bool interp_retape(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) X(n);
// loop over argument values
size_t k;
for(k = 0; k < TableLength - 1; k++)
{
X[0] = .4 * ArgumentValue[k] + .6 * ArgumentValue[k+1];
// declare independent variables and start tape recording
// (use a different tape for each argument value)
CppAD::Independent(X);
// evaluate piecewise linear interpolant at X[0]
AD<double> A = Argument(X[0]);
AD<double> F = Function(X[0]);
AD<double> S = Slope(X[0]);
AD<double> I = F + (X[0] - A) * S;
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = I;
// create f: X -> Y and stop tape recording
CppAD::ADFun<double> f(X, Y);
// vectors for arguments to the function object f
CPPAD_TESTVECTOR(double) x(n); // argument values
CPPAD_TESTVECTOR(double) y(m); // function values
CPPAD_TESTVECTOR(double) dx(n); // differentials in x space
CPPAD_TESTVECTOR(double) dy(m); // differentials in y space
// to check function value we use the fact that X[0] is between
// ArgumentValue[k] and ArgumentValue[k+1]
double delta, check;
x[0] = Value(X[0]);
delta = ArgumentValue[k+1] - ArgumentValue[k];
check = FunctionValue[k+1] * (x[0]-ArgumentValue[k]) / delta
+ FunctionValue[k] * (ArgumentValue[k+1]-x[0]) / delta;
ok &= NearEqual(Y[0], check, 1e-10, 1e-10);
// evaluate partials w.r.t. x[0]
dx[0] = 1.;
dy = f.Forward(1, dx);
// check that the derivative is the slope
check = (FunctionValue[k+1] - FunctionValue[k])
/ (ArgumentValue[k+1] - ArgumentValue[k]);
ok &= NearEqual(dy[0], check, 1e-10, 1e-10);
}
return ok;
}
bool opt_val_hes(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// temporary indices
size_t j, k;
// x space vector
size_t n = 1;
BaseVector x(n);
x[0] = 2. * 3.141592653;
// y space vector
size_t m = 1;
BaseVector y(m);
y[0] = 1.;
// t and z vectors
size_t ell = 10;
BaseVector t(ell);
BaseVector z(ell);
for(k = 0; k < ell; k++)
{ t[k] = double(k) / double(ell); // time of measurement
z[k] = y[0] * sin( x[0] * t[k] ); // data without noise
}
// construct the function object
Fun fun(t, z);
// evaluate the Jacobian and Hessian
BaseVector jac(n), hes(n * n);
int signdet = CppAD::opt_val_hes(x, y, fun, jac, hes);
// we know that F_yy is positive definate for this case
assert( signdet == 1 );
// create ADFun object g corresponding to V(x)
ADVector a_x(n), a_v(1);
for(j = 0; j < n; j++)
a_x[j] = x[j];
Independent(a_x);
a_v[0] = V(a_x, t, z);
CppAD::ADFun<double> g(a_x, a_v);
// accuracy for checks
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// check Jacobian
BaseVector check_jac = g.Jacobian(x);
for(j = 0; j < n; j++)
ok &= NearEqual(jac[j], check_jac[j], eps, eps);
// check Hessian
BaseVector check_hes = g.Hessian(x, 0);
for(j = 0; j < n*n; j++)
ok &= NearEqual(hes[j], check_hes[j], eps, eps);
return ok;
}
/*!
Fetch the next operator during a forward sweep.
Use forward_start to initialize to the first operator; i.e.,
the BeginOp at the beginning of the recording.
We use the notation forward_routine to denote the set
forward_start, forward_next, forward_csum, forward_cskip.
\param op [in,out]
The input value of \c op must be its output value from the
previous call to a forward_routine.
Its output value is the next operator in the recording.
For speed, \c forward_next does not check for the special cases
where <tt>op == CSumOp</tt> or <tt>op == CSkipOp</tt>. In these cases,
the other return values from \c forward_next must be corrected by a call
to \c forward_csum or \c forward_cskip respectively.
\param op_arg [in,out]
The input value of \c op_arg must be its output value form the
previous call to a forward routine.
Its output value is the
beginning of the vector of argument indices for this operation.
\param op_index [in,out]
The input value of \c op_index must be its output value form the
previous call to a forward routine.
Its output value is the index of the next operator in the recording.
Thus the ouput value following the previous call to forward_start is one.
In addition,
the output value increases by one with each call to forward_next.
\param var_index [in,out]
The input value of \c var_index must be its output value form the
previous call to a forward routine.
Its output value is the
index of the primary (last) result corresponding to the operator op.
