This file is indexed.

/usr/share/gnudatalanguage/mpfit/mpfitfun.pro is in gdl-mpfit 1.85+2017.01.03-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
;+
; NAME:
;   MPFITFUN
;
; AUTHOR:
;   Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
;   craigm@lheamail.gsfc.nasa.gov
;   UPDATED VERSIONs can be found on my WEB PAGE: 
;      http://cow.physics.wisc.edu/~craigm/idl/idl.html
;
; PURPOSE:
;   Perform Levenberg-Marquardt least-squares fit to IDL function
;
; MAJOR TOPICS:
;   Curve and Surface Fitting
;
; CALLING SEQUENCE:
;   parms = MPFITFUN(MYFUNCT, X, Y, ERR, start_params, ...)
;
; DESCRIPTION:
;
;  MPFITFUN fits a user-supplied model -- in the form of an IDL
;  function -- to a set of user-supplied data.  MPFITFUN calls
;  MPFIT, the MINPACK-1 least-squares minimizer, to do the main
;  work.
;
;  Given the data and their uncertainties, MPFITFUN finds the best set
;  of model parameters which match the data (in a least-squares
;  sense) and returns them in an array.
;  
;  The user must supply the following items:
;   - An array of independent variable values ("X").
;   - An array of "measured" *dependent* variable values ("Y").
;   - An array of "measured" 1-sigma uncertainty values ("ERR").
;   - The name of an IDL function which computes Y given X ("MYFUNCT").
;   - Starting guesses for all of the parameters ("START_PARAMS").
;
;  There are very few restrictions placed on X, Y or MYFUNCT.  Simply
;  put, MYFUNCT must map the "X" values into "Y" values given the
;  model parameters.  The "X" values may represent any independent
;  variable (not just Cartesian X), and indeed may be multidimensional
;  themselves.  For example, in the application of image fitting, X
;  may be a 2xN array of image positions.
;
;  Data values of NaN or Infinity for "Y", "ERR" or "WEIGHTS" will be
;  ignored as missing data if the NAN keyword is set.  Otherwise, they
;  may cause the fitting loop to halt with an error message.  Note
;  that the fit will still halt if the model function, or its
;  derivatives, produces infinite or NaN values.
;
;  MPFITFUN carefully avoids passing large arrays where possible to
;  improve performance.
;
;  See below for an example of usage.
;
; USER FUNCTION
;
;  The user must define a function which returns the model value.  For
;  applications which use finite-difference derivatives -- the default
;  -- the user function should be declared in the following way:
;
;    FUNCTION MYFUNCT, X, P
;     ; The independent variable is X
;     ; Parameter values are passed in "P"
;     YMOD = ... computed model values at X ...
;     return, YMOD
;    END
;
;  The returned array YMOD must have the same dimensions and type as
;  the "measured" Y values.
;
;  User functions may also indicate a fatal error condition
;  using the ERROR_CODE common block variable, as described
;  below under the MPFIT_ERROR common block definition.
;
;  MPFIT by default calculates derivatives numerically via a finite
;  difference approximation.  However, the user function *may*
;  calculate the derivatives if desired, but only if the model
;  function is declared with an additional position parameter, DP, as
;  described below.
;
;  To enable explicit derivatives for all parameters, set
;  AUTODERIVATIVE=0.
;
;  When AUTODERIVATIVE=0, the user function is responsible for
;  calculating the derivatives of the user function with respect to
;  each parameter.  The user function should be declared as follows:
;
;    ;
;    ; MYFUNCT - example user function
;    ;   P - input parameter values (N-element array)
;    ;   DP - upon input, an N-vector indicating which parameters
;    ;          to compute derivatives for; 
;    ;        upon output, the user function must return
;    ;          an ARRAY(M,N) of derivatives in this keyword
;    ;   (keywords) - any other keywords specified by FUNCTARGS
;    ; RETURNS - function values
;    ;
;    FUNCTION MYFUNCT, x, p, dp [, (additional keywords if desired)]
;     model = F(x, p)         ;; Model function
;     
;     if n_params() GT 2 then begin
;       ; Create derivative and compute derivative array
;       requested = dp   ; Save original value of DP
;       dp = make_array(n_elements(x), n_elements(p), value=x[0]*0)
;
;       ; Compute derivative if requested by caller
;       for i = 0, n_elements(p)-1 do if requested(i) NE 0 then $
;         dp(*,i) = FGRAD(x, p, i)
;     endif
;    
;     return, resid
;    END
;
;  where FGRAD(x, p, i) is a model function which computes the
;  derivative of the model F(x,p) with respect to parameter P(i) at X.
;
;  Derivatives should be returned in the DP array. DP should be an
;  ARRAY(m,n) array, where m is the number of data points and n is the
;  number of parameters.  DP[i,j] is the derivative of the ith
;  function value with respect to the jth parameter.
;
;  MPFIT may not always request derivatives from the user function.
;  In those cases, the parameter DP is not passed.  Therefore
;  functions can use N_PARAMS() to indicate whether they must compute
