// Pixels to RA,Dec in degrees.
void sip_pixelxy2radec(const sip_t* sip, double px, double py,
double *ra, double *dec) {
if (has_distortions(sip)) {
double U, V;
sip_distortion(sip, px, py, &U, &V);
// Run a normal TAN conversion on the distorted pixel coords.
tan_pixelxy2radec(&(sip->wcstan), U, V, ra, dec);
} else
// Run a normal TAN conversion
tan_pixelxy2radec(&(sip->wcstan), px, py, ra, dec);
}
// Pixels to RA,Dec in degrees.
void tpv_pixelxy2radec(const tpv_t* tpv, double px, double py,
double *ra, double *dec) {
double U, V;
tpv_distortion(tpv, px, py, &U, &V);
// Run a normal TAN conversion on the distorted pixel coords.
tan_pixelxy2radec(&(tpv->wcstan), U, V, ra, dec);
}
int fit_sip_wcs_2(const double* starxyz,
const double* fieldxy,
const double* weights,
int M,
int sip_order,
int inv_order,
int W, int H,
int crpix_center,
double* crpix,
int doshift,
sip_t* sipout) {
tan_t wcs;
memset(&wcs, 0, sizeof(tan_t));
// Start with a TAN
if (fit_tan_wcs(starxyz, fieldxy, M, &wcs, NULL)) {
ERROR("Failed to fit for TAN WCS");
return -1;
}
if (crpix || crpix_center) {
double cx,cy;
double cr,cd;
if (crpix) {
cx = crpix[0];
cy = crpix[1];
} else {
int i;
if (W == 0) {
for (i=0; i<M; i++) {
W = MAX(W, (int)ceil(fieldxy[2*i + 0]));
}
}
if (H == 0) {
for (i=0; i<M; i++) {
H = MAX(H, (int)ceil(fieldxy[2*i + 1]));
}
}
cx = 1. + 0.5 * W;
cy = 1. + 0.5 * H;
}
tan_pixelxy2radec(&wcs, cx, cy, &cr, &cd);
wcs.crpix[0] = cx;
wcs.crpix[1] = cy;
wcs.crval[0] = cr;
wcs.crval[1] = cd;
}
wcs.imagew = W;
wcs.imageh = H;
return fit_sip_wcs(starxyz, fieldxy, weights, M, &wcs,
sip_order, inv_order, doshift, sipout);
}
// Given a pixel offset (shift in image plane), adjust the WCS
// CRVAL to the position given by CRPIX + offset.
// Why not just
// sip_pixelxy2radec(wcs, crpix0 +- xs, crpix1 +- ys,
// wcs->wcstan.crval+0, wcs->wcstan.crval+1);
// The answer is that "North" changes when you move the reference point.
void wcs_shift(tan_t* wcs, double xs, double ys) {
// UNITS: xs/ys in pixels
// crvals in degrees, nx/nyref and theta in degrees
double crpix0, crpix1, crval0;
double theta, sintheta, costheta;
double newcrval0, newcrval1;
double newcd00,newcd01,newcd10,newcd11;
// Save old vals
crpix0 = wcs->crpix[0];
crpix1 = wcs->crpix[1];
crval0 = wcs->crval[0];
// compute the desired projection of the new tangent point by
// shifting the projection of the current tangent point
wcs->crpix[0] += xs;
wcs->crpix[1] += ys;
// now reproject the old crpix[xy] into shifted wcs
tan_pixelxy2radec(wcs, crpix0, crpix1, &newcrval0, &newcrval1);
// Restore crpix
wcs->crpix[0] = crpix0;
wcs->crpix[1] = crpix1;
// RA,DEC coords of new tangent point
wcs->crval[0] = newcrval0;
wcs->crval[1] = newcrval1;
theta = -deg2rad(newcrval0 - crval0);
// deltaRA = new minus old RA;
theta *= sin(deg2rad(newcrval1));
// multiply by the sin of the NEW Dec; at equator this correctly
// evals to zero
sintheta = sin(theta);
costheta = cos(theta);
// Fix the CD matrix since "northwards" has changed due to moving RA
newcd00 = costheta * wcs->cd[0][0] - sintheta * wcs->cd[0][1];
