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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_sparsity.cpp}
{xrst_spell
cccccccc
cccccccccc
rvec
}
Atomic Matrix Multiply Sparsity Patterns: Example and Test
##########################################################
Purpose
*******
This example demonstrates computing sparsity patterns with
the :ref:`atomic_four_mat_mul-name` class.
f(x)
****
For a matrix :math:`A` we define the function :math:`\R{rvec} ( A )`
to be the elements of :math:`A` in row major order.
For this example, the function :math:`f(x)` is
.. math::
f(x) =
\R{rvec} \left[
\left( \begin{array}{cc}
x_0 & x_1 \\
x_2 & x_3 \\
\end{array} \right)
\left( \begin{array}{cc}
x_4 & x_5 \\
x_6 & x_7
\end{array} \right)
\right]
=
\R{rvec}
\left( \begin{array}{cc}
x_0 x_4 + x_1 x_6 & x_0 x_5 + x_1 x_7 \\
x_2 x_4 + x_3 x_6 & x_2 x_5 + x_3 x_7 \\
\end{array} \right)
.. math::
f(x)
=
\left( \begin{array}{c}
x_0 x_4 + x_1 x_6 \\
x_0 x_5 + x_1 x_7 \\
x_2 x_4 + x_3 x_6 \\
x_2 x_5 + x_3 x_7
\end{array} \right)
Jacobian of f(x)
****************
The Jacobian of :math:`f(x)` is
.. math::
f^{(1)} (x) = \left( \begin{array}{cccccccc}
% 0 1 2 3 4 5 6 7
x_4 & x_6 & 0 & 0 & x_0 & 0 & x_1 & 0 \\ % 0
x_5 & x_7 & 0 & 0 & 0 & x_0 & 0 & x_1 \\ % 1
0 & 0 & x_4 & x_6 & x_2 & 0 & x_3 & 0 \\ % 2
0 & 0 & x_5 & x_7 & 0 & x_2 & 0 & x_3 \\ % 3
\end{array} \right)
Hessian
*******
The function :math:`f_2 (x)` is
.. math::
f_2 (x) = x_2 x_4 + x_3 x_6
The Hessian of :math:`f_2(x)` is
.. math::
f_2^{(2)} (x)
=
\left( \begin{array}{cccccccccc}
& 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
& - & - & - & - & - & - & - & - \\
0 \; | & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 \; | & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
2 \; | & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
3 \; | & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
4 \; | & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
5 \; | & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
6 \; | & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
7 \; | & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\end{array} \right)
where the first row is the column index,
and the first column is the row index,
for the corresponding matrix entries above.
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atomic_four_mat_mul_sparsity.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/mat_mul/mat_mul.hpp>
bool sparsity(void)
{ // ok, eps
bool ok = true;
//
// AD
using CppAD::AD;
using CppAD::sparse_rc;
// -----------------------------------------------------------------------
// Record f
// -----------------------------------------------------------------------
//
// afun
CppAD::atomic_mat_mul<double> afun("atomic_mat_mul");
//
// nleft, n_middle, n_right
size_t n_left = 2, n_middle = 2, n_right = 2;
//
// 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);
//
// s_vector
typedef CPPAD_TESTVECTOR(size_t) s_vector;
//
// eye_sparsity
// nx by nx identitty matrix
sparse_rc<s_vector> eye_sparsity;
eye_sparsity.resize(nx, nx, nx);
for(size_t i = 0; i < nx; ++i)
eye_sparsity.set(i, i, i);
//
// -----------------------------------------------------------------------
// jac_sparsity
bool transpose = false;
bool dependency = false;
bool internal_bool = false;
sparse_rc<s_vector> jac_sparsity;
f.for_jac_sparsity(
eye_sparsity, transpose, dependency, internal_bool, jac_sparsity
);
{ // check jac_sparsity
//
// row, col
const s_vector& row = jac_sparsity.row();
const s_vector& col = jac_sparsity.col();
s_vector row_major = jac_sparsity.row_major();
//
// ok
ok &= jac_sparsity.nnz() == 16;
for(size_t k = 0; k < jac_sparsity.nnz(); ++k)
ok &= row[ row_major[k] ] == k / 4;
// row 0
ok &= col[ row_major[0] ] == 0;
ok &= col[ row_major[1] ] == 1;
ok &= col[ row_major[2] ] == 4;
ok &= col[ row_major[3] ] == 6;
// row 1
ok &= col[ row_major[4] ] == 0;
ok &= col[ row_major[5] ] == 1;
ok &= col[ row_major[6] ] == 5;
ok &= col[ row_major[7] ] == 7;
// row 2
ok &= col[ row_major[8] ] == 2;
ok &= col[ row_major[9] ] == 3;
ok &= col[ row_major[10] ] == 4;
ok &= col[ row_major[11] ] == 6;
// row 3
ok &= col[ row_major[12] ] == 2;
ok &= col[ row_major[13] ] == 3;
ok &= col[ row_major[14] ] == 5;
ok &= col[ row_major[15] ] == 7;
}
// ----------------------------------------------------------------
//
// select_y
// corresponding to f_2
CPPAD_TESTVECTOR(bool) select_y(ny);
for(size_t i = 0; i < ny; ++i)
select_y[i] = false;
select_y[2] = true;
//
// hes_sparsity
transpose = false;
internal_bool = false;
sparse_rc<s_vector> hes_sparsity;
f.rev_hes_sparsity(select_y, transpose, internal_bool, hes_sparsity);
{ // check hes_sparsity
//
// row, col
const s_vector& row = hes_sparsity.row();
const s_vector& col = hes_sparsity.col();
s_vector row_major = hes_sparsity.row_major();
//
// ok
ok &= hes_sparsity.nnz() == 4;
//
ok &= row[ row_major[0] ] == 2;
ok &= col[ row_major[0] ] == 4;
//
ok &= row[ row_major[1] ] == 3;
ok &= col[ row_major[1] ] == 6;
//
ok &= row[ row_major[2] ] == 4;
ok &= col[ row_major[2] ] == 2;
//
ok &= row[ row_major[3] ] == 6;
ok &= col[ row_major[3] ] == 3;
}
return ok;
}
// END C++
|
