_tx_all[k_all];
}
}
// set user_ty
for(i = 0; i < user_m; i++)
{ size_t i_all = i * (q * r + 1);
size_t i_one = i * user_q1;
user_ty_one[i_one+0] = user_ty_all[i_all+0];
for(k = 1; k < q; k++)
{ size_t k_all = i_all + (k-1)*r+1+ell;
size_t k_one = i_one + k;
user_ty_one[k_one] = user_ty_all[k_all];
}
}
CPPAD_ATOMIC_CALL(
q, q, user_vx, user_vy, user_tx_one, user_ty_one
);
# ifndef NDEBUG
if( ! user_ok )
{ std::string msg =
atomic_base<Base>::class_name(user_index)
+ ": atomic_base.forward: returned false";
CPPAD_ASSERT_KNOWN(false, msg.c_str() );
}
# endif
for(i = 0; i < user_m; i++)
{ if( user_iy[i] > 0 )
{ size_t i_taylor = user_iy[i]*((J-1)*r+1);
size_t q_taylor = i_taylor + (q-1)*r+1+ell;
size_t q_one = i * user_q1 + q;
taylor[q_taylor] = user_ty_one[q_one];
}
}
}
# if CPPAD_FORWARD2SWEEP_TRACE
user_state = user_trace;
# else
user_state = user_start;
# endif
}
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 );
user_tx_all[user_j*(q*r+1) + 0] = parameter[ arg[0]];
for(ell = 0; ell < r; ell++)
for(k = 1; k < user_q1; k++)
user_tx_all[user_j*(q*r+1) + (k-1)*r+1+ell] = Base(0);
++user_j;
if( user_j == user_n )
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 );
user_tx_all[user_j*(q*r+1)+0] = taylor[arg[0]*((J-1)*r+1)+0];
for(ell = 0; ell < r; ell++)
{ for(k = 1; k < user_q1; k++)
{ user_tx_all[user_j*(q*r+1) + (k-1)*r+1+ell] =
taylor[arg[0]*((J-1)*r+1) + (k-1)*r+1+ell];
}
}
++user_j;
if( user_j == user_n )
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_iy[user_i] = 0;
user_ty_all[user_i*(q*r+1) + 0] = parameter[ arg[0]];
for(ell = 0; ell < r; ell++)
for(k = 1; k < user_q1; k++)
user_ty_all[user_i*(q*r+1) + (k-1)*r+1+ell] = Base(0);
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 );
user_iy[user_i] = i_var;
user_ty_all[user_i*(q*r+1)+0] = taylor[i_var*((J-1)*r+1)+0];
for(ell = 0; ell < r; ell++)
{ for(k = 1; k < user_q1; k++)
{ user_ty_all[user_i*(q*r+1) + (k-1)*r+1+ell] =
taylor[i_var*((J-1)*r+1) + (k-1)*r+1+ell];
}
}
user_i++;
if( user_i == user_m )
user_state = user_end;
break;
// -------------------------------------------------
default:
CPPAD_ASSERT_UNKNOWN(0);
}
# if CPPAD_FORWARD2SWEEP_TRACE
if( user_state == user_trace )
{ user_state = user_start;
CPPAD_ASSERT_UNKNOWN( op == UserOp );
CPPAD_ASSERT_UNKNOWN( NumArg(UsrrvOp) == 0 );
for(i = 0; i < user_m; i++) if( user_iy[i] > 0 )
{ size_t i_tmp = (i_op + i) - user_m;
printOp(
std::cout,
play,
i_tmp,
user_iy[i],
UsrrvOp,
CPPAD_NULL
);
Base* Z_tmp = taylor + user_iy[i]*((J-1) * r + 1);
{ Z_vec[0] = Z_tmp[0];
for(ell = 0; ell < r; ell++)
{ std::cout << std::endl << " ";
for(size_t p_tmp = 1; p_tmp <= q; p_tmp++)
Z_vec[p_tmp] = Z_tmp[(p_tmp-1)*r+ell+1];
printOpResult(
std::cout,
q + 1,
Z_vec.data(),
0,
(Base *) CPPAD_NULL
);
}
}
std::cout << std::endl;
}
}
const addr_t* arg_tmp = arg;
if( op == CSumOp )
arg_tmp = arg - arg[-1] - 4;
if( op == CSkipOp )
arg_tmp = arg - arg[-1] - 7;
if( op != UsrrvOp )
{ printOp(
std::cout,
play,
i_op,
i_var,
op,
arg_tmp
);
Base* Z_tmp = CPPAD_NULL;
if( op == UsravOp )
Z_tmp = taylor + arg[0]*((J-1) * r + 1);
else if( NumRes(op) > 0 )
Z_tmp = taylor + i_var*((J-1)*r + 1);
if( Z_tmp != CPPAD_NULL )
{ Z_vec[0] = Z_tmp[0];
for(ell = 0; ell < r; ell++)
{ std::cout << std::endl << " ";
for(size_t p_tmp = 1; p_tmp <= q; p_tmp++)
