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; NAME:
; TNMIN
;
; 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:
; Performs function minimization (Truncated-Newton Method)
;
; MAJOR TOPICS:
; Optimization and Minimization
;
; CALLING SEQUENCE:
; parms = TNMIN(MYFUNCT, X, FUNCTARGS=fcnargs, NFEV=nfev,
; MAXITER=maxiter, ERRMSG=errmsg, NPRINT=nprint,
; QUIET=quiet, XTOL=xtol, STATUS=status,
; FGUESS=fguess, PARINFO=parinfo, BESTMIN=bestmin,
; ITERPROC=iterproc, ITERARGS=iterargs, niter=niter)
;
; DESCRIPTION:
;
; TNMIN uses the Truncated-Newton method to minimize an arbitrary IDL
; function with respect to a given set of free parameters. The
; user-supplied function must compute the gradient with respect to
; each parameter. TNMIN is based on TN.F (TNBC) by Stephen Nash.
;
; If you want to solve a least-squares problem, to perform *curve*
; *fitting*, then you will probably want to use the routines MPFIT,
; MPFITFUN and MPFITEXPR. Those routines are specifically optimized
; for the least-squares problem. TNMIN is suitable for constrained
; and unconstrained optimization problems with a medium number of
; variables. Function *maximization* can be performed using the
; MAXIMIZE keyword.
;
; TNMIN is similar to MPFIT in that it allows parameters to be fixed,
; simple bounding limits to be placed on parameter values, and
; parameters to be tied to other parameters. One major difference
; between MPFIT and TNMIN is that TNMIN does not compute derivatives
; automatically by default. See PARINFO and AUTODERIVATIVE below for
; more discussion and examples.
;
; USER FUNCTION
;
; The user must define an IDL function which returns the desired
; value as a single scalar. The IDL function must accept a list of
; numerical parameters, P. Additionally, keyword parameters may be
; used to pass more data or information to the user function, via the
; FUNCTARGS keyword.
;
; The user function should be declared in the following way:
;
; FUNCTION MYFUNCT, p, dp [, keywords permitted ]
; ; Parameter values are passed in "p"
; f = .... ; Compute function value
; dp = .... ; Compute partial derivatives (optional)
; return, f
; END
;
; The function *must* accept at least one argument, the parameter
; list P. The vector P is implicitly assumed to be a one-dimensional
; array. Users may pass additional information to the function by
; composing and _EXTRA structure and passing it in the FUNCTARGS
; keyword.
;
; User functions may also indicate a fatal error condition using the
; ERROR_CODE common block variable, as described below under the
; TNMIN_ERROR common block definition (by setting ERROR_CODE to a
; number between -15 and -1).
;
; EXPLICIT vs. NUMERICAL DERIVATIVES
;
; By default, the user must compute the function gradient components
; explicitly using AUTODERIVATIVE=0. As explained below, numerical
; derivatives can also be calculated using AUTODERIVATIVE=1.
;
; For explicit derivatives, the user should call TNMIN using the
; default keyword value AUTODERIVATIVE=0. [ This is different
; behavior from MPFIT, where AUTODERIVATIVE=1 is the default. ] The
; IDL user routine should compute the gradient of the function as a
; one-dimensional array of values, one for each of the parameters.
; They are passed back to TNMIN via "dp" as shown above.
;
; The derivatives with respect to fixed parameters are ignored; zero
; is an appropriate value to insert for those derivatives. Upon
; input to the user function, DP is set to a vector with the same
; length as P, with a value of 1 for a parameter which is free, and a
; value of zero for a parameter which is fixed (and hence no
; derivative needs to be calculated). This input vector may be
; overwritten as needed.
;
; For numerical derivatives, a finite differencing approximation is
; used to estimate the gradient values. Users can activate this
; feature by passing the keyword AUTODERIVATIVE=1. Fine control over
; this behavior can be achieved using the STEP, RELSTEP and TNSIDE
; fields of the PARINFO structure.
;
; When finite differencing is used for computing derivatives (ie,
; when AUTODERIVATIVE=1), the parameter DP is not passed. Therefore
; functions can use N_PARAMS() to indicate whether they must compute
; the derivatives or not. However there is no penalty (other than
; computation time) for computing the gradient values and users may
; switch between AUTODERIVATIVE=0 or =1 in order to test both
; scenarios.
;
; CONSTRAINING PARAMETER VALUES WITH THE PARINFO KEYWORD
;
; The behavior of TNMIN can be modified with respect to each
; parameter to be optimized. 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 TNMIN.
;
; 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
; TNMIN, 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 TNMIN does not use this tag in any
; way.
;
; .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.
;
; .TNSIDE - 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.
;
; .TIED - a string expression which "ties" the parameter to other
; free or fixed parameters. 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 expressions. ]
;
; Future modifications to the PARINFO structure, if any, will involve
; adding structure tags beginning with the two letters "MP" or "TN".
; Therefore programmers are urged to avoid using tags starting with
; these two combinations of letters; otherwise they are free to
; include their own fields within the PARINFO structure, and they
; will be ignored.
;
; 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.
;
;
; INPUTS:
;
; MYFUNCT - a string variable containing the name of the function to
; be minimized (see USER FUNCTION above). The IDL routine
; should return the value of the function and optionally
; its gradients.
;
; X - An array of starting values for each of the parameters of the
; model.
;
; This parameter is optional if the PARINFO keyword is used.
; See above. The PARINFO keyword provides a mechanism to fix or
; constrain individual parameters. If both X and PARINFO are
; passed, then the starting *value* is taken from X, but the
; *constraints* are taken from PARINFO.
;
;
; RETURNS:
;
; Returns the array of best-fit parameters.
;
;
; KEYWORD PARAMETERS:
;
; AUTODERIVATIVE - If this is set, derivatives of the function will
; be computed automatically via a finite
; differencing procedure. If not set, then MYFUNCT
; must provide the (explicit) derivatives.
; Default: 0 (explicit derivatives required)
;
; BESTMIN - upon return, the best minimum function value that TNMIN
; could find.
;
; EPSABS - a nonnegative real variable. Termination occurs when the
; absolute error between consecutive iterates is at most
; EPSABS. Note that using EPSREL is normally preferable
; over EPSABS, except in cases where ABS(F) is much larger
; than 1 at the optimal point. A value of zero indicates
; the absolute error test is not applied. If EPSABS is
; specified, then both EPSREL and EPSABS tests are applied;
; if either succeeds then termination occurs.
; Default: 0 (i.e., only EPSREL is applied).
;
; EPSREL - a nonnegative input variable. Termination occurs when the
; relative error between two consecutive iterates is at
; most EPSREL. Therefore, EPSREL measures the relative
; error desired in the function. An additional, more
; lenient, stopping condition can be applied by specifying
; the EPSABS keyword.
; Default: 100 * Machine Precision
;
; ERRMSG - a string error or warning message is returned.
;
; FGUESS - provides the routine a guess to the minimum value.
; Default: 0
;
; 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.
;
; Consider the following example:
; if FUNCTARGS = { XVAL:[1.D,2,3], YVAL:[1.D,4,9]}
; then the user supplied function should be declared
; like this:
; FUNCTION MYFUNCT, P, XVAL=x, YVAL=y
;
; By default, no extra parameters are passed to the
; user-supplied function.
;
; 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.
;
; ITERDERIV - Intended to print function gradient information. If
; set, then the ITERDERIV keyword is set in each call to
; ITERPROC. In the default ITERPROC, parameter values
; and gradient information are both printed when this
; keyword is set.
;
; ITERPROC - The name of a procedure to be called upon each NPRINT
; iteration of the TNMIN routine. It should be declared
; in the following way:
;
; PRO ITERPROC, MYFUNCT, p, iter, fnorm, FUNCTARGS=fcnargs, $
; PARINFO=parinfo, QUIET=quiet, _EXTRA=extra
; ; perform custom iteration update
; END
;
; ITERPROC must accept the _EXTRA keyword, in case of
; future changes to the calling procedure.
;
; 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 is should be the function
; 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
; between -15 and -1 (see TNMIN_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 TNMIN returns.
; Default: 200 iterations
;
; MAXIMIZE - If set, the function is maximized instead of
; minimized.
;
; MAXNFEV - The maximum number of function evaluations to perform.
; If the number is exceeded, then the STATUS value is set
; to -17 and TNMIN returns. A value of zero indicates no
; maximum.
; Default: 0 (no maximum)
;
; NFEV - upon return, the number of MYFUNCT function evaluations
; performed.
;
; NITER - upon return, number of iterations completed.
;
; 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.
; 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 TNMIN.
;
; See description above for the structure of PARINFO.
;
; Default value: all parameters are free and unconstrained.
;
; QUIET - set this keyword when no textual output should be printed
; by TNMIN
;
; STATUS - an integer status code is returned. All values greater
; than zero can represent success (however STATUS EQ 5 may
; indicate failure to converge). Gaps in the numbering
; system below are to maintain compatibility with MPFIT.
; Upon return, STATUS can have one of the following values:
;
; -18 a fatal internal error occurred during optimization.
;
; -17 the maximum number of function evaluations has been
; reached without convergence.
;
; -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 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 TNMIN_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 TNMIN.
;
; 0 improper input parameters.
;
; 1 convergence was reached.
;
; 2-4 (RESERVED)
;
; 5 the maximum number of iterations has been reached
;
; 6-8 (RESERVED)
;
;
; EXAMPLE:
;
; FUNCTION F, X, DF, _EXTRA=extra ;; *** MUST ACCEPT KEYWORDS
; F = (X(0)-1)^2 + (X(1)+7)^2
; DF = [ 2D * (X(0)-1), 2D * (X(1)+7) ] ; Gradient
; RETURN, F
; END
;
; P = TNMIN('F', [0D, 0D], BESTMIN=F0)
; Minimizes the function F(x0,x1) = (x0-1)^2 + (x1+7)^2.
