/*
 * 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;
    	}
    }
}