// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// this list of conditions and the following disclaimer.
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// this list of conditions and the following disclaimer in the documentation
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//
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//
// 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/internal/macros.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 {
double x1[5];
double x2[5];
} 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 < CERES_ARRAYSIZE(kTests); ++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.
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 < CERES_ARRAYSIZE(kTests); ++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 {
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 < CERES_ARRAYSIZE(kTests); ++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