;
;
; COMMON BLOCKS:
;
; COMMON TNMIN_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, TNMIN 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:
;
; TRUNCATED-NEWTON METHOD, TN.F
; Stephen G. Nash, Operations Research and Applied Statistics
; Department
; http://www.netlib.org/opt/tn
;
; Nash, S. G. 1984, "Newton-Type Minimization via the Lanczos
; Method," SIAM J. Numerical Analysis, 21, p. 770-778
;
;
; MODIFICATION HISTORY:
; Derived from TN.F by Stephen Nash with many changes and additions,
; to conform to MPFIT paradigm, 19 Jan 1999, CM
; Changed web address to COW, 25 Sep 1999, CM
; Alphabetized documented keyword parameters, 02 Oct 1999, CM
; Changed to ERROR_CODE for error condition, 28 Jan 2000, CM
; Continued and fairly major improvements (CM, 08 Jan 2001):
; - calling of user procedure is now concentrated in TNMIN_CALL,
; and arguments are reduced by storing a large number of them
; in common blocks;
; - finite differencing is done within TNMIN_CALL; added
; AUTODERIVATIVE=1 so that finite differencing can be enabled,
; both one and two sided;
; - a new procedure to parse PARINFO fields, borrowed from MPFIT;
; brought PARINFO keywords up to date with MPFIT;
; - go through and check for float vs. double discrepancies;
; - add explicit MAXIMIZE keyword, and support in TNMIN_CALL and
; TNMIN_DEFITER to print the correct values in that case;
; TNMIN_DEFITER now prints function gradient values if
; requested;
; - convert to common-based system of MPFIT for storing machine
; constants; revert TNMIN_ENORM to simple sum of squares, at
; least for now;
; - remove limit on number of function evaluations, at least for
; now, and until I can understand what happens when we do
; numerical derivatives.
; Further changes: more float vs double; disable TNMINSTEP for now;
; experimented with convergence test in case of function
; maximization, 11 Jan 2001, CM
; TNMINSTEP is parsed but not enabled, 13 Mar 2001
; Major code cleanups; internal docs; reduced commons, CM, 08 Apr
; 2001
; Continued code cleanups; documentation; the STATUS keyword
; actually means something, CM, 10 Apr 2001
; Added reference to Nash paper, CM, 08 Feb 2002
; Fixed 16-bit loop indices, D. Schelgel, 22 Apr 2003
; Changed parens to square brackets because of conflicts with
; limits function. K. Tolbert, 23 Feb 2005
; Some documentation clarifications, CM, 09 Nov 2007
; Ensure that MY_FUNCT returns a scalar; make it more likely that
; error messages get back out to the user; fatal CATCH'd error
; now returns STATUS = -18, CM, 17 Sep 2008
; Fix TNMIN_CALL when parameters are TIEd (thanks to Alfred de
; Wijn), CM, 22 Nov 2009
; Remember to TIE the parameters before final return (thanks to
; Michael Smith), CM, 20 Jan 2010
;
; TODO
; - scale derivatives semi-automatically;
; - ability to scale and offset parameters;
;
; $Id: tnmin.pro,v 1.20 2016/05/19 16:08:08 cmarkwar Exp $
;-
; Copyright (C) 1998-2001,2002,2003,2007,2008,2009 Craig Markwardt
; This software is provided as is without any warranty whatsoever.
; Permission to use, copy and distribute unmodified copies for
; non-commercial purposes, and to modify and use for personal or
; internal use, is granted. All other rights are reserved.
;-
;%% TRUNCATED-NEWTON METHOD: SUBROUTINES
; FOR OTHER MACHINES, MODIFY ROUTINE MCHPR1 (MACHINE EPSILON)
; WRITTEN BY: STEPHEN G. NASH
; OPERATIONS RESEARCH AND APPLIED STATISTICS DEPT.
; GEORGE MASON UNIVERSITY
; FAIRFAX, VA 22030
;******************************************************************
;; Routine which declares functions and common blocks
pro tnmin_dummy
forward_function tnmin_enorm, tnmin_step1, tnmin
forward_function tnmin_call, tnmin_autoder
common tnmin_error, error_code
common tnmin_machar, tnmin_machar_vals
common tnmin_config, tnmin_tnconfig
common tnmin_fcnargs, tnmin_tnfcnargs
common tnmin_work, lsk, lyk, ldiagb, lsr, lyr
a = 1
return
end
;; Following are machine constants that can be loaded once. I have
;; found that bizarre underflow messages can be produced in each call
;; to MACHAR(), so this structure minimizes the number of calls to
;; one.
pro tnmin_setmachar, double=isdouble
common tnmin_machar, tnmin_machar_vals
;; In earlier versions of IDL, MACHAR itself could produce a load of
;; error messages. We try to mask some of that out here.
if (!version.release) LT 5 then dummy = check_math(1, 1)
mch = 0.
mch = machar(double=keyword_set(isdouble))
dmachep = mch.eps
dmaxnum = mch.xmax
dminnum = mch.xmin
dmaxlog = alog(mch.xmax)
dminlog = alog(mch.xmin)
if keyword_set(isdouble) then $
dmaxgam = 171.624376956302725D $
else $
dmaxgam = 171.624376956302725
drdwarf = sqrt(dminnum*1.5) * 10
drgiant = sqrt(dmaxnum) * 0.1
tnmin_machar_vals = {machep: dmachep, maxnum: dmaxnum, minnum: dminnum, $
maxlog: dmaxlog, minlog: dminlog, maxgam: dmaxgam, $
rdwarf: drdwarf, rgiant: drgiant}
if (!version.release) LT 5 then dummy = check_math(0, 0)
return
end
;; Procedure to parse the parameter values in PARINFO
pro tnmin_parinfo, parinfo, tnames, tag, values, default=def, status=status, $
n_param=n
status = 0
if n_elements(n) EQ 0 then n = n_elements(parinfo)
if n EQ 0 then begin
if n_elements(def) EQ 0 then return
values = def
status = 1
return
endif
if n_elements(parinfo) EQ 0 then goto, DO_DEFAULT
if n_elements(tnames) EQ 0 then tnames = tag_names(parinfo)
wh = where(tnames EQ tag, ct)
if ct EQ 0 then begin
DO_DEFAULT:
if n_elements(def) EQ 0 then return
values = make_array(n, value=def(0))
values(0) = def
endif else begin
values = parinfo.(wh(0))
endelse
status = 1
return
end
;; Procedure to tie one parameter to another.
pro tnmin_tie, p, _ptied
_wh = where(_ptied NE '', _ct)
if _ct EQ 0 then return
for _i = 0L, _ct-1 do begin
_cmd = 'p('+strtrim(_wh(_i),2)+') = '+_ptied(_wh(_i))
_err = execute(_cmd)
if _err EQ 0 then begin
message, 'ERROR: Tied expression "'+_cmd+'" failed.'
return
endif
endfor
end
function tnmin_autoder, fcn, x, dx, dside=dside
common tnmin_machar, machvals
common tnmin_config, tnconfig
MACHEP0 = machvals.machep
DWARF = machvals.minnum
if n_elements(dside) NE n_elements(x) then dside = tnconfig.dside
eps = sqrt(MACHEP0)
h = eps * (1. + abs(x))
;; if STEP is given, use that
wh = where(tnconfig.step GT 0, ct)
if ct GT 0 then h(wh) = tnconfig.step(wh)
;; if relative step is given, use that
wh = where(tnconfig.dstep GT 0, ct)
if ct GT 0 then h(wh) = abs(tnconfig.dstep(wh)*x(wh))
;; In case any of the step values are zero
wh = where(h EQ 0, ct)
if ct GT 0 then h(wh) = eps
;; Reverse the sign of the step if we are up against the parameter
;; limit, or if the user requested it.
mask = (dside EQ -1 OR (tnconfig.ulimited AND (x GT tnconfig.ulimit-h)))
wh = where(mask, ct)
if ct GT 0 then h(wh) = -h(wh)
dx = x * 0.
f = tnmin_call(fcn, x)
for i = 0L, n_elements(x)-1 do begin
if tnconfig.pfixed(i) EQ 1 then goto, NEXT_PAR
hh = h(i)
RESTART_PAR:
xp = x
xp(i) = xp(i) + hh
fp = tnmin_call(fcn, xp)
if abs(dside(i)) LE 1 then begin
;; COMPUTE THE ONE-SIDED DERIVATIVE
dx(i) = (fp-f)/hh
endif else begin
;; COMPUTE THE TWO-SIDED DERIVATIVE
xp(i) = x(i) - hh
fm = tnmin_call(fcn, xp)
dx(i) = (fp-fm)/(2*hh)
endelse
NEXT_PAR:
endfor
return, f
end
;; Call user function or procedure, with _EXTRA or not, with
;; derivatives or not.
function tnmin_call, fcn, x1, dx, fullparam_=xall
; on_error, 2
common tnmin_config, tnconfig
common tnmin_fcnargs, fcnargs
ifree = tnconfig.ifree
;; Following promotes the byte array to a floating point array so
;; that users who simply re-fill the array aren't surprised when
;; their gradient comes out as bytes. :-)
dx = tnconfig.pfixed + x1(0)*0.
if n_elements(xall) GT 0 then begin
x = xall
x(ifree) = x1
endif else begin
x = x1
endelse
;; Enforce TIEd parameters
if keyword_set(tnconfig.qanytied) then tnmin_tie, x, tnconfig.ptied
;; Decide whether we are calling a procedure or function
if tnconfig.proc then proc = 1 else proc = 0
tnconfig.nfev = tnconfig.nfev + 1
if n_params() EQ 3 then begin
if tnconfig.autoderiv then $
f = tnmin_autoder(fcn, x, dx) $
else if n_elements(fcnargs) GT 0 then $
f = call_function(fcn, x, dx, _EXTRA=fcnargs) $
else $
f = call_function(fcn, x, dx)
dx = dx(ifree)
if tnconfig.max then begin
dx = -dx
f = -f
endif
endif else begin
if n_elements(fcnargs) GT 0 then $
f = call_function(fcn, x, _EXTRA=fcnargs) $
else $
f = call_function(fcn, x)
if n_elements(f) NE 1 then begin
message, 'ERROR: function "'+fcn+'" returned a vector when '+$
'a scalar was expected.'
endif
endelse
if n_elements(f) GT 1 then return, f $
else return, f(0)
end
function tnmin_enorm, vec
common tnmin_config, tnconfig
;; Very simple-minded sum-of-squares
if n_elements(tnconfig) GT 0 then if tnconfig.fastnorm then begin
ans = sqrt(total(vec^2,1))
goto, TERMINATE
endif
common tnmin_machar, machvals
agiant = machvals.rgiant / n_elements(vec)
adwarf = machvals.rdwarf * n_elements(vec)
;; This is hopefully a compromise between speed and robustness.
