Squashed 'third_party/ceres/' content from commit e51e9b4
Change-Id: I763587619d57e594d3fa158dc3a7fe0b89a1743b
git-subtree-dir: third_party/ceres
git-subtree-split: e51e9b46f6ca88ab8b2266d0e362771db6d98067
diff --git a/internal/ceres/numeric_diff_test_utils.cc b/internal/ceres/numeric_diff_test_utils.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. 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 DIRECT, 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.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+// tbennun@gmail.com (Tal Ben-Nun)
+
+#include "ceres/numeric_diff_test_utils.h"
+
+#include <algorithm>
+#include <cmath>
+#include "ceres/cost_function.h"
+#include "ceres/test_util.h"
+#include "ceres/types.h"
+#include "gtest/gtest.h"
+
+
+namespace ceres {
+namespace internal {
+
+bool EasyFunctor::operator()(const double* x1,
+ const double* x2,
+ double* residuals) const {
+ residuals[0] = residuals[1] = residuals[2] = 0;
+ for (int i = 0; i < 5; ++i) {
+ residuals[0] += x1[i] * x2[i];
+ residuals[2] += x2[i] * x2[i];
+ }
+ residuals[1] = residuals[0] * residuals[0];
+ return true;
+}
+
+void EasyFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function,
+ NumericDiffMethodType method) const {
+ // The x1[0] is made deliberately small to test the performance near
+ // zero.
+ double x1[] = { 1e-64, 2.0, 3.0, 4.0, 5.0 };
+ double x2[] = { 9.0, 9.0, 5.0, 5.0, 1.0 };
+ double *parameters[] = { &x1[0], &x2[0] };
+
+ double dydx1[15]; // 3 x 5, row major.
+ double dydx2[15]; // 3 x 5, row major.
+ double *jacobians[2] = { &dydx1[0], &dydx2[0] };
+
+ double residuals[3] = {-1e-100, -2e-100, -3e-100 };
+
+ ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
+ &residuals[0],
+ &jacobians[0]));
+
+ double expected_residuals[3];
+ EasyFunctor functor;
+ functor(x1, x2, expected_residuals);
+ EXPECT_EQ(expected_residuals[0], residuals[0]);
+ EXPECT_EQ(expected_residuals[1], residuals[1]);
+ EXPECT_EQ(expected_residuals[2], residuals[2]);
+
+ double tolerance = 0.0;
+ switch (method) {
+ default:
+ case CENTRAL:
+ tolerance = 3e-9;
+ break;
+
+ case FORWARD:
+ tolerance = 2e-5;
+ break;
+
+ case RIDDERS:
+ tolerance = 1e-13;
+ break;
+ }
+
+ for (int i = 0; i < 5; ++i) {
+ ExpectClose(x2[i], dydx1[5 * 0 + i], tolerance); // y1
+ ExpectClose(x1[i], dydx2[5 * 0 + i], tolerance);
+ ExpectClose(2 * x2[i] * residuals[0], dydx1[5 * 1 + i], tolerance); // y2
+ ExpectClose(2 * x1[i] * residuals[0], dydx2[5 * 1 + i], tolerance);
+ ExpectClose(0.0, dydx1[5 * 2 + i], tolerance); // y3
+ ExpectClose(2 * x2[i], dydx2[5 * 2 + i], tolerance);
+ }
+}
+
+bool TranscendentalFunctor::operator()(const double* x1,
+ const double* x2,
+ double* residuals) const {
+ double x1x2 = 0;
+ for (int i = 0; i < 5; ++i) {
+ x1x2 += x1[i] * x2[i];
+ }
+ residuals[0] = sin(x1x2);
+ residuals[1] = exp(-x1x2 / 10);
+ return true;
+}
+
+void TranscendentalFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function,
+ NumericDiffMethodType method) const {
+
+ struct TestParameterBlocks {
+ double x1[5];
+ double x2[5];
+ };
+
+ std::vector<TestParameterBlocks> kTests = {
+ { { 1.0, 2.0, 3.0, 4.0, 5.0 }, // No zeros.
+ { 9.0, 9.0, 5.0, 5.0, 1.0 },
+ },
+ { { 0.0, 2.0, 3.0, 0.0, 5.0 }, // Some zeros x1.
+ { 9.0, 9.0, 5.0, 5.0, 1.0 },
+ },
+ { { 1.0, 2.0, 3.0, 1.0, 5.0 }, // Some zeros x2.
