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File fitdocs.txt, 32.1 KB (added by pcr, 13 years ago)
documentation for model fitting procedures

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1
2	----- Documentation for Fit\average_parameters.pro -----
3	NAME:
4	AVERAGE_PARAMETERS
5
6	AUTHOR:
7	pierre.cruzalebes@oca.eu
8
9	PURPOSE:
10	average parameter vector estimates using weighted mean,
11	calculate errors from direct bootstrap (if enough parameter
12	vectors to average)
13
14	CATEGORY:
15	fitting
16
17	INPUTS:
18	need text input file (in OBS_PATH/INP/ directory) with:
19	- number of model parameter file(s) to average
20	- input model parameter file name(s)
21	- observation parameter file name(s) associated
22
23	REQUIREMENTS:
24	data read in input model parameter file(s) (in OBS_PATH/ subdirectory,
25	.out extension) must be in ASCII format and contain (in this order) :
26	- model flag, flux flag, synthetic exitance+radiance file names,
27	data format flag, starting parameters, free parameter flags,
28	goodness-of-fit parameter, input parameters, inferior errors,
29	superior errors, confidence level
30
31	data read in input observation parameter file(s) (in OBS_PATH/ subdirectory,
32	.obs extension, one row per observation) are of complex type :
33	- (DIT[s] , NDIT), (RA[deg] , DEC[deg]), (START_UTC[h] , END_UTC[h]),
34	(START_FWHM["] , END_FWHM), (START_TAU0[s] , START_TAU0[s]), (MJD@Oh , 0)
35
36	OUPUTS:
37	data written in output file (in OBS_PATH/OUT/ directory) must be in
38	ASCII format and contain (in this order) :
39	- model flag, flux flag, synthetic exitance+radiance file name,
40	data format flag, starting parameters, free parameter flags,
41	goodness-of-fit parameter, output parameters, inferior errors,
42	superior errors, nber of degrees of freedom
43
44	LOCAL PROCEDURE CALLED:
45	RESET_PLOT
46
47	LOCAL FUNCTION USED:
48	EXTRACT_PROHEADER
49	GET_OUTLIER_FENCES
50	TRI_STDEV
51	WAVG
52	WSTDEV
53	WSTERR
54
55	LOCAL SYSTEM VARIABLE USED:
56	EPSILON
57	FORMAT_OUT
58	MAX_REL_ERR
59	NB_BOOT_LOOPS
60	NB_DATA_BOOT
61	NB_MAX_PARAM
62	NB_OB_MAX
63	NB_TARG_MAX
64	OBS_PATH
65	PLOT_DEV
66	SPIDAST_PATH
67
68	REVISION HISTORY:
69	Written by pcr 2010/10/22
70	last modification by pcr 2010/12/12
71
72	----- Documentation for Fit\boot_fit.pro -----
73	NAME:
74	BOOT_FIT
75
76	AUTHOR:
77	pierre.cruzalebes@oca.eu
78
79	PURPOSE:
80	Proceed nonparametric residual bootstrap iterations (random shoot
81	of centered residuals with replacement) of gradient-expansion fits
82	calculate free-parameter confidence intervals.
83
84	CATEGORY:
85	fitting.
86
87	CALLING SEQUENCE:
88	DPAR = BOOT_FIT(XX,BSL,BWARR,MEAS,WGHT,PAR,PAR0,IDXF,NMODEL,VISI,
89	TEFF,REF,CLEVEL,NBOOT,PAROUT,DCHISQR,IDXC,PAR_ARR)
90
91	INPUTS:
92	XX = Row vector of synthetic wavelengths,
93	or structure with synthetic wavelength vector XX.WVL
94	and relative impact parameter vect. XX.RIP
95	BSL = Row vector of baselengths.
96	BWARR = 2-D ARRAY WITH # OF BASELENGTHS AND # OF WAVELENGTHS FOR EACH PART
97	(DEFINED BY P2VM SETTING).
98	BWARR(I,0) = # OF BASELENGTHS FOR PART I
99	BWARR(I,1) = # OF WAVELENGTHS FOR PART I
100	MEAS = Row vector of measurements, length(MEAS)=length(XX or XX.WVL)
101	*length(BSL).
102	WGHT = Row vector of experimental weight, same length as MEAS.
103	PAR = Row vector of parameter values.
104	PAR0 = Row vector of starting parameter values.
105	IDXF = Row vector of free parameter indexes, length lower or equal to PAR.
106	NMODEL = Nber of model used for fit.
107	VISI = Visibility flag ( 1:vis / 0:no vis ),
108	for bispectrum calculation VISI=table.
109	TEFF = Effective temperature used with MARCS flux or intensity tabulated data.
110	REF = Row vector of reference synthetic fluxes, same length as XX,
111	or 2-dim array of ref. synth. intensities, dim=(length(XX.WVL),
112	length(XX.RIP)).
