29 #include <cxmessages.h>
33 #include "gimath_lm.h"
34 #include "gimessages.h"
50 #define SWAP(a,b) {swap=(a);(a)=(b);(b)=swap;}
61 {LMRQ_GAUSSUM, mrqgaussum, 4, 1,
"gaussum", LINE_MODEL},
62 {LMRQ_XOPTMOD, mrqxoptmod, 7, 3,
"xoptmod", XOPT_MODEL},
63 {LMRQ_XOPTMODGS, mrqxoptmodGS, 7, 3,
"xoptmodGS", XOPT_MODEL},
64 {LMRQ_XOPTMOD2, mrqxoptmod2, 10, 3,
"xoptmod2", XOPT_MODEL},
65 {LMRQ_PSFCOS, mrqpsfcos, 5, 1,
"psfcos", LINE_MODEL},
66 {LMRQ_PSFEXP, mrqpsfexp, 5, 1,
"psfexp", LINE_MODEL},
67 {LMRQ_YOPTMOD, mrqyoptmod, 7, 3,
"yoptmod", YOPT_MODEL},
68 {LMRQ_YOPTMOD2, mrqyoptmod2, 10, 3,
"yoptmod2", YOPT_MODEL},
69 {LMRQ_LOCYWARP, mrqlocywarp, 5, 4,
"locywarp", LOCY_MODEL},
70 {LMRQ_PSFEXP2, mrqpsfexp2, 5, 1,
"psfexp2", LINE_MODEL},
71 {LMRQ_TEST, mrqtest, 2, 1,
"test", LINE_MODEL}
74 cxint nr_lmrq_models = CX_N_ELEMENTS(lmrq_models);
94 covariance_sort(cpl_matrix *covar, cxint ma, cxint ia[], cxint mfit)
97 register cxint i, j, k;
98 register cxdouble swap;
100 cxdouble *pd_covar = NULL;
103 pd_covar = cpl_matrix_get_data(covar);
104 nr_covar = cpl_matrix_get_nrow(covar);
106 for (i = mfit; i < ma; i++)
107 for (j = 0; j <= i; j++)
108 pd_covar[i * nr_covar + j] = pd_covar[j * nr_covar + i] = 0.0;
111 for (j = (ma-1); j >= 0; j--) {
113 for (i = 0; i < ma; i++)
114 SWAP(pd_covar[i * nr_covar + k],pd_covar[i * nr_covar + j])
116 for (i = 0;i < ma; i++)
117 SWAP(pd_covar[k * nr_covar + i],pd_covar[j * nr_covar + i])
154 mrqdydaweight(cxdouble x, cxdouble x0, cxdouble dx)
158 w = exp(-pow(fabs(x-x0),DW_DEGREE)/pow(dx,DW_DEGREE/DW_LOG001));
204 lmrq_params fit_params,
215 cpl_matrix *beta = NULL;
221 beta = cpl_matrix_new(ma,ma);
225 res = mymrqmin(x, y, sig, ndata, a, r, ia, ma, alpha, beta, chisq,
229 cpl_matrix_delete(beta); beta = NULL;
235 for (n = 1; n <= fit_params.imax; n++) {
239 res = mymrqmin(x, y, sig, ndata, a, r, ia, ma, alpha, beta, chisq,
243 cpl_matrix_delete(beta); beta = NULL;
249 else if (fabs(ochisq-*chisq) < fit_params.dchsq)
252 if (itst > fit_params.tmax)
259 res = mymrqmin(x, y, sig, ndata, a, r, ia, ma, alpha, beta, chisq,
263 cpl_matrix_delete(beta); beta = NULL;
267 cpl_matrix_delete(beta); beta = NULL;
346 register cxint gj, j, k, l, m;
348 static cxdouble *pd_a, *pd_covar, *pd_alpha;
349 static cxint nr_covar, nr_alpha, nr_moneda, mfit;
351 static cpl_matrix *matry, *mbeta, *mda, *moneda;
352 static cxdouble *atry, *beta, *da, *oneda, ochisq;
358 pd_a = cpl_matrix_get_data(a);
359 pd_covar = cpl_matrix_get_data(covar);
360 pd_alpha = cpl_matrix_get_data(alpha);
361 nr_covar = cpl_matrix_get_nrow(covar);
362 nr_alpha = cpl_matrix_get_nrow(alpha);
366 matry = cpl_matrix_new(ma,1);
367 atry = cpl_matrix_get_data(matry);
369 mbeta = cpl_matrix_new(ma,1);
370 beta = cpl_matrix_get_data(mbeta);
372 mda = cpl_matrix_new(ma,1);
373 da = cpl_matrix_get_data(mda);
375 for (mfit = 0, j = 0; j < ma; j++)
379 moneda = cpl_matrix_new(1,mfit);
380 oneda = cpl_matrix_get_data(moneda);
384 gj = mymrqcof(x, y, sig, ndata, a, r, ia, ma, alpha, mbeta,
388 cpl_matrix_delete(moneda); moneda = NULL; oneda = NULL;
