add liblbfgs, which is much less crappy than the current one

1 files changed, 745 insertions, 0 deletions

diff --git a/training/liblbfgs/lbfgs.h b/training/liblbfgs/lbfgs.h
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+/*
+ *      C library of Limited memory BFGS (L-BFGS).
+ *
+ * Copyright (c) 1990, Jorge Nocedal
+ * Copyright (c) 2007-2010 Naoaki Okazaki
+ * All rights reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+
+/* $Id$ */
+
+#ifndef __LBFGS_H__
+#define __LBFGS_H__
+
+#ifdef  __cplusplus
+extern "C" {
+#endif/*__cplusplus*/
+
+/*
+ * The default precision of floating point values is 64bit (double).
+ */
+#ifndef LBFGS_FLOAT
+#define LBFGS_FLOAT     64
+#endif/*LBFGS_FLOAT*/
+
+/*
+ * Activate optimization routines for IEEE754 floating point values.
+ */
+#ifndef LBFGS_IEEE_FLOAT
+#define LBFGS_IEEE_FLOAT    1
+#endif/*LBFGS_IEEE_FLOAT*/
+
+#if     LBFGS_FLOAT == 32
+typedef float lbfgsfloatval_t;
+
+#elif   LBFGS_FLOAT == 64
+typedef double lbfgsfloatval_t;
+
+#else
+#error "libLBFGS supports single (float; LBFGS_FLOAT = 32) or double (double; LBFGS_FLOAT=64) precision only."
+
+#endif
+
+
+/** 
+ * \addtogroup liblbfgs_api libLBFGS API
+ * @{
+ *
+ *  The libLBFGS API.
+ */
+
+/**
+ * Return values of lbfgs().
+ * 
+ *  Roughly speaking, a negative value indicates an error.
+ */
+enum {
+    /** L-BFGS reaches convergence. */
+    LBFGS_SUCCESS = 0,
+    LBFGS_CONVERGENCE = 0,
+    LBFGS_STOP,
+    /** The initial variables already minimize the objective function. */
+    LBFGS_ALREADY_MINIMIZED,
+
+    /** Unknown error. */
+    LBFGSERR_UNKNOWNERROR = -1024,
+    /** Logic error. */
+    LBFGSERR_LOGICERROR,
+    /** Insufficient memory. */
+    LBFGSERR_OUTOFMEMORY,
+    /** The minimization process has been canceled. */
+    LBFGSERR_CANCELED,
+    /** Invalid number of variables specified. */
+    LBFGSERR_INVALID_N,
+    /** Invalid number of variables (for SSE) specified. */
+    LBFGSERR_INVALID_N_SSE,
+    /** The array x must be aligned to 16 (for SSE). */
+    LBFGSERR_INVALID_X_SSE,
+    /** Invalid parameter lbfgs_parameter_t::epsilon specified. */
+    LBFGSERR_INVALID_EPSILON,
+    /** Invalid parameter lbfgs_parameter_t::past specified. */
+    LBFGSERR_INVALID_TESTPERIOD,
+    /** Invalid parameter lbfgs_parameter_t::delta specified. */
+    LBFGSERR_INVALID_DELTA,
+    /** Invalid parameter lbfgs_parameter_t::linesearch specified. */
+    LBFGSERR_INVALID_LINESEARCH,
+    /** Invalid parameter lbfgs_parameter_t::max_step specified. */
+    LBFGSERR_INVALID_MINSTEP,
+    /** Invalid parameter lbfgs_parameter_t::max_step specified. */
+    LBFGSERR_INVALID_MAXSTEP,
+    /** Invalid parameter lbfgs_parameter_t::ftol specified. */
+    LBFGSERR_INVALID_FTOL,
+    /** Invalid parameter lbfgs_parameter_t::wolfe specified. */
+    LBFGSERR_INVALID_WOLFE,
+    /** Invalid parameter lbfgs_parameter_t::gtol specified. */
+    LBFGSERR_INVALID_GTOL,
+    /** Invalid parameter lbfgs_parameter_t::xtol specified. */
+    LBFGSERR_INVALID_XTOL,
+    /** Invalid parameter lbfgs_parameter_t::max_linesearch specified. */
+    LBFGSERR_INVALID_MAXLINESEARCH,
+    /** Invalid parameter lbfgs_parameter_t::orthantwise_c specified. */
+    LBFGSERR_INVALID_ORTHANTWISE,
+    /** Invalid parameter lbfgs_parameter_t::orthantwise_start specified. */
+    LBFGSERR_INVALID_ORTHANTWISE_START,
