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File modeldocs.txt, 36.0 KB (added by pcr, 13 years ago)
documentation for model generation procedures

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1
2	----- Documentation for Model\abs_eff.pro -----
3	NAME:
4	ABS_EFF
5
6	AUTHOR:
7	pierre.cruzalebes@oca.eu
8
9	PURPOSE:
10	EVALUATE THE WAVELENGTH DISTRIBUTION OF THE ABSORPTION EFFICIENCY
11	(THIN DUSTY SHELL MODEL)
12	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
13
14	CATEGORY:
15	MODELLING.
16
17	CALLING SEQUENCE:
18	ABS_EFF,XX,A,F,PD_F
19
20	INPUTS:.
21	XX = VALUES OF INDEPENDENT VARIABLES
22	= WAVELENGTHS + IMPACT PARAMETER RELATIVE TO STELLAR DIAM (STRUCTURE).
23	A = PARAMETER.
24
25	OUTPUTS:
26	F = VALUE OF FUNCTION AT EACH WAVELENGTH.
27
28
29	OPTIONAL OUTPUT PARAMETERS:
30	PD_F = VECTOR CONTAINING THE PARTIAL DERIVATIVE. PD_F(I)
31	= DERIVATIVE AT ITH WAVELENGTH W/RESPECT TO A.
32
33	COMMON BLOCKS:
34	NONE.
35
36	SIDE EFFECTS:
37	NONE.
38
39	RESTRICTIONS:
40	NONE.
41
42	PROCEDURE:
43	F = X^(-A)
44	WITH: X = XX.WVL = WAVELENGTH
45	A = SPECTRAL INDEX
46	PD_F = -LN(X)*F ;PARTIAL DERIVATIVE W/RESPECT TO A
47
48	LOCAL PROCEDURE CALLED:
49	NONE
50
51	LOCAL FUNCTION USED:
52	NONE
53
54	LOCAL SYSTEM VARIABLE USED:
55	NONE
56
57	REVISION HISTORY:
58	Written by pcr 2008/01/08
59	last modification by pcr 2008/02/12
60
61	----- Documentation for Model\central_depth.pro -----
62	NAME:
63	CENTRAL_DEPTH
64
65	AUTHOR:
66	pierre.cruzalebes@oca.eu
67
68	PURPOSE:
69	EVALUATE OPTICAL DEPTH RADIAL DISTRIBUTION IN CENTRAL DIRECTION
70	(RADIATIVE-TRANSFER ANALYTICAL MODEL)
71	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
72
73	CATEGORY:
74	MODELLING.
75
76	CALLING SEQUENCE:
77	CENTRAL_DEPTH,XX,A,F,PD_F
78
79	INPUTS:.
80	XX = VALUES OF INDEPENDENT VARIABLES
81	= WAVELENGTHS + RELATIVE IMPACT PARAMETERS (STRUCTURE).
82	A = ROW VECTOR OF PARAMETERS.
83
84	OUTPUTS:
85	F = VALUE OF FUNCTION AT EACH WAVELENGTH AND SIGHT ANGLE.
86
87	OPTIONAL OUTPUT PARAMETERS:
88	PD_F = ARRAY CONTAINING PARTIAL DERIVATIVE.
89	PD_F(I,J,K) = DERIVATIVE AT ITH WAVELENGTH AND JTH SIGHT ANGLE
90	W/RESPECT TO KTH PARAMETER.
91
92	COMMON BLOCKS:
93	NONE.
94
95	SIDE EFFECTS:
96	NONE.
97
98	RESTRICTIONS:
99	NONE.
100
101	PROCEDURE:
102	F = NB_DENS(A1,A2,A4)ABS_EFF(A3)CENT_PATH(A0,A1,A2)/A5
103	WITH: NB_DENS = RELATIVE NUMBER DENSITY AT OUTER BOUNDARY = (A2/A1)^A4
104	ABS_EFF = WAVELENGTH DISTRIBUTION OF ABSORPTION EFFICIENCY = (1/X)^A3
105	CENT_PATH = ANGULAR OPTICAL PATH IN CENTRAL DIRECTION = A0*(SQRT((A2/A0)^2-R^2)-SQRT((A1/A0)^2-R^2))/2
106	X = XX.WVL = WAVELENGTH
107	R = XX.RIP = RELATIVE IMPACT PARAMETER
108	A0 = STELLAR DIAMETER
109	A1 = SHELL INNER DIAMETER
110	A2 = SHELL OUTER DIAMETER
111	A3 = SPECTRAL INDEX
112	A4 = POWER-LAW DENSITY INDEX
113	A5 = REFERENCE GEOMETRICAL PATH
114	PD_F_0 = F*PD_CENT_PATH_0/CENT_PATH ;PARTIAL DERIVATIVE W/RESPECT TO A0
115	PD_F_1 = F*(PD_NB_DENS_1/NB_DENS+PD_CENT_PATH_1/CENT_PATH) ;PARTIAL DERIVATIVE W/RESPECT TO A1
116	PD_F_2 = F*(PD_NB_DENS_2/NB_DENS+PD_CENT_PATH_2/CENT_PATH) ;PARTIAL DERIVATIVE W/RESPECT TO A2
117	PD_F_3 = F*PD_ABS_EFF_3/ABS_EFF ;PARTIAL DERIVATIVE W/RESPECT TO A3
118	PD_F_4 = F*PD_NB_DENS_4/NB_DENS ;PARTIAL DERIVATIVE W/RESPECT TO A4
119	PD_F_5 = -F/A5 ;PARTIAL DERIVATIVE W/RESPECT TO A5
120
121	LOCAL PROCEDURE CALLED:
122	ABS_EFF
123	CENT_PATH
124	NB_DENS
125
126	LOCAL FUNCTION USED:
127	NONE
128
129	LOCAL SYSTEM VARIABLE USED:
130	NONE
131
132	REVISION HISTORY:
133	Written by pcr 2008/01/08
134	last modification by pcr 2009/03/18
135
136	----- Documentation for Model\cent_path.pro -----
137	NAME:
138	CENT_PATH
139
140	AUTHOR:
141	pierre.cruzalebes@oca.eu
142
143	PURPOSE:
144	EVALUATE GEOMETRICAL-THICKNESS RADIAL DISTRIBUTION IN CENTRAL DIRECTION
145	(RADIATIVE-TRANSFER ANALYTICAL MODEL)
146	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
147
148	CATEGORY:
149	MODELLING.
150
151	CALLING SEQUENCE:
152	CENT_PATH,XX,A,F,PD_F
153
154	INPUTS:.
155	XX = VALUES OF INDEPENDENT VARIABLES
156	= WAVELENGTHS + RELATIVE IMPACT PARAMETERS (STRUCTURE).
