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///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2012-2018 DreamWorks Animation LLC
//
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
//
// Redistributions of source code must retain the above copyright
// and license notice and the following restrictions and disclaimer.
//
// * Neither the name of DreamWorks Animation nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
// LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
//
///////////////////////////////////////////////////////////////////////////
#include <cppunit/extensions/HelperMacros.h>
#include <openvdb/openvdb.h>
#include <openvdb/version.h>
#include <openvdb/math/ConjGradient.h>
class TestConjGradient: public CppUnit::TestCase
{
public:
CPPUNIT_TEST_SUITE(TestConjGradient);
CPPUNIT_TEST(testJacobi);
CPPUNIT_TEST(testIncompleteCholesky);
CPPUNIT_TEST(testVectorDotProduct);
CPPUNIT_TEST_SUITE_END();
void testJacobi();
void testIncompleteCholesky();
void testVectorDotProduct();
};
CPPUNIT_TEST_SUITE_REGISTRATION(TestConjGradient);
////////////////////////////////////////
void
TestConjGradient::testJacobi()
{
using namespace openvdb;
typedef math::pcg::SparseStencilMatrix<double, 7> MatrixType;
const math::pcg::SizeType rows = 5;
MatrixType A(rows);
A.setValue(0, 0, 24.0);
A.setValue(0, 2, 6.0);
A.setValue(1, 1, 8.0);
A.setValue(1, 2, 2.0);
A.setValue(2, 0, 6.0);
A.setValue(2, 1, 2.0);
A.setValue(2, 2, 8.0);
A.setValue(2, 3, -6.0);
A.setValue(2, 4, 2.0);
A.setValue(3, 2, -6.0);
A.setValue(3, 3, 24.0);
A.setValue(4, 2, 2.0);
A.setValue(4, 4, 8.0);
CPPUNIT_ASSERT(A.isFinite());
MatrixType::VectorType
x(rows, 0.0),
b(rows, 1.0),
expected(rows);
expected[0] = 0.0104167;
expected[1] = 0.09375;
expected[2] = 0.125;
expected[3] = 0.0729167;
expected[4] = 0.09375;
math::pcg::JacobiPreconditioner<MatrixType> precond(A);
// Solve A * x = b for x.
math::pcg::State result = math::pcg::solve(
A, b, x, precond, math::pcg::terminationDefaults<double>());
CPPUNIT_ASSERT(result.success);
CPPUNIT_ASSERT(result.iterations <= 20);
CPPUNIT_ASSERT(x.eq(expected, 1.0e-5));
}
void
TestConjGradient::testIncompleteCholesky()
{
using namespace openvdb;
typedef math::pcg::SparseStencilMatrix<double, 7> MatrixType;
typedef math::pcg::IncompleteCholeskyPreconditioner<MatrixType> CholeskyPrecond;
const math::pcg::SizeType rows = 5;
MatrixType A(5);
A.setValue(0, 0, 24.0);
A.setValue(0, 2, 6.0);
A.setValue(1, 1, 8.0);
A.setValue(1, 2, 2.0);
A.setValue(2, 0, 6.0);
A.setValue(2, 1, 2.0);
A.setValue(2, 2, 8.0);
A.setValue(2, 3, -6.0);
A.setValue(2, 4, 2.0);
A.setValue(3, 2, -6.0);
A.setValue(3, 3, 24.0);
A.setValue(4, 2, 2.0);
A.setValue(4, 4, 8.0);
CPPUNIT_ASSERT(A.isFinite());
CholeskyPrecond precond(A);
{
const CholeskyPrecond::TriangularMatrix lower = precond.lowerMatrix();
CholeskyPrecond::TriangularMatrix expected(5);
expected.setValue(0, 0, 4.89898);
expected.setValue(1, 1, 2.82843);
expected.setValue(2, 0, 1.22474);
expected.setValue(2, 1, 0.707107);
expected.setValue(2, 2, 2.44949);
expected.setValue(3, 2, -2.44949);
expected.setValue(3, 3, 4.24264);
expected.setValue(4, 2, 0.816497);
expected.setValue(4, 4, 2.70801);
#if 0
std::cout << "Expected:\n";
for (int i = 0; i < 5; ++i) {
std::cout << " " << expected.getConstRow(i).str() << std::endl;
}
std::cout << "Actual:\n";
for (int i = 0; i < 5; ++i) {
std::cout << " " << lower.getConstRow(i).str() << std::endl;
}
#endif
CPPUNIT_ASSERT(lower.eq(expected, 1.0e-5));
}
{
const CholeskyPrecond::TriangularMatrix upper = precond.upperMatrix();
CholeskyPrecond::TriangularMatrix expected(5);
{
expected.setValue(0, 0, 4.89898);
expected.setValue(0, 2, 1.22474);
expected.setValue(1, 1, 2.82843);
expected.setValue(1, 2, 0.707107);
expected.setValue(2, 2, 2.44949);
expected.setValue(2, 3, -2.44949);
expected.setValue(2, 4, 0.816497);
expected.setValue(3, 3, 4.24264);
expected.setValue(4, 4, 2.70801);
}
#if 0
std::cout << "Expected:\n";
for (int i = 0; i < 5; ++i) {
std::cout << " " << expected.getConstRow(i).str() << std::endl;
}
std::cout << "Actual:\n";
for (int i = 0; i < 5; ++i) {
std::cout << " " << upper.getConstRow(i).str() << std::endl;
}
#endif
CPPUNIT_ASSERT(upper.eq(expected, 1.0e-5));
}
MatrixType::VectorType
x(rows, 0.0),
b(rows, 1.0),
expected(rows);
expected[0] = 0.0104167;
expected[1] = 0.09375;
expected[2] = 0.125;
expected[3] = 0.0729167;
expected[4] = 0.09375;
// Solve A * x = b for x.
math::pcg::State result = math::pcg::solve(
A, b, x, precond, math::pcg::terminationDefaults<double>());
CPPUNIT_ASSERT(result.success);
CPPUNIT_ASSERT(result.iterations <= 20);
CPPUNIT_ASSERT(x.eq(expected, 1.0e-5));
}
void
TestConjGradient::testVectorDotProduct()
{
using namespace openvdb;
typedef math::pcg::Vector<double> VectorType;
// Test small vector - runs in series
{
const size_t length = 1000;
VectorType aVec(length, 2.0);
VectorType bVec(length, 3.0);
VectorType::ValueType result = aVec.dot(bVec);
CPPUNIT_ASSERT_DOUBLES_EQUAL(result, 6.0 * length, 1.0e-7);
}
// Test long vector - runs in parallel
{
const size_t length = 10034502;
VectorType aVec(length, 2.0);
VectorType bVec(length, 3.0);
VectorType::ValueType result = aVec.dot(bVec);
CPPUNIT_ASSERT_DOUBLES_EQUAL(result, 6.0 * length, 1.0e-7);
}
}
// Copyright (c) 2012-2018 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
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