openjpeg/src/lib/openjp2/invert.c

/*
 * The copyright in this software is being made available under the 2-clauses
 * BSD License, included below. This software may be subject to other third
 * party and contributor rights, including patent rights, and no such rights
 * are granted under this license.
 *
 * Copyright (c) 2008, Jerome Fimes, Communications & Systemes <jerome.fimes@c-s.fr>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS `AS IS'
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

#include "opj_includes.h"

/**
 * LUP decomposition
 */
static OPJ_BOOL opj_lupDecompose(OPJ_FLOAT32 * matrix,
                                 OPJ_UINT32 * permutations,
                                 OPJ_FLOAT32 * p_swap_area,
                                 OPJ_UINT32 nb_compo);
/**
 * LUP solving
 */
static void opj_lupSolve(OPJ_FLOAT32 * pResult,
                         OPJ_FLOAT32* pMatrix,
                         OPJ_FLOAT32* pVector,
                         OPJ_UINT32* pPermutations,
                         OPJ_UINT32 nb_compo,
                         OPJ_FLOAT32 * p_intermediate_data);

/**
 *LUP inversion (call with the result of lupDecompose)
 */
static void opj_lupInvert(OPJ_FLOAT32 * pSrcMatrix,
                          OPJ_FLOAT32 * pDestMatrix,
                          OPJ_UINT32 nb_compo,
                          OPJ_UINT32 * pPermutations,
                          OPJ_FLOAT32 * p_src_temp,
                          OPJ_FLOAT32 * p_dest_temp,
                          OPJ_FLOAT32 * p_swap_area);

/*
==========================================================
   Matric inversion interface
==========================================================
*/
/**
 * Matrix inversion.
 */
OPJ_BOOL opj_matrix_inversion_f(OPJ_FLOAT32 * pSrcMatrix,
                                OPJ_FLOAT32 * pDestMatrix,
                                OPJ_UINT32 nb_compo)
{
    OPJ_BYTE * l_data = 00;
    OPJ_UINT32 l_permutation_size = nb_compo * (OPJ_UINT32)sizeof(OPJ_UINT32);
    OPJ_UINT32 l_swap_size = nb_compo * (OPJ_UINT32)sizeof(OPJ_FLOAT32);
    OPJ_UINT32 l_total_size = l_permutation_size + 3 * l_swap_size;
    OPJ_UINT32 * lPermutations = 00;
    OPJ_FLOAT32 * l_double_data = 00;

    l_data = (OPJ_BYTE *) opj_malloc(l_total_size);
    if (l_data == 0) {
        return OPJ_FALSE;
    }
    lPermutations = (OPJ_UINT32 *) l_data;
    l_double_data = (OPJ_FLOAT32 *)(l_data + l_permutation_size);
    memset(lPermutations, 0, l_permutation_size);

    if (! opj_lupDecompose(pSrcMatrix, lPermutations, l_double_data, nb_compo)) {
        opj_free(l_data);
        return OPJ_FALSE;
    }

    opj_lupInvert(pSrcMatrix, pDestMatrix, nb_compo, lPermutations, l_double_data,
                  l_double_data + nb_compo, l_double_data + 2 * nb_compo);
    opj_free(l_data);

    return OPJ_TRUE;
}


/*
==========================================================
   Local functions
==========================================================
*/
static OPJ_BOOL opj_lupDecompose(OPJ_FLOAT32 * matrix,
                                 OPJ_UINT32 * permutations,
                                 OPJ_FLOAT32 * p_swap_area,
                                 OPJ_UINT32 nb_compo)
{
    OPJ_UINT32 * tmpPermutations = permutations;
    OPJ_UINT32 * dstPermutations;
    OPJ_UINT32 k2 = 0, t;
    OPJ_FLOAT32 temp;
    OPJ_UINT32 i, j, k;
    OPJ_FLOAT32 p;
    OPJ_UINT32 lLastColum = nb_compo - 1;
    OPJ_UINT32 lSwapSize = nb_compo * (OPJ_UINT32)sizeof(OPJ_FLOAT32);
    OPJ_FLOAT32 * lTmpMatrix = matrix;
    OPJ_FLOAT32 * lColumnMatrix, * lDestMatrix;
    OPJ_UINT32 offset = 1;
    OPJ_UINT32 lStride = nb_compo - 1;

    /*initialize permutations */
    for (i = 0; i < nb_compo; ++i) {
        *tmpPermutations++ = i;
    }
    /* now make a pivot with column switch */
    tmpPermutations = permutations;
    for (k = 0; k < lLastColum; ++k) {
        p = 0.0;

        /* take the middle element */
        lColumnMatrix = lTmpMatrix + k;

        /* make permutation with the biggest value in the column */
        for (i = k; i < nb_compo; ++i) {
            temp = ((*lColumnMatrix > 0) ? *lColumnMatrix : -(*lColumnMatrix));
            if (temp > p) {
                p = temp;
                k2 = i;
            }
            /* next line */
            lColumnMatrix += nb_compo;
        }

        /* a whole rest of 0 -> non singular */
        if (p == 0.0) {
            return OPJ_FALSE;
        }

        /* should we permute ? */
        if (k2 != k) {
            /*exchange of line */
            /* k2 > k */
            dstPermutations = tmpPermutations + k2 - k;
            /* swap indices */
            t = *tmpPermutations;
            *tmpPermutations = *dstPermutations;
            *dstPermutations = t;