+    /** Invalid parameter lbfgs_parameter_t::orthantwise_end specified. */
+    LBFGSERR_INVALID_ORTHANTWISE_END,
+    /** The line-search step went out of the interval of uncertainty. */
+    LBFGSERR_OUTOFINTERVAL,
+    /** A logic error occurred; alternatively, the interval of uncertainty
+        became too small. */
+    LBFGSERR_INCORRECT_TMINMAX,
+    /** A rounding error occurred; alternatively, no line-search step
+        satisfies the sufficient decrease and curvature conditions. */
+    LBFGSERR_ROUNDING_ERROR,
+    /** The line-search step became smaller than lbfgs_parameter_t::min_step. */
+    LBFGSERR_MINIMUMSTEP,
+    /** The line-search step became larger than lbfgs_parameter_t::max_step. */
+    LBFGSERR_MAXIMUMSTEP,
+    /** The line-search routine reaches the maximum number of evaluations. */
+    LBFGSERR_MAXIMUMLINESEARCH,
+    /** The algorithm routine reaches the maximum number of iterations. */
+    LBFGSERR_MAXIMUMITERATION,
+    /** Relative width of the interval of uncertainty is at most
+        lbfgs_parameter_t::xtol. */
+    LBFGSERR_WIDTHTOOSMALL,
+    /** A logic error (negative line-search step) occurred. */
+    LBFGSERR_INVALIDPARAMETERS,
+    /** The current search direction increases the objective function value. */
+    LBFGSERR_INCREASEGRADIENT,
+};
+
+/**
+ * Line search algorithms.
+ */
+enum {
+    /** The default algorithm (MoreThuente method). */
+    LBFGS_LINESEARCH_DEFAULT = 0,
+    /** MoreThuente method proposd by More and Thuente. */
+    LBFGS_LINESEARCH_MORETHUENTE = 0,
+    /**
+     * Backtracking method with the Armijo condition.
+     *  The backtracking method finds the step length such that it satisfies
+     *  the sufficient decrease (Armijo) condition,
+     *    - f(x + a * d) <= f(x) + lbfgs_parameter_t::ftol * a * g(x)^T d,
+     *
+     *  where x is the current point, d is the current search direction, and
+     *  a is the step length.
+     */
+    LBFGS_LINESEARCH_BACKTRACKING_ARMIJO = 1,
+    /** The backtracking method with the defualt (regular Wolfe) condition. */
+    LBFGS_LINESEARCH_BACKTRACKING = 2,
+    /**
+     * Backtracking method with regular Wolfe condition.
+     *  The backtracking method finds the step length such that it satisfies
+     *  both the Armijo condition (LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
+     *  and the curvature condition,
+     *    - g(x + a * d)^T d >= lbfgs_parameter_t::wolfe * g(x)^T d,
+     *
+     *  where x is the current point, d is the current search direction, and
+     *  a is the step length.
+     */
+    LBFGS_LINESEARCH_BACKTRACKING_WOLFE = 2,
+    /**
+     * Backtracking method with strong Wolfe condition.
+     *  The backtracking method finds the step length such that it satisfies
+     *  both the Armijo condition (LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
+     *  and the following condition,
+     *    - |g(x + a * d)^T d| <= lbfgs_parameter_t::wolfe * |g(x)^T d|,
+     *
+     *  where x is the current point, d is the current search direction, and
+     *  a is the step length.
+     */
+    LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE = 3,
+};
+
+/**
+ * L-BFGS optimization parameters.
+ *  Call lbfgs_parameter_init() function to initialize parameters to the
+ *  default values.
+ */
+typedef struct {
+    /**
+     * The number of corrections to approximate the inverse hessian matrix.