157	A = ROW VECTOR OF PARAMETERS.
158
159	OUTPUTS:
160	F = VALUE OF THICKNESS AT EACH SIGHT ANGLE.
161
162
163	OPTIONAL OUTPUT PARAMETERS:
164	PD_F = ARRAY CONTAINING PARTIAL DERIVATIVE.
165	PD_F(I,J) = DERIVATIVE AT ITH SIGHT ANGLE W/RESPECT TO JTH PARAMETER.
166
167	COMMON BLOCKS:
168	NONE.
169
170	SIDE EFFECTS:
171	NONE.
172
173	RESTRICTIONS:
174	NONE.
175
176	PROCEDURE:
177	F = A0*(R2-R1)/2
178	WITH: R = XX.RIP = RELATIVE IMPACT PARAMETER
179	A0 = STELLAR DIAMETER
180	A1 = SHELL INNER DIAMETER
181	A2 = SHELL OUTER DIAMETER
182	AA1 = A1/A0
183	AA2 = A2/A0
184	R1 = SQRT(AA1^2-R^2)
185	R2 = SQRT(AA2^2-R^2)
186	PD_F_0 = (AA1^2/R1-AA2^2/R2+R2-R1)/2 ;PARTIAL DERIVATIVE W/RESPECT TO A0
187	PD_F_1 = -AA1/R1/2 ;PARTIAL DERIVATIVE W/RESPECT TO A1
188	PD_F_2 = AA2/R2/2 ;PARTIAL DERIVATIVE W/RESPECT TO A2
189
190	LOCAL PROCEDURE CALLED:
191	NONE
192
193	LOCAL FUNCTION USED:
194	NONE
195
196	LOCAL SYSTEM VARIABLE USED:
197	NONE
198
199	REVISION HISTORY:
200	Written by pcr 2008/01/08
201	last modification by pcr 2008/12/28
202
203	----- Documentation for Model\core_depth.pro -----
204	NAME:
205	CORE_DEPTH
206
207	AUTHOR:
208	pierre.cruzalebes@oca.eu
209
210	PURPOSE:
211	EVALUATE OPTICAL DEPTH RADIAL DISTRIBUTION IN CORE DIRECTION
212	(RADIATIVE-TRANSFER ANALYTICAL MODEL)
213	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
214
215	CATEGORY:
216	MODELLING.
217
218	CALLING SEQUENCE:
219	CORE_DEPTH,XX,A,F,PD_F
220
221	INPUTS:.
222	XX = VALUES OF INDEPENDENT VARIABLES
223	= WAVELENGTHS + IMPACT PARAMETER RELATIVE TO INNER DIAM (STRUCTURE).
224	A = ROW VECTOR OF PARAMETERS.
225
226	OUTPUTS:
227	F = VALUE OF FUNCTION AT EACH WAVELENGTH AND SIGHT ANGLE.
228
229
230	OPTIONAL OUTPUT PARAMETERS:
231	PD_F = ARRAY CONTAINING PARTIAL DERIVATIVE.
232	PD_F(I,J,K) = DERIVATIVE AT ITH WAVELENGTH AND JTH SIGHT ANGLE
233	W/RESPECT TO KTH PARAMETER.
234
235	COMMON BLOCKS:
236	NONE.
237
238	SIDE EFFECTS:
239	NONE.
240
241	RESTRICTIONS:
242	NONE.
243
244	PROCEDURE:
245	F = NB_DENS(A0,A1,A3)ABS_EFF(A2)CORE_PATH(A0,A1,A2)/A4
246	WITH: NB_DENS = RELATIVE NUMBER DENSITY AT OUTER BOUNDARY = (A1/A0)^A3
247	ABS_EFF = WAVELENGTH DISTRIBUTION OF ABSORPTION EFFICIENCY = X^(-A2)
248	CORE_PATH = ANGULAR OPTICAL PATH IN CORE DIRECTION = 2*(SQRT(A1^2-R^2)-SQRT(A0^2-R^2))
249	X = XX.WVL = WAVELENGTH
250	R = A0/2*XX.RIP = IMPACT PARAMETER
251	A0 = SHELL INNER DIAMETER
252	A1 = SHELL OUTER DIAMETER
253	A2 = SPECTRAL INDEX
254	A3 = POWER-LAW DENSITY INDEX
255	A4 = REFERENCE GEOMETRICAL DEPTH
256	PD_F_0 = F*(PD_NB_DENS_0/NB_DENS+PD_CENT_PATH_0/CENT_PATH) ;PARTIAL DERIVATIVE W/RESPECT TO A0
257	PD_F_1 = F*(PD_NB_DENS_1/NB_DENS+PD_CENT_PATH_1/CENT_PATH) ;PARTIAL DERIVATIVE W/RESPECT TO A1
258	PD_F_2 = F*PD_ABS_EFF_2/ABS_EFF ;PARTIAL DERIVATIVE W/RESPECT TO A2
259	PD_F_3 = F*PD_NB_DENS_3/NB_DENS ;PARTIAL DERIVATIVE W/RESPECT TO A3
260	PD_F_4 = -F/A4 ;PARTIAL DERIVATIVE W/RESPECT TO A4
261
262	LOCAL PROCEDURE CALLED:
263	ABS_EFF
264	CORE_PATH
265	NB_DENS
266
267	LOCAL FUNCTION USED:
268	NONE
269
270	LOCAL SYSTEM VARIABLE USED:
271	NONE
272
273	REVISION HISTORY:
274	Written by pcr 2008/01/10
275	last modification by pcr 2009/03/18
276
277	----- Documentation for Model\core_path.pro -----
278	NAME:
279	CORE_PATH
280
281	AUTHOR:
282	pierre.cruzalebes@oca.eu
283
284	PURPOSE:
285	EVALUATE GEOMETRICAL-THICKNESS RADIAL DISTRIBUTION IN CORE DIRECTION
286	(RADIATIVE-TRANSFER ANALYTICAL MODEL)
287	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
288
289	CATEGORY:
290	MODELLING.
291
292	CALLING SEQUENCE:
293	CORE_PATH,XX,A,F,PD_F
294
295	INPUTS:.
296	XX = VALUES OF INDEPENDENT VARIABLES
297	= WAVELENGTHS + IMPACT PARAMETER RELATIVE TO INNER DIAM (STRUCTURE).
298	A = ROW VECTOR OF PARAMETERS.
299
300	OUTPUTS:
301	F = VALUE OF THICKNESS AT EACH SIGHT ANGLE.
302
303	OPTIONAL OUTPUT PARAMETERS:
304	PD_F = ARRAY CONTAINING PARTIAL DERIVATIVE.
305	PD_F(I,J) = DERIVATIVE AT ITH SIGHT ANGLE W/RESPECT TO JTH PARAMETER.
306
307	COMMON BLOCKS:
308	NONE.
309
310	SIDE EFFECTS:
311	NONE.
312
313	RESTRICTIONS:
314	NONE.
315
316	PROCEDURE:
317	F = A0*(R1-R0)
318	WITH: R = XX.RIP = RELATIVE IMPACT PARAMETER
319	A0 = SHELL INNER DIAMETER
320	A1 = SHELL OUTER DIAMETER
321	AA = A1/A0
322	R0 = SQRT(1-R^2)
323	R1 = SQRT(AA^2-R^2)
324	PD_F_0 = R1-R0-AA^2/R1 ;PARTIAL DERIVATIVE W/RESPECT TO A0
325	PD_F_1 = AA/R1 ;PARTIAL DERIVATIVE W/RESPECT TO A1
326
327	LOCAL PROCEDURE CALLED:
328	NONE
329
330	LOCAL FUNCTION USED:
331	NONE
332
333	LOCAL SYSTEM VARIABLE USED:
334	NONE
335
336	REVISION HISTORY:
337	Written by pcr 2008/01/10
338	last modification by pcr 2008/12/28
339
340	----- Documentation for Model\delta_ring.pro -----
341	NAME:
342	DELTA_RING
343
344	AUTHOR:
345	pierre.cruzalebes@oca.eu
346
347	PURPOSE:
348	EVALUATE "DELTA RING" FUNCTION
349	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVE.
