;+
; NAME:
; MPFITEXPR
;
; 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 arbitrary expression
;
; MAJOR TOPICS:
; Curve and Surface Fitting
;
; CALLING SEQUENCE:
; MYFUNCT = 'X*(1-X)+3'
; parms = MPFITEXPR(MYFUNCT, XVAL, YVAL, ERR, start_parms, ...)
;
; DESCRIPTION:
;
; MPFITEXPR fits a user-supplied model -- in the form of an arbitrary IDL
; expression -- to a set of user-supplied data. MPFITEXPR calls
; MPFIT, the MINPACK-1 least-squares minimizer, to do the main
; work.
;
; Given the data and their uncertainties, MPFITEXPR 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").
; - A text IDL expression which computes Y given X.
; - Starting guesses for all of the parameters ("START_PARAMS").
;
; There are very few restrictions placed on X, Y or the expression of
; the model. Simply put, the expression 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.
;
; Some rules must be obeyed in constructing the expression. First,
; the independent variable name *MUST* be "X" in the expression,
; regardless of the name of the variable being passed to MPFITEXPR.
; This is demonstrated in the above calling sequence, where the X
; variable passed in is called "XVAL" but the expression still refers
; to "X". Second, parameter values must be referred to as an array
; named "P".
;
; If you do not pass in starting values for the model parameters,
; MPFITEXPR will attempt to determine the number of parameters you
; intend to have (it does this by looking for references to the array
; variable named "P"). When no starting values are passed in, the
; values are assumed to start at zero.
;
; MPFITEXPR carefully avoids passing large arrays where possible to
; improve performance.
;
; See below for an example of usage.
;
; EVALUATING EXPRESSIONS
;
; This source module also provides a function called MPEVALEXPR. You
; can use this function to evaluate your expression, given a list of
; parameters. This is one of the easier ways to compute the model
; once the best-fit parameters have been found. Here is an example:
;
; YMOD = MPEVALEXPR(MYFUNCT, XVAL, PARMS)
;
; where MYFUNCT is the expression (see MYFUNCT below), XVAL is the
; list of "X" values, and PARMS is an array of parameters. The
; returned array YMOD contains the expression MYFUNCT evaluated at
; each point in XVAL.
;
; PASSING PRIVATE DATA TO AN EXPRESSION
;
; The most complicated optimization problems typically involve other
; external parameters, in addition to the fitted parameters. While
; it is extremely easy to rewrite an expression dynamically, in case
; one of the external parameters changes, the other possibility is to
; use the PRIVATE data structure.
;
; The user merely passes a structure to the FUNCTARGS keyword. The
; user expression receives this value as the variable PRIVATE.
; MPFITEXPR nevers accesses this variable so it can contain any
; desired values. Usually it would be an IDL structure so that any
; named external parameters can be passed to the expression.
;
;
; 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
; this function uses the IDL EXECUTE() function, it will not work
; with the free version of the IDL Virtual machine.
;
;
; INPUTS:
; MYFUNCT - a string variable containing an IDL expression. The
; only restriction is that the independent variable *must*
; be referred to as "X" and model parameters *must* be
; referred to as an array called "P". Do not use symbol
; names beginning with the underscore, "_".
;
; The expression should calculate "model" Y values given
; the X values and model parameters. Using the vector
; notation of IDL, this can be quite easy to do. If your
; expression gets complicated, you may wish to make an IDL
; function which will improve performance and readibility.
;
; The resulting array should be of the same size and
; dimensions as the "measured" Y values.
;
; 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.
;
; 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.
;
; 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.
;
; If no parameters are given, then MPFITEXPR attempts
; to determine the number of parameters by scanning
; the expression. Parameters determined this way are
; initialized to zero. This technique is not fully
; reliable, so users are advised to pass explicit
; parameter starting values.
;
;
; RETURNS:
;
; Returns the array of best-fit parameters.
;
;
; KEYWORD PARAMETERS:
;
; BESTNORM - the value of the summed, squared, weighted residuals
; for the returned parameter values, i.e. the chi-square value.
;
; 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:
; IDL> PCOR = COV * 0
; IDL> 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])
;
; If NOCOVAR is set or MPFIT terminated abnormally, then
; COVAR is set to a scalar with value !VALUES.D_NAN.
;
; DOF - number of degrees of freedom, computed as
; DOF = N_ELEMENTS(DEVIATES) - NFREE
; Note that this doesn't account for pegged parameters (see
; NPEGGED).
;
; 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 - passed directly to the expression as the variable
; PRIVATE. Any user-private data can be communicated to
; the user expression using this keyword.
; Default: PRIVATE is undefined in user expression
;
; 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 is exceeded, then the STATUS value is set to 5
; and MPFIT returns.
