271 lines
8.6 KiB
C++
271 lines
8.6 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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// tbennun@gmail.com (Tal Ben-Nun)
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#include "ceres/numeric_diff_test_utils.h"
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#include <algorithm>
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#include <cmath>
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#include "ceres/cost_function.h"
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#include "ceres/internal/macros.h"
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#include "ceres/test_util.h"
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#include "ceres/types.h"
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#include "gtest/gtest.h"
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namespace ceres {
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namespace internal {
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bool EasyFunctor::operator()(const double* x1,
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const double* x2,
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double* residuals) const {
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residuals[0] = residuals[1] = residuals[2] = 0;
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for (int i = 0; i < 5; ++i) {
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residuals[0] += x1[i] * x2[i];
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residuals[2] += x2[i] * x2[i];
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}
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residuals[1] = residuals[0] * residuals[0];
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return true;
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}
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void EasyFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
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const CostFunction& cost_function,
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NumericDiffMethodType method) const {
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// The x1[0] is made deliberately small to test the performance near
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// zero.
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double x1[] = { 1e-64, 2.0, 3.0, 4.0, 5.0 };
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double x2[] = { 9.0, 9.0, 5.0, 5.0, 1.0 };
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double *parameters[] = { &x1[0], &x2[0] };
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double dydx1[15]; // 3 x 5, row major.
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double dydx2[15]; // 3 x 5, row major.
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double *jacobians[2] = { &dydx1[0], &dydx2[0] };
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double residuals[3] = {-1e-100, -2e-100, -3e-100 };
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ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
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&residuals[0],
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&jacobians[0]));
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double expected_residuals[3];
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EasyFunctor functor;
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functor(x1, x2, expected_residuals);
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EXPECT_EQ(expected_residuals[0], residuals[0]);
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EXPECT_EQ(expected_residuals[1], residuals[1]);
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EXPECT_EQ(expected_residuals[2], residuals[2]);
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double tolerance = 0.0;
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switch (method) {
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default:
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case CENTRAL:
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tolerance = 3e-9;
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break;
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case FORWARD:
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tolerance = 2e-5;
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break;
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case RIDDERS:
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tolerance = 1e-13;
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break;
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}
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for (int i = 0; i < 5; ++i) {
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ExpectClose(x2[i], dydx1[5 * 0 + i], tolerance); // y1
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ExpectClose(x1[i], dydx2[5 * 0 + i], tolerance);
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ExpectClose(2 * x2[i] * residuals[0], dydx1[5 * 1 + i], tolerance); // y2
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ExpectClose(2 * x1[i] * residuals[0], dydx2[5 * 1 + i], tolerance);
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ExpectClose(0.0, dydx1[5 * 2 + i], tolerance); // y3
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ExpectClose(2 * x2[i], dydx2[5 * 2 + i], tolerance);
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}
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}
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bool TranscendentalFunctor::operator()(const double* x1,
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const double* x2,
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double* residuals) const {
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double x1x2 = 0;
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for (int i = 0; i < 5; ++i) {
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x1x2 += x1[i] * x2[i];
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}
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residuals[0] = sin(x1x2);
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residuals[1] = exp(-x1x2 / 10);
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return true;
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}
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void TranscendentalFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
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const CostFunction& cost_function,
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NumericDiffMethodType method) const {
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struct {
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double x1[5];
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double x2[5];
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} kTests[] = {
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{ { 1.0, 2.0, 3.0, 4.0, 5.0 }, // No zeros.
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{ 9.0, 9.0, 5.0, 5.0, 1.0 },
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},
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{ { 0.0, 2.0, 3.0, 0.0, 5.0 }, // Some zeros x1.
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{ 9.0, 9.0, 5.0, 5.0, 1.0 },
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},
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{ { 1.0, 2.0, 3.0, 1.0, 5.0 }, // Some zeros x2.
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{ 0.0, 9.0, 0.0, 5.0, 0.0 },
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},
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{ { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros x1.
