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/*

 * linear least squares model

 *

 * Copyright (c) 2006 Michael Niedermayer 

 *

 * This file is part of FFmpeg.

 *

 * FFmpeg is free software; you can redistribute it and/or

 * modify it under the terms of the GNU Lesser General Public

 * License as published by the Free Software Foundation; either

 * version 2.1 of the License, or (at your option) any later version.

 *

 * FFmpeg 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

 * Lesser General Public License for more details.

 *

 * You should have received a copy of the GNU Lesser General Public

 * License along with FFmpeg; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

 */

/**

 * @file

 * linear least squares model

 */

#include 

#include 

#include "attributes.h"

#include "version.h"

#include "lls1.h"

#if FF_API_LLS1

av_cold void avpriv_init_lls(LLSModel *m, int indep_count)

{

    memset(m, 0, sizeof(LLSModel));

    m->indep_count = indep_count;

}

void avpriv_update_lls(LLSModel *m, double *var, double decay)

{

    int i, j;

    for (i = 0; i <= m->indep_count; i++) {

        for (j = i; j <= m->indep_count; j++) {

            m->covariance[i][j] *= decay;

            m->covariance[i][j] += var[i] * var[j];

        }

    }

}

void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order)

{

    int i, j, k;

    double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0];

    double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1];

    double *covar_y                = m->covariance[0];

    int count                      = m->indep_count;

    for (i = 0; i < count; i++) {

        for (j = i; j < count; j++) {

            double sum = covar[i][j];

            for (k = i - 1; k >= 0; k--)

                sum -= factor[i][k] * factor[j][k];

            if (i == j) {

                if (sum < threshold)

                    sum = 1.0;

                factor[i][i] = sqrt(sum);

            } else {

                factor[j][i] = sum / factor[i][i];

            }

        }

    }

    for (i = 0; i < count; i++) {

        double sum = covar_y[i + 1];

        for (k = i - 1; k >= 0; k--)

            sum -= factor[i][k] * m->coeff[0][k];

        m->coeff[0][i] = sum / factor[i][i];

    }

    for (j = count - 1; j >= min_order; j--) {

        for (i = j; i >= 0; i--) {

            double sum = m->coeff[0][i];

            for (k = i + 1; k <= j; k++)

                sum -= factor[k][i] * m->coeff[j][k];

            m->coeff[j][i] = sum / factor[i][i];

        }

        m->variance[j] = covar_y[0];

        for (i = 0; i <= j; i++) {

            double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];

            for (k = 0; k < i; k++)

                sum += 2 * m->coeff[j][k] * covar[k][i];

            m->variance[j] += m->coeff[j][i] * sum;

        }

    }

}

double avpriv_evaluate_lls(LLSModel *m, double *param, int order)

{

    int i;

    double out = 0;

    for (i = 0; i <= order; i++)

        out += param[i] * m->coeff[order][i];

    return out;

}

#if FF_API_LLS_PRIVATE

av_cold void av_init_lls(LLSModel *m, int indep_count)

{

    avpriv_init_lls(m, indep_count);

}

void av_update_lls(LLSModel *m, double *param, double decay)

{

    avpriv_update_lls(m, param, decay);

}

void av_solve_lls(LLSModel *m, double threshold, int min_order)

{

    avpriv_solve_lls(m, threshold, min_order);

}

double av_evaluate_lls(LLSModel *m, double *param, int order)

{

    return avpriv_evaluate_lls(m, param, order);

}

#endif /* FF_API_LLS_PRIVATE */

#endif /* FF_API_LLS1 */

#ifdef TEST

#include 

#include 

#include "lfg.h"

int main(void)

{

    LLSModel m;

    int i, order;

    AVLFG lfg;

    av_lfg_init(&lfg, 1);

    avpriv_init_lls(&m, 3);

    for (i = 0; i < 100; i++) {

        double var[4];

        double eval;

        var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;

        var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;

        var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;

        var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;

        avpriv_update_lls(&m, var, 0.99);

        avpriv_solve_lls(&m, 0.001, 0);

        for (order = 0; order < 3; order++) {

            eval = avpriv_evaluate_lls(&m, var + 1, order);

            printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",

                   var[0], order, eval, sqrt(m.variance[order] / (i + 1)),

                   m.coeff[order][0], m.coeff[order][1],

                   m.coeff[order][2]);

        }

    }

    return 0;

}

#endif