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mexSG_WLS_opt.cpp
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mexSG_WLS_opt.cpp
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#include <math.h>
#include <time.h>
#include <string.h>
#include "mex.h"
#define min(X, Y) ((X) < (Y) ? (X) : (Y))
// size of input image, guidance image and SG_WLS
int rowNum, colNum, rc, ccImg, ccGuide, ccImgMinusChaNum, ccImgPlusChaNum, ccGuideMinusChaNum, ccGuidePlusChaNum;
int chaNumImg, chaNumGuide, chaNumImgX2, chaNumGuideX2;
int r, sysLen_row, sysLen_col;
// memory management
double *** memAllocDouble3(int row, int col, int cha);
double ** memAllocDouble2(int row, int col);
void memFreeDouble3(double ***p);
void memFreeDouble2(double **p);
// functions
void expLUT(double *LUT, double sigma, int chaNum, int len);
void fracLUT(double *LUT, double sigma, int chaNum, int len);
void img2vector_col(double ***img, double ***imgGuide, double **vectorImg, double **vectorGuide, int col);
void img2vector_row(double ***img, double ***imgGuide, double **vectorImg, double **vectorGuide, int row);
void vector2img_col(double ***img, double **vector, int col);
void vector2img_row(double ***img, double **vector, int row);
void getCount(double *count, int len, int r, int step);
void getLaplacian(double **vectorGuide, double *a, double **b, double **c, double lambda, double *rangeLUT, double *spatialLUT, int sysLen);
void pointDiv(double ***imgInter, double ***imgFiltered, double *count, int colDir);
// solvers
void solverForRadius1(double *a, double **b, double **c, double *alpha, double **gamma, double **beta, double **F, double **Y, double **X, int sysLen);
void solverForRadius2(double *a, double **b, double **c, double *alpha, double **gamma, double **beta, double **F, double **Y, double **X, int sysLen);
void solverForRadiusLargerThan2(double *a, double **b, double **c, double *alpha, double **gamma, double **beta, double **F, double **Y, double **X, int sysLen);
// main function
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
////// Input images ////////
double *img = (double*)mxGetData(prhs[0]), *guidance = (double*)mxGetData(prhs[1]); // input image to be filtered and the guidance image
if((mxGetDimensions(prhs[0])[0] != mxGetDimensions(prhs[1])[0]) || (mxGetDimensions(prhs[0])[1] != mxGetDimensions(prhs[1])[1]))
mexErrMsgTxt("The input image and the guidance image should be of the same size.");
// Get row, column and channel number
rowNum = mxGetDimensions(prhs[0])[0]; // row number
colNum = mxGetDimensions(prhs[0])[1]; // column number
rc = rowNum * colNum;
if(mxGetNumberOfDimensions(prhs[0]) == 2) // channel number of image to be filtered
chaNumImg = 1; // single channel image
else
chaNumImg = 3; // rgb image
ccImg = colNum * chaNumImg;
chaNumImgX2 = 2 * chaNumImg;
ccImgMinusChaNum = ccImg - chaNumImg;
ccImgPlusChaNum = ccImg + chaNumImg;
if(mxGetNumberOfDimensions(prhs[1]) == 2) // channel number of guidance image
chaNumGuide = 1; // single channel image
else
chaNumGuide = 3; // rgb image
ccGuide = colNum * chaNumGuide;
chaNumGuideX2 = 2 * chaNumGuide;
ccGuideMinusChaNum = ccGuide - chaNumGuide;
ccGuidePlusChaNum = ccGuide + chaNumGuide;
//////// SG_WLS parameters ///////////////
double lambda = mxGetScalar(prhs[2]); // lambda of the SG_WLS
double sigmaR = mxGetScalar(prhs[3]); // range sigma for the guidance weight
double sigmaS = mxGetScalar(prhs[4]); // spatial sigma for the guidance weight
r = (int)mxGetScalar(prhs[5]); // raius of the neighborhood
int step = (int)mxGetScalar(prhs[6]); // the step size between each SG_WLS
int iterNum = (int)mxGetScalar(prhs[7]); // number of iterations
int weightChoice = (int)mxGetScalar(prhs[8]); // 0 for exp weight, 1 for frac weight
// Transfer the input image and the guidance image into 3-dimention arrays
double ***imgFiltered = memAllocDouble3(rowNum, colNum, chaNumImg); // initialize the filtered image with the input image
