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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
g_0 (x) = x_0 * x_0
g_1 (x) = x_0 * x_1
g_2 (x) = x_1 * x_2
g_3 (x) = x_2 * x_2
*/
# include <cppad/cppad.hpp> // CppAD include file
namespace { // start empty namespace
using CppAD::vector; // abbreviate CppAD::vector using vector
// ============================================================================
// Testing dynamic parameters in atomic_three functions.
// ============================================================================
class dynamic_optimize : public CppAD::atomic_three<double> {
public:
// can use const char* name when calling this constructor
dynamic_optimize(const std::string& name) : // can have more arguments
CppAD::atomic_three<double>(name) // inform base class of name
{ }
private:
// calculate type_y
virtual bool for_type(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
vector<CppAD::ad_type_enum>& type_y )
{ assert( parameter_x.size() == type_x.size() );
bool ok = type_x.size() == 3; // n
ok &= type_y.size() == 4; // m
if( ! ok )
return false;
type_y[0] = type_x[0];
type_y[1] = std::max( type_x[0], type_x[1] );
type_y[2] = std::max( type_x[1], type_x[2] );
type_y[3] = type_x[2];
return true;
}
// calculate depend_x
virtual bool rev_depend(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
vector<bool>& depend_x ,
const vector<bool>& depend_y )
{ assert( parameter_x.size() == depend_x.size() );
bool ok = depend_x.size() == 3; // n
ok &= depend_y.size() == 4; // m
if( ! ok )
return false;
depend_x[0] = depend_y[0] || depend_y[1];
depend_x[1] = depend_y[1] || depend_y[2];
depend_x[2] = depend_y[2] || depend_y[3];
return true;
}
virtual bool forward(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
size_t need_y ,
size_t order_low ,
size_t order_up ,
const vector<double>& taylor_x ,
vector<double>& taylor_y
)
{
# ifndef NDEBUG
size_t n = taylor_x.size() / (order_up + 1);
size_t m = taylor_y.size() / (order_up + 1);
# endif
assert( n == 3 );
assert( m == 4 );
assert( order_low <= order_up );
// return flag
bool ok = order_up == 0;
if( ! ok )
return ok;
// g_0 = x_0 * x_0
taylor_y[0] = taylor_x[0] * taylor_x[0];
// g_1 = x_0 * x_1
taylor_y[1] = taylor_x[0] * taylor_x[1];
// g_2 = x_1 * x_2
taylor_y[2] = taylor_x[1] * taylor_x[2];
// g_3 = x_2 * x_2
taylor_y[3] = taylor_x[2] * taylor_x[2];
return ok;
}
}; // End of dynamic_optimize class
// ---------------------------------------------------------------------------
bool optimize_dynamic_one(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
dynamic_optimize afun("dynamic_optimize");
//
// constant parameter
double c_0 = 2.0;
//
// independent dynamic parameter vector
size_t np = 1;
CPPAD_TESTVECTOR(double) p(np);
CPPAD_TESTVECTOR( AD<double> ) ap(np);
ap[0] = p[0] = 3.0;
//
// independent variable vector
size_t nu = 1;
double u_0 = 0.5;
CPPAD_TESTVECTOR( AD<double> ) au(nu);
au[0] = u_0;
// declare independent variables and start tape recording
CppAD::Independent(au, ap);
// create a dynamic parameter that is not used
AD<double> ar = 2.0 * ap[0];
// call atomic function and store result in ay
CPPAD_TESTVECTOR( AD<double> ) ax(3), av(4);
ax[0] = c_0; // x_0 = c
ax[1] = ap[0]; // x_1 = p
ax[2] = au[0]; // x_2 = u
afun(ax, av);
// check type of result
ok &= Constant( av[0] ); // v_0 = c * c
ok &= Dynamic( av[1] ); // v_1 = c * p
ok &= Variable( av[2] ); // v_2 = p * u
ok &= Variable( av[3] ); // v_3 = u * u
// range space vector