350
351	CATEGORY:
352	MODELLING.
353
354	CALLING SEQUENCE:
355	DELTA_RING,X,A,F,PD_F
356
357	INPUTS:.
358	X = VALUES OF INDEPENDENT VARIABLES (SPATIAL FREQUENCIES).
359	A = PARAMETER OF EQUATION DESCRIBED BELOW (RING DIAMETER IN MAS).
360
361	OUTPUTS:
362	F = VALUE OF FUNCTION AT EACH X(I).
363
364	OPTIONAL OUTPUT PARAMETERS:
365	PD_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
366	PD_F(I) = DERIVATIVE AT ITH POINT W/RESPECT TO A.
367
368	COMMON BLOCKS:
369	NONE.
370
371	SIDE EFFECTS:
372	NONE.
373
374	RESTRICTIONS:
375	NONE.
376
377	PROCEDURE:
378	F = AJ0(PIA*X)
379	PD_F = J0(PIAX)-(PIAX)J1(PIA*X)
380
381	LOCAL PROCEDURE CALLED:
382	NONE
383
384	LOCAL FUNCTION USED:
385	NONE
386
387	LOCAL SYSTEM VARIABLE USED:
388	MAS2RADIAN
389
390	REVISION HISTORY:
391	Written by pcr 2006/09/18
392	last modification by pcr 2008/01/23
393
394	----- Documentation for Model\engelke.pro -----
395	NAME:
396	ENGELKE
397
398	AUTHOR:
399	pierre.cruzalebes@oca.eu
400
401	PURPOSE:
402	EVALUATE "ENGELKE" (=MODIFIED PLANCK) SPECTRAL RADIANT EXITANCE
403	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVE
404	(ENGELKE, AJ 104, 1248 (1992)).
405
406	CATEGORY:
407	MODELLING.
408
409	CALLING SEQUENCE:
410	ENGELKE,X,A,F,PDER_F
411
412	INPUTS:.
413	X = ROW VALUES OF INDEPENDENT VARIABLES (WAVELENGTHS IN MU).
414	A = PARAMETER OF EQUATION DESCRIBED BELOW (TEMPERATURE IN KELVIN).
415
416	OUTPUTS:
417	F = ROW VALUES OF FUNCTION (in W.m^-2.mu^-1).
418
419
420	OPTIONAL OUTPUT PARAMETERS:
421	PDER_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
422	PD_F(I) = DERIVATIVE AT ITH POINT W/RESPECT TO A.
423
424	COMMON BLOCKS:
425	NONE.
426
427	SIDE EFFECTS:
428	NONE.
429
430	RESTRICTIONS:
431	NONE.
432
433	PROCEDURE:
434	F=PIC1/(X^5)/(EXP(C2/(XB))-1)
435	PDER_F=F(C2/(XB))/B/(1-EXP(-C2/(XB)))B/A(1-C5(C4/(XA))/(1+(C4/(XA))))
436	where B=(C3A(1+C4/(A*X))^C5
437
438	LOCAL PROCEDURE CALLED:
439	NONE
440
441	LOCAL FUNCTION USED:
442	NONE
443
444	LOCAL SYSTEM VARIABLE USED:
445	NONE
446
447	REVISION HISTORY:
448	Written by pcr 2007/01/03
449	last modification by pcr 2008/02/12
450
451	----- Documentation for Model\gaussian_disk.pro -----
452	NAME:
453	GAUSSIAN_DISK
454
455	AUTHOR:
456	pierre.cruzalebes@oca.eu
457
458	PURPOSE:
459	EVALUATE "GAUSSIAN_DISK" FUNCTION
460	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVE.
461
462	CATEGORY:
463	MODELLING.
464
465	CALLING SEQUENCE:
466	GAUSSIAN_DISK,X,A,F,PD_F
467
468	INPUTS:.
469	X = VALUES OF INDEPENDENT VARIABLES (SPATIAL FREQUENCIES).
470	A = PARAMETER OF EQUATION DESCRIBED BELOW (DISK FWHM IN MAS).
471
472	OUTPUTS:
473	F = VALUE OF FUNCTION AT EACH X(I).
474
475	OPTIONAL OUTPUT PARAMETERS:
476	PD_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
477	PD_F(I) = DERIVATIVE AT ITH POINT W/RESPECT TO A.
478
479	COMMON BLOCKS:
480	NONE.
481
482	SIDE EFFECTS:
483	NONE.
484
485	RESTRICTIONS:
486	NONE.
487
488	PROCEDURE:
489	F = (A^2)/4/LN(2)EXP(-((PIA*X)^2)/4/LN(2))
490	PD_F = F2/A(1-((PIAX)^2)/4/LN(2))
491
492	LOCAL PROCEDURE CALLED:
493	NONE
494
495	LOCAL FUNCTION USED:
496	GAUSSIAN
497
498	LOCAL SYSTEM VARIABLE USED:
499	MAS2RADIAN
500
501	REVISION HISTORY:
502	Written by pcr 2006/09/18
503	last modification by pcr 2009/01/28
504
505	----- Documentation for Model\inner_temp.pro -----
506	NAME:
507	INNER_TEMP
508
509	AUTHOR:
510	pierre.cruzalebes@oca.eu
511
512	PURPOSE:
513	EVALUATE DUST EFFECTIVE TEMPERATURE AT INNER BOUNDARY
514	(THIN DUSTY SHELL MODEL)
515	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
516
517	CATEGORY:
518	MODELLING.
519
520	CALLING SEQUENCE:
521	INNER_TEMP,A,F,PD_F
522
523	INPUTS:
524	A = ROW VECTOR OF PARAMETERS.
525
526	OUTPUTS:
527	F = VALUE OF FUNCTION.
528
529	OPTIONAL OUTPUT PARAMETERS:
530	PD_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
531	PD_F(K) = DERIVATIVE W/RESPECT TO KTH PARAMETER.
532
533	COMMON BLOCKS:
534	NONE.
535
536	SIDE EFFECTS:
537	NONE.
538
539	RESTRICTIONS:
540	NONE.
541
542	PROCEDURE:
543	F = A0*(1-MU)^(1/(A3+4))
544	WITH: A0 = STELLAR EFFECTIVE TEMPERATURE
545	A1 = STELLAR DIAMETER
546	A2 = SHELL INNER DIAMETER
547	A3 = SPECTRAL INDEX
548	MU = SQRT(1-(A1/A2)^2)
549	PD_F_0 = F/A0 ;PARTIAL DERIVATIVE W/RESPECT TO A0
550	PD_F_1 = F/(A3+4)*A1/A2^2/MU/(1-MU) ;PARTIAL DERIVATIVE W/RESPECT TO A1
551	PD_F_2 = -F/(A3+4)*A1^2/A2^3/MU/(1-MU) ;PARTIAL DERIVATIVE W/RESPECT TO A2
552	PD_F_3 = -F/(A3+4)^2*LN(1-MU) ;PARTIAL DERIVATIVE W/RESPECT TO A3
553
554	LOCAL PROCEDURE CALLED:
555	NONE
556
557	LOCAL FUNCTION USED:
558	NONE
559
560	LOCAL SYSTEM VARIABLE USED:
561	NONE
562
563	REVISION HISTORY:
564	Written by pcr 2008/01/10
565	last modficiation by pcr 2008/02/12
566
567	----- Documentation for Model\marcs_disk.pro -----
568	NAME:
569	MARCS_DISK
570
571	AUTHOR:
572	pierre.cruzalebes@oca.eu
573
574	PURPOSE:
575	EVALUATE TRAPEZOIDAL TRANSFER FUNCTION OF MARCS INTENSITY
576	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVE.
