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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_mat_mul_reverse.cpp}
{xrst_spell
ccccccccc
cccccccccc
}
Atomic Matrix Multiply Reverse Mode: Example and Test
#####################################################
Purpose
*******
This example demonstrates using reverse mode
with the :ref:`atomic_four_mat_mul-name` class.
f(x)
****
For this example, the function :math:`f(x)` is
.. math::
f(x) =
\left( \begin{array}{ccc}
x_0 & x_1 & x_2 \\
x_3 & x_4 & x_5
\end{array} \right)
\left( \begin{array}{c}
x_6 \\
x_7 \\
x_8
\end{array} \right)
=
\left( \begin{array}{c}
x_0 * x_6 + x_1 * x_7 + x_2 * x_8 \\
x_3 * x_6 + x_4 * x_7 + x_5 * x_8
\end{array} \right)
Jacobian of f(x)
****************
The Jacobian of :math:`f(x)` is
.. math::
f^{(1)} (x) = \left( \begin{array}{cccccccccc}
x_6 & x_7 & x_8 & 0 & 0 & 0 & x_0 & x_1 & x_2 \\
0 & 0 & 0 & x_6 & x_7 & x_8 & x_3 & x_4 & x_5
\end{array} \right)
g(x)
****
We define the function :math:`g(x) = f_0^{(1)} (x)^\R{T}`; i.e.,
.. math::
g(x) = ( x_6, x_7, x_8, 0, 0, 0, x_0, x_1, x_2 )^\R{T}
Hessian
*******
The Hessian of :math:`f_1(x)` is the Jacobian
of :math:`g(x)`; i.e.,
.. math::
f_1^{(2)} (x)
=
g^{(1)} (x)
=
\left( \begin{array}{ccccccccc}
% 0 1 2 3 4 5 6 7 8
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ % 0
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ % 1
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ % 2
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ % 3
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ % 4
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ % 5
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ % 6
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ % 7
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ % 8
\end{array} \right)
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atomic_four_mat_mul_reverse.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/mat_mul/mat_mul.hpp>
bool reverse(void)
{ // ok, eps
bool ok = true;
//
// AD, NearEqual
using CppAD::AD;
using CppAD::NearEqual;
// -----------------------------------------------------------------------
// Record f
// -----------------------------------------------------------------------
//
// afun
CppAD::atomic_mat_mul<double> afun("atomic_mat_mul");
//
// nleft, n_middle, n_right
size_t n_left = 2, n_middle = 3, n_right = 1;
//
// nx, ax
size_t nx = n_middle * (n_left + n_right);
CPPAD_TESTVECTOR( AD<double> ) ax(nx);
for(size_t j = 0; j < nx; ++j)
ax[j] = AD<double>(j + 2);
CppAD::Independent(ax);
//
// ny, ay
size_t ny = n_left * n_right;
CPPAD_TESTVECTOR( AD<double> ) ay(ny);
//
// ay
size_t call_id = afun.set(n_left, n_middle, n_right);
afun(call_id, ax, ay);
//
// f
CppAD::ADFun<double> f(ax, ay);
// -----------------------------------------------------------------------
// Reverse mode on f
// -----------------------------------------------------------------------
//
// x
CPPAD_TESTVECTOR(double) x(nx);
for(size_t j = 0; j < nx; ++j)
x[j] = double(3 + nx - j);
//
// y
// zero order forward mode computation of f(x)
CPPAD_TESTVECTOR(double) y(nx);
y = f.Forward(0, x);
//
// check_y
double check_y[] = {
x[0] * x[6] + x[1] * x[7] + x[2] * x[8],
x[3] * x[6] + x[4] * x[7] + x[5] * x[8]
};
for(size_t i = 0; i < ny; ++i)
ok &= y[i] == check_y[i];
//
// J
// first order reverse mode computation of f'(x)
CPPAD_TESTVECTOR(double) w1(ny), dw1(nx), J(ny * nx);
for(size_t i = 0; i < ny; ++i)
w1[i] = 0.0;
for(size_t i = 0; i < ny; ++i)
{ w1[i] = 1.0;
dw1 = f.Reverse(1, w1);
w1[i] = 0.0;
for(size_t j = 0; j < nx; ++j)
J[i * nx + j] = dw1[j];
}
//
// check_J
double check_J[] = {
x[6], x[7], x[8], 0.0, 0.0, 0.0, x[0], x[1], x[2],
0.0, 0.0, 0.0, x[6], x[7], x[8], x[3], x[4], x[5]
};
for(size_t ij = 0; ij < ny * nx; ij++)
ok &= J[ij] == check_J[ij];
//
// H_0
// Second order reverse mode computaiton of f_0^2 (x)
CPPAD_TESTVECTOR(double) x1(nx), w2(ny), dw2(2 * nx), H_0(nx * nx);
for(size_t i = 0; i < ny; ++i)
w2[i] = 0.0;
w2[0] = 1.0;
for(size_t j = 0; j < nx; ++j)
x1[j] = 0.0;
for(size_t i = 0; i < nx; ++i)
{ x1[i] = 1.0;
f.Forward(1, x1);
x1[i] = 0.0;
dw2 = f.Reverse(2, w2);
for(size_t j = 0; j < nx; ++j)
H_0[i * nx + j] = dw2[2 * j + 1];
}
//
// check_H_0
assert( nx == 9 );
double check_H_0[] = {
0., 0., 0., 0., 0., 0., 1., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 1., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 1.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
1., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 1., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 1., 0., 0., 0., 0., 0., 0,
};
for(size_t ij = 0; ij < nx * nx; ij++)
ok &= H_0[ij] == check_H_0[ij];
// -----------------------------------------------------------------------
// Record g
// -----------------------------------------------------------------------
//
// af
CppAD::ADFun< AD<double>, double> af = f.base2ad();
//
// az
CppAD::Independent(ax);
CPPAD_TESTVECTOR( AD<double> ) aw(ny), az(nx);
af.Forward(0, ax);
for(size_t i = 0; i < ny; ++i)
aw[i] = 0.0;
aw[0] = 1.0;
az = af.Reverse(1, aw);
// g
CppAD::ADFun<double> g(ax, az);
// -----------------------------------------------------------------------
// Forward mode on g
// -----------------------------------------------------------------------
//
// z
// zero order forward mode computation of g(x)
CPPAD_TESTVECTOR(double) z(nx);
z = g.Forward(0, x);
//
// check z
for(size_t j = 0; j < nx; ++j)
ok &= z[j] == J[0 * nx + j];
//
// z1
CPPAD_TESTVECTOR(double) w(nx), dw(nx);
for(size_t i = 0; i < nx; ++i)
w[i] = 0.0;
for(size_t i = 0; i < nx; ++i)
{ w[i] = 1.0;
dw = g.Reverse(1, w);
w[i] = 0.0;
for(size_t j = 0; j < nx; ++j)
ok &= dw[j] == check_H_0[i * nx + j];
}
// ----------------------------------------------------------------
return ok;
}
// END C++
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