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alard.c
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alard.c
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#include<stdio.h>
#include<string.h>
#include<math.h>
#include<malloc.h>
#include<stdlib.h>
#include<fitsio.h>
#include "defaults.h"
#include "globals.h"
#include "functions.h"
/*
Several of these subroutines appear originally in code created by
Cristophe Alard for ISIS, but have been modified and/or rewritten
for the current software package. In particular, the construction
of the least squares matrices have been taken directly from the ISIS
code.
08/20/01 acbecker@physics.bell-labs.com
*/
void getKernelVec() {
/*****************************************************
* Fills kernel_vec with kernel weight filter, called only once
*****************************************************/
int ig, idegx, idegy, nvec;
int ren;
nvec = 0;
for (ig = 0; ig < ngauss; ig++) {
for (idegx = 0; idegx <= deg_fixe[ig]; idegx++) {
for (idegy = 0; idegy <= deg_fixe[ig]-idegx; idegy++) {
/* stores kernel weight mask for each order */
kernel_vec[nvec] = kernel_vector(nvec, idegx, idegy, ig, &ren);
nvec++;
}
}
}
}
int fillStamp(stamp_struct *stamp, float *imConv, float *imRef) {
/*****************************************************
* Fills stamp->vectors with convolved images, and
* pixel indices multiplied by each other for background fit
*****************************************************/
int ren = 0;
int i,j,xi,yi,dx,dy,idegx,idegy,di,dj,nv,ig,nvec;
double ax,ay,xf,yf;
double *im;
float rPixX2, rPixY2;
rPixX2 = 0.5 * rPixX;
rPixY2 = 0.5 * rPixY;
if (verbose >= 1)
fprintf(stderr, " xs : %4i ys : %4i sig: %6.3f sscnt: %4i nss: %4i \n",
stamp->x, stamp->y, stamp->chi2, stamp->sscnt, stamp->nss);
if (stamp->sscnt >= stamp->nss) {
/* have gone through all the good substamps, reject this stamp */
/*if (verbose >= 2) fprintf(stderr, " ******** REJECT stamp (out of substamps)\n");*/
if (verbose >= 1)
fprintf(stderr, " Reject stamp\n");
return 1;
}
nvec = 0;
for (ig = 0; ig < ngauss; ig++) {
for (idegx = 0; idegx <= deg_fixe[ig]; idegx++) {
for (idegy = 0; idegy <= deg_fixe[ig]-idegx; idegy++) {
ren = 0;
dx = (idegx / 2) * 2 - idegx;
dy = (idegy / 2) * 2 - idegy;
if (dx == 0 && dy == 0 && nvec > 0)
ren = 1;
/* fill stamp->vectors[nvec] with convolved image */
/* image is convolved with functional form of kernel, fit later for amplitude */
xy_conv_stamp(stamp, imConv, nvec, ren);
++nvec;
}
}
}
/* get the krefArea data */
if (cutSStamp(stamp, imRef))
return 1;
/* fill stamp->vectors[nvec+++] with x^(bg) * y^(bg) for background fit */
xi = stamp->xss[stamp->sscnt];
yi = stamp->yss[stamp->sscnt];
di = xi - hwKSStamp;
dj = yi - hwKSStamp;
for (i = xi - hwKSStamp; i <= xi + hwKSStamp; i++) {
xf = (i - rPixX2) / rPixX2;
for (j = yi - hwKSStamp; j <= yi + hwKSStamp; j++) {
/* fprintf(stderr, "%d %d %d %d %d %d\n", k, xi, yi,i, j, fwKSStamp); */
yf = (j - rPixY2) / rPixY2;
ax = 1.0;
nv = nvec;
for (idegx = 0; idegx <= bgOrder; idegx++) {
ay = 1.0;
for (idegy = 0; idegy <= bgOrder - idegx; idegy++) {
im = stamp->vectors[nv];
im[i-di+fwKSStamp*(j-dj)] = ax * ay;
ay *= yf;
++nv;
}
