| Re: Problems getting CURVEFIT to work [message #32848] |
Wed, 13 November 2002 07:41  |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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Jonathan Greenberg wrote:
>
> Thanks!
>
> On 11/12/02 5:14 PM, in article onk7jiuv7e.fsf@cow.physics.wisc.edu, "Craig
> Markwardt" <craigmnet@cow.physics.wisc.edu> wrote:
>
>>
>> Jonathan Greenberg <greenberg@ucdavis.edu> writes:
>>> Hi there, I'm trying to use CURVEFIT to fit data to a decay function of the
>>> form:
>>> f(x) = a(1-e^(bx))+c
>>
>> Problem 1. Your parameters A and C are very highly (anti) correlated
>> with each other. It would be better to recast as A*EXP(B*X) + C.
>
> The problem is I need a curve that starts low and asymptotes higher -- I
Which is precisely what a*exp(b*x)+c will do, for the appropriate values
of a, b, and c. For example, y=-80690323.0D*exp(-0.0006D*x)+1.340D is a
curve with those features, which makes a rough match to your data. It
can be converted to the form of your equation by re-writing it as:
y = 80690323.0D*(1.0D - exp(-0.0006D*x))-80690321.66D
But as you can see, that form obscures the assymptotic value, which is
1.34 for this curve. The assymptote in your form is a-c, which is a
small difference of two very large numbers. That causes problems for any
numerical approach to
fitting this equation to data.
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| Re: Problems getting CURVEFIT to work [message #32849 is a reply to message #32848] |
Wed, 13 November 2002 07:18  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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Jonathan Greenberg <greenberg@ucdavis.edu> writes:
> On 11/12/02 5:14 PM, in article onk7jiuv7e.fsf@cow.physics.wisc.edu, "Craig
> Markwardt" <craigmnet@cow.physics.wisc.edu> wrote:
>> Jonathan Greenberg <greenberg@ucdavis.edu> writes:
>>> Hi there, I'm trying to use CURVEFIT to fit data to a decay function of the
>>> form:
>>> f(x) = a(1-e^(bx))+c
>>
>> Problem 1. Your parameters A and C are very highly (anti) correlated
>> with each other. It would be better to recast as A*EXP(B*X) + C.
>
> The problem is I need a curve that starts low and asymptotes higher -- I
> have a reason to believe it will asymptote at some maximum, hence the
> a(1-e^(bx))+c --> given this, how can I get this to work?
A*EXP(B*X) + D will suit you just fine. It's the same function after
all, with (D=C+A). The fit you were doing had C and A almost
perfectly anti-correlated, so combining the two will relieve some of
that problem.
Craig
--
------------------------------------------------------------ --------------
Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
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| Re: Problems getting CURVEFIT to work [message #32853 is a reply to message #32849] |
Tue, 12 November 2002 23:43 |
Jonathan Greenberg
Messages: 91
Registered: November 2002
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Member |
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Thanks!
On 11/12/02 5:14 PM, in article onk7jiuv7e.fsf@cow.physics.wisc.edu, "Craig
Markwardt" <craigmnet@cow.physics.wisc.edu> wrote:
>
> Jonathan Greenberg <greenberg@ucdavis.edu> writes:
>> Hi there, I'm trying to use CURVEFIT to fit data to a decay function of the
>> form:
>> f(x) = a(1-e^(bx))+c
>
> Problem 1. Your parameters A and C are very highly (anti) correlated
> with each other. It would be better to recast as A*EXP(B*X) + C.
The problem is I need a curve that starts low and asymptotes higher -- I
have a reason to believe it will asymptote at some maximum, hence the
a(1-e^(bx))+c --> given this, how can I get this to work?
>
>
>> My code is as follows:
>>
>> pro decayfunc, X,A,F,pder
>> bx=EXP(A[1]*X)
>> F=A[0]*(1-bx)+A[2]
>> if N_PARAMS() GE 4 THEN $
>> pder=[[1-bx],[-A[0]*X*bx],[replicate(1.0,N_ELEMENTS(X))]]
>> end
>> X=[30185.0,33897.0,35089.0,35377.0,35665.0]
>> Y=[0.3002,1.3849,1.3004,1.226,1.3118]
>> A=[1.25,-1.0,-0.1]
>
> Problem 2. Your initial value of "B" of -1 is not a good choice.
