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gnn_affine.c

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/***************************************************************************
 *  @file gnn_affine.c
 *  @brief gnn_affine Implementation.
 *
 *  @date   : 05-10-03 11:56
 *  @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_affine_doc gnn_affine : Affine Activation Function.
 * @ingroup gnn_atomic_doc
 *
 * This node type implements an Affine activatino function given by:
 *
 * \f[ y_i = a_i x_i + b_i \f]
 *
 * where the index \f$i = 1,\ldots,n\f$ runs over all inputs / outputs.
 * The amplitude factors \f$a_i\f$ and the biases \f$b_i\f$ are independent
 * and can be trained. Usually, this activation function is placed after
 * a non-linear activation function which is limited in its output range,
 * like a gaussian, logistic sigmoid or a hyperbolic tangent activation
 * function, to scale the outputs to the correct magnitudes.
 *
 * The function's gradients are:
 * \f[ \frac{\partial E}{\partial x_i}
 *     = a_i \frac{\partial E}{\partial y_i}
 * \f]
 * with respect to its inputs, and
 * \f[ \frac{\partial E}{\partial a_i}
 *     = x_i \frac{\partial E}{\partial y_i}
 * \f]
 * \f[ \frac{\partial E}{\partial b_i}
 *     = \frac{\partial E}{\partial y_i}
 * \f]
 * with respect to its parameters.
 */


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

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



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

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

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

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

static void
gnn_affine_destroy (gnn_node *node);



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

/**
 * @brief Computes the output.
 * @ingroup gnn_affine_doc
 *
 * @param   node A pointer to the \ref gnn_affine 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_affine_f (gnn_node *node,
              const gsl_vector *x,
              const gsl_vector *w,
              gsl_vector *y)
{
    size_t i;
    size_t size;
    gnn_affine *anode;

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

    /* get views */
    anode = (gnn_affine *) node;

    /* evaluate */
    gsl_vector_memcpy (y, x);
    gsl_vector_mul (y, anode->a);
    gsl_vector_add (y, anode->b);

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial x} \f$.
 * @ingroup gnn_affine_doc
 *
 * @param    node A pointer to the \ref gnn_affine node.
 * @param x  The input vector \f$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_affine_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_affine *anode;

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

    /* get views */
    anode = (gnn_affine *) node;

    /* evaluate */
    gsl_vector_memcpy (dx, anode->a);
    gsl_vector_mul (dx, dy);

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial w} \f$.
 * @ingroup gnn_affine_doc
 *
 * @param    node A pointer to the \ref gnn_affine node.
 * @param x  The input vector \f$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_affine_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_affine *anode;

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

    /* get views */
    anode = (gnn_affine *) node;

    /* evaluate */
    gsl_vector_memcpy (anode->buf, x);
    gsl_vector_mul (anode->buf, dy);
    gsl_vector_add (anode->da, anode->buf);
    
    gsl_vector_add (anode->db, dy);

    return 0;
}

/**
 * @brief Destructor function.
 * @ingroup gnn_affine_doc
 *
 * @param node A pointer to the \ref gnn_affine node.
 */
static void
gnn_affine_destroy (gnn_node *node)
{
    gnn_affine *anode;

    anode = (gnn_affine *) node;

    if (anode->buf != NULL)
        gsl_vector_free (anode->buf);
}



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

/**
 * @brief Creates an Affine Activation Function node.
 * @ingroup gnn_affine_doc
 *
 * This function creates a node of the gnn_affine type. Although the parameters
 * \f$a_i\f$ and \f$b_i\f$, \f$i=1,\ldots,n=m\f$ are all equal initially, they
 * change during training.
 *
 * @param input_size The input size \f$n\f$.
 * @param a The \f$a_i\f$ (amplitude) factors.
 * @param v The biases \f$b_i\f$.
 * @return A pointer to a new \ref gnn_divergence node.
 */
gnn_node *
gnn_affine_new (int input_size, double a, double b)
{
    int status;
    gnn_node *node;
    gnn_affine *anode;
    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);
    }

    /* allocate the node */
    anode = (gnn_affine *) malloc (sizeof (gnn_affine));
    if (anode == NULL)
    {
        GSL_ERROR_VAL ("could not allocate memory for gnn_affine node",
                       GSL_ENOMEM, NULL);
    }

    /* get view as a gnn_node */
    node = (gnn_node *) anode;

    /* Initialize the node */
    status = gnn_node_init (node,
                            "gnn_affine",
                            gnn_affine_f,
                            gnn_affine_dx,
                            gnn_affine_dw,
                            NULL);
    if (status)
    {
        GSL_ERROR_VAL ("could not initialize gnn_affine 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_affine node",
                       GSL_EFAILED, NULL);
    }

    /* create buffer */
    anode->buf = gsl_vector_alloc (input_size);
    if (anode->buf == NULL)
    {
        gnn_node_destroy (node);
        GSL_ERROR_VAL ("could not allocate buffer for gnn_affine 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);

    anode->a_view  = gsl_vector_subvector (w,  0, input_size);
    anode->da_view = gsl_vector_subvector (dw, 0, input_size);
    anode->af_view = gsl_vector_int_subvector (f, 0, input_size);

    anode->b_view  = gsl_vector_subvector (w, input_size, input_size);
    anode->db_view = gsl_vector_subvector (dw, input_size, input_size);
    anode->bf_view = gsl_vector_int_subvector (f, input_size, input_size);

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

    anode->b  = &(anode->b_view.vector);
    anode->db = &(anode->db_view.vector);
    anode->bf = &(anode->bf_view.vector);

    /* initialize values */
    gsl_vector_set_all (anode->a, a);
    gsl_vector_set_all (anode->b, b);

    /* update parameters */
    gnn_node_local_update (node);

    return node;
}

/**
 * @brief Creates a standard Affine Activation Function node.
 * @ingroup gnn_affine_doc
 *
 * This function creates a node of the gnn_affine type. The parameters
 * are initialized with amplitudes \f$a_i = 1\f$ and biases \f$b_i = 0\f$.
 *
 * @param input_size The input size \f$n\f$.
 * @return A pointer to a new \ref gnn_tanh node.
 */
gnn_node *
gnn_affine_standard_new (int input_size)
{
    return gnn_affine_new (input_size, 1.0, 0.0);
}

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