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gnn_logistic.c

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/***************************************************************************
 *  @file gnn_logistic.c
 *  @brief Logistic Sigmoid transfer function.
 *
 *  @date   : 10-08-03 01:09
 *  @author : Pedro Ortega C. <peortega@dcc.uchile.cl>
 *  Copyright  2003  Pedro Ortega C.
 ****************************************************************************/
/*
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Library General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */



/**
 * @defgroup gnn_logistic_doc gnn_logistic : Logistic Sigmoid Activation Function.
 * @ingroup gnn_atomic_doc
 *
 * The \ref gnn_logistic datatype implements a node that computes the function:
 * \f[ y_i = a \frac{1}{1 + \exp(-bx)} \f]
 * where \f$i = 1,\ldots,n\f$.
 *
 * This function is a member of the more general class of sigmoid functions,
 * which have the property to "squash" its inputs to a very restricted output
 * interval.
 *
 * The Logistic Sigmoid is assymmetric and its outputs lie between \f$[0,a]\f$.
 * It has been said that it leads to slower convergence in training than the
 * Hyperbolic Tangent.
 */



/******************************************/
/* Include Files                          */
/******************************************/

#include "gnn_logistic.h"
#include <math.h>



/******************************************/
/* Macros and Definitions                 */
/******************************************/

#define GNN_LOGISTIC_A(node) (((gnn_logistic *)(node))->a)
#define GNN_LOGISTIC_B(node) (((gnn_logistic *)(node))->b)



/******************************************/
/* Static Declaration                     */
/******************************************/

typedef struct _gnn_logistic
{
    gnn_node node;
    double a;
    double b;
} gnn_logistic;

static int
gnn_logistic_f (gnn_node *node,
                const gsl_vector *x,
                const gsl_vector *w,
                gsl_vector *y);

static int
gnn_logistic_dx (gnn_node *node,
                 const gsl_vector *x,
                 const gsl_vector *w,
                 const gsl_vector *dy,
                 gsl_vector *dx);



/******************************************/
/* Static Implementation                  */
/******************************************/

/**
 * @brief Computes the output.
 * @ingroup gnn_logistic_doc
 *
 * This functions evaluates the logistic sigmoid function.
 *
 * @param node  A pointer to a \ref gnn_logistic node.
 * @param x The input vector \f$x\f$.
 * @param w The parameter vector \f$w\f$ (which is empty in this case).
 * @param y The output buffer vector \f$y\f$.
 * @return Returns 0 on success.
 */
static int
gnn_logistic_f (gnn_node *node,
                const gsl_vector *x,
                const gsl_vector *w,
                gsl_vector *y)
{
    size_t i;
    size_t size;
    double a;
    double b;

    /* get the size */
    size = gnn_node_input_get_size (node);

    /* get the parameters */
    a = GNN_LOGISTIC_A (node);
    b = GNN_LOGISTIC_B (node);

    /* evaluate */
    for (i=0; i<size; ++i)
    {
        double xi;
        double yi;

        xi = gsl_vector_get (x, i);
        yi = a * 1 / (1 + exp (- b * xi));
        gsl_vector_set (y, i, yi);
    }

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial X} \f$.
 * @ingroup gnn_logistic_doc
 *
 * This functions computes the gradient of the logistic sigmoid function,
 * given dedy (\f$ \frac{\partial E}{\partial Y} \f$). The function is,
 * \f[ \frac{\partial E}{\partial x_i}
 *     = ab \frac{ x_i e^{-bx_i} }{ \left ( 1 + e^{-bx_i} \right )^2 }
 *       \frac{\partial E}{\partial y_i}
 *     = b y_i \left ( 1 - \frac{y_i}{a} \right )
 *       \frac{\partial E}{\partial y_i}
 * \f]
 *
 * @param node  A pointer to a \ref gnn_logistic node.
 * @param x  The input vector \f$x\f$.
 * @param w  The parameter vector \f$w\f$ (which is empty in this case).
 * @param dy The vector \f$\frac{\partial E}{\partial y}\f$.
 * @param dx The output buffer vector \f$\frac{\partial E}{\partial x}\f$.
 * @return Returns 0 on success.
 */
static int
gnn_logistic_dx (gnn_node *node,
                 const gsl_vector *x,
                 const gsl_vector *w,
                 const gsl_vector *dy,
                 gsl_vector *dx)
{
    size_t i;
    size_t size;
    double a;
    double b;

    /* get the size */
    size = gnn_node_input_get_size (node);

