static int fit_tan_wcs_solve(const double* starxyz, const double* fieldxy, const double* weights, int N, const double* crpix, const tan_t* tanin, tan_t* tanout, double* p_scale) { int i, j, k; double field_cm[2] = {0, 0}; double cov[4] = {0, 0, 0, 0}; double R[4] = {0, 0, 0, 0}; double scale; // projected star coordinates double* p; // relative field coordinates double* f; double pcm[2] = {0, 0}; double w = 0; double totalw; gsl_matrix* A; gsl_matrix* U; gsl_matrix* V; gsl_vector* S; gsl_vector* work; gsl_matrix_view vcov; gsl_matrix_view vR; double crxyz[3]; double star_cm[3] = {0, 0, 0}; assert(((tanin != NULL) && (crpix != NULL)) || ((tanin == NULL) && (crpix == NULL))); if (tanin) { // default vals... memcpy(tanout, tanin, sizeof(tan_t)); } else { memset(tanout, 0, sizeof(tan_t)); } // -allocate and fill "p" and "f" arrays. ("projected" and "field") p = malloc(N * 2 * sizeof(double)); f = malloc(N * 2 * sizeof(double)); // -get field center-of-mass totalw = 0.0; for (i=0; i<N; i++) { w = (weights ? weights[i] : 1.0); field_cm[0] += w * fieldxy[i*2 + 0]; field_cm[1] += w * fieldxy[i*2 + 1]; totalw += w; } field_cm[0] /= totalw; field_cm[1] /= totalw; // Subtract it out. for (i=0; i<N; i++) { f[2*i+0] = fieldxy[2*i+0] - field_cm[0]; f[2*i+1] = fieldxy[2*i+1] - field_cm[1]; } if (tanin) { // Use original WCS to set the center of projection to the new crpix. tan_pixelxy2xyzarr(tanin, crpix[0], crpix[1], crxyz); for (i=0; i<N; i++) { Unused anbool ok; // -project the stars around crval ok = star_coords(starxyz + i*3, crxyz, TRUE, p + 2*i, p + 2*i + 1); assert(ok); } } else { // -get the star center-of-mass (this will become the tangent point CRVAL) for (i=0; i<N; i++) { w = (weights ? weights[i] : 1.0); star_cm[0] += w * starxyz[i*3 + 0]; star_cm[1] += w * starxyz[i*3 + 1]; star_cm[2] += w * starxyz[i*3 + 2]; } normalize_3(star_cm); // -project the stars around their center of mass for (i=0; i<N; i++) { Unused anbool ok; ok = star_coords(starxyz + i*3, star_cm, TRUE, p + 2*i, p + 2*i + 1); assert(ok); } } // -compute the center of mass of the projected stars and subtract it out. for (i=0; i<N; i++) { w = (weights ? weights[i] : 1.0); pcm[0] += w * p[2*i + 0]; pcm[1] += w * p[2*i + 1]; } pcm[0] /= totalw; pcm[1] /= totalw; for (i=0; i<N; i++) { p[2*i + 0] -= pcm[0]; p[2*i + 1] -= pcm[1]; } // -compute the covariance between field positions and projected // positions of the corresponding stars. for (i=0; i<N; i++) for (j=0; j<2; j++) for (k=0; k<2; k++) cov[j*2 + k] += p[i*2 + k] * f[i*2 + j]; for (i=0; i<4; i++) assert(isfinite(cov[i])); // -run SVD V = gsl_matrix_alloc(2, 2); S = gsl_vector_alloc(2); work = gsl_vector_alloc(2); vcov = gsl_matrix_view_array(cov, 2, 2); vR = gsl_matrix_view_array(R, 2, 2); A = &(vcov.matrix); // The Jacobi version doesn't always compute an orthonormal U if S has zeros. //gsl_linalg_SV_decomp_jacobi(A, V, S); gsl_linalg_SV_decomp(A, V, S, work); // the U result is written to A. U = A; gsl_vector_free(S); gsl_vector_free(work); // R = V U' gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, V, U, 