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{ 9.0, 9.0, 5.0, 5.0, 1.0 },
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},
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{ { 1.0, 2.0, 3.0, 4.0, 5.0 }, // All zeros x2.
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{ 0.0, 0.0, 0.0, 0.0, 0.0 },
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},
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{ { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros.
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{ 0.0, 0.0, 0.0, 0.0, 0.0 },
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},
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};
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for (int k = 0; k < CERES_ARRAYSIZE(kTests); ++k) {
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double *x1 = &(kTests[k].x1[0]);
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double *x2 = &(kTests[k].x2[0]);
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double *parameters[] = { x1, x2 };
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double dydx1[10];
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double dydx2[10];
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double *jacobians[2] = { &dydx1[0], &dydx2[0] };
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double residuals[2];
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ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
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&residuals[0],
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&jacobians[0]));
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double x1x2 = 0;
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for (int i = 0; i < 5; ++i) {
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x1x2 += x1[i] * x2[i];
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}
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double tolerance = 0.0;
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switch (method) {
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default:
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case CENTRAL:
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tolerance = 2e-7;
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break;
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case FORWARD:
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tolerance = 2e-5;
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break;
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case RIDDERS:
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tolerance = 3e-12;
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break;
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}
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for (int i = 0; i < 5; ++i) {
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ExpectClose( x2[i] * cos(x1x2), dydx1[5 * 0 + i], tolerance);
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ExpectClose( x1[i] * cos(x1x2), dydx2[5 * 0 + i], tolerance);
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ExpectClose(-x2[i] * exp(-x1x2 / 10.) / 10., dydx1[5 * 1 + i], tolerance);
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ExpectClose(-x1[i] * exp(-x1x2 / 10.) / 10., dydx2[5 * 1 + i], tolerance);
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}
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}
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}
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bool ExponentialFunctor::operator()(const double* x1,
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double* residuals) const {
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residuals[0] = exp(x1[0]);
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return true;
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}
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void ExponentialFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
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const CostFunction& cost_function) const {
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// Evaluating the functor at specific points for testing.
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double kTests[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
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// Minimal tolerance w.r.t. the cost function and the tests.
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const double kTolerance = 2e-14;
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for (int k = 0; k < CERES_ARRAYSIZE(kTests); ++k) {
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double *parameters[] = { &kTests[k] };
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double dydx;
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double *jacobians[1] = { &dydx };
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double residual;
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ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
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&residual,
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&jacobians[0]));
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double expected_result = exp(kTests[k]);
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// Expect residual to be close to exp(x).
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ExpectClose(residual, expected_result, kTolerance);
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// Check evaluated differences. dydx should also be close to exp(x).
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ExpectClose(dydx, expected_result, kTolerance);
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}
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}
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bool RandomizedFunctor::operator()(const double* x1,
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double* residuals) const {
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double random_value = static_cast<double>(rand()) /
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static_cast<double>(RAND_MAX);
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// Normalize noise to [-factor, factor].
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random_value *= 2.0;
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random_value -= 1.0;
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random_value *= noise_factor_;
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residuals[0] = x1[0] * x1[0] + random_value;
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return true;
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}
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void RandomizedFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
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const CostFunction& cost_function) const {
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double kTests[] = { 0.0, 1.0, 3.0, 4.0, 50.0 };
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const double kTolerance = 2e-4;
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// Initialize random number generator with given seed.
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srand(random_seed_);
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for (int k = 0; k < CERES_ARRAYSIZE(kTests); ++k) {
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double *parameters[] = { &kTests[k] };
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double dydx;
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double *jacobians[1] = { &dydx };
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double residual;
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ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
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&residual,
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&jacobians[0]));
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// Expect residual to be close to x^2 w.r.t. noise factor.
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ExpectClose(residual, kTests[k] * kTests[k], noise_factor_);
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// Check evaluated differences. (dy/dx = ~2x)
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ExpectClose(dydx, 2 * kTests[k], kTolerance);
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}
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}
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} // namespace internal
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} // namespace ceres
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