;; Need to do this because of the possibility of over- or underflow.
mx = max(vec, min=mn)
mx = max(abs([mx,mn]))
if mx EQ 0 then return, vec(0)* 0.
if mx GT agiant OR mx LT adwarf then ans = mx * sqrt(total((vec/mx)^2)) $
else ans = sqrt( total(vec^2) )
TERMINATE:
return, ans
end
;
; ROUTINES TO INITIALIZE PRECONDITIONER
;
pro tnmin_initpc, diagb, emat, n, upd1, yksk, gsk, yrsr, lreset
;; Rename common variables as they appear in INITP3. Those
;; indicated in all caps are not used or renamed here.
; common tnmin_work, lsk, lyk, ldiagb, lsr, lyr
common tnmin_work, sk, yk, LDIAGB, sr, yr
; I I I I
;; From INITP3
if keyword_set(upd1) then begin
EMAT = DIAGB
endif else if keyword_set(lreset) then begin
BSK = DIAGB*SK
SDS = TOTAL(SK*BSK)
EMAT = DIAGB - DIAGB*DIAGB*SK*SK/SDS + YK*YK/YKSK
endif else begin
BSK = DIAGB * SR
SDS = TOTAL(SR*BSK)
SRDS = TOTAL(SK*BSK)
YRSK = TOTAL(YR*SK)
BSK = DIAGB*SK - BSK*SRDS/SDS+YR*YRSK/YRSR
EMAT = DIAGB-DIAGB*DIAGB*SR*SR/SDS+YR*YR/YRSR
SDS = TOTAL(SK*BSK)
EMAT = EMAT - BSK*BSK/SDS+YK*YK/YKSK
endelse
return
end
pro tnmin_ssbfgs, n, gamma, sj, yj, hjv, hjyj, yjsj, yjhyj, $
vsj, vhyj, hjp1v
;
; SELF-SCALED BFGS
;
DELTA = (1. + GAMMA*YJHYJ/YJSJ)*VSJ/YJSJ - GAMMA*VHYJ/YJSJ
BETA = -GAMMA*VSJ/YJSJ
HJP1V = GAMMA*HJV + DELTA*SJ + BETA*HJYJ
RETURN
end
;
; THIS ROUTINE ACTS AS A PRECONDITIONING STEP FOR THE
; LINEAR CONJUGATE-GRADIENT ROUTINE. IT IS ALSO THE
; METHOD OF COMPUTING THE SEARCH DIRECTION FROM THE
; GRADIENT FOR THE NON-LINEAR CONJUGATE-GRADIENT CODE.
; IT REPRESENTS A TWO-STEP SELF-SCALED BFGS FORMULA.
;
pro tnmin_msolve, g, y, n, upd1, yksk, gsk, yrsr, lreset, first, $
hyr, hyk, ykhyk, yrhyr
;; Rename common variables as they appear in MSLV
; common tnmin_work, lsk, lyk, ldiagb, lsr, lyr
common tnmin_work, sk, yk, diagb, sr, yr
; I I I I I
;; From MSLV
if keyword_set(UPD1) then begin
Y = G / DIAGB
RETURN
endif
ONE = G(0)*0 + 1.
GSK = TOTAL(G*SK)
if keyword_set(lreset) then begin
;
; COMPUTE GH AND HY WHERE H IS THE INVERSE OF THE DIAGONALS
;
HG = G/DIAGB
if keyword_set(FIRST) then begin
HYK = YK/DIAGB
YKHYK = TOTAL(YK*HYK)
endif
GHYK = TOTAL(G*HYK)
TNMIN_SSBFGS,N,ONE,SK,YK,HG,HYK,YKSK, YKHYK,GSK,GHYK,Y
RETURN
endif
;
; COMPUTE HG AND HY WHERE H IS THE INVERSE OF THE DIAGONALS
;
HG = G/DIAGB
if keyword_set(FIRST) then begin
HYK = YK/DIAGB
HYR = YR/DIAGB
YKSR = TOTAL(YK*SR)
YKHYR = TOTAL(YK*HYR)
endif
GSR = TOTAL(G*SR)
GHYR = TOTAL(G*HYR)
if keyword_set(FIRST) then begin
YRHYR = TOTAL(YR*HYR)
endif
TNMIN_SSBFGS,N,ONE,SR,YR,HG,HYR,YRSR, YRHYR,GSR,GHYR,HG
if keyword_set(FIRST) then begin
TNMIN_SSBFGS,N,ONE,SR,YR,HYK,HYR,YRSR, YRHYR,YKSR,YKHYR,HYK
endif
YKHYK = TOTAL(HYK*YK)
GHYK = TOTAL(HYK*G)
TNMIN_SSBFGS,N,ONE,SK,YK,HG,HYK,YKSK, YKHYK,GSK,GHYK,Y
RETURN
end
;
; THIS ROUTINE COMPUTES THE PRODUCT OF THE MATRIX G TIMES THE VECTOR
; V AND STORES THE RESULT IN THE VECTOR GV (FINITE-DIFFERENCE VERSION)
;
pro tnmin_gtims, v, gv, n, x, g, fcn, first, delta, accrcy, xnorm, $
xnew
IF keyword_set(FIRST) THEN BEGIN
;; Extra factor of ten is to avoid clashing with the finite
;; difference scheme which computes the derivatives
DELTA = SQRT(100*ACCRCY)*(1.+XNORM) ;; XXX diff than TN.F
; DELTA = SQRT(ACCRCY)*(1.+XNORM)
FIRST = 0
ENDIF
DINV = 1. /DELTA
F = tnmin_call(FCN, X + DELTA*V, GV, fullparam_=xnew)
GV = (GV-G)*DINV
return
end
;
; UPDATE THE PRECONDITIOING MATRIX BASED ON A DIAGONAL VERSION
; OF THE BFGS QUASI-NEWTON UPDATE.
;
pro tnmin_ndia3, n, e, v, gv, r, vgv
VR = TOTAL(V*R)
E = E - R*R/VR + GV*GV/VGV
wh = where(e LE 1D-6, ct)
if ct GT 0 then e(wh) = 1
return
end
pro tnmin_fix, whlpeg, whupeg, z
if whlpeg(0) NE -1 then z(whlpeg) = 0
if whupeg(0) NE -1 then z(whupeg) = 0
end
;
; THIS ROUTINE PERFORMS A PRECONDITIONED CONJUGATE-GRADIENT
; ITERATION IN ORDER TO SOLVE THE NEWTON EQUATIONS FOR A SEARCH
; DIRECTION FOR A TRUNCATED-NEWTON ALGORITHM. WHEN THE VALUE OF THE
; QUADRATIC MODEL IS SUFFICIENTLY REDUCED,
; THE ITERATION IS TERMINATED.
;
; PARAMETERS
;
; ZSOL - COMPUTED SEARCH DIRECTION
; G - CURRENT GRADIENT
; GV,GZ1,V - SCRATCH VECTORS
; R - RESIDUAL
; DIAGB,EMAT - DIAGONAL PRECONDITONING MATRIX
; NITER - NONLINEAR ITERATION #
; FEVAL - VALUE OF QUADRATIC FUNCTION
pro tnmin_modlnp, zsol, gv, r, v, diagb, emat, $
x, g, zk, n, niter, maxit, nmodif, nlincg, $
upd1, yksk, gsk, yrsr, lreset, fcn, whlpeg, whupeg, $
accrcy, gtp, gnorm, xnorm, xnew
;
; GENERAL INITIALIZATION
;
zero = x(0)* 0.
one = zero + 1
IF (MAXIT EQ 0) THEN RETURN
FIRST = 1
RHSNRM = GNORM
TOL = zero + 1.E-12
QOLD = zero
;
; INITIALIZATION FOR PRECONDITIONED CONJUGATE-GRADIENT ALGORITHM
;
tnmin_initpc, diagb, emat, n, upd1, yksk, gsk, yrsr, lreset
R = -G
V = G*0.
ZSOL = V
;
; ************************************************************
; MAIN ITERATION
; ************************************************************
;
FOR K = 1L, MAXIT DO BEGIN
NLINCG = NLINCG + 1
;
; CG ITERATION TO SOLVE SYSTEM OF EQUATIONS
;
tnmin_fix, whlpeg, whupeg, r
TNMIN_MSOLVE, R, ZK, N, UPD1, YKSK, GSK, YRSR, LRESET, FIRST, $
HYR, HYK, YKHYK, YRHYR
tnmin_fix, whlpeg, whupeg, zk
RZ = TOTAL(R*ZK)
IF (RZ/RHSNRM LT TOL) THEN GOTO, MODLNP_80
IF (K EQ 1) THEN BETA = ZERO $
ELSE BETA = RZ/RZOLD
V = ZK + BETA*V
tnmin_fix, whlpeg, whupeg, v
TNMIN_GTIMS, V, GV, N, X, G, FCN, FIRST, DELTA, ACCRCY, XNORM, XNEW
tnmin_fix, whlpeg, whupeg, gv
VGV = TOTAL(V*GV)
IF (VGV/RHSNRM LT TOL) THEN GOTO, MODLNP_50
TNMIN_NDIA3, N,EMAT,V,GV,R,VGV
;
; COMPUTE LINEAR STEP LENGTH
;
ALPHA = RZ / VGV
;
; COMPUTE CURRENT SOLUTION AND RELATED VECTORS
;
ZSOL = ZSOL + ALPHA*V
R = R - ALPHA*GV
;
; TEST FOR CONVERGENCE
;
GTP = TOTAL(ZSOL*G)
PR = TOTAL(R*ZSOL)
QNEW = 5.E-1 * (GTP + PR)
QTEST = K * (1.E0 - QOLD/QNEW)
IF (QTEST LT 0.D0) THEN GOTO, MODLNP_70
QOLD = QNEW
IF (QTEST LE 5.D-1) THEN GOTO, MODLNP_70
;
; PERFORM CAUTIONARY TEST
;
IF (GTP GT 0) THEN GOTO, MODLNP_40
RZOLD = RZ
ENDFOR
;
; TERMINATE ALGORITHM
;
K = K-1
goto, MODLNP_70
MODLNP_40:
ZSOL = ZSOL - ALPHA*V
GTP = TOTAL(ZSOL*G)
goto, MODLNP_90
MODLNP_50:
;; printed output
MODLNP_60:
IF (K GT 1) THEN GOTO, MODLNP_70
TNMIN_MSOLVE,G,ZSOL,N,UPD1,YKSK,GSK,YRSR,LRESET,FIRST, $
HYR, HYK, YKHYK, YRHYR
ZSOL = -ZSOL
tnmin_fix, whlpeg, whupeg, zsol
GTP = TOTAL(ZSOL*G)
MODLNP_70:
goto, MODLNP_90
MODLNP_80:
IF (K GT 1) THEN GOTO, MODLNP_70
ZSOL = -G
tnmin_fix, whlpeg, whupeg, zsol
GTP = TOTAL(ZSOL*G)
goto, MODLNP_70
;
; STORE (OR RESTORE) DIAGONAL PRECONDITIONING
;
MODLNP_90:
diagb = emat
return
end
function tnmin_step1, fnew, fm, gtp, smax, epsmch
; ********************************************************
; STEP1 RETURNS THE LENGTH OF THE INITIAL STEP TO BE TAKEN ALONG THE
; VECTOR P IN THE NEXT LINEAR SEARCH.