*/
void forward_next(
OpCode& op, const addr_t*& op_arg, size_t& op_index, size_t& var_index)
{ using CppAD::NumRes;
using CppAD::NumArg;
CPPAD_ASSERT_UNKNOWN( op_ == op );
CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ );
CPPAD_ASSERT_UNKNOWN( op_index == op_index_ );
CPPAD_ASSERT_UNKNOWN( var_index == var_index_ );
// index for the next operator
op_index = ++op_index_;
// first argument for next operator
op_arg = op_arg_ += NumArg(op_);
// next operator
op = op_ = OpCode( op_rec_[ op_index_ ] );
// index for last result for next operator
var_index = var_index_ += NumRes(op);
CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ );
CPPAD_ASSERT_UNKNOWN(
op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size()
);
CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ );
}
/*!
Correct \c forward_next return values when <tt>op == CSkipOp</tt>.
\param op [in]
The input value of op must be the return value from the previous
call to \c forward_next and must be \c CSkipOp. It is not modified.
\param op_arg [in,out]
The input value of \c op_arg must be the return value from the
previous call to \c forward_next. Its output value is the
beginning of the vector of argument indices for the next operation.
\param op_index [in]
The input value of \c op_index does must be the return value from the
previous call to \c forward_next. Its is not modified.
\param var_index [in,out]
The input value of \c var_index must be the return value from the
previous call to \c forward_next. It is not modified.
*/
void forward_cskip(
OpCode& op, const addr_t*& op_arg, size_t& op_index, size_t& var_index)
{ using CppAD::NumRes;
using CppAD::NumArg;
CPPAD_ASSERT_UNKNOWN( op_ == op );
CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ );
CPPAD_ASSERT_UNKNOWN( op_index == op_index_ );
CPPAD_ASSERT_UNKNOWN( var_index == var_index_ );
CPPAD_ASSERT_UNKNOWN( op == CSkipOp );
CPPAD_ASSERT_UNKNOWN( NumArg(CSkipOp) == 0 );
CPPAD_ASSERT_UNKNOWN(
op_arg[4] + op_arg[5] == op_arg[ 6 + op_arg[4] + op_arg[5] ]
);
/*
The only thing that really needs fixing is op_arg_.
Actual number of arugments for this operator is
7 + op_arg[4] + op_arg[5]
We must change op_arg_ so that when you add NumArg(CSkipOp)
you get first argument for next operator in sequence.
*/
op_arg = op_arg_ += 7 + op_arg[4] + op_arg[5];
CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ );
CPPAD_ASSERT_UNKNOWN(
op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size()
);
CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ );
}
/*!
Fetch the next operator during a reverse sweep.
Use reverse_start to initialize to reverse play back.
The first call to reverse_next (after reverse_start) will give the
last operator in the recording.
We use the notation reverse_routine to denote the set
reverse_start, reverse_next, reverse_csum, reverse_cskip.
\param op [in,out]
The input value of \c op must be its output value from the
previous call to a reverse_routine.
Its output value is the next operator in the recording (in reverse order).
The last operator sets op equal to EndOp.
\param op_arg [in,out]
The input value of \c op_arg must be its output value from the
previous call to a reverse_routine.
Its output value is the
beginning of the vector of argument indices for this operation.
The last operator sets op_arg equal to the beginning of the
argument indices for the entire recording.
For speed, \c reverse_next does not check for the special cases
<tt>op == CSumOp</tt> or <tt>op == CSkipOp</tt>. In these cases, the other
return values from \c reverse_next must be corrected by a call to
\c reverse_csum or \c reverse_cskip respectively.
\param op_index [in,out]
The input value of \c op_index must be its output value from the
previous call to a reverse_routine.
Its output value
is the index of this operator in the recording. Thus the output
value following the previous call to reverse_start is equal to
the number of variables in the recording minus one.
In addition, the output value decreases by one with each call to
reverse_next.
The last operator sets op_index equal to 0.
\param var_index [in,out]
The input value of \c var_index must be its output value from the
previous call to a reverse_routine.
Its output value is the
index of the primary (last) result corresponding to the operator op.
The last operator sets var_index equal to 0 (corresponding to BeginOp
at beginning of operation sequence).