double *ptr_imgFiltered = &imgFiltered[0][0][0];
for(int i=0; i<rowNum; i++)
for(int j=0; j<colNum; j++)
for(int k=0; k<chaNumImg; k++)
*ptr_imgFiltered++ = img[k * rc + j *rowNum + i];
double ***imgGuide = memAllocDouble3(rowNum, colNum, chaNumGuide);
double *ptr_imgGuide = &imgGuide[0][0][0];
for(int i=0; i<rowNum; i++)
for(int j=0; j<colNum; j++)
for(int k=0; k<chaNumGuide; k++)
*ptr_imgGuide++ = guidance[k * rc + j * rowNum + i];
// Intermediate output
double *** imgInter = memAllocDouble3(rowNum, colNum, chaNumImg);
// Output
plhs[0] = mxDuplicateArray(prhs[0]); // the output has the same size as the input image
double *imgResult = (double*) mxGetData(plhs[0]);
// SG-WLS related variables
sysLen_row = colNum * (2 * r + 1); // the size of the SG-WLS along the row direction
sysLen_col = rowNum * (2 * r + 1); // the size of the SG-WLS along the column direction
double *a_row = (double*) mxGetData(mxCreateDoubleMatrix(sysLen_row, 1, mxREAL));
double **b_row = memAllocDouble2(sysLen_row, r);
double **c_row = memAllocDouble2(sysLen_row, r);
double *a_col = (double*) mxGetData(mxCreateDoubleMatrix(sysLen_col, 1, mxREAL));
double **b_col = memAllocDouble2(sysLen_col, r);
double **c_col = memAllocDouble2(sysLen_col, r);
double *alpha_row = (double*) mxGetData(mxCreateDoubleMatrix(sysLen_row, 1, mxREAL));
double **gamma_row = memAllocDouble2(sysLen_row, r);
double **beta_row = memAllocDouble2(sysLen_row, r);
double *alpha_col = (double*) mxGetData(mxCreateDoubleMatrix(sysLen_col, 1, mxREAL));
double **gamma_col = memAllocDouble2(sysLen_col, r);
double **beta_col = memAllocDouble2(sysLen_col, r);
double **vectorImg_row = memAllocDouble2(sysLen_row, chaNumImg);
double **vectorGuide_row = memAllocDouble2(sysLen_row, chaNumGuide + 2); // RGB pixel values + x/y coordinates for spatial weight computation
double **vectorInter_row = memAllocDouble2(sysLen_row, chaNumImg); // intermediate variables 'F' in solving P*Y=F, Q*U=F
double **vectorFiltered_row = memAllocDouble2(sysLen_row, chaNumImg); // smoothed output 'U' in solving P*Y=F, Q*U=F
double **vectorImg_col = memAllocDouble2(sysLen_col, chaNumImg);
double **vectorGuide_col = memAllocDouble2(sysLen_col, chaNumGuide + 2);
double **vectorInter_col = memAllocDouble2(sysLen_col, chaNumImg);
double **vectorFiltered_col = memAllocDouble2(sysLen_col, chaNumImg);
// accumulate the count of the filtered value at the same location
double *count_row = (double *)mxGetData(mxCreateDoubleMatrix(rowNum, 1, mxREAL));
double *count_col = (double *)mxGetData(mxCreateDoubleMatrix(colNum, 1, mxREAL));
// weight lookup table
int maxRange = 255 + 10;
maxRange = chaNumGuide * maxRange * maxRange;
int maxSpatial = 2 * (2 * r + 1) * (2 * r + 1);
double *rangeLUT = (double *)mxGetData(mxCreateDoubleMatrix(maxRange, 1, mxREAL));
double *spatialLUT = (double *)mxGetData(mxCreateDoubleMatrix(maxSpatial, 1, mxREAL));
if(weightChoice == 0){
expLUT(rangeLUT, sigmaR, chaNumGuide, maxRange);
expLUT(spatialLUT, sigmaS, 1, maxSpatial);}
else if(weightChoice ==1){
fracLUT(rangeLUT, sigmaR, chaNumGuide, maxRange);
fracLUT(spatialLUT, sigmaS, 1, maxSpatial);}
else mexErrMsgTxt("Weight choice should be 0 (exponential) or 1 (fractional)\n.");
// maximum row/column number
int maxIterColNum = r + 1 + ((colNum - r - r - 1)/step)*step;
int maxIterRowNum = r + 1 + ((rowNum - r - r - 1)/step)*step;
int col, row, iter;
// do filtering
clock_t tStart = clock(); // time measurement;
for(iter=0; iter<iterNum; iter++)
{
/////////////// column direction //////////////
memset(count_col, 0.0, sizeof(double)*colNum);
memset(imgInter[0][0], 0.0, sizeof(double)*rc*chaNumImg);
getCount(count_col, colNum, r, step);
for(col=r; col<maxIterColNum; col+=step)
{
img2vector_col(imgFiltered, imgGuide, vectorImg_col, vectorGuide_col, col);
