// RA,Dec in degrees to Pixels. anbool sip_radec2pixelxy_check(const sip_t* sip, double ra, double dec, double *px, double *py) { double u, v; double U, V; double U2, V2; if (!tan_radec2pixelxy(&(sip->wcstan), ra, dec, px, py)) return FALSE; if (!has_distortions(sip)) return TRUE; // Subtract crpix, invert SIP distortion, add crpix. // Sanity check: if (sip->a_order != 0 && sip->ap_order == 0) { fprintf(stderr, "suspicious inversion; no inversion SIP coeffs " "yet there are forward SIP coeffs\n"); } U = *px - sip->wcstan.crpix[0]; V = *py - sip->wcstan.crpix[1]; sip_calc_inv_distortion(sip, U, V, &u, &v); // Check that we're dealing with the right range of the polynomial by inverting it and // checking that we end up back in the right place. sip_calc_distortion(sip, u, v, &U2, &V2); if (fabs(U2 - U) + fabs(V2 - V) > 10.0) return FALSE; *px = u + sip->wcstan.crpix[0]; *py = v + sip->wcstan.crpix[1]; return TRUE; }
void sip_pixel_undistortion(const sip_t* sip, double x, double y, double* X, double *Y) { if (!has_distortions(sip)) { *X = x; *Y = y; return; } // Sanity check: if (sip->a_order != 0 && sip->ap_order == 0) { fprintf(stderr, "suspicious inversion; no inverse SIP coeffs " "yet there are forward SIP coeffs\n"); } // Get pixel coordinates relative to reference pixel double u = x - sip->wcstan.crpix[0]; double v = y - sip->wcstan.crpix[1]; sip_calc_inv_distortion(sip, u, v, X, Y); *X += sip->wcstan.crpix[0]; *Y += sip->wcstan.crpix[1]; }
int fit_sip_wcs(const double* starxyz, const double* fieldxy, const double* weights, int M, const tan_t* tanin1, int sip_order, int inv_order, sip_t* sipout) { int sip_coeffs; double xyzcrval[3]; double cdinv[2][2]; double sx, sy, sU, sV, su, sv; int N; int i, j, p, q, order; double totalweight; int rtn; gsl_matrix *mA; gsl_vector *b1, *b2, *x1, *x2; gsl_vector *r1=NULL, *r2=NULL; tan_t tanin2; int ngood; const tan_t* tanin = &tanin2; // We need at least the linear terms to compute CD. if (sip_order < 1) sip_order = 1; // convenience: allow the user to call like: // fit_sip_wcs(... &(sipout.wcstan), ..., sipout); memcpy(&tanin2, tanin1, sizeof(tan_t)); memset(sipout, 0, sizeof(sip_t)); memcpy(&(sipout->wcstan), tanin, sizeof(tan_t)); sipout->a_order = sipout->b_order = sip_order; sipout->ap_order = sipout->bp_order = inv_order; // The SIP coefficients form an (order x order) upper triangular // matrix missing the 0,0 element. sip_coeffs = (sip_order + 1) * (sip_order + 2) / 2; N = sip_coeffs; if (M < N) { ERROR("Too few correspondences for the SIP order specified (%i < %i)\n", M, N); return -1; } mA = gsl_matrix_alloc(M, N); b1 = gsl_vector_alloc(M); b2 = gsl_vector_alloc(M); assert(mA); assert(b1); assert(b2); /* * We use a clever trick to estimate CD, A, and B terms in two * seperated least squares fits, then finding A and B by multiplying * the found parameters by CD inverse. * * Rearranging the SIP equations (see sip.h) we get the following * matrix operation to compute x and y in world intermediate * coordinates, which is convienently written in a way which allows * least squares estimation of CD and terms related to A and B. * * First use the x's to find the first set