113	CLEVEL = Desired confidence level.
114	NBOOT = number of bootstrap loops.
115
116	OUTPUTS:
117	CLEVEL = Final confidence level.
118	PAROUT = 2-dim array of final parameters, dim=(length(PAR),!NB_BOOT_LOOPS).
119	DCHISQR = Row vector of final chi-square differences sorted
120	by ascending order, length=!NB_BOOT_LOOPS.
121	IDXC = Row vector of success indexes (parameters in confidence region),
122	length lower or equal to !NB_BOOT_LOOPS.
123	PAR_ARR = 2-dim array of confid lev/nb of chi2 val in
124	68.3%/95.4%/99.7%/99.99%-CI,
125	and param(s) at lower/upper fences of each CI, dim=(length(PAR)+1,3)
126
127	FUNCTION RESULT:
128	DPAR = Row array of parameter inferior/superior error estimate(s),
129	dim=(length(PAR),2).
130
131	COMMON BLOCKS:
132	NONE.
133
134	SIDE EFFECTS:
135	NONE.
136
137	REQUIREMENTS:
138	The function to be fit must be defined and called in MODEL_DATA_FUNCT_PROJ.
139	For an example see FUNCT in the PV-WAVE User's Library.
140	Call to MODEL_DATA_FUNCT_PROJ is:
141	MODEL_DATA_FUNCT_PROJ,XX,BSL,BWARR,PAR,IDXF,NMODEL,VISI,TEFF,REF,
142	DEPTH_INTENS_DATA,DATA_FIT
143	where:
144	XX = row vector or structure of independant variables
145	(wavelength or wavelength + relative inpact parameter), input.
146	BSL = row vector of baselength, input.
147	BWARR = 2-D array, input
148	PAR = row vector of parameters, input.
149	IDXF = row vector unforzen-parameter indexes, input.
150	NMODEL = number of model used for calculation of function, input.
151	VISI = visibility flag or bispectrum index table, input.
152	TEFF = temperature, input.
153	REF = row vector of synthetic fluxes or 2-dim array of synthetic
154	intensities, input.
155	DEPTH_INTENS_DATA = 2-dim complex array with optical depth
156	and intensity
157	or flag (=1/0) for opt. depth based models, output.
158	DATA_FIT = row vector of projected function values at each projected
159	frequency (or proj. wavelength if base=0), output.
160	RESTRICTIONS:
161	NONE.
162
163	PROCEDURE:
164	SEE CODE.
165
166	LOCAL PROCEDURE CALLED:
167	LOCA_SCALE_CHI2
168	LOCA_SCALE_NORM
169	MODEL_DATA_FUNCT_PROJ
170
171	LOCAL FUNCTION USED:
172	GET_OUTLIER_FENCES
173	LM_FIT
174
175	LOCAL SYSTEM VARIABLE USED:
176	EPSILON
177	MAX_REL_ERR
178	NB_BASE_STEP
179	NB_BOOT_MIN
180	NB_DATA_BOOT
181	NB_DATA_MAX
182	NB_MAX_BOOTS
183	NB_DATA_MAX
184	NB_RES_STEP
185
186	REVISION HISTORY:
187	Written by pcr 2007/12/17
188	last modification by pcr 2011/01/04
189
190	----- Documentation for Fit\create_fitting_batch.pro -----
191	NAME:
192	CREATE_FITTING_BATCH
193
194	AUTHOR:
195	pierre.cruzalebes@oca.eu
196
197	PURPOSE:
198	create program batch for model fitting processing and make input files
199	used by programs :
200	- limb-darkened spectral radiance conversion
201	- model fitting
202	- model parameter averaging
203
204	CATEGORY:
205	fitting
206
207	INPUTS:
208	needs text input file (in OBS_PATH/INP/ directory) with :
209	- target name
210	- data format ('vis', 'spec', 'coh', 'bisp', 'trip' or 'clos')
211	- model number used for fitting
212	- starting parameters (for LM)
213	- parameter flags (0:frozen / 1:unfrozen)
214	- name of synthetic spectrum ('none' if not needed)
215	- min and max wavelengths of global spectral range covered
216	with all bandwidths in all parts [mum] (in same row)
217	- fit format ('ob', 'part', 'dir', 'run', or 'all' for fit of model
218	with individual OBs, with target files contained in each data
219	part, directory (=day) or run, or with all target files)
220	- allocation programme information file (used only if fit format = 'run')
221
222	REQUIREMENTS:
223	individual OB files and dir/run/global concatenated obs parameter
224	files (in SCIENCE/ sub-directory) must have been previously created by
225	concatenate_observations call(s)
226
227	data read in allocation programme file (in OBS_PATH/ directory) must be in ASCII format
228	and contain 2*nrun+1 rows with :
229	- total number of run(s) allocated for the observing programme and obs run name(s) (same row)
230	then for each run :
231	- nber of allocated night(s) in run and name(s) of obs data directory(ies) (1 dir per obs night)
232
233	OUTPUTS:
234	model fitting processing batch text file (in SPIDAST_PATH/ directory)
235	and needed text input files (in OBS_PATH/INP/ directory)
236
237	LOCAL PROCEDURE CALLED:
238	EXTRACT_PROHEADER
239
240	LOCAL FUNCTION USED:
241	NONE
242
243	LOCAL SYSTEM VARIABLE USED:
244	MAX_HEADER
245	NB_BAND_MAX
246	NB_PAIR_MAX
247	NB_OB_MAX
248	NB_PART_MAX
249	NB_TARG_MAX
250	NB_TRIPLE_MAX
251	OBS_PATH
252	SPEC_RES
253	SPIDAST_PATH
254
255	REVISION HISTORY:
256	Written by pcr 2010/11/03
257	last modification by pcr 2011/01/11
258
259	----- Documentation for Fit\fit_model.pro -----
260	NAME:
261	FIT_MODEL
262
263	AUTHOR:
264	pierre.cruzalebes@oca.eu
265
266	PURPOSE:
267	fit model parameter(s)on calibrated spectro-interferometric data
268	use bootstrap loops of non-linear least squares fit (gradient-expansion
269	algorithm) combining gradient search with analytical solution
270	developed from linearizing fitting function.
