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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: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin sparse_sub_hes.cpp}
Subset of a Sparse Hessian: Example and Test
############################################
Purpose
*******
This example uses a
:ref:`sparse_hessian@p@Column Subset` of the sparsity pattern
to compute a subset of the Hessian.
See Also
********
:ref:`sub_sparse_hes.cpp-name`
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end sparse_sub_hes.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool sparse_sub_hes(void)
{ bool ok = true;
using CppAD::AD;
typedef CPPAD_TESTVECTOR(size_t) SizeVector;
typedef CPPAD_TESTVECTOR(double) DoubleVector;
typedef CppAD::sparse_rc<SizeVector> sparsity;
//
// domain space vector
size_t n = 4;
CPPAD_TESTVECTOR(AD<double>) ax(n);
for(size_t j = 0; j < n; j++)
ax[j] = double(j);
// declare independent variables and start recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = 0.0;
for(size_t j = 0; j < n; j++)
ay[0] += double(j+1) * ax[0] * ax[j];
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// sparsity pattern for the identity matrix
size_t nr = n;
size_t nc = n;
size_t nnz_in = n;
sparsity pattern_in(nr, nc, nnz_in);
for(size_t k = 0; k < nnz_in; k++)
{ size_t r = k;
size_t c = k;
pattern_in.set(k, r, c);
}
// compute sparsity pattern for J(x) = f'(x)
bool transpose = false;
bool dependency = false;
bool internal_bool = false;
sparsity pattern_out;
f.for_jac_sparsity(
pattern_in, transpose, dependency, internal_bool, pattern_out
);
//
// compute sparsity pattern for H(x) = f''(x)
CPPAD_TESTVECTOR(bool) select_range(m);
select_range[0] = true;
CppAD::sparse_hes_work work;
f.rev_hes_sparsity(
select_range, transpose, internal_bool, pattern_out
);
size_t nnz = pattern_out.nnz();
ok &= nnz == 7;
ok &= pattern_out.nr() == n;
ok &= pattern_out.nc() == n;
{ // check results
const SizeVector& row( pattern_out.row() );
const SizeVector& col( pattern_out.col() );
SizeVector row_major = pattern_out.row_major();
//
ok &= row[ row_major[0] ] == 0 && col[ row_major[0] ] == 0;
ok &= row[ row_major[1] ] == 0 && col[ row_major[1] ] == 1;
ok &= row[ row_major[2] ] == 0 && col[ row_major[2] ] == 2;
ok &= row[ row_major[3] ] == 0 && col[ row_major[3] ] == 3;
//
ok &= row[ row_major[4] ] == 1 && col[ row_major[4] ] == 0;
ok &= row[ row_major[5] ] == 2 && col[ row_major[5] ] == 0;
ok &= row[ row_major[6] ] == 3 && col[ row_major[6] ] == 0;
}
//
// Only interested in cross-terms. Since we are not computing rwo 0,
// we do not need sparsity entries in row 0.
CppAD::sparse_rc<SizeVector> subset_pattern(n, n, 3);
for(size_t k = 0; k < 3; k++)
subset_pattern.set(k, k+1, 0);
CppAD::sparse_rcv<SizeVector, DoubleVector> subset( subset_pattern );
//
// argument and weight values for computation
CPPAD_TESTVECTOR(double) x(n), w(m);
for(size_t j = 0; j < n; j++)
x[j] = double(n) / double(j+1);
w[0] = 1.0;
//
std::string coloring = "cppad.general";
size_t n_sweep = f.sparse_hes(
x, w, subset, subset_pattern, coloring, work
);
ok &= n_sweep == 1;
for(size_t k = 0; k < 3; k++)
{ size_t i = k + 1;
ok &= subset.val()[k] == double(i + 1);
}
//
// convert subset from lower triangular to upper triangular
for(size_t k = 0; k < 3; k++)
subset_pattern.set(k, 0, k+1);
subset = CppAD::sparse_rcv<SizeVector, DoubleVector>( subset_pattern );
//
// This will require more work because the Hessian is computed
// column by column (not row by row).
work.clear();
n_sweep = f.sparse_hes(
x, w, subset, subset_pattern, coloring, work
);
ok &= n_sweep == 3;
//
// but it will get the right answer
for(size_t k = 0; k < 3; k++)
{ size_t i = k + 1;
ok &= subset.val()[k] == double(i + 1);
}
return ok;
}
// END C++
|