Z_vec[p_tmp] = Z_tmp[ (p_tmp-1)*r + ell + 1];
printOpResult(
std::cout,
q + 1,
Z_vec.data(),
0,
(Base *) CPPAD_NULL
);
}
}
std::cout << std::endl;
}
}
std::cout << std::endl;
# else
}
int LuRatio(SizeVector &ip, SizeVector &jp, ADvector &LU, AD<Base> &ratio) //
{
typedef ADvector FloatVector; //
typedef AD<Base> Float; //
// check numeric type specifications
CheckNumericType<Float>();
// check simple vector class specifications
CheckSimpleVector<Float, FloatVector>();
CheckSimpleVector<size_t, SizeVector>();
size_t i, j; // some temporary indices
const Float zero( 0 ); // the value zero as a Float object
size_t imax; // row index of maximum element
size_t jmax; // column indx of maximum element
Float emax; // maximum absolute value
size_t p; // count pivots
int sign; // sign of the permutation
Float etmp; // temporary element
Float pivot; // pivot element
// -------------------------------------------------------
size_t n = size_t(ip.size());
CPPAD_ASSERT_KNOWN(
size_t(jp.size()) == n,
"Error in LuFactor: jp must have size equal to n"
);
CPPAD_ASSERT_KNOWN(
size_t(LU.size()) == n * n,
"Error in LuFactor: LU must have size equal to n * m"
);
// -------------------------------------------------------
// initialize row and column order in matrix not yet pivoted
for(i = 0; i < n; i++)
{ ip[i] = i;
jp[i] = i;
}
// initialize the sign of the permutation
sign = 1;
// initialize the ratio //
ratio = Float(1); //
// ---------------------------------------------------------
// Reduce the matrix P to L * U using n pivots
for(p = 0; p < n; p++)
{ // determine row and column corresponding to element of
// maximum absolute value in remaining part of P
imax = jmax = n;
emax = zero;
for(i = p; i < n; i++)
{ for(j = p; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN(
(ip[i] < n) & (jp[j] < n)
);
etmp = LU[ ip[i] * n + jp[j] ];
// check if maximum absolute value so far
if( AbsGeq (etmp, emax) )
{ imax = i;
jmax = j;
emax = etmp;
}
}
}
for(i = p; i < n; i++) //
{ for(j = p; j < n; j++) //
{ etmp = abs(LU[ ip[i] * n + jp[j] ] / emax); //
ratio = //
CondExpGt(etmp, ratio, etmp, ratio); //
} //
} //
CPPAD_ASSERT_KNOWN(
(imax < n) & (jmax < n) ,
"AbsGeq must return true when second argument is zero"
);
if( imax != p )
{ // switch rows so max absolute element is in row p
i = ip[p];
ip[p] = ip[imax];
ip[imax] = i;
sign = -sign;
}
if( jmax != p )
{ // switch columns so max absolute element is in column p
j = jp[p];
jp[p] = jp[jmax];
jp[jmax] = j;
sign = -sign;
}
// pivot using the max absolute element
pivot = LU[ ip[p] * n + jp[p] ];
// check for determinant equal to zero
if( pivot == zero )
{ // abort the mission
return 0;
}
// Reduce U by the elementary transformations that maps
// LU( ip[p], jp[p] ) to one. Only need transform elements
// above the diagonal in U and LU( ip[p] , jp[p] ) is
// corresponding value below diagonal in L.
for(j = p+1; j < n; j++)
LU[ ip[p] * n + jp[j] ] /= pivot;
// Reduce U by the elementary transformations that maps
// LU( ip[i], jp[p] ) to zero. Only need transform elements
// above the diagonal in U and LU( ip[i], jp[p] ) is
// corresponding value below diagonal in L.
for(i = p+1; i < n; i++ )
{ etmp = LU[ ip[i] * n + jp[p] ];
for(j = p+1; j < n; j++)
{ LU[ ip[i] * n + jp[j] ] -=
etmp * LU[ ip[p] * n + jp[j] ];
}
}
}
return sign;
}