getLaplacian(vectorGuide_col, a_col, b_col, c_col, lambda, rangeLUT, spatialLUT, sysLen_col);
if(r==1)
solverForRadius1(a_col, b_col, c_col, alpha_col, gamma_col, beta_col, vectorImg_col, vectorInter_col, vectorFiltered_col, sysLen_col);
else if(r==2)
solverForRadius2(a_col, b_col, c_col, alpha_col, gamma_col, beta_col, vectorImg_col, vectorInter_col, vectorFiltered_col, sysLen_col);
else
solverForRadiusLargerThan2(a_col, b_col, c_col, alpha_col, gamma_col, beta_col, vectorImg_col, vectorInter_col, vectorFiltered_col, sysLen_col);
vector2img_col(imgInter, vectorFiltered_col, col);
}
// the last 2 * r + 1 columns
col = colNum - 1 - r;
img2vector_col(imgFiltered, imgGuide, vectorImg_col, vectorGuide_col, col);
getLaplacian(vectorGuide_col, a_col, b_col, c_col, lambda, rangeLUT, spatialLUT, sysLen_col);
if(r==1)
solverForRadius1(a_col, b_col, c_col, alpha_col, gamma_col, beta_col, vectorImg_col, vectorInter_col, vectorFiltered_col, sysLen_col);
else if(r==2)
solverForRadius2(a_col, b_col, c_col, alpha_col, gamma_col, beta_col, vectorImg_col, vectorInter_col, vectorFiltered_col, sysLen_col);
else
solverForRadiusLargerThan2(a_col, b_col, c_col, alpha_col, gamma_col, beta_col, vectorImg_col, vectorInter_col, vectorFiltered_col, sysLen_col);
vector2img_col(imgInter, vectorFiltered_col, col);
pointDiv(imgInter, imgFiltered, count_col, 1);
///////////////////// row direction //////////////////////
memset(count_row, 0.0, sizeof(double)*rowNum);
memset(imgInter[0][0], 0.0, sizeof(double)*rc*chaNumImg);
getCount(count_row, rowNum, r, step);
for(row=r; row<maxIterRowNum; row+=step)
{
img2vector_row(imgFiltered, imgGuide, vectorImg_row, vectorGuide_row, row);
getLaplacian(vectorGuide_row, a_row, b_row, c_row, lambda, rangeLUT, spatialLUT, sysLen_row);
if(r==1)
solverForRadius1(a_row, b_row, c_row, alpha_row, gamma_row, beta_row, vectorImg_row, vectorInter_row, vectorFiltered_row, sysLen_row);
else if(r==2)
solverForRadius2(a_row, b_row, c_row, alpha_row, gamma_row, beta_row, vectorImg_row, vectorInter_row, vectorFiltered_row, sysLen_row);
else
solverForRadiusLargerThan2(a_row, b_row, c_row, alpha_row, gamma_row, beta_row, vectorImg_row, vectorInter_row, vectorFiltered_row, sysLen_row);
vector2img_row(imgInter, vectorFiltered_row, row);
}
// the last 2 * r + 1 rows
row = rowNum - 1 - r;
img2vector_row(imgFiltered, imgGuide, vectorImg_row, vectorGuide_row, row);
getLaplacian(vectorGuide_row, a_row, b_row, c_row, lambda, rangeLUT, spatialLUT, sysLen_row);
if(r==1)
solverForRadius1(a_row, b_row, c_row, alpha_row, gamma_row, beta_row, vectorImg_row, vectorInter_row, vectorFiltered_row, sysLen_row);
else if(r==2)
solverForRadius2(a_row, b_row, c_row, alpha_row, gamma_row, beta_row, vectorImg_row, vectorInter_row, vectorFiltered_row, sysLen_row);
else
solverForRadiusLargerThan2(a_row, b_row, c_row, alpha_row, gamma_row, beta_row, vectorImg_row, vectorInter_row, vectorFiltered_row, sysLen_row);
vector2img_row(imgInter, vectorFiltered_row, row);
pointDiv(imgInter, imgFiltered, count_row, 0);
}
mexPrintf("Elapsed time is %f seconds.\n", double(clock() - tStart)/CLOCKS_PER_SEC);
// transfer to the output
ptr_imgFiltered = &(imgFiltered[0][0][0]);
for(int i=0; i<rowNum; i++)
{
for(int j=0; j<colNum; j++)
{
for(int k=0; k<chaNumImg; k++)
imgResult[k * rc + j * rowNum + i] = *ptr_imgFiltered++;
}
}
memFreeDouble3(imgFiltered);
memFreeDouble3(imgGuide);
memFreeDouble3(imgInter);
a_row = NULL;
a_col = NULL;
memFreeDouble2(b_row);
memFreeDouble2(b_col);
memFreeDouble2(c_row);
memFreeDouble2(c_col);
alpha_row = NULL;
alpha_col = NULL;
memFreeDouble2(beta_row);
memFreeDouble2(beta_col);
memFreeDouble2(gamma_row);
memFreeDouble2(gamma_col);
memFreeDouble2(vectorImg_row);
memFreeDouble2(vectorImg_col);
memFreeDouble2(vectorGuide_row);
memFreeDouble2(vectorGuide_col);
memFreeDouble2(vectorFiltered_row);
memFreeDouble2(vectorFiltered_col);
memFreeDouble2(vectorInter_row);