;  the derivatives or not.
;
;  For additional information about explicit derivatives, including
;  additional settings and debugging options, see the discussion under
;  "EXPLICIT DERIVATIVES" and AUTODERIVATIVE in MPFIT.PRO.
;
; CONSTRAINING PARAMETER VALUES WITH THE PARINFO KEYWORD
;
;  The behavior of MPFIT can be modified with respect to each
;  parameter to be fitted.  A parameter value can be fixed; simple
;  boundary constraints can be imposed; limitations on the parameter
;  changes can be imposed; properties of the automatic derivative can
;  be modified; and parameters can be tied to one another.
;
;  These properties are governed by the PARINFO structure, which is
;  passed as a keyword parameter to MPFIT.
;
;  PARINFO should be an array of structures, one for each parameter.
;  Each parameter is associated with one element of the array, in
;  numerical order.  The structure can have the following entries
;  (none are required):
;  
;     .VALUE - the starting parameter value (but see the START_PARAMS
;              parameter for more information).
;  
;     .FIXED - a boolean value, whether the parameter is to be held
;              fixed or not.  Fixed parameters are not varied by
;              MPFIT, but are passed on to MYFUNCT for evaluation.
;  
;     .LIMITED - a two-element boolean array.  If the first/second
;                element is set, then the parameter is bounded on the
;                lower/upper side.  A parameter can be bounded on both
;                sides.  Both LIMITED and LIMITS must be given
;                together.
;  
;     .LIMITS - a two-element float or double array.  Gives the
;               parameter limits on the lower and upper sides,
;               respectively.  Zero, one or two of these values can be
;               set, depending on the values of LIMITED.  Both LIMITED
;               and LIMITS must be given together.
;  
;     .PARNAME - a string, giving the name of the parameter.  The
;                fitting code of MPFIT does not use this tag in any
;                way.  However, the default ITERPROC will print the
;                parameter name if available.
;  
;     .STEP - the step size to be used in calculating the numerical
;             derivatives.  If set to zero, then the step size is
;             computed automatically.  Ignored when AUTODERIVATIVE=0.
;             This value is superceded by the RELSTEP value.
;
;     .RELSTEP - the *relative* step size to be used in calculating
;                the numerical derivatives.  This number is the
;                fractional size of the step, compared to the
;                parameter value.  This value supercedes the STEP
;                setting.  If the parameter is zero, then a default
;                step size is chosen.
;
;     .MPSIDE - the sidedness of the finite difference when computing
;               numerical derivatives.  This field can take four
;               values:
;
;                  0 - one-sided derivative computed automatically
;                  1 - one-sided derivative (f(x+h) - f(x)  )/h
;                 -1 - one-sided derivative (f(x)   - f(x-h))/h
;                  2 - two-sided derivative (f(x+h) - f(x-h))/(2*h)
;
;              Where H is the STEP parameter described above.  The
;              "automatic" one-sided derivative method will chose a
;              direction for the finite difference which does not
;              violate any constraints.  The other methods do not
;              perform this check.  The two-sided method is in
;              principle more precise, but requires twice as many
;              function evaluations.  Default: 0.
;
;     .MPMAXSTEP - the maximum change to be made in the parameter
;                  value.  During the fitting process, the parameter
;                  will never be changed by more than this value in
;                  one iteration.
;
;                  A value of 0 indicates no maximum.  Default: 0.
;  
;     .TIED - a string expression which "ties" the parameter to other
;             free or fixed parameters as an equality constraint.  Any
;             expression involving constants and the parameter array P
;             are permitted.
;             Example: if parameter 2 is always to be twice parameter
;             1 then use the following: parinfo[2].tied = '2 * P[1]'.
;             Since they are totally constrained, tied parameters are
;             considered to be fixed; no errors are computed for them.
;             [ NOTE: the PARNAME can't be used in a TIED expression. ]
;
;     .MPPRINT - if set to 1, then the default ITERPROC will print the
;                parameter value.  If set to 0, the parameter value
;                will not be printed.  This tag can be used to
;                selectively print only a few parameter values out of
;                many.  Default: 1 (all parameters printed)
;
;     .MPFORMAT - IDL format string to print the parameter within
;                 ITERPROC.  Default: '(G20.6)'  (An empty string will