577
578	CATEGORY:
579	MODELLING.
580
581	CALLING SEQUENCE:
582	MARCS_DISK,XX,A,FORI,F,PD_F
583
584	INPUTS:.
585	XX = ROW VECTOR OF SPATIAL FREQUENCIES (FOR A GIVEN BASELINE)
586	OR FREQUENCIES + RELATIVE IMPACT PARAMETERS (STRUCTURE).
587	A = PARAMETER VECTOR (WITH 1 ELEMENT = STELLAR DISK).
588	FORI = FLUX OR INTENSITY VALUES (SAME DIMENSION AS XX).
589
590	OUTPUTS:
591	FF = VALUE OF FUNCTION AT EACH FREQUENCY.
592
593	OPTIONAL OUTPUT PARAMETERS:
594	PD_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
595	PD_FF(I,K) = DERIVATIVE AT ITH SPATIAL FREQUENCY
596	W/RESPECT TO STELLAR DIAMETER.
597
598	COMMON BLOCKS:
599	NONE.
600
601	SIDE EFFECTS:
602	NONE.
603
604	RESTRICTIONS:
605	NONE.
606
607	PROCEDURE:
608	IF FORI=INTENSITY (AND FREQ=XX.WVL AND RIP=XX.RIP):
609	FF = TRAPEZ_HANKEL(FREQ,A,RIP,FORI)
610	PD_F = PD_TRAPEZ_HANKEL(FREQ,A,RIP,FORI)
611	IF FORI=FLUX (AND FREQ=XX):
612	FF = FORI*UNIFORM_DISK(FREQ,A)
613	PD_F = FORI*PD_UNIFORM_DISK(FREQ,A)
614
615	LOCAL PROCEDURE CALLED:
616	TRAPEZ_HANKEL
617	UNIFORM_DISK
618
619	LOCAL FUNCTION USED:
620	NONE
621
622	LOCAL SYSTEM VARIABLE USED:
623	NONE
624
625	REVISION HISTORY:
626	Written by pcr 2007/12/03
627	last modification by pcr 2008/01/23
628
629	----- Documentation for Model\model_data_funct.pro -----
630	NAME:
631	MODEL_DATA_FUNCT
632
633	AUTHOR:
634	pierre.cruzalebes@oca.eu
635
636	PURPOSE:
637	EVALUATE ANALYTICAL MODEL DATA FUNCTION (FLUX/VISI/BISP)
638	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
639	NORMALLY, PROCEDURE USED BY LM_FIT TO FIT MODEL
640	ON INTERFEROMETRIC CALIBRATED DATA.
641
642	CATEGORY:
643	MODELLING.
644
645	CALLING SEQUENCE:
646	MODEL_DATA_FUNCT,X,B,BWARR,PAR,MODEL,VIS,TEFF,REF,DID,FCT,PDER
647
648	INPUTS:
649	X = ROW VECTOR OR STRUCTURE OF INDEPENDENT VARIABLES
650	(WAVELENGTH OR WAVELENGTH AND RELATIVE IMPACT PARAMETER).
651	B = ROW COMPLEX VECTOR OF BASELINES (LENGTH/ANGLE).
652	BWARR = 2-D ARRAY WITH # OF BASELENGTHS AND # OF WAVELENGTHS
653	FOR EACH PART (DEFINED BY P2VM SETTING).
654	BWARR(I,0) = # OF BASELENGTHS FOR PART I
655	BWARR(I,1) = # OF WAVELENGTHS FOR PART I
656	PAR = ROW VECTOR OF PARAMETERS OF EQUATION DESCRIBED BELOW.
657	IDXF = ROW VECTOR OF UNFREEZE-PARAMETER INDEXES.
658	MODEL = MODEL NUMBER FOR CALCULATION OF FCTION (AND PARTIAL DERIVATIVES).
659	VIS = FLAG FOR VISIBILITY AND PARTIAL DERIVATIVES CALCULATION (0:FLUX/1:VISI),
660	FOR BISPECTRUM/TRIPLE PRODUCT CALCULATION VIS=+/-TABLE.
661	TEFF = EFFECTIVE TEMPERATURE USED WITH MARCS TABULATED FLUX/INTENSITY.
662	REF = ROW VECTOR OF NB_LAMBDA REFERENCE FLUXES
663	OR MATRIX OF NB_LAMBDA*(NB_LUMIN+1) INTENSITIES AND ROSS2LD RATIOS.
664	OUTPUTS:
665	PAR = ROW VECTOR OF PARAMETERS.
666	DID = 2-DIM COMPLEX ARRAY WITH OPTICAL DEPTH AND INTENSITY
667	OR FLAG (=1/0) FOR OPT.DEPTH BASED MODELS.
668	FCT = ROW REAL(COMPLEX) VECTOR OF NB_FREQ=NB_LAMBDA*NB_BASE FCTION VALUES
669	(OF NB_BISP=NB_LAMBDA*NB_BASE^3 BISP VALUES)
670
671	OPTIONAL OUTPUT PARAMETERS:
672	PDER = 2-D REAL(COMPLEX) ARRAY CONTAINING THE
673	PARTIAL DERIVATIVES. PDER(I,J) = DERIVATIVE
674	AT ITH SPATIAL FREQUENCY (OR ITH FREQ. TRIPLET)
675	W/RESPECT TO JTH PARAMETER.
676
677	COMMON BLOCKS:
678	NONE.
679
680	SIDE EFFECTS:
681	NONE.
682
683	RESTRICTIONS:
684	NONE.
685
686	PROCEDURE:
687	X = WAVELENGTH VECTOR OR WAVELENGTH AND RELATIVE IMPACT PARAMETER STRUCTURE.
688	B = COMPLEX BASELINE VECTOR (LENGTH/ANGLE).
689	REF = REFERENCE FLUX VECTOR OR INTENSITY + DIAM RATIO ARRAY.
690	IF VIS=0:
691	FCT = ABS(SPEC).
692	PDER = SIGN(SPEC)*PDSPEC.
693	IF VIS=1:
694	FCT = ABS(SPEC/SPEC0).
695	PDER = SIGN(SPEC)(PDSPEC/SPEC0-SPEC/SPEC0PDSPEC0/SPEC0).
696	IF VIS=TAB:
697	FCT = SPEC1CONJ(SPEC2)SPEC3.
698	PDER = PDSPEC1CONJ(SPEC2)SPEC3+SPEC1CONJ(PDSPEC2)SPEC3
699	+SPEC1SPEC2PDSPEC3.
700	IF VIS=(-1)*TAB:
701	FCT = (SPEC1/SPEC0)CONJ(SPEC2/SPEC0)(SPEC3/SPEC0).
702	PDER = (PDSPEC1/SPEC0-SPEC1/SPEC0PDSPEC0/SPEC0)CONJ(SPEC2/SPEC0)*(SPEC3/SPEC0)
703	+ (SPEC1/SPEC0)CONJ(PDSPEC2/SPEC0-SPEC2/SPEC0PDSPEC0/SPEC0)*(SPEC3/SPEC0)
704	+ (SPEC1/SPEC0)CONJ(SPEC2/SPEC0)(PDSPEC3/SPEC0-SPEC3/SPEC0*PDSPEC0/SPEC0).
705	WHERE: SPEC,SPEC0,SPEC1,SPEC2,SPEC3,
706	AND PDSPEC,PDSPEC0,PDSPEC1,PDSPEC2,PDSPEC2,
707	GIVEN BY MODEL_SPECTRUM
708	AND INDEX OF TAB GIVEN BY MAKE_TAB3.
709
710	COMMENTS:
711	BASED ON FCT.PRO
712
713	LOCAL PROCEDURE CALLED:
714	MODEL_SPECTRUM
715
716	LOCAL FUNCTION USED:
717	NONE
718
719	LOCAL SYSTEM VARIABLES USED:
720	NB_BASE_STEP
721	NB_RAD_MAX
722
723	REVISION HISTORY:
724	Written by pcr 2006/09/25
725	last modification by pcr 2010/08/25
726
727	----- Documentation for Model\model_data_funct_proj.pro -----
728	NAME:
729	MODEL_DATA_FUNCT_PROJ
730
731	AUTHOR:
732	pierre.cruzalebes@oca.eu
733
734	PURPOSE:
735	EVALUATE ANALYTICAL MODEL PROJECTED DATA FUNCTION
736	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
737	NORMALLY, FUNCTION USED BY LM_FIT TO FIT
738	MODEL ON INTERFEROMETRIC CALIBRATED DATA.
739
740	CATEGORY:
741	MODELLING.
742
743	CALLING SEQUENCE:
744	MODEL_DATA_FUNCT_PROJ,XX,BASE,BW_ARR,PARAM,INDEX_FREE,
745	MODEL_NUMBER,VISI_FLAG,TEMP,REF_DATA,DEPTH_INTENS_DATA,
746	PROJ_FUNCT,PROJ_PDER
747
748	INPUTS:
749	XX = ROW VECTOR OR STRUCTURE OF INDEPENDENT VARIABLES
750	(WAVELENGTH OR WAVELENGTH AND RELATIVE IMPACT PARAMETER).