+ { 0.0, 9.0, 0.0, 5.0, 0.0 },
+ },
+ { { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros x1.
+ { 9.0, 9.0, 5.0, 5.0, 1.0 },
+ },
+ { { 1.0, 2.0, 3.0, 4.0, 5.0 }, // All zeros x2.
+ { 0.0, 0.0, 0.0, 0.0, 0.0 },
+ },
+ { { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros.
+ { 0.0, 0.0, 0.0, 0.0, 0.0 },
+ },
+ };
+
+ for (int k = 0; k < kTests.size(); ++k) {
+ double *x1 = &(kTests[k].x1[0]);
+ double *x2 = &(kTests[k].x2[0]);
+ double *parameters[] = { x1, x2 };
+
+ double dydx1[10];
+ double dydx2[10];
+ double *jacobians[2] = { &dydx1[0], &dydx2[0] };
+
+ double residuals[2];
+
+ ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
+ &residuals[0],
+ &jacobians[0]));
+ double x1x2 = 0;
+ for (int i = 0; i < 5; ++i) {
+ x1x2 += x1[i] * x2[i];
+ }
+
+ double tolerance = 0.0;
+ switch (method) {
+ default:
+ case CENTRAL:
+ tolerance = 2e-7;
+ break;
+
+ case FORWARD:
+ tolerance = 2e-5;
+ break;
+
+ case RIDDERS:
+ tolerance = 3e-12;
+ break;
+ }
+
+ for (int i = 0; i < 5; ++i) {
+ ExpectClose( x2[i] * cos(x1x2), dydx1[5 * 0 + i], tolerance);
+ ExpectClose( x1[i] * cos(x1x2), dydx2[5 * 0 + i], tolerance);
+ ExpectClose(-x2[i] * exp(-x1x2 / 10.) / 10., dydx1[5 * 1 + i], tolerance);
+ ExpectClose(-x1[i] * exp(-x1x2 / 10.) / 10., dydx2[5 * 1 + i], tolerance);
+ }
+ }
+}
+
+bool ExponentialFunctor::operator()(const double* x1,
+ double* residuals) const {
+ residuals[0] = exp(x1[0]);
+ return true;
+}
+
+
+void ExponentialFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function) const {
+ // Evaluating the functor at specific points for testing.
+ std::vector<double> kTests = { 1.0, 2.0, 3.0, 4.0, 5.0 };
+
+ // Minimal tolerance w.r.t. the cost function and the tests.
+ const double kTolerance = 2e-14;
+
+ for (int k = 0; k < kTests.size(); ++k) {
+ double *parameters[] = { &kTests[k] };
+ double dydx;
+ double *jacobians[1] = { &dydx };
+ double residual;
+
+ ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
+ &residual,
+ &jacobians[0]));
+
+
+ double expected_result = exp(kTests[k]);
+
+ // Expect residual to be close to exp(x).
+ ExpectClose(residual, expected_result, kTolerance);
+
+ // Check evaluated differences. dydx should also be close to exp(x).
+ ExpectClose(dydx, expected_result, kTolerance);
+ }
+}
+
+bool RandomizedFunctor::operator()(const double* x1,
+ double* residuals) const {
+ double random_value = static_cast<double>(rand()) /
+ static_cast<double>(RAND_MAX);
+
+ // Normalize noise to [-factor, factor].
+ random_value *= 2.0;
+ random_value -= 1.0;
+ random_value *= noise_factor_;
+
+ residuals[0] = x1[0] * x1[0] + random_value;
+ return true;
+}
+
+void RandomizedFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function) const {
+ std::vector<double> kTests = { 0.0, 1.0, 3.0, 4.0, 50.0 };
+
+ const double kTolerance = 2e-4;
+
+ // Initialize random number generator with given seed.
+ srand(random_seed_);
+
+ for (int k = 0; k < kTests.size(); ++k) {
+ double *parameters[] = { &kTests[k] };
+ double dydx;
+ double *jacobians[1] = { &dydx };
+ double residual;
+
+ ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
+ &residual,
+ &jacobians[0]));
+
+ // Expect residual to be close to x^2 w.r.t. noise factor.
+ ExpectClose(residual, kTests[k] * kTests[k], noise_factor_);
+
+ // Check evaluated differences. (dy/dx = ~2x)
+ ExpectClose(dydx, 2 * kTests[k], kTolerance);
+ }
+}
+
+} // namespace internal
+} // namespace ceres