*/
void reverse_next(
OpCode& op, const addr_t*& op_arg, size_t& op_index, size_t& var_index)
{ using CppAD::NumRes;
using CppAD::NumArg;
CPPAD_ASSERT_UNKNOWN( op_ == op );
CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ );
CPPAD_ASSERT_UNKNOWN( op_index == op_index_ );
CPPAD_ASSERT_UNKNOWN( var_index == var_index_ );
// index of the last result for the next operator
CPPAD_ASSERT_UNKNOWN( var_index_ >= NumRes(op_) );
var_index = var_index_ -= NumRes(op_);
// next operator
CPPAD_ASSERT_UNKNOWN( op_index_ > 0 );
op_index = --op_index_; // index
op = op_ = OpCode( op_rec_[ op_index_ ] ); // value
// first argument for next operator
op_arg = op_arg_ -= NumArg(op);
CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ );
CPPAD_ASSERT_UNKNOWN(
op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size()
);
}
bool BenderQuad(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// temporary indices
size_t i, j;
// x space vector
size_t n = 1;
BAvector x(n);
x[0] = 2. * 3.141592653;
// y space vector
size_t m = 1;
BAvector y(m);
y[0] = 1.;
// t and z vectors
size_t N = 10;
BAvector t(N);
BAvector z(N);
for(i = 0; i < N; i++)
{ t[i] = double(i) / double(N); // time of measurement
z[i] = y[0] * sin( x[0] * t[i] ); // data without noise
}
// construct the function object
Fun fun(t, z);
// evaluate the G(x), G'(x) and G''(x)
BAvector g(1), gx(n), gxx(n * n);
CppAD::BenderQuad(x, y, fun, g, gx, gxx);
// create ADFun object Gfun corresponding to G(x)
ADvector a_x(n), a_g(1);
for(j = 0; j < n; j++)
a_x[j] = x[j];
Independent(a_x);
a_g[0] = G(a_x, t, z);
CppAD::ADFun<double> Gfun(a_x, a_g);
// accuracy for checks
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// check Jacobian
BAvector check_gx = Gfun.Jacobian(x);
for(j = 0; j < n; j++)
ok &= NearEqual(gx[j], check_gx[j], eps, eps);
// check Hessian
BAvector check_gxx = Gfun.Hessian(x, 0);
for(j = 0; j < n*n; j++)
ok &= NearEqual(gxx[j], check_gxx[j], eps, eps);
return ok;
}
bool forward_order(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.;
ax[1] = 1.;
// declare independent variables and starting recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = ax[0] * ax[0] * ax[1];
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// initially, the variable values during taping are stored in f
ok &= f.size_order() == 1;
// Compute three forward orders at one
size_t q = 2, q1 = q+1;
CPPAD_TESTVECTOR(double) xq(n*q1), yq;
xq[q1*0 + 0] = 3.; xq[q1*1 + 0] = 4.; // x^0 (order zero)
xq[q1*0 + 1] = 1.; xq[q1*1 + 1] = 0.; // x^1 (order one)
xq[q1*0 + 2] = 0.; xq[q1*1 + 2] = 0.; // x^2 (order two)
// X(t) = x^0 + x^1 * t + x^2 * t^2
// = [ 3 + t, 4 ]
yq = f.Forward(q, xq);
ok &= size_t( yq.size() ) == m*q1;
// Y(t) = F[X(t)]
// = (3 + t) * (3 + t) * 4
// = y^0 + y^1 * t + y^2 * t^2 + o(t^3)
//
// check y^0 (order zero)
CPPAD_TESTVECTOR(double) x0(n);
x0[0] = xq[q1*0 + 0];
x0[1] = xq[q1*1 + 0];
ok &= NearEqual(yq[q1*0 + 0] , x0[0]*x0[0]*x0[1], eps, eps);
//
// check y^1 (order one)
ok &= NearEqual(yq[q1*0 + 1] , 2.*x0[0]*x0[1], eps, eps);
//
// check y^2 (order two)
double F_00 = 2. * yq[q1*0 + 2]; // second partial F w.r.t. x_0, x_0
ok &= NearEqual(F_00, 2.*x0[1], eps, eps);
// check number of orders per variable
ok &= f.size_order() == 3;
return ok;
}
bool mul_level(void)
{ bool ok = true;
using CppAD::checkpoint;
using CppAD::ADFun;
using CppAD::Independent;
// domain dimension for this problem
size_t n = 10;
size_t m = 1;
// checkpoint version of the function F(x)
a2vector a2x(n), a2y(m);
for(size_t j = 0; j < n; j++)
a2x[j] = a2double(j + 1);
//
// could also use bool_sparsity_enum or set_sparsity_enum
checkpoint<a1double> atom_f("atom_f", f_algo, a2x, a2y);
//
// Record a version of y = f(x) without checkpointing
Independent(a2x);
f_algo(a2x, a2y);
ADFun<a1double> check_not(a2x, a2y);
//
// number of variables in a tape of f_algo that does not use checkpointing
size_t size_not = check_not.size_var();
//
// Record a version of y = f(x) with checkpointing
Independent(a2x);
atom_f(a2x, a2y);
ADFun<a1double> check_yes(a2x, a2y);
//
// f_algo is represented by one atomic operation in this tape
ok &= check_yes.size_var() < size_not;
//
// now record operations at a1double level
a1vector a1x(n), a1y(m);
for(size_t j = 0; j < n; j++)
a1x[j] = a1double(j + 1);
//
// without checkpointing
Independent(a1x);
a1y = check_not.Forward(0, a1x);
ADFun<double> with_not(a1x, a1y);
//
// should have the same size
ok &= with_not.size_var() == size_not;
//
// with checkpointing
Independent(a1x);
a1y = check_yes.Forward(0, a1x);
ADFun<double> with_yes(a1x, a1y);
//
// f_algo is nolonger represented by one atomic operation in this tape
ok &= with_yes.size_var() == size_not;
//
return ok;
}
bool atanh(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// 10 times machine epsilon
double eps = 10. * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// a temporary value