memFreeDouble2(vectorInter_col);
}
//============ Functions =============https://
double *** memAllocDouble3(int row, int col, int cha)
{
// allocate the memory for a 3-dimension array which can be indexed as pp[row][col][cha]
int padding=10;
double *a, **p, ***pp;
a=(double*) malloc(sizeof(double) * (row * col * cha + padding));
if(a==NULL) {mexErrMsgTxt("memAllocDouble: Memory allocate failure.\n"); }
p=(double**) malloc(sizeof(double*) * row * col);
pp=(double***) malloc(sizeof(double**) * row);
int cc = col * cha;
int i, j;
for(i=0; i<row; i++)
for(j=0; j<col; j++)
p[i * col + j] = &a[i * cc + j * cha];
for(i=0; i<row; i++)
pp[i] = &p[i* col];
return(pp);
}
///////////////////////////////
void memFreeDouble3(double ***p)
{
// free the memory of an allocated 3-dimension array
if(p!=NULL)
{
free(p[0][0]);
free(p[0]);
free(p);
p=NULL;
}
}
////////////////////////////////
double** memAllocDouble2(int row, int col)
{
// allocate the memory for a 2-dimension array which can be indexed as p[row][col]
int padding=10;
double *a, **p;
a=(double*) malloc(sizeof(double) * (row * col + padding));
if(a==NULL) {mexErrMsgTxt("memAllocDouble: Memory allocate failure.\n"); }
p=(double**) malloc(sizeof(double*) * row);
for(int i=0; i<row; i++) p[i] = &a[i * col];
return(p);
}
//////////////////////////////////
void memFreeDouble2(double **p)
{
// free the memory of an allocated 2-demision array
if(p!=NULL)
{
free(p[0]);
free(p);
p=NULL;
}
}
////////////////////////////////////////////////////
void expLUT(double *LUT, double sigma, int chaNum, int len)
{
double *ptr=&LUT[0];
for(int i=0; i<len; i++) *ptr++ = exp(double(-i) / (double(chaNum) * 2 * sigma * sigma));
}
///////////////////////////////////////////////////
void fracLUT(double *LUT, double sigma, int chaNum, int len)
{
double *ptr=&LUT[0];
for(int i=0; i<len; i++) *ptr++ = 1 / (pow(sqrt(double(i) / double(chaNum)), sigma) + 0.00001);
}
////////////////////////////////////////////////////
void img2vector_col(double ***img, double ***imgGuide, double **vectorImg, double **vectorGuide, int col)
{
// transform the block centered along column 'col' with radius 'r' into a vector whose length is 'rowNum * (2 * r + 1)'.
double *ptr_img, *ptr_guide, *ptr_vecImg, *ptr_vecGuide;
int i, j, k, colSlide;
bool forward=true;
colSlide = col - r;
ptr_vecImg = &vectorImg[0][0];
ptr_vecGuide = &vectorGuide[0][0];
ptr_img = &img[0][colSlide][0];
ptr_guide = &imgGuide[0][colSlide][0];
for(i=0; i<rowNum; i++)
{
for(j=-r; j<=r; j++)
{
if(forward){ // left-to-right extraction sliding direction
// for the image to be filtered
for(k=0; k<chaNumImg; k++)
*ptr_vecImg++ = *ptr_img++;
// for the guidance image
for(k=0; k<chaNumGuide; k++)
*ptr_vecGuide++ = *ptr_guide++;
// store the x/y pixel coordinate in the image coordinate system, to compute the spatial weight
*ptr_vecGuide++ = i;
*ptr_vecGuide++ = colSlide++;
}
else { // right-to-left extraction sliding direction
// for the image to be filtered
ptr_img -= chaNumImgX2;
for(k=0; k<chaNumImg; k++)
*ptr_vecImg++ = *ptr_img++;
// for the guidance image
ptr_guide -= chaNumGuideX2;
for(k=0; k<chaNumGuide; k++)
*ptr_vecGuide++ = *ptr_guide++;
// store the x/y pixel coordinate in the image coordinate system, to compute the spatial weight
*ptr_vecGuide++ = i;
*ptr_vecGuide++ = colSlide--;
}
}
if(forward){
// move to the next row
ptr_img += ccImgPlusChaNum;
ptr_guide += ccGuidePlusChaNum;
colSlide--;
}
else{
// move to the next row
ptr_img += ccImgMinusChaNum;
ptr_guide += ccGuideMinusChaNum;
colSlide++;
}
forward = !forward; // change sliding direction between left-to-right and right-to-left
}
}
//////////////////////////////////////////////////
void img2vector_row(double ***img, double ***imgGuide, double **vectorImg, double **vectorGuide, int row)
{
// transform the block centered along row 'row' with radius 'r' into a vector whose length is 'colNum * (2 * r + 1)'.
