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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
// ----------------------------------------------------------------------------
/*
{xrst_begin atomic_four_vector_div.cpp}
Atomic Vector Division Example
##############################
f(u, v, w)
**********
For this example,
:math:`f : \B{R}^{2m} \rightarrow \B{R}^m`
is defined by :math:`f(u, v) = u * u / v`.
where *u* and *v* are in :math:`\B{R}^m`.
g(u, v)
*******
For this example :math:`g : \B{R}^{2m} \rightarrow \B{R}^m`
is defined by :math:`g_i (u, v) = \partial_{v[i]} f_i (u, v)`
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atomic_four_vector_div.cpp}
*/
// BEGIN C++
# 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;
}
// END C++
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