AD<double> tanh_of_x0 = CppAD::tanh(ax[0]);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = CppAD::atanh(tanh_of_x0);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// check value
ok &= NearEqual(ay[0] , x0, eps, eps);
// forward computation of first partial w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 1., eps, eps);
// forward computation of higher order partials w.r.t. x[0]
size_t n_order = 5;
for(size_t order = 2; order < n_order; order++)
{ dx[0] = 0.;
dy = f.Forward(order, dx);
ok &= NearEqual(dy[0], 0., eps, eps);
}
// reverse computation of derivatives
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n_order * n);
w[0] = 1.;
dw = f.Reverse(n_order, w);
ok &= NearEqual(dw[0], 1., eps, eps);
for(size_t order = 1; order < n_order; order++)
ok &= NearEqual(dw[order * n + 0], 0., eps, eps);
return ok;
}
bool atan2(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// a temporary value
AD<double> sin_of_x0 = CppAD::sin(x[0]);
AD<double> cos_of_x0 = CppAD::cos(x[0]);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = CppAD::atan2(sin_of_x0, cos_of_x0);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0, eps99, eps99);
// forward computation of first partial w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 1., eps99, eps99);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 1., eps99, eps99);
// use a VecAD<Base>::reference object with atan2
CppAD::VecAD<double> v(2);
AD<double> zero(0);
AD<double> one(1);
v[zero] = sin_of_x0;
v[one] = cos_of_x0;
AD<double> result = CppAD::atan2(v[zero], v[one]);
ok &= NearEqual(result, x0, eps99, eps99);
return ok;
}
bool Div(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// some binary division operations
AD<double> a = x[0] / 1.; // AD<double> / double
AD<double> b = a / 2; // AD<double> / int
AD<double> c = 3. / b; // double / AD<double>
AD<double> d = 4 / c; // int / AD<double>
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = (x[0] * x[0]) / d; // AD<double> / AD<double>
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0], x0*x0*3.*2.*1./(4.*x0), eps99, eps99);
// forward computation of partials w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 3.*2.*1./4., eps99, eps99);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 3.*2.*1./4., eps99, eps99);
// use a VecAD<Base>::reference object with division
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = d;
AD<double> result = (x[0] * x[0]) / v[zero];
ok &= (result == y[0]);
return ok;
}
bool AddEq(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = .5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// range space vector
size_t m = 2;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = x[0]; // initial value
y[0] += 2; // AD<double> += int
y[0] += 4.; // AD<double> += double
y[1] = y[0] += x[0]; // use the result of a compound assignment
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0+2.+4.+x0, eps99, eps99);
ok &= NearEqual(y[1] , y[0], eps99, eps99);
// forward computation of partials w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 2., eps99, eps99);
ok &= NearEqual(dy[1], 2., eps99, eps99);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
w[1] = 0.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 2., eps99, eps99);
// use a VecAD<Base>::reference object with computed addition
CppAD::VecAD<double> v(1);
AD<double> zero(0);
AD<double> result = 1;
v[zero] = 2;
result += v[zero];
ok &= (result == 3);
return ok;
}
bool MulEq(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
double x0 = .5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// range space vector
size_t m = 2;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = x[0]; // initial value
y[0] *= 2; // AD<double> *= int
y[0] *= 4.; // AD<double> *= double
y[1] = y[0] *= x[0]; // use the result of a computed assignment
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0*2.*4.*x0, 1e-10 , 1e-10);
ok &= NearEqual(y[1] , y[0], 1e-10 , 1e-10);
// forward computation of partials w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 8.*2.*x0, 1e-10, 1e-10);
ok &= NearEqual(dy[1], 8.*2.*x0, 1e-10, 1e-10);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
w[1] = 0.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 8.*2.*x0, 1e-10, 1e-10);
// use a VecAD<Base>::reference object with computed multiplication
CppAD::VecAD<double> v(1);
AD<double> zero(0);
AD<double> result = 1;
v[zero] = 2;
result *= v[zero];
ok &= (result == 2);
return ok;
}
/* $$
$head Use Atomic Function$$
$codep */
bool get_started(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
/* $$
$subhead Constructor$$
$codep */
// Create the atomic get_started object
atomic_get_started afun("atomic_get_started");
/* $$
$subhead Recording$$
$codep */
// Create the function f(x)
//
// domain space vector
size_t n = 1;
double x0 = 0.5;
vector< AD<double> > ax(n);