size_t ny = 3;
CPPAD_TESTVECTOR( AD<double> ) ay(ny);
for(size_t i = 0; i < ny; ++i)
ay[i] = av[i];
// create f: u -> y and stop tape recording
CppAD::ADFun<double> f;
f.Dependent (au, ay); // f(u) = (c * c, c * p, p * u)
// sequence properties
ok &= f.size_dyn_ind() == 1; // p
ok &= f.size_dyn_par() == 3; // p, r, c * p
// Three constant parameters: nan, c, c * c
ok &= f.size_par() == 6;
// Normal variables: u, p * u, u * u
// Extra variables: phanton at index 0, y[0], y[1]
ok &= f.size_var() == 6;
// optimize
f.optimize();
// sequence properties
ok &= f.size_dyn_ind() == 1; // p
ok &= f.size_dyn_par() == 2; // c * p
// Four constant parameters: nan, zero, c, c * c
ok &= f.size_par() == 6;
// Normal variables: u, p * u
// Extra variables: phanton at index 0, y[0], y[1]
ok &= f.size_var() == 5;
// check
double check;
// check zero order forward mode
size_t q;
CPPAD_TESTVECTOR( double ) u_q(nu), y_q(ny);
q = 0;
u_q[0] = u_0;
y_q = f.Forward(q, u_q);
check = c_0 * c_0;
ok &= NearEqual(y_q[0] , check, eps, eps);
check = c_0 * p[0];
ok &= NearEqual(y_q[1] , check, eps, eps);
check = p[0] * u_0;
ok &= NearEqual(y_q[2] , check, eps, eps);
// set new value for dynamic parameters
p[0] = 2.0 * p[0];
f.new_dynamic(p);
y_q = f.Forward(q, u_q);
check = c_0 * c_0;
ok &= NearEqual(y_q[0] , check, eps, eps);
check = c_0 * p[0];
ok &= NearEqual(y_q[1] , check, eps, eps);
check = p[0] * u_0;
ok &= NearEqual(y_q[2] , check, eps, eps);
return ok;
}
// ---------------------------------------------------------------------------
bool optimize_dynamic_two(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
dynamic_optimize afun("dynamic_optimize");
//
// independent dynamic parameter vector
size_t np = 1;
CPPAD_TESTVECTOR(double) p(np);
CPPAD_TESTVECTOR( AD<double> ) ap(np);
ap[0] = p[0] = 3.0;
//
// independent variable vector
size_t nu = 1;
double u_0 = 0.5;
CPPAD_TESTVECTOR( AD<double> ) au(nu);
au[0] = u_0;
// declare independent variables and start tape recording
CppAD::Independent(au, ap);
// create a dynamic parameter that is used by atomic function
// but not needed to compute f(u)
AD<double> ar = 2.0 * ap[0];
// call atomic function and store result in ay
CPPAD_TESTVECTOR( AD<double> ) ax(3), av(4);
ax[0] = au[0]; // x_0 = u
ax[1] = ap[0]; // x_1 = p
ax[2] = ar; // x_2 = r
afun(ax, av);
// check type of result
ok &= Variable( av[0] ); // v_0 = u * u , used
ok &= Variable( av[1] ); // v_1 = u * p , used
ok &= Dynamic( av[2] ); // v_2 = r * p , not used
ok &= Dynamic( av[3] ); // v_3 = r * r , not used
// range space vector
size_t ny = 2;
CPPAD_TESTVECTOR( AD<double> ) ay(ny);
for(size_t i = 0; i < ny; ++i)
ay[i] = av[i];
// create f: u -> y and stop tape recording
CppAD::ADFun<double> f;
f.Dependent (au, ay); // f(u) = (u * u, u * p)
// sequence properties
ok &= f.size_dyn_ind() == 1; // p
ok &= f.size_dyn_par() == 4; // p, r, r * p, r * r
// Two constant parameters: nan, 2.0 in computation of r
ok &= f.size_par() == 6;
// optimize
f.optimize();
// sequence properties
ok &= f.size_dyn_ind() == 1; // p
ok &= f.size_dyn_par() == 1; // p
// Two constant parameter: nan, zero
ok &= f.size_par() == 3;
// check
double check;
// check zero order forward mode
size_t q;
CPPAD_TESTVECTOR( double ) u_q(nu), y_q(ny);
q = 0;
u_q[0] = u_0;
y_q = f.Forward(q, u_q);
check = u_0 * u_0;
ok &= NearEqual(y_q[0] , check, eps, eps);
check = u_0 * p[0];
ok &= NearEqual(y_q[1] , check, eps, eps);
// set new value for dynamic parameters
p[0] = 2.0 * p[0];
