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gnn_tanh.c

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/***************************************************************************
 *  @file gnn_tanh.c
 *  @brief Hyperbolic Tangent transfer function.
 *
 *  @date   : 06-08-03 18:17, 21-08-03 20:00
 *  @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_tanh_doc gnn_tanh : Hyperbolic Tangent Activation Function.
 * @ingroup gnn_atomic_doc
 *
 * This node type implements the Hyperbolic Tangent activation function given
 * by:
 * \f[ y_i = a \tanh (b x_i) \f]
 * where the index \f$i = 1,\ldots,n\f$ runs over all inputs / outputs.
 *
 * 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 Hyperbolic Tangent is symmetric and its outputs lie between \f$[-a,a]\f$.
 * It has been said that it leads to faster convergence in training than the
 * Logistic Sigmoid.
 */


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

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

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

#define GNN_TANH_A(node) (((gnn_tanh *)(node))->a)
#define GNN_TANH_B(node) (((gnn_tanh *)(node))->b)

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

typedef struct _gnn_tanh
{
    gnn_node node;
    double a;
    double b;
} gnn_tanh;

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

static int
gnn_tanh_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_tanh_doc
 *
 * This functions evaluates the hyperbolic tangent function.
 *
 * @param   node A pointer to the \ref gnn_tanh 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_tanh_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_TANH_A (node);
    b = GNN_TANH_B (node);

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

        xi = gsl_vector_get (x, i);
        yi = a * tanh (b * xi);
        gsl_vector_set (y, i, yi);
    }

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial X} \f$.
 * @ingroup gnn_tanh_doc
 *
 * This functions computes the gradient of the hyperbolic tangent function,
 * given dedy (\f$ \frac{\partial E}{\partial Y} \f$). The function is,
 * \f[ \frac{\partial E}{\partial x_i} =
 *     ab \, sech^2 (bx_i) \frac{\partial E}{\partial y_i} =
 *     ab \left ( 1 - \tanh^2(bx_i) \right ) \frac{\partial E}{\partial y_i} \f]
 *
 * @param    node A pointer to the \ref gnn_tanh node.
 * @param x  The input vector \f$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_tanh_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_TANH_A (node);
    b = GNN_TANH_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 * tanh (b * xi);
        dyi = gsl_vector_get (dy, i);
        dxi = a * b * (1.0 - yi * yi) * dyi;

        gsl_vector_set (dx, i, dxi);
    }

    return 0;
}


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

/**
 * @brief Creates a Hyperbolic Tangent Activation Function node.
 * @ingroup gnn_tanh_doc
 *
 * This function creates a node of the gnn_tanh type. This node computes
 * \f[ y_i = a \tanh (b x_i) \f]
 * where \f$i = 1, \ldots, n\f$, \f$a\f$ and \f$b\f$ constant parameters.
 *
 * @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_tanh node.
 */
gnn_node *
gnn_tanh_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 strictly positive",
                       GSL_EINVAL, NULL);
    }

    /* allocate the node */
    node = (gnn_node *) malloc (sizeof (gnn_tanh));
    if (node == NULL)
    {
        GSL_ERROR_VAL ("could not allocate memory for gnn_tanh node",
                       GSL_ENOMEM, NULL);
    }
    
    /* Initialize the node */
    status = gnn_node_init (node,
                            "gnn_tanh",
                            gnn_tanh_f,
                            gnn_tanh_dx,
                            NULL,
                            NULL);
    if (status)
    {
        GSL_ERROR_VAL ("could not initialize gnn_tanh 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_tanh node",
                       GSL_EFAILED, NULL);
    }
    
    /* set the constants */
    GNN_TANH_A (node) = a;
    GNN_TANH_B (node) = b;

    return node;
}

/**
 * @brief Creates a standard Hyperbolic Tangent function node.
 * @ingroup gnn_tanh_doc
 *
 * This function creates a layer of the gnn_tanh type:
 * \f[ y_i = \tanh (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_tanh node.
 */
gnn_node *
gnn_tanh_standard_new (int input_size)
{
    return gnn_tanh_new (input_size, 1.0, 1.0);
}

/**
 * @brief Creates a Hyperbolic Tangent function node.
 * @ingroup gnn_tanh_doc
 *
 * This function creates a node of the gnn_tanh type.
 * \f[ y_i = 1.7159 \tanh (\frac{2}{3} x_i) \f]
 * where \f$i = 1, \ldots, n\f$. The constants are chosen so that
 * when the layer is feed with a linear combination layer with
 * normalized outputs its own outputs have an effective gain of 1.
 *
 * @param input_size The input size \f$n\f$.
 * @return A pointer to a new \ref gnn_tanh node.
 */
gnn_node *
gnn_tanh_enhanced_new (int input_size)
{
    return gnn_tanh_new (input_size, 1.7159, 2.0 / 3.0);
}

/**
 * @brief Returns the amplitude constant \f$a\f$.
 * @ingroup gnn_tanh_doc
 *
 * @param  node A pointer to the \ref gnn_tanh node.
 * @return The amplitude \f$a\f$ of the sigmoid.
 */
double
gnn_tanh_get_a (gnn_node *node)
{
    return GNN_TANH_A (node);
}

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

/**
 * @brief Gets the streching factor \f$b\f$.
 * @ingroup gnn_tanh_doc
 *
 * @param  node A pointer to the \ref gnn_tanh node.
 * @return The streching factor \f$b\f$.
 */
double
gnn_tanh_get_b (gnn_node *node)
{
    return GNN_TANH_B (node);
}

/**
 * @brief Sets the streching factor \f$b\f$.
 * @ingroup gnn_tanh_doc
 *
 * @param node A pointer to the \ref gnn_tanh node.
 * @param b    The new streching factor \f$b\f$.
 */
void
gnn_tanh_set_b (gnn_node *node, double b)
{
    GNN_TANH_B (node) = b;
}

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