271
272	CATEGORY:
273	fitting
274
275	INPUTS:
276	need text input file (in OBS_PATH/INP/ directory) with:
277	- data format ('vis', 'spec', 'coh', 'bisp', 'trip' or 'clos')
278	- number of part(s) (one file per P2VM setting)
279	spec data :
280	- input calibrated spec file name(s) (1 name per row)
281	other data :
282	- baselength file name(s)
283	- input calibrated data file name(s) (1 name per row, same order
284	than in baselength files : NTEL*(NTEL-1)/2 baselines per OB)
285	then, for all data formats :
286	- model number used for fitting
287	- starting parameters (for LM)
288	- parameter flags (0:frozen / 1:unfrozen)
289	- synthetic exitance and radiance file names ('none' if not needed,
290	in same row)
291	- number of values per parameter, used for chi-square plots
292	- desired confidence level (between 0 and 1)
293	- number of bootstrap iterations (-1 for no fit)
294	- optionaly : final spectral resolution at mean wavelength
295
296	REQUIREMENTS:
297	type of data used for fitting must be:
298	'vis' for visibility data
299	'spec' for spectrum data
300	'coh' for coherent spectrum data
301	'bisp' for bispectrum data
302	'trip' for triple product data
303	'clos' for closure phase data
304
305	spec data:
306	data read/written in input/output calibrated/fitted spec file (in
307	subdirectory of OBS_DATA/) must be in ASCII format and contain
308	(1 row per spectral channel):
309	- wavelength and bandwidth [m], flux and error [W/m^2/mum]
310	for each data file
311
312	data read in input baseline file(s) (in subdirectory of OBS_PATH/)
313	must be in ASCII format and contain (2NBASE=NTEL(NTEL-1) columns, one
314	row per obs file):
315	- (length[m] , angle[deg]) of each projected baseline
316	at obs file start/end
317
318	vis data:
319	data read/written in input/output calibrated/fitted vis. file (in
320	subdirectory of OBS_PATH/) must be in ASCII format and contain (1 row per
321	spectral channel):
322	- wavelength and bandwidth [m], visibility and error for each data file
323
324	coh spec data:
325	data read/written in input/output calibrated/fitted coh. spec. file (in
326	subdirectory of OBS_PATH/) must be in ASCII format and contain (1 row per
327	spectral channel):
328	- wavelength and bandwidth [m], coherent flux and error [W/m^2/mum]
329	for each data file
330
331	bisp data:
332	data read/written in input/output calibrated/fitted bisp. file (in
333	subdirectory of OBS_PATH/) must be in ASCII format and contain (1 row per
334	spectral channel):
335	- wavelength and bandwidth [m], real part of bispectrum and error,
336	imaginary part of bispectrum and error [(W/m^2/mum)^3]
337	for each data file
338
339	trip data:
340	data read/written in input/output calibrated/fitted triple prod. file (in
341	subdirectory of OBS_PATH/) must be in ASCII format and contain (1 row per
342	spectral channel):
343	- wavelength and bandwidth [m], real part of triple product and error,
344	imaginary part of triple product and error for each data file
345
346	clos data:
347	data read/written in input/output calibrated/fitted clos. phase file (in
348	subdirectory of OBS_PATH) must be in ASCII format and contain (1 row per
349	spectral channel):
350	- wavelength and bandwidth [m], closure phase and error [deg]
351	for each data file
352
353	flag for model are defined in model_spectrum.pro as well as order of starting