ax *= xf;
}
}
}
/* build stamp->mat from stamp->vectors */
build_matrix0(stamp);
/* build stamp->scprod from stamp->vectors and imRef */
build_scprod0(stamp, imRef);
return 0;
}
double *kernel_vector(int n, int deg_x, int deg_y, int ig, int *ren) {
/*****************************************************
* Creates kernel sized entry for kernel_vec for each kernel degree
* Mask of filter_x * filter_y, filter = exp(-x**2 sig) * x^deg
* Subtract off kernel_vec[0] if n > 0
* NOTE: this does not use any image
******************************************************/
double *vector=NULL,*kernel0=NULL;
int i,j,k,dx,dy,ix;
double sum_x,sum_y,x,qe;
if (usePCA) {
return kernel_vector_PCA(n, deg_x, deg_y, ig, ren);
}
vector = (double *)malloc(fwKernel*fwKernel*sizeof(double));
dx = (deg_x / 2) * 2 - deg_x;
dy = (deg_y / 2) * 2 - deg_y;
sum_x = sum_y = 0.0;
*ren = 0;
for (ix = 0; ix < fwKernel; ix++) {
x = (double)(ix - hwKernel);
k = ix+n*fwKernel;
qe = exp(-x * x * sigma_gauss[ig]);
filter_x[k] = qe * pow(x, deg_x);
filter_y[k] = qe * pow(x, deg_y);
sum_x += filter_x[k];
sum_y += filter_y[k];
}
if (n > 0)
kernel0 = kernel_vec[0];
sum_x = 1. / sum_x;
sum_y = 1. / sum_y;
if (dx == 0 && dy == 0) {
for (ix = 0; ix < fwKernel; ix++) {
filter_x[ix+n*fwKernel] *= sum_x;
filter_y[ix+n*fwKernel] *= sum_y;
}
for (i = 0; i < fwKernel; i++) {
for (j = 0; j < fwKernel; j++) {
vector[i+fwKernel*j] = filter_x[i+n*fwKernel] * filter_y[j+n*fwKernel];
}
}
if (n > 0) {
for (i = 0; i < fwKernel * fwKernel; i++) {
vector[i] -= kernel0[i];
}
*ren = 1;
}
} else {
for (i = 0; i < fwKernel; i++) {
for (j = 0; j < fwKernel; j++) {
vector[i+fwKernel*j] = filter_x[i+n*fwKernel] * filter_y[j+n*fwKernel];
}
}
}
return vector;
}
double *kernel_vector_PCA(int n, int deg_x, int deg_y, int ig, int *ren) {
/*****************************************************
* Creates kernel sized entry for kernel_vec for each kernel degree
* Mask of filter_x * filter_y, filter = exp(-x**2 sig) * x^deg
* Subtract off kernel_vec[0] if n > 0
* NOTE: this does not use any image
******************************************************/
double *vector=NULL,*kernel0=NULL;
int i,j;
vector = (double *)malloc(fwKernel*fwKernel*sizeof(double));
for (i = 0; i < fwKernel; i++) {
for (j = 0; j < fwKernel; j++) {
vector[i+fwKernel*j] = PCA[n][i+fwKernel*j];
}
}
if (n > 0)
kernel0 = kernel_vec[0];
if (n > 0) {
for (i = 0; i < fwKernel * fwKernel; i++) {
vector[i] -= kernel0[i];
}
*ren = 1;
}
return vector;
}
void xy_conv_stamp(stamp_struct *stamp, float *image, int n, int ren) {
/*****************************************************
* Called for each degree of convolution, ngauss by deg_gauss
* Each convolution is stored in stamp->vectors[n], imc here
******************************************************/
int i,j,xc,yc,xij,sub_width,xi,yi;
double *v0,*imc;
if (usePCA) {
xy_conv_stamp_PCA(stamp, image, n, ren);
return;
}
xi = stamp->xss[stamp->sscnt];
yi = stamp->yss[stamp->sscnt];
imc = stamp->vectors[n];
sub_width = fwKSStamp + fwKernel - 1;
/* pull area to convolve out of full reference image region */
/* convolve with y filter */
for(i = xi - hwKSStamp - hwKernel; i <= xi + hwKSStamp + hwKernel; i++) {