            /* and swap entire line. */
            lColumnMatrix = lTmpMatrix + (k2 - k) * nb_compo;
            memcpy(p_swap_area, lColumnMatrix, lSwapSize);
            memcpy(lColumnMatrix, lTmpMatrix, lSwapSize);
            memcpy(lTmpMatrix, p_swap_area, lSwapSize);
        }

        /* now update data in the rest of the line and line after */
        lDestMatrix = lTmpMatrix + k;
        lColumnMatrix = lDestMatrix + nb_compo;
        /* take the middle element */
        temp = *(lDestMatrix++);

        /* now compute up data (i.e. coeff up of the diagonal). */
        for (i = offset; i < nb_compo; ++i)  {
            /*lColumnMatrix; */
            /* divide the lower column elements by the diagonal value */

            /* matrix[i][k] /= matrix[k][k]; */
            /* p = matrix[i][k] */
            p = *lColumnMatrix / temp;
            *(lColumnMatrix++) = p;

            for (j = /* k + 1 */ offset; j < nb_compo; ++j) {
                /* matrix[i][j] -= matrix[i][k] * matrix[k][j]; */
                *(lColumnMatrix++) -= p * (*(lDestMatrix++));
            }
            /* come back to the k+1th element */
            lDestMatrix -= lStride;
            /* go to kth element of the next line */
            lColumnMatrix += k;
        }

        /* offset is now k+2 */
        ++offset;
        /* 1 element less for stride */
        --lStride;
        /* next line */
        lTmpMatrix += nb_compo;
        /* next permutation element */
        ++tmpPermutations;
    }
    return OPJ_TRUE;
}

static void opj_lupSolve(OPJ_FLOAT32 * pResult,
                         OPJ_FLOAT32 * pMatrix,
                         OPJ_FLOAT32 * pVector,
                         OPJ_UINT32* pPermutations,
                         OPJ_UINT32 nb_compo, OPJ_FLOAT32 * p_intermediate_data)
{
    OPJ_INT32 k;
    OPJ_UINT32 i, j;
    OPJ_FLOAT32 sum;
    OPJ_FLOAT32 u;
    OPJ_UINT32 lStride = nb_compo + 1;
    OPJ_FLOAT32 * lCurrentPtr;
    OPJ_FLOAT32 * lIntermediatePtr;
    OPJ_FLOAT32 * lDestPtr;
    OPJ_FLOAT32 * lTmpMatrix;
    OPJ_FLOAT32 * lLineMatrix = pMatrix;
    OPJ_FLOAT32 * lBeginPtr = pResult + nb_compo - 1;
    OPJ_FLOAT32 * lGeneratedData;
    OPJ_UINT32 * lCurrentPermutationPtr = pPermutations;


    lIntermediatePtr = p_intermediate_data;
    lGeneratedData = p_intermediate_data + nb_compo - 1;

    for (i = 0; i < nb_compo; ++i) {
        sum = 0.0;
        lCurrentPtr = p_intermediate_data;
        lTmpMatrix = lLineMatrix;
        for (j = 1; j <= i; ++j) {
            /* sum += matrix[i][j-1] * y[j-1]; */
            sum += (*(lTmpMatrix++)) * (*(lCurrentPtr++));
        }
        /*y[i] = pVector[pPermutations[i]] - sum; */
        *(lIntermediatePtr++) = pVector[*(lCurrentPermutationPtr++)] - sum;
        lLineMatrix += nb_compo;
    }

    /* we take the last point of the matrix */
    lLineMatrix = pMatrix + nb_compo * nb_compo - 1;

    /* and we take after the last point of the destination vector */
    lDestPtr = pResult + nb_compo;


    assert(nb_compo != 0);
    for (k = (OPJ_INT32)nb_compo - 1; k != -1 ; --k) {
        sum = 0.0;
        lTmpMatrix = lLineMatrix;
        u = *(lTmpMatrix++);
        lCurrentPtr = lDestPtr--;
        for (j = (OPJ_UINT32)(k + 1); j < nb_compo; ++j) {
            /* sum += matrix[k][j] * x[j] */
            sum += (*(lTmpMatrix++)) * (*(lCurrentPtr++));
        }
        /*x[k] = (y[k] - sum) / u; */
        *(lBeginPtr--) = (*(lGeneratedData--) - sum) / u;
        lLineMatrix -= lStride;
    }
}


static void opj_lupInvert(OPJ_FLOAT32 * pSrcMatrix,
                          OPJ_FLOAT32 * pDestMatrix,
                          OPJ_UINT32 nb_compo,
                          OPJ_UINT32 * pPermutations,
                          OPJ_FLOAT32 * p_src_temp,
                          OPJ_FLOAT32 * p_dest_temp,
                          OPJ_FLOAT32 * p_swap_area)
{
    OPJ_UINT32 j, i;
    OPJ_FLOAT32 * lCurrentPtr;
    OPJ_FLOAT32 * lLineMatrix = pDestMatrix;
    OPJ_UINT32 lSwapSize = nb_compo * (OPJ_UINT32)sizeof(OPJ_FLOAT32);

    for (j = 0; j < nb_compo; ++j) {
        lCurrentPtr = lLineMatrix++;
        memset(p_src_temp, 0, lSwapSize);
        p_src_temp[j] = 1.0;
        opj_lupSolve(p_dest_temp, pSrcMatrix, p_src_temp, pPermutations, nb_compo,
                     p_swap_area);

        for (i = 0; i < nb_compo; ++i) {
            *(lCurrentPtr) = p_dest_temp[i];
            lCurrentPtr += nb_compo;
        }
    }
}