newcd01 = sintheta * wcs->cd[0][0] + costheta * wcs->cd[0][1];
newcd10 = costheta * wcs->cd[1][0] - sintheta * wcs->cd[1][1];
newcd11 = sintheta * wcs->cd[1][0] + costheta * wcs->cd[1][1];
wcs->cd[0][0] = newcd00;
wcs->cd[0][1] = newcd01;
wcs->cd[1][0] = newcd10;
wcs->cd[1][1] = newcd11;
}
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;
}
void tan_pixelxy2radecarr(const tan_t* wcs_tan, double px, double py, double *radec) {
tan_pixelxy2radec(wcs_tan, px, py, radec+0, radec+1);
}
void test_wcslib_equals_tan(CuTest* tc) {
#ifndef WCSLIB_EXISTS
printf("\n\nWarning, WCSLIB support was not compiled in, so no WCSLIB functionality will be tested.\n\n\n");
return;
#endif
anwcs_t* anwcs = NULL;
tan_t* tan;
char* tmpfile = create_temp_file("test-anwcs-wcs", "/tmp");
double x, y, x2, y2, ra, dec, ra2, dec2;
int ok, ok2;
int i;
// from http://live.astrometry.net/status.php?job=alpha-201004-29242410
// test-anwcs-1.wcs
const char* wcsliteral =
"SIMPLE = T / Standard FITS file BITPIX = 8 / ASCII or bytes array NAXIS = 0 / Minimal header EXTEND = T / There may be FITS ext CTYPE1 = 'RA---TAN' / TAN (gnomic) projection CTYPE2 = 'DEC--TAN' / TAN (gnomic) projection WCSAXES = 2 / no comment EQUINOX = 2000.0 / Equatorial coordinates definition (yr) LONPOLE = 180.0 / no comment LATPOLE = 0.0 / no comment CRVAL1 = 83.7131676182 / RA of reference point CRVAL2 = -5.10104333945 / DEC of reference point CRPIX1 = 221.593284607 / X reference pixel CRPIX2 = 169.655508041 / Y reference pixel CUNIT1 = 'deg ' / X pixel scale units CUNIT2 = 'deg ' / Y pixel scale units CD1_1 = 1.55258090814E-06 / Transformation matrix CD1_2 = 0.00081692280013 / no comment CD2_1 = -0.00081692280013 / no comment CD2_2 = 1.55258090814E-06 / no comment IMAGEW = 900 / Image width, in pixels. IMAGEH = 600 / Image height, in pixels. DATE = '2010-04-14T12:12:18' / Date this file was created. HISTORY Created by the Astrometry.net suite. HISTORY For more details, see http://astrometry.net . HISTORY Subversion URL HISTORY http://astrometry.net/svn/branches/astrometry/alpha/quads/ HISTORY Subversion revision 5409 HISTORY Subversion date 2007-10-09 13:49:13 -0400 (Tue, 09 Oct HISTORY 2007) HISTORY This WCS header was created by the program \"blind\". COMMENT -- blind solver parameters: -- COMMENT Index(0): /data1/INDEXES/200/index-219 COMMENT Index(1): /data1/INDEXES/200/index-218 COMMENT Index(2): /data1/INDEXES/200/index-217 COMMENT Index(3): /data1/INDEXES/200/index-216 COMMENT Index(4): /data1/INDEXES/200/index-215 COMMENT Index(5): /data1/INDEXES/200/index-214 COMMENT Index(6): /data1/INDEXES/200/index-213 COMMENT Index(7): /data1/INDEXES/200/index-212 COMMENT Index(8): /data1/INDEXES/200/index-211 COMMENT Index(9): /data1/INDEXES/200/index-210 COMMENT Index(10): /data1/INDEXES/200/index-209 COMMENT Index(11): /data1/INDEXES/200/index-208 COMMENT Index(12): /data1/INDEXES/200/index-207 COMMENT Index(13): /data1/INDEXES/200/index-206 COMMENT Index(14): /data1/INDEXES/200/index-205 COMMENT Index(15): /data1/INDEXES/200/index-204-00 COMMENT Index(16): /data1/INDEXES/200/index-204-01 COMMENT