389 cpl_matrix_delete(mda); mda = NULL; da = NULL;
390 cpl_matrix_delete(mbeta); mbeta = NULL; beta = NULL;
391 cpl_matrix_delete(matry); matry = NULL; atry = NULL;
397 for (j = 0; j < ma; j++)
402 nr_moneda = cpl_matrix_get_nrow(moneda);
404 for (j = -1, l = 0; l < ma; l++) {
406 for (j++, k = -1, m = 0; m < ma; m++) {
409 pd_covar[j * nr_covar + k] = pd_alpha[j * nr_alpha + k];
413 pd_covar[j * nr_covar + j] =
414 pd_alpha[j * nr_alpha + j] * (1.0 + (*alamda));
416 oneda[j * nr_moneda + 0] = beta[j];
420 gj = giraffe_gauss_jordan(covar, mfit, moneda, 1);
423 cpl_matrix_delete(moneda); moneda = NULL; oneda = NULL;
424 cpl_matrix_delete(mda); mda = NULL; da = NULL;
425 cpl_matrix_delete(mbeta); mbeta = NULL; beta = NULL;
426 cpl_matrix_delete(matry); matry = NULL; atry = NULL;
430 for (j = 0; j < mfit; j++)
431 da[j] = oneda[j * nr_moneda + 0];
433 if (*alamda == 0.0) {
434 covariance_sort(covar, ma, ia, mfit);
435 cpl_matrix_delete(moneda); moneda = NULL; oneda = NULL;
436 cpl_matrix_delete(mda); mda = NULL; da = NULL;
437 cpl_matrix_delete(mbeta); mbeta = NULL; beta = NULL;
438 cpl_matrix_delete(matry); matry = NULL; atry = NULL;
442 for (j = -1, l = 0; l < ma; l++)
444 atry[l] = pd_a[l] + da[++j];
446 gj = mymrqcof(x, y, sig, ndata, matry, r, ia, ma, covar, mda,
450 cpl_matrix_delete(moneda); moneda = NULL; oneda = NULL;
451 cpl_matrix_delete(mda); mda = NULL; da = NULL;
452 cpl_matrix_delete(mbeta); mbeta = NULL; beta = NULL;
453 cpl_matrix_delete(matry); matry = NULL; atry = NULL;
457 if (*chisq < ochisq) {
462 for (j = -1, l = 0; l < ma; l++) {
464 for (j++, k = -1, m = 0; m < ma; m++) {
467 pd_alpha[j * nr_alpha + k] =
468 pd_covar[j * nr_covar + k];
529 register cxint i, j, k, l, m, mfit = 0;
531 cxdouble ymod, wt, sig2i, dy, *dyda;
533 cxdouble *pd_x = NULL,
540 cxint nr_alpha, nc_x;
546 pd_x = cpl_matrix_get_data(x);
547 nc_x = cpl_matrix_get_ncol(x);
548 pd_y = cpl_matrix_get_data(y);
549 pd_sig = cpl_matrix_get_data(sig);
550 pd_a = cpl_matrix_get_data(a);
551 pd_alpha = cpl_matrix_get_data(alpha);
552 nr_alpha = cpl_matrix_get_nrow(alpha);
553 pd_beta = cpl_matrix_get_data(beta);
555 for (j = 0; j < ma; j++) {
560 for (j = 0; j < mfit; j++) {
561 for (k = 0; k <= j; k++)
562 pd_alpha[j * nr_alpha + k] = 0.0;
569 dyda = (cxdouble *) cx_calloc(ma,
sizeof(cxdouble));
571 for (i = 0; i < ndata; i++) {
573 (*funcs)(&(pd_x[i*nc_x]), pd_a, r, &ymod, dyda, ma);
575 if (pd_sig[i]==0.0) {
579 sig2i = 1.0 / (pd_sig[i] * pd_sig[i]);
583 for (j = -1, l = 0; l < ma; l++) {
586 wt = dyda[l] * sig2i;
587 for (j++, k = -1, m = 0; m <= l; m++) {
590 pd_alpha[j * nr_alpha + k] += (wt * dyda[m]);
594 pd_beta[j] += (dy * wt);
599 *chisq += (dy * dy * sig2i);
603 for (j = 1; j < mfit; j++)
604 for (k = 0; k < j; k++)
605 pd_alpha[k * nr_alpha + j] = pd_alpha[j * nr_alpha + k];
631 r_squared(cxdouble resSS, cpl_matrix *y, cxint n)
634 register cxdouble Sy, Syy, SS;
635 cxdouble res, *pd_y = NULL;
637 pd_y = cpl_matrix_get_data(y);
642 for (i=0, Sy=0.0, Syy=0.0; i<n; i++) {
644 Syy += pd_y[i]*pd_y[i];
692 mrqgaussum(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
