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+/*
+ * 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
+==========================================================
+*/
+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 colum 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;
+}
+
+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;
+ }
+}
+
+
+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;
+ }
+ }
+}
+
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