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gnn_gaussian.c

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/***************************************************************************
 *  @file gnn_gaussian.c
 *  @brief Gaussian Kernel transfer function.
 *
 *  @date   : 18-09-03 10:33
 *  @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_gaussian_doc gnn_gaussian : Gaussian Kernel Activation Function.
 * @ingroup gnn_atomic_doc
 *
 * This node type implements a Gaussian Kernel activation function given
 * by:
 * \f[ y_i = a_i e^{-\frac{x_i^2}{v_i}} \f]
 * where the index \f$i = 1,\ldots,n\f$ runs over all inputs / outputs, and
 * \f$v_i = \sigma_i^2\f$
 *
 * This function is a member of the more general class of kernel functions.
 * They are intended to work in combination with a prototype node
 * (\ref gnn_prototype).
 *
 * The function's gradients are:
 * \f[ \frac{\partial E}{\partial x_i}
 *     = - \frac{2 x_i y_i}{v_i} \frac{\partial E}{\partial y_i}
 * \f]
 * with respect to its inputs, and
 * \f[ \frac{\partial E}{\partial a_i}
 *     = \frac{y_i}{a_i} \frac{\partial E}{\partial y_i}
 * \f]
 * \f[ \frac{\partial E}{\partial v_i}
 *     = \frac{x_i^2 y_i}{v_i^2} \frac{\partial E}{\partial y_i}
 * \f]
 * with respect to its parameters.
 */


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

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



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

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

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

static int
gnn_gaussian_dw (gnn_node *node,
                 const gsl_vector *x,
                 const gsl_vector *w,
                 const gsl_vector *dy,
                 gsl_vector *dw);

static void
gnn_gaussian_destroy (gnn_node *node);



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

/**
 * @brief Computes the output.
 * @ingroup gnn_gaussian_doc
 *
 * This functions evaluates the Gaussian Kernel activation function.
 *
 * @param   node A pointer to the \ref gnn_gaussian node.
 * @param x The input vector \f$x\f$.
 * @param w The parameter vector \f$w\f$.
 * @param y The output buffer vector \f$y\f$.
 * @return Returns 0 on success.
 */
static int
gnn_gaussian_f (gnn_node *node,
                const gsl_vector *x,
                const gsl_vector *w,
                gsl_vector *y)
{
    size_t i;
    size_t size;
    gnn_gaussian *gnode;

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

    /* get views */
    gnode = (gnn_gaussian *) node;

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

        xi  = gsl_vector_get (x, i);
        ai  = gsl_vector_get (gnode->a, i);
        vi  = gsl_vector_get (gnode->v, i);
        yi  = ai * exp (- xi * xi / vi);
        gsl_vector_set (gnode->y, i, yi);
    }
    /* copy to outputs */
    gsl_vector_memcpy (y, gnode->y);

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial x} \f$.
 * @ingroup gnn_gaussian_doc
 *
 * This functions computes the gradient with respect to the inputs of the
 * Gaussian Kernel function.
 *
 * @param    node A pointer to the \ref gnn_gaussian node.
 * @param x  The input vector \f$x\f$.
 * @param w  The parameter vector \f$w\f$.
 * @param dy The vector \f$\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_gaussian_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;
    gnn_gaussian *gnode;

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

    /* get views */
    gnode = (gnn_gaussian *) node;

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

        xi  = gsl_vector_get (x, i);
        yi  = gsl_vector_get (gnode->y, i);
        vi  = gsl_vector_get (gnode->v, i);
        //dxi = gsl_vector_get (dx, i);
        dyi = gsl_vector_get (dy, i);

        //dxi += - 2 * xi * yi / vi * dyi;
        dxi = - 2 * xi * yi / vi * dyi;
        gsl_vector_set (dx, i, dxi);
    }

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial w} \f$.
 * @ingroup gnn_gaussian_doc
 *
 * This functions computes the gradient with respect to the parameters of the
 * Gaussian Kernel function. That is, it computes
 * \f$\frac{\partial E}{\partial a_i}\f$ and
 * \f$\frac{\partial E}{\partial v_i}\f$.
 *
 * @param    node A pointer to the \ref gnn_gaussian node.
 * @param x  The input vector \f$x\f$.
 * @param w  The parameter vector \f$w\f$.
 * @param dy The vector \f$\frac{\partial E}{\partial y}\f$.
 * @param dx The output buffer vector \f$\frac{\partial E}{\partial w}\f$.
 * @return Returns 0 on success.
 */
static int
gnn_gaussian_dw (gnn_node *node,
                 const gsl_vector *x,
                 const gsl_vector *w,
                 const gsl_vector *dy,
                 gsl_vector *dw)
{
    size_t i;
    size_t size;
    gnn_gaussian *gnode;

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

    /* get views */
    gnode = (gnn_gaussian *) node;