693 cxdouble dyda[], cxint na)
697 register cxdouble fac,ex,amplitude,center,backg,width,xred;
702 for (j = 0, i = 0; i < na; i += 4, j += 4) {
707 xred = (x[0] - center) / width;
708 ex = exp(-xred * xred / 2.);
709 fac = amplitude * xred * ex;
710 *y += (amplitude * ex + backg);
713 if (dyda == NULL)
continue;
717 dyda[j + 1] = fac / width;
719 dyda[j + 3] = (fac * xred) / width;
776 mrqxoptmod(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
777 cxdouble dyda[], cxint na)
780 const cxchar *fctid =
"mrqxoptmod";
782 register cxdouble xccd, d, X;
783 register cxdouble lambda,xfibre,yfibre,pixsize,nx;
785 register cxdouble fcoll,cfact;
787 register cxdouble gtheta,gorder,gspace;
788 register cxdouble yfibre2,tmp,tmp2,d2,X2,gspace2,sqtmp,costheta,sintheta;
792 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
798 dyda[0] = dyda[1] = dyda[2] = dyda[3] =
799 dyda[4] = dyda[5] = dyda[6] = 0.0;
802 lambda = x[LMI_WLEN];
803 xfibre = x[LMI_XFIB];
804 yfibre = x[LMI_YFIB];
807 pixsize = a[LMP_PXSIZ];
808 fcoll = a[LMP_FCOLL];
809 cfact = a[LMP_CFACT];
810 gtheta = a[LMP_THETA];
811 gorder = a[LMP_ORDER];
812 gspace = a[LMP_SPACE];
814 yfibre2 = yfibre * yfibre;
815 gspace2 = gspace * gspace;
816 costheta = cos(gtheta);
817 sintheta = sin(gtheta);
818 d2 = xfibre * xfibre + yfibre2 + (fcoll * fcoll);
820 X = (-lambda*gorder/gspace) + (xfibre*costheta/d) + (fcoll*sintheta/d);
822 sqtmp = sqrt(1.0 - yfibre2/d2 - X2);
823 tmp = -sintheta*X + costheta*sqtmp;
825 xccd = (cfact * fcoll * (X*costheta + sintheta*sqtmp))/tmp;
829 *y = (xccd / pixsize - 0.5*nx);
831 *y = (-xccd / pixsize + 0.5*nx);
839 dyda[LMP_PXSIZ] = 0.0;
841 dyda[LMP_FCOLL] = cfact*(costheta*X+sintheta*sqtmp)/tmp +
842 cfact*fcoll*(costheta*(-X*fcoll/d2+sintheta/d -
843 gorder*lambda*fcoll/(d2*gspace)) +
844 0.5*sintheta*(-2.0*X*(-X*fcoll/d2+sintheta/d -
845 gorder*lambda*fcoll/(d2*gspace))+2.0*yfibre2*fcoll/(d2*d2))/sqtmp)/tmp -
846 cfact*fcoll*(costheta*X+sintheta*sqtmp)*(-sintheta*(-X*fcoll/d2 +
847 sintheta/d-gorder*lambda*fcoll/(d2*gspace)) +
848 0.5*costheta*(-2.0*X*(-X*fcoll/d2+sintheta/d -
849 gorder*lambda*fcoll/(d2*gspace))+2.0*yfibre2*fcoll/(d2*d2))/sqtmp)/tmp2;
850 dyda[LMP_FCOLL] /= pixsize;
852 dyda[LMP_CFACT] = (xccd/cfact)/pixsize;
854 dyda[LMP_THETA] = cfact*fcoll*((-xfibre*sintheta/d+fcoll*costheta/d)*costheta -
855 sintheta*X-sintheta*X*(-xfibre*sintheta/d+fcoll*costheta/d)/sqtmp +
856 costheta*sqtmp)/tmp -
857 cfact*fcoll*(costheta*X+sintheta*sqtmp)*(-(-xfibre*sintheta/d +
858 fcoll*costheta/d)*sintheta-costheta*X -
859 costheta*X*(-xfibre*sintheta/d+fcoll*costheta/d)/sqtmp -
860 sintheta*sqtmp)/tmp2;
861 dyda[LMP_THETA] /= pixsize;
863 dyda[LMP_ORDER] = 0.0;
864 dyda[LMP_SPACE] = cfact*fcoll*(lambda*gorder*costheta/gspace2-sintheta*X*lambda*gorder/(sqtmp*gspace2))/tmp -
865 cfact*fcoll*(X*costheta+sintheta*sqtmp) *
866 (-lambda*gorder*sintheta/gspace2-costheta*X*lambda*gorder/(sqtmp*gspace2))/tmp2;
867 dyda[LMP_SPACE] /= pixsize;
870 dyda[LMP_NX] = -dyda[LMP_NX];
871 dyda[LMP_PXSIZ] = -dyda[LMP_PXSIZ];
872 dyda[LMP_FCOLL] = -dyda[LMP_FCOLL];