for(j = yi - hwKSStamp; j <= yi + hwKSStamp; j++) {
xij = i - xi + sub_width / 2 + sub_width * (j - yi + hwKSStamp);
temp[xij] = 0.0;
for(yc = -hwKernel; yc <= hwKernel; yc++) {
temp[xij] += image[i+rPixX*(j+yc)] * filter_y[hwKernel-yc+n*fwKernel];
}
}
}
/* convolve with x filter */
for(j = -hwKSStamp; j <= hwKSStamp; j++) {
for(i = -hwKSStamp; i <= hwKSStamp;i++) {
xij = i + hwKSStamp + fwKSStamp * (j + hwKSStamp);
imc[xij] = 0.0;
for(xc = -hwKernel; xc <= hwKernel; xc++) {
imc[xij] += temp[i+xc+sub_width/2+sub_width*(j+hwKSStamp)] * filter_x[hwKernel-xc+n*fwKernel];
}
}
}
if (ren) {
v0 = stamp->vectors[0];
for(i = 0; i < fwKSStamp * fwKSStamp; i++) imc[i] -= v0[i];
}
return;
}
void xy_conv_stamp_PCA(stamp_struct *stamp, float *image, int n, int ren) {
/*****************************************************
* Called for each degree of convolution, ngauss by deg_gauss
* Each convolution is stored in stamp->vectors[n], imc here
******************************************************/
int i,j,xc,yc,xij,xi,yi;
double *v0,*imc;
xi = stamp->xss[stamp->sscnt];
yi = stamp->yss[stamp->sscnt];
imc = stamp->vectors[n];
/* pull area to convolve out of full reference image region */
for(j = yi - hwKSStamp; j <= yi + hwKSStamp; j++) {
for(i = xi - hwKSStamp; i <= xi + hwKSStamp; i++) {
xij = i - (xi - hwKSStamp) + fwKSStamp * (j - (yi - hwKSStamp));
imc[xij] = 0.;
for(yc = -hwKernel; yc <= hwKernel; yc++) {
for(xc = -hwKernel; xc <= hwKernel; xc++) {
imc[xij] += image[(i+xc)+rPixX*(j+yc)] * PCA[n][(xc+hwKernel) + fwKernel*(yc+hwKernel)];
}
}
}
}
if (ren) {
v0 = stamp->vectors[0];
for(i = 0; i < fwKSStamp * fwKSStamp; i++) imc[i] -= v0[i];
}
return;
}
void fitKernel(stamp_struct *stamps, float *imRef, float *imConv, float *imNoise, double *kernelSol,
double *meansigSubstamps, double *scatterSubstamps, int *NskippedSubstamps) {
/*****************************************************
* Complete fit for kernel solution
*****************************************************/
double d, **matrix;
char check;
int i,mat_size;
int ncomp1, ncomp2, ncomp, nbg_vec;
ncomp1 = nCompKer - 1;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
mat_size = ncomp1 * ncomp2 + nbg_vec + 1;
if (verbose >= 2) fprintf(stderr, " Mat_size: %i ncomp2: %i ncomp1: %i nbg_vec: %i \n",
mat_size, ncomp2, ncomp1, nbg_vec);
/* allocate fitting matrix */
matrix = (double **)malloc((mat_size + 1)*sizeof(double *));
for (i = 0; i <= mat_size; i++)
matrix[i] = (double *)malloc((mat_size + 1)*sizeof(double));
/* allocate weight matrix */
wxy = (double **)malloc(nS*sizeof(double *));
for (i = 0; i < nS; i++)
wxy[i] = (double *)malloc(ncomp2*sizeof(double));
if (verbose>=2) fprintf(stderr, " Expanding Matrix For Full Fit\n");
build_matrix(stamps, nS, matrix);
build_scprod(stamps, nS, imRef, kernelSol);
ludcmp(matrix, mat_size, indx, &d);
lubksb(matrix, mat_size, indx, kernelSol);
if (verbose>=2) fprintf(stderr, " Checking again\n");
check = check_again(stamps, kernelSol, imConv, imRef, imNoise, meansigSubstamps, scatterSubstamps, NskippedSubstamps);
while(check) {
fprintf(stderr, "\n Re-Expanding Matrix\n");
build_matrix(stamps, nS, matrix);
build_scprod(stamps, nS, imRef, kernelSol);
