Add a rough implementation of LBFGS.

Change-Id: I2bc816adfe0c02773a23035ea31de3cddc1322a4

include/ceres/types.h

@@ -167,6 +167,20 @@ enum LineSearchDirectionType {
   // precise choice of the non-linear conjugate gradient algorithm
   // used is determined by NonlineConjuateGradientType.
   NONLINEAR_CONJUGATE_GRADIENT,
+
+  // A limited memory approximation to the inverse Hessian is
+  // maintained and used to compute a quasi-Newton step.
+  //
+  // For more details see
+  //
+  // Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited
+  // Storage". Mathematics of Computation 35 (151): 773–782.
+  //
+  // Byrd, R. H.; Nocedal, J.; Schnabel, R. B. (1994).
+  // "Representations of Quasi-Newton Matrices and their use in
+  // Limited Memory Methods". Mathematical Programming 63 (4):
+  // 129–156.
+  LBFGS,
 };
 
 // Nonliner conjugate gradient methods are a generalization of the

internal/ceres/CMakeLists.txt

@@ -57,6 +57,7 @@ SET(CERES_INTERNAL_SRC
     gradient_checking_cost_function.cc
     implicit_schur_complement.cc
     iterative_schur_complement_solver.cc
+    lbfgs.cc
     levenberg_marquardt_strategy.cc
     line_search.cc
     line_search_minimizer.cc

internal/ceres/lbfgs.cc

@@ -0,0 +1,106 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// 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)
+
+#include "glog/logging.h"
+#include "ceres/lbfgs.h"
+#include "ceres/internal/eigen.h"
+
+namespace ceres {
+namespace internal {
+
+LBFGS::LBFGS(int num_parameters, int max_num_corrections)
+    : num_parameters_(num_parameters),
+      max_num_corrections_(max_num_corrections),
+      num_corrections_(0),
+      diagonal_(1.0),
+      delta_x_history_(num_parameters, max_num_corrections),
+      delta_gradient_history_(num_parameters, max_num_corrections),
+      delta_x_dot_delta_gradient_(max_num_corrections) {
+}
+
+bool LBFGS::Update(const Vector& delta_x, const Vector& delta_gradient) {
+  const double delta_x_dot_delta_gradient = delta_x.dot(delta_gradient);
+  if (delta_x_dot_delta_gradient <= 1e-10) {
+    VLOG(2) << "Skipping LBFGS Update. " << delta_x_dot_delta_gradient;
+    return false;
+  }
+
+  if (num_corrections_ == max_num_corrections_) {
+    // TODO(sameeragarwal): This can be done more efficiently using
+    // a circular buffer/indexing scheme, but for simplicity we will
+    // do the expensive copy for now.
+    delta_x_history_.block(0, 0, num_parameters_, max_num_corrections_ - 2) =
+        delta_x_history_
+        .block(0, 1, num_parameters_, max_num_corrections_ - 1);
+
+    delta_gradient_history_
+        .block(0, 0, num_parameters_, max_num_corrections_ - 2) =
+        delta_gradient_history_
+        .block(0, 1, num_parameters_, max_num_corrections_ - 1);
+
+    delta_x_dot_delta_gradient_.head(num_corrections_ - 2) =
+        delta_x_dot_delta_gradient_.tail(num_corrections_ - 1);
+  } else {
+    ++num_corrections_;
+  }
+
+  delta_x_history_.col(num_corrections_ - 1) = delta_x;
+  delta_gradient_history_.col(num_corrections_ - 1) = delta_gradient;
+  delta_x_dot_delta_gradient_(num_corrections_ - 1) =
+      delta_x_dot_delta_gradient;
+  diagonal_ = delta_x_dot_delta_gradient / delta_gradient.squaredNorm();
+  return true;
+}
+
+void LBFGS::RightMultiply(const double* x_ptr, double* y_ptr) const {
+  ConstVectorRef gradient(x_ptr, num_parameters_);
+  VectorRef search_direction(y_ptr, num_parameters_);
+
+  search_direction = gradient;
+
+  Vector alpha(num_corrections_);
+
+  for (int i = num_corrections_ - 1; i >= 0; --i) {
+    alpha(i) = delta_x_history_.col(i).dot(search_direction) /
+        delta_x_dot_delta_gradient_(i);
+    search_direction -= alpha(i) * delta_gradient_history_.col(i);
+  }
+
+  search_direction *= diagonal_;
+
+  for (int i = 0; i < num_corrections_; ++i) {
+    const double beta = delta_gradient_history_.col(i).dot(search_direction) /
+        delta_x_dot_delta_gradient_(i);
+    search_direction += delta_x_history_.col(i) * (alpha(i) - beta);
+  }
+}
+
+}  // namespace internal
+}  // namespace ceres