873 dyda[LMP_CFACT] = -dyda[LMP_CFACT];
874 dyda[LMP_THETA] = -dyda[LMP_THETA];
875 dyda[LMP_ORDER] = -dyda[LMP_ORDER];
876 dyda[LMP_SPACE] = -dyda[LMP_SPACE];
884 dyda[LMP_FCOLL] *= mrqdydaweight(a[LMP_FCOLL],r[k],r[k+1]);
888 dyda[LMP_CFACT] *= mrqdydaweight(a[LMP_CFACT],r[k],r[k+1]);
892 dyda[LMP_THETA] *= mrqdydaweight(a[LMP_THETA],r[k],r[k+1]);
896 dyda[LMP_SPACE] *= mrqdydaweight(a[LMP_SPACE],r[k],r[k+1]);
964 mrqxoptmod2(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
965 cxdouble dyda[], cxint na)
968 const cxchar *fctid =
"mrqxoptmod2";
970 register cxdouble lambda,xfibre,yfibre,pixsize,nx;
972 register cxdouble fcoll,cfact;
974 register cxdouble gtheta,gorder,gspace;
976 cxdouble slitdx,slitdy,slitphi;
978 register cxdouble t1,t10,t104,t107,t11,t113,t119,t12,t120,t121,t124,t136,
979 t137,t138,t14,t143,t148,t16,t161,t162,t166,t168,t17,t173,
980 t18,t19,t191,t195,t196,t2,t20,t201,t21,t210,t23,t24,t26,
981 t27,t28,t3,t30,t32,t33,t34,t35,t36,t37,t38,t39,t4,t40,t44,
982 t49,t52,t58,t60,t61,t62,t64,t68,t75,t76,t78,t80,t9,t91,t93;
986 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
992 dyda[0] = dyda[1] = dyda[2] = dyda[3] =
993 dyda[4] = dyda[5] = dyda[6] =
994 dyda[7] = dyda[8] = dyda[9] = 0.0;
997 lambda = x[LMI_WLEN];
998 xfibre = x[LMI_XFIB];
999 yfibre = x[LMI_YFIB];
1002 pixsize = a[LMP_PXSIZ];
1003 fcoll = a[LMP_FCOLL];
1004 cfact = a[LMP_CFACT];
1005 gtheta = a[LMP_THETA];
1006 gorder = a[LMP_ORDER];
1007 gspace = a[LMP_SPACE];
1008 slitdx = a[LMP_SOFFX];
1009 slitdy = a[LMP_SOFFY];
1010 slitphi = a[LMP_SPHI];
1016 t9 = xfibre*(1.0+slitphi*yfibre)+slitdx;
1019 t12 = slitphi*slitphi;
1020 t14 = sqrt(1.0-t12);
1021 t16 = yfibre*t14+slitdy;
1029 t26 = -t3*t4+t10*t21+t24*t21;
1033 t32 = sqrt(1.0-t17*t28-t30);
1042 t44 = pixsize*pixsize;
1045 t58 = -t10*t52*fcoll+t23*t21-t18*t23*t52;
1050 t68 = 2.0*t64*fcoll-2.0*t26*t58;
1055 t91 = -t9*t23*t21+fcoll*t2*t21;
1058 t107 = t26*lambda*t4;
1060 t119 = gspace*gspace;
1067 t143 = t136-t10*t138/2.0-t24*t138/2.0;
1068 t148 = t64*t137-2.0*t26*t143;
1071 t166 = -t10*t162/2.0-t24*t162/2.0;
1073 t173 = -2.0*t168+t64*t161-2.0*t26*t166;
1075 t195 = 2.0*t9*xfibre*yfibre-2.0*t16*yfibre*t191*slitphi;
1077 t201 = xfibre*yfibre*t136-t10*t196/2.0-t24*t196/2.0;
1078 t210 = 2.0*t168*yfibre*t191*slitphi+t64*t195-2.0*t26*t201;
1082 *y = t1*t39*t40-0.5*nx;
1084 *y = -t1*t39*t40+0.5*nx;
1092 dyda[LMP_PXSIZ] = -t1*t39/t44;
1094 cfact*t34*t49+t1*(t2*t58+t61*t68/2.0)*t38*t40 -
1095 t75*t78*(-t23*t58+t80*t68/2.0);
1099 t1*(-t35+t2*t91+t36-t61*t93)*t38*t40 -
1100 t75*t78*(-t27-t23*t91-t33-t80*t93);
1102 t1*(-t104*t4+t61*t107)*t38*t40-t75*t78*(t113*t4+t80*t107);
1104 t1*(t104*t121-t61*t26*t124)*t38*t40 -
1105 t75*t78*(-t113*t121-t80*t26*t124);
1107 t1*(t2*t143+t61*t148/2.0)*t38*t40 -
1108 t75*t78*(-t23*t143+t80*t148/2.0);
1110 t1*(t2*t166+t61*t173/2.0)*t38*t40 -
1111 t75*t78*(-t23*t166+t80*t173/2.0);
1113 t1*(t2*t201+t61*t210/2.0)*t38*t40 -
1114 t75*t78*(-t23*t201+t80*t210/2.0);
1117 dyda[LMP_NX] = -dyda[LMP_NX];
1118 dyda[LMP_PXSIZ] = -dyda[LMP_PXSIZ];
1119 dyda[LMP_FCOLL] = -dyda[LMP_FCOLL];