ludcmp(matrix, mat_size, indx, &d);
lubksb(matrix, mat_size, indx, kernelSol);
fprintf(stderr, " Checking again\n");
check = check_again(stamps, kernelSol, imConv, imRef, imNoise, meansigSubstamps, scatterSubstamps, NskippedSubstamps);
}
fprintf(stderr, " Sigma clipping of bad stamps converged, kernel determined\n");
for (i = 0; i <= mat_size; i++)
free(matrix[i]);
for (i = 0; i < nS; i++)
free(wxy[i]);
free(matrix);
free(wxy);
return;
}
void build_matrix0(stamp_struct *stamp) {
/*****************************************************
* Build least squares matrix for each stamp
*****************************************************/
int i,j,pixStamp,k,i1,ivecbg=0;
int ncomp1, ncomp2, ncomp, nbg_vec;
double p0,q;
double **vec;
ncomp1 = nCompKer;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
pixStamp = fwKSStamp * fwKSStamp;
vec = stamp->vectors;
/* loop over the convolved images created by xy_conv_stamp() */
/* each level represents ngauss and deg_gauss */
for (i = 0; i < ncomp1; i++) {
for (j = 0; j <= i; j++) {
q = 0.0;
/* integrate W_m1 and W_m2 (sum over all pixels) */
for (k = 0; k < pixStamp; k++)
q += vec[i][k] * vec[j][k];
/* Q from Eqn 3. in Alard */
stamp->mat[i+1][j+1] = q;
}
}
for (i1 = 0; i1 < ncomp1; i1++) {
ivecbg = ncomp1;
p0 = 0.0;
/* integrate convolved images and first order background (equals 1 everywhere!)*/
for (k = 0; k < pixStamp; k++)
p0 += vec[i1][k] * vec[ivecbg][k];
stamp->mat[ncomp1+1][i1+1] = p0;
}
/* integrate first order background with itself */
/* NOTE : DON'T MASK K HERE - BACKGROUND! */
for (k = 0, q = 0.0; k < pixStamp; k++)
q += vec[ivecbg][k] * vec[ncomp1][k];
stamp->mat[ncomp1+1][ncomp1+1] = q;
return;
}
void build_scprod0(stamp_struct *stamp, float *image) {
/*****************************************************
* Build the right side of each stamp's least squares matrix
* stamp.scprod = degree of kernel fit + 1 bg term
*****************************************************/
int xc,yc,xi,yi,i1,k;
int ncomp1, ncomp2, ncomp, nbg_vec;
double p0,q;
double **vec;
ncomp1 = nCompKer;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
vec = stamp->vectors;
xi = stamp->xss[stamp->sscnt];
yi = stamp->yss[stamp->sscnt];
/* Do eqn 4. in Alard */
/* Multiply each order's convolved image with reference image */
for (i1 = 0; i1 < ncomp1; i1++) {
p0 = 0.0;
for (xc = -hwKSStamp; xc <= hwKSStamp; xc++) {
for (yc = -hwKSStamp; yc <= hwKSStamp; yc++) {
k = xc + hwKSStamp + fwKSStamp * (yc + hwKSStamp);
p0 += vec[i1][k] * image[xc+xi+rPixX*(yc+yi)];
}
}
stamp->scprod[i1+1] = p0;
}
/* Multiply first order background model with reference image */
q = 0.0;
for (xc = -hwKSStamp; xc <= hwKSStamp; xc++) {
for (yc = -hwKSStamp; yc <= hwKSStamp; yc++) {
k = xc + hwKSStamp + fwKSStamp * (yc + hwKSStamp);
q += vec[ncomp1][k] * image[xc+xi+rPixX*(yc+yi)];
}
}
stamp->scprod[ncomp1+1] = q;
return;
}
double check_stamps(stamp_struct *stamps, int nS, float *imRef, float *imNoise) {
/*****************************************************
* Fit each stamp independently, reject significant outliers
* Next fit good stamps globally
* Returns a merit statistic, smaller for better fits