354	parameters
355
356	data read in input synthetic exitance file (of name exitance_file_stem.spec,
357	in SYNTHE_PATH/ directory) must be in ASCII format and contain:
358	- wavelength [AA = 10^-4 mum] and exitance [erg/cm^2/s/AA =
359	10*W/m^2/mum)
360
361	if input synthetic radiance available (in SYNTHE_PATH/ directory)
362	use also radiance data composed of !NB_LUMIN+1 columns with:
363	- zero and relative impact parameters
364	(!NB_LUMIN values between 0. and 1., in first row)
365	- wavelength [mum] and !NB_LUMIN values of absolute radiance
366	[W/m^2/mum/sr] (one row per spectral channel)
367
368	OUTPUTS:
369	data written in output fit file (of name input_file_stem.out, in
370	OBS_PATH/OUT/ directory) must be in ASCII format and contain
371	(in this order):
372	- model flag, flux flag, synthetic exitance+radiance file names,
373	data format flag, starting parameters, free flags, final
374	goodness-of-fit parameter, fitted parameters, inferior errors,
375	superior errors, number of degrees of freedom
376
377	data written in covariance file (of name input_file_stem.cova, in
378	OBS_PATH/OUT/ directory) must be in ASCII format and contain
379	the covariance matrix (of size NB_MAX_PARAM*NB_MAX_PARAM)
380
381	data written in output first parameter file (of name input_file_stem.par,
382	in OBS_PATH/OUT/ directory) must be in ASCII format and contain (in this
383	order) :
384	- delta(chi-square) and free parameter vector(s) (1 row per vector)
385
386	data written in output second parameter file (of name input_file_stem.param,
387	in OBS_PATH/OUT/ directory) must be in ASCII format and contain
388	(in this order, one row per confid level) :
389	- confid lev/nb of chi2 val in confidence interval, and free param(s)
390	at lower/upper fences of each CI
391
392	LOCAL PROGRAM CALLED:
393	ENGELKE
394	GET_SYN_REF
395	LOCA_SCALE_NORM
396	MODEL_DATA_FUNCT
397	MODEL_DATA_FUNCT_PROJ
398	MODEL_SPECTRUM
399	PLANCK
400	PLOT_DISTRI
401	RESET_PLOT
402	UNIFORM_DISK
403
404	LOCAL FUNCTION USED:
405	BOOT_FIT
406	EXTRACT_PROHEADER
407	FUNCTPROJ
408	GET_OUTLIER_FENCES
409	LM_FIT
410	MAKE_TAB3
411	SYM
412	TRAP
413
414	LOCAL SYSTEM VARIABLE USED:
415	EPSILON
416	FORMAT_OUT
417	MAS2RADIAN
418	MAX_LONG
419	MAX_REL_ERR
420	NB_BASE_STEP
421	NB_BOOT_MIN
422	NB_DATA_MAX
423	NB_LAMBDA_MAX
424	NB_MAX_FITS
425	NB_MAX_PARAM
426	NB_OB_MAX
427	NB_PAIR_MAX
428	NB_RES_STEP
429	OBS_PATH
430	PARAM_REL_DIST
431	PLOT_DEV
432	SPEC_RES
433	SPIDAST_PATH
434	SYNTHE_PATH
435
436	REVISION HISTORY:
437	Written by pcr 2006/09/15
438	last modification by pcr 2011/01/22
439
440	----- Documentation for Fit\fit_sed.pro -----
441	NAME:
442	FIT_SED
443
444	AUTHOR:
445	pierre.cruzalebes@oca.eu
446
447	PURPOSE:
448	fit model parameter(s) on SED data
449	use bootstrap loops of non-linear least squares method (gradient-expansion
450	algorithm) combining gradient search with analytical solution
451	developed from linearizing fitting function
452
453	INPUTS:
454	need text input file with :
455	- input SED and broadband effective parameter file name ('none' if
456	not needed, in same row)
457	- flag for model to be used for fitting
458	- starting parameters (for LM)
459	- parameter flags (0:frozen / 1:unfrozen)
460	- synthetic exitance file name
461	- number of values per parameter, used for chi-squared plots
462	- desired confidence level (between 0. and 1.)