0.0, &(vR.matrix)); gsl_matrix_free(V); for (i=0; i<4; i++) assert(isfinite(R[i])); // -compute scale: make the variances equal. { double pvar, fvar; pvar = fvar = 0.0; for (i=0; i<N; i++) { w = (weights ? weights[i] : 1.0); for (j=0; j<2; j++) { pvar += w * square(p[i*2 + j]); fvar += w * square(f[i*2 + j]); } } scale = sqrt(pvar / fvar); } // -compute WCS parameters. scale = rad2deg(scale); tanout->cd[0][0] = R[0] * scale; // CD1_1 tanout->cd[0][1] = R[1] * scale; // CD1_2 tanout->cd[1][0] = R[2] * scale; // CD2_1 tanout->cd[1][1] = R[3] * scale; // CD2_2 assert(isfinite(tanout->cd[0][0])); assert(isfinite(tanout->cd[0][1])); assert(isfinite(tanout->cd[1][0])); assert(isfinite(tanout->cd[1][1])); if (tanin) { // CRPIX is fixed. tanout->crpix[0] = crpix[0]; tanout->crpix[1] = crpix[1]; // Set CRVAL temporarily... tan_pixelxy2radec(tanin, crpix[0], crpix[1], tanout->crval+0, tanout->crval+1); // Shift CRVAL so that the center of the quad is in the right place. { double ix,iy; double dx,dy; double dxyz[3]; tan_pixelxy2iwc(tanout, field_cm[0], field_cm[1], &ix, &iy); dx = rad2deg(pcm[0]) - ix; dy = rad2deg(pcm[1]) - iy; tan_iwc2xyzarr(tanout, dx, dy, dxyz); xyzarr2radecdeg(dxyz, tanout->crval + 0, tanout->crval + 1); } } else { tanout->crpix[0] = field_cm[0]; tanout->crpix[1] = field_cm[1]; xyzarr2radecdegarr(star_cm, tanout->crval); // FIXME -- we ignore pcm. It should get added back in (after // multiplication by CD in the appropriate units) to either crval or // crpix. It's a very small correction probably of the same size // as the other approximations we're making. } if (p_scale) *p_scale = scale; free(p); free(f); return 0; }
// Pixels to XYZ unit vector. void tan_pixelxy2xyzarr(const tan_t* tan, double px, double py, double *xyz) { double x,y; tan_pixelxy2iwc(tan, px, py, &x, &y); tan_iwc2xyzarr(tan, x, y, xyz); }
int wcs_pv2sip(const char* wcsinfn, int ext, const char* wcsoutfn, anbool scamp_head_file, double* xy, int Nxy, int imageW, int imageH, anbool forcetan) { qfits_header* hdr = NULL; double* radec = NULL; int rtn = -1; tan_t tanwcs; double x,y, px,py; double xyz[3]; double* xorig = NULL; double* yorig = NULL; double* rddist = NULL; int i, j; // 1 x y r x2 xy y2 x3 x2y xy2 y3 r3 x4 x3y x2y2 xy3 y4 // x5 x4y x3y2 x2y3 xy4 y5 r5 x6 x5y x4y2, x3y3 x2y4 xy5 y6 // x7 x6y x5y2 x4y3 x3y4 x2y5 xy6 y7 r7 int xp[] = { 0, 1, 0, 0, 2, 1, 0, 3, 2, 1, 0, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 5, 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 0}; int yp[] = { 0, 0, 1, 0, 0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0}; int rp[] = { 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7}; double xpows[8]; double ypows[8]; double rpows[8]; double pv1[40]; double pv2[40]; double r; if (scamp_head_file) { size_t sz = 0; char* txt; char* prefix; int np; int nt; unsigned char* txthdr; sl* lines; int i; txt = file_get_contents(wcsinfn, &sz, TRUE); if (!txt) { ERROR("Failed to read file %s", wcsinfn); goto bailout; } lines = sl_split(NULL, txt, "\n"); prefix = "SIMPLE = T / Standard FITS file " "BITPIX = 8 / ASCII or bytes array " "NAXIS = 0 / Minimal header " "EXTEND = T / There may be FITS ext " "WCSAXES = 2 / "; np = strlen(prefix); nt = np + FITS_LINESZ * sl_size(lines); txthdr = malloc(nt); memset(txthdr, ' ', np + FITS_LINESZ * sl_size(lines)); memcpy(txthdr, prefix, np); for (i=0; i<sl_size(lines); i++) memcpy(txthdr + np + i*FITS_LINESZ, sl_get(lines, i), strlen(sl_get(lines, i))); sl_free2(lines); hdr = qfits_header_read_hdr_string(txthdr, nt); free(txthdr); free(txt); } else { char* ct; hdr = anqfits_get_header2(wcsinfn, ext); ct = fits_get_dupstring(hdr, "CTYPE1"); if ((ct && streq(ct, "RA---TPV")) || forcetan) { // http://iraf.noao.edu/projects/ccdmosaic/tpv.html logmsg("Replacing CTYPE1 = %s header with RA---TAN\n", ct); fits_update_value(hdr, "CTYPE1", "RA---TAN"); } ct = fits_get_dupstring(hdr, "CTYPE2"); if ((ct && streq(ct, "DEC--TPV")) || forcetan) { logmsg("Replacing CTYPE2 = %s header with DEC--TAN\n", ct); fits_update_value(hdr, "CTYPE2", "DEC--TAN"); } } if (!hdr) { ERROR("Failed to read header: file %s, ext %i\n", wcsinfn, ext); goto bailout; } tan_read_header(hdr, &tanwcs); for (i=0; i<sizeof(pv1)/sizeof(double); i++) { char key[10]; sprintf(key, "PV1_%i", i); pv1[i] = qfits_header_getdouble(hdr, key, 0.0); sprintf(key, "PV2_%i", i); pv2[i] = qfits_header_getdouble(hdr, key, 0.0); } xorig = malloc(Nxy * sizeof(double)); yorig = malloc(Nxy * sizeof(double)); rddist = malloc(2 * Nxy * sizeof(double)); for (j=0; j<Nxy; j++) { xorig[j] = xy[2*j+0]; yorig[j] = xy[2*j+1]; tan_pixelxy2iwc(&tanwcs, xorig[j], yorig[j], &x, &y); r = sqrt(x*x + y*y); xpows[0] = ypows[0] = rpows[0] = 1.0; for (i=1; i<sizeof(xpows)/sizeof(double); i++) { xpows[i] = xpows[i-1]*x; ypows[i] = ypows[i-1]*y; rpows[i] = rpows[i-1]*r; } px = py = 0; for (i=0; i<sizeof(xp)/sizeof(int); i++) { px += pv1[i] * xpows[xp[i]] * ypows[yp[i]] * rpows[rp[i]]; py += pv2[i] * ypows[xp[i]] * xpows[yp[i]] * rpows[rp[i]]; } tan_iwc2xyzarr(&tanwcs, px, py, xyz); xyzarr2radecdeg(xyz, rddist+2*j, rddist+2*j+1); } // { starxy_t sxy; tweak_t* t; il* imgi; il* refi; int sip_order = 5; int sip_inv_order = 5; sxy.N = Nxy; sxy.x = xorig; sxy.y = yorig; imgi = il_new(256); refi = il_new(256); for (i=0; i<Nxy; i++) { il_append(imgi, i); il_append(refi, i); } t = tweak_new(); t->sip->a_order = t->sip->b_order = sip_order; t->sip->ap_order = t->sip->bp_order = sip_inv_order; tweak_push_wcs_tan(t, &tanwcs); tweak_push_ref_ad_array(t, rddist, Nxy); tweak_push_image_xy(t, &sxy); tweak_push_correspondence_indices(t, imgi, refi, NULL, NULL); tweak_go_to(t, TWEAK_HAS_LINEAR_CD); if (imageW) t->sip->wcstan.imagew = imageW; if (imageH) t->sip->wcstan.imageh = imageH; sip_write_to_file(t->sip, wcsoutfn); tweak_free(t); } rtn = 0; bailout: free(xorig); free(yorig); free(rddist); qfits_header_destroy(hdr); free(radec); return rtn; }
void tan_iwc2radec(const tan_t* tan, double x, double y, double *p_ra, double *p_dec) { double xyz[3]; tan_iwc2xyzarr(tan, x, y, xyz); xyzarr2radecdeg(xyz, p_ra, p_dec); }