// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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//
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// Copyright 2007 Google Inc. All Rights Reserved.
//
// Author: wjr@google.com (William Rucklidge)
//
// This file contains a class that exercises a cost function, to make sure
// that it is computing reasonable derivatives. It compares the Jacobians
// computed by the cost function with those obtained by finite
// differences.
#ifndef CERES_PUBLIC_GRADIENT_CHECKER_H_
#define CERES_PUBLIC_GRADIENT_CHECKER_H_
#include <cstddef>
#include <algorithm>
#include <vector>
#include "ceres/internal/eigen.h"
#include "ceres/internal/fixed_array.h"
#include "ceres/internal/macros.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/numeric_diff_cost_function.h"
#include "glog/logging.h"
namespace ceres {
// An object that exercises a cost function, to compare the answers that it
// gives with derivatives estimated using finite differencing.
//
// The only likely usage of this is for testing.
//
// How to use: Fill in an array of pointers to parameter blocks for your
// CostFunction, and then call Probe(). Check that the return value is
// 'true'. See prober_test.cc for an example.
//
// This is templated similarly to NumericDiffCostFunction, as it internally
// uses that.
template <typename CostFunctionToProbe,
int M = 0, int N0 = 0, int N1 = 0, int N2 = 0, int N3 = 0, int N4 = 0>
class GradientChecker {
public:
// Here we stash some results from the probe, for later
// inspection.
struct GradientCheckResults {
// Computed cost.
Vector cost;
// The sizes of these matrices are dictated by the cost function's
// parameter and residual block sizes. Each vector's length will
// term->parameter_block_sizes().size(), and each matrix is the
// Jacobian of the residual with respect to the corresponding parameter
// block.
// Derivatives as computed by the cost function.
vector<Matrix> term_jacobians;
// Derivatives as computed by finite differencing.
vector<Matrix> finite_difference_jacobians;
// Infinity-norm of term_jacobians - finite_difference_jacobians.
double error_jacobians;
};
// Checks the Jacobian computed by a cost function.
//
// probe_point: The parameter values at which to probe.
// error_tolerance: A threshold for the infinity-norm difference
// between the Jacobians. If the Jacobians differ by more than
// this amount, then the probe fails.
//
// term: The cost function to test. Not retained after this call returns.
//
// results: On return, the two Jacobians (and other information)
// will be stored here. May be NULL.
//
// Returns true if no problems are detected and the difference between the
// Jacobians is less than error_tolerance.
static bool Probe(double const* const* probe_point,
double error_tolerance,
CostFunctionToProbe *term,
GradientCheckResults* results) {
CHECK_NOTNULL(probe_point);
CHECK_NOTNULL(term);
LOG(INFO) << "-------------------- Starting Probe() --------------------";
// We need a GradientCheckeresults, whether or not they supplied one.
internal::scoped_ptr<GradientCheckResults> owned_results;
if (results == NULL) {
owned_results.reset(new GradientCheckResults);
results = owned_results.get();
}
// Do a consistency check between the term and the template parameters.
CHECK_EQ(M, term->num_residuals());
const int num_residuals = M;
const vector<int32>& block_sizes = term->parameter_block_sizes();
const int num_blocks = block_sizes.size();
CHECK_LE(num_blocks, 5) << "Unable to test functions that take more "
<< "than 5 parameter blocks";
if (N0) {
CHECK_EQ(N0, block_sizes[0]);
CHECK_GE(num_blocks, 1);
} else {
CHECK_LT(num_blocks, 1);
}
if (N1) {
CHECK_EQ(N1, block_sizes[1]);
CHECK_GE(num_blocks, 2);
} else {
CHECK_LT(num_blocks, 2);
}
if (N2) {
CHECK_EQ(N2, block_sizes[2]);
CHECK_GE(num_blocks, 3);
} else {
CHECK_LT(num_blocks, 3);
}
if (N3) {
CHECK_EQ(N3, block_sizes[3]);
CHECK_GE(num_blocks, 4);
} else {
CHECK_LT(num_blocks, 4);
}
if (N4) {
CHECK_EQ(N4, block_sizes[4]);
CHECK_GE(num_blocks, 5);
} else {
CHECK_LT(num_blocks, 5);
}
results->term_jacobians.clear();
results->term_jacobians.resize(num_blocks);
results->finite_difference_jacobians.clear();
results->finite_difference_jacobians.resize(num_blocks);
internal::FixedArray<double*> term_jacobian_pointers(num_blocks);
internal::FixedArray<double*>
finite_difference_jacobian_pointers(num_blocks);
for (int i = 0; i < num_blocks; i++) {
results->term_jacobians[i].resize(num_residuals, block_sizes[i]);
term_jacobian_pointers[i] = results->term_jacobians[i].data();
results->finite_difference_jacobians[i].resize(
num_residuals, block_sizes[i]);
finite_difference_jacobian_pointers[i] =
results->finite_difference_jacobians[i].data();
}
results->cost.resize(num_residuals, 1);
CHECK(term->Evaluate(probe_point, results->cost.data(),
term_jacobian_pointers.get()));
NumericDiffCostFunction<CostFunctionToProbe, CENTRAL, M, N0, N1, N2, N3, N4>
numeric_term(term, DO_NOT_TAKE_OWNERSHIP);
CHECK(numeric_term.Evaluate(probe_point, results->cost.data(),
finite_difference_jacobian_pointers.get()));
results->error_jacobians = 0;
for (int i = 0; i < num_blocks; i++) {
Matrix jacobian_difference = results->term_jacobians[i] -
results->finite_difference_jacobians[i];
results->error_jacobians =
std::max(results->error_jacobians,
jacobian_difference.lpNorm<Eigen::Infinity>());
}
LOG(INFO) << "========== term-computed derivatives ==========";
for (int i = 0; i < num_blocks; i++) {
LOG(INFO) << "term_computed block " << i;
LOG(INFO) << "\n" << results->term_jacobians[i];
}
LOG(INFO) << "========== finite-difference derivatives ==========";
for (int i = 0; i < num_blocks; i++) {
LOG(INFO) << "finite_difference block " << i;
LOG(INFO) << "\n" << results->finite_difference_jacobians[i];
}
LOG(INFO) << "========== difference ==========";
for (int i = 0; i < num_blocks; i++) {
LOG(INFO) << "difference block " << i;
LOG(INFO) << (results->term_jacobians[i] -
results->finite_difference_jacobians[i]);
}
LOG(INFO) << "||difference|| = " << results->error_jacobians;
return results->error_jacobians < error_tolerance;
}
private:
CERES_DISALLOW_IMPLICIT_CONSTRUCTORS(GradientChecker);
};
} // namespace ceres
#endif // CERES_PUBLIC_GRADIENT_CHECKER_H_