1120 dyda[LMP_CFACT] = -dyda[LMP_CFACT];
1121 dyda[LMP_THETA] = -dyda[LMP_THETA];
1122 dyda[LMP_ORDER] = -dyda[LMP_ORDER];
1123 dyda[LMP_SPACE] = -dyda[LMP_SPACE];
1124 dyda[LMP_SOFFX] = -dyda[LMP_SOFFX];
1125 dyda[LMP_SOFFY] = -dyda[LMP_SOFFY];
1126 dyda[LMP_SPHI] = -dyda[LMP_SPHI];
1134 dyda[LMP_PXSIZ] *= mrqdydaweight(a[LMP_PXSIZ],r[k],r[k+1]);
1138 dyda[LMP_FCOLL] *= mrqdydaweight(a[LMP_FCOLL],r[k],r[k+1]);
1142 dyda[LMP_CFACT] *= mrqdydaweight(a[LMP_CFACT],r[k],r[k+1]);
1146 dyda[LMP_THETA] *= mrqdydaweight(a[LMP_THETA],r[k],r[k+1]);
1150 dyda[LMP_ORDER] *= mrqdydaweight(a[LMP_ORDER],r[k],r[k+1]);
1154 dyda[LMP_SPACE] *= mrqdydaweight(a[LMP_SPACE],r[k],r[k+1]);
1158 dyda[LMP_SOFFX] *= mrqdydaweight(a[LMP_SOFFX],r[k],r[k+1]);
1162 dyda[LMP_SOFFY] *= mrqdydaweight(a[LMP_SOFFY],r[k],r[k+1]);
1166 dyda[LMP_SPHI] *= mrqdydaweight(a[LMP_SPHI],r[k],r[k+1]);
1237 mrqyoptmod(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
1238 cxdouble dyda[], cxint na)
1241 const cxchar *fctid =
"mrqyoptmod";
1243 register cxdouble lambda,xfibre,yfibre,pixsize,ny;
1245 register cxdouble fcoll,cfact;
1247 register cxdouble gtheta,gorder,gspace;
1249 cxdouble t10,t12,t13,t15,t18,t2,t22,t24,t26,t27,t28,t29,t3,t30,t33,
1250 t4,t41,t45,t47,t5,t53,t56,t57,t6,t7,t76,t8,t9,t93,t94;
1256 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
1262 dyda[LMP_NX] = dyda[LMP_PXSIZ] = dyda[LMP_FCOLL] = dyda[LMP_CFACT] =
1263 dyda[LMP_THETA] = dyda[LMP_ORDER] = dyda[LMP_SPACE] = 0.0;
1266 lambda = x[LMI_WLEN];
1267 xfibre = x[LMI_XFIB];
1268 yfibre = x[LMI_YFIB];
1271 pixsize = a[LMP_PXSIZ];
1272 fcoll = a[LMP_FCOLL];
1273 cfact = a[LMP_CFACT];
1274 gtheta = a[LMP_THETA];
1275 gorder = a[LMP_ORDER];
1276 gspace = a[LMP_SPACE];
1278 t2 = cfact*fcoll*yfibre;
1290 t18 = -t9*t10+t13*t8+fcoll*t15*t8;
1292 t24 = sqrt(1.0-t4/t6-t22);
1293 t26 = -t18*t15+t12*t24;
1298 t33 = pixsize*pixsize;
1302 t53 = -t13*t41*fcoll+t15*t8-t5*t15*t41;
1305 t76 = -xfibre*t15*t8+fcoll*t12*t8;
1306 t93 = gspace*gspace;
1309 *y = -t2*t30+0.5*ny;
1312 if (dyda == NULL)
return;
1317 dyda[LMP_PXSIZ] = t2*t28/t33;
1318 dyda[LMP_FCOLL] = -cfact*yfibre*t30+cfact*t5*yfibre*t41*t27*t29+t2*t47*t29*
1319 (-t53*t15+t56*(2.0*t4/t57*fcoll-2.0*t18*t53)/2.0);
1320 dyda[LMP_CFACT] = -fcoll*yfibre*t30;
1321 dyda[LMP_THETA] = t2*t47*t29*(-t76*t15-t18*t12-t15*t24-t56*t18*t76);
1322 dyda[LMP_ORDER] = t2*t47*t29*(lambda*t10*t15+t56*t18*lambda*t10);
1323 dyda[LMP_SPACE] = t2*t47*t29*(-t9*t94*t15-t56*t18*t9*t94);
1400 mrqyoptmod2(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
1401 cxdouble dyda[], cxint na)
1404 const cxchar *fctid =
"mrqyoptmod2";
1406 register cxdouble lambda,xfibre,yfibre,pixsize,ny;
1408 register cxdouble fcoll,cfact;
1410 register cxdouble gtheta,gorder,gspace;
1412 cxdouble slitdx,slitdy,slitphi;
1414 double t1,t102,t103,t11,t112,t117,t118,t12,t123,t13,t136,t14,t141,t145,
1415 t147,t15,t159,t16,t160,t17,t172,t179,t18,t184,t19,t2,t21,t22,t24,
1416 t25,t27,t29,t31,t33,t35,t36,t37,t38,t39,t4,t42,t50,t51,t54,t56,t6,
1417 t62,t65,t66,t68,t7,t85;
1423 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