; Default: 200 iterations
;
; 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. Note that
; several Levenberg-Marquardt attempts can be made in a
; single iteration.
; Default value: 1
;
; PARINFO - 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
;
; 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:
;
; 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:
;
; 1D/ERR^2 - Normal weighting (ERR is the measurement error)
; 1D/Y - Poisson weighting (counting statistics)
; 1D - Unweighted
;
; 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
; x = dindgen(200) * 0.1 - 10. ; Independent variable
; yi = gauss1(x, [2.2D, 1.4, 3000.]) + 1000 ; "Ideal" Y variable
; y = yi + randomn(seed, 200) * sqrt(yi) ; Measured, w/ noise
; sy = sqrt(y) ; Poisson errors
;
; ; Now fit a Gaussian to see how well we can recover
; expr = 'P[0] + GAUSS1(X, P[1:3])' ; fitting function
; p0 = [800.D, 1.D, 1., 500.] ; Initial guess
; p = mpfitexpr(expr, x, y, sy, p0) ; Fit the expression
; print, p
;
; plot, x, y ; Plot data
; oplot, x, mpevalexpr(expr, x, p) ; Plot model
;
; Generates a synthetic data set with a Gaussian peak, and Poisson
; statistical uncertainty. Then a model consisting of a constant
; plus Gaussian is fit to the data.
;
;
; 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 NITER 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
; Parameter values can be tied to others, 09 Nov 1998
; Added MPEVALEXPR utility function, 09 Dec 1998
; Cosmetic documentation updates, 16 Apr 1999, CM
; More cosmetic documentation updates, 14 May 1999, CM
; Made sure to update STATUS value, 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
; Check to be sure that X and Y are present, 02 Nov 1999, CM
; Documented PERROR for unweighted fits, 03 Nov 1999, CM
; Removed ITERPROC='' when quiet EQ 1, 10 Jan 2000, CM
; Changed to ERROR_CODE for error condition, 28 Jan 2000, CM
; Updated the EXAMPLE, 26 Mar 2000, CM
; Copying permission terms have been liberalized, 26 Mar 2000, CM
; Propagated improvements from MPFIT, 17 Dec 2000, CM
; Correct reference to _WTS in MPFITEXPR_EVAL, 25 May 2001, CM
; (thanks to Mark Fardal)
; Added useful FUNCTARGS behavior (as yet undocumented), 04 Jul
; 2002, CM
; Documented FUNCTARGS/PRIVATE behavior, 22 Jul 2002, CM
; Added NFREE and NPEGGED keywords, 13 Sep 2002, CM
; Documented RELSTEP field of PARINFO (!!), CM, 25 Oct 2002
; Add DOF keyword, CM, 31 Jul 2003
; Add FUNCTARGS keyword to MPEVALEXPR, CM 08 Aug 2003
; Minor documentation adjustment, 03 Feb 2004, CM
; Move STRICTARR compile option inside each function/procedure, 9 Oct 2006
; Clarify documentation on user-function, derivatives, and PARINFO,
; 27 May 2007
; Add COMPATIBILITY section, CM, 13 Dec 2007
; Remove obsolete STR_SEP in favor of STRSPLIT, CM, 2015-03-18
; Better documentation for STATUS, CM, 2016-04-29
;
; $Id: mpfitexpr.pro,v 1.16 2016/05/19 16:08:49 cmarkwar Exp $
;-
; Copyright (C) 1997-2001, 2002, 2003, 2004, 2007, 2015, 2016 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 mpevalexpr, mpfitexpr_eval, mpfitexpr, mpfit
; Utility function which simply returns the value of the expression,
; evaluated at each point in x, using the parameters p.
function mpevalexpr, _expr, x, p, functargs=private
COMPILE_OPT strictarr
_cmd = '_f = '+_expr
_err = execute(_cmd)
return, _f
end
; This is the call-back function for MPFIT. It evaluates the
; expression, subtracts the data, and returns the residuals.
function mpfitexpr_eval, p, _EXTRA=private
COMPILE_OPT strictarr
common mpfitexpr_common, _expr, x, y, err, _wts, _f
;; Compute the model value by executing the expression
_f = 0.D
_cmd = '_f = '+_expr
_xxx = execute(_cmd)
if _xxx EQ 0 then message, 'ERROR: command execution failed.'