Index(17): /data1/INDEXES/200/index-204-02 COMMENT Index(18): /data1/INDEXES/200/index-204-03 COMMENT Index(19): /data1/INDEXES/200/index-204-04 COMMENT Index(20): /data1/INDEXES/200/index-204-05 COMMENT Index(21): /data1/INDEXES/200/index-204-06 COMMENT Index(22): /data1/INDEXES/200/index-204-07 COMMENT Index(23): /data1/INDEXES/200/index-204-08 COMMENT Index(24): /data1/INDEXES/200/index-204-09 COMMENT Index(25): /data1/INDEXES/200/index-204-10 COMMENT Index(26): /data1/INDEXES/200/index-204-11 COMMENT Index(27): /data1/INDEXES/200/index-203-00 COMMENT Index(28): /data1/INDEXES/200/index-203-01 COMMENT Index(29): /data1/INDEXES/200/index-203-02 COMMENT Index(30): /data1/INDEXES/200/index-203-03 COMMENT Index(31): /data1/INDEXES/200/index-203-04 COMMENT Index(32): /data1/INDEXES/200/index-203-05 COMMENT Index(33): /data1/INDEXES/200/index-203-06 COMMENT Index(34): /data1/INDEXES/200/index-203-07 COMMENT Index(35): /data1/INDEXES/200/index-203-08 COMMENT Index(36): /data1/INDEXES/200/index-203-09 COMMENT Index(37): /data1/INDEXES/200/index-203-10 COMMENT Index(38): /data1/INDEXES/200/index-203-11 COMMENT Index(39): /data1/INDEXES/200/index-202-00 COMMENT Index(40): /data1/INDEXES/200/index-202-01 COMMENT Index(41): /data1/INDEXES/200/index-202-02 COMMENT Index(42): /data1/INDEXES/200/index-202-03 COMMENT Index(43): /data1/INDEXES/200/index-202-04 COMMENT Index(44): /data1/INDEXES/200/index-202-05 COMMENT Index(45): /data1/INDEXES/200/index-202-06 COMMENT Index(46): /data1/INDEXES/200/index-202-07 COMMENT Index(47): /data1/INDEXES/200/index-202-08 COMMENT Index(48): /data1/INDEXES/200/index-202-09 COMMENT Index(49): /data1/INDEXES/200/index-202-10 COMMENT Index(50): /data1/INDEXES/200/index-202-11 COMMENT Index(51): /data1/INDEXES/200/index-201-00 COMMENT Index(52): /data1/INDEXES/200/index-201-01 COMMENT Index(53): /data1/INDEXES/200/index-201-02 COMMENT Index(54): /data1/INDEXES/200/index-201-03 COMMENT Index(55): /data1/INDEXES/200/index-201-04 COMMENT Index(56): /data1/INDEXES/200/index-201-05 COMMENT Index(57): /data1/INDEXES/200/index-201-06 COMMENT Index(58): /data1/INDEXES/200/index-201-07 COMMENT Index(59): /data1/INDEXES/200/index-201-08 COMMENT Index(60): /data1/INDEXES/200/index-201-09 COMMENT Index(61): /data1/INDEXES/200/index-201-10 COMMENT Index(62): /data1/INDEXES/200/index-201-11 COMMENT Index(63): /data1/INDEXES/200/index-200-00 COMMENT Index(64): /data1/INDEXES/200/index-200-01 COMMENT Index(65): /data1/INDEXES/200/index-200-02 COMMENT Index(66): /data1/INDEXES/200/index-200-03 COMMENT Index(67): /data1/INDEXES/200/index-200-04 COMMENT Index(68): /data1/INDEXES/200/index-200-05 COMMENT Index(69): /data1/INDEXES/200/index-200-06 COMMENT Index(70): /data1/INDEXES/200/index-200-07 COMMENT Index(71): /data1/INDEXES/200/index-200-08 COMMENT Index(72): /data1/INDEXES/200/index-200-09 COMMENT Index(73): /data1/INDEXES/200/index-200-10 COMMENT Index(74): /data1/INDEXES/200/index-200-11 COMMENT Field name: field.xy.fits COMMENT Field scale lower: 0.4 arcsec/pixel COMMENT Field scale upper: 720 arcsec/pixel COMMENT X col name: X