+     *  The L-BFGS routine stores the computation results of previous \ref m
+     *  iterations to approximate the inverse hessian matrix of the current
+     *  iteration. This parameter controls the size of the limited memories
+     *  (corrections). The default value is \c 6. Values less than \c 3 are
+     *  not recommended. Large values will result in excessive computing time.
+     */
+    int             m;
+
+    /**
+     * Epsilon for convergence test.
+     *  This parameter determines the accuracy with which the solution is to
+     *  be found. A minimization terminates when
+     *      ||g|| < \ref epsilon * max(1, ||x||),
+     *  where ||.|| denotes the Euclidean (L2) norm. The default value is
+     *  \c 1e-5.
+     */
+    lbfgsfloatval_t epsilon;
+
+    /**
+     * Distance for delta-based convergence test.
+     *  This parameter determines the distance, in iterations, to compute
+     *  the rate of decrease of the objective function. If the value of this
+     *  parameter is zero, the library does not perform the delta-based
+     *  convergence test. The default value is \c 0.
+     */
+    int             past;
+
+    /**
+     * Delta for convergence test.
+     *  This parameter determines the minimum rate of decrease of the
+     *  objective function. The library stops iterations when the
+     *  following condition is met:
+     *      (f' - f) / f < \ref delta,
+     *  where f' is the objective value of \ref past iterations ago, and f is
+     *  the objective value of the current iteration.
+     *  The default value is \c 0.
+     */
+    lbfgsfloatval_t delta;
+
+    /**
+     * The maximum number of iterations.
+     *  The lbfgs() function terminates an optimization process with
+     *  ::LBFGSERR_MAXIMUMITERATION status code when the iteration count
+     *  exceedes this parameter. Setting this parameter to zero continues an
+     *  optimization process until a convergence or error. The default value
+     *  is \c 0.
+     */
+    int             max_iterations;
+
+    /**
+     * The line search algorithm.
+     *  This parameter specifies a line search algorithm to be used by the
+     *  L-BFGS routine.
+     */
+    int             linesearch;
+
+    /**
+     * The maximum number of trials for the line search.
+     *  This parameter controls the number of function and gradients evaluations
+     *  per iteration for the line search routine. The default value is \c 20.
+     */
+    int             max_linesearch;
+
+    /**
+     * The minimum step of the line search routine.
+     *  The default value is \c 1e-20. This value need not be modified unless
+     *  the exponents are too large for the machine being used, or unless the
+     *  problem is extremely badly scaled (in which case the exponents should
+     *  be increased).
+     */
+    lbfgsfloatval_t min_step;
+
+    /**
+     * The maximum step of the line search.
+     *  The default value is \c 1e+20. This value need not be modified unless
+     *  the exponents are too large for the machine being used, or unless the
+     *  problem is extremely badly scaled (in which case the exponents should
+     *  be increased).
+     */
+    lbfgsfloatval_t max_step;
+
+    /**
+     * A parameter to control the accuracy of the line search routine.
+     *  The default value is \c 1e-4. This parameter should be greater
+     *  than zero and smaller than \c 0.5.
+     */
+    lbfgsfloatval_t ftol;
+
+    /**
+     * A coefficient for the Wolfe condition.
+     *  This parameter is valid only when the backtracking line-search
+     *  algorithm is used with the Wolfe condition,
+     *  ::LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE or
+     *  ::LBFGS_LINESEARCH_BACKTRACKING_WOLFE .
+     *  The default value is \c 0.9. This parameter should be greater
+     *  the \ref ftol parameter and smaller than \c 1.0.
+     */
+    lbfgsfloatval_t wolfe;
+
+    /**
+     * A parameter to control the accuracy of the line search routine.
+     *  The default value is \c 0.9. If the function and gradient
+     *  evaluations are inexpensive with respect to the cost of the
+     *  iteration (which is sometimes the case when solving very large
+     *  problems) it may be advantageous to set this parameter to a small
+     *  value. A typical small value is \c 0.1. This parameter shuold be
+     *  greater than the \ref ftol parameter (\c 1e-4) and smaller than
+     *  \c 1.0.
+     */
+    lbfgsfloatval_t gtol;
+
+    /**
+     * The machine precision for floating-point values.