463	- number of bootstrap iterations (-1 for no fit)
464
465	REQUIREMENTS:
466	data read in SED file (in subdirectory of OBS_PATH/)
467	must be in ASCII format and contain (in this order) :
468	- wavelength and bandwidth [mum], measured flux and error [W/m^2/mum]
469
470	data read in broadband effective parameter file (in ALL_DATA_PATH/
471	directory) must be in ASCII format and contain (in this order) :
472	- effective wavelength and bandwidth [mum] in each band for the used
473	model
474
475	flag for model are defined in model_spectrum.pro
476	as well as start-parameter order
477
478	data read in input synthetic exitance file (of name exitance_file_stem.spec
479	in SYNTHE_PATH/ directory) must be in ASCII format and contain :
480	- wavelength [AA = 10^-4 mum] and exitance [erg/cm^2/s/AA =
481	10*W/m^2/mum]
482
483	OUTPUTS:
484	data written in output file (of name input_file_stem.out in OBS_PATH/OUT/
485	directory) must be in ASCII format and contain (in this order) :
486	- model flag , flux flag, synthetic exitance+radiance file names, data
487	format flag, starting parameters, free flags, final goodness-of-fit
488	parameter, fitted parameters, inferior errors, superior errors, number
489	of degrees of freedom
490
491	data written in covariance file (of name input_file_stem.cova in
492	OBS_PATH/OUT/ directory) must be in ASCII format and contain the covariance
493	matrix (of size NB_MAX_PARAM*NB_MAX_PARAM)
494
495	data written in first parameter file (of name input_file_stem.par in
496	OBS_PATH/OUT/ directory) must be in ASCII format and contain
497	(in this order) :
498	- delta(chi2) and free parameter vector(s) (1 row per vector)
499
500	data written in second parameter file (of name input_file_stem.param in
501	OBS_PATH/OUT/ directory) must be in ASCII format and contain (in this order,
502	one row per confid level) :
503	- confid lev/nb of chi2 val in confidence interval, and free param(s)
504	at lower/upper fences of each CI
505
506	LOCAL PROCEDURE_CALLED:
507	ENGELKE
508	GET_SYN_REF
509	LOCA_SCALE_NORM
510	MODEL_DATA_FUNCT_PROJ
511	MODEL_SPECTRUM
512	PLANCK
513	PLOT_DISTRI
514	RESET_PLOT
515
516	LOCAL FUNCTION USED:
517	BOOT_FIT
518	EXTRACT_PROHEADER
519	FUNCTPROJ
520	GET_OUTLIER_FENCES
521	LM_FIT
522	TRAP
523
524	LOCAL SYSTEM VARIABLE USED:
525	ALL_DATA_PATH
526	EPSILON
527	FORMAT_OUT
528	MARCS_RES
529	MAX_LONG
530	MAX_REL_ERR
531	NB_BOOT_MIN
532	NB_DATA_MAX
533	NB_MAX_FITS
534	NB_MAX_PARAM
535	NB_RES_STEP
536	OBS_PATH
537	PARAM_REL_DIST
538	PLOT_DEV
539	SPIDAST_PATH
540	SYNTHE_PATH
541
542	REVISION HISTORY:
543	Written by pcr 2007/02/01
544	last modification by pcr 2011/01/22
545
546	----- Documentation for Fit\ld_poly_fit.pro -----
547	NAME: LD_POLY_FIT
548
549	PURPOSE: Non-linear least squares fit to a function of an arbitrary number
550	of parameters. The function may be any non-linear function where
551	the partial derivatives are known or can be approximated.
552
553	CATEGORY:
554	fitting.
555
556	USAGE: yfit = LD_POLY_FIT(x, y, w, params [,sigmas])
557
558	INPUT:
559	x - A vector of independent variables
560	y - A vector of dependent variable, same length as x
561	w - A vector of weights, same length as x. For no weighting set
562	w(i) = 1., for instrumental weighting w(i) = 1./y(i), etc
563	params - On input, a vector containing the initial estimates of the
564	parameters. The length of params must equal the number of
565	parameters in the function that is trying to be fit to the
566	x,y data
567
568	OUTPUT:
569	params - A vector of the calculated parameters of the fitted
570	function
571	sigmas - (Optional) a vector of standard deviations of the
572	parameters
573
574	RETURNED
575	yfit - A vector of fitted dependent variable values
576
577	SIDE EFFECTS:
578	The function to be fit must be defined and called LD_POLY_FUNCT. The call
579	to LD_POLY_FUNCT is LD_POLY_FUNCT, x,p,f, pder where:
580	x - Input, a vector of independent variables
581	p - Input, a vector of function parameters
582	f - Output, a vector of values of the function, f(i)=ld_poly_funct(x(i))
583	pder - Optional output, an array of size length_of_x by
584	number_of_parameters containing the partial derivatives
585	of funct. pder(i,j) is the derivative of the function at
586	the ith point with respect to the jth parameter.
587
588	PROCEDURE:
589	Copied from "CURFIT", least squares fit to a non-linear function,
590	pages 237-239, Bevington, Data Reduction and Error Analysis for the
591	Physical Sciences.
592
593	"This method is the Gradient-expansion algorithm which combines the
594	best features of the gradient search with the method of linearizing
595	the fitting function."
596
597	Iterations are perform until the chi square changes by only 0.1% or
598	until 20 iterations have been performed. The initial guess of the
599	parameter values should be as close to the actual values as
600	possible or the solution may not converge.