*****************************************************/
int nComps,i,im,jm,mcnt1,mcnt2,mcnt3;
double d,sum=0,kmean,kstdev;
double merit1,merit2,merit3,sig1,sig2,sig3;
float *m1,*m2,*m3,*ks;
int xc, yc, nks;
double **matrix;
int mat_size;
int ncomp1, ncomp2, ncomp, nbg_vec;
int ntestStamps;
double *testKerSol = NULL;
stamp_struct *testStamps = NULL;
/* kernel sum */
ks = (float *)calloc(nS, sizeof(float));
nks = 0;
ncomp1 = nCompKer - 1;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
mat_size = ncomp1 * ncomp2 + nbg_vec + 1;
if (verbose>=2) fprintf(stderr, " Mat_size0: %i ncomp2: %i ncomp1: %i nbg_vec: %i \n"
, mat_size, ncomp2, ncomp1, nbg_vec);
/* for inital fit */
nComps = nCompKer + 1;
for (i = 0; i < nS; i++) {
xc = stamps[i].xss[stamps[i].sscnt];
yc = stamps[i].yss[stamps[i].sscnt];
/* extract check_mat to solve one particular stamp */
for (im = 1; im <= nComps; im++) {
check_vec[im] = stamps[i].scprod[im];
for (jm = 1; jm <= im; jm++) {
check_mat[im][jm] = stamps[i].mat[im][jm];
check_mat[jm][im] = check_mat[im][jm];
}
}
/* fit stamp, the constant kernel coefficients end up in check_vec */
ludcmp(check_mat,nComps,indx,&d);
lubksb(check_mat,nComps,indx,check_vec);
/* find kernel sum */
sum = check_vec[1];
check_stack[i] = sum;
stamps[i].norm = sum;
ks[nks++] = sum;
if (verbose >= 2) fprintf(stderr, " # %d xss: %4i yss: %4i ksum: %f\n", i,
stamps[i].xss[stamps[i].sscnt],
stamps[i].yss[stamps[i].sscnt], sum);
}
sigma_clip(ks, nks, &kmean, &kstdev, 10);
fprintf(stderr, " %.1f sigma clipped mean ksum : %.3f, stdev : %.3f, n : %i\n",
kerSigReject, kmean, kstdev, nks);
/* so we need some way to reject bad stamps here in the first test,
we decided to use kernel sum. is there a better way? part of
the trick is that if some things are variable, you get different
kernel sums, but the subtraction itself should come out ok. */
/* stamps.diff : delta ksum in sigma */
/* here we want to reject high sigma points on the HIGH and LOW
side, since we want things with the same normalization */
for (i = 0; i < nS; i++) {
stamps[i].diff = fabs((stamps[i].norm - kmean) / kstdev);
}
/*****************************************************
* Global fit for kernel solution
*****************************************************/
/* do only if necessary */
if ((strncmp(forceConvolve, "b", 1)==0)) {
/* allocate fitting matrix */
matrix = (double **)calloc((mat_size + 1), sizeof(double *));
for (i = 0; i <= mat_size; i++)
matrix[i] = (double *)calloc((mat_size + 1), sizeof(double));
/* allocate weight matrix */
wxy = (double **)calloc(nS, sizeof(double *));
for (i = 0; i < nS; i++)
wxy[i] = (double *)calloc(ncomp2, sizeof(double));
/* first find out how many good stamps to allocate */
ntestStamps = 0;
for (i = 0; i < nS; i++)
if (stamps[i].diff < kerSigReject) {
ntestStamps++;
}
else {
if (verbose >= 2) fprintf(stderr, " # %d skipping xss: %4i yss: %4i ksum: %f sigma: %f\n", i,
stamps[i].xss[stamps[i].sscnt],
stamps[i].yss[stamps[i].sscnt],
stamps[i].norm, stamps[i].diff);
}
/* then allocate test stamp structure */
if(!(testStamps = (stamp_struct *)calloc(ntestStamps, sizeof(stamp_struct)))) {
printf("Cannot Allocate Test Stamp List\n");
exit (1);
}