+     *  This parameter must be a positive value set by a client program to
+     *  estimate the machine precision. The line search routine will terminate
+     *  with the status code (::LBFGSERR_ROUNDING_ERROR) if the relative width
+     *  of the interval of uncertainty is less than this parameter.
+     */
+    lbfgsfloatval_t xtol;
+
+    /**
+     * Coeefficient for the L1 norm of variables.
+     *  This parameter should be set to zero for standard minimization
+     *  problems. Setting this parameter to a positive value activates
+     *  Orthant-Wise Limited-memory Quasi-Newton (OWL-QN) method, which
+     *  minimizes the objective function F(x) combined with the L1 norm |x|
+     *  of the variables, {F(x) + C |x|}. This parameter is the coeefficient
+     *  for the |x|, i.e., C. As the L1 norm |x| is not differentiable at
+     *  zero, the library modifies function and gradient evaluations from
+     *  a client program suitably; a client program thus have only to return
+     *  the function value F(x) and gradients G(x) as usual. The default value
+     *  is zero.
+     */
+    lbfgsfloatval_t orthantwise_c;
+
+    /**
+     * Start index for computing L1 norm of the variables.
+     *  This parameter is valid only for OWL-QN method
+     *  (i.e., \ref orthantwise_c != 0). This parameter b (0 <= b < N)
+     *  specifies the index number from which the library computes the
+     *  L1 norm of the variables x,
+     *      |x| := |x_{b}| + |x_{b+1}| + ... + |x_{N}| .
+     *  In other words, variables x_1, ..., x_{b-1} are not used for
+     *  computing the L1 norm. Setting b (0 < b < N), one can protect
+     *  variables, x_1, ..., x_{b-1} (e.g., a bias term of logistic
+     *  regression) from being regularized. The default value is zero.
+     */
+    int             orthantwise_start;
+
+    /**
+     * End index for computing L1 norm of the variables.
+     *  This parameter is valid only for OWL-QN method
+     *  (i.e., \ref orthantwise_c != 0). This parameter e (0 < e <= N)
+     *  specifies the index number at which the library stops computing the
+     *  L1 norm of the variables x,
+     */
+    int             orthantwise_end;
+} lbfgs_parameter_t;
+
+
+/**
+ * Callback interface to provide objective function and gradient evaluations.
+ *
+ *  The lbfgs() function call this function to obtain the values of objective
+ *  function and its gradients when needed. A client program must implement
+ *  this function to evaluate the values of the objective function and its
+ *  gradients, given current values of variables.
+ *  
+ *  @param  instance    The user data sent for lbfgs() function by the client.
+ *  @param  x           The current values of variables.
+ *  @param  g           The gradient vector. The callback function must compute
+ *                      the gradient values for the current variables.
+ *  @param  n           The number of variables.
+ *  @param  step        The current step of the line search routine.
+ *  @retval lbfgsfloatval_t The value of the objective function for the current
+ *                          variables.
+ */
+typedef lbfgsfloatval_t (*lbfgs_evaluate_t)(
+    void *instance,
+    const lbfgsfloatval_t *x,
+    lbfgsfloatval_t *g,
+    const int n,
+    const lbfgsfloatval_t step
+    );
+
+/**
+ * Callback interface to receive the progress of the optimization process.
+ *
+ *  The lbfgs() function call this function for each iteration. Implementing
+ *  this function, a client program can store or display the current progress
+ *  of the optimization process.
+ *
+ *  @param  instance    The user data sent for lbfgs() function by the client.
+ *  @param  x           The current values of variables.
+ *  @param  g           The current gradient values of variables.
+ *  @param  fx          The current value of the objective function.
+ *  @param  xnorm       The Euclidean norm of the variables.
+ *  @param  gnorm       The Euclidean norm of the gradients.
+ *  @param  step        The line-search step used for this iteration.
+ *  @param  n           The number of variables.
+ *  @param  k           The iteration count.
+ *  @param  ls          The number of evaluations called for this iteration.
+ *  @retval int         Zero to continue the optimization process. Returning a
+ *                      non-zero value will cancel the optimization process.
