| Robust curve fitting [message #12464] |
Mon, 03 August 1998 00:00  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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There has been some recent discussion on this newgroup about curve
fitting. Specifically, people wanted a faster system with more
features. I also wanted a curve fitting routine that didn't cause IDL
to crash.
I recently had an opportunity to translate the MINPACK-1 curve-fitting
package into IDL. MINPACK is a minimization package available from
netlib, and has an excellent reputation. I have found that it is much
more robust, able to cope with singular matrices, etc. Since people
have been requesting, I polished it up a little bit, and am making it
available via my IDL web page:
http://astrog.physics.wisc.edu/~craigm/idl/idl.html
In addition to three IDL procedures (MPFIT, MPFITFUN, and MPFITEXPR)
which are extensively documented, I have written a short tutorial page
on how to use them
(http://astrog.physics.wisc.edu/~craigm/idl/fittut.html). You should
download all three routines.
The easiest to use routine, MPFITEXPR, does not even require you to
compile a separate IDL function. You just type the expression you
want, as a string! I have found this indispensable for interactive
analysis.
Benefits:
* can fit arbitrary expressions from the command line without
compiling a special IDL function (see MPFITEXPR).
* you can fix any parameters you wish (see PARINFO keyword).
* you can place upper and lower limits on parameter values.
(see PARINFO keyword).
* you can pass additional keywords to your function in a manner
similar to the _EXTRA mechanism (see the FUNCTARGS keyword).
* the function evaluation is a vector operation, so it avoids
time-consuming FOR loops.
* it computes the entire covariance matrix (see COVAR keyword)
* partial derivatives are calculated automatically and numerically,
freeing you from the need to compute them analytically yourself.
I get very good performance on my machine! Download them and give a
try. As always, feedback is appreciated.
Craig
--
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Craig B. Markwardt, Ph.D. EMAIL: craigmnet@astrog.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
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| Re: Robust curve fitting [message #12674 is a reply to message #12464] |
Thu, 06 August 1998 00:00  |
address
Messages: 3
Registered: August 1998
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Junior Member |
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In article <ond8ag5et2.fsf@cow.physics.wisc.edu>,
craigmnet@astrog.physics.wisc.edu wrote:
> Mark Elliott <mark@mail.mmrrcc.upenn.edu> writes:
>>
>> Do you or anyone reading this know if there are similar IDL (or
>> MINPACK) routines which perform Levenberg-Marquardt fitting to COMPLEX
>> functions?
>>
>
> I'm not an expert in the field, I just translated the program!
>
> I can tell you that MPFIT itself does not understand complex
> variables; they have to be either FLOAT or DOUBLE. I am not even sure
> what the least-squares problem means when you talk about complex
> numbers. If you want to minimize the Euclidean distance between data
> and model points on the complex plane, and if your data have
> independent errors in the real and imaginary components, then the
> solution should be easy.
>
Hi,
We routinely fit complex variables by putting the real part in the first
part of an array and the imaginary part after that. We calculate the
function and the derivatives the same way, real part first then the imaginary.
See the added example which we use with a slightly adapted curvefit. You
just consider the imaginary part as another set of data, since -indeed- in
our case the errors are independent. Good luck.
;*********************************************************** ****************
;+
; CALLING SEQUENCE:
; FUNCT, f_nr, X,FPAR,FUN,PDER
; INPUTS:
; f_nr = function nr 1: single complex spectral line
; T = VALUES OF INDEPENDENT VARIABLE. (time here)
; FPAR = PARAMETERS OF EQUATION DESCRIBED BELOW.
; X = PARAMETERS (depends on function nr)
; OUTPUTS:
; FUN = VALUE OF FUNCTION AT EACH X(I).
;
; OPTIONAL OUTPUT PARAMETERS:
; DFUN = (N_ELEMENTS(X), npar) ARRAY CONTAINING THE
; PARTIAL DERIVATIVES. DFUN(I,J) = DERIVATIVE
; AT ITH POINT W/RESPECT TO JTH PARAMETER.
; PROCEDURE:
; function nr = 2:
; FUN(0:cut-1) = sum(i) (A1i sin((w0+wi)t) + A2i cos((w0+wi)t)) exp(-bt)
; FUN(cut:* ) = sum(i) (A1i cos((w0+wi)t) - A2i sin((w0+wi)t)) exp(-bt)
;
; MODIFICATION HISTORY:
; WRITTEN, DMS, RSI, SEPT, 1982.
; Jan Willem van der Veen, jan 1998
;-
PRO FUNCT, f_nr,T,FPAR,FUN,DFUN
s = N_ELEMENTS(T)
NTERMS = N_ELEMENTS(FPAR)
cut = s/2
type = size(FPAR)
type = type(type(0)+1)
dpar = type eq 5
if dpar then begin
FUN = dblarr(s)
IF (N_PARAMS(0) GT 4) THEN DFUN = dblarr(s, nterms)
endif else begin
FUN = fltarr(s)
IF (N_PARAMS(0) GT 4) THEN DFUN = fltarr(s, nterms)
endelse
if (f_nr EQ 1) then begin
A1 = FPAR(0) ; amplitude cos 1
A2 = FPAR(1) ; amplitude sin 1
B = FPAR(2) ; damping
W = FPAR(3) ; frequency
T2 = T(0:cut-1)
BEXP = EXP(-B*T2) ; decay
FS = SIN(W*T2) ; sin part
FC = COS(W*T2) ; cos part
FUN(0:cut-1) = ( A1*FS+A2*FC )*BEXP
FUN(cut:s-1) = ( A1*FC-A2*FS )*BEXP
IF N_PARAMS(0) LE 4 THEN RETURN ; need derivatives
DFUN(0:cut-1,0) = FS*BEXP ; d FUN / d A11
DFUN(cut:s-1,0) = FC*BEXP
DFUN(0:cut-1,1) = FC*BEXP ; d FUN / d A21
DFUN(cut:s-1,1) =-FS*BEXP
DFUN(0:cut-1,2) = FUN(0:cut-1)*(-T2)
DFUN(cut:s-1,2) = FUN(cut:s-1)*(-T2)
DFUN(0:cut-1,3) = ( A1*FC-A2*FS)*T2*BEXP
DFUN(cut:s-1,3) = (-A1*FS-A2*FC)*T2*BEXP
endif
RETURN
END
--
\|||/ email: prlkovsky at newsguy dot com
>|- o|< I was never sure about anything anyway...
-----oo0 U -Ooo---------------------------------------------------
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