testKerSol = (double *)calloc((nCompTotal+1), sizeof(double));
/* and point test stamp structure to good stamps */
ntestStamps = 0;
for (i = 0; i < nS; i++)
if (stamps[i].diff < kerSigReject)
testStamps[ntestStamps++] = stamps[i];
/* finally do fit */
if (verbose >= 2) fprintf(stderr, " Expanding Test Matrix For Fit\n");
build_matrix(testStamps, ntestStamps, matrix);
build_scprod(testStamps, ntestStamps, imRef, testKerSol);
ludcmp(matrix, mat_size, indx, &d);
lubksb(matrix, mat_size, indx, testKerSol);
/* get the kernel sum to normalize figures of merit! */
kmean = make_kernel(0, 0, testKerSol);
/* determine figure of merit from good stamps */
/* average of sum (diff**2 / value), ~variance */
m1 = (float *)calloc(ntestStamps, sizeof(float));
/* standard deviation of pixel distribution */
m2 = (float *)calloc(ntestStamps, sizeof(float));
/* noise sd based on histogram distribution width */
m3 = (float *)calloc(ntestStamps, sizeof(float));
mcnt1 = 0;
mcnt2 = 0;
mcnt3 = 0;
for (i = 0; i < ntestStamps; i++) {
getStampSig(&testStamps[i], testKerSol, imNoise, &sig1, &sig2, &sig3);
if ((sig1 != -1) && (sig1 <= MAXVAL)) {
m1[mcnt1++] = sig1;
}
if ((sig2 != -1) && (sig2 <= MAXVAL)) {
m2[mcnt2++] = sig2;
}
if ((sig3 != -1) && (sig3 <= MAXVAL)) {
m3[mcnt3++] = sig3;
}
}
sigma_clip(m1, mcnt1, &merit1, &sig1, 10);
sigma_clip(m2, mcnt2, &merit2, &sig2, 10);
sigma_clip(m3, mcnt3, &merit3, &sig3, 10);
/* normalize by kernel sum */
merit1 /= kmean;
merit2 /= kmean;
merit3 /= kmean;
/* clean up this mess */
if (testKerSol) free(testKerSol);
if (testStamps) free(testStamps);
for (i = 0; i <= mat_size; i++)
free(matrix[i]);
for (i = 0; i < nS; i++)
free(wxy[i]);
free(matrix);
free(wxy);
free(m1);
free(m2);
free(m3);
free(ks);
/* average value of figures of merit across stamps */
fprintf(stderr, " <var_merit> = %.3f, <sd_merit> = %.3f, <hist_merit> = %.3f\n", merit1, merit2, merit3);
/* return what is asked for if possible, if not use backup */
if (strncmp(figMerit, "v", 1)==0) {
if (mcnt1 > 0) {
return merit1;
}
else if (mcnt2 > 0) {
return merit2;
}
else if (mcnt3 > 0) {
return merit3;
}
else {
return 666;
}
}
else if (strncmp(figMerit, "s", 1)==0) {
if (mcnt2 > 0) {
return merit2;
}
else if (mcnt1 > 0) {
return merit1;
}
else if (mcnt3 > 0) {
return merit3;
}
else {
return 666;
}
}
else if (strncmp(figMerit, "h", 1)==0) {
if (mcnt3 > 0) {
return merit3;
}
else if (mcnt1 > 0) {
return merit1;
}
else if (mcnt2 > 0) {
return merit2;
}
else {
return 666;
}
}
}
else
return 0;
return 0;
}
void build_matrix_new(stamp_struct *stamps, int nS, double **matrix) {
/*****************************************************
* Build overall matrix including spatial variations
*****************************************************/
int mat_size,i,j,pixStamp,istamp,k,i1,i2,j1,j2,ibg,jbg,ivecbg,jj;
int ncomp1, ncomp2, ncomp, nbg_vec;
double **matrix0,p0,q,fx,fy;
double **vec;
int ideg1, ideg2, xstamp, ystamp;
double a1, a2;
ncomp1 = nCompKer - 1;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
pixStamp = fwKSStamp * fwKSStamp;
mat_size = ncomp1 * ncomp2 + nbg_vec + 1;
if (verbose >= 2) fprintf(stderr, " Mat_size: %i ncomp2: %i ncomp1: %i nbg_vec: %i \n",mat_size,ncomp2,ncomp1,nbg_vec);