;                 also use the default.)
;
;  Future modifications to the PARINFO structure, if any, will involve
;  adding structure tags beginning with the two letters "MP".
;  Therefore programmers are urged to avoid using tags starting with
;  "MP", but otherwise they are free to include their own fields
;  within the PARINFO structure, which will be ignored by MPFIT.
;  
;  PARINFO Example:
;  parinfo = replicate({value:0.D, fixed:0, limited:[0,0], $
;                       limits:[0.D,0]}, 5)
;  parinfo[0].fixed = 1
;  parinfo[4].limited[0] = 1
;  parinfo[4].limits[0]  = 50.D
;  parinfo[*].value = [5.7D, 2.2, 500., 1.5, 2000.]
;  
;  A total of 5 parameters, with starting values of 5.7,
;  2.2, 500, 1.5, and 2000 are given.  The first parameter
;  is fixed at a value of 5.7, and the last parameter is
;  constrained to be above 50.
;
; COMPATIBILITY
;
;  This function is designed to work with IDL 5.0 or greater.
;  
;  Because TIED parameters rely on the EXECUTE() function, they cannot
;  be used with the free version of the IDL Virtual Machine.
;
;
; INPUTS:
;   MYFUNCT - a string variable containing the name of an IDL function.
;             This function computes the "model" Y values given the
;             X values and model parameters, as desribed above.
;
;   X - Array of independent variable values.
;
;   Y - Array of "measured" dependent variable values.  Y should have
;       the same data type as X.  The function MYFUNCT should map
;       X->Y.
;         NOTE: the following special cases apply:
;                * if Y is NaN or Infinite, and the NAN keyword is
;                  set, then the corresponding data point is ignored
;
;   ERR - Array of "measured" 1-sigma uncertainties.  ERR should have
;         the same data type as Y.  ERR is ignored if the WEIGHTS
;         keyword is specified.
;         NOTE: the following special cases apply:
;                * if ERR is zero, then the corresponding data point
;                  is ignored
;                * if ERR is NaN or Infinite, and the NAN keyword is
;                  set, then the corresponding data point is ignored
;                * if ERR is negative, then the absolute value of 
;                  ERR is used.
;
;   START_PARAMS - An array of starting values for each of the
;                  parameters of the model.  The number of parameters
;                  should be fewer than the number of measurements.
;                  Also, the parameters should have the same data type
;                  as the measurements (double is preferred).
;
;                  This parameter is optional if the PARINFO keyword
;                  is used (see MPFIT).  The PARINFO keyword provides
;                  a mechanism to fix or constrain individual
;                  parameters.  If both START_PARAMS and PARINFO are
;                  passed, then the starting *value* is taken from
;                  START_PARAMS, but the *constraints* are taken from
;                  PARINFO.
; 
;
; RETURNS:
;
;   Returns the array of best-fit parameters.
;
;
; KEYWORD PARAMETERS:
;
;   BESTNORM - the value of the summed squared residuals for the
;              returned parameter values.
;
;   BEST_FJAC - upon return, BEST_FJAC contains the Jacobian, or
;               partial derivative, matrix for the best-fit model.
;               The values are an array,
;               ARRAY(N_ELEMENTS(DEVIATES),NFREE) where NFREE is the
;               number of free parameters.  This array is only
;               computed if /CALC_FJAC is set, otherwise BEST_FJAC is
;               undefined.
;
;               The returned array is such that BEST_FJAC[I,J] is the
;               partial derivative of the model with respect to
;               parameter PARMS[PFREE_INDEX[J]].
;
;   BEST_RESID - upon return, an array of best-fit deviates,
;                normalized by the weights or errors.
;
;   COVAR - the covariance matrix for the set of parameters returned
;           by MPFIT.  The matrix is NxN where N is the number of
;           parameters.  The square root of the diagonal elements
;           gives the formal 1-sigma statistical errors on the
;           parameters IF errors were treated "properly" in MYFUNC.
;           Parameter errors are also returned in PERROR.
;
;           To compute the correlation matrix, PCOR, use this example:
;                  PCOR = COV * 0
;                  FOR i = 0, n-1 DO FOR j = 0, n-1 DO $
;                    PCOR[i,j] = COV[i,j]/sqrt(COV[i,i]*COV[j,j])
;           or equivalently, in vector notation,
;                  PCOR = COV / (PERROR # PERROR)
;
;           If NOCOVAR is set or MPFIT terminated abnormally, then
;           COVAR is set to a scalar with value !VALUES.D_NAN.
;
;   CASH - when set, the fit statistic is changed to a derivative of
;          the CASH statistic.  The model function must be strictly
;          positive. WARNING: this option is incomplete and untested.
;
;   DOF - number of degrees of freedom, computed as