751	BASE = ROW COMPLEX VECTOR OF BASELINES (LENGTH/ANGLE).
752	BW_ARR = 2-D ARRAY WITH # OF BASELENGTHS AND # OF WAVELENGTHS
753	FOR EACH PART (DEFINED BY P2VM SETTING).
754	BW_ARR(I,0) = # OF BASELENGTHS FOR PART I
755	BW_ARR(I,1) = # OF WAVELENGTHS FOR PART I
756	PARAM = ROW VECTOR OF PARAMETERS OF EQUATION DESCRIBED BELOW.
757	INDEX_FREE = ROW VECTOR OF FREE-PARAMETER INDEXES.
758	MODEL_NUMBER = NBER OF MODEL USED FOR CALCULATION OF FUNCTION
759	(AND PARTIAL DERIVATIVES).
760	VISI_FLAG = FLAG FOR VISIBILITY AND PARTIAL DERIVATIVES CALCULATION
761	(0:FLUX/1:VISI),
762	FOR BISPECTRUM/TRIPLE PRODUCT CALCULATION VISI_FLAG=+/-TAB3.
763	TEMP = EFFECTIVE TEMPERATURE USED WITH MARCS TABULATED FLUX/INTENSITY.
764	REF_DATA = ROW VECTOR OF LENGTH(XX) REFERENCE FLUXES
765	OR MATRIX OF LENGTH(XX.WVL)*(NB_LUMIN+1) REFERENCE INTENSITIES
766	AND ROSS2LD RATIO.
767
768	OUTPUTS:
769	PARAM = ROW VECTOR OF PARAMETERS.
770	DEPTH_INTENS_DATA = 2-DIM COMPLEX ARRAY WITH OPTICAL DEPTH AND INTENSITY
771	OR FLAG (=1/0) FOR OPT.DEPTH BASED MODELS.
772	PROJ_FUNCT = ROW VECTOR OF PROJECTED FUNCTION VALUES AT EACH
773	PROJECTED FREQUENCY (OR PROJECTED WAVELENGTH IF NULL BASE)
774
775	OPTIONAL OUTPUT PARAMETERS:
776	PROJ_PDER = 2-D ARRAY CONTAINING PROJECTED PARTIAL DERIVATIVES
777	PROJ_PDER(I,J) = PROJECTED DERIVATIVE AT ITH PROJECTED FREQUENCY/WAVELENGTH
778	W/RESPECT TO JTH PARAMETER.
779
780	COMMON BLOCKS:
781	NONE.
782
783	SIDE EFFECTS:
784	NONE.
785
786	RESTRICTIONS:
787	NONE.
788
789	PROCEDURE:
790	PROJ_FUNCT = FUNCTPROJ(FUNCT) OR BISP_PROJ(FUNCT)
791	PROJ_PDER = FUNCTPROJ(PDER) OR BISP_PROJ(PDER)
792	WHERE: FUNCT AND PDER ARE GIVEN BY MODEL_DATA_FUNCT
793
794	COMMENTS:
795	BASED ON FUNCT.PRO
796
797	LOCAL PROCEDURE CALLED:
798	MODEL_DATA_FUNCT
799
800	LOCAL FUNCTION USED:
801	FUNCTPROJ
802	BISP_PROJ
803
804	LOCAL SYSTEM VARIABLE USED:
805	EPSILON
806	NB_BASE_STEP
807	NB_DATA_MAX
808	NB_RES_STEP
809
810	MODIFICATION HISTORY:
811	Written by pcr 2007/11/30
812	last modification by pcr 2010/08/25
813
814	----- Documentation for Model\model_spectrum.pro -----
815	NAME:
816	MODEL_SPECTRUM
817
818	AUTHOR:
819	pierre.cruzalebes@oca.eu
820
821	PURPOSE:
822	PRINT PARAMETER SIGNIFICANCE AND VALUES, RETURN FLUX,
823	CREATE PARAMETER SETS FOR TEST MODEL, AND CALCULATE OPTICAL
824	DEPTH AND INTENSITY
825	OR
826	EVALUATE MODEL COMPLEX SPATIAL SPECTRUM FOR GIVEN COMPLEX BASELINE
827	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
828	PROCEDURE USED BY LM_FIT TO FIT MODEL TO INTERFEROMETRIC CALIBRATED DATA.
829
830	CATEGORY:
831	MODELLING.
832
833	CALLING SEQUENCE:
834	MODEL_SPECTRUM,A,MODEL,FLUX,ODEPTH,PRANGE,DIAM_INDEX,PTIT,
835	XX,BASE,EM,SPEC,PDER_SPEC
836
837	INPUTS:
838	A = ROW VECTOR OF MODEL PARAMETERS OF EQUATION DESCRIBED BELOW.
839	MODEL = USED-MODEL NUMBER.
840	XX = VALUES OF INDEPENDENT VARIABLES = WAVELENGTHS (VECTOR, IN MU)
841	OR WAVELENGTHS + RELATIVE IMPACT PARAMETERS (STRUCTURE).
842	BASE = COMPLEX BASELINE (LENGTH IN M / ANGLE IN DEG).
843	EM = SPECTRAL EXITANCE OR SPECTRAL RADIANCE.
844
845	OUTPUTS:
846	A = ROW VECTOR OF MODEL PARAMETERS.
847	FLUX = STELLAR FLUX FLAG (1 FOR BLACKBODY, 0 FOR ENGELKE, -1 FOR MARCS).
848	ODEPTH = 2-DIM COMPLEX ARRAY WITH OPTICAL DEPTH AND INTENSITY
849	OR FLAG (=1/0) FOR OPT.DEPTH BASED MODELS.
850	PRANGE = 2-DIM ARRAY OF PARAMETER MIN AND MAX VALUES (SIZE=2*LENGTH(A)),
851	USED WITH TEST_MODEL AND CREATE_DATA,
852	OR EFFECTIVE TEMPERATURE USED WITH MARCS FLUX/INTENSITY TABULATED DATA.
853	DIAM_INDEX = INDEX OF PARAMETER USED AS CENTRAL DIAMETER,
854	USED WITH TEST_MODEL, CREATE_DATA AND FIT_MODEL.
855	PSTRING = 2-DIM ARRAY OF PARAMETER NAME AND UNIT STRINGS (SIZE=2*LENGTH(A)),
856	FOR PLOT OF PARAMETER AXIS TITLE.
857	SPEC = COMPLEX VALUE OF SPATIAL SPECTRUM AT EACH SPATIAL FREQUENCY B/X
858	(X = WAVELENGTH VECTOR).
