inline void reverse_erf_op(
size_t d ,
size_t i_z ,
const addr_t* arg ,
const Base* parameter ,
size_t cap_order ,
const Base* taylor ,
size_t nc_partial ,
Base* partial )
{
// check assumptions
CPPAD_ASSERT_UNKNOWN( NumArg(ErfOp) == 3 );
CPPAD_ASSERT_UNKNOWN( NumRes(ErfOp) == 5 );
CPPAD_ASSERT_UNKNOWN( d < cap_order );
// array used to pass parameter values for sub-operations
addr_t addr[2];
// If pz is zero, make sure this operation has no effect
// (zero times infinity or nan would be non-zero).
Base* pz = partial + i_z * nc_partial;
bool skip(true);
for(size_t i_d = 0; i_d <= d; i_d++)
skip &= IdenticalZero(pz[i_d]);
if( skip )
return;
// convert from final result to first result
i_z -= 4; // 4 = NumRes(ErfOp) - 1;
// Taylor coefficients and partials corresponding to x
const Base* x = taylor + arg[0] * cap_order;
Base* px = partial + arg[0] * nc_partial;
// Taylor coefficients and partials corresponding to z_3
const Base* z_3 = taylor + (i_z+3) * cap_order;
Base* pz_3 = partial + (i_z+3) * nc_partial;
// Taylor coefficients and partials corresponding to z_4
Base* pz_4 = partial + (i_z+4) * nc_partial;
// Reverse z_4
size_t j = d;
while(j)
{ pz_4[j] /= Base(j);
for(size_t k = 1; k <= j; k++)
{ px[k] += pz_4[j] * z_3[j-k] * Base(k);
pz_3[j-k] += pz_4[j] * x[k] * Base(k);
}
j--;
}
px[0] += pz_4[0] * z_3[0];
// z_3 = (2 / sqrt(pi)) * exp( - x * x )
addr[0] = arg[2]; // 2 / sqrt(pi)
addr[1] = i_z + 2; // z_2
reverse_mulpv_op(
d, i_z+3, addr, parameter, cap_order, taylor, nc_partial, partial
);
// z_2 = exp( - x * x )
reverse_exp_op(
d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial
);
// z_1 = - x * x
addr[0] = arg[1]; // zero
addr[1] = i_z; // z_0
reverse_subpv_op(
d, i_z+1, addr, parameter, cap_order, taylor, nc_partial, partial
);
// z_0 = x * x
addr[0] = arg[0]; // x
addr[1] = arg[0]; // x
reverse_mulvv_op(
d, i_z+0, addr, parameter, cap_order, taylor, nc_partial, partial
);
}
void ReverseSweep(
size_t d,
size_t n,
size_t numvar,
player<Base>* play,
size_t J,
const Base* Taylor,
size_t K,
Base* Partial,
bool* cskip_op,
const pod_vector<addr_t>& var_by_load_op
)
{
OpCode op;
size_t i_op;
size_t i_var;
const addr_t* arg = CPPAD_NULL;
// check numvar argument
CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar );
CPPAD_ASSERT_UNKNOWN( numvar > 0 );
// 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();
// work space used by UserOp.
const size_t user_k = d; // highest order we are differentiating
const size_t user_k1 = d+1; // number of orders for this calculation
vector<size_t> user_ix; // variable indices for argument vector
vector<Base> user_tx; // argument vector Taylor coefficients
vector<Base> user_ty; // result vector Taylor coefficients
vector<Base> user_px; // partials w.r.t argument vector
vector<Base> user_py; // partials w.r.t. result vector
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_state = user_end;
// temporary indices
size_t j, ell;
// Initialize
play->reverse_start(op, arg, i_op, i_var);
CPPAD_ASSERT_UNKNOWN( op == EndOp );
# if CPPAD_REVERSE_SWEEP_TRACE
std::cout << std::endl;
# endif
bool more_operators = true;
while(more_operators)
{ // next op
play->reverse_next(op, arg, i_op, i_var);
CPPAD_ASSERT_UNKNOWN((i_op > n) | (op == InvOp) | (op == BeginOp));
CPPAD_ASSERT_UNKNOWN((i_op <= n) | (op != InvOp) | (op != BeginOp));
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->reverse_csum(op, arg, i_op, i_var);
}
CPPAD_ASSERT_UNKNOWN( op != CSkipOp );
// if( op == CSkipOp )
// { // CSkip has a variable number of arguments
// play->reverse_cskip(op, arg, i_op, i_var);
// }
CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
play->reverse_next(op, arg, i_op, i_var);
}
// rest of informaiton depends on the case
# if CPPAD_REVERSE_SWEEP_TRACE
if( op == CSumOp )
{ // CSumOp has a variable number of arguments
play->reverse_csum(op, arg, i_op, i_var);
}
if( op == CSkipOp )
{ // CSkip has a variable number of arguments
play->reverse_cskip(op, arg, i_op, i_var);
}
size_t i_tmp = i_var;
const Base* Z_tmp = Taylor + i_var * J;
const Base* pZ_tmp = Partial + i_var * K;
printOp(
std::cout,
play,
i_op,
i_tmp,
op,
arg
);
if( NumRes(op) > 0 && op != BeginOp ) printOpResult(
std::cout,
d + 1,
Z_tmp,
d + 1,
pZ_tmp
);
std::cout << std::endl;
# endif
switch( op )
{
case AbsOp:
reverse_abs_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case AcosOp:
// sqrt(1 - x * x), acos(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_acos_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case AddvvOp:
reverse_addvv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case AddpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
reverse_addpv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case AsinOp:
// sqrt(1 - x * x), asin(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_asin_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case AtanOp:
// 1 + x * x, atan(x)
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_atan_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case BeginOp:
CPPAD_ASSERT_NARG_NRES(op, 1, 1);
more_operators = false;
break;
// --------------------------------------------------
case CSkipOp:
// CSkipOp has a variable number of arguments and
// forward_next thinks it one has one argument.