;             DOF = N_ELEMENTS(DEVIATES) - NFREE
;         Note that this doesn't account for pegged parameters (see
;         NPEGGED).  It also does not account for data points which
;         are assigned zero weight, for example if :
;           * WEIGHTS[i] EQ 0, or
;           * ERR[i] EQ infinity, or 
;           * any of the values is "undefined" and /NAN is set.
;
;   ERRMSG - a string error or warning message is returned.
;
;   FTOL - a nonnegative input variable. Termination occurs when both
;          the actual and predicted relative reductions in the sum of
;          squares are at most FTOL (and STATUS is accordingly set to
;          1 or 3).  Therefore, FTOL measures the relative error
;          desired in the sum of squares.  Default: 1D-10
;
;   FUNCTARGS - A structure which contains the parameters to be passed
;               to the user-supplied function specified by MYFUNCT via
;               the _EXTRA mechanism.  This is the way you can pass
;               additional data to your user-supplied function without
;               using common blocks.
;
;               By default, no extra parameters are passed to the
;               user-supplied function.
;
;   GTOL - a nonnegative input variable. Termination occurs when the
;          cosine of the angle between fvec and any column of the
;          jacobian is at most GTOL in absolute value (and STATUS is
;          accordingly set to 4). Therefore, GTOL measures the
;          orthogonality desired between the function vector and the
;          columns of the jacobian.  Default: 1D-10
;
;   ITERARGS - The keyword arguments to be passed to ITERPROC via the
;              _EXTRA mechanism.  This should be a structure, and is
;              similar in operation to FUNCTARGS.
;              Default: no arguments are passed.
;
;   ITERPROC - The name of a procedure to be called upon each NPRINT
;              iteration of the MPFIT routine.  It should be declared
;              in the following way:
;
;              PRO ITERPROC, MYFUNCT, p, iter, fnorm, FUNCTARGS=fcnargs, $
;                PARINFO=parinfo, QUIET=quiet, ...
;                ; perform custom iteration update
;              END
;         
;              ITERPROC must either accept all three keyword
;              parameters (FUNCTARGS, PARINFO and QUIET), or at least
;              accept them via the _EXTRA keyword.
;          
;              MYFUNCT is the user-supplied function to be minimized,
;              P is the current set of model parameters, ITER is the
;              iteration number, and FUNCTARGS are the arguments to be
;              passed to MYFUNCT.  FNORM should be the
;              chi-squared value.  QUIET is set when no textual output
;              should be printed.  See below for documentation of
;              PARINFO.
;
;              In implementation, ITERPROC can perform updates to the
;              terminal or graphical user interface, to provide
;              feedback while the fit proceeds.  If the fit is to be
;              stopped for any reason, then ITERPROC should set the
;              common block variable ERROR_CODE to negative value (see
;              MPFIT_ERROR common block below).  In principle,
;              ITERPROC should probably not modify the parameter
;              values, because it may interfere with the algorithm's
;              stability.  In practice it is allowed.
;
;              Default: an internal routine is used to print the
;                       parameter values.
;
;   MAXITER - The maximum number of iterations to perform.  If the
;             number of calculation iterations exceeds MAXITER, then
;             the STATUS value is set to 5 and MPFIT returns.  
;
;             If MAXITER EQ 0, then MPFIT does not iterate to adjust
;             parameter values; however, the user function is evaluated
;             and parameter errors/covariance/Jacobian are estimated
;             before returning.
;             Default: 200 iterations
;
;   NAN - ignore infinite or NaN values in the Y, ERR or WEIGHTS
;         parameters.  These values will be treated as missing data.
;         However, the fit will still halt with an error condition
;         if the model function becomes infinite.
;
;   NFEV - the number of MYFUNCT function evaluations performed.
;
;   NFREE - the number of free parameters in the fit.  This includes
;           parameters which are not FIXED and not TIED, but it does
;           include parameters which are pegged at LIMITS.
;
;   NITER - the number of iterations completed.
;
;   NOCOVAR - set this keyword to prevent the calculation of the
;             covariance matrix before returning (see COVAR)
;
;   NPEGGED - the number of free parameters which are pegged at a
;             LIMIT.
;
;   NPRINT - The frequency with which ITERPROC is called.  A value of
;            1 indicates that ITERPROC is called with every iteration,
;            while 2 indicates every other iteration, etc.  Be aware
