Prev Next json_get_started.cpp

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@This is cppad-20221105 documentation. Here is a link to its current documentation .
Json Get Started: Example and Test

Notation
Notation Description size
p vector of dynamic parameters 1
x vector of independent variables 1
c vector of constants 1
y vector of dependent variables 1

Node Table
index value
1 p[0]
2 x[0]
3 c[0]
4 sin(p[0])
5 sin(x[0])
6 sin(c[0])
7 sin(p[0]) + sin(x[0]) + sin(c[0])
y[0] sin(p[0]) + sin(x[0]) + sin(c[0])

Include
Include the CppAD core functions: 

# include <cppad/cppad.hpp>

Syntax
ok = get_started() 

bool get_started(void)
{

Setup 
    bool ok = true;
    using CppAD::vector;
    using CppAD::AD;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

Function

Begin Function
See function : 

    std::string json =
        "{\n"
        "   'function_name'  : 'get_started example',\n"

Begin op_define_vec
see op_define_vec : 

        "   'op_define_vec'  : [ 2, [\n"

Define Unary
see unary operators : 

        "       { 'op_code':1, 'name':'sin', 'n_arg':1 } ,\n"

Define Sum
see sum : 

        "       { 'op_code':2, 'name':'sum'            } ]\n"

End op_define_vec 

        "   ],\n"

n_dynamic_ind
see n_dynamic_ind : 

        "   'n_dynamic_ind'  : 1,\n"

n_variable_ind
see n_variable_ind : 

        "   'n_variable_ind' : 1,\n"

constant_vec
see constant_vec : 

        "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]

Begin op_usage_vec
see op_usage_vec : 

        "   'op_usage_vec'   : [ 4, [\n"

op_usage
see op_usage with n_arg in definition : 

        "       [ 1, 1]                ,\n" // sin(p[0])
        "       [ 1, 2]                ,\n" // sin(x[0])
        "       [ 1, 3]                ,\n" // sin(c[0])
see op_usage with n_arg not in definition : 

        "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // sin(p[0])+sin(x[0])+sin(c[0])

End op_usage_vec 

        "   ],\n"

dependent_vec
see dependent_var 

        "   'dependent_vec' : [ 1, [7] ] \n"

End Function 

        "}\n";

Convert Single to Double Quotes 

    for(size_t i = 0; i < json.size(); ++i)
        if( json[i] == '\'' ) json[i] = '"';

double f(x, p) 

    CppAD::ADFun<double> f;
    f.from_json(json);

Check f(x, p) 
    vector<double> c(1), p(1), x(1), y(1);
    c[0] = -0.1; // must match value in graph
    p[0] = 0.2;  // can be any value
    x[0] = 0.3;  // can be any value
    //
    // compute y = f(x, p)
    f.new_dynamic(p);
    y = f.Forward(0, x);
    //
    // f(x, p) = sin(p_0) + sin(x_0) + sin(c_0)
    double check = std::sin(p[0]) + std::sin(x[0]) + std::sin(c[0]);
    ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
AD<double> f(x, p) 

    CppAD::ADFun< AD<double>, double > af( f.base2ad() );

Evaluate Derivative 
    // set independent variables and parameters
    vector< AD<double> > ap(1), ax(1);
    ap[0] = 0.2;
    ax[0] = 0.3;
    //
    // record computation of z = d/dx f(x, p)
    CppAD::Independent(ax, ap);
    af.new_dynamic(ap);
    vector< AD<double> > az = af.Jacobian(ax);

double g(x, p) = d/dx f(x, p) 

    CppAD::ADFun<double> g(ax, az);

Convert to Json and Back 

    json = g.to_json();
    g.from_json(json);

Check g(x, p) 
    c[0] = -0.1; // must match value in graph
    p[0] = 0.3;  // can be any value
    x[0] = 0.4;  // can be any value
    //
    // compute z = g(x, p)
    g.new_dynamic(p);
    vector<double> z = g.Forward(0, x);
    //
    // g(x, p) = d/dx f(x, p) = d/dx sin(x) = cos(x)
    check = std::cos(x[0]);
    ok &= CppAD::NearEqual(z[0], check, eps99, eps99);
    //
    return ok;
}
Input File: example/json/get_started.cpp