859
860	OPTIONAL OUTPUT PARAMETERS:
861	PDER_SPEC = (NLAMBDA,NPARAM) COMPLEX ARRAY CONTAINING PARTIAL DERIVATIVES.
862	SPEC_PDER(I,J) = DERIVATIVE AT ITH WAVELENGTH W/RESPECT TO JTH PARAMETER.
863
864	COMMON BLOCKS:
865	NONE.
866
867	SIDE EFFECTS:
868	NONE.
869
870	RESTRICTIONS:
871	NONE.
872
873	PROCEDURE:
874
875	CENTRAL_DEPTH = optical depth in the central direction (thin-shell model)
876	CORE_DEPTH = optical depth in the core direction (thin-shell model)
877	DELTA_RING(D) = delta ring Hankel transform of diameter D
878	GAUSSIAN_DISK(W) = gaussian disk Hankel transform of full width
879	at half maximum W
880	ENGELKE(T) = Engelke exitance (modified Planck) with temperature T
881	INNER_TEMP = dust effective temperature at the inner boundary (thin-shell model)
882	PLANCK(T) = blackbody exitance (Planck) with surface temperature T
883	SHELL_DEPTH = optical depth in the shell direction (thin-shell model)
884	TRAPEZ_HANKEL(I) = trapezoidal Hankel transform of intensity I
885	UNIFORM_DISK(D) = Hankel transform of uniform disk of diameter D
886
887	*****************************************
888	SINGLE COMPONENT 1-D MODELS (MODEL<100):
889	*****************************************
890
891	MODEL=1 (stellar disk with tabulated exitance/radiance)
892	if P0 = spectral radiance:
893	SPEC = TRAPEZ_HANKEL(A0,P0)
894	if P0 = spectral exitance:
895	SPEC = P0*UNIFORM_DISK(A0)
896	where A0 = disk diameter
897	MODEL=10 (single ud bb model)
898	SPEC = PLANCK(A0)*UNIFORM_DISK(A1)
899	where A0 = effective temperature
900	A1 = disk diameter
901	MODEL=11 (single gd bb)
902	SPEC = PLANCK(A0)*GAUSSIAN_DISK(A1)
903	where A0 = effective temperature
904	A1 = disk fwhm
905	MODEL=12 (single dr bb)
906	SPEC = PLANCK(A0)*DELTA_RING(A1)
907	where A0 = effective temperature
908	A1 = ring diameter
909	MODEL=13 (single ud Engelke model)
910	SPEC = ENGELKE(A0)*UNIFORM_DISK(A1)
911	where A0 = effective temperature
912	A1 = disk diameter
913	MODEL=20 (single ur bb)
914	SPEC = PLANCK(A0)*(UNIFORM_DISK(A2)-UNIFORM_DISK(A1))
915	where A0 = effective temperature
916	A1 = outer ring internal diameter
917	A2 = outer ring external diameter
918	MODEL=21 (single ud bb model, increas pow law of diam vs lambda)
919	SPEC = PLANCK(A0)UNIFORM_DISK(A1X^A2)
920	where A0 = effective temperature
921	A1 = disk diameter @ 1 mu
922	A2 = spectral index
923	MODEL=51 (radiative-transfer analytical model, central direction)
924	TRM = EXP(-CENTRAL_DEPTH(A)) = central transmittance
925	if P0 = spectral radiance:
926	SPEC = TRAPEZ_HANKEL(P0*TRM)
927	if P0 = spectral exitance:
928	SPEC = P0*TRAPEZ_HANKEL(TRM)
929	where A0 = central source diameter
930	A1 = shell inner diameter
931	A2 = shell outer diameter
932	A3 = spectral index
933	A4 = grain density index
934	A5 = reference geometrical thickness
935	MODEL=52 (radiative-transfer analytical model, core direction)
936	TRM = 1-EXP(-CORE_DEPTH(B)) = core transmittance
937	SPEC = PLANCK(A0)*TRAPEZ_HANKEL(TRM)
938	where A0 = dust temperature
939	A1 = B0 = shell inner diameter
940	A2 = B1 = shell outer diameter
941	A3 = B2 = spectral index
942	A4 = B3 = grain density index
943	A5 = B4 = reference geometrical thickness
944	MODEL=53 (radiative-transfer analytical model, shell direction)
945	TRM = 1-EXP(-SHELL_DEPTH(B)) = shell transmittance
946	SPEC = PLANCK(A0)*TRAPEZ_HANKEL(TRM)
947	where A0 = dust temperature
948	A1 = B0 = shell inner diameter
949	A2 = B1 = shell outer diameter
950	A3 = B2 = spectral index
951	A4 = B3 = grain density index
952	A5 = B4 = reference geometrical thickness
953	MODEL=54 (radiative-transfer analytical model, core+shell directions)
954	TRM1 = 1-EXP(-CORE_DEPTH(B)) = core transmittance
955	TRM2 = 1-EXP(-SHELL_DEPTH_1(B)) = shell transmittance, inner direction (until inner diam A1)
956	TRM3 = 1-EXP(-SHELL_DEPTH_2(B)) = shell transmittance, outer direction (until outer diam A2)
957	SPEC = PLANCK(A0)*(TRAPEZ_HANKEL(TRM2)-TRAPEZ_HANKEL(TRM1)+TRAPEZ_HANKEL(TRM3))
958	where A0 = dust temperature
959	A1 = B0 = shell inner diameter
960	A2 = B1 = shell outer diameter
961	A3 = B2 = spectral index
962	A4 = B3 = grain density index
963	A5 = B4 = reference geometrical thickness
964
965
966	*********************************
967	COMPOSITE 1-D MODELS (MODEL>99):
968	*********************************
969
970	MODEL=130 (stellar disk with tabulated exitance/radiance + 1 ud bb)
971	if P0 = spectral radiance:
972	SPEC = TRAPEZ_HANKEL(A0,P0)EXP(-A3)+PLANCK(A1)UNIFORM_DISK(A2)*(1-EXP(-A3))
973	if P0 = spectral exitance:
974	SPEC = P0UNIFORM_DISK(A0)EXP(-A3)+PLANCK(A1)UNIFORM_DISK(A2)(1-EXP(-A3))
975	where A0 = disk diameter
976	A1 = outer effective temperature
977	A2 = outer diameter
978	A3 = global optical depth
979	MODEL=140 (2 ud bbs)
980	SPEC = PLANCK(A0)UNIFORM_DISK(A1)EXP(-A4)+PLANCK(A2)UNIFORM_DISK(A3)(1-EXP(-A4))
981	where A0 = inner effective temperature
982	A1 = inner diameter
983	A2 = outer effective temperature
984	A3 = outer diameter
985	A4 = global optical depth
986	MODEL=141 (1 ud bb + 1 gd bb)
987	SPEC = PLANCK(A0)UNIFORM_DISK(A1)EXP(-A4))+PLANCK(A2)GAUSSIAN_DISK(A3)(1-EXP(-A4))
988	where A0 = inner effective temperature
989	A1 = inner diameter
990	A2 = outer effective temperature
991	A3 = outer fwhm
992	A4 = global optical depth
993	MODEL=142 (stellar disk with tabulated exitance/radiance + 1 ud bb, decreas pow law of opt depth vs lambda)
994	if P0 = spectral radiance:
995	SPEC = TRAPEZ_HANKEL(A0,P0)EXP(-(A3X^(-A4)))+PLANCK(A1)UNIFORM_DISK(A2)(1-EXP(-(A3*X^(-A4))))
996	if P0 = spectral exitance:
997	SPEC = P0UNIFORM_DISK(A0)EXP(-(A3X^(-A4)))+PLANCK(A1)UNIFORM_DISK(A2)(1-EXP(-(A3X^(-A4))))
998	where A0 = disk diameter
