// RA,Dec in degrees to Pixels.
anbool tan_radec2pixelxy(const tan_t* tan, double a, double d, double *px, double *py)
{
double xyzpt[3];
radecdeg2xyzarr(a,d,xyzpt);
return tan_xyzarr2pixelxy(tan, xyzpt, px, py);
}
int fit_sip_coefficients(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;
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
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're going to fit for the "forward" SIP coefficients
* A, B.
*
* SIP converts (x,y) -> distort with A,B -> (x',y') -> TAN -> RA,Dec
*
* We are going to hold TAN fixed here, so first convert RA,Dec
* to (x',y'), and then compute A,B terms.
*
* Set up the matrix equation
* [ SIP polynomial terms ] [ SIP coeffs ] - [x'] ~ 0
*
* Where SIP polynomial terms are powers of x.
*
* Though rather than x, x' we'll work in CRPIX-relative units,
* since that's what SIP does.
*/
// Fill in matrix mA:
totalweight = 0.0;
ngood = 0;
for (i=0; i<M; i++) {
double xprime, yprime;
double x, y;
double weight = 1.0;
anbool ok;
ok = tan_xyzarr2pixelxy(tanin, starxyz + 3*i, &xprime, &yprime);
if (!ok)
continue;
xprime -= tanin->crpix[0];
yprime -= tanin->crpix[1];
x = fieldxy[2*i ] - tanin->crpix[0];
y = fieldxy[2*i+1] - tanin->crpix[1];
if (weights) {
weight = weights[i];
assert(weight >= 0.0);
assert(weight <= 1.0);
totalweight += weight;
if (weight == 0.0)
continue;
}
/// AHA!, since SIP computes an "fuv","guv" to ADD to
/// x,y to get x',y', b is the DIFFERENCE!
gsl_vector_set(b1, ngood, weight * (xprime - x));
gsl_vector_set(b2, ngood, weight * (yprime - y));
/* 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(x, (double)p) * pow(y, (double)q));
j++;
}
}
assert(j == N);
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;
}
// Extract the SIP coefficients.
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] = gsl_vector_get(x1, j);
sipout->b[p][q] = gsl_vector_get(x2, j);
j++;
}
}
assert(j == N);
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;
}