double *ptr_img, *ptr_guide, *ptr_vecImg, *ptr_vecGuide;
int i, j, k, rowSlide;
bool forward=true;
rowSlide = row - r;
ptr_vecImg = &vectorImg[0][0];
ptr_vecGuide = &vectorGuide[0][0];
ptr_img = &img[rowSlide][0][0];
ptr_guide = &imgGuide[rowSlide][0][0];
for(j=0; j<colNum; j++)
{
for(i=-r; i<=r; i++)
{
if(forward){ // up-bottom extraction sliding direction
// for the image to be filtered
for(k=0; k<chaNumImg; k++)
*ptr_vecImg++ = *ptr_img++;
ptr_img += ccImgMinusChaNum;
// for the guidance image
for(k=0; k<chaNumGuide; k++)
*ptr_vecGuide++ = *ptr_guide++;
ptr_guide += ccGuideMinusChaNum;
// store the x/y pixel coordinate in the image coordinate system, to compute the spatial weight
*ptr_vecGuide++ = rowSlide++;
*ptr_vecGuide++ = j;
}
else{ // bottom-up extraction sliding direction
// for the image to be filtered
for(k=0; k<chaNumImg; k++)
*ptr_vecImg++ = *ptr_img++;
ptr_img -= ccImgPlusChaNum;
// for the guidance image
for(k=0; k<chaNumGuide; k++)
*ptr_vecGuide++ = *ptr_guide++;
ptr_guide -= ccGuidePlusChaNum;
// store the x/y pixel coordinate in the image coordinate system, to compute the spatial weight
*ptr_vecGuide++ = rowSlide--;
*ptr_vecGuide++ = j;
}
}
if(forward){
// move to the next column
ptr_img -= ccImgMinusChaNum;
ptr_guide -= ccGuideMinusChaNum;
rowSlide--;
}
else{
// move to the next column
ptr_img += ccImgPlusChaNum;
ptr_guide += ccGuidePlusChaNum;
rowSlide++;
}
forward = !forward; // change the extraction sliding direction between bottom-up and up-bottom in each column of the image
}
}
///////////////////////////////////////////////////
void vector2img_col(double ***img, double **vector, int col)
{
// the inverse transform of 'img2vector_column'
double *ptr_img, *ptr_vec;
int i, j, k, colSlide;
bool forward=true;
colSlide = col - r;
ptr_vec = &vector[0][0];
ptr_img = &img[0][colSlide][0];
for(i=0; i<rowNum; i++)
{
for(j=-r; j<=r; j++)
{
if(forward){
// for image
for(k=0; k<chaNumImg; k++)
*ptr_img++ += *ptr_vec++;}
else {
// for image
ptr_img -= chaNumImgX2;
for(k=0; k<chaNumImg; k++)
*ptr_img++ += *ptr_vec++;}
}
if(forward)
// move to the next row
ptr_img += ccImgPlusChaNum;
else
// move to the next row
ptr_img += ccImgMinusChaNum;
forward = !forward; // change the extraction sliding direction between left-to-right and right-to-left in each row of the image
}
}
///////////////////////////////////////////////////
void vector2img_row(double ***img, double **vector, int row)
{
// the inverse transform of 'img2vector_column'
double *ptr_img, *ptr_vec;
int i, j, k, rowSlide;
bool forward=true;
rowSlide = row - r;
ptr_img = &img[rowSlide][0][0];
ptr_vec = &vector[0][0];
for(j=0; j<colNum; j++)
{
for(i=-r; i<=r; i++)
{
if(forward){ // up-bottom extraction sliding direction
// for image to be filtered
for(k=0; k<chaNumImg; k++)
*ptr_img++ += *ptr_vec++;
ptr_img += ccImgMinusChaNum;}
else{ // bottom-up extraction sliding direction
// for image to be filtered
for(k=0; k<chaNumImg; k++)
*ptr_img++ += *ptr_vec++;
ptr_img -= ccImgPlusChaNum;}
}
if(forward)
// move to the next column
ptr_img -= ccImgMinusChaNum;
else
// move to the next column
ptr_img += ccImgPlusChaNum;
forward = !forward; // change the extraction sliding direction between bottom-up and up-bottom in each column of the image