; ********************************************************
D = ABS(FNEW-FM)
ALPHA = FNEW(0)*0 + 1.
IF (2.D0*D LE (-GTP) AND D GE EPSMCH) THEN $
ALPHA = -2.*D/GTP
IF (ALPHA GE SMAX) THEN ALPHA = SMAX
return, alpha
end
;
; ************************************************************
; GETPTC, AN ALGORITHM FOR FINDING A STEPLENGTH, CALLED REPEATEDLY BY
; ROUTINES WHICH REQUIRE A STEP LENGTH TO BE COMPUTED USING CUBIC
; INTERPOLATION. THE PARAMETERS CONTAIN INFORMATION ABOUT THE INTERVAL
; IN WHICH A LOWER POINT IS TO BE FOUND AND FROM THIS GETPTC COMPUTES A
; POINT AT WHICH THE FUNCTION CAN BE EVALUATED BY THE CALLING PROGRAM.
; THE VALUE OF THE INTEGER PARAMETERS IENTRY DETERMINES THE PATH TAKEN
; THROUGH THE CODE.
; ************************************************************
pro tnmin_getptc, big, small, rtsmll, reltol, abstol, tnytol, $
fpresn, eta, rmu, xbnd, u, fu, gu, xmin, fmin, gmin, $
xw, fw, gw, a, b, oldf, b1, scxbnd, e, step, factor, $
braktd, gtest1, gtest2, tol, ientry, itest
;; This chicanery is so that we get the data types right
ZERO = fu(0)* 0.
; a1 = zero & scale = zero & chordm = zero
; chordu = zero & d1 = zero & d2 = zero
; denom = zero
POINT1 = ZERO + 0.1
HALF = ZERO + 0.5
ONE = ZERO + 1
THREE = ZERO + 3
FIVE = ZERO + 5
ELEVEN = ZERO + 11
if ientry EQ 1 then begin ;; else clause = 20 (OK)
;
; IENTRY=1
; CHECK INPUT PARAMETERS
;
;; GETPTC_10:
ITEST = 2
IF (U LE ZERO OR XBND LE TNYTOL OR GU GT ZERO) THEN RETURN
ITEST = 1
IF (XBND LT ABSTOL) THEN ABSTOL = XBND
TOL = ABSTOL
TWOTOL = TOL + TOL
;
; A AND B DEFINE THE INTERVAL OF UNCERTAINTY, X AND XW ARE POINTS
; WITH LOWEST AND SECOND LOWEST FUNCTION VALUES SO FAR OBTAINED.
; INITIALIZE A,SMIN,XW AT ORIGIN AND CORRESPONDING VALUES OF
; FUNCTION AND PROJECTION OF THE GRADIENT ALONG DIRECTION OF SEARCH
; AT VALUES FOR LATEST ESTIMATE AT MINIMUM.
;
A = ZERO
XW = ZERO
XMIN = ZERO
OLDF = FU
FMIN = FU
FW = FU
GW = GU
GMIN = GU
STEP = U
FACTOR = FIVE
;
; THE MINIMUM HAS NOT YET BEEN BRACKETED.
;
BRAKTD = 0
;
; SET UP XBND AS A BOUND ON THE STEP TO BE TAKEN. (XBND IS NOT COMPUTED
; EXPLICITLY BUT SCXBND IS ITS SCALED VALUE.) SET THE UPPER BOUND
; ON THE INTERVAL OF UNCERTAINTY INITIALLY TO XBND + TOL(XBND).
;
SCXBND = XBND
B = SCXBND + RELTOL*ABS(SCXBND) + ABSTOL
E = B + B
B1 = B
;
; COMPUTE THE CONSTANTS REQUIRED FOR THE TWO CONVERGENCE CRITERIA.
;
GTEST1 = -RMU*GU
GTEST2 = -ETA*GU
;
; SET IENTRY TO INDICATE THAT THIS IS THE FIRST ITERATION
;
IENTRY = 2
goto, GETPTC_210
endif
;
; IENTRY = 2
;
; UPDATE A,B,XW, AND XMIN
;
;; GETPTC_20:
IF (FU GT FMIN) THEN GOTO, GETPTC_60
;
; IF FUNCTION VALUE NOT INCREASED, NEW POINT BECOMES NEXT
; ORIGIN AND OTHER POINTS ARE SCALED ACCORDINGLY.
;
CHORDU = OLDF - (XMIN + U)*GTEST1
if NOT (FU LE CHORDU) then begin
;
; THE NEW FUNCTION VALUE DOES NOT SATISFY THE SUFFICIENT DECREASE
; CRITERION. PREPARE TO MOVE THE UPPER BOUND TO THIS POINT AND
; FORCE THE INTERPOLATION SCHEME TO EITHER BISECT THE INTERVAL OF
; UNCERTAINTY OR TAKE THE LINEAR INTERPOLATION STEP WHICH ESTIMATES
; THE ROOT OF F(ALPHA)=CHORD(ALPHA).
;
CHORDM = OLDF - XMIN*GTEST1
GU = -GMIN
DENOM = CHORDM-FMIN
IF (ABS(DENOM) LT 1.D-15) THEN BEGIN
DENOM = ZERO + 1.E-15
IF (CHORDM-FMIN LT 0.D0) THEN DENOM = -DENOM
ENDIF
IF (XMIN NE ZERO) THEN GU = GMIN*(CHORDU-FU)/DENOM
FU = (HALF*U*(GMIN+GU) + FMIN) > FMIN
;
; IF FUNCTION VALUE INCREASED, ORIGIN REMAINS UNCHANGED
; BUT NEW POINT MAY NOW QUALIFY AS W.
;
GETPTC_60:
IF (U GE ZERO) THEN BEGIN
B = U
BRAKTD = 1
ENDIF ELSE BEGIN
A = U
ENDELSE
XW = U
FW = FU
GW = GU
endif else begin
;; GETPTC_30:
FW = FMIN
FMIN = FU
GW = GMIN
GMIN = GU
XMIN = XMIN + U
A = A-U
B = B-U
XW = -U
SCXBND = SCXBND - U
IF (GU GT ZERO) THEN BEGIN
B = ZERO
BRAKTD = 1
ENDIF ELSE BEGIN
A = ZERO
ENDELSE
TOL = ABS(XMIN)*RELTOL + ABSTOL
endelse
TWOTOL = TOL + TOL
XMIDPT = HALF*(A + B)
;
; CHECK TERMINATION CRITERIA
;
CONVRG = ABS(XMIDPT) LE TWOTOL - HALF*(B-A) OR $
ABS(GMIN) LE GTEST2 AND FMIN LT OLDF AND $
(ABS(XMIN - XBND) GT TOL OR NOT BRAKTD)
IF CONVRG THEN BEGIN
ITEST = 0
IF (XMIN NE ZERO) THEN RETURN
;
; IF THE FUNCTION HAS NOT BEEN REDUCED, CHECK TO SEE THAT THE RELATIVE
; CHANGE IN F(X) IS CONSISTENT WITH THE ESTIMATE OF THE DELTA-
; UNIMODALITY CONSTANT, TOL. IF THE CHANGE IN F(X) IS LARGER THAN
; EXPECTED, REDUCE THE VALUE OF TOL.
;
ITEST = 3
IF (ABS(OLDF-FW) LE FPRESN*(ONE + ABS(OLDF))) THEN RETURN
TOL = POINT1*TOL
IF (TOL LT TNYTOL) THEN RETURN
RELTOL = POINT1*RELTOL
ABSTOL = POINT1*ABSTOL
TWOTOL = POINT1*TWOTOL
endif
;
; CONTINUE WITH THE COMPUTATION OF A TRIAL STEP LENGTH
;
;; GETPTC_100:
R = ZERO
Q = ZERO
S = ZERO
IF (ABS(E) GT TOL) THEN BEGIN
;
; FIT CUBIC THROUGH XMIN AND XW
;
R = THREE*(FMIN-FW)/XW + GMIN + GW
ABSR = ABS(R)
Q = ABSR
IF (GW EQ ZERO OR GMIN EQ ZERO) EQ 0 THEN BEGIN ;; else clause = 140 (OK)
;
; COMPUTE THE SQUARE ROOT OF (R*R - GMIN*GW) IN A WAY
; WHICH AVOIDS UNDERFLOW AND OVERFLOW.
;
ABGW = ABS(GW)
ABGMIN = ABS(GMIN)
S = SQRT(ABGMIN)*SQRT(ABGW)
IF ((GW/ABGW)*GMIN LE ZERO) THEN BEGIN
;
; COMPUTE THE SQUARE ROOT OF R*R + S*S.
;
SUMSQ = ONE
P = ZERO
IF (ABSR LT S) THEN BEGIN ;; else clause = 110 (OK)
;
; THERE IS A POSSIBILITY OF OVERFLOW.
;
IF (S GT RTSMLL) THEN P = S*RTSMLL
IF (ABSR GE P) THEN SUMSQ = ONE +(ABSR/S)^2
SCALE = S
endif else begin ;; flow to 120 (OK)
;
; THERE IS A POSSIBILITY OF UNDERFLOW.