ax[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
vector< AD<double> > ay(m);
// call user function and store get_started(x) in au[0]
vector< AD<double> > au(m);
afun(ax, au); // u = 1 / x
// now use AD division to invert to invert the operation
ay[0] = 1.0 / au[0]; // y = 1 / u = x
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f;
f.Dependent (ax, ay); // f(x) = x
/* $$
$subhead forward$$
$codep */
// check function value
double check = x0;
ok &= NearEqual( Value(ay[0]) , check, eps, eps);
// check zero order forward mode
size_t p;
vector<double> x_p(n), y_p(m);
p = 0;
x_p[0] = x0;
y_p = f.Forward(p, x_p);
ok &= NearEqual(y_p[0] , check, eps, eps);
return ok;
}
bool Add(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// some binary addition operations
AD<double> a = x[0] + 1.; // AD<double> + double
AD<double> b = a + 2; // AD<double> + int
AD<double> c = 3. + b; // double + AD<double>
AD<double> d = 4 + c; // int + AD<double>
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = d + x[0]; // AD<double> + AD<double>
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , 2. * x0 + 10, eps99, eps99);
// forward computation of partials w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 2., eps99, eps99);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 2., eps99, eps99);
// use a VecAD<Base>::reference object with addition
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = a;
AD<double> result = v[zero] + 2;
ok &= (result == b);
return ok;
}
bool pow_int(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// declare independent variables and start tape recording
size_t n = 1;
double x0 = -0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
CppAD::Independent(x);
// dependent variable vector
size_t m = 7;
CPPAD_TESTVECTOR(AD<double>) y(m);
int i;
for(i = 0; i < int(m); i++)
y[i] = CppAD::pow(x[0], i - 3);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
double check;
for(i = 0; i < int(m); i++)
{ check = std::pow(x0, double(i - 3));
ok &= NearEqual(y[i] , check, 1e-10 , 1e-10);
}
// forward computation of first partial w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
for(i = 0; i < int(m); i++)
{ check = double(i-3) * std::pow(x0, double(i - 4));
ok &= NearEqual(dy[i] , check, 1e-10 , 1e-10);
}
// reverse computation of derivative of y[i]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
for(i = 0; i < int(m); i++)
w[i] = 0.;
for(i = 0; i < int(m); i++)
{ w[i] = 1.;
dw = f.Reverse(1, w);
check = double(i-3) * std::pow(x0, double(i - 4));
ok &= NearEqual(dw[0] , check, 1e-10 , 1e-10);
w[i] = 0.;
}
return ok;
}
bool SubEq(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
double x0 = .5;
CPPAD_TEST_VECTOR< AD<double> > x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// range space vector
size_t m = 2;
CPPAD_TEST_VECTOR< AD<double> > y(m);
y[0] = 3. * x[0]; // initial value
y[0] -= 2; // AD<double> -= int
y[0] -= 4.; // AD<double> -= double
y[1] = y[0] -= x[0]; // use the result of a computed assignment
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , 3.*x0-(2.+4.+x0), 1e-10 , 1e-10);
ok &= NearEqual(y[1] , y[0], 1e-10 , 1e-10);
// forward computation of partials w.r.t. x[0]
CPPAD_TEST_VECTOR<double> dx(n);
CPPAD_TEST_VECTOR<double> dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 2., 1e-10, 1e-10);
ok &= NearEqual(dy[1], 2., 1e-10, 1e-10);
// reverse computation of derivative of y[0]
CPPAD_TEST_VECTOR<double> w(m);
CPPAD_TEST_VECTOR<double> dw(n);
w[0] = 1.;
w[1] = 0.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 2., 1e-10, 1e-10);
// use a VecAD<Base>::reference object with computed subtraction
CppAD::VecAD<double> v(1);
AD<double> zero(0);
AD<double> result = 1;
v[zero] = 2;
result -= v[zero];
ok &= (result == -1);
return ok;
}
bool print_for(void)
{ bool ok = true;
using CppAD::PrintFor;
std::stringstream stream_out; // stream that output is written to
std::string string_check; // what we expect the output to be
// independent variable vector
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 1.;
Independent(ax);
// print a VecAD<double>::reference object that is a parameter
CppAD::VecAD<double> av(1);
AD<double> Zero(0);
av[Zero] = 0.;
PrintFor("v[0] = ", av[Zero]);
string_check += "v[0] = 0"; // v[0] == 0 during Forward(0, x)
// Print a newline to separate this from previous output,
// then print an AD<double> object that is a variable.
PrintFor("\nv[0] + x[0] = ", av[0] + ax[0]);
string_check += "\nv[0] + x[0] = 2"; // x[0] == 2 during Forward(0, x)
// A conditional print that will not generate output when x[0] = 2.
PrintFor(ax[0], "\n 2. + x[0] = ", 2. + ax[0], "\n");
// A conditional print that will generate output when x[0] = 2.
PrintFor(ax[0] - 2., "\n 3. + x[0] = ", 3. + ax[0], "\n");
string_check += "\n 3. + x[0] = 5\n";
// A log evaluations that will result in an error message when x[0] = 2.