}
}
////////////////////
void getLaplacian(double **vectorGuide, double *a, double **b, double **c, double lambda, double *rangeLUT, double *spatialLUT, int sysLen)
{
double *ptr_guide_cur, *ptr_guide_nei, *ptr_a, *ptr_b, *ptr_c;
double diffR, temp, diffS, weightR, weightS, weight;
int i, j, k, n=sysLen, colNumGuideVector = chaNumGuide + 2;
ptr_guide_cur = &vectorGuide[0][0];
ptr_guide_nei = &vectorGuide[1][0];
ptr_a = &a[0];
ptr_b = &b[0][0];
ptr_c = &c[0][0];
// compute b and c first
for(i=0; i<n-1; i++)
{
for(j=1; j<=min(r, n - 1 - i); j++)
{
// range weight
diffR = 0;
for(k=0; k<chaNumGuide; k++){
temp = *ptr_guide_cur++ - *ptr_guide_nei++;
diffR += temp * temp;}
weightR = rangeLUT[(int)diffR];
// spatial weight
diffS = 0;
for(k=chaNumGuide; k<colNumGuideVector; k++){
temp = *ptr_guide_cur++ - *ptr_guide_nei++;
diffS += temp * temp; }
weightS = spatialLUT[(int)diffS];
weight = -lambda * weightR * weightS;
*ptr_b = weight;
*ptr_c = weight;
ptr_b++; ptr_c++;
ptr_guide_cur -= colNumGuideVector;
}
ptr_b += r - j + 1;
ptr_c += r - j + 1;
ptr_guide_cur += colNumGuideVector;
ptr_guide_nei = ptr_guide_cur + colNumGuideVector;
}
// compute a with the computed b and c
double *ptr_c_anchor;
ptr_a = &a[0];
ptr_b = &b[0][0];
ptr_c_anchor = &c[0][0];
temp = 0;
for(j=1; j<=r; j++)
temp -= *ptr_b++;
*ptr_a++ = 1 + temp;
///////////////
for(i=1; i<r+1; i++)
{
ptr_c = ptr_c_anchor++;
temp = 0;
for(j=1; j<=i; j++){
temp -= *ptr_c;
ptr_c += r - 1;}
for(j=1; j<=r; j++)
temp -= *ptr_b++;
*ptr_a++ = 1 + temp;
}
//////////
ptr_c_anchor--;
for(i=r + 1; i<n - r; i++)
{
ptr_c_anchor += r;
ptr_c = ptr_c_anchor;
temp = 0;
for(j=1; j<=r; j++){
temp -= *ptr_c + *ptr_b++;
ptr_c += r - 1;}
*ptr_a++ = 1 + temp;
}
////////////////
for(i=n - r; i<n - 1; i++)
{
ptr_c_anchor += r;
ptr_c = ptr_c_anchor;
temp = 0;
for(j=1; j<=r; j++){
temp -= *ptr_c;
ptr_c += r - 1;}
for(j=1; j<=n - 1 - i; j++)
temp -= *ptr_b++;
ptr_b += r - j + 1;
*ptr_a++ = 1 + temp;
}
////////////////////////
i = n - 1;
ptr_c_anchor += r;
ptr_c = ptr_c_anchor;
temp = 0;
for(j=1; j<=r; j++){
temp -= *ptr_c;
ptr_c += r - 1;}
*ptr_a = 1 + temp;
}
/////////////////////////////////////
void solverForRadius1(double *a, double **b, double **c, double *alpha, double **gamma, double **beta, double **F, double **Y, double **X, int sysLen)
{
int k, cha, n=sysLen;
double *ptr_a, *ptr_b, *ptr_c, *ptr_alpha, *ptr_gamma, *ptr_beta;
double tempAlpha, tempGamma, tempBeta;
ptr_a = &a[0]; ptr_b = &b[0][0]; ptr_c = &c[0][0];
ptr_alpha = &alpha[0]; ptr_beta = &beta[0][0];
// LU decomposition
tempAlpha = *ptr_a++;
tempGamma = *ptr_c++;
tempBeta = tempGamma / tempAlpha;
// tempBeta = *ptr_b++ / tempAlpha;
*ptr_alpha++ = tempAlpha;
*ptr_beta++ = tempBeta;
for(k=1; k<n - 1; k++)
{
tempAlpha = *ptr_a++ - tempGamma * tempBeta;
*ptr_alpha++ = tempAlpha;
tempGamma = *ptr_c++;
tempBeta = tempGamma / tempAlpha;
// tempBeta = *ptr_b++ / tempAlpha;
*ptr_beta++ = tempBeta;
}
*ptr_alpha = *ptr_a - tempGamma * tempBeta;
/////// Solve ///////////
double *ptr_F, *ptr_Y, *ptr_X, *ptr_Y_pre;
ptr_alpha = &alpha[0];
ptr_gamma = &c[0][0]; // ptr_gamma = &gamma[0][0]; we always have \gamma_k,i = c_k,i when r=1