+ */
+typedef int (*lbfgs_progress_t)(
+    void *instance,
+    const lbfgsfloatval_t *x,
+    const lbfgsfloatval_t *g,
+    const lbfgsfloatval_t fx,
+    const lbfgsfloatval_t xnorm,
+    const lbfgsfloatval_t gnorm,
+    const lbfgsfloatval_t step,
+    int n,
+    int k,
+    int ls
+    );
+
+/*
+A user must implement a function compatible with ::lbfgs_evaluate_t (evaluation
+callback) and pass the pointer to the callback function to lbfgs() arguments.
+Similarly, a user can implement a function compatible with ::lbfgs_progress_t
+(progress callback) to obtain the current progress (e.g., variables, function
+value, ||G||, etc) and to cancel the iteration process if necessary.
+Implementation of a progress callback is optional: a user can pass \c NULL if
+progress notification is not necessary.
+
+In addition, a user must preserve two requirements:
+    - The number of variables must be multiples of 16 (this is not 4).
+    - The memory block of variable array ::x must be aligned to 16.
+
+This algorithm terminates an optimization
+when:
+
+    ||G|| < \epsilon \cdot \max(1, ||x||) .
+
+In this formula, ||.|| denotes the Euclidean norm.
+*/
+
+/**
+ * Start a L-BFGS optimization.
+ *
+ *  @param  n           The number of variables.
+ *  @param  x           The array of variables. A client program can set
+ *                      default values for the optimization and receive the
+ *                      optimization result through this array. This array
+ *                      must be allocated by ::lbfgs_malloc function
+ *                      for libLBFGS built with SSE/SSE2 optimization routine
+ *                      enabled. The library built without SSE/SSE2
+ *                      optimization does not have such a requirement.
+ *  @param  ptr_fx      The pointer to the variable that receives the final
+ *                      value of the objective function for the variables.
+ *                      This argument can be set to \c NULL if the final
+ *                      value of the objective function is unnecessary.
+ *  @param  proc_evaluate   The callback function to provide function and
+ *                          gradient evaluations given a current values of
+ *                          variables. A client program must implement a
+ *                          callback function compatible with \ref
+ *                          lbfgs_evaluate_t and pass the pointer to the
+ *                          callback function.
+ *  @param  proc_progress   The callback function to receive the progress
+ *                          (the number of iterations, the current value of
+ *                          the objective function) of the minimization
+ *                          process. This argument can be set to \c NULL if
+ *                          a progress report is unnecessary.
+ *  @param  instance    A user data for the client program. The callback
+ *                      functions will receive the value of this argument.
+ *  @param  param       The pointer to a structure representing parameters for
+ *                      L-BFGS optimization. A client program can set this
+ *                      parameter to \c NULL to use the default parameters.
+ *                      Call lbfgs_parameter_init() function to fill a
+ *                      structure with the default values.
+ *  @retval int         The status code. This function returns zero if the
+ *                      minimization process terminates without an error. A
+ *                      non-zero value indicates an error.
+ */
+int lbfgs(
+    int n,
+    lbfgsfloatval_t *x,
+    lbfgsfloatval_t *ptr_fx,
+    lbfgs_evaluate_t proc_evaluate,
+    lbfgs_progress_t proc_progress,
+    void *instance,
+    lbfgs_parameter_t *param
+    );
+
+/**
+ * Initialize L-BFGS parameters to the default values.
+ *
+ *  Call this function to fill a parameter structure with the default values
+ *  and overwrite parameter values if necessary.
+ *
+ *  @param  param       The pointer to the parameter structure.
+ */
+void lbfgs_parameter_init(lbfgs_parameter_t *param);
+
+/**
+ * Allocate an array for variables.
+ *
+ *  This function allocates an array of variables for the convenience of
+ *  ::lbfgs function; the function has a requreiemt for a variable array
+ *  when libLBFGS is built with SSE/SSE2 optimization routines. A user does
+ *  not have to use this function for libLBFGS built without SSE/SSE2
+ *  optimization.
+ *  
+ *  @param  n           The number of variables.
+ */
+lbfgsfloatval_t* lbfgs_malloc(int n);
+
+/**
+ * Free an array of variables.
+ *  
+ *  @param  x           The array of variables allocated by ::lbfgs_malloc
+ *                      function.