    /* get the parameters */
    a = GNN_LOGISTIC_A (node);
    b = GNN_LOGISTIC_B (node);

    /* evaluate */
    for (i=0; i<size; ++i)
    {
        double xi;
        double yi;
        double dxi;
        double dyi;

        xi  = gsl_vector_get (x, i);
        yi  = a * 1 / (1 + exp (- b * xi));
        dyi = gsl_vector_get (dy, i);
        dxi = b * yi * (1.0 - yi / a) * dyi;

        gsl_vector_set (dx, i, dxi);
    }

    return 0;
}


/******************************************/
/* Public Interface                       */
/******************************************/

/**
 * @brief Creates a Logistic Sigmoid activation function node.
 * @ingroup gnn_logistic_doc
 *
 * This function creates a node of the \ref gnn_logistic type. This node
 * computes
 * \f[ y_i = a \frac{ 1 }{ 1 + e^{-b x_i} } \f]
 * where \f$i = 1, \ldots, n\f$, \f$a\f$ and \f$b\f$ constants.
 *
 * @param input_size The input size \f$n\f$.
 * @param a The \f$a\f$ factor.
 * @param b The \f$b\f$ factor.
 * @return A pointer to a new \ref gnn_logistic node.
 */
gnn_node *
gnn_logistic_new (int input_size, double a, double b)
{
    int status;
    gnn_node *node;

    /* check if sizes are positive */
    if (input_size < 1)
    {
        GSL_ERROR_VAL ("input size should be stricly positive",
                       GSL_EINVAL, NULL);
    }

    /* allocate the node */
    node = (gnn_node *) malloc (sizeof (gnn_logistic));
    if (node == NULL)
    {
        GSL_ERROR_VAL ("could not allocate memory for gnn_logistic",
                       GSL_ENOMEM, NULL);
    }
    
    /* Initialize the node */
    status = gnn_node_init (node,
                            "gnn_logistic",
                            gnn_logistic_f,
                            gnn_logistic_dx,
                            NULL,
                            NULL);
    if (status)
    {
        GSL_ERROR_VAL ("could not initialize gnn_logistic node",
                       GSL_EFAILED, NULL);
    }
    
    status = gnn_node_set_sizes (node, input_size, input_size, 0);
    if (status)
    {
        GSL_ERROR_VAL ("could not set sizes for gnn_logistic node",
                       GSL_EFAILED, NULL);
    }
    /* set the constants */
    GNN_LOGISTIC_A (node) = a;
    GNN_LOGISTIC_B (node) = b;

    return node;
}

/**
 * @brief Creates a standard Logistic Sigmoid function node.
 * @ingroup gnn_logistic_doc
 *
 * This function creates a node of the \ref gnn_logistic type:
 * \f[ y_i = \frac { 1 } { 1 + e^{-x_i}} \f]
 * where \f$i = 1, \ldots, n\f$.
 *
 * @param input_size The input size \f$n\f$.
 * @return A pointer to a new \ref gnn_logistic node.
 */
gnn_node *
gnn_logistic_standard_new (int input_size)
{
    return gnn_logistic_new (input_size, 1.0, 1.0);
}

/**
 * @brief Returns the amplitude constant \f$a\f$.
 * @ingroup gnn_logistic_doc
 *
 * @param node  A pointer to a \ref gnn_logistic node.
 * @return The amplitude \f$a\f$ of the sigmoid.
 */
double
gnn_logistic_get_a (gnn_node *node)
{
    return GNN_LOGISTIC_A (node);
}

/**
 * @brief Sets the amplitude constant \f$a\f$.
 * @ingroup gnn_logistic_doc
 *
 * @param node  A pointer to a \ref gnn_logistic node.
 * @param a     The amplitude factor.
 */
void
gnn_logistic_set_a (gnn_node *node, double a)
{
    GNN_LOGISTIC_A (node) = a;
}

/**
 * @brief Gets the streching factor \f$b\f$.
 * @ingroup gnn_logistic_doc
 *
 * @param node  A pointer to a \ref gnn_logistic node.
 * @return The streching factor \f$b\f$.
 */
double
gnn_logistic_get_b (gnn_node *node)
{
    return GNN_LOGISTIC_B (node);
}

/**
 * @brief Sets the streching factor \f$b\f$.
 * @ingroup gnn_logistic_doc
 *
 * @param node  A pointer to a \ref gnn_logistic node.
 * @param b     The new streching factor \f$b\f$.
 */
void
gnn_logistic_set_b (gnn_node *node, double b)
{
    GNN_LOGISTIC_B (node) = b;
}

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