ptr_Y_pre=&Y[0][0];
ptr_Y = &Y[0][0];
ptr_F = &F[0][0];
// L * Y = F
tempAlpha = *ptr_alpha++;
for(cha=0; cha<chaNumImg; cha++)
*ptr_Y++ = *ptr_F++ / tempAlpha;
for(k=1; k<n; k++)
{
tempAlpha = *ptr_alpha++;
tempGamma = *ptr_gamma++;
for(cha=0; cha<chaNumImg; cha++)
*ptr_Y++ = (*ptr_F++ - tempGamma * (*ptr_Y_pre++)) / tempAlpha;
}
// U*X = Y;
double *ptr_X_pre=&X[n-1][chaNumImg - 1];
ptr_X = ptr_X_pre;
ptr_Y = &Y[n-1][chaNumImg - 1];
for(cha=0; cha<chaNumImg; cha++)
*ptr_X-- = *ptr_Y--;
ptr_beta = &beta[n-2][0];
for(k=n-2; k>=0; k--)
{
tempBeta = *ptr_beta--;
for(cha=0; cha<chaNumImg; cha++)
*ptr_X-- = *ptr_Y-- - tempBeta * (*ptr_X_pre--);
}
}
//////////////////////////////
void solverForRadius2(double *a, double **b, double **c, double *alpha, double **gamma, double **beta, double **F, double **Y, double **X, int sysLen)
{
int i, k, t, n=sysLen;
double *ptr_a, *ptr_b, *ptr_c,*ptr_alpha, *ptr_gamma, *ptr_beta, *ptr_gamma_temp, *ptr_beta_temp;
double tempAlpha, tempGamma, tempBeta;
ptr_a = &a[0]; ptr_b = &b[0][0]; ptr_c = &c[0][0];
ptr_alpha = &alpha[0]; ptr_gamma = &gamma[0][0]; ptr_beta = &beta[0][0];
ptr_gamma_temp = ptr_gamma; ptr_beta_temp = ptr_beta;
//////////////////// LU decomposition ///////////////////
// k = 0;
tempAlpha = *ptr_a++;
*ptr_alpha++ = tempAlpha;
for(i=0; i<r; i++){
*ptr_gamma++ = *ptr_c++;
*ptr_beta++ = *ptr_b++ / tempAlpha;
}
//////////
// k = 1;
tempAlpha = *ptr_a++ - *ptr_gamma_temp * (*ptr_beta_temp);
*ptr_alpha++ = tempAlpha;
*ptr_gamma++ = *ptr_c++ - *(ptr_gamma_temp + 1) * *ptr_beta_temp;
*ptr_beta++ = (*ptr_b++ - *ptr_gamma_temp * (*(ptr_beta_temp + 1))) / tempAlpha;
*ptr_gamma++ = *ptr_c++;
*ptr_beta++ = *ptr_b++ / tempAlpha;
ptr_gamma_temp++;
ptr_beta_temp++;
///////////
for(k=2; k<n-r; k++)
{
// alpha
tempAlpha = 0;
for(t=1; t<=r; t++)
tempAlpha += *ptr_gamma_temp++ * (*ptr_beta_temp++);
tempAlpha = *ptr_a++ - tempAlpha;
*ptr_alpha++ = tempAlpha;
//gamma, beta
*ptr_gamma++ = *ptr_c++ - *ptr_gamma_temp * (*(ptr_beta_temp - 1));
*ptr_beta++ = (*ptr_b++ - *(ptr_gamma_temp - 1) * (*ptr_beta_temp)) / tempAlpha;
*ptr_gamma++ = *ptr_c++;
*ptr_beta++ = *ptr_b++ / tempAlpha;
}
////////
// k=n-2
//// alpha
tempAlpha = 0;
for(t=1; t<=r; t++)
tempAlpha += *ptr_gamma_temp++ * (*ptr_beta_temp++);
tempAlpha = *ptr_a++ - tempAlpha;
*ptr_alpha++ = tempAlpha;
//gamma, beta
*ptr_gamma++ = *ptr_c++ - *ptr_gamma_temp * (*(ptr_beta_temp - 1));
*ptr_beta++ = (*ptr_b++ - *(ptr_gamma_temp - 1) * (*ptr_beta_temp)) / tempAlpha;
////////
// k = n - 1;
tempAlpha = 0;
for(t=1; t<=r; t++)
tempAlpha += *ptr_gamma_temp++ * (*ptr_beta_temp++);
*ptr_alpha = *ptr_a - tempAlpha;
///////////////////////////// Solve /////////////////////////
int cha;
double tempX, tempY;//, tempGamma, tempBeta;
double *ptr_X, *ptr_X_pre, *ptr_F, *ptr_Y, *ptr_Y_pre;
ptr_Y = &Y[0][0]; ptr_Y_pre = ptr_Y; ptr_F = &F[0][0];
ptr_alpha = &alpha[0]; ptr_gamma = &gamma[0][0];
////////////////// L*Y = F ///////////////////
// k = 0;
tempAlpha = *ptr_alpha++;
for(cha=0; cha<chaNumImg; cha++)
*ptr_Y++ = *ptr_F++ / tempAlpha;
// k = 1;
tempGamma = *ptr_gamma++;
tempAlpha = *ptr_alpha++;
for(cha=0; cha<chaNumImg; cha++)
*ptr_Y++ = (*ptr_F++ - tempGamma * (*ptr_Y_pre++)) / tempAlpha;