601
602	LOCAL PROCEDURE CALLED:
603	NONE
604
605	LOCAL FUNCTION USED:
606	LD_POLY_FUNCT
607
608	LOCAL SYSTEM VARIABLE USED:
609	EPSILON
610
611	REVISION HISTORY:
612	Written by pcr 2008/04/23
613	last modification by pcr 2010/06/28
614
615	----- Documentation for Fit\ld_poly_funct.pro -----
616	NAME:
617	LD_POLY_FUNCT
618
619	AUTHOR:
620	pierre.cruzalebes@oca.eu
621
622	PURPOSE:
623	EVALUATE THE POLYNOMIAL LIMB-DARKENED LAW DERIVED FROM MANDUCA ET AL. (1997)
624	AND OPTIONALLY RETURN THE VALUE OF IT'S PARTIAL DERIVATIVES.
625	NORMALLY, THIS FUNCTION IS USED BY LD_POLY_FIT TO FIT THE
626	POLYNOMIAL LAW TO ACTUAL LIMB-DARKENED DATA.
627
628	CATEGORY:
629	FITTING.
630
631	CALLING SEQUENCE:
632	LD_POLY_FUNCT,X,A,F,PDER
633
634	INPUTS:
635	X = VALUES OF INDEPENDENT VARIABLE (= 1-MU).
636	A = PARAMETERS OF EQUATION DESCRIBED BELOW.
637
638	OUTPUTS:
639	F = VALUE OF FUNCTION AT EACH X(I).
640
641	OPTIONAL OUTPUT PARAMETERS:
642	PDER = (N_ELEMENTS(X),NDEGREE) ARRAY CONTAINING THE
643	PARTIAL DERIVATIVES. P(I,J) = DERIVATIVE
644	AT ITH POINT W/RESPECT TO JTH PARAMETER.
645
646	COMMON BLOCKS:
647	NONE.
648
649	SIDE EFFECTS:
650	NONE.
651
652	RESTRICTIONS:
653	NONE.
654
655	PROCEDURE:
656	F = 1-A(0)X-A(1)X^2-A(2)X^3-A(3)X^4+...
657
658	LOCAL PROCEDURE CALLED:
659	NONE
660
661	LOCAL FUNCTION USED:
662	NONE
663
664	LOCAL SYSTEM VARIABLE USED:
665	NONE
666
667	REVISION HISTORY:
668	Written by pcr 2008/04/23
669	last modification by pcr 2010/07/01
670
671	----- Documentation for Fit\lm_fit.pro -----
672	NAME:
673	LM_FIT
674
675	PURPOSE:
676	Non-linear least squares fit to a synthetic function of an
677	arbitrary number of parameters.
678	Function may be any non-linear function where
679	the partial derivatives are known or can be approximated.
680
681	CATEGORY:
682	Fitting
683
684	CALLING SEQUENCE:
685	YFIT = LM_FIT(SX,BL,BWA,VY,WG,PA,IDX,MNB,VIS,TEMP,SRF,COVAA)
686
687	INPUTS:
688	SX = Independent variables = Row vector of synthetic wavelengths,
689	or structure with wavelengths and impact parameters.
690	BL = Row vector of baselengths.
691	BWA= 2-D array with # of baselengths and # of wavelengths for each part
692	(defined by P2VM setting).
693	BWA(I,0) = # of baselengths for part I
694	BWA(I,1) = # of wavelengths for part I
695	VY = Row vector of dependent variables (can be complex).
696	WG = Row vector of weights (can be complex), same length as VY.
697	PA = Row vector containing the initial parameter estimates.
698	IDX = Row vector of unfrozen-parameter indexes.
699	MNB = Model nber.
700	VIS = Visibility flag (if null no vis, else vis),
701	for bispectrum calculation VIS = bispectrum index table .
702	TEMP = Effective temperature used with MARCS flux/intensity data.
703	SRF = Row vector (or matrix) of synthetic fluxes (or intensities).
704	PRINT_INFO = Flag for LM-info printing ( 0: no print / 1: print ).
705
706	OUTPUTS:
707	PA = Row vector of parameters containing fit.
708	IDX = Row vector of output unfrozen-parameter indexes.
709	PRINT_INFO = Flag for LM-info printing ( -1: fit failed ).
710	COVAA = Formal covariance matrix of the fit.
711
712
713	FUNCTION RESULT:
714	YFIT = Row vector of calculated values (same length as Y).
715
716	COMMON BLOCKS:
717	NONE.
718
719	SIDE EFFECTS:
720	The function to be fit must be defined and called in MODEL_DATA_FUNCT_PROJ.
721	For an example see FUNCT in the PV-WAVE User's Library.
722	Call to MODEL_DATA_FUNCT_PROJ is:
723	MODEL_DATA_FUNCT_PROJ,XX,BASE,BWA,PA,IDX,MNB,VIS,TEMP,R0,
724	DEPTH_INTENS_DATA,F_PROJ,PDER_PROJ
725	where:
726	XX = row vector or structure of independant variables
727	(wavelength or wavelength + relative inpact parameter), input.
728	BASE = row vector of baselength, input.
729	BWA = 2-D array, input
730	PA = row vector of parameters, input.
731	IDX = row vector unfrozen-parameter indexes, input.
732	MNB = model flag for calculation of function (and partial derivatives), input.
733	VIS = visibility flag or bispectrum index table, input.
734	TEMP = temperature, input.
735	R0 = row vector of synthetic fluxes or 2-D array of synthetic intensities, input.
736	DEPTH_INTENS_DATA = 2-dim complex array with optical depth and intensity
737	or flag (=1/0) for opt. depth based models, output.
738	F_PROJ = row vector of projected function values at each projected frequency
739	(or proj. wavelength if base=0), output.
740	PDER_PROJ = 2-dim array containing the projected partial derivatives, optional output.
741	PDER_PROJ(I,J) = projected derivative at Ith projected frequency (or wavelength)
742	w/respect to JTH parameter.