AD<double> var = 2. - ax[0];
AD<double> log_var = check_log(var);
string_check += "check_log: y == 0 which is <= 0\n";
// dependent variable vector
size_t m = 2;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = av[Zero] + ax[0];
// define f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// zero order forward with x[0] = 2
CPPAD_TESTVECTOR(double) x(n);
x[0] = 2.;
f.Forward(0, x, stream_out);
std::string string_out = stream_out.str();
ok &= string_out == string_check;
return ok;
}
bool Sub(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = .5;
CPPAD_TESTVECTOR(AD<double>) x(1);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
AD<double> a = 2. * x[0] - 1.; // AD<double> - double
AD<double> b = a - 2; // AD<double> - int
AD<double> c = 3. - b; // double - AD<double>
AD<double> d = 4 - c; // int - AD<double>
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = x[0] - d; // AD<double> - AD<double>
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0], x0-4.+3.+2.-2.*x0+1., eps99, eps99);
// forward computation of partials w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], -1., eps99, eps99);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], -1., eps99, eps99);
// use a VecAD<Base>::reference object with subtraction
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = b;
AD<double> result = 3. - v[zero];
ok &= (result == c);
return ok;
}
bool Mul(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
double x0 = .5;
CPPAD_TEST_VECTOR< AD<double> > x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// some binary multiplication operations
AD<double> a = x[0] * 1.; // AD<double> * double
AD<double> b = a * 2; // AD<double> * int
AD<double> c = 3. * b; // double * AD<double>
AD<double> d = 4 * c; // int * AD<double>
// range space vector
size_t m = 1;
CPPAD_TEST_VECTOR< AD<double> > y(m);
y[0] = x[0] * d; // AD<double> * AD<double>
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0*(4.*3.*2.*1.)*x0, 1e-10 , 1e-10);
// forward computation of partials w.r.t. x[0]
CPPAD_TEST_VECTOR<double> dx(n);
CPPAD_TEST_VECTOR<double> dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10);
// reverse computation of derivative of y[0]
CPPAD_TEST_VECTOR<double> w(m);
CPPAD_TEST_VECTOR<double> dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10);
// use a VecAD<Base>::reference object with multiplication
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = c;
AD<double> result = 4 * v[zero];
ok &= (result == d);
return ok;
}
bool Tanh(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = CppAD::tanh(x[0]);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
double check = std::tanh(x0);
ok &= NearEqual(y[0] , check, eps, eps);
// forward computation of first partial w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
check = 1. - std::tanh(x0) * std::tanh(x0);
ok &= NearEqual(dy[0], check, eps, eps);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], check, eps, eps);
// use a VecAD<Base>::reference object with tan
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = x0;
AD<double> result = CppAD::tanh(v[zero]);
check = std::tanh(x0);
ok &= NearEqual(result, check, eps, eps);
return ok;
}
bool log10(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// ten raised to the x0 power
AD<double> ten = 10.;
AD<double> pow_10_x0 = CppAD::pow(ten, x[0]);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = CppAD::log10(pow_10_x0);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0, 1e-10 , 1e-10);
// forward computation of first partial w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 1., 1e-10, 1e-10);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 1., 1e-10, 1e-10);
// use a VecAD<Base>::reference object with log10
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = pow_10_x0;
AD<double> result = CppAD::log10(v[zero]);
ok &= NearEqual(result, x0, 1e-10, 1e-10);
return ok;
}
bool Asin(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TEST_VECTOR< AD<double> > x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// a temporary value
AD<double> sin_of_x0 = CppAD::sin(x[0]);
// range space vector
size_t m = 1;
CPPAD_TEST_VECTOR< AD<double> > y(m);
y[0] = CppAD::asin(sin_of_x0);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0, 1e-10 , 1e-10);
// forward computation of first partial w.r.t. x[0]
CPPAD_TEST_VECTOR<double> dx(n);
CPPAD_TEST_VECTOR<double> dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 1., 1e-10, 1e-10);
// reverse computation of derivative of y[0]
CPPAD_TEST_VECTOR<double> w(m);
CPPAD_TEST_VECTOR<double> dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], 1., 1e-10, 1e-10);
// use a VecAD<Base>::reference object with asin
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = sin_of_x0;
AD<double> result = CppAD::asin(v[zero]);
ok &= NearEqual(result, x0, 1e-10, 1e-10);
return ok;
}
bool mul_level(void)
{ bool ok = true; // initialize test result
using CppAD::NearEqual;
double eps = 10. * std::numeric_limits<double>::epsilon();
typedef CppAD::AD<double> ADdouble; // for one level of taping
typedef CppAD::AD<ADdouble> ADDdouble; // for two levels of taping
size_t n = 2; // dimension for example
CPPAD_TEST_VECTOR<ADdouble> a_x(n);
CPPAD_TEST_VECTOR<ADDdouble> aa_x(n);
// value of the independent variables
a_x[0] = 2.; a_x[1] = 3.;
Independent(a_x);
aa_x[0] = a_x[0]; aa_x[1] = a_x[1];
CppAD::Independent(aa_x);
// compute the function f(x) = 2 * x[0] * x[1]
CPPAD_TEST_VECTOR<ADDdouble> aa_f(1);
aa_f[0] = 2. * aa_x[0] * aa_x[1];
CppAD::ADFun<ADdouble> F(aa_x, aa_f);
// re-evaluate f(2, 3) (must get proper deepedence on a_x).