;            that several Levenberg-Marquardt attempts can be made in
;            a single iteration.  Also, the ITERPROC is *always*
;            called for the final iteration, regardless of the
;            iteration number.
;            Default value: 1
;
;   PARINFO - A one-dimensional array of structures.
;             Provides a mechanism for more sophisticated constraints
;             to be placed on parameter values.  When PARINFO is not
;             passed, then it is assumed that all parameters are free
;             and unconstrained.  Values in PARINFO are never 
;             modified during a call to MPFIT.
;
;             See description above for the structure of PARINFO.
;
;             Default value:  all parameters are free and unconstrained.
;
;   PERROR - The formal 1-sigma errors in each parameter, computed
;            from the covariance matrix.  If a parameter is held
;            fixed, or if it touches a boundary, then the error is
;            reported as zero.
;
;            If the fit is unweighted (i.e. no errors were given, or
;            the weights were uniformly set to unity), then PERROR
;            will probably not represent the true parameter
;            uncertainties.  
;
;            *If* you can assume that the true reduced chi-squared
;            value is unity -- meaning that the fit is implicitly
;            assumed to be of good quality -- then the estimated
;            parameter uncertainties can be computed by scaling PERROR
;            by the measured chi-squared value.
;
;              DOF     = N_ELEMENTS(X) - N_ELEMENTS(PARMS) ; deg of freedom
;              PCERROR = PERROR * SQRT(BESTNORM / DOF)   ; scaled uncertainties
;
;   PFREE_INDEX - upon return, PFREE_INDEX contains an index array
;                 which indicates which parameter were allowed to
;                 vary.  I.e. of all the parameters PARMS, only
;                 PARMS[PFREE_INDEX] were varied.
;
;   QUERY - if set, then MPFIT() will return immediately with one of
;           the following values:
;                 1 - if MIN_VERSION is not set
;                 1 - if MIN_VERSION is set and MPFIT satisfies the minimum
;                 0 - if MIN_VERSION is set and MPFIT does not satisfy it
;           Default: not set.
;
;   QUIET - set this keyword when no textual output should be printed
;           by MPFIT
;
;   STATUS - an integer status code is returned.  All values greater
;            than zero can represent success (however STATUS EQ 5 may
;            indicate failure to converge).  It can have one of the
;            following values:
;
;        -18  a fatal execution error has occurred.  More information
;             may be available in the ERRMSG string.
;
;        -16  a parameter or function value has become infinite or an
;             undefined number.  This is usually a consequence of
;             numerical overflow in the user's model function, which
;             must be avoided.
;
;        -15 to -1 
;             these are error codes that either MYFUNCT or ITERPROC
;             may return to terminate the fitting process (see
;             description of MPFIT_ERROR common below).  If either
;             MYFUNCT or ITERPROC set ERROR_CODE to a negative number,
;             then that number is returned in STATUS.  Values from -15
;             to -1 are reserved for the user functions and will not
;             clash with MPFIT.
;
;	   0  improper input parameters.
;         
;	   1  both actual and predicted relative reductions
;	      in the sum of squares are at most FTOL.
;         
;	   2  relative error between two consecutive iterates
;	      is at most XTOL
;         
;	   3  conditions for STATUS = 1 and STATUS = 2 both hold.
;         
;	   4  the cosine of the angle between fvec and any
;	      column of the jacobian is at most GTOL in
;	      absolute value.
;         
;	   5  the maximum number of iterations has been reached
;         
;	   6  FTOL is too small. no further reduction in
;	      the sum of squares is possible.
;         
;	   7  XTOL is too small. no further improvement in
;	      the approximate solution x is possible.
;         
;	   8  GTOL is too small. fvec is orthogonal to the
;	      columns of the jacobian to machine precision.
;
;   WEIGHTS - Array of weights to be used in calculating the
;             chi-squared value.  If WEIGHTS is specified then the ERR
;             parameter is ignored.  The chi-squared value is computed
;             as follows:
;
;                CHISQ = TOTAL( (Y-MYFUNCT(X,P))^2 * ABS(WEIGHTS) )
;
;             Here are common values of WEIGHTS for standard weightings:
;
;                1D/ERR^2 - Normal weighting (ERR is the measurement error)
;                1D/Y     - Poisson weighting (counting statistics)
;                1D       - Unweighted
;
;         NOTE: the following special cases apply:
;                * if WEIGHTS is zero, then the corresponding data point
;                  is ignored
