XGFIT s Curve Fitting Algorithm with GSL

Transcription

1 XGFIT s Curv Fitti Alorithm ith GSL Ovrvi XGFIT is a GTK+ aliatio that taks as iut a st o (, y) oits, rodus a li rah, ad rorms a aussia it o th data. XGFIT uss th GNU Sitii Lirary (GSL) to rorm th urv it. GSL may doloadd rly via RdHat at htt://sours.rdhat.om/sl. This doumt dsris th aussia quatio, th us o GSL to rorm th urv it, ad doumts th mathmatial ork do to dvlo th od. Curv Fitti Imlmtatio As mtiod aov, th urv itti is o imlmtd usi GSL. Th utio ar itti is ( ) +, hr,, ad rrst th as, ak, tr ad idth o, rstivly. Th atual task rormd y th urv itti alorithm is to id valus or th 4 aramtrs. Th thiqu usd to imlmt th it is th Lvr-Marquardt Mthod. I ordr to rorm th it, GSL rquirs that th rorammr suly thr rodurs:. A utio that ill alulat ad stor () or ah iv valu o.. A utio that ill alulat ad stor () or ah iv valu o. Not that aus ar dali ith a utio o 4 aramtrs, is a vtor utio ad () is th vtor drivativ o. 3. A utio that ill ivok () ad () ith th aroriat aramtrs. Produrs ad 3 ar rlativly asy to udrstad. Hovr, rodur ivolvs advad alulus ad is laid i dtail rstly. Fidi th drivativ o Th drivativ o a vtor v is alulatd y taki artial drivativs ith rst to ah omot i v. I our as, this ivolvs 4 artial drivativs, o ah or,,, ad. I hav data oits, ostrut a 4 matri ad ill ah ro ith th orrsodi artial drivativs o i. This 4 matri is th Jaoia matri o. Th artial drivativs ar rrstd as

2 ,,, ad. Th irst artial drivativ aov is rad th artial drivativ o ith rst to. Th rmaii thr artial drivativs ar rad i a similar ashio. Calulati a artial drivativ is ot muh dirt rom alulati a ormal drivativ. Eah aramtr, t th o i dirtiatd aaist, is tratd lik a ostat. Normal dirtiatio ruls th aly. Th artial drivativ o ith rst to is sho lo. Not that si trat as th oly varial aramtr, th omliatd sod trm alls o omltly. + Nt, s th artial drivativ o ith rst to. This alulatio is oly slihtly mor omliatd tha th rvious o. Baus it is ot rlatd to, th trm disaars omltly. Also, i lt r, ar lt ith r, hih dirtiats to r. + No this i to t a it mor omliatd. Fidi th drivativ ith rst to ivolvs usi th hai rul. Rall that th hai rul ivs us a ay o alulati th drivativ o a omosit utio, F, suh that Hr, lt ( ) '( ) '( ( ) ) ' ( ) F '( ) o. F, ()

3 hih a rok ito th omots ( ) ad (). Noti that () () ( ) F. No, alulat () ad () i ordr to aly th hai rul. For, may i dirtiati immdiatly. () d ' Bor dirtiati, hovr, lt s mak it look mor lik a olyomial. () ( ) + No, a s that ( ) ( ) ' + d. No that hav oth ad, a aly th hai rul. () ( ) ( ) ' ' '

4 At this oit, hav th drivativ o F. Nt, must rmmr to multily this drivativ y i ordr to id th artial drivativ o our oriial ith rst to. Thus, Calulati th artial drivativ o ith rst to is vry similar, ad atr a it o ork arriv at ( ) 3 Poulati th Jaoia Matri No that hav alulatd all our artial drivativs, ill al to oulat our 4 Jaoia matri. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) I th atual imlmtatio, divid ah lmt o th Jaoia matri y a sima i valu. Iitially, ah valu o sima is st to 0.. Usi FitGSL FitGSL is a utility ratd to rmov th omlity o GSL rom th rorammr. Th olloi aml dmostrats th us o FitGSL.

5 #ilud "itsl.h" #di N_DATA 5 it mai(it ar, har *arv[]) itsl_data *d; it i, r; loat [4]; d itsl_allo_data(n_data); or( i 0; i < N_DATA / ; i++ ) d->t[i]. i; d->t[i].y (loat)(i + ((rad() % 5) - )); } or( i N_DATA / ; i < N_DATA; i++ ) d->t[i]. i; d->t[i].y (loat)((n_data - i) + ((rad() % 5) - )); } r itsl_lm(d,, 0); itsl_r_data(d); rit("\"); rit(" %, ", [B_INDEX]); rit(" %, ", [P_INDEX]); rit(" %, ", [C_INDEX]); rit(" %\\", [W_INDEX]); } rtur EXIT_SUCCESS; First, alloat a ista o a itls_data strutur that ill hold N_DATA data oits. Nt, rod to oulat th strutur ith (, y) valus. Normally, ths valus ould om rom a il or som kid o maiul alulatio. Fially, ivok th it usi th itsl_lm() utio, ad outut th alulatd valus. Not: For a rr o th utios ad tys did y FitGSL, las s Adi A. Th outut rom th rdi roram should 0.588,.86546,.47790, I you ould lik to uild th saml aliatio, sur to lik ith th olloi las: -lsl -lsllas lm Also, sur that GSL is istalld o your systm ad that you hav a oy o th FitGSL modul.

6 A itrsti oit to ot is that th urv it i this as aild. Hovr, rui XGFIT ith th sam data shos that th alulatd valus do it th urv rlativly ll. S Fiur lo. Fiur : A usal it, v o ailur O ours, it s u to th usr to did hthr or ot to us th alulatd valus i th it ails.

7 Adi A: FitGSL Rr Data Tys itsl_oitd - A to-dimsioal oit o th Cartsia lai ith loatioit omots. tyd strut _itsl_oitd loat ; loat y; }itsl_oitd; itsl_data Stors th data that ill it y FitGSL. tyd strut _itsl_data it ; itsl_oitd *t; }itsl_data; S Also: itsl_allo_data(), itsl_r_data() Futios it itsl_lm(ost itsl_data *dat, loat *rsults, it vros); Fid,, ad asd o th data sulid i dat. Th rsults ar stord i rsults, hih is a 4-lmt array o loats. Us th maros B_INDEX, P_INDEX, C_INDEX, ad W_INDEX (did i itsl.h) to t at th idividual omots. Th vros la should st to 0 to surss vros status outut. itsl_data *itsl_allo_data(it ); Alloats a itsl_data strutur ith suiit stora or data oits. void itsl_r_data(itsl_data *dat); Frs a itsl_data strutur. loat itsl_(loat, loat, loat, loat, loat ); Ivok (), usi th siid valus or,,, ad. Usul or rahially omari th urv it to th iut data oits.