for(i = 0; i <= mat_size; i++)
for(j = 0; j <= mat_size; j++)
matrix[i][j] = 0.0;
for(i = 0; i < nS; i++)
for(j = 0; j < ncomp2; j++)
wxy[i][j] = 0.0;
for (istamp = 0; istamp < nS; istamp++) {
/* skip over any bad stamps along the way */
while(stamps[istamp].sscnt >= stamps[istamp].nss) {
++istamp;
if (istamp >= nS) break;
}
if (istamp >= nS) break;
vec = stamps[istamp].vectors;
xstamp = stamps[istamp].xss[stamps[istamp].sscnt];
ystamp = stamps[istamp].yss[stamps[istamp].sscnt];
/* build weight function *HERE*, implicitly giving bad stamps zero weight */
/* because we skip them over above... */
k = 0;
fx = (xstamp - rPixX/2) / rPixX/2;
fy = (ystamp - rPixY/2) / rPixY/2;
for (ideg1 = 0, a1 = 1.0; ideg1 <= kerOrder; ideg1++, a1 *= fx)
for (ideg2 = 0, a2 = 1.0; ideg2 <= kerOrder - ideg1; ideg2++, a2 *= fy)
wxy[istamp][k++] = a1 * a2;
matrix0 = stamps[istamp].mat;
for (i = 0; i < ncomp; i++) {
i1 = i / ncomp2;
i2 = i - i1 * ncomp2;
for (j = 0; j <= i; j++) {
j1 = j / ncomp2;
j2 = j - j1 * ncomp2;
/* spatially weighted W_m1 and W_m2 integrals */
matrix[i+2][j+2] += wxy[istamp][i2] * wxy[istamp][j2] * matrix0[i1+2][j1+2];
}
}
matrix[1][1] += matrix0[1][1];
for (i = 0; i < ncomp; i++) {
i1 = i / ncomp2;
i2 = i - i1 * ncomp2;
matrix[i+2][1] += wxy[istamp][i2] * matrix0[i1+2][1];
}
for (ibg = 0; ibg < nbg_vec; ibg++) {
i = ncomp + ibg + 1;
ivecbg = ncomp1 + ibg + 1;
for (i1 = 1; i1 < ncomp1 + 1; i1++) {
p0 = 0.0;
/* integrate convolved images over all order backgrounds */
for (k = 0; k < pixStamp; k++)
p0 += vec[i1][k] * vec[ivecbg][k];
/* spatially weighted image * background terms */
for (i2 = 0; i2 < ncomp2; i2++) {
jj = (i1 - 1) * ncomp2 + i2 + 1;
matrix[i+1][jj+1] += p0 * wxy[istamp][i2];
}
}
p0 = 0.0;
for (k = 0; k < pixStamp; k++)
p0 += vec[0][k] * vec[ivecbg][k];
matrix[i+1][1] += p0;
/* background * background */
for (jbg = 0;jbg <= ibg; jbg++) {
for (k = 0, q = 0.0; k < pixStamp; k++)
q += vec[ivecbg][k] * vec[ncomp1+jbg+1][k];
matrix[i+1][ncomp+jbg+2] += q;
}
}
}
/* fill lower half of matrix */
for (i = 0; i < mat_size; i++) {
for (j = 0; j <= i; j++) {
matrix[j+1][i+1] = matrix[i+1][j+1];
/* fprintf(stderr, "matrix[%i][%i]: %lf\n", i,j,matrix[i+1][j+1]); */
}
}
return;
}
void build_matrix(stamp_struct *stamps, int nS, double **matrix) {
/*****************************************************
* Build overall matrix including spatial variations
*****************************************************/
int mat_size,i,j,pixStamp,istamp,k,i1,i2,j1,j2,ibg,jbg,ivecbg,jj;
int ncomp1, ncomp2, ncomp, nbg_vec;
double **matrix0,p0,q;
double **vec;
float rPixX2, rPixY2;
int ideg1, ideg2, xstamp, ystamp;
double a1, a2, fx, fy;
ncomp1 = nCompKer - 1;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
pixStamp = fwKSStamp * fwKSStamp;
rPixX2 = 0.5 * rPixX;
rPixY2 = 0.5 * rPixY;
mat_size = ncomp1 * ncomp2 + nbg_vec + 1;
if (verbose >= 2) fprintf(stderr, " Mat_size: %i ncomp2: %i ncomp1: %i nbg_vec: %i \n",mat_size,ncomp2,ncomp1,nbg_vec);
for(i = 0; i <= mat_size; i++)
for(j = 0; j <= mat_size; j++)
matrix[i][j] = 0.0;
for(i = 0; i < nS; i++)
for(j = 0; j < ncomp2; j++)
wxy[i][j] = 0.0;
for (istamp = 0; istamp < nS; istamp++) {