;                * if WEIGHTS is NaN or Infinite, and the NAN keyword is
;                  set, then the corresponding data point is ignored
;                * if WEIGHTS is negative, then the absolute value of 
;                  WEIGHTS is used.
;
;   XTOL - a nonnegative input variable. Termination occurs when the
;          relative error between two consecutive iterates is at most
;          XTOL (and STATUS is accordingly set to 2 or 3).  Therefore,
;          XTOL measures the relative error desired in the approximate
;          solution.  Default: 1D-10
;
;   YFIT - the best-fit model function, as returned by MYFUNCT.
;
;   
; EXAMPLE:
;
;   ; First, generate some synthetic data
;   npts = 200
;   x  = dindgen(npts) * 0.1 - 10.                  ; Independent variable 
;   yi = gauss1(x, [2.2D, 1.4, 3000.])              ; "Ideal" Y variable
;   y  = yi + randomn(seed, npts) * sqrt(1000. + yi); Measured, w/ noise
;   sy = sqrt(1000.D + y)                           ; Poisson errors
;
;   ; Now fit a Gaussian to see how well we can recover
;   p0 = [1.D, 1., 1000.]                   ; Initial guess (cent, width, area)
;   p = mpfitfun('GAUSS1', x, y, sy, p0)    ; Fit a function
;   print, p
;
;   Generates a synthetic data set with a Gaussian peak, and Poisson
;   statistical uncertainty.  Then the same function is fitted to the
;   data (with different starting parameters) to see how close we can
;   get.
;
;
; COMMON BLOCKS:
;
;   COMMON MPFIT_ERROR, ERROR_CODE
;
;     User routines may stop the fitting process at any time by
;     setting an error condition.  This condition may be set in either
;     the user's model computation routine (MYFUNCT), or in the
;     iteration procedure (ITERPROC).
;
;     To stop the fitting, the above common block must be declared,
;     and ERROR_CODE must be set to a negative number.  After the user
;     procedure or function returns, MPFIT checks the value of this
;     common block variable and exits immediately if the error
;     condition has been set.  By default the value of ERROR_CODE is
;     zero, indicating a successful function/procedure call.
;
; REFERENCES:
;
;   MINPACK-1, Jorge More', available from netlib (www.netlib.org).
;   "Optimization Software Guide," Jorge More' and Stephen Wright, 
;     SIAM, *Frontiers in Applied Mathematics*, Number 14.
;
; MODIFICATION HISTORY:
;   Written, Apr-Jul 1998, CM
;   Added PERROR keyword, 04 Aug 1998, CM
;   Added COVAR keyword, 20 Aug 1998, CM
;   Added ITER output keyword, 05 Oct 1998
;      D.L Windt, Bell Labs, windt@bell-labs.com;
;   Added ability to return model function in YFIT, 09 Nov 1998
;   Analytical derivatives allowed via AUTODERIVATIVE keyword, 09 Nov 1998
;   Parameter values can be tied to others, 09 Nov 1998
;   Cosmetic documentation updates, 16 Apr 1999, CM
;   More cosmetic documentation updates, 14 May 1999, CM
;   Made sure to update STATUS, 25 Sep 1999, CM
;   Added WEIGHTS keyword, 25 Sep 1999, CM
;   Changed from handles to common blocks, 25 Sep 1999, CM
;     - commons seem much cleaner and more logical in this case.
;   Alphabetized documented keywords, 02 Oct 1999, CM
;   Added QUERY keyword and query checking of MPFIT, 29 Oct 1999, CM
;   Corrected EXAMPLE (offset of 1000), 30 Oct 1999, CM
;   Check to be sure that X and Y are present, 02 Nov 1999, CM
;   Documented PERROR for unweighted fits, 03 Nov 1999, CM
;   Changed to ERROR_CODE for error condition, 28 Jan 2000, CM
;   Corrected errors in EXAMPLE, 26 Mar 2000, CM
;   Copying permission terms have been liberalized, 26 Mar 2000, CM
;   Propagated improvements from MPFIT, 17 Dec 2000, CM
;   Added CASH statistic, 10 Jan 2001
;   Added NFREE and NPEGGED keywords, 11 Sep 2002, CM
;   Documented RELSTEP field of PARINFO (!!), CM, 25 Oct 2002
;   Add DOF keyword to return degrees of freedom, CM, 23 June 2003
;   Convert to IDL 5 array syntax (!), 16 Jul 2006, CM
;   Move STRICTARR compile option inside each function/procedure, 9
;     Oct 2006
;   Add NAN keyword, to ignore non-finite data values, 28 Oct 2006, CM
;   Clarify documentation on user-function, derivatives, and PARINFO,
;     27 May 2007
;   Fix bug in handling of explicit derivatives with errors/weights
;     (the weights were not being applied), CM, 03 Sep 2007
;   Add COMPATIBILITY section, CM, 13 Dec 2007
;   Add documentation about NAN behavior, CM, 30 Mar 2009
;   Add keywords BEST_RESIDS, CALC_FJAC, BEST_FJAC, PFREE_INDEX;
;     update some documentation that had become stale, CM, 2010-10-28
;   Documentation corrections, CM, 2011-08-26
;   Additional documentation about explicit derivatives, CM, 2012-07-23
;
;  $Id: mpfitfun.pro,v 1.19 2012/09/27 23:59:31 cmarkwar Exp $
;-
; Copyright (C) 1997-2002, 2003, 2006, 2007, 2009, 2010, 2011, 2012, Craig Markwardt
; This software is provided as is without any warranty whatsoever.
; Permission to use, copy, modify, and distribute modified or
; unmodified copies is granted, provided this copyright and disclaimer
; are included unchanged.
;-