999	A1 = outer effective temperature
1000	A2 = outer diameter
1001	A3 = global optical depth @ 1 mum
1002	A4 = spectral index
1003	MODEL=150 (1 ud bb + 1 ur bb)
1004	SPEC = PLANCK(A0)UNIFORM_DISK(A1)EXP(-A5)+PLANCK(A2)(UNIFORM_DISK(A4)-UNIFORM_DISK(A3))(1-EXP(-A5))
1005	where A0 = inner effective temperature
1006	A1 = inner disk diameter
1007	A2 = outer effective temperature
1008	A3 = outer ring internal diameter
1009	A4 = outer ring external diameter
1010	A5 = global optical depth
1011	MODEL=151 (2 ud bbs, decreas pow law of opt depth vs lambda)
1012	SPEC = PLANCK(A0)UNIFORM_DISK(A1)EXP(-(A4X^(-A5)))+PLANCK(A2)UNIFORM_DISK(A3)(1-EXP(-(A4X^(-A5))))
1013	where A0 = inner effective temperature
1014	A1 = inner diameter
1015	A2 = outer effective temperature
1016	A3 = outer diameter
1017	A4 = global optical depth @ 1 mum
1018	A5 = spectral index
1019	MODEL=152 (MARCS disk + dust thin shell = radiative-transfer full analytical model)
1020	T1 = INNER_TEMP(AA)
1021	TRM0 = EXP(-CENTRAL_DEPTH(A)) = central transmittance
1022	TRM1 = 1-EXP(-CORE_DEPTH_0(B)) = core transmittance, central direction (until stellar diam A0)
1023	TRM2 = 1-EXP(-CORE_DEPTH_1(B)) = core transmittance, inner direction (until inner diam A1)
1024	TRM3 = 1-EXP(-SHELL_DEPTH_1(B)) = shell transmittance, inner direction (until inner diam A1)
1025	TRM4 = 1-EXP(-SHELL_DEPTH_2(B)) = shell transmittance, outer direction (until outer diam A2)
1026	if P0 = spectral radiance:
1027	SPEC0 = TRAPEZ_HANKEL(P0*TRM0)
1028	if P0 = spectral exitance:
1029	SPEC0 = P0*TRAPEZ_HANKEL(TRM0)
1030	SPEC1 = TRAPEZ_HANKEL(TRM1)
1031	SPEC2 = TRAPEZ_HANKEL(TRM2)
1032	SPEC3 = TRAPEZ_HANKEL(TRM3)
1033	SPEC4 = TRAPEZ_HANKEL(TRM4)
1034	SPEC = SPEC0+PLANCK(T1)*(SPEC2-SPEC1+SPEC4-SPEC3)
1035	where T0 = AA0 = central source temperature (fixed, not a model parameter)
1036	A0 = AA1 = central source diameter
1037	A1 = AA2 = B0 = shell inner diameter
1038	A2 = B1 = shell outer diameter
1039	A3 = AA3 = B2 = spectral index
1040	A4 = B3 = grain density index
1041	A5 = B4 = reference geometrical thickness
1042
1043	LOCAL PROCEDURE CALLED:
1044	CENTRAL_DEPTH
1045	CORE_DEPTH
1046	DELTA_RING
1047	ENGELKE
1048	GAUSSIAN_DISK
1049	INNER_TEMP
1050	MARCS_DISK
1051	PLANCK
1052	SHELL_DEPTH
1053	UNIFORM_DISK
1054	LOCAL FUNCTION USED:
1055	COSD
1056	SIND
1057	LOCAL SYSTEM VARIABLE USED:
1058	EPSILON
1059	MAS2RADIAN
1060	NB_CORE
1061	NB_MAX_PARAM
1062	NB_RES_STEP
1063	NB_SHELL
1064	NB_STAR
1065	OBS_PATH
1066	PARAM_REL_DIST
1067
1068	REVISION HISTORY:
1069	Written by pcr 2006/09/16
1070	last modification by pcr 2011/01/18
1071
1072	----- Documentation for Model\nb_dens.pro -----
1073	NAME:
1074	NB_DENS
1075
1076	AUTHOR:
1077	pierre.cruzalebes@oca.eu
1078
1079	PURPOSE:
1080	EVALUATE RELATIVE NUMBER DENSITY AT OUTER BOUNDARY
1081	(THIN DUSTY SHELL MODEL)
1082	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
1083
1084	CATEGORY:
1085	MODELLING.
1086
1087	CALLING SEQUENCE:
1088	NB_DENS,A,F,PD_F
1089
1090	INPUTS:.
1091	A = ROW VECTOR OF PARAMETERS.
1092
1093	OUTPUTS:
1094	F = VALUE OF FUNCTION.
1095
1096	OPTIONAL OUTPUT PARAMETERS:
1097	PD_F = VECTOR CONTAINING PARTIAL DERIVATIVE
1098	PD_F(K) = DERIVATIVE W/RESPECT TO KTH PARAMETER.
1099
1100	COMMON BLOCKS:
1101	NONE.
1102
1103	SIDE EFFECTS:
1104	NONE.
1105
1106	RESTRICTIONS:
1107	NONE.
1108
1109	PROCEDURE:
1110	F = (A1/A0)^A2
1111	WITH: A0 = SHELL INNER DIAMETER
1112	A1 = SHELL OUTER DIAMETER
1113	A2 = POWER-LAW DENSITY INDEX
1114	PD_F_0 = -A2/A0*F ;PARTIAL DERIVATIVE W/RESPECT TO A0
1115	PD_F_1 = A2/A1*F ;PARTIAL DERIVATIVE W/RESPECT TO A1
1116	PD_F_2 = LN(A1/A0)*F ;PARTIAL DERIVATIVE W/RESPECT TO A2
1117
1118	LOCAL PROCEDURE CALLED:
1119	NONE
1120
1121	LOCAL FUNCTION USED:
1122	NONE
1123
1124	LOCAL SYSTEM VARIABLE USED:
1125	NONE
1126
1127	REVISION HISTORY:
1128	Written by pcr 2008/01/08
1129	last modification by pcr 2008/02/12
1130
1131	----- Documentation for Model\planck.pro -----
1132	NAME:
1133	PLANCK
1134
1135	AUTHOR:
1136	pierre.cruzalebes@oca.eu
1137
1138	PURPOSE:
1139	EVALUATE "PLANCK" (BLACK BODY) SPECTRAL RADIANT EXITANCE
1140	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVE.
1141
1142	CATEGORY:
1143	MODELLING.
1144
1145	CALLING SEQUENCE:
1146	PLANCK,X,A,F,PDER_F
1147
1148	INPUTS:.
1149	X = ROW VALUES OF INDEPENDENT VARIABLES (WAVELENGTHS IN MU).
1150	A = PARAMETER OF EQUATION DESCRIBED BELOW (TEMPERATURE IN KELVIN).
1151
1152	OUTPUTS:
1153	F = ROW VALUES OF FUNCTION (IN W.m^-2.mu^-1).
1154
1155	OPTIONAL OUTPUT PARAMETERS:
1156	PDER_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
1157	PDER_F(I) = DERIVATIVE AT ITH POINT W/RESPECT TO A.
1158
1159	COMMON BLOCKS:
1160	NONE.
1161
1162	SIDE EFFECTS:
1163	NONE.
1164
1165	RESTRICTIONS:
1166	NONE.
1167
1168	PROCEDURE:
1169	F=PIC1/(X^5)/(EXP(C2/(XA))-1)
1170	PDER_F=F(C2/(XA))/A/(1-EXP(-C2/(X*A)))
1171
1172	LOCAL PROCEDURE CALLED:
1173	NONE
1174
1175	LOCAL FUNCTION USED:
1176	NONE
1177
1178	LOCAL SYSTEM VARIABLE USED:
1179	NONE
1180
1181	REVISION HISTORY:
1182	Written by pcr 2006/08/20
1183	last modification by pcr 2008/02/12
1184
1185	----- Documentation for Model\shell_depth.pro -----
1186	NAME:
1187	SHELL_DEPTH
1188
1189	AUTHOR:
1190	pierre.cruzalebes@oca.eu
1191
1192	PURPOSE:
1193	EVALUATE OPTICAL DEPTH RADIAL DISTRIBUTION IN SHELL DIRECTION
1194	(RADIATIVE-TRANSFER ANALYTICAL MODEL)
1195	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
1196
1197	CATEGORY:
1198	MODELLING.
1199
1200	CALLING SEQUENCE:
1201	SHELL_DEPTH,XX,A,F,PD_F
1202
1203	INPUTS:.
1204	XX = VALUES OF INDEPENDENT VARIABLES
1205	= WAVELENGTHS + IMPACT PARAMETER RELATIVE TO OUTER DIAM (STRUCTURE).