1429 dyda[LMP_NY] = dyda[LMP_PXSIZ] = dyda[LMP_FCOLL] = dyda[LMP_CFACT] =
1430 dyda[LMP_THETA] = dyda[LMP_ORDER] = dyda[LMP_SPACE] =
1431 dyda[LMP_SOFFX] = dyda[LMP_SOFFY] = dyda[LMP_SPHI] = 0.0;
1434 lambda = x[LMI_WLEN];
1435 xfibre = x[LMI_XFIB];
1436 yfibre = x[LMI_YFIB];
1439 pixsize = a[LMP_PXSIZ];
1440 fcoll = a[LMP_FCOLL];
1441 cfact = a[LMP_CFACT];
1442 gtheta = a[LMP_THETA];
1443 gorder = a[LMP_ORDER];
1444 gspace = a[LMP_SPACE];
1445 slitdx = a[LMP_SOFFX];
1446 slitdy = a[LMP_SOFFY];
1447 slitphi = a[LMP_SPHI];
1450 t2 = slitphi*slitphi;
1452 t6 = yfibre*t4+slitdy;
1454 t11 = xfibre*(1.0+slitphi*yfibre)+slitdx;
1461 t18 = lambda*gorder;
1467 t27 = -t18*t19+t22*t17+t25*t17;
1470 t33 = sqrt(1.0-t13*t29-t31);
1471 t35 = -t27*t24+t21*t33;
1476 t42 = pixsize*pixsize;
1481 t62 = -t22*t50*fcoll+t24*t17-t14*t24*t50;
1485 t85 = -t11*t24*t17+fcoll*t21*t17;
1486 t102 = gspace*gspace;
1491 t123 = t117-t22*t118/2.0-t25*t118/2.0;
1494 t145 = -t22*t141/2.0-t25*t141/2.0;
1498 t172 = 2.0*t11*xfibre*yfibre-2.0*t6*yfibre*t159*slitphi;
1500 t184 = xfibre*yfibre*t117-t22*t179/2.0-t25*t179/2.0;
1502 *y = -t7*t39+0.5*ny;
1505 if (dyda == NULL)
return;
1509 dyda[LMP_PXSIZ] = t7*t37/t42;
1511 -cfact*t6*t39+cfact*t14*t6*t51*t38+
1512 t7*t56*t38*(-t62*t24+t65*(2.0*t68*fcoll-2.0*t27*t62)/2.0);
1516 t7*t56*t38*(-t85*t24-t27*t21-t24*t33-t65*t27*t85);
1518 t7*t56*t38*(lambda*t19*t24+t65*t27*lambda*t19);
1520 t7*t56*t38*(-t18*t103*t24-t65*t27*t18*t103);
1522 t7*t51*t38*t112/2.0+t7*t56*t38*(-t123*t24+t65*
1523 (t68*t112-2.0*t27*t123)/2.0);
1525 -t1*t39+t7*t51*t38*t136/2.0+t7*t56*t38*(-t145*t24+t65*
1526 (-2.0*t147+t68*t136-2.0*t27*t145)/2.0);
1528 t1*t160*slitphi*t17*t36*t38+t7*t51*t38*t172/2.0+
1529 t7*t56*t38*(-t184*t24+t65*(2.0*t147*t160*slitphi+t68*t172-
1560 mrqpsfcos(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
1561 cxdouble dyda[], cxint na)
1564 const cxchar *fctid =
"mrqpsfcos";
1566 cxdouble t1,t10,t13,t14,t15,t16,t2,t26,t3,t4,t5,t6,t7,t8,t9;
1568 cxdouble amplitude = a[LMP_AMPL];
1569 cxdouble center = a[LMP_CENT];
1570 cxdouble background = a[LMP_BACK];
1571 cxdouble width1 = a[LMP_WID1];
1572 cxdouble width2 = a[LMP_WID2];
1578 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
1584 dyda[LMP_AMPL] = dyda[LMP_CENT] = dyda[LMP_BACK] = dyda[LMP_WID1] =
1585 dyda[LMP_WID2] = 0.0;
1592 t5 = pow(t4,width1);
1602 t26 = (t1>0.0)? 1.0:-1.0;
1608 if (dyda == NULL)
return;
1610 dyda[LMP_AMPL] = dyda[LMP_CENT] = dyda[LMP_BACK] = dyda[LMP_WID1] = 0.0;
1611 dyda[LMP_WID2] = 1.0;
1613 *y = amplitude*t10/8.0+background;
1619 dyda[LMP_AMPL] = t10/8.0;
1621 dyda[LMP_CENT] = 3.0/8.0*t13*t14*CX_PI*t5*width1*t26/t2;
1622 dyda[LMP_BACK] = 1.0;
1623 dyda[LMP_WID1] = -3.0/8.0*t15*t6*t16;
1624 dyda[LMP_WID2] = 3.0/8.0*t15*t6*width1*t3;
1657 mrqpsfexp(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
1658 cxdouble dyda[], cxint na)
1661 const cxchar *fctid =
"mrqpsfexp";
1663 cxdouble t1,t2,t3,t4,t6,t8,t10,t15,t18;
1665 cxdouble amplitude = a[LMP_AMPL];
1666 cxdouble center = a[LMP_CENT];
1667 cxdouble background = a[LMP_BACK];
1668 cxdouble width1 = a[LMP_WID1];
