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-// Ceres Solver - A fast non-linear least squares minimizer
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-// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
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-// http://code.google.com/p/ceres-solver/
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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: keir@google.com (Keir Mierle)
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-//
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-// Based on the tests in numeric_diff_cost_function.cc.
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-//
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-// TODO(keir): See about code duplication.
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-
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-#include "ceres/runtime_numeric_diff_cost_function.h"
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-
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-#include <algorithm>
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-#include <cmath>
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-#include <string>
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-#include <vector>
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-#include "ceres/cost_function.h"
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-#include "ceres/internal/macros.h"
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-#include "ceres/internal/scoped_ptr.h"
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-#include "ceres/stringprintf.h"
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-#include "ceres/test_util.h"
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-#include "glog/logging.h"
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-#include "gtest/gtest.h"
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-
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-namespace ceres {
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-namespace internal {
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-
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-const double kRelativeEps = 1e-6;
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-
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-// y1 = x1'x2 -> dy1/dx1 = x2, dy1/dx2 = x1
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-// y2 = (x1'x2)^2 -> dy2/dx1 = 2 * x2 * (x1'x2), dy2/dx2 = 2 * x1 * (x1'x2)
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-// y3 = x2'x2 -> dy3/dx1 = 0, dy3/dx2 = 2 * x2
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-class TestCostFunction : public CostFunction {
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- public:
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- TestCostFunction() {
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- set_num_residuals(3);
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- mutable_parameter_block_sizes()->push_back(5); // x1.
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- mutable_parameter_block_sizes()->push_back(5); // x2.
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- }
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- virtual bool Evaluate(double const* const* parameters,
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- double* residuals,
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- double** jacobians) const {
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- (void) jacobians; // Ignored.
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-
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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] += parameters[0][i] * parameters[1][i];
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- residuals[2] += parameters[1][i] * parameters[1][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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-};
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-
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-TEST(NumericDiffCostFunction, EasyCase) {
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- // Try both central and forward difference.
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- TestCostFunction term;
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- scoped_ptr<CostFunction> cfs[2];
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- cfs[0].reset(
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- CreateRuntimeNumericDiffCostFunction(&term, CENTRAL, kRelativeEps));
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-
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- cfs[1].reset(
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- CreateRuntimeNumericDiffCostFunction(&term, FORWARD, kRelativeEps));
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-
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-
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- for (int c = 0; c < 2; ++c) {
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- CostFunction *cost_function = cfs[c].get();
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-
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- double x1[] = { 1.0, 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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-
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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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-
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- double residuals[3] = {-1e-100, -2e-100, -3e-100 };
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-
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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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-
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- EXPECT_EQ(residuals[0], 67);
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- EXPECT_EQ(residuals[1], 4489);
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- EXPECT_EQ(residuals[2], 213);
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-
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- for (int i = 0; i < 5; ++i) {
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- LOG(INFO) << "c = " << c << " i = " << i;
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- const double kEps = c == 0 ? /* central */ 3e-9 : /* forward */ 2e-5;
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-
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- ExpectClose(x2[i], dydx1[5 * 0 + i], kEps); // y1
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- ExpectClose(x1[i], dydx2[5 * 0 + i], kEps);
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- ExpectClose(2 * x2[i] * residuals[0], dydx1[5 * 1 + i], kEps); // y2
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- ExpectClose(2 * x1[i] * residuals[0], dydx2[5 * 1 + i], kEps);
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- ExpectClose(0.0, dydx1[5 * 2 + i], kEps); // y3
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- ExpectClose(2 * x2[i], dydx2[5 * 2 + i], kEps);
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- }
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- }
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-}
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-
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-// y1 = sin(x1'x2)
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-// y2 = exp(-x1'x2 / 10)
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-//
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-// dy1/dx1 = x2 * cos(x1'x2), dy1/dx2 = x1 * cos(x1'x2)
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-// dy2/dx1 = -x2 * exp(-x1'x2 / 10) / 10, dy2/dx2 = -x2 * exp(-x1'x2 / 10) / 10
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-class TranscendentalTestCostFunction : public CostFunction {
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- public:
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- TranscendentalTestCostFunction() {
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- set_num_residuals(2);
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- mutable_parameter_block_sizes()->push_back(5); // x1.
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- mutable_parameter_block_sizes()->push_back(5); // x2.
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- }
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- virtual bool Evaluate(double const* const* parameters,
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- double* residuals,
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- double** jacobians) const {
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- (void) jacobians; // Ignored.
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-
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- double x1x2 = 0;
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- for (int i = 0; i < 5; ++i) {
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- x1x2 += parameters[0][i] * parameters[1][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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-};
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-
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-TEST(NumericDiffCostFunction, TransendentalOperationsInCostFunction) {
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- // Try both central and forward difference.
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- TranscendentalTestCostFunction term;
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- scoped_ptr<CostFunction> cfs[2];
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- cfs[0].reset(
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- CreateRuntimeNumericDiffCostFunction(&term, CENTRAL, kRelativeEps));
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-
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- cfs[1].reset(
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- CreateRuntimeNumericDiffCostFunction(&term, FORWARD, kRelativeEps));
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-
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- for (int c = 0; c < 2; ++c) {
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- CostFunction *cost_function = cfs[c].get();
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-
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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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-
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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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-
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- double residuals[2];
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-
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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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- LOG(INFO) << "Ran evaluate for test k=" << k << " c=" << c;
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-
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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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-
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- for (int i = 0; i < 5; ++i) {
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- const double kEps = (c == 0 ? /* central */ 3e-9 : /* forward */ 2e-5);
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-
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- ExpectClose( x2[i] * cos(x1x2), dydx1[5 * 0 + i], kEps); // NOLINT
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- ExpectClose( x1[i] * cos(x1x2), dydx2[5 * 0 + i], kEps); // NOLINT
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- ExpectClose(-x2[i] * exp(-x1x2 / 10.) / 10., dydx1[5 * 1 + i], kEps);
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- ExpectClose(-x1[i] * exp(-x1x2 / 10.) / 10., dydx2[5 * 1 + i], kEps);
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- }
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- }
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- }
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-}
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-
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-} // namespace internal
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-} // namespace ceres
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Sameer Agarwal