openjpeg/libopenjpeg/invert.c

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/*
* 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 "invert.h"
#include "opj_malloc.h"
bool opj_lupDecompose(OPJ_FLOAT32 * matrix,OPJ_UINT32 * permutations, OPJ_FLOAT32 * p_swap_area,OPJ_UINT32 n);
void opj_lupSolve(OPJ_FLOAT32 * pResult, OPJ_FLOAT32* pMatrix, OPJ_FLOAT32* pVector, OPJ_UINT32* pPermutations, OPJ_UINT32 n,OPJ_FLOAT32 * p_intermediate_data);
void opj_lupInvert (OPJ_FLOAT32 * pSrcMatrix,
OPJ_FLOAT32 * pDestMatrix,
OPJ_UINT32 n,
OPJ_UINT32 * pPermutations,
OPJ_FLOAT32 * p_src_temp,
OPJ_FLOAT32 * p_dest_temp,
OPJ_FLOAT32 * p_swap_area);
/**
* Matrix inversion.
*/
bool opj_matrix_inversion_f(OPJ_FLOAT32 * pSrcMatrix,OPJ_FLOAT32 * pDestMatrix, OPJ_UINT32 n)
{
OPJ_BYTE * l_data = 00;
OPJ_UINT32 l_permutation_size = n * sizeof(OPJ_UINT32);
OPJ_UINT32 l_swap_size = n * 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 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,n))
{
opj_free(l_data);
return false;
}
opj_lupInvert(pSrcMatrix,pDestMatrix,n,lPermutations,l_double_data,l_double_data + n,l_double_data + 2*n);
opj_free(l_data);
return true;
}
/**
* LUP decomposition
*/
bool opj_lupDecompose(OPJ_FLOAT32 * matrix,OPJ_UINT32 * permutations, OPJ_FLOAT32 * p_swap_area,OPJ_UINT32 n)
{
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 = n - 1;
OPJ_UINT32 lSwapSize = n * sizeof(OPJ_FLOAT32);
OPJ_FLOAT32 * lTmpMatrix = matrix;
OPJ_FLOAT32 * lColumnMatrix,* lDestMatrix;
OPJ_UINT32 offset = 1;
OPJ_UINT32 lStride = n-1;
//initialize permutations
for
(i = 0; i < n; ++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 < n; ++i)
{
temp = ((*lColumnMatrix > 0) ? *lColumnMatrix : -(*lColumnMatrix));
if
(temp > p)
{
p = temp;
k2 = i;
}
// next line
lColumnMatrix += n;
}
// a whole rest of 0 -> non singular
if
(p == 0.0)
{
return 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) * n;
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 + n;
// take the middle element
temp = *(lDestMatrix++);
// now compute up data (i.e. coeff up of the diagonal).
for (i = offset; i < n; ++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 < n; ++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+=n;
// next permutation element
++tmpPermutations;
}
return true;
}
/**
* LUP solving
*/
void opj_lupSolve (OPJ_FLOAT32 * pResult, OPJ_FLOAT32 * pMatrix, OPJ_FLOAT32 * pVector, OPJ_UINT32* pPermutations, OPJ_UINT32 n,OPJ_FLOAT32 * p_intermediate_data)
{
OPJ_UINT32 i,j;
OPJ_FLOAT32 sum;
OPJ_FLOAT32 u;
OPJ_UINT32 lStride = n+1;
OPJ_FLOAT32 * lCurrentPtr;
OPJ_FLOAT32 * lIntermediatePtr;
OPJ_FLOAT32 * lDestPtr;
OPJ_FLOAT32 * lTmpMatrix;
OPJ_FLOAT32 * lLineMatrix = pMatrix;
OPJ_FLOAT32 * lBeginPtr = pResult + n - 1;
OPJ_FLOAT32 * lGeneratedData;
OPJ_UINT32 * lCurrentPermutationPtr = pPermutations;
lIntermediatePtr = p_intermediate_data;
lGeneratedData = p_intermediate_data + n - 1;
for
(i = 0; i < n; ++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 += n;
}
// we take the last point of the matrix
lLineMatrix = pMatrix + n*n - 1;
// and we take after the last point of the destination vector
lDestPtr = pResult + n;
for
(i = n - 1; i != -1 ; --i)
{
sum = 0.0;
lTmpMatrix = lLineMatrix;
u = *(lTmpMatrix++);
lCurrentPtr = lDestPtr--;
for
(j = i + 1; j < n; ++j)
{
// sum += matrix[i][j] * x[j]
sum += (*(lTmpMatrix++)) * (*(lCurrentPtr++));
}
//x[i] = (y[i] - sum) / u;
*(lBeginPtr--) = (*(lGeneratedData--) - sum) / u;
lLineMatrix -= lStride;
}
}
/** LUP inversion (call with the result of lupDecompose)
*/
void opj_lupInvert (
OPJ_FLOAT32 * pSrcMatrix,
OPJ_FLOAT32 * pDestMatrix,
OPJ_UINT32 n,
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 = n * sizeof(OPJ_FLOAT32);
for
(j = 0; j < n; ++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, n , p_swap_area);
for
(i = 0; i < n; ++i)
{
*(lCurrentPtr) = p_dest_temp[i];
lCurrentPtr+=n;
}
}
}