743	RESTRICTIONS:
744	NONE.
745
746	PROCEDURE:
747	Copied from "CURFIT", least squares fit to a non-linear
748	function, pages 237-239, Bevington, Data Reduction and Error
749	Analysis for the Physical Sciences.
750	Modified, to output covariance matrix and make final function
751	call, Amara Graps, August 1987
752
753	"This method is the Gradient-expansion algorithm which
754	combines the best features of the gradient search with
755	the method of linearizing the fitting function."
756
757	Iterations are performed until the chi square changes by
758	only TOL_CHI2 (in absolute or fractional) or until NITER iterations have been performed.
759
760	The initial guess of the parameter values should be
761	as close to the actual values as possible or the solution
762	may not converge.
763
764	LOCAL PROCEDURE CALLED:
765	MODEL_DATA_FUNCT_PROJ
766
767	LOCAL FUNCTION USED:
768	COMPLEX2REAL
769
770	LOCAL SYSTEM VARIABLE USED:
771	EPSILON
772	CHI2_LM_TOLE
773	DEL_FLAMBDA_LM
774	FLAMBDA_LM
775	MAX_REL_ERR
776	NB_LM_ITER
777
778	REVISION HISTORY:
779	Written by pcr 2006/10/24
780	last modification by pcr 2011/01/22
781
782	----- Documentation for Fit\polybootw.pro -----
783	NAME:
784	POLYBOOTW
785
786	AUTHOR:
787	pierre.cruzalebes@oca.eu
788
789	PURPOSE:
790	Proceed nonparametric residual bootstrap iterations (ramdom shoot of
791	residuals with replacement) of polynomial weighted fits
792	giving estimates of upper and lower coefficient errors.
793
794	CATEGORY:
795	fitting.
796
797	CALLING SEQUENCE:
798	DCOEFF = POLYBOOTW(X,Y,WEIGHT,DEG,CLEVEL,COEFF)
799
800	INPUTS:
801	X = Row vector of independent coordinates.
802	Y = Row vector of data, same length as X.
803	WEIGHT = Row vector of experimental weights, same length as Y
804	(e.g. proportional to (meas errors)^-2).
805	DEG = Degree of polynomial to be fitted to data.
806	CLEVEL = Desired confidence level (between 0 and 1).
807	COEFF = Row vector of polynomial coefficients, length=DEG+1.
808
809	OUTPUTS:
810	None.
811
812	FUNCTION RESULT:
813	DCOEFF = Row array of parameter inferior/superior error estimate(s),
814	dim=(DEG+1,2).
815
816	COMMON BLOCKS:
817	NONE.
818
819	SIDE EFFECTS:
820	NONE.
821
822	RESTRICTIONS:
823	NONE.
824
825	PROCEDURE:
826	SEE CODE.
827
828	LOCAL PROCEDURE CALLED:
829	LOCA_SCALE_CHI2
830
831	LOCAL FUNCTION USED:
832	GET_OUTLIER_FENCES
833
834	LOCAL SYSTEM VARIABLE USED:
835	NB_BOOT_LOOPS
836	NB_DATA_BOOT
837	NB_MAX_BOOTS
838
839	REVISION HISTORY:
840	written by pcr 2008/06/05
841	last modification by pcr 2010/12/12
842
843	----- Documentation for Fit\poly_boot.pro -----
844	NAME:
845	POLY_BOOT
846
847	AUTHOR:
848	pierre.cruzalebes@oca.eu
849
850	PURPOSE:
851	Proceed nonparametric residual bootstrap iterations (ramdom shoot of
852	residuals with replacement) of polynomial fits
853	giving estimates of upper and lower coefficient errors.
854
855	CATEGORY:
856	fitting.
857
858	CALLING SEQUENCE:
859	DCOEFF = POLY_BOOT(X,Y,DEG,CLEVEL,COEFF)
860
861	INPUTS:
862	X = Row vector of independent coordinates.
863	Y = Row vector of data, same length as X.
864	DEG = Degree of polynomial to be fitted to data.
865	CLEVEL = Desired confidence level (between 0 and 1).
866	COEFF = Row vector of polynomial coefficients, length=DEG+1.
867
868	OUTPUTS:
869	None.
870
871	FUNCTION RESULT:
872	DCOEFF = Row array of parameter inferior/superior error estimate(s),
873	dim=(DEG+1,2).