+ */
+void lbfgs_free(lbfgsfloatval_t *x);
+
+/** @} */
+
+#ifdef  __cplusplus
+}
+#endif/*__cplusplus*/
+
+
+
+/**
+@mainpage libLBFGS: a library of Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)
+
+@section intro Introduction
+
+This library is a C port of the implementation of Limited-memory
+Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method written by Jorge Nocedal.
+The original FORTRAN source code is available at:
+http://www.ece.northwestern.edu/~nocedal/lbfgs.html
+
+The L-BFGS method solves the unconstrainted minimization problem,
+
+<pre>
+    minimize F(x), x = (x1, x2, ..., xN),
+</pre>
+
+only if the objective function F(x) and its gradient G(x) are computable. The
+well-known Newton's method requires computation of the inverse of the hessian
+matrix of the objective function. However, the computational cost for the
+inverse hessian matrix is expensive especially when the objective function
+takes a large number of variables. The L-BFGS method iteratively finds a
+minimizer by approximating the inverse hessian matrix by information from last
+m iterations. This innovation saves the memory storage and computational time
+drastically for large-scaled problems.
+
+Among the various ports of L-BFGS, this library provides several features:
+- <b>Optimization with L1-norm (Orthant-Wise Limited-memory Quasi-Newton
+  (OWL-QN) method)</b>:
+  In addition to standard minimization problems, the library can minimize
+  a function F(x) combined with L1-norm |x| of the variables,
+  {F(x) + C |x|}, where C is a constant scalar parameter. This feature is
+  useful for estimating parameters of sparse log-linear models (e.g.,
+  logistic regression and maximum entropy) with L1-regularization (or
+  Laplacian prior).
+- <b>Clean C code</b>:
+  Unlike C codes generated automatically by f2c (Fortran 77 into C converter),
+  this port includes changes based on my interpretations, improvements,
+  optimizations, and clean-ups so that the ported code would be well-suited
+  for a C code. In addition to comments inherited from the original code,
+  a number of comments were added through my interpretations.
+- <b>Callback interface</b>:
+  The library receives function and gradient values via a callback interface.
+  The library also notifies the progress of the optimization by invoking a
+  callback function. In the original implementation, a user had to set
+  function and gradient values every time the function returns for obtaining
+  updated values.
+- <b>Thread safe</b>:
+  The library is thread-safe, which is the secondary gain from the callback
+  interface.
+- <b>Cross platform.</b> The source code can be compiled on Microsoft Visual
+  Studio 2010, GNU C Compiler (gcc), etc.
+- <b>Configurable precision</b>: A user can choose single-precision (float)
+  or double-precision (double) accuracy by changing ::LBFGS_FLOAT macro.
+- <b>SSE/SSE2 optimization</b>:
+  This library includes SSE/SSE2 optimization (written in compiler intrinsics)
+  for vector arithmetic operations on Intel/AMD processors. The library uses
+  SSE for float values and SSE2 for double values. The SSE/SSE2 optimization
+  routine is disabled by default.
+
+This library is used by:
+- <a href="http://www.chokkan.org/software/crfsuite/">CRFsuite: A fast implementation of Conditional Random Fields (CRFs)</a>
+- <a href="http://www.chokkan.org/software/classias/">Classias: A collection of machine-learning algorithms for classification</a>
+- <a href="http://www.public.iastate.edu/~gdancik/mlegp/">mlegp: an R package for maximum likelihood estimates for Gaussian processes</a>
+- <a href="http://infmath.uibk.ac.at/~matthiasf/imaging2/">imaging2: the imaging2 class library</a>
+- <a href="http://search.cpan.org/~laye/Algorithm-LBFGS-0.16/">Algorithm::LBFGS - Perl extension for L-BFGS</a>
+- <a href="http://www.cs.kuleuven.be/~bernd/yap-lbfgs/">YAP-LBFGS (an interface to call libLBFGS from YAP Prolog)</a>
+
+@section download Download
+
+- <a href="https://github.com/downloads/chokkan/liblbfgs/liblbfgs-1.10.tar.gz">Source code</a>
+- <a href="https://github.com/chokkan/liblbfgs">GitHub repository</a>
+
+libLBFGS is distributed under the term of the
+<a href="http://opensource.org/licenses/mit-license.php">MIT license</a>.