1669 cxdouble width2 = a[LMP_WID2];
1673 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
1679 dyda[LMP_AMPL] = dyda[LMP_CENT] = dyda[LMP_BACK] = dyda[LMP_WID1] =
1680 dyda[LMP_WID2] = 0.0;
1693 t3 = pow(t2,width2);
1697 t15 = width1*width1;
1700 *y = amplitude*t6+background;
1706 dyda[LMP_AMPL] = t6;
1707 dyda[LMP_CENT] = t8*width2*t10/t2*t4*t6;
1709 if (isnan(dyda[LMP_CENT]))
1710 dyda[LMP_CENT] = 0.;
1712 dyda[LMP_BACK] = 1.0;
1713 dyda[LMP_WID1] = t8/t15*t6;
1714 dyda[LMP_WID2] = -t8*t18*t4*t6;
1716 if (isnan(dyda[LMP_WID2]))
1717 dyda[LMP_WID2] = 0.;
1724 dyda[LMP_AMPL] *= mrqdydaweight(a[LMP_AMPL],r[k],r[k+1]);
1728 dyda[LMP_CENT] *= mrqdydaweight(a[LMP_CENT],r[k],r[k+1]);
1732 dyda[LMP_WID1] *= mrqdydaweight(a[LMP_WID1],r[k],r[k+1]);
1736 dyda[LMP_WID2] *= mrqdydaweight(a[LMP_WID2],r[k],r[k+1]);
1770 mrqpsfexp2(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
1771 cxdouble dyda[], cxint na)
1774 const cxchar *fctid =
"mrqpsfexp2";
1776 cxdouble t1,t2,t3,t4,t5,t6,t8,t10,t16;
1778 cxdouble amplitude = a[LMP_AMPL];
1779 cxdouble center = a[LMP_CENT];
1780 cxdouble background = a[LMP_BACK];
1781 cxdouble width1 = a[LMP_WID1];
1782 cxdouble width2 = a[LMP_WID2];
1786 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
1792 dyda[LMP_AMPL] = dyda[LMP_CENT] = dyda[LMP_BACK] = dyda[LMP_WID1] =
1793 dyda[LMP_WID2] = 0.0;
1808 t5 = pow(t4,width2);
1813 *y = amplitude*t6+background;
1819 dyda[LMP_AMPL] = t6;
1820 dyda[LMP_CENT] = t8*width2*t10/t2*t6;
1822 if (isnan(dyda[LMP_CENT]))
1823 dyda[LMP_CENT] = 0.0;
1825 dyda[LMP_BACK] = 1.0;
1826 dyda[LMP_WID1] = t8*width2*t3*t6;
1827 dyda[LMP_WID2] = -t8*t16*t6;
1829 if (isnan(dyda[LMP_WID2]))
1830 dyda[LMP_WID2] = 0.0;
1837 dyda[LMP_AMPL] *= mrqdydaweight(a[LMP_AMPL],r[k],r[k+1]);
1841 dyda[LMP_CENT] *= mrqdydaweight(a[LMP_CENT],r[k],r[k+1]);
1845 dyda[LMP_WID1] *= mrqdydaweight(a[LMP_WID1],r[k],r[k+1]);
1849 dyda[LMP_WID2] *= mrqdydaweight(a[LMP_WID2],r[k],r[k+1]);
1878 mrqlocywarp(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
1879 cxdouble dyda[], cxint na)
1882 const cxchar *fctid =
"mrqlocywarp";
1884 cxdouble xccd, nx, startx;
1885 register cxint i,ncoef;
1886 cxdouble Tx, Ty, cx, Ky, tt, xx;
1887 cpl_matrix *mBase = NULL, *mX = NULL;
1888 register cxdouble fxx = 0.0, f1xx = 0.0, f2xx = 0.0, z1;
1889 cxdouble *pd_x = NULL, *pd_mbase = NULL;
1893 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
1899 dyda[LMP_TX] = dyda[LMP_TY] = dyda[LMP_CX] = dyda[LMP_KY] =
1905 startx = x[LMI_STRX];
1906 ncoef = (cxint) x[LMI_NCOF];
1916 mX = cpl_matrix_new(1,1);
1917 pd_x = cpl_matrix_get_data(mX);
1920 mBase = giraffe_chebyshev_base1d(startx, nx, ncoef, mX);
1922 pd_mbase = cpl_matrix_get_data(mBase);
1924 for (i = 0; i < ncoef; i++)
1925 fxx += pd_mbase[i] * x[i+4];
1928 for (i = 0; i < (ncoef - 1); i++)
1929 f1xx += pd_mbase[i] * (i+1)*x[i+5];
1933 for (i = 0; i < (ncoef - 2); i++)
1934 f2xx += pd_mbase[i] * (i+2)*x[i+6];
1937 if (mX!=NULL) { cpl_matrix_delete(mX); mX = NULL; pd_x = NULL; }
1938 if (mBase!=NULL) { cpl_matrix_delete(mBase); mBase = NULL; pd_mbase = NULL; }