//////////
ptr_Y_pre -= chaNumImg;
for(k=2; k<n; k++)
{
tempAlpha = *ptr_alpha++;
for(cha=0; cha<chaNumImg; cha++){
tempY = 0;
for(t=1; t<=r; t++) {
tempY += *ptr_gamma++ * (*ptr_Y_pre);
ptr_Y_pre += chaNumImg;}
*ptr_Y++ = (*ptr_F++ - tempY) / tempAlpha;
ptr_gamma -= r; ptr_Y_pre -= r * chaNumImg - 1;
}
ptr_gamma += r;
}
////////////// U*X = Y ////////////////////
ptr_X = &X[n - 1][chaNumImg - 1]; ptr_X_pre = ptr_X; ptr_Y = &Y[n - 1][chaNumImg - 1];
// k = n - 1
for(cha=0; cha<chaNumImg; cha++)
*ptr_X-- = *ptr_Y--;
// k = n - 2;
ptr_beta = &beta[n - 2][0];
tempBeta = *ptr_beta--;
for(cha=0; cha<chaNumImg; cha++)
*ptr_X-- = *ptr_Y-- - tempBeta * (*ptr_X_pre--);
//////////
ptr_X_pre += chaNumImg;
for(k=n-3; k>=0; k--)
{
for(cha=0; cha<chaNumImg; cha++){
tempX = 0;
for(t=1; t<=r; t++){
tempX += *ptr_beta-- * (*ptr_X_pre);
ptr_X_pre -= chaNumImg;}
*ptr_X-- = *ptr_Y-- - tempX;
ptr_beta += r; ptr_X_pre += r * chaNumImg - 1;
}
ptr_beta -= r;
}
}
//////////////////////////////
void solverForRadiusLargerThan2(double *a, double **b, double **c, double *alpha, double **gamma, double **beta, double **F, double **Y, double **X, int sysLen)
{
int i, maxt, k, t, n=sysLen, rMinusOne = r - 1;
double *ptr_a, *ptr_b, *ptr_c, *ptr_alpha, *ptr_gamma, *ptr_beta, *ptr_gamma_temp, *ptr_beta_temp;
double tempAlpha, tempGamma, tempBeta;
ptr_a = &a[0]; ptr_b = &b[0][0]; ptr_c = &c[0][0];
ptr_alpha = &alpha[0]; ptr_gamma = &gamma[0][0]; ptr_beta = &beta[0][0];
ptr_gamma_temp = ptr_gamma; ptr_beta_temp = ptr_beta;
//////////////////// Decomposition ///////////////////
// k = 0;
tempAlpha = *ptr_a++;
*ptr_alpha++ = tempAlpha;
for(i=0; i<r; i++){
*ptr_gamma++ = *ptr_c++;
*ptr_beta++ = *ptr_b++ / tempAlpha;}
//////////
// k = 1;
//// alpha
tempAlpha = *ptr_a++ - *ptr_gamma_temp * (*ptr_beta_temp);
*ptr_alpha++ = tempAlpha;
////// gamma, beta
for(i=0; i<r-1; i++){
*ptr_gamma++ = *ptr_c++ - *(ptr_gamma_temp + i + 1) * (*ptr_beta_temp);
*ptr_beta++ =(*ptr_b++ - *ptr_gamma_temp * (*(ptr_beta_temp + i + 1))) / tempAlpha;}
*ptr_gamma++ = *ptr_c++;
*ptr_beta++ = *ptr_b++ / tempAlpha;
//////////
for(k=2; k<r; k++)
{
ptr_gamma_temp += r;
ptr_beta_temp += r;
//// alpha
tempAlpha = 0;
for(t=1; t<=k; t++){
tempAlpha += *ptr_gamma_temp * (*ptr_beta_temp);
ptr_gamma_temp -= rMinusOne;
ptr_beta_temp -= rMinusOne;}
tempAlpha = *ptr_a++ - tempAlpha;
*ptr_alpha++ = tempAlpha;
ptr_gamma_temp += k * rMinusOne;
ptr_beta_temp += k * rMinusOne;
////// gamma, beta
for(i=0; i<r-1; i++)
{
maxt = min(k, r - i - 1);
tempGamma = 0;
tempBeta = 0;
for(t=1; t<=maxt; t++){
tempGamma += *(ptr_gamma_temp + i + 1) * (*ptr_beta_temp);
tempBeta += *ptr_gamma_temp * (*(ptr_beta_temp + i + 1));
ptr_gamma_temp -= rMinusOne;
ptr_beta_temp -= rMinusOne;}
*ptr_gamma++ = *ptr_c++ - tempGamma;
*ptr_beta++ = (*ptr_b++ - tempBeta) / tempAlpha;
ptr_gamma_temp += maxt * rMinusOne;
ptr_beta_temp += maxt * rMinusOne;
}
*ptr_gamma++ = *ptr_c++;
*ptr_beta++ = *ptr_b++ / tempAlpha;
}
/////////////
for(k=r; k<n-r; k++)
{
ptr_gamma_temp += r;
ptr_beta_temp += r;
//// alpha
tempAlpha = 0;
for(t=1; t<=r; t++){
tempAlpha += *ptr_gamma_temp * (*ptr_beta_temp);
ptr_gamma_temp -= rMinusOne;
ptr_beta_temp -= rMinusOne;}