internal/ceres/lbfgs.h

@@ -0,0 +1,84 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// 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)
+//
+// Limited memory positive definite approximation to the inverse
+// Hessian, using the work of
+//
+// Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited
+// Storage". Mathematics of Computation 35 (151): 773–782.
+//
+// Byrd, R. H.; Nocedal, J.; Schnabel, R. B. (1994).
+// "Representations of Quasi-Newton Matrices and their use in
+// Limited Memory Methods". Mathematical Programming 63 (4):
+
+#include "ceres/internal/eigen.h"
+#include "ceres/linear_operator.h"
+
+namespace ceres {
+namespace internal {
+
+// Right multiplying with an LBFGS operator is equivalent to
+// multiplying by the inverse Hessian.
+class LBFGS : public LinearOperator {
+ public:
+  // num_parameters is the row/column size of the Hessian.
+  // max_num_corrections is the rank of the Hessian approximation.
+  // The approximation uses:
+  // 2 * max_num_corrections * num_parameters + max_num_corrections
+  // doubles.
+  LBFGS(int num_parameters, int max_num_corrections);
+  virtual ~LBFGS() {}
+
+  // Update the low rank approximation, i.e. store delta_x and
+  // delta_gradient, and get rid of the oldest delta_x and
+  // delta_gradient vectors if the number of corrections is already
+  // equal to max_num_corrections.
+  bool Update(const Vector& delta_x, const Vector& delta_gradient);
+
+  // LinearOperator interface
+  virtual void RightMultiply(const double* x, double* y) const;
+  virtual void LeftMultiply(const double* x, double* y) const {
+    RightMultiply(x,y);
+  }
+  virtual int num_rows() const { return num_parameters_; }
+  virtual int num_cols() const { return num_parameters_; }
+
+ private:
+  const int num_parameters_;
+  const int max_num_corrections_;
+  int num_corrections_;
+  double diagonal_;
+  Matrix delta_x_history_;
+  Matrix delta_gradient_history_;
+  Vector delta_x_dot_delta_gradient_;
+};
+
+}  // namespace internal
+}  // namespace ceres

internal/ceres/line_search.cc

@@ -73,7 +73,7 @@ LineSearchFunction::LineSearchFunction(Evaluator* evaluator)
 }
 
 void LineSearchFunction::Init(const Vector& position,
-                               const Vector& direction) {
+                              const Vector& direction) {
   position_ = position;
   direction_ = direction;
 }

internal/ceres/line_search_minimizer.cc

@@ -51,6 +51,7 @@
 
 #include "Eigen/Dense"
 #include "ceres/array_utils.h"
+#include "ceres/lbfgs.h"
 #include "ceres/evaluator.h"
 #include "ceres/internal/eigen.h"
 #include "ceres/internal/scoped_ptr.h"
@@ -191,6 +192,11 @@ void LineSearchMinimizer::Minimize(const Minimizer::Options& options,
   ArmijoLineSearch line_search;
   LineSearch::Summary line_search_summary;
 
+  scoped_ptr<LBFGS> lbfgs;
+  if (options_.line_search_direction_type == ceres::LBFGS) {
+    lbfgs.reset(new LBFGS(num_effective_parameters, 20));
+  }
+
   while (true) {
     iteration_start_time = WallTimeInSeconds();
     if (iteration_summary.iteration >= options_.max_num_iterations) {
@@ -218,6 +224,11 @@ void LineSearchMinimizer::Minimize(const Minimizer::Options& options,
       search_direction = -gradient;
       directional_derivative = -gradient_squared_norm;
     } else {
+
+      if (lbfgs.get() != NULL) {
+        lbfgs->Update(delta, gradient_change);
+      }
+
       // TODO(sameeragarwal): This should probably be refactored into
       // a set of functions. But we will do that once things settle
       // down in this solver.
@@ -266,6 +277,13 @@ void LineSearchMinimizer::Minimize(const Minimizer::Options& options,
           }
           break;
 
+        case ceres::LBFGS:
+          search_direction.setZero();
+          lbfgs->RightMultiply(gradient.data(), search_direction.data());
+          search_direction *= -1.0;
+          directional_derivative =  gradient.dot(search_direction);
+          break;
+
         default:
           LOG(FATAL) << "Unknown line search direction type: "
                      << options_.line_search_direction_type;