f.new_dynamic(p);
y_q = f.Forward(q, u_q);
check = u_0 * u_0;
ok &= NearEqual(y_q[0] , check, eps, eps);
check = u_0 * p[0];
ok &= NearEqual(y_q[1] , check, eps, eps);
return ok;
}
// ---------------------------------------------------------------------------
bool optimize_dynamic_three(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
dynamic_optimize afun("dynamic_optimize");
//
// independent dynamic parameter vector
size_t np = 1;
CPPAD_TESTVECTOR(double) p(np);
CPPAD_TESTVECTOR( AD<double> ) ap(np);
ap[0] = p[0] = 3.0;
//
// independent variable vector
size_t nu = 1;
double u_0 = 0.5;
CPPAD_TESTVECTOR( AD<double> ) au(nu);
au[0] = u_0;
// declare independent variables and start tape recording
CppAD::Independent(au, ap);
// create a dynamic parameter that is used by atomic function
// but not needed to compute f(u)
AD<double> ar = 2.0 * ap[0];
// call atomic function and store result in ay
CPPAD_TESTVECTOR( AD<double> ) ax(3), av(4);
ax[0] = au[0]; // x_0 = u
ax[1] = ar; // x_1 = r
ax[2] = ap[0]; // x_2 = p
afun(ax, av);
// check type of result
ok &= Variable( av[0] ); // v_0 = u * u , used
ok &= Variable( av[1] ); // v_1 = u * r , used
ok &= Dynamic( av[2] ); // v_2 = r * p , not used
ok &= Dynamic( av[3] ); // v_3 = p * p , not used
// range space vector
size_t ny = 2;
CPPAD_TESTVECTOR( AD<double> ) ay(ny);
for(size_t i = 0; i < ny; ++i)
ay[i] = av[i];
// create f: u -> y and stop tape recording
CppAD::ADFun<double> f;
f.Dependent (au, ay); // f(u) = (u * u, u * p)
// sequence properties
ok &= f.size_dyn_ind() == 1; // p
ok &= f.size_dyn_par() == 4; // p, r, r * p, p * p
// Two constant parameters: nan, 2.0 in computation of r
ok &= f.size_par() == 6;
// optimize
f.optimize();
// sequence properties
ok &= f.size_dyn_ind() == 1; // p
ok &= f.size_dyn_par() == 2; // p, r
// Three constant parameters: nan, zero, 2.0 in computation of r
ok &= f.size_par() == 5;
// check
double check;
// check zero order forward mode
double r = 2.0 * p[0];
size_t q;
CPPAD_TESTVECTOR( double ) u_q(nu), y_q(ny);
q = 0;
u_q[0] = u_0;
y_q = f.Forward(q, u_q);
check = u_0 * u_0;
ok &= NearEqual(y_q[0] , check, eps, eps);
check = u_0 * r;
ok &= NearEqual(y_q[1] , check, eps, eps);
// set new value for dynamic parameters
p[0] = 2.0 * p[0];
r = 2.0 * p[0];
f.new_dynamic(p);
y_q = f.Forward(q, u_q);
check = u_0 * u_0;
ok &= NearEqual(y_q[0] , check, eps, eps);
check = u_0 * r;
ok &= NearEqual(y_q[1] , check, eps, eps);
return ok;
}
// ============================================================================
// Testing Variables that get removed
// ============================================================================
class variable_optimize : public CppAD::atomic_three<double> {
public:
// can use const char* name when calling this constructor
variable_optimize(const std::string& name) : // can have more arguments
CppAD::atomic_three<double>(name) // inform base class of name
{ }
private:
// calculate type_y
virtual bool for_type(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
vector<CppAD::ad_type_enum>& type_y )
{ assert( parameter_x.size() == type_x.size() );
bool ok = type_x.size() == 2; // n
ok &= type_y.size() == 2; // m
if( ! ok )
return false;
type_y[0] = type_x[0];
type_y[1] = std::max( type_x[0], type_x[1] );
return true;
}
// calculate depend_x
virtual bool rev_depend(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
vector<bool>& depend_x ,
const vector<bool>& depend_y )
{ assert( parameter_x.size() == depend_x.size() );