size_t p = 0;
CPPAD_TEST_VECTOR<ADdouble> a_fp(1);
a_fp = F.Forward(p, a_x);
ok &= NearEqual(a_fp[0], 2. * a_x[0] * a_x[1], eps, eps);
// compute the function g(x) = 2 * partial_x[0] f(x) = 4 * x[1]
p = 1;
CPPAD_TEST_VECTOR<ADdouble> a_dx(n), a_g(1);
a_dx[0] = 1.; a_dx[1] = 0.;
a_fp = F.Forward(p, a_dx);
a_g[0] = 2. * a_fp[0];
CppAD::ADFun<double> G(a_x, a_g);
// compute partial_x[1] g(x)
CPPAD_TEST_VECTOR<double> xp(n), gp(1);
p = 0;
xp[0] = 4.; xp[1] = 5.;
gp = G.Forward(p, xp);
ok &= NearEqual(gp[0], 4. * xp[1], eps, eps);
p = 1;
xp[0] = 0.; xp[1] = 1.;
gp = G.Forward(p, xp);
ok &= NearEqual(gp[0], 4., eps, eps);
return ok;
}
bool Erf(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::atan;
using CppAD::exp;
using CppAD::sqrt;
// Construct function object corresponding to erf
CPPAD_TEST_VECTOR< AD<double> > X(1);
CPPAD_TEST_VECTOR< AD<double> > Y(1);
X[0] = 0.;
Independent(X);
Y[0] = erf(X[0]);
ADFun<double> Erf(X, Y);
// vectors to use with function object
CPPAD_TEST_VECTOR<double> x(1);
CPPAD_TEST_VECTOR<double> y(1);
CPPAD_TEST_VECTOR<double> dx(1);
CPPAD_TEST_VECTOR<double> dy(1);
// check value at zero
x[0] = 0.;
y = Erf.Forward(0, x);
ok &= NearEqual(0., y[0], 4e-4, 0.);
// check the derivative of error function
dx[0] = 1.;
double pi = 4. * atan(1.);
double factor = 2. / sqrt( pi );
int i;
for(i = -10; i <= 10; i++)
{ x[0] = i / 4.;
y = Erf.Forward(0, x);
// check derivative
double derf = factor * exp( - x[0] * x[0] );
dy = Erf.Forward(1, dx);
ok &= NearEqual(derf, dy[0], 0., 2e-3);
// test using erf with AD< AD<double> >
AD< AD<double> > X0 = x[0];
AD< AD<double> > Y0 = erf(X0);
ok &= ( y[0] == Value( Value(Y0) ) );
}
return ok;
}
bool OdeErrControl_three(void)
{ bool ok = true; // initial return value
using CppAD::NearEqual;
double alpha = 10.;
Method_three method(alpha);
CppAD::vector<double> xi(2);
xi[0] = 1.;
xi[1] = 0.;
CppAD::vector<double> eabs(2);
eabs[0] = 1e-4;
eabs[1] = 1e-4;
// inputs
double ti = 0.;
double tf = 1.;
double smin = 1e-4;
double smax = 1.;
double scur = 1.;
double erel = 0.;
// outputs
CppAD::vector<double> ef(2);
CppAD::vector<double> xf(2);
CppAD::vector<double> maxabs(2);
size_t nstep;
xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
double x0 = exp( alpha * tf * tf );
ok &= NearEqual(x0, xf[0], 1e-4, 1e-4);
ok &= NearEqual(0., ef[0], 1e-4, 1e-4);
double root_pi = sqrt( 4. * atan(1.));
double root_alpha = sqrt( alpha );
double x1 = CppAD::erf(alpha * tf) * root_pi / (2 * root_alpha);
ok &= NearEqual(x1, xf[1], 1e-4, 1e-4);
ok &= NearEqual(0., ef[1], 1e-4, 1e-4);
ok &= method.F.was_negative();
return ok;
}
void reverse_csum(
OpCode& op, const addr_t*& op_arg, size_t& op_index, size_t& var_index)
{ using CppAD::NumRes;
using CppAD::NumArg;
CPPAD_ASSERT_UNKNOWN( op_ == op );
CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ );
CPPAD_ASSERT_UNKNOWN( op_index == op_index_ );
CPPAD_ASSERT_UNKNOWN( var_index == var_index_ );
CPPAD_ASSERT_UNKNOWN( op == CSumOp );
CPPAD_ASSERT_UNKNOWN( NumArg(CSumOp) == 0 );
/*
The variables that need fixing are op_arg_ and op_arg. Currently,
op_arg points to the last argument for the previous operator.