FORWARD_FUNCTION mpfitfun_eval, mpfitfun, mpfit

; This is the call-back function for MPFIT.  It evaluates the
; function, subtracts the data, and returns the residuals.
function mpfitfun_eval, p, dp, _EXTRA=extra

  COMPILE_OPT strictarr
  common mpfitfun_common, fcn, x, y, err, wts, f, fcnargs

  ;; Save the original DP matrix for later use
  if n_params() GT 1 then if n_elements(dp) GT 0 then dp0 = dp

  ;; The function is evaluated here.  There are four choices,
  ;; depending on whether (a) FUNCTARGS was passed to MPFITFUN, which
  ;; is passed to this function as "hf"; or (b) the derivative
  ;; parameter "dp" is passed, meaning that derivatives should be
  ;; calculated analytically by the function itself.
  if n_elements(fcnargs) GT 0 then begin
      if n_params() GT 1 then f = call_function(fcn, x, p, dp, _EXTRA=fcnargs)$
      else                    f = call_function(fcn, x, p, _EXTRA=fcnargs)
  endif else begin
      if n_params() GT 1 then f = call_function(fcn, x, p, dp) $
      else                    f = call_function(fcn, x, p)
  endelse

  np = n_elements(p)
  nf = n_elements(f)

  ;; Compute the deviates, applying either errors or weights
  if n_elements(wts) GT 0 then begin
      result = (y-f)*wts
      if n_elements(dp0) GT 0 AND n_elements(dp) EQ np*nf then begin
          for j = 0L, np-1 do dp[j*nf] = dp[j*nf:j*nf+nf-1] * wts
      endif
  endif else if n_elements(err) GT 0 then begin
      result = (y-f)/err
      if n_elements(dp0) GT 0 AND n_elements(dp) EQ np*nf then begin
          for j = 0L, np-1 do dp[j*nf] = dp[j*nf:j*nf+nf-1] / err
      endif
  endif else begin
      result = (y-f)
  endelse
      
  ;; Make sure the returned result is one-dimensional.
  result = reform(result, n_elements(result), /overwrite)
  return, result
  
end

;; Implement residual and gradient scaling according to the
;; prescription of Cash (ApJ, 228, 939)
pro mpfitfun_cash, resid, dresid
  COMPILE_OPT strictarr
  common mpfitfun_common, fcn, x, y, err, wts, f, fcnargs

  sz = size(dresid)
  m = sz[1]
  n = sz[2]

  ;; Do rudimentary dimensions checks, so we don't do something stupid
  if n_elements(y) NE m OR n_elements(f) NE m OR n_elements(resid) NE m then begin
      DIM_ERROR:
      message, 'ERROR: dimensions of Y, F, RESID or DRESID are not consistent'
  endif

  ;; Scale gradient by sqrt(y)/f
  gfact = temporary(dresid) * rebin(reform(sqrt(y)/f,m,1),m,n)
  dresid = reform(dresid, m, n, /overwrite)
  
  ;; Scale residuals by 1/sqrt(y)
  resid = temporary(resid)/sqrt(y)

  return
end

function mpfitfun, fcn, x, y, err, p, WEIGHTS=wts, FUNCTARGS=fa, $
                   BESTNORM=bestnorm, nfev=nfev, STATUS=status, $
                   best_resid=best_resid, pfree_index=ifree, $
                   calc_fjac=calc_fjac, best_fjac=best_fjac, $
                   parinfo=parinfo, query=query, CASH=cash, $
                   covar=covar, perror=perror, yfit=yfit, $
                   niter=niter, nfree=nfree, npegged=npegged, dof=dof, $
                   quiet=quiet, ERRMSG=errmsg, NAN=NAN, _EXTRA=extra

  COMPILE_OPT strictarr
  status = 0L
  errmsg = ''