    /* evaluate */
    for (i=0; i<size; ++i)
    {
        double xi;
        double yi;
        double ai;
        double vi;
        double dyi;
        double dai;
        double dvi;

        xi  = gsl_vector_get (x, i);
        yi  = gsl_vector_get (gnode->y, i);
        ai  = gsl_vector_get (gnode->a, i);
        vi  = gsl_vector_get (gnode->v, i);
        dyi = gsl_vector_get (dy, i);
        dai = gsl_vector_get (gnode->da, i);
        dvi = gsl_vector_get (gnode->dv, i);

        dai += (yi / ai) * dyi;
        dvi += (xi * xi * yi / (vi * vi)) * dyi;

        gsl_vector_set (gnode->da, i, dai);
        gsl_vector_set (gnode->dv, i, dvi);
    }

    return 0;
}

/**
 * @brief Computes the output.
 * @ingroup gnn_gaussian_doc
 *
 * This is the destructor for a \ref gnn_gaussian node.
 *
 * @param   node A pointer to the \ref gnn_gaussian node.
 */
static void
gnn_gaussian_destroy (gnn_node *node)
{
    gnn_gaussian *gnode;

    gnode = (gnn_gaussian *) node;
    
    if (gnode->y != NULL)
        gsl_vector_free (gnode->y);
}



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

/**
 * @brief Creates a Gaussian Kernel Activation Function node.
 * @ingroup gnn_gaussian_doc
 *
 * This function creates a node of the gnn_gaussian type. All kernels are
 * initialized with the same amplitude and variance.
 *
 * @param input_size The input size \f$n\f$.
 * @param a The \f$a\f$ (amplitude) factor.
 * @param v The variance \f$\sigma^2\f$.
 * @return A pointer to a new \ref gnn_divergence node.
 */
gnn_node *
gnn_gaussian_new (int input_size, double a, double v)
{
    int status;
    gnn_node *node;
    gnn_gaussian *gnode;
    gsl_vector *w;
    gsl_vector *dw;
    gsl_vector_int *f;

    /* check if sizes are positive */
    if (input_size < 1)
    {
        GSL_ERROR_VAL ("input size should be strictly positive",
                       GSL_EINVAL, NULL);
    }
    
    /* check amplitude */
    if (a <= 0.0)
    {
        GSL_ERROR_VAL ("amplitude factor a should be stricly positive",
                       GSL_EINVAL, NULL);
    }

    /* check variance */
    if (v <= 0.0)
    {
        GSL_ERROR_VAL ("variance factor a should be stricly positive",
                       GSL_EINVAL, NULL);
    }

    /* allocate the node */
    gnode = (gnn_gaussian *) malloc (sizeof (gnn_gaussian));
    if (gnode == NULL)
    {
        GSL_ERROR_VAL ("could not allocate memory for gnn_gaussian node",
                       GSL_ENOMEM, NULL);
    }
    
    /* get view as a gnn_node */
    node = (gnn_node *) gnode;

    /* Initialize the node */
    status = gnn_node_init (node,
                            "gnn_gaussian",
                            gnn_gaussian_f,
                            gnn_gaussian_dx,
                            gnn_gaussian_dw,
                            gnn_gaussian_destroy);
    if (status)
    {
        GSL_ERROR_VAL ("could not initialize gnn_gaussian node",
                       GSL_EFAILED, NULL);
    }

    status = gnn_node_set_sizes (node, input_size, input_size, 2 * input_size);
    if (status)
    {
        GSL_ERROR_VAL ("could not set sizes for gnn_gaussian node",
                       GSL_EFAILED, NULL);
    }

    /* create buffer */
    gnode->y = gsl_vector_alloc (input_size);
    if (gnode->y == NULL)
    {
        gnn_node_destroy (node);
        GSL_ERROR_VAL ("could not allocate buffer for gnn_gaussian node",
                       GSL_ENOMEM, NULL);
    }

    /* get parameter views */
    w  = gnn_node_local_get_w (node);
    dw = gnn_node_local_get_dw (node);
    f  = gnn_node_local_get_f (node);
    
    gnode->a_view  = gsl_vector_subvector (w,  0, input_size);
    gnode->da_view = gsl_vector_subvector (dw, 0, input_size);
    gnode->af_view = gsl_vector_int_subvector (f, 0, input_size);
                                           
    gnode->v_view  = gsl_vector_subvector (w, input_size, input_size);
    gnode->dv_view = gsl_vector_subvector (dw, input_size, input_size);
    gnode->vf_view = gsl_vector_int_subvector (f, input_size, input_size);

    gnode->a  = &(gnode->a_view.vector);
    gnode->da = &(gnode->da_view.vector);
    gnode->af = &(gnode->af_view.vector);

    gnode->v  = &(gnode->v_view.vector);
    gnode->dv = &(gnode->dv_view.vector);
    gnode->vf = &(gnode->vf_view.vector);

    /* initialize values */
    gsl_vector_set_all (gnode->a, a);
    gsl_vector_set_all (gnode->v, v);

    /* update parameters */
    gnn_node_local_update (node);
    
    return node;
}

/**
 * @brief Creates a standard Gaussian Kernel Activation Function node.
 * @ingroup gnn_gaussian_doc
 *
 * This function creates a node of the gnn_gaussian type. All kernels are
 * initialized with amplitude \f$a_i = 1\f$ and variance \f$v_i = 1\f$.
 *
 * @param input_size The input size \f$n\f$.
 * @return A pointer to a new \ref gnn_tanh node.
 */
gnn_node *
gnn_gaussian_standard_new (int input_size)
{
    return gnn_gaussian_new (input_size, 1.0, 1.0);
}

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