/* skip over any bad stamps along the way */
while(stamps[istamp].sscnt >= stamps[istamp].nss) {
++istamp;
if (istamp >= nS) break;
}
if (istamp >= nS) break;
vec = stamps[istamp].vectors;
xstamp = stamps[istamp].xss[stamps[istamp].sscnt];
ystamp = stamps[istamp].yss[stamps[istamp].sscnt];
/* RANGE FROM -1 to 1 */
fx = (xstamp - rPixX2) / rPixX2;
fy = (ystamp - rPixY2) / rPixY2;
/* build weight function *HERE* */
k = 0;
a1 = 1.0;
for (ideg1 = 0; ideg1 <= kerOrder; ideg1++) {
a2 = 1.0;
for (ideg2 = 0; ideg2 <= kerOrder - ideg1; ideg2++) {
wxy[istamp][k++] = a1 * a2;
a2 *= fy;
}
a1 *= fx;
}
matrix0 = stamps[istamp].mat;
for (i = 0; i < ncomp; i++) {
i1 = i / ncomp2;
i2 = i - i1 * ncomp2;
for (j = 0; j <= i; j++) {
j1 = j / ncomp2;
j2 = j - j1 * ncomp2;
/* spatially weighted W_m1 and W_m2 integrals */
matrix[i+2][j+2] += wxy[istamp][i2] * wxy[istamp][j2] * matrix0[i1+2][j1+2];
}
}
matrix[1][1] += matrix0[1][1];
for (i = 0; i < ncomp; i++) {
i1 = i / ncomp2;
i2 = i - i1 * ncomp2;
matrix[i+2][1] += wxy[istamp][i2] * matrix0[i1+2][1];
}
for (ibg = 0; ibg < nbg_vec; ibg++) {
i = ncomp + ibg + 1;
ivecbg = ncomp1 + ibg + 1;
for (i1 = 1; i1 < ncomp1 + 1; i1++) {
p0 = 0.0;
/* integrate convolved images over all order backgrounds */
for (k = 0; k < pixStamp; k++)
p0 += vec[i1][k] * vec[ivecbg][k];
/* spatially weighted image * background terms */
for (i2 = 0; i2 < ncomp2; i2++) {
jj = (i1 - 1) * ncomp2 + i2 + 1;
matrix[i+1][jj+1] += p0 * wxy[istamp][i2];
}
}
p0 = 0.0;
for (k = 0; k < pixStamp; k++)
p0 += vec[0][k] * vec[ivecbg][k];
matrix[i+1][1] += p0;
/* background * background */
for (jbg = 0;jbg <= ibg; jbg++) {
for (k = 0, q = 0.0; k < pixStamp; k++)
q += vec[ivecbg][k] * vec[ncomp1+jbg+1][k];
matrix[i+1][ncomp+jbg+2] += q;
}
}
}
/* fill lower half of matrix */
for (i = 0; i < mat_size; i++) {
for (j = 0; j <= i; j++) {
matrix[j+1][i+1] = matrix[i+1][j+1];
/* fprintf(stderr, "matrix[%i][%i]: %lf\n", i,j,matrix[i+1][j+1]); */
}
}
return;
}
void build_scprod(stamp_struct *stamps, int nS, float *image, double *kernelSol) {
/*****************************************************
* Build the right side of the complete least squares matrix
*****************************************************/
int istamp,xc,yc,xi,yi,i1,i2,k,ibg,i,ii;
int ncomp1, ncomp2, ncomp, nbg_vec;
double p0,q;
double **vec;
ncomp1 = nCompKer - 1;
ncomp2 = ((kerOrder + 1) * (kerOrder + 2)) / 2;
ncomp = ncomp1 * ncomp2;
nbg_vec = ((bgOrder + 1) * (bgOrder + 2)) / 2;
for (i = 0; i <= ncomp + nbg_vec + 1; i++)
kernelSol[i]=0.0;
for (istamp = 0; istamp < nS; istamp++) {
/* skip over any bad stamps along the way */
while(stamps[istamp].sscnt >= stamps[istamp].nss) {
++istamp;
if (istamp >= nS) break;
}
if (istamp >= nS) break;
vec= stamps[istamp].vectors;
xi = stamps[istamp].xss[stamps[istamp].sscnt];
yi = stamps[istamp].yss[stamps[istamp].sscnt];
p0 = stamps[istamp].scprod[1];
kernelSol[1] += p0;
/* spatially weighted convolved image * ref image */
for (i1 = 1; i1 < ncomp1 + 1; i1++) {
p0 = stamps[istamp].scprod[i1+1];
for (i2 = 0; i2 < ncomp2; i2++) {
ii = (i1-1) * ncomp2 + i2 + 1;
/* no need for weighting here */
kernelSol[ii+1] += p0 * wxy[istamp][i2];