+
+@section changelog History
+- Version 1.10 (2010-12-22):
+    - Fixed compiling errors on Mac OS X; this patch was kindly submitted by
+      Nic Schraudolph.
+    - Reduced compiling warnings on Mac OS X; this patch was kindly submitted
+      by Tamas Nepusz.
+    - Replaced memalign() with posix_memalign().
+    - Updated solution and project files for Microsoft Visual Studio 2010.
+- Version 1.9 (2010-01-29):
+    - Fixed a mistake in checking the validity of the parameters "ftol" and
+      "wolfe"; this was discovered by Kevin S. Van Horn.
+- Version 1.8 (2009-07-13):
+    - Accepted the patch submitted by Takashi Imamichi;
+      the backtracking method now has three criteria for choosing the step
+      length:
+        - ::LBFGS_LINESEARCH_BACKTRACKING_ARMIJO: sufficient decrease (Armijo)
+          condition only
+        - ::LBFGS_LINESEARCH_BACKTRACKING_WOLFE: regular Wolfe condition
+          (sufficient decrease condition + curvature condition)
+        - ::LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE: strong Wolfe condition
+    - Updated the documentation to explain the above three criteria.
+- Version 1.7 (2009-02-28):
+    - Improved OWL-QN routines for stability.
+    - Removed the support of OWL-QN method in MoreThuente algorithm because
+      it accidentally fails in early stages of iterations for some objectives.
+      Because of this change, <b>the OW-LQN method must be used with the
+      backtracking algorithm (::LBFGS_LINESEARCH_BACKTRACKING)</b>, or the
+      library returns ::LBFGSERR_INVALID_LINESEARCH.
+    - Renamed line search algorithms as follows:
+        - ::LBFGS_LINESEARCH_BACKTRACKING: regular Wolfe condition.
+        - ::LBFGS_LINESEARCH_BACKTRACKING_LOOSE: regular Wolfe condition.
+        - ::LBFGS_LINESEARCH_BACKTRACKING_STRONG: strong Wolfe condition.
+    - Source code clean-up.
+- Version 1.6 (2008-11-02):
+    - Improved line-search algorithm with strong Wolfe condition, which was
+      contributed by Takashi Imamichi. This routine is now default for
+      ::LBFGS_LINESEARCH_BACKTRACKING. The previous line search algorithm
+      with regular Wolfe condition is still available as
+      ::LBFGS_LINESEARCH_BACKTRACKING_LOOSE.
+    - Configurable stop index for L1-norm computation. A member variable
+      ::lbfgs_parameter_t::orthantwise_end was added to specify the index
+      number at which the library stops computing the L1 norm of the
+      variables. This is useful to prevent some variables from being
+      regularized by the OW-LQN method.
+    - A sample program written in C++ (sample/sample.cpp).
+- Version 1.5 (2008-07-10):
+    - Configurable starting index for L1-norm computation. A member variable
+      ::lbfgs_parameter_t::orthantwise_start was added to specify the index
+      number from which the library computes the L1 norm of the variables.
+      This is useful to prevent some variables from being regularized by the
+      OWL-QN method.
+    - Fixed a zero-division error when the initial variables have already
+      been a minimizer (reported by Takashi Imamichi). In this case, the
+      library returns ::LBFGS_ALREADY_MINIMIZED status code.
+    - Defined ::LBFGS_SUCCESS status code as zero; removed unused constants,
+      LBFGSFALSE and LBFGSTRUE.
+    - Fixed a compile error in an implicit down-cast.
+- Version 1.4 (2008-04-25):
+    - Configurable line search algorithms. A member variable
+      ::lbfgs_parameter_t::linesearch was added to choose either MoreThuente
+      method (::LBFGS_LINESEARCH_MORETHUENTE) or backtracking algorithm
+      (::LBFGS_LINESEARCH_BACKTRACKING).
+    - Fixed a bug: the previous version did not compute psuedo-gradients
+      properly in the line search routines for OWL-QN. This bug might quit
+      an iteration process too early when the OWL-QN routine was activated
+      (0 < ::lbfgs_parameter_t::orthantwise_c).
+    - Configure script for POSIX environments.
+    - SSE/SSE2 optimizations with GCC.