  ;; Detect MPFIT and crash if it was not found
  catch, catcherror
  if catcherror NE 0 then begin
      MPFIT_NOTFOUND:
      catch, /cancel
      message, 'ERROR: the required function MPFIT must be in your IDL path', /info
      return, !values.d_nan
  endif
  if mpfit(/query) NE 1 then goto, MPFIT_NOTFOUND
  catch, /cancel
  if keyword_set(query) then return, 1

  if n_params() EQ 0 then begin
      message, "USAGE: PARMS = MPFITFUN('MYFUNCT', X, Y, ERR, "+ $
        "START_PARAMS, ... )", /info
      return, !values.d_nan
  endif
  if n_elements(x) EQ 0 OR n_elements(y) EQ 0 then begin
      message, 'ERROR: X and Y must be defined', /info
      return, !values.d_nan
  endif

  if n_elements(err) GT 0 OR n_elements(wts) GT 0 AND keyword_set(cash) then begin
      message, 'ERROR: WEIGHTS or ERROR cannot be specified with CASH', /info
      return, !values.d_nan
  endif
  if keyword_set(cash) then begin
      scalfcn = 'mpfitfun_cash'
  endif

  ;; Use common block to pass data back and forth
  common mpfitfun_common, fc, xc, yc, ec, wc, mc, ac
  fc = fcn & xc = x & yc = y & mc = 0L
  ;; These optional parameters must be undefined first
  ac = 0 & dummy = size(temporary(ac))
  ec = 0 & dummy = size(temporary(ec))
  wc = 0 & dummy = size(temporary(wc))

  ;; FUNCTARGS
  if n_elements(fa) GT 0 then ac = fa

  ;; WEIGHTS or ERROR
  if n_elements(wts) GT 0 then begin
      wc = sqrt(abs(wts))
  endif else if n_elements(err) GT 0 then begin
      wh = where(err EQ 0, ct)
      if ct GT 0 then begin
          errmsg = 'ERROR: ERROR value must not be zero.  Use WEIGHTS instead.'
          message, errmsg, /info
          return, !values.d_nan
      endif
      ;; Appropriate weight for gaussian errors
      wc = 1/abs(err)
  endif

  ;; Check for weights/errors which do not match the dimension
  ;; of the data points
  if n_elements(wc) GT 0 AND $
    n_elements(wc) NE 1 AND $
    n_elements(wc) NE n_elements(yc) then begin
      errmsg = 'ERROR: ERROR/WEIGHTS must either be a scalar or match the number of Y values'
      message, errmsg, /info
      return, !values.d_nan
  endif

  ;; If the weights/errors are a scalar value, and not finite, then 
  ;; the fit will surely fail
  if n_elements(wc) EQ 1 then begin
      if finite(wc[0]) EQ 0 then begin
          errmsg = 'ERROR: the supplied scalar WEIGHT/ERROR value was not finite'
          message, errmsg, /info
          return, !values.d_nan
      endif
  endif

  ;; Handle the cases of non-finite data points or weights
  if keyword_set(nan) then begin
      ;; Non-finite data points
      wh = where(finite(yc) EQ 0, ct)
      if ct GT 0 then begin
          yc[wh] = 0
          ;; Careful: handle case when weights were a scalar...
          ;;   ... promote to a vector
          if n_elements(wc) EQ 1 then wc = replicate(wc[0], n_elements(yc))
          wc[wh] = 0
      endif

      ;; Non-finite weights
      wh = where(finite(wc) EQ 0, ct)
      if ct GT 0 then wc[wh] = 0
  endif

  result = mpfit('mpfitfun_eval', p, SCALE_FCN=scalfcn, $
                 parinfo=parinfo, STATUS=status, nfev=nfev, BESTNORM=bestnorm,$
                 covar=covar, perror=perror, $
                 best_resid=best_resid, pfree_index=ifree, $
                 calc_fjac=calc_fjac, best_fjac=best_fjac, $
                 niter=niter, nfree=nfree, npegged=npegged, dof=dof, $
                 ERRMSG=errmsg, quiet=quiet, _EXTRA=extra)

  ;; Retrieve the fit value
  yfit = temporary(mc)

  ;; Rescale the Jacobian according to parameter uncertainties
  if keyword_set(calc_fjac) AND nfree GT 0 AND status GT 0 then begin
      ec = 1/wc  ;; Per-data-point errors (could be INF or NAN!)
      for i = 0, nfree-1 do best_fjac[*,i] = - best_fjac[*,i] * ec
  endif

  ;; Some cleanup
  xc = 0 & yc = 0 & wc = 0 & ec = 0 & mc = 0 & ac = 0

  ;; Print error message if there is one.
  if NOT keyword_set(quiet) AND errmsg NE '' then $
    message, errmsg, /info

  return, result
end