1206	A = ROW VECTOR OF PARAMETERS.
1207
1208	OUTPUTS:
1209	F = VALUE OF FUNCTION AT EACH WAVELENGTH AND SIGHT ANGLE.
1210
1211	OPTIONAL OUTPUT PARAMETERS:
1212	PD_F = ARRAY CONTAINING PARTIAL DERIVATIVE.
1213	PD_F(I,J,K) = DERIVATIVE AT ITH WAVELENGTH AND JTH SIGHT ANGLE
1214	W/RESPECT TO KTH PARAMETER.
1215
1216	COMMON BLOCKS:
1217	NONE.
1218
1219	SIDE EFFECTS:
1220	NONE.
1221
1222	RESTRICTIONS:
1223	NONE.
1224
1225	PROCEDURE:
1226	F = NB_DENS(A0,A1,A3)ABS_EFF(A2)SHELL_PATH(A1)/A4
1227	WITH: NB_DENS = RELATIVE NUMBER DENSITY AT OUTER BOUNDARY = (A1/A0)^A3
1228	ABS_EFF = WAVELENGTH DISTRIBUTION OF ABSORPTION EFFICIENCY = (1/X)^A2
1229	SHELL_PATH = ANGULAR OPTICAL PATH IN SHELL DIRECTION = A1*SQRT(1-R^2)
1230	X = XX.WVL = WAVELENGTH
1231	R = XX.RIP = RELATIVE IMPACT PARAMETER
1232	A0 = SHELL INNER DIAMETER
1233	A1 = SHELL OUTER DIAMETER
1234	A2 = SPECTRAL INDEX
1235	A3 = POWER-LAW DENSITY INDEX
1236	A4 = REFERENCE GEOMETRICAL PATH
1237	PD_F_0 = F*PD_NB_DENS_0/NB_DENS ;PARTIAL DERIVATIVE W/RESPECT TO A0
1238	PD_F_1 = F*(PD_NB_DENS_1/NB_DENS+PD_SHELL_PATH_1/SHELL_PATH) ;PARTIAL DERIVATIVE W/RESPECT TO A1
1239	PD_F_2 = F*PD_ABS_EFF_2/ABS_EFF ;PARTIAL DERIVATIVE W/RESPECT TO A2
1240	PD_F_3 = F*PD_NB_DENS_3/NB_DENS ;PARTIAL DERIVATIVE W/RESPECT TO A3
1241	PD_F_4 = -F/A4 ;PARTIAL DERIVATIVE W/RESPECT TO A4
1242
1243	LOCAL PROCEDURE CALLED:
1244	ABS_EFF
1245	NB_DENS
1246	SHELL_PATH
1247
1248	LOCAL FUNCTION USED:
1249	NONE
1250
1251	LOCAL SYSTEM VARIABLE USED:
1252	NONE
1253
1254	MODIFICATION HISTORY:
1255	Written by pcr 2008/01/10
1256	last modification by pcr 2009/03/18
1257
1258	----- Documentation for Model\shell_path.pro -----
1259	NAME:
1260	SHELL_PATH
1261
1262	AUTHOR:
1263	pierre.cruzalebes@oca.eu
1264
1265	PURPOSE:
1266	EVALUATE GEOMETRICAL-THICKNESS RADIAL DISTRIBUTION IN SHELL DIRECTION
1267	(RADIATIVE-TRANSFER ANALYTICAL MODEL)
1268	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVES.
1269
1270	CATEGORY:
1271	MODELLING.
1272
1273	CALLING SEQUENCE:
1274	SHELL_PATH,XX,A,F,PD_F
1275
1276	INPUTS:
1277	XX = VALUES OF INDEPENDENT VARIABLES
1278	= WAVELENGTHS + IMPACT PARAMETER RELATIVE TO OUTER DIAM (STRUCTURE).
1279	A = PARAMETER.
1280
1281	OUTPUTS:
1282	F = VALUE OF THICKNESS AT EACH SIGHT ANGLE.
1283
1284	OPTIONAL OUTPUT PARAMETERS:
1285	PD_F = VECTOR CONTAINING PARTIAL DERIVATIVE.
1286	PD_F(I) = DERIVATIVE AT ITH SIGHT ANGLE W/RESPECT TO PARAMETER.
1287
1288	COMMON BLOCKS:
1289	NONE.
1290
1291	SIDE EFFECTS:
1292	NONE.
1293
1294	RESTRICTIONS:
1295	NONE.
1296
1297	PROCEDURE:
1298	F = A*SQRT(1-R^2)
1299	WITH: R = XX.RIP = RELATIVE IMPACT PARAMETER
1300	A = SHELL OUTER DIAMETER
1301	PD_F = SQRT(1-R^2) ;PARTIAL DERIVATIVE W/RESPECT TO A
1302
1303	LOCAL PROCEDURE CALLED:
1304	NONE
1305
1306	LOCAL FUNCTION USED:
1307	NONE
1308
1309	LOCAL SYSTEM VARIABLE USED:
1310	NONE
1311
1312	REVISION HISTORY:
1313	Written by pcr 2008/01/10
1314	last modification by pcr 2008/12/28
1315
1316	----- Documentation for Model\uniform_disk.pro -----
1317	NAME:
1318	UNIFORM_DISK
1319
1320	AUTHOR:
1321	pierre.cruzalebes@oca.eu
1322
1323	PURPOSE:
1324	EVALUATE "UNIFORM_DISK" FUNCTION
1325	AND OPTIONALLY RETURN VALUE OF PARTIAL DERIVATIVE.
1326
1327	CATEGORY:
1328	MODELLING.
1329
1330	CALLING SEQUENCE:
1331	UNIFORM_DISK,X,A,FCT,PD_FCT
1332
1333	INPUTS:.
1334	X = VALUES OF INDEPENDENT VARIABLES (SPATIAL FREQUENCIES, IN RAD^-1).
1335	A = PARAMETER OF EQUATION DESCRIBED BELOW (DISK DIAMETER, IN MAS).
1336
1337	OUTPUTS:
1338	FCT = VALUE OF FUNCTION AT EACH X(I).
1339
1340	OPTIONAL OUTPUT PARAMETERS:
1341	PD_FCT = VECTOR CONTAINING THE PARTIAL DERIVATIVE.
1342	PD_F(I) = DERIVATIVE AT ITH POINT W/RESPECT TO A.
1343
1344	COMMON BLOCKS:
1345	NONE.
1346
1347	SIDE EFFECTS:
1348	NONE.
1349
1350	RESTRICTIONS:
1351	NONE.
1352
1353	PROCEDURE:
1354	FCT = (A^2)/42J1(PIAX)/(PIAX)
1355	PD_FCT = (A/2)J0(PIA*X)
1356
1357	LOCAL PROCEDURE CALLED:
1358	NONE
1359
1360	LOCAL FUNCTION USED:
1361	NONE
1362
1363	LOCAL SYSTEM VARIABLE USED:
1364	EPSILON
1365	MAS2RADIAN
1366
1367	REVISION HISTORY:
1368	Written by pcr 2006/09/18
1369	last modification by pcr 2011/01/13
1370

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