;
;; GETPTC_110:
IF (ABSR GT RTSMLL) THEN P = ABSR*RTSMLL
IF (S GE P) THEN SUMSQ = ONE + (S/ABSR)^2
SCALE = ABSR
ENDELSE ;; flow to 120 (OK)
;; GETPTC_120:
SUMSQ = SQRT(SUMSQ)
Q = BIG
IF (SCALE LT BIG/SUMSQ) THEN Q = SCALE*SUMSQ
endif else begin ;; flow to 140
;
; COMPUTE THE SQUARE ROOT OF R*R - S*S
;
;; GETPTC_130:
Q = SQRT(ABS(R+S))*SQRT(ABS(R-S))
IF (R GE S OR R LE (-S)) EQ 0 THEN BEGIN
R = ZERO
Q = ZERO
goto, GETPTC_150
endif
endelse
endif
;
; COMPUTE THE MINIMUM OF FITTED CUBIC
;
;; GETPTC_140:
IF (XW LT ZERO) THEN Q = -Q
S = XW*(GMIN - R - Q)
Q = GW - GMIN + Q + Q
IF (Q GT ZERO) THEN S = -S
IF (Q LE ZERO) THEN Q = -Q
R = E
IF (B1 NE STEP OR BRAKTD) THEN E = STEP
endif
;
; CONSTRUCT AN ARTIFICIAL BOUND ON THE ESTIMATED STEPLENGTH
;
GETPTC_150:
A1 = A
B1 = B
STEP = XMIDPT
IF (BRAKTD) EQ 0 THEN BEGIN ;; else flow to 160 (OK)
STEP = -FACTOR*XW
IF (STEP GT SCXBND) THEN STEP = SCXBND
IF (STEP NE SCXBND) THEN FACTOR = FIVE*FACTOR
;; flow to 170 (OK)
endif else begin
;
; IF THE MINIMUM IS BRACKETED BY 0 AND XW THE STEP MUST LIE
; WITHIN (A,B).
;
;; GETPTC_160:
if (a NE zero OR xw GE zero) AND (b NE zero OR xw LE zero) then $
goto, GETPTC_180
;
; IF THE MINIMUM IS NOT BRACKETED BY 0 AND XW THE STEP MUST LIE
; WITHIN (A1,B1).
;
D1 = XW
D2 = A
IF (A EQ ZERO) THEN D2 = B
; THIS LINE MIGHT BE
; IF (A EQ ZERO) THEN D2 = E
U = - D1/D2
STEP = FIVE*D2*(POINT1 + ONE/U)/ELEVEN
IF (U LT ONE) THEN STEP = HALF*D2*SQRT(U)
endelse
;; GETPTC_170:
IF (STEP LE ZERO) THEN A1 = STEP
IF (STEP GT ZERO) THEN B1 = STEP
;
; REJECT THE STEP OBTAINED BY INTERPOLATION IF IT LIES OUTSIDE THE
; REQUIRED INTERVAL OR IT IS GREATER THAN HALF THE STEP OBTAINED
; DURING THE LAST-BUT-ONE ITERATION.
;
GETPTC_180:
if NOT (abs(s) LE abs(half*q*r) OR s LE q*a1 OR s GE q*b1) then begin
;; else clause = 200 (OK)
;
; A CUBIC INTERPOLATION STEP
;
STEP = S/Q
;
; THE FUNCTION MUST NOT BE EVALUTATED TOO CLOSE TO A OR B.
;
if NOT (step - a GE twotol AND b - step GE twotol) then begin
;; else clause = 210 (OK)
IF (XMIDPT LE ZERO) THEN STEP = -TOL ELSE STEP = TOL
endif ;; flow to 210 (OK)
endif else begin
;; GETPTC_200:
E = B-A
endelse
;
; IF THE STEP IS TOO LARGE, REPLACE BY THE SCALED BOUND (SO AS TO
; COMPUTE THE NEW POINT ON THE BOUNDARY).
;
GETPTC_210:
if (step GE scxbnd) then begin ;; else clause = 220 (OK)
STEP = SCXBND
;
; MOVE SXBD TO THE LEFT SO THAT SBND + TOL(XBND) = XBND.
;
SCXBND = SCXBND - (RELTOL*ABS(XBND)+ABSTOL)/(ONE + RELTOL)
endif
;; GETPTC_220:
U = STEP
IF (ABS(STEP) LT TOL AND STEP LT ZERO) THEN U = -TOL
IF (ABS(STEP) LT TOL AND STEP GE ZERO) THEN U = TOL
ITEST = 1
RETURN
end
;
; LINE SEARCH ALGORITHMS OF GILL AND MURRAY
;
pro tnmin_linder, n, fcn, small, epsmch, reltol, abstol, $
tnytol, eta, sftbnd, xbnd, p, gtp, x, f, alpha, g, $
iflag, xnew
zero = f(0) * 0.
one = zero + 1.
LSPRNT = 0L
NPRNT = 10000L
RTSMLL = SQRT(SMALL)
BIG = 1./SMALL
ITCNT = 0L
;
; SET THE ESTIMATED RELATIVE PRECISION IN F(X).
;
FPRESN = 10.*EPSMCH
U = ALPHA
FU = F
FMIN = F
GU = GTP
RMU = zero + 1E-4
;
; FIRST ENTRY SETS UP THE INITIAL INTERVAL OF UNCERTAINTY.
;
IENTRY = 1L
LINDER_10:
;
; TEST FOR TOO MANY ITERATIONS
;
ITCNT = ITCNT + 1
IF (ITCNT GT 30) THEN BEGIN
;; deviation from Nash: allow optimization to continue in outer
;; loop even if we fail to converge, if IFLAG EQ 0. A value of
;; 1 indicates failure. I believe that I tried IFLAG=0 once and
;; there was some problem, but I forget what it was.
IFLAG = 1
F = FMIN
ALPHA = XMIN
X = X + ALPHA*P
RETURN
ENDIF
IFLAG = 0
TNMIN_GETPTC,BIG,SMALL,RTSMLL,RELTOL,ABSTOL,TNYTOL, $
FPRESN,ETA,RMU,XBND,U,FU,GU,XMIN,FMIN,GMIN, $
XW,FW,GW,A,B,OLDF,B1,SCXBND,E,STEP,FACTOR, $
BRAKTD,GTEST1,GTEST2,TOL,IENTRY,ITEST
;
; IF ITEST=1, THE ALGORITHM REQUIRES THE FUNCTION VALUE TO BE
; CALCULATED.
;
IF (ITEST EQ 1) THEN BEGIN
UALPHA = XMIN + U
FU = TNMIN_CALL(FCN, X + UALPHA*P, LG, fullparam_=xnew)
GU = TOTAL(LG*P)
;
; THE GRADIENT VECTOR CORRESPONDING TO THE BEST POINT IS
; OVERWRITTEN IF FU IS LESS THAN FMIN AND FU IS SUFFICIENTLY
; LOWER THAN F AT THE ORIGIN.
;
IF (FU LE FMIN AND FU LE OLDF-UALPHA*GTEST1) THEN $
G = LG
; print, 'fu = ', fu
GOTO, LINDER_10
ENDIF
;
; IF ITEST=2 OR 3 A LOWER POINT COULD NOT BE FOUND
;
IFLAG = 1
IF (ITEST NE 0) THEN RETURN
;
; IF ITEST=0 A SUCCESSFUL SEARCH HAS BEEN MADE
;
; print, 'itcnt = ', itcnt
IFLAG = 0
F = FMIN
ALPHA = XMIN
X = X + ALPHA*P
RETURN
END
pro tnmin_defiter, fcn, x, iter, fnorm, fmt=fmt, FUNCTARGS=fcnargs, $
quiet=quiet, deriv=df, dprint=dprint, pfixed=pfixed, $
maximize=maximize, _EXTRA=iterargs
if keyword_set(quiet) then return
if n_params() EQ 3 then begin
fnorm = tnmin_call(fcn, x, df)
endif
if keyword_set(maximize) then f = -fnorm else f = fnorm
print, iter, f, format='("Iter ",I6," FUNCTION = ",G20.8)'
if n_elements(fmt) GT 0 then begin
print, x, format=fmt
endif else begin
n = n_elements(x)
ii = lindgen(n)
p = ' P('+strtrim(ii,2)+') = '+string(x,format='(G)')
if keyword_set(dprint) then begin
p1 = strarr(n)
wh = where(pfixed EQ 0, ct)
if ct GT 0 AND n_elements(df) GE ct then begin
if keyword_set(maximize) then df1 = -df else df1 = df
p1(wh) = string(df1, format='(G)')
endif
wh = where(pfixed EQ 1, ct)
if ct GT 0 then $
p1(wh) = ' (FIXED)'
p = p + ' : DF/DP('+strtrim(ii,2)+') = '+p1
endif
print, p, format='(A)'
endelse
return
end
; SUBROUTINE TNBC (IERROR, N, X, F, G, W, LW, SFUN, LOW, UP, IPIVOT)
; IMPLICIT DOUBLE PRECISION (A-H,O-Z)
; INTEGER IERROR, N, LW, IPIVOT(N)
; DOUBLE PRECISION X(N), G(N), F, W(LW), LOW(N), UP(N)
;
; THIS ROUTINE SOLVES THE OPTIMIZATION PROBLEM
;
; MINIMIZE F(X)
; X
; SUBJECT TO LOW <= X <= UP
;
; WHERE X IS A VECTOR OF N REAL VARIABLES. THE METHOD USED IS
; A TRUNCATED-NEWTON ALGORITHM (SEE "NEWTON-TYPE MINIMIZATION VIA
; THE LANCZOS ALGORITHM" BY S.G. NASH (TECHNICAL REPORT 378, MATH.
; THE LANCZOS METHOD" BY S.G. NASH (SIAM J. NUMER. ANAL. 21 (1984),
; PP. 770-778). THIS ALGORITHM FINDS A LOCAL MINIMUM OF F(X). IT DOES
; NOT ASSUME THAT THE FUNCTION F IS CONVEX (AND SO CANNOT GUARANTEE A
; GLOBAL SOLUTION), BUT DOES ASSUME THAT THE FUNCTION IS BOUNDED BELOW.
; IT CAN SOLVE PROBLEMS HAVING ANY NUMBER OF VARIABLES, BUT IT IS
; ESPECIALLY USEFUL WHEN THE NUMBER OF VARIABLES (N) IS LARGE.