;; Compute the deviates, applying either errors or weights
if n_elements(err) GT 0 then begin
result = (y-_f)/err
endif else if n_elements(_wts) GT 0 then begin
result = (y-_f)*_wts
endif else begin
result = (y-_f)
endelse
;; The returned result should be one-dimensional
result = reform(result, n_elements(result), /overwrite)
return, result
end
;; This is the main entry point for this module
function mpfitexpr, expr, x, y, err, p, WEIGHTS=wts, $
BESTNORM=bestnorm, STATUS=status, nfev=nfev, $
parinfo=parinfo, query=query, functargs=fcnargs, $
covar=covar, perror=perror, yfit=yfit, $
niter=niter, nfree=nfree, npegged=npegged, dof=dof, $
quiet=quiet, _EXTRA=extra, errmsg=errmsg
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 = MPFITEXPR('EXPR', 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 no parameters are given, then parse the input expression,
;; and determine the number of parameters automatically.
if (n_elements(parinfo) GT 0) AND (n_elements(p) EQ 0) then $
p = parinfo[*].value
if (n_elements(p) EQ 0) then begin
pos = 0L
nparams = 0L
ee = strupcase(expr)
;; These are character constants representing the boundaries of
;; variable names.
ca = (byte('A'))[0]
cz = (byte('Z'))[0]
c0 = (byte('0'))[0]
c9 = (byte('9'))[0]
c_ = (byte('_'))[0] ;; Underscore can be in a variable name
ll = strlen(ee)
pnames = ['']
;; Now step through, looking for variables looking like p[0], etc.
repeat begin
i = [strpos(ee, 'P(', pos), strpos(ee, 'P[', pos)]
wh = where(i GE 0, ct)
if ct LE 0 then goto, DONE_PARAMS
i = min(i[wh])
;; None found, finished
if i LT 0 then goto, DONE_PARAMS
;; Too close to the end of the string
if i GT ll-4 then goto, DONE_PARAMS
;; Have to be careful here, to be sure that this isn't just
;; a variable name ending in "p"
maybe = 0
;; If this is the first character
if i EQ 0 then maybe = 1 $
else begin
;; Or if the preceding character is a non-variable character
c = (byte(strmid(ee, i-1, 1)))[0]
if NOT ( (c GE ca AND c LE cz) OR (c GE c0 AND c LE c9) $
OR c EQ c_ ) then maybe = 1
endelse
if maybe then begin
;; If we found one, then strip out the value inside the
;; parentheses.
rest = strmid(ee, i+2, ll-i-2)
next = strtrim(strsplit(rest,')',/extract),2)
next = next[0]
pnames = [pnames, next]
endif
pos = i+1
endrep until pos GE ll
DONE_PARAMS:
if n_elements(pnames) EQ 1 then begin
message, 'ERROR: no parameters to fit', /info
return, !values.d_nan
endif
;; Finally, we take the maximum parameter number
pnames = pnames[1:*]
nparams = max(long(pnames)) + 1
if NOT keyword_set(quiet) then $
message, ' Number of parameters: '+strtrim(nparams,2) $
+ ' (initialized to zero)', /info
;; Create a parameter vector, starting at zero
p = dblarr(nparams)
endif
;; Use common block to pass data back and forth
common mpfitexpr_common, fc, xc, yc, ec, wc, mc
fc = expr & xc = x & yc = y & mc = 0L
;; These optional parameters must be undefined first
ec = 0 & dummy = size(temporary(ec))
wc = 0 & dummy = size(temporary(wc))
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
message, 'ERROR: ERROR value must not be zero. Use WEIGHTS.', $
/info
return, !values.d_nan
endif
ec = err
endif
;; Test out the function, as mpfit would call it, to see if it works
;; okay. There is no sense in calling the fitter if the function
;; itself doesn't work.
catch, catcherror
if catcherror NE 0 then begin
CATCH_ERROR:
catch, /cancel
message, 'ERROR: execution of "'+expr+'" failed.', /info
message, ' check syntax and parameter usage', /info
xc = 0 & yc = 0 & ec = 0 & wc = 0 & ac = 0
return, !values.d_nan
endif
;; Initialize. Function that is actually called is mpfitexpr_eval,
;; which is a wrapper that sets up the expression evaluation.
fcn = 'mpfitexpr_eval'
;; FCNARGS are passed by MPFIT directly to MPFITEXPR_EVAL. These
;; actually contain the data, the expression, and a slot to return
;; the model function.
fvec = call_function(fcn, p, _EXTRA=fcnargs)
if n_elements(fvec) EQ 1 then $
if NOT finite(fvec[0]) then goto, CATCH_ERROR
;; No errors caught if reached this stage
catch, /cancel
;; Call MPFIT
result = mpfit(fcn, p, $
parinfo=parinfo, STATUS=status, nfev=nfev, BESTNORM=bestnorm,$
covar=covar, perror=perror, functargs=fcnargs, $
niter=niter, nfree=nfree, npegged=npegged, dof=dof, $
ERRMSG=errmsg, quiet=quiet, _EXTRA=extra)
;; Retrieve the fit value
yfit = temporary(mc)
;; 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