*/
// last argument for this csum operation
--op_arg;
// first argument for this csum operation
op_arg = op_arg_ -= (op_arg[0] + 4);
// now op_arg points to the first argument for this csum operator
CPPAD_ASSERT_UNKNOWN(
op_arg[0] + op_arg[1] == op_arg[ 3 + op_arg[0] + op_arg[1] ]
);
CPPAD_ASSERT_UNKNOWN( op_index_ < op_rec_.size() );
CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ );
CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ );
}
void reverse_cskip(
OpCode& op, const addr_t*& op_arg, size_t& op_index, size_t& var_index)
{ using CppAD::NumRes;
using CppAD::NumArg;
CPPAD_ASSERT_UNKNOWN( op_ == op );
CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ );
CPPAD_ASSERT_UNKNOWN( op_index == op_index_ );
CPPAD_ASSERT_UNKNOWN( var_index == var_index_ );
CPPAD_ASSERT_UNKNOWN( op == CSkipOp );
CPPAD_ASSERT_UNKNOWN( NumArg(CSkipOp) == 0 );
/*
The variables that need fixing are op_arg_ and op_arg. Currently,
op_arg points first arugment for the previous operator.
*/
--op_arg;
op_arg = op_arg_ -= (op_arg[0] + 4);
CPPAD_ASSERT_UNKNOWN(
op_arg[1] + op_arg[2] == op_arg[ 3 + op_arg[1] + op_arg[2] ]
);
CPPAD_ASSERT_UNKNOWN( op_index_ < op_rec_.size() );
CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ );
CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ );
}
bool compare_op(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps10 = 10.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.5;
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
for(size_t k = 0; k < 2; k++)
{ // optimization options
std::string options = "";
if( k == 0 )
options = "no_compare_op";
// declare independent variables and start tape recording
CppAD::Independent(ax);
// compute function value
tape_size before, after;
fun(options, ax, ay, before, after);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
ok &= f.size_var() == before.n_var;
ok &= f.size_op() == before.n_op;
// Optimize the operation sequence
f.optimize(options);
ok &= f.size_var() == after.n_var;
ok &= f.size_op() == after.n_op;
// Check result for a zero order calculation for a different x,
// where the result of the comparison is he same.
CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
x[0] = 0.75;
y = f.Forward(0, x);
if ( options == "" )
ok &= f.compare_change_number() == 0;
fun(options, x, check, before, after);
ok &= NearEqual(y[0], check[0], eps10, eps10);
// Check case where result of the comparision is differnent
// (hence one needs to re-tape to get correct result)
x[0] = 2.0;
y = f.Forward(0, x);
if ( options == "" )
ok &= f.compare_change_number() == 1;
fun(options, x, check, before, after);
ok &= std::fabs(y[0] - check[0]) > 0.5;
}
return ok;
}
bool CompareChange(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::ADFun;
using CppAD::Independent;
// domain space vector
size_t n = 2;
CPPAD_TEST_VECTOR< AD<double> > X(n);
X[0] = 3.;
X[1] = 4.;
// declare independent variables and start tape recording
CppAD::Independent(X);
// range space vector
size_t m = 1;
CPPAD_TEST_VECTOR< AD<double> > Y(m);
Y[0] = Minimum(X[0], X[1]);
// create f: x -> y and stop tape recording
ADFun<double> f(X, Y);
// evaluate zero mode Forward where conditional has the same result
// note that f.CompareChange is not defined when NDEBUG is true
CPPAD_TEST_VECTOR<double> x(n);
CPPAD_TEST_VECTOR<double> y(m);
x[0] = 3.5;
x[1] = 4.;
y = f.Forward(0, x);
ok &= (y[0] == x[0]);
ok &= (y[0] == Minimum(x[0], x[1]));
ok &= (f.CompareChange() == 0);
// evaluate zero mode Forward where conditional has different result
x[0] = 4.;
x[1] = 3.;
y = f.Forward(0, x);
ok &= (y[0] == x[0]);
ok &= (y[0] != Minimum(x[0], x[1]));
ok &= (f.CompareChange() == 1);
// re-tape to obtain the new AD operation sequence
X[0] = 4.;
X[1] = 3.;
Independent(X);
Y[0] = Minimum(X[0], X[1]);
// stop tape and store result in f
f.Dependent(Y);
// evaluate the function at new argument values
y = f.Forward(0, x);
ok &= (y[0] == x[1]);
ok &= (y[0] == Minimum(x[0], x[1]));
ok &= (f.CompareChange() == 0);
return ok;
}