;
; SUBROUTINE PARAMETERS:
;
; IERROR - (INTEGER) ERROR CODE
; ( 0 => NORMAL RETURN
; ( 2 => MORE THAN MAXFUN EVALUATIONS
; ( 3 => LINE SEARCH FAILED TO FIND LOWER
; ( POINT (MAY NOT BE SERIOUS)
; (-1 => ERROR IN INPUT PARAMETERS
; N - (INTEGER) NUMBER OF VARIABLES
; X - (REAL*8) VECTOR OF LENGTH AT LEAST N; ON INPUT, AN INITIAL
; ESTIMATE OF THE SOLUTION; ON OUTPUT, THE COMPUTED SOLUTION.
; G - (REAL*8) VECTOR OF LENGTH AT LEAST N; ON OUTPUT, THE FINAL
; VALUE OF THE GRADIENT
; F - (REAL*8) ON INPUT, A ROUGH ESTIMATE OF THE VALUE OF THE
; OBJECTIVE FUNCTION AT THE SOLUTION; ON OUTPUT, THE VALUE
; OF THE OBJECTIVE FUNCTION AT THE SOLUTION
; W - (REAL*8) WORK VECTOR OF LENGTH AT LEAST 14*N
; LW - (INTEGER) THE DECLARED DIMENSION OF W
; SFUN - A USER-SPECIFIED SUBROUTINE THAT COMPUTES THE FUNCTION
; AND GRADIENT OF THE OBJECTIVE FUNCTION. IT MUST HAVE
; THE CALLING SEQUENCE
; SUBROUTINE SFUN (N, X, F, G)
; INTEGER N
; DOUBLE PRECISION X(N), G(N), F
; LOW, UP - (REAL*8) VECTORS OF LENGTH AT LEAST N CONTAINING
; THE LOWER AND UPPER BOUNDS ON THE VARIABLES. IF
; THERE ARE NO BOUNDS ON A PARTICULAR VARIABLE, SET
; THE BOUNDS TO -1.D38 AND 1.D38, RESPECTIVELY.
; IPIVOT - (INTEGER) WORK VECTOR OF LENGTH AT LEAST N, USED
; TO RECORD WHICH VARIABLES ARE AT THEIR BOUNDS.
;
; THIS IS AN EASY-TO-USE DRIVER FOR THE MAIN OPTIMIZATION ROUTINE
; LMQNBC. MORE EXPERIENCED USERS WHO WISH TO CUSTOMIZE PERFORMANCE
; OF THIS ALGORITHM SHOULD CALL LMQBC DIRECTLY.
;
;----------------------------------------------------------------------
; THIS ROUTINE SETS UP ALL THE PARAMETERS FOR THE TRUNCATED-NEWTON
; ALGORITHM. THE PARAMETERS ARE:
;
; ETA - SEVERITY OF THE LINESEARCH
; MAXFUN - MAXIMUM ALLOWABLE NUMBER OF FUNCTION EVALUATIONS
; XTOL - DESIRED ACCURACY FOR THE SOLUTION X*
; STEPMX - MAXIMUM ALLOWABLE STEP IN THE LINESEARCH
; ACCRCY - ACCURACY OF COMPUTED FUNCTION VALUES
; MSGLVL - CONTROLS QUANTITY OF PRINTED OUTPUT
; 0 = NONE, 1 = ONE LINE PER MAJOR ITERATION.
; MAXIT - MAXIMUM NUMBER OF INNER ITERATIONS PER STEP
;
function tnmin, fcn, xall, fguess=fguess, functargs=fcnargs, parinfo=parinfo, $
epsrel=epsrel0, epsabs=epsabs0, fastnorm=fastnorm, $
nfev=nfev, maxiter=maxiter0, maxnfev=maxfun0, maximize=fmax, $
errmsg=errmsg, nprint=nprint, status=status, nocatch=nocatch, $
iterproc=iterproc, iterargs=iterargs, niter=niter,quiet=quiet,$
autoderivative=autoderiv, iterderiv=iterderiv, bestmin=f
if n_elements(nprint) EQ 0 then nprint = 1
if n_elements(iterproc) EQ 0 then iterproc = 'TNMIN_DEFITER'
if n_elements(autoderiv) EQ 0 then autoderiv = 0
if n_elements(msglvl) EQ 0 then msglvl = 0
if n_params() EQ 0 then begin
message, "USAGE: PARMS = TNMIN('MYFUNCT', START_PARAMS, ... )", /info
return, !values.d_nan
endif
iterd = keyword_set(iterderiv)
maximize = keyword_set(fmax)
status = 0L
nfev = 0L
errmsg = ''
catch_msg = 'in TNMIN'
common tnmin_config, tnconfig
tnconfig = {fastnorm: keyword_set(fastnorm), proc: 0, nfev: 0L, $
autoderiv: keyword_set(autoderiv), max: maximize}
;; Handle error conditions gracefully
if NOT keyword_set(nocatch) then begin
catch, catcherror
if catcherror NE 0 then begin
catch, /cancel
err_string = ''+!error_state.msg
message, /cont, 'Error detected while '+catch_msg+':'
message, /cont, err_string
message, /cont, 'Error condition detected. Returning to MAIN level.'
if errmsg EQ '' then $
errmsg = 'Error detected while '+catch_msg+': '+err_string
if status EQ 0 then status = -18
return, !values.d_nan
endif
endif
;; Parinfo:
;; --------------- STARTING/CONFIG INFO (passed in to routine, not changed)
;; .value - starting value for parameter
;; .fixed - parameter is fixed
;; .limited - a two-element array, if parameter is bounded on
;; lower/upper side
;; .limits - a two-element array, lower/upper parameter bounds, if
;; limited vale is set
;; .step - step size in Jacobian calc, if greater than zero
catch_msg = 'parsing input parameters'
;; Parameters can either be stored in parinfo, or x. Parinfo takes
;; precedence if it exists.
if n_elements(xall) EQ 0 AND n_elements(parinfo) EQ 0 then begin
errmsg = 'ERROR: must pass parameters in X or PARINFO'
goto, TERMINATE
endif
;; Be sure that PARINFO is of the right type
if n_elements(parinfo) GT 0 then begin
parinfo_size = size(parinfo)
if parinfo_size(parinfo_size(0)+1) NE 8 then begin
errmsg = 'ERROR: PARINFO must be a structure.'
goto, TERMINATE
endif
if n_elements(xall) GT 0 AND n_elements(xall) NE n_elements(parinfo) $
then begin
errmsg = 'ERROR: number of elements in PARINFO and X must agree'
goto, TERMINATE
endif
endif
;; If the parameters were not specified at the command line, then
;; extract them from PARINFO
if n_elements(xall) EQ 0 then begin
tnmin_parinfo, parinfo, tagnames, 'VALUE', xall, status=stx
if stx EQ 0 then begin
errmsg = 'ERROR: either X or PARINFO(*).VALUE must be supplied.'
goto, TERMINATE
endif
sz = size(xall)
;; Convert to double if parameters are not float or double
if sz(sz(0)+1) NE 4 AND sz(sz(0)+1) NE 5 then $
xall = double(xall)
endif
npar = n_elements(xall)
zero = xall(0) * 0.
one = zero + 1
ten = zero + 10
twothird = (zero+2)/(zero+3)
quarter = zero + 0.25
half = zero + 0.5
;; Extract machine parameters
sz = size(xall)
tp = sz(sz(0)+1)
if tp NE 4 AND tp NE 5 then begin
if NOT keyword_set(quiet) then begin
message, 'WARNING: input parameters must be at least FLOAT', /info
message, ' (converting parameters to FLOAT)', /info
endif
xall = float(xall)
sz = size(xall)
endif
isdouble = (sz(sz(0)+1) EQ 5)
common tnmin_machar, machvals
tnmin_setmachar, double=isdouble
MCHPR1 = machvals.machep
;; TIED parameters?
tnmin_parinfo, parinfo, tagnames, 'TIED', ptied, default='', n=npar
ptied = strtrim(ptied, 2)
wh = where(ptied NE '', qanytied)
qanytied = qanytied GT 0
tnconfig = create_struct(tnconfig, 'QANYTIED', qanytied, 'PTIED', ptied)
;; FIXED parameters ?
tnmin_parinfo, parinfo, tagnames, 'FIXED', pfixed, default=0, n=npar
pfixed = pfixed EQ 1
pfixed = pfixed OR (ptied NE '') ;; Tied parameters are also effectively fixed
;; Finite differencing step, absolute and relative, and sidedness of derivative
tnmin_parinfo, parinfo, tagnames, 'STEP', step, default=zero, n=npar
tnmin_parinfo, parinfo, tagnames, 'RELSTEP', dstep, default=zero, n=npar
tnmin_parinfo, parinfo, tagnames, 'TNSIDE', dside, default=2, n=npar
;; Maximum and minimum steps allowed to be taken in one iteration
tnmin_parinfo, parinfo, tagnames, 'TNMAXSTEP', maxstep, default=zero, n=npar
tnmin_parinfo, parinfo, tagnames, 'TNMINSTEP', minstep, default=zero, n=npar
qmin = minstep * 0 ;; Disable minstep for now
qmax = maxstep NE 0
wh = where(qmin AND qmax AND maxstep LT minstep, ct)
if ct GT 0 then begin
errmsg = 'ERROR: TNMINSTEP is greater than TNMAXSTEP'
goto, TERMINATE
endif
wh = where(qmin AND qmax, ct)
qminmax = ct GT 0
;; Finish up the free parameters
ifree = where(pfixed NE 1, ct)
if ct EQ 0 then begin
errmsg = 'ERROR: no free parameters'
goto, TERMINATE
endif
;; Compose only VARYING parameters
xnew = xall ;; xnew is the set of parameters to be returned
x = xnew(ifree) ;; x is the set of free parameters
;; LIMITED parameters ?