+    - New functions ::lbfgs_malloc and ::lbfgs_free to use SSE/SSE2 routines
+      transparently. It is uncessary to use these functions for libLBFGS built
+      without SSE/SSE2 routines; you can still use any memory allocators if
+      SSE/SSE2 routines are disabled in libLBFGS.
+- Version 1.3 (2007-12-16):
+    - An API change. An argument was added to lbfgs() function to receive the
+      final value of the objective function. This argument can be set to
+      \c NULL if the final value is unnecessary.
+    - Fixed a null-pointer bug in the sample code (reported by Takashi Imamichi).
+    - Added build scripts for Microsoft Visual Studio 2005 and GCC.
+    - Added README file.
+- Version 1.2 (2007-12-13):
+    - Fixed a serious bug in orthant-wise L-BFGS.
+      An important variable was used without initialization.
+- Version 1.1 (2007-12-01):
+    - Implemented orthant-wise L-BFGS.
+    - Implemented lbfgs_parameter_init() function.
+    - Fixed several bugs.
+    - API documentation.
+- Version 1.0 (2007-09-20):
+    - Initial release.
+
+@section api Documentation
+
+- @ref liblbfgs_api "libLBFGS API"
+
+@section sample Sample code
+
+@include sample.c
+
+@section ack Acknowledgements
+
+The L-BFGS algorithm is described in:
+    - Jorge Nocedal.
+      Updating Quasi-Newton Matrices with Limited Storage.
+      <i>Mathematics of Computation</i>, Vol. 35, No. 151, pp. 773--782, 1980.
+    - Dong C. Liu and Jorge Nocedal.
+      On the limited memory BFGS method for large scale optimization.
+      <i>Mathematical Programming</i> B, Vol. 45, No. 3, pp. 503-528, 1989.
+
+The line search algorithms used in this implementation are described in:
+    - John E. Dennis and Robert B. Schnabel.
+      <i>Numerical Methods for Unconstrained Optimization and Nonlinear
+      Equations</i>, Englewood Cliffs, 1983.
+    - Jorge J. More and David J. Thuente.
+      Line search algorithm with guaranteed sufficient decrease.
+      <i>ACM Transactions on Mathematical Software (TOMS)</i>, Vol. 20, No. 3,
+      pp. 286-307, 1994.
+
+This library also implements Orthant-Wise Limited-memory Quasi-Newton (OWL-QN)
+method presented in:
+    - Galen Andrew and Jianfeng Gao.
+      Scalable training of L1-regularized log-linear models.
+      In <i>Proceedings of the 24th International Conference on Machine
+      Learning (ICML 2007)</i>, pp. 33-40, 2007.
+
+Special thanks go to:
+    - Yoshimasa Tsuruoka and Daisuke Okanohara for technical information about
+      OWL-QN
+    - Takashi Imamichi for the useful enhancements of the backtracking method
+    - Kevin S. Van Horn, Nic Schraudolph, and Tamas Nepusz for bug fixes
+
+Finally I would like to thank the original author, Jorge Nocedal, who has been
+distributing the effieicnt and explanatory implementation in an open source
+licence.
+
+@section reference Reference
+
+- <a href="http://www.ece.northwestern.edu/~nocedal/lbfgs.html">L-BFGS</a> by Jorge Nocedal.
+- <a href="http://research.microsoft.com/en-us/downloads/b1eb1016-1738-4bd5-83a9-370c9d498a03/default.aspx">Orthant-Wise Limited-memory Quasi-Newton Optimizer for L1-regularized Objectives</a> by Galen Andrew.
+- <a href="http://chasen.org/~taku/software/misc/lbfgs/">C port (via f2c)</a> by Taku Kudo.
+- <a href="http://www.alglib.net/optimization/lbfgs.php">C#/C++/Delphi/VisualBasic6 port</a> in ALGLIB.
+- <a href="http://cctbx.sourceforge.net/">Computational Crystallography Toolbox</a> includes
+  <a href="http://cctbx.sourceforge.net/current_cvs/c_plus_plus/namespacescitbx_1_1lbfgs.html">scitbx::lbfgs</a>.
+*/
+
+#endif/*__LBFGS_H__*/