COMMENT Y col name: Y COMMENT Start obj: 0 COMMENT End obj: 200 COMMENT Solved_in: solved COMMENT Solved_out: solved COMMENT Solvedserver: (null) COMMENT Parity: 2 COMMENT Codetol: 0.01 COMMENT Verify distance: 0 arcsec COMMENT Verify pixels: 1 pix COMMENT Maxquads: 0 COMMENT Maxmatches: 0 COMMENT Cpu limit: 0 s COMMENT Time limit: 0 s COMMENT Total time limit: 0 s COMMENT Total CPU limit: 600 s COMMENT Tweak: no COMMENT -- COMMENT -- properties of the matching quad: -- COMMENT quadno: 686636 COMMENT stars: 1095617,1095660,1095623,1095618 COMMENT field: 6,5,24,35 COMMENT code error: 0.00868071 COMMENT noverlap: 42 COMMENT nconflict: 1 COMMENT nfield: 88 COMMENT nindex: 139 COMMENT scale: 2.94093 arcsec/pix COMMENT parity: 1 COMMENT quads tried: 2166080 COMMENT quads matched: 2079562 COMMENT quads verified: 1747182 COMMENT objs tried: 0 COMMENT cpu time: 117.82 COMMENT -- AN_JOBID= 'alpha-201004-29242410' / Astrometry.net job ID END ";
if (write_file(tmpfile, wcsliteral, strlen(wcsliteral))) {
ERROR("Failed to write WCS to temp file %s", tmpfile);
CuFail(tc, "failed to write WCS to temp file");
}
tan = tan_read_header_file(tmpfile, NULL);
CuAssertPtrNotNull(tc, tan);
for (i=0; i<2; i++) {
if (i == 0) {
anwcs = anwcs_open_wcslib(tmpfile, 0);
} else if (i == 1) {
anwcs = anwcs_open_sip(tmpfile, 0);
}
CuAssertPtrNotNull(tc, anwcs);
/*
printf("ANWCS:\n");
anwcs_print(anwcs, stdout);
printf("TAN:\n");
tan_print_to(tan, stdout);
*/
/* this wcs has:
crval=(83.7132, -5.10104)
crpix=(221.593, 169.656)
CD = ( 1.5526e-06 0.00081692 )
( -0.00081692 1.5526e-06 )
*/
// check crval <-> crpix.
x = tan->crpix[0];
y = tan->crpix[1];
ra = 1; ra2 = 2; dec = 3; dec2 = 4;
tan_pixelxy2radec(tan, x, y, &ra, &dec);
CuAssertDblEquals(tc, tan->crval[0], ra, 1e-6);
CuAssertDblEquals(tc, tan->crval[1], dec, 1e-6);
ok = anwcs_pixelxy2radec(anwcs, x, y, &ra2, &dec2);
CuAssertIntEquals(tc, 0, ok);
CuAssertDblEquals(tc, tan->crval[0], ra2, 1e-6);
CuAssertDblEquals(tc, tan->crval[1], dec2, 1e-6);
ra = tan->crval[0];
dec = tan->crval[1];
x = 1; x2 = 2; y = 3; y2 = 4;
ok = tan_radec2pixelxy(tan, ra, dec, &x, &y);
CuAssertIntEquals(tc, TRUE, ok);
CuAssertDblEquals(tc, tan->crpix[0], x, 1e-6);
CuAssertDblEquals(tc, tan->crpix[1], y, 1e-6);
ok2 = anwcs_radec2pixelxy(anwcs, ra, dec, &x2, &y2);
CuAssertIntEquals(tc, 0, ok2);
CuAssertDblEquals(tc, tan->crpix[0], x2, 1e-6);
CuAssertDblEquals(tc, tan->crpix[1], y2, 1e-6);
// check pixel (0,0).
x = y = 0.0;
ra = 1; ra2 = 2; dec = 3; dec2 = 4;
tan_pixelxy2radec(tan, x, y, &ra, &dec);
ok = anwcs_pixelxy2radec(anwcs, x, y, &ra2, &dec2);
CuAssertIntEquals(tc, 0, ok);
CuAssertDblEquals(tc, ra, ra2, 1e-6);
CuAssertDblEquals(tc, dec, dec2, 1e-6);
// check RA,Dec (85, -4)
ra = 85;
dec = -4;
x = 1; x2 = 2; y = 3; y2 = 4;
ok = tan_radec2pixelxy(tan, ra, dec, &x, &y);
CuAssertIntEquals(tc, TRUE, ok);
ok2 = anwcs_radec2pixelxy(anwcs, ra, dec, &x2, &y2);
CuAssertIntEquals(tc, 0, ok2);
printf("x,y (%g,%g) vs (%g,%g)\n", x, y, x2, y2);
CuAssertDblEquals(tc, x, x2, 1e-6);
CuAssertDblEquals(tc, y, y2, 1e-6);
anwcs_free(anwcs);
}
free(tan);
}