of parametetrs * * +--------------------- Intermediate world coordinates in DEGREES * | +--------- Pixel coordinates u and v in PIXELS * | | +--- Polynomial u,v terms in powers of PIXELS * v v v * ( x1 ) ( 1 u1 v1 p1 ) (sx ) * ( x2 ) = ( 1 u2 v2 p2 ) * (cd11 ) : * ( x3 ) ( 1 u3 v3 p3 ) (cd12 ) : * ( ...) ( ... ) (cd11*A + cd12*B ) : * cd11 is a scalar, degrees per pixel * cd12 is a scalar, degrees per pixel * cd11*A and cs12*B are mixture of SIP terms (A,B) and CD matrix * (cd11,cd12) * * Then find cd21 and cd22 with the y's * * ( y1 ) ( 1 u1 v1 p1 ) (sy ) * ( y2 ) = ( 1 u2 v2 p2 ) * (cd21 ) : * ( y3 ) ( 1 u3 v3 p3 ) (cd22 ) : * ( ...) ( ... ) (cd21*A + cd22*B ) : (Y4) * y2: scalar, degrees per pixel * y3: scalar, degrees per pixel * Y4: mixture of SIP terms (A,B) and CD matrix (cd21,cd22) * * These are both standard least squares problems which we solve with * QR decomposition, ie * min_{cd,A,B} || x - [1,u,v,p]*[s;cd;cdA+cdB]||^2 with * x reference, cd,A,B unrolled parameters. * * We get back (for x) a vector of optimal * [sx;cd11;cd12; cd11*A + cd12*B] * Now we can pull out sx, cd11 and cd12 from the beginning of this vector, * and call the rest of the vector [cd11*A] + [cd12*B]; * similarly for the y fit, we get back a vector of optimal * [sy;cd21;cd22; cd21*A + cd22*B] * once we have all those we can figure out A and B as follows * -1 * A' = [cd11 cd12] * [cd11*A' + cd12*B'] * B' [cd21 cd22] [cd21*A' + cd22*B'] * * which recovers the A and B's. * */ /* * Dustin's interpretation of the above: * We want to solve: * * min || b[M-by-1] - A[M-by-N] x[N-by-1] ||_2 * * M = the number of correspondences. * N = the number of SIP terms. * * And we want an overdetermined system, so M >= N. * * [ 1 u_1 v_1 u_1^2 u_1 v_1 v_1^2 ... ] * mA = [ 1 u_2 v_2 u_2^2 u_2 v_2 v_2^2 ... ] * [ ...... ] * * Where (u_i, v_i) are *undistorted* pixel positions minus CRPIX. * * The answers we want are: * * [ sx ] * x1 = [ cd11 ] * [ cd12 ] * [ (A) (B) ] * [ cd11*(A) + cd12*(B) ] * [ (A) (B) ] * * [ sy ] * x2 = [ cd21 ] * [ cd22 ] * [ (A) (B) ] * [ cd21*(A) + cd22*(B) ] * [ (A) (B) ] * * And the target vectors are the intermediate world coords of the * reference stars, in degrees. * * [ ix_1 ] * b1 = [ ix_2 ] * [ ... ] * * [ iy_1 ] * b2 = [ iy_2 ] * [ ... ] * * * (where A and B are tall vectors of SIP coefficients of order 2 * and above) * */ // Fill in matrix mA: radecdeg2xyzarr(tanin->crval[0], tanin->crval[1], xyzcrval); totalweight = 0.0; ngood = 0; for (i=0; i<M; i++) { double x=0, y=0; double weight = 1.0; double u; double v; Unused anbool ok; u = fieldxy[2*i + 0] - tanin->crpix[0]; v = fieldxy[2*i + 1] - tanin->crpix[1]; // B contains Intermediate World Coordinates (in degrees) // tangent-plane projection ok = star_coords(starxyz + 3*i, xyzcrval, TRUE, &x, &y); if (!ok) { logverb("Skipping star that cannot be projected to tangent plane\n"); continue; } gsl_vector_set(b1, ngood, weight * rad2deg(x)); gsl_vector_set(b2, ngood, weight * rad2deg(y)); if (weights) { weight = weights[i]; assert(weight >= 0.0); assert(weight <= 1.0); totalweight += weight; if (weight == 0.0) continue; } /* The coefficients are stored in this order: * p q * (0,0) = 1 <- order 0 * (1,0) = u <- order 1 * (0,1) = v * (2,0) = u^2 <- order 2 * (1,1) = uv * (0,2) = v^2 * ... */ j = 0; for (order=0; order<=sip_order; order++) { for (q=0; q<=order; q++) { p = order - q; assert(j >= 0); assert(j < N); assert(p >= 0); assert(q >= 0); assert(p + q <= sip_order); gsl_matrix_set(mA, ngood, j, weight * pow(u, (double)p) * pow(v, (double)q)); j++; } } assert(j == N); // The shift - aka (0,0) - SIP coefficient must be 1. assert(gsl_matrix_get(mA, i, 0) == 1.0 * weight); assert(fabs(gsl_matrix_get(mA, i, 1) - u * weight) < 1e-12); assert(fabs(gsl_matrix_get(mA, i, 2) - v * weight) < 1e-12); ngood++; } if (ngood == 0) { ERROR("No stars projected within the image\n"); return -1; } if (weights) logverb("Total weight: %g\n", totalweight); if (ngood < M) { _gsl_vector_view sub_b1 = gsl_vector_subvector(b1, 0, ngood); _gsl_vector_view sub_b2 = gsl_vector_subvector(b2, 0, ngood); _gsl_matrix_view sub_mA = gsl_matrix_submatrix(mA, 0, 0, ngood, N); rtn = gslutils_solve_leastsquares_v(&(sub_mA.matrix), 2, &(sub_b1.vector), &x1, NULL, &(sub_b2.vector), &x2, NULL); } else { // Solve the equation. rtn = gslutils_solve_leastsquares_v(mA, 2, b1, &x1, NULL, b2, &x2, NULL); } if (rtn) { ERROR("Failed to solve SIP matrix equation!"); return -1; } // Row 0 of X are the shift (p=0, q=0) terms. // Row 1 of X are the terms that multiply "u". // Row 2 of X are the terms that multiply "v". // Grab CD. sipout->wcstan.cd[0][0] = gsl_vector_get(x1, 1); sipout->wcstan.cd[0][1] = gsl_vector_get(x1, 2); sipout->wcstan.cd[1][0] = gsl_vector_get(x2, 1); sipout->wcstan.cd[1][1] = gsl_vector_get(x2, 2); // Compute inv(CD) i = invert_2by2_arr((const double*)(sipout->wcstan.cd), (double*)cdinv); assert(i == 0); // Grab the shift. sx = gsl_vector_get(x1, 0); sy = gsl_vector_get(x2, 0); // Extract the SIP coefficients. // (this includes the 0 and 1 order terms, which we later overwrite) j = 0; for (order=0; order<=sip_order; order++) { for (q=0; q<=order; q++) { p = order - q; assert(j >= 0); assert(j < N); assert(p >= 0); assert(q >= 0); assert(p + q <= sip_order); sipout->a[p][q] = cdinv[0][0] * gsl_vector_get(x1, j) + cdinv[0][1] * gsl_vector_get(x2, j); sipout->b[p][q] = cdinv[1][0] * gsl_vector_get(x1, j) + cdinv[1][1] * gsl_vector_get(x2, j); j++; } } assert(j == N); // We have already dealt with the shift and linear terms, so zero them out // in the SIP coefficient matrix. sipout->a[0][0] = 0.0; sipout->a[0][1] = 0.0; sipout->a[1][0] = 0.0; sipout->b[0][0] = 0.0; sipout->b[0][1] = 0.0; sipout->b[1][0] = 0.0; sip_compute_inverse_polynomials(sipout, 0, 0, 0, 0, 0, 0); sU = cdinv[0][0] * sx + cdinv[0][1] * sy; sV = cdinv[1][0] * sx + cdinv[1][1] * sy; logverb("Applying shift of sx,sy = %g,%g deg (%g,%g pix) to CRVAL and CD.\n", sx, sy, sU, sV); sip_calc_inv_distortion(sipout, sU, sV, &su, &sv); debug("sx = %g, sy = %g\n", sx, sy); debug("sU = %g, sV = %g\n", sU, sV); debug("su = %g, sv = %g\n", su, sv); wcs_shift(&(sipout->wcstan), -su, -sv); if (r1) gsl_vector_free(r1); if (r2) gsl_vector_free(r2); gsl_matrix_free(mA); gsl_vector_free(b1); gsl_vector_free(b2); gsl_vector_free(x1); gsl_vector_free(x2); return 0; }