Prev Next atomic_four_vector_div.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 .
Atomic Vector Division Example

f(u, v, w)
For this example, @(@ f : \B{R}^{2m} \rightarrow \B{R}^m @)@ is defined by @(@ f(u, v) = u * u / v @)@. where u and v are in @(@ \B{R}^m @)@.

g(u, v)
For this example @(@ g : \B{R}^{2m} \rightarrow \B{R}^m @)@ is defined by @(@ g_i (u, v) = \partial_{v[i]} f_i (u, v) @)@

Source 

# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/vector/vector.hpp>
bool div(void)
{   bool ok = true;
    using CppAD::NearEqual;
    using CppAD::AD;
    double eps99 = 99.0 * CppAD::numeric_limits<double>::epsilon();
    //
    // vec_op
    // atomic vector_op object
    CppAD::atomic_vector<double> vec_op("atomic_vector");
    //
    // m
    // size of u and v
    size_t m = 4;
    //
    // mul_op, div_op
    typedef CppAD::atomic_vector<double>::op_enum_t op_enum_t;
    op_enum_t mul_op = CppAD::atomic_vector<double>::mul_enum;
    op_enum_t div_op = CppAD::atomic_vector<double>::div_enum;
    // -----------------------------------------------------------------------
    // Record f(u, v) = u * u / v
    // -----------------------------------------------------------------------
    // Independent variable vector
    CPPAD_TESTVECTOR( CppAD::AD<double> ) auv(2 * m);
    for(size_t j = 0; j < 2 * m; ++j)
        auv[j] = AD<double>(1 + j);
    CppAD::Independent(auv);
    //
    // au, av, aw
    CPPAD_TESTVECTOR( CppAD::AD<double> ) au(m), av(m);
    for(size_t i = 0; i < m; ++i)
    {   au[i] = auv[0 * m + i];
        av[i] = auv[1 * m + i];
    }
    //
    // ax = (mul_op, au, au)
    CPPAD_TESTVECTOR( CppAD::AD<double> ) ax(2 * m);
    for(size_t i = 0; i < m; ++i)
    {   ax[i]     = au[i];
        ax[m + i] = au[i];
    }
    //
    // ay = u * u
    CPPAD_TESTVECTOR( CppAD::AD<double> ) ay(m);
    vec_op(mul_op, ax, ay);
    //
    // ax = (ay, av)
    for(size_t i = 0; i < m; ++i)
    {   ax[i]     = ay[i];
        ax[m + i] = av[i];
    }
    //
    // az = au / ay
    CPPAD_TESTVECTOR( CppAD::AD<double> ) az(m);
    vec_op(div_op, ax, az);
    //
    // f
    CppAD::ADFun<double> f(auv, az);
    // -----------------------------------------------------------------------
    // check forward mode on f
    // -----------------------------------------------------------------------
    //
    // uv, duv
    CPPAD_TESTVECTOR(double) uv(2 * m), duv(2 * m);
    for(size_t j = 0; j < 2 * m; ++j)
    {   uv[j]  = double(2 + j);
        duv[j] = 1.0;
    }
    //
    // z, dz
    CPPAD_TESTVECTOR(double) z(m), dz(m);
    z  = f.Forward(0, uv);
    dz = f.Forward(1, duv);
    //
    // ok
    for(size_t i = 0; i < m; ++i)
    {   double ui     = uv[0 * m + i];
        double vi     = uv[1 * m + i];
        double check  = ui * ui / vi;
        ok           &= NearEqual( z[i] ,  check,  eps99, eps99);
        check         = 2.0 * ui / vi - ui * ui / (vi * vi);
        ok         &= NearEqual( dz[i] ,  check,  eps99, eps99);
    }
    // -----------------------------------------------------------------------
    // check reverse mode on f
    // -----------------------------------------------------------------------
    //
    // weight
    CPPAD_TESTVECTOR(double) weight(m);
    for(size_t i = 0; i < m; ++i)
        weight[i] = 1.0;
    //
    // dweight
    CPPAD_TESTVECTOR(double) dweight(2 * m);
    f.Forward(0, uv);
    dweight = f.Reverse(1, weight);
    //
    // ok
    for(size_t i = 0; i < m; ++i)
    {   double ui      = uv[0 * m + i];
        double vi      = uv[1 * m + i];
        double dfi_dui = 2.0 * ui / vi;
        ok           &= NearEqual(dweight[0 * m + i], dfi_dui, eps99, eps99);
        double dfi_dvi = - ui * ui / (vi * vi);
        ok           &= NearEqual(dweight[1 * m + i], dfi_dvi, eps99, eps99);
    }
    // -----------------------------------------------------------------------
    // Record g_i (u, v) = \partial d/dv[i] f_i (u, v)
    // -----------------------------------------------------------------------
    //
    // af
    CppAD::ADFun< AD<double>, double > af = f.base2ad();
    //
    // auv
    CppAD::Independent(auv);
    //
    // aduv
    CPPAD_TESTVECTOR( AD<double> ) aduv(2 * m);
    for(size_t i = 0; i < m; ++i)
    {   aduv[0 * m + i]  = 0.0; // du[i]
        aduv[1 * m + i]  = 1.0; // dv[i]
    }
    //
    // az
    // use the fact that d_u[i] f_k (u, v, w) is zero when i != k
    af.Forward(0, auv);
    az = af.Forward(1, aduv);
    CppAD::ADFun<double> g(auv, az);
    // -----------------------------------------------------------------------
    // Record h (u, v) = sum f_i^(1) (u , v)
    // -----------------------------------------------------------------------
    //
    // auv
    CppAD::Independent(auv);
    //
    // aweight
    CPPAD_TESTVECTOR( AD<double> ) aweight(m);
    for(size_t i = 0; i < m; ++i)
        aweight[i] = 1.0;
    //
    // az
    CPPAD_TESTVECTOR( AD<double> ) adweight(3 * m);
    af.Forward(0, auv);
    az = af.Reverse(1, aweight);
    CppAD::ADFun<double> h(auv, az);
    // -----------------------------------------------------------------------
    // check forward mode on g
    // -----------------------------------------------------------------------
    //
    // z
    z = g.Forward(0, uv);
    //
    // ok
    for(size_t i = 0; i < m; ++i)
    {   double ui      = uv[0 * m + i];
        double vi      = uv[1 * m + i];
        double check   = - ui * ui / (vi * vi);
        ok           &= NearEqual( z[i] ,  check,  eps99, eps99);
    }
    // -----------------------------------------------------------------------
    // check forward mode on h
    // -----------------------------------------------------------------------
    //
    // z
    z = h.Forward(0, uv);
    //
    // ok
    for(size_t i = 0; i < m; ++i)
    {   double ui  = uv[0 * m + i];
        double vi  = uv[1 * m + i];
        //
        double dfi_dui  = 2.0 * ui / vi;
        ok             &= NearEqual(z[0 * m + i] ,  dfi_dui,  eps99, eps99);
        //
        double dfi_dvi  = - ui * ui / (vi * vi);
        ok             &= NearEqual(z[1 * m + i] ,  dfi_dvi,  eps99, eps99);
    }
    return ok;
}
Input File: example/atomic_four/vector/div.cpp