tnmin_parinfo, parinfo, tagnames, 'LIMITED', limited, status=st1
tnmin_parinfo, parinfo, tagnames, 'LIMITS', limits, status=st2
if st1 EQ 1 AND st2 EQ 1 then begin
;; Error checking on limits in parinfo
wh = where((limited[0,*] AND xall LT limits[0,*]) OR $
(limited[1,*] AND xall GT limits[1,*]), ct)
if ct GT 0 then begin
errmsg = 'ERROR: parameters are not within PARINFO limits'
goto, TERMINATE
endif
wh = where(limited[0,*] AND limited[1,*] AND $
limits[0,*] GE limits[1,*] AND pfixed EQ 0, ct)
if ct GT 0 then begin
errmsg = 'ERROR: PARINFO parameter limits are not consistent'
goto, TERMINATE
endif
;; Transfer structure values to local variables
qulim = limited[1, ifree]
ulim = limits [1, ifree]
qllim = limited[0, ifree]
llim = limits [0, ifree]
wh = where(qulim OR qllim, ct)
if ct GT 0 then qanylim = 1 else qanylim = 0
endif else begin
;; Fill in local variables with dummy values
qulim = lonarr(n_elements(ifree))
ulim = x * 0.
qllim = qulim
llim = x * 0.
qanylim = 0
endelse
tnconfig = create_struct(tnconfig, $
'PFIXED', pfixed, 'IFREE', ifree, $
'STEP', step, 'DSTEP', dstep, 'DSIDE', dside, $
'ULIMITED', qulim, 'ULIMIT', ulim)
common tnmin_fcnargs, tnfcnargs
tnfcnargs = 0 & dummy = temporary(tnfcnargs)
if n_elements(fcnargs) GT 0 then tnfcnargs = fcnargs
;; SET UP CUSTOMIZING PARAMETERS
;; ETA - SEVERITY OF THE LINESEARCH
;; MAXFUN - MAXIMUM ALLOWABLE NUMBER OF FUNCTION EVALUATIONS
;; XTOL - DESIRED ACCURACY FOR THE SOLUTION X*
;; STEPMX - MAXIMUM ALLOWABLE STEP IN THE LINESEARCH
;; ACCRCY - ACCURACY OF COMPUTED FUNCTION VALUES
;; MSGLVL - DETERMINES QUANTITY OF PRINTED OUTPUT
;; 0 = NONE, 1 = ONE LINE PER MAJOR ITERATION.
;; MAXIT - MAXIMUM NUMBER OF INNER ITERATIONS PER STEP
n = n_elements(x)
if n_elements(maxit) EQ 0 then begin
maxit = (n/2) < 50 > 2 ;; XXX diff than TN.F
endif
if n_elements(maxfun0) EQ 0 then $
maxfun = 0L $
else $
maxfun = floor(maxfun0(0)) > 1
; maxfun = 150L*n
; if keyword_set(autoderiv) then $
; maxfun = maxfun*(1L + round(total(abs(dside)> 1 < 2)))
eta = zero + 0.25
stepmx = zero + 10
if n_elements(maxiter0) EQ 0 then $
maxiter = 200L $
else $
maxiter = floor(maxiter0(0)) > 1
g = replicate(x(0)* 0., n)
;; call minimizer
;
; THIS ROUTINE IS A BOUNDS-CONSTRAINED TRUNCATED-NEWTON METHOD.
; THE TRUNCATED-NEWTON METHOD IS PRECONDITIONED BY A LIMITED-MEMORY
; QUASI-NEWTON METHOD (THIS PRECONDITIONING STRATEGY IS DEVELOPED
; IN THIS ROUTINE) WITH A FURTHER DIAGONAL SCALING (SEE ROUTINE NDIA3).
; FOR FURTHER DETAILS ON THE PARAMETERS, SEE ROUTINE TNBC.
;
;
; initialize variables
;
common tnmin_work, lsk, lyk, ldiagb, lsr, lyr
; I/O I/O I/O I/O I/O
lsk = 0 & lyk = 0 & ldiagb = 0 & lsr = 0 & lyr = 0
zero = x(0)* 0.
one = zero + 1
if n_elements(fguess) EQ 0 then fguess = one
if maximize then f = -fguess else f = fguess
conv = 0 & lreset = 0 & upd1 = 0 & newcon = 0
gsk = zero & yksk = zero & gtp = zero & gtpnew = zero & yrsr = zero
upd1 = 1
ireset = 0L
nmodif = 0L
nlincg = 0L
fstop = f
conv = 0
nm1 = n - 1
;; From CHKUCP
;
; CHECKS PARAMETERS AND SETS CONSTANTS WHICH ARE COMMON TO BOTH
; DERIVATIVE AND NON-DERIVATIVE ALGORITHMS
;
EPSMCH = MCHPR1
SMALL = EPSMCH*EPSMCH
TINY = SMALL
NWHY = -1L
;
; SET CONSTANTS FOR LATER
;
;; Some of these constants have been moved around for clarity (!)
if n_elements(epsrel0) EQ 0 then epsrel = 100*MCHPR1 $
else epsrel = epsrel0(0)+0.
if n_elements(epsabs0) EQ 0 then epsabs = zero $
else epsabs = abs(epsabs0(0))+0.
ACCRCY = epsrel
XTOL = sqrt(ACCRCY)
RTEPS = SQRT(EPSMCH)
RTOL = XTOL
IF (ABS(RTOL) LT ACCRCY) THEN RTOL = 10. *RTEPS
FTOL2 = 0
FTOL1 = RTOL^2 + EPSMCH ;; For func chg convergence test (U1a)
if epsabs NE 0 then $
FTOL2 = EPSABS + EPSMCH ;; For absolute func convergence test (U1b)
PTOL = RTOL + RTEPS ;; For parm chg convergence test (U2)
GTOL1 = ACCRCY^TWOTHIRD ;; For gradient convergence test (U3, squared)
GTOL2 = (1D-2*XTOL)^2 ;; For gradient convergence test (U4, squared)
;
; CHECK FOR ERRORS IN THE INPUT PARAMETERS
;
IF (ETA LT 0.D0 OR STEPMX LT RTOL) THEN BEGIN
errmsg = 'ERROR: input keywords are inconsistent'
goto, TERMINATE
endif
;; Check input parameters for errors
if (n LE 0) OR (xtol LE 0) OR (maxit LE 0) then begin
errmsg = 'ERROR: input keywords are inconsistent'
goto, TERMINATE
endif
NWHY = 0L
XNORM = TNMIN_ENORM(X)
ALPHA = zero
TEST = zero
; From SETUCR
;
; CHECK INPUT PARAMETERS, COMPUTE THE INITIAL FUNCTION VALUE, SET
; CONSTANTS FOR THE SUBSEQUENT MINIMIZATION
;
fm = f
;
; COMPUTE THE INITIAL FUNCTION VALUE
;
catch_msg = 'calling TNMIN_CALL'
fnew = tnmin_call(fcn, x, g, fullparam_=xnew)
;
; SET CONSTANTS FOR LATER
;
NITER = 0L
OLDF = FNEW
GTG = TOTAL(G*G)
common tnmin_error, tnerr
if nprint GT 0 AND iterproc NE '' then begin
iflag = 0L
if (niter-1) MOD nprint EQ 0 then begin
catch_msg = 'calling '+iterproc
tnerr = 0
call_procedure, iterproc, fcn, xnew, niter, fnew, $
FUNCTARGS=fcnargs, parinfo=parinfo, quiet=quiet, $
dprint=iterd, deriv=g, pfixed=pfixed, maximize=maximize, $
_EXTRA=iterargs
iflag = tnerr
if iflag LT 0 then begin
errmsg = 'WARNING: premature termination by "'+iterproc+'"'
nwhy = 4L
goto, CLEANUP
endif
endif
endif
fold = fnew
flast = fnew
; From LMQNBC
;
; TEST THE LAGRANGE MULTIPLIERS TO SEE IF THEY ARE NON-NEGATIVE.
; BECAUSE THE CONSTRAINTS ARE ONLY LOWER BOUNDS, THE COMPONENTS
; OF THE GRADIENT CORRESPONDING TO THE ACTIVE CONSTRAINTS ARE THE
; LAGRANGE MULTIPLIERS. AFTERWORDS, THE PROJECTED GRADIENT IS FORMED.
;
catch_msg = 'zeroing derivatives of pegged parameters'
lmask = qllim AND (x EQ llim) AND (g GE 0)
umask = qulim AND (x EQ ulim) AND (g LE 0)
whlpeg = where(lmask, nlpeg)
whupeg = where(umask, nupeg)
tnmin_fix, whlpeg, whupeg, g
GTG = TOTAL(G*G)
;
; CHECK IF THE INITIAL POINT IS A LOCAL MINIMUM.
;
FTEST = ONE + ABS(FNEW)
IF (GTG LT GTOL2*FTEST*FTEST) THEN GOTO, CLEANUP
;
; SET INITIAL VALUES TO OTHER PARAMETERS
;
ICYCLE = NM1
GNORM = SQRT(GTG)
DIFNEW = ZERO
EPSRED = HALF/TEN
FKEEP = FNEW
;
; SET THE DIAGONAL OF THE APPROXIMATE HESSIAN TO UNITY.
;
LDIAGB = replicate(one, n)
;
; ..................START OF MAIN ITERATIVE LOOP..........
;
; COMPUTE THE NEW SEARCH DIRECTION
;
catch_msg = 'calling TNMIN_MODLNP'
tnmin_modlnp, lpk, lgv, lz1, lv, ldiagb, lemat, $
x, g, lzk, n, niter, maxit, nmodif, nlincg, upd1, yksk, $
gsk, yrsr, lreset, fcn, whlpeg, whupeg, accrcy, gtpnew, gnorm, xnorm, $
xnew
ITER_LOOP:
catch_msg = 'computing step length'
LOLDG = G
PNORM = tnmin_enorm(LPK)
OLDF = FNEW
OLDGTP = GTPNEW
;
; PREPARE TO COMPUTE THE STEP LENGTH
;
PE = PNORM + EPSMCH
;
; COMPUTE THE ABSOLUTE AND RELATIVE TOLERANCES FOR THE LINEAR SEARCH
;
RELTOL = RTEPS*(XNORM + ONE)/PE
ABSTOL = - EPSMCH*FTEST/(OLDGTP - EPSMCH)
;
; COMPUTE THE SMALLEST ALLOWABLE SPACING BETWEEN POINTS IN
; THE LINEAR SEARCH
;
TNYTOL = EPSMCH*(XNORM + ONE)/PE
;; From STPMAX
SPE = STEPMX/PE
mmask = (NOT lmask AND NOT umask)
wh = where(mmask AND (lpk GT 0) AND qulim AND (ulim - x LT spe*lpk), ct)
if ct GT 0 then begin
spe = min( (ulim(wh)-x(wh)) / lpk(wh))
endif
wh = where(mmask AND (lpk LT 0) AND qllim AND (llim - x GT spe*lpk), ct)
if ct GT 0 then begin
spe = min( (llim(wh)-x(wh)) / lpk(wh))
endif
;; From LMQNBC
;
; SET THE INITIAL STEP LENGTH.