// we must inform reverse_next of this special case.
# if ! CPPAD_REVERSE_SWEEP_TRACE
play->reverse_cskip(op, arg, i_op, i_var);
# endif
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.
# if ! CPPAD_REVERSE_SWEEP_TRACE
play->reverse_csum(op, arg, i_op, i_var);
# endif
reverse_csum_op(
d, i_var, arg, K, Partial
);
// end of a cummulative summation
break;
// -------------------------------------------------
case CExpOp:
reverse_cond_op(
d,
i_var,
arg,
num_par,
parameter,
J,
Taylor,
K,
Partial
);
break;
// --------------------------------------------------
case CosOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_cos_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case CoshOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_cosh_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case DisOp:
// Derivative of discrete operation is zero so no
// contribution passes through this operation.
break;
// --------------------------------------------------
case DivvvOp:
reverse_divvv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case DivpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
reverse_divpv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case DivvpOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
reverse_divvp_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
# if CPPAD_COMPILER_HAS_ERF
case ErfOp:
reverse_erf_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
# endif
// --------------------------------------------------
case ExpOp:
reverse_exp_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case InvOp:
break;
// --------------------------------------------------
case LdpOp:
reverse_load_op(
op, d, i_var, arg, J, Taylor, K, Partial, var_by_load_op.data()
);
break;
// -------------------------------------------------
case LdvOp:
reverse_load_op(
op, d, i_var, arg, J, Taylor, K, Partial, var_by_load_op.data()
);
break;
// --------------------------------------------------
case EqpvOp:
case EqvvOp:
case LtpvOp:
case LtvpOp:
case LtvvOp:
case LepvOp:
case LevpOp:
case LevvOp:
case NepvOp:
case NevvOp:
break;
// -------------------------------------------------
case LogOp:
reverse_log_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case MulvvOp:
reverse_mulvv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case MulpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
reverse_mulpv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case ParOp:
break;
// --------------------------------------------------
case PowvpOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
reverse_powvp_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case PowpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
reverse_powpv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case PowvvOp:
reverse_powvv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case PriOp:
// no result so nothing to do
break;
// --------------------------------------------------
case SignOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_sign_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case SinOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_sin_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case SinhOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_sinh_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case SqrtOp:
reverse_sqrt_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case StppOp:
break;
// --------------------------------------------------
case StpvOp:
break;
// -------------------------------------------------
case StvpOp:
break;
// -------------------------------------------------
case StvvOp:
break;
// --------------------------------------------------
case SubvvOp:
reverse_subvv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case SubpvOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
reverse_subpv_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// --------------------------------------------------
case SubvpOp:
CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
reverse_subvp_op(
d, i_var, arg, parameter, J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case TanOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_tan_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
break;
// -------------------------------------------------
case TanhOp:
CPPAD_ASSERT_UNKNOWN( i_var < numvar );
reverse_tanh_op(
d, i_var, arg[0], J, Taylor, K, Partial
);
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_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
if(user_ix.size() != user_n)
user_ix.resize(user_n);
if(user_tx.size() != user_n * user_k1)
{ user_tx.resize(user_n * user_k1);
user_px.resize(user_n * user_k1);
}
if(user_ty.size() != user_m * user_k1)
{ user_ty.resize(user_m * user_k1);
user_py.resize(user_m * user_k1);
}
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]) );
// call users function for this operation
user_atom->set_id(user_id);
CPPAD_ATOMIC_CALL(
user_k, user_tx, user_ty, user_px, user_py
);
# ifndef NDEBUG
if( ! user_ok )
{ std::string msg =
atomic_base<Base>::class_name(user_index)
+ ": atomic_base.reverse: returned false";
CPPAD_ASSERT_KNOWN(false, msg.c_str() );
}
# endif
for(j = 0; j < user_n; j++) if( user_ix[j] > 0 )
{ for(ell = 0; ell < user_k1; ell++)
Partial[user_ix[j] * K + ell] +=
user_px[j * user_k1 + ell];
}
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;
user_ix[user_j] = 0;
user_tx[user_j * user_k1 + 0] = parameter[ arg[0]];
for(ell = 1; ell < user_k1; ell++)
user_tx[user_j * user_k1 + ell] = Base(0.);
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;
user_ix[user_j] = arg[0];
for(ell = 0; ell < user_k1; ell++)
user_tx[user_j*user_k1 + ell] = Taylor[ arg[0] * J + ell];
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;
for(ell = 0; ell < user_k1; ell++)
{ user_py[user_i * user_k1 + ell] = Base(0.);
user_ty[user_i * user_k1 + ell] = Base(0.);
}
user_ty[user_i * user_k1 + 0] = parameter[ arg[0] ];
if( user_i == 0 )
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;
for(ell = 0; ell < user_k1; ell++)
{ user_py[user_i * user_k1 + ell] =
Partial[i_var * K + ell];
user_ty[user_i * user_k1 + ell] =
Taylor[i_var * J + ell];
}
if( user_i == 0 )
user_state = user_arg;
break;
// ------------------------------------------------------------
default:
CPPAD_ASSERT_UNKNOWN(false);
}
}
# if CPPAD_REVERSE_SWEEP_TRACE
std::cout << std::endl;
# endif
// values corresponding to BeginOp
CPPAD_ASSERT_UNKNOWN( i_op == 0 );
CPPAD_ASSERT_UNKNOWN( i_var == 0 );
}