/*
* 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;
}
}
}