874
875	COMMON BLOCKS:
876	NONE.
877
878	SIDE EFFECTS:
879	NONE.
880
881	RESTRICTIONS:
882	NONE.
883
884	PROCEDURE:
885	SEE CODE.
886
887	LOCAL PROCEDURE CALLED:
888	LOCA_SCALE_CHI2
889
890	LOCAL FUNCTION USED:
891	GET_OUTLIER_FENCES
892
893	LOCAL SYSTEM VARIABLE USED:
894	NB_BOOT_LOOPS
895	NB_DATA_BOOT
896	NB_MAX_BOOTS
897
898	REVISION HISTORY:
899	Written by pcr 2008/06/04
900	last modification by pcr 2010/12/12
901
902	----- Documentation for Fit\test_model.pro -----
903	NAME:
904	TEST_MODEL
905
906	AUTHOR:
907	pierre.cruzalebes@oca.eu
908
909	PURPOSE:
910	test model and partial derivatives vs parameters
911	and also test Levenberg-Marquardt (LM) algorithm
912
913	CATEGORY:
914	fitting
915
916	INPUTS:
917	need text input file (in OBS_PATH/INP/ directory) with:
918	- number of baselength file(s) (one file per P2VM setting,
919	null if not needed, e.g. for flux or sed fit)
920	- baselength file name(s) (if needed)
921	- nber of wavelength bands
922	for each baselength file:
923	- name(s) of wavelength list(s) (1 row per spectral band)
924	then:
925	- data format
926	- model number used for fitting
927	- number of values per parameter, band number, pair number
928	(used for derivative test)
929	- parameter value(s) (= starting parameters used for fit)
930	- parameter flags (0:frozen / 1:unfrozen) (used for fit)
931	- synthetic exitance and radiance file names ('none' if not needed,
932	in same row)
933	- parameter relative error used for fit (null if no fit)
934
935	REQUIREMENTS:
936	data read in input baseline file(s) (in subdirectory of OBS_PATH/)
937	must be in ASCII format and contain (2NBASE=NTEL(NTEL-1) columns, one
938	row per obs file) :
939	- (length[m] , angle[deg]) of each projected baseline at obs file start/end
940
941	data read in wavelength list(s) (in subdirectory of OBS_PATH/)
942	must be in ASCII format and contain (one row per spectral channel,
943	decreasing order of wavelength):
944	- wavelength and bandwith [m]
945
946	data format must be:
947	'vis' for visibility data
948	'spec' for spectrum data
949	'coh' for coherent spectrum data
950	'bisp' for bispectrum data
951	'sed' for sed data
952
953	model number is defined in model_spectrum.pro
954	as well as order of starting parameters
955
956	data read in input synthetic exitance file (.spec, 4 first
957	characters=temperature, in SYNTHE_PATH/ directory)
958	must be in ASCII format and contain 2 columns of data:
959	- wavelength (in AA = 10^-4 mu) and spectral exitance (in
960	erg.cm^-2.s^-1.AA^-1 = 10*W.m^-2.mu^-1)
961
962	if input synthetic radiance available (in SYNTHE_PATH/ directory)
963	use also radiance data composed of !NB_LUMIN+1 columns with:
964	- zero and relative impact parameters (!NB_LUMIN values between 0.
965	and 1., in first row)
966	- wavelength [mum] and !NB_LUMIN values of absolute radiance
967	[W/m^2/mum/sr] (one row per spectral channel)
968
969	also use relative impact parameter list of name RIP_LIST_NAME composed of:
970	- 1 column of NB_LUMIN values (between 0. and 1.)
971
972	OUTPUTS:
973	data written in test data file(s) (in the same subdirectory of OBS_PATH/,
974	one file per baseline/triplet) must be in ASCII format and contain
975	(in this order, one row per wavelength):
976	for visibility data (.vis):
977	- wavelength and bandwidth (in m), visibility and error
978	for flux data (.spec):
979	- wavelength and bandwidth (in m), flux and error (in W.m^-2.mu^-1)
980	for coherent flux data (.coh):
981	- wavelength and bandwidth (in m), coherent flux and error
982	(in W.m^-2.mu^-1),
983	for bispectral data (.bisp):
984	- wavelength and bandwidth (in m), bispectrum real part and error,
985	bispectrum imaginary part and error (all in W^3.m^6.mu^-3)
986	for sed data (.sed):
987	- wavelength and bandwidth (in m), flux and error (in W.m^-2.mu^-1)
988
989	LOCAL PROCEDURE CALLED:
990	ENGELKE
991	GET_SYN_REF
992	MODEL_DATA_FUNCT_PROJ
993	MODEL_SPECTRUM
994	PLANCK
995	RESET_PLOT
996
997	LOCAL FUNCTION USED:
998	COSD
999	EXTRACT_PROHEADER
1000	FUNCTPROJ
1001	LM_FIT
1002	MAKE_TAB3
1003	SIND
1004	TRAP
1005
1006	LOCAL SYSTEM VARIABLE USED:
1007	EPSILON
1008	MARCS_RES
1009	MAS2RADIAN
1010	NB_BASE_STEP
1011	NB_DATA_MAX
1012	NB_LAMBDA_MAX
1013	NB_MAX_PARAM
1014	NB_OB_MAX
1015	NB_PAIR_MAX
1016	NB_RES_STEP
1017	OBS_PATH
1018	PLOT_DEV
1019	SPIDAST_PATH
1020	SYNTHE_PATH
1021
1022	REVISION HISTORY:
1023	Written by pcr 2006/09/22
1024	last modification by pcr 2011/01/13
1025

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