;
ALPHA = TNMIN_STEP1(FNEW,FM,OLDGTP,SPE, epsmch)
;
; PERFORM THE LINEAR SEARCH
;
catch_msg = 'performing linear search'
tnmin_linder, n, fcn, small, epsmch, reltol, abstol, tnytol, $
eta, zero, spe, lpk, oldgtp, x, fnew, alpha, g, nwhy, xnew
NEWCON = 0
IF (ABS(ALPHA-SPE) GT 1.D1*EPSMCH) EQ 0 THEN BEGIN
NEWCON = 1
NWHY = 0L
;; From MODZ
mmask = (NOT lmask AND NOT umask)
wh = where(mmask AND (lpk LT 0) AND qllim $
AND (x-llim LE 10*epsmch*(abs(llim)+one)),ct)
if ct GT 0 then begin
flast = fnew
lmask(wh) = 1
x(wh) = llim(wh)
whlpeg = where(lmask, nlpeg)
endif
wh = where(mmask AND (lpk GT 0) AND qulim $
AND (ulim-x LE 10*epsmch*(abs(ulim)+one)),ct)
if ct GT 0 then begin
flast = fnew
umask(wh) = 1
x(wh) = ulim(wh)
whupeg = where(umask, nupeg)
endif
xnew(ifree) = x
;; From LMQNBC
FLAST = FNEW
endif
FOLD = FNEW
NITER = NITER + 1
;
; IF REQUIRED, PRINT THE DETAILS OF THIS ITERATION
;
if nprint GT 0 AND iterproc NE '' then begin
iflag = 0L
xx = xnew
xx(ifree) = x
if (niter-1) MOD nprint EQ 0 then begin
catch_msg = 'calling '+iterproc
tnerr = 0
call_procedure, iterproc, fcn, xx, niter, fnew, $
FUNCTARGS=fcnargs, parinfo=parinfo, quiet=quiet, $
dprint=iterd, deriv=g, pfixed=pfixed, maximize=maximize, $
_EXTRA=iterargs
iflag = tnerr
if iflag LT 0 then begin
errmsg = 'WARNING: premature termination by "'+iterproc+'"'
nwhy = 4L
goto, CLEANUP
endif
endif
endif
catch_msg = 'testing for convergence'
IF (NWHY LT 0) THEN BEGIN
NWHY = -2L
goto, CLEANUP
ENDIF
IF (NWHY NE 0 AND NWHY NE 2) THEN BEGIN
;; THE LINEAR SEARCH HAS FAILED TO FIND A LOWER POINT
NWHY = 3L
goto, CLEANUP
endif
if nwhy GT 1 then begin
fnew = tnmin_call(fcn, x, g, fullparam_=xnew)
endif
wh = where(finite(x) EQ 0, ct)
if ct GT 0 OR finite(fnew) EQ 0 then begin
nwhy = -3L
goto, CLEANUP
endif
;
; TERMINATE IF MORE THAN MAXFUN EVALUATIONS HAVE BEEN MADE
;
NWHY = 2L
if maxfun GT 0 AND tnconfig.nfev GT maxfun then goto, CLEANUP
if niter GT maxiter then goto, CLEANUP
NWHY = 0L
;
; SET UP PARAMETERS USED IN CONVERGENCE AND RESETTING TESTS
;
DIFOLD = DIFNEW
DIFNEW = OLDF - FNEW
;
; IF THIS IS THE FIRST ITERATION OF A NEW CYCLE, COMPUTE THE
; PERCENTAGE REDUCTION FACTOR FOR THE RESETTING TEST.
;
IF (ICYCLE EQ 1) THEN BEGIN
IF (DIFNEW GT 2.D0*DIFOLD) THEN EPSRED = EPSRED + EPSRED
IF (DIFNEW LT 5.0D-1*DIFOLD) THEN EPSRED = HALF*EPSRED
ENDIF
LGV = G
tnmin_fix, whlpeg, whupeg, lgv
GTG = TOTAL(LGV*LGV)
GNORM = SQRT(GTG)
FTEST = ONE + ABS(FNEW)
XNORM = tnmin_enorm(X)
;; From CNVTST
LTEST = (FLAST - FNEW) LE (-5.D-1*GTPNEW)
wh = where((lmask AND g LT 0) OR (umask AND g GT 0), ct)
if ct GT 0 then begin
conv = 0
if NOT ltest then begin
mx = max(abs(g(wh)), wh2)
lmask(wh(wh2)) = 0 & umask(wh(wh2)) = 0
FLAST = FNEW
goto, CNVTST_DONE
endif
endif
;; Gill Murray and Wright tests are listed to the right.
;; Modifications due to absolute function value test are done here.
fconv = abs(DIFNEW) LT FTOL1*FTEST ;; U1a
if ftol2 EQ 0 then begin
pconv = ALPHA*PNORM LT PTOL*(ONE + XNORM) ;; U2
gconv = GTG LT GTOL1*FTEST*FTEST ;; U3
endif else begin
;; Absolute tolerance implies a loser constraint on parameters
fconv = fconv OR (abs(difnew) LT ftol2) ;; U1b
acc2 = (FTOL2/FTEST + EPSMCH)
pconv = ALPHA*PNORM LT SQRT(acc2)*(ONE + XNORM) ;; U2
gconv = GTG LT (acc2^twothird)*FTEST*FTEST ;; U3
endelse
IF ((PCONV AND FCONV AND GCONV) $ ;; U1 + U2 + U3
OR (GTG LT GTOL2*FTEST*FTEST)) THEN BEGIN ;; U4
CONV = 1
ENDIF ELSE BEGIN
;; Convergence failed
CONV = 0
ENDELSE
;
; FOR DETAILS, SEE GILL, MURRAY, AND WRIGHT (1981, P. 308) AND
; FLETCHER (1981, P. 116). THE MULTIPLIER TESTS (HERE, TESTING
; THE SIGN OF THE COMPONENTS OF THE GRADIENT) MAY STILL NEED TO
; MODIFIED TO INCORPORATE TOLERANCES FOR ZERO.
;
CNVTST_DONE:
;; From LMQNBC
IF (CONV) THEN GOTO, CLEANUP
tnmin_fix, whlpeg, whupeg, g
;
; COMPUTE THE CHANGE IN THE ITERATES AND THE CORRESPONDING CHANGE
; IN THE GRADIENTS
;
IF NEWCON EQ 0 THEN BEGIN
LYK = G - LOLDG
LSK = ALPHA*LPK
;
; SET UP PARAMETERS USED IN UPDATING THE PRECONDITIONING STRATEGY.
;
YKSK = TOTAL(LYK*LSK)
LRESET = 0
IF (ICYCLE EQ NM1 OR DIFNEW LT EPSRED*(FKEEP-FNEW)) THEN LRESET = 1
IF (LRESET EQ 0) THEN BEGIN
YRSR = TOTAL(LYR*LSR)
IF (YRSR LE ZERO) THEN LRESET = 1
ENDIF
UPD1 = 0
ENDIF
;
; COMPUTE THE NEW SEARCH DIRECTION
;
;; TNMIN_90:
catch_msg = 'calling TNMIN_MODLNP'
tnmin_modlnp, lpk, lgv, lz1, lv, ldiagb, lemat, $
x, g, lzk, n, niter, maxit, nmodif, nlincg, upd1, yksk, $
gsk, yrsr, lreset, fcn, whlpeg, whupeg, accrcy, gtpnew, gnorm, xnorm, $
xnew
IF (NEWCON) THEN GOTO, ITER_LOOP
; IF (NOT LRESET) OR ICYCLE EQ 1 AND n_elements(LSR) GT 0 THEN BEGIN ;; For testing
IF (LRESET EQ 0) THEN BEGIN
;
; COMPUTE THE ACCUMULATED STEP AND ITS CORRESPONDING
; GRADIENT DIFFERENCE.
;
LSR = LSR + LSK
LYR = LYR + LYK
ICYCLE = ICYCLE + 1
goto, ITER_LOOP
ENDIF
;
; RESET
;
;; TNMIN_110:
IRESET = IRESET + 1
;
; INITIALIZE THE SUM OF ALL THE CHANGES IN X.
;
LSR = LSK
LYR = LYK
FKEEP = FNEW
ICYCLE = 1L
goto, ITER_LOOP
;
; ...............END OF MAIN ITERATION.......................
;
CLEANUP:
nfev = tnconfig.nfev
tnfcnargs = 0
catch, /cancel
case NWHY of
-3: begin
;; INDEFINITE VALUE
status = -16L
if errmsg EQ '' then $
errmsg = ('ERROR: parameter or function value(s) have become '+$
'infinite; check model function for over- '+$
'and underflow')
return, !values.d_nan
end
-2: begin
;; INTERNAL ERROR IN LINE SEARCH
status = -18L
if errmsg EQ '' then $
errmsg = 'ERROR: Fatal error during line search'
return, !values.d_nan
end
-1: begin
TERMINATE:
;; FATAL TERMINATION
status = 0L
if errmsg EQ '' then errmsg = 'ERROR: Invalid inputs'
return, !values.d_nan
end
0: begin
CONVERGED:
status = 1L
end
2: begin
;; MAXIMUM NUMBER of FUNC EVALS or ITERATIONS REACHED
if maxfun GT 0 AND nfev GT maxfun then begin
status = -17L
if errmsg EQ '' then $
errmsg = ('WARNING: no convergence within maximum '+$
'number of function calls')
endif else begin
status = 5L
if errmsg EQ '' then $
errmsg = ('WARNING: no convergence within maximum '+$
'number of iterations')
endelse
FNEW = OLDF
end
3: begin
status = -18L
if errmsg EQ '' then errmsg = 'ERROR: Line search failed to converge'
end
4: begin
;; ABNORMAL TERMINATION BY USER ROUTINE
status = iflag
end
endcase
;; Successful return
F = FNEW
xnew(ifree) = x
if keyword_set(tnconfig.qanytied) then tnmin_tie, xnew, tnconfig.ptied
return, xnew
end
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