bool ok = depend_x.size() == 2; // n
ok &= depend_y.size() == 2; // m
if( ! ok )
return false;
depend_x[0] = depend_y[0] || depend_y[1];
depend_x[1] = depend_y[1];
return true;
}
virtual bool forward(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
size_t need_y ,
size_t order_low ,
size_t order_up ,
const vector<double>& taylor_x ,
vector<double>& taylor_y
)
{
# ifndef NDEBUG
size_t n = taylor_x.size() / (order_up + 1);
size_t m = taylor_y.size() / (order_up + 1);
# endif
assert( n == 2 );
assert( m == 2 );
assert( order_low <= order_up );
// return flag
bool ok = order_up == 0;
if( ! ok )
return ok;
// g_0 = exp( x_0 )
taylor_y[0] = std::exp( taylor_x[0] );
// g_1 = exp( x_0 * x_1 )
taylor_y[1] = std::exp( taylor_x[0] * taylor_x[1] );
return ok;
}
virtual bool reverse(
const vector<double>& parameter_x ,
const vector<CppAD::ad_type_enum>& type_x ,
size_t order_up ,
const vector<double>& taylor_x ,
const vector<double>& taylor_y ,
vector<double>& partial_x ,
const vector<double>& partial_y
)
{
size_t q1 = order_up + 1;
size_t n = taylor_x.size() / q1;
# ifndef NDEBUG
size_t m = taylor_y.size() / q1;
# endif
assert( n == 2 );
assert( m == 2 );
// return flag
bool ok = order_up == 0;
if( ! ok )
return ok;
// initialize summation as zero
for(size_t j = 0; j < n; ++j)
partial_x[j] = 0.0;
// g_0 = exp( x_0 )
partial_x[0] += partial_y[0] * taylor_y[0];
// g_1 = exp( x_0 * x_1 )
partial_x[0] += partial_y[1] * taylor_y[1] * taylor_x[1];
partial_x[1] += partial_y[1] * taylor_y[1] * taylor_x[0];
//
return ok;
}
}; // End of variable_optimize class
// ---------------------------------------------------------------------------
bool optimize_variable_one(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
variable_optimize afun("variable_optimize");
//
// independent variable vector
size_t nu = 2;
CPPAD_TESTVECTOR( AD<double> ) au(nu);
for(size_t j = 0; j < nu; ++j)
au[j] = double(j + 1);
// declare independent variables and start tape recording
CppAD::Independent(au);
// call atomic function and store result in ay
CPPAD_TESTVECTOR( AD<double> ) ax(nu), av(nu);
for(size_t j = 0; j < nu; ++j)
ax[j] = au[j] / 2.0; // x = u / 2
afun(ax, av);
// check type of result
for(size_t j = 0; j < nu; ++j)
ok &= Variable( av[j] );
// range space vector
size_t ny = 1;
CPPAD_TESTVECTOR( AD<double> ) ay(ny);
//
// only the first component of av affects the function value
ay[0] = av[0];
// create f: u -> y and stop tape recording
CppAD::ADFun<double> f;
f.Dependent (au, ay); // f(u) = exp( u[0] / 2 )
// optimize
f.optimize();
// check
double check;
// check zero order forward mode
CPPAD_TESTVECTOR( double ) u(nu), y(ny);
for(size_t j = 0; j < nu; ++j)
u[j] = double(j + 1) / double(nu);
y = f.Forward(0, u);
check = std::exp( u[0] / 2.0 );
ok &= NearEqual(y[0] , check, eps, eps);
// Check first order reverse mode. This test would vaile when
// nan was used for argument and function values that were optimized out
// because they were not used.
CPPAD_TESTVECTOR( double ) w(ny), dw(nu);
w[0] = 1.0;
dw = f.Reverse(1, w);
check = std::exp( u[0] / 2.0 ) / 2.0;
ok &= NearEqual(dw[0] , check, eps, eps);
check = 0.0;
ok &= NearEqual(dw[1] , check, eps, eps);
//
return ok;
}
} // End empty namespace
bool atomic_three(void)
{ bool ok = true;
ok &= optimize_dynamic_one();
ok &= optimize_dynamic_two();
ok &= optimize_dynamic_three();
ok &= optimize_variable_one();
return ok;
}
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