1940 z1 = 1.0 - tt*tt + tt*f1xx;
1941 *y = Ky*(fxx-tt*xx)/z1 + Ty;
1948 (cx*Ky/z1)*((tt-f1xx) + tt*f2xx*(fxx-tt*xx)/z1);
1953 (Ky*(xccd-Tx)/z1)*((f1xx-tt) - tt*f2xx*(fxx-tt*xx)/z1);
1955 dyda[LMP_KY] = (fxx-tt*xx)/z1;
1957 (Ky/(z1*z1))*(-xx*(1.+tt*tt)+2.*tt*fxx-fxx*f1xx);
1964 dyda[LMP_TX] *= mrqdydaweight(a[LMP_TX],r[k],r[k+1]);
1968 dyda[LMP_CX] *= mrqdydaweight(a[LMP_CX],r[k],r[k+1]);
1972 dyda[LMP_KY] *= mrqdydaweight(a[LMP_KY],r[k],r[k+1]);
1976 dyda[LMP_TT] *= mrqdydaweight(a[LMP_TT],r[k],r[k+1]);
2005 mrqxoptmodGS(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
2006 cxdouble dyda[], cxint na)
2009 const cxchar *fctid =
"mrqxoptmodGS";
2011 register cxdouble lambda,xfibre,yfibre,pixsize,nx;
2013 register cxdouble fcoll,cfact;
2015 register cxdouble gtheta,gorder,gspace;
2017 register cxdouble t1,t10,t109,t11,t110,t114,t12,t14,t17,t18,t2,t21,t23,t24;
2018 register cxdouble t25,t26,t27,t28,t29,t3,t30,t31,t35,t40,t43,t49,t5,t51,t52;
2019 register cxdouble t53,t59,t6,t66,t67,t69,t7,t71,t8,t82,t84,t9,t95,t98;
2023 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
2029 dyda[LMP_NX] = dyda[LMP_PXSIZ] = dyda[LMP_FCOLL] = dyda[LMP_CFACT] =
2030 dyda[LMP_THETA] = dyda[LMP_ORDER] = dyda[LMP_SPACE] = 0.0;
2033 lambda = x[LMI_WLEN];
2034 xfibre = x[LMI_XFIB];
2035 yfibre = x[LMI_YFIB];
2038 pixsize = a[LMP_PXSIZ];
2039 fcoll = a[LMP_FCOLL];
2040 cfact = a[LMP_CFACT];
2041 gtheta = a[LMP_THETA];
2042 gorder = a[LMP_ORDER];
2043 gspace = a[LMP_SPACE];
2057 t17 = -t2*t3+t12*t6+fcoll*t14*t12;
2060 t23 = sqrt(1.0-t8/t10-t21);
2069 t35 = pixsize*pixsize;
2072 t49 = -t6*t43*fcoll+t14*t12-t9*t14*t43;
2076 t59 = 2.0*t8/t53*fcoll-2.0*t17*t49;
2081 t82 = -xfibre*t14*t12+fcoll*t5*t12;
2084 t98 = t17*lambda*t3;
2085 t109 = gspace*gspace;
2091 *y = t1*t30*t31-0.5*nx;
2093 *y = -t1*t30*t31+0.5*nx;
2101 dyda[LMP_PXSIZ] = -t1*t30/t35;
2103 cfact*t25*t40+t1*(t49*t5+t52*t59/2.0)*t29*t31-
2104 t66*t69*(-t49*t14+t71*t59/2.0);
2108 t1*(t82*t5-t26+t27-t52*t84)*t29*t31-
2109 t66*t69*(-t82*t14-t18-t24-t71*t84);
2111 t1*(-t95*t5+t52*t98)*t29*t31-t66*t69*(t95*t14+t71*t98);
2113 t1*(t2*t110*t5-t52*t17*t114)*t29*t31-
2114 t66*t69*(-t2*t110*t14-t71*t17*t114);
2117 dyda[LMP_NX] = -dyda[LMP_NX];
2118 dyda[LMP_PXSIZ] = -dyda[LMP_PXSIZ];
2119 dyda[LMP_FCOLL] = -dyda[LMP_FCOLL];
2120 dyda[LMP_CFACT] = -dyda[LMP_CFACT];
2121 dyda[LMP_THETA] = -dyda[LMP_THETA];
2122 dyda[LMP_ORDER] = -dyda[LMP_ORDER];
2123 dyda[LMP_SPACE] = -dyda[LMP_SPACE];
2131 dyda[LMP_PXSIZ] *= mrqdydaweight(a[LMP_PXSIZ],r[k],r[k+1]);
2135 dyda[LMP_FCOLL] *= mrqdydaweight(a[LMP_FCOLL],r[k],r[k+1]);
2139 dyda[LMP_CFACT] *= mrqdydaweight(a[LMP_CFACT],r[k],r[k+1]);
2143 dyda[LMP_THETA] *= mrqdydaweight(a[LMP_THETA],r[k],r[k+1]);
2147 dyda[LMP_ORDER] *= mrqdydaweight(a[LMP_ORDER],r[k],r[k+1]);
2151 dyda[LMP_SPACE] *= mrqdydaweight(a[LMP_SPACE],r[k],r[k+1]);
2181 mrqtest(cxdouble x[], cxdouble a[], cxdouble r[], cxdouble *y,
2182 cxdouble dyda[], cxint na)
2185 const cxchar *fctid =
"mrqtest";
2194 cpl_error_set(fctid, CPL_ERROR_ILLEGAL_INPUT);
2199 *y = a1 * x[0] + b1;
struct definition to handle model functions