> When the fitter tries to evaluate EXP(-1.0*30185.) the result is zero.
> A better choice would be about -1./30000.
I'll try that out!
>
> Problem 3. Your data don't look very exponential to me! There is
> just one low point. You are going to have to live with some very
> large confidence intervals...
>
>> weight=[1.0,1.0,1.0,1.0,1.0]
>> yfit=CURVEFIT[X,Y,weights,A,SIGMA,FUNCTION_NAME='decayfunc', /DOUBLE]
Yeah, I have more data now, and will try this!
>
> Suggestion. It might be worth trying MPCURVEFIT or MPFITFUN from my
> web page. The fitting routines appear to be much more robust than the
> stock CURVEFIT.
I'll try them. Thanks!
>
> Good luck,
> Craig
>
> http://cow.physics.wisc.edu/~craigm/idl/idl.html (under curve fitting)
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| Re: Problems getting CURVEFIT to work [message #32857 is a reply to message #32853] |
Tue, 12 November 2002 17:14 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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Jonathan Greenberg <greenberg@ucdavis.edu> writes:
> Hi there, I'm trying to use CURVEFIT to fit data to a decay function of the
> form:
> f(x) = a(1-e^(bx))+c
Problem 1. Your parameters A and C are very highly (anti) correlated
with each other. It would be better to recast as A*EXP(B*X) + C.
> My code is as follows:
>
> pro decayfunc, X,A,F,pder
> bx=EXP(A[1]*X)
> F=A[0]*(1-bx)+A[2]
> if N_PARAMS() GE 4 THEN $
> pder=[[1-bx],[-A[0]*X*bx],[replicate(1.0,N_ELEMENTS(X))]]
> end
> X=[30185.0,33897.0,35089.0,35377.0,35665.0]
> Y=[0.3002,1.3849,1.3004,1.226,1.3118]
> A=[1.25,-1.0,-0.1]
Problem 2. Your initial value of "B" of -1 is not a good choice.
When the fitter tries to evaluate EXP(-1.0*30185.) the result is zero.
A better choice would be about -1./30000.
Problem 3. Your data don't look very exponential to me! There is
just one low point. You are going to have to live with some very
large confidence intervals...
> weight=[1.0,1.0,1.0,1.0,1.0]
> yfit=CURVEFIT[X,Y,weights,A,SIGMA,FUNCTION_NAME='decayfunc', /DOUBLE]
Suggestion. It might be worth trying MPCURVEFIT or MPFITFUN from my
web page. The fitting routines appear to be much more robust than the
stock CURVEFIT.
Good luck,
Craig
http://cow.physics.wisc.edu/~craigm/idl/idl.html (under curve fitting)
--
------------------------------------------------------------ --------------
Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
------------------------------------------------------------ --------------
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| Re: Problems getting CURVEFIT to work [message #32897 is a reply to message #32857] |
Fri, 15 November 2002 10:35 |
Jonathan Greenberg
Messages: 91
Registered: November 2002
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Member |
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Hello again Craig:
You MPCURVEFIT function is terrific! I've started using it instead of
CURVEFIT. One quick question, how does it deal with NaN values? I started
including NaN values in my regressions, and I noticed some strange behavior
from the output -- ideally it should just ignore the X,Y that has a NaN for
the X value, but is this actually the case?
--j
On 11/12/02 5:14 PM, in article onk7jiuv7e.fsf@cow.physics.wisc.edu, "Craig
Markwardt" <craigmnet@cow.physics.wisc.edu> wrote:
>
> Jonathan Greenberg <greenberg@ucdavis.edu> writes:
>> Hi there, I'm trying to use CURVEFIT to fit data to a decay function of the
>> form:
>> f(x) = a(1-e^(bx))+c
>
> Problem 1. Your parameters A and C are very highly (anti) correlated
> with each other. It would be better to recast as A*EXP(B*X) + C.
>
>
>> My code is as follows:
>>
>> pro decayfunc, X,A,F,pder
>> bx=EXP(A[1]*X)
>> F=A[0]*(1-bx)+A[2]
>> if N_PARAMS() GE 4 THEN $
>> pder=[[1-bx],[-A[0]*X*bx],[replicate(1.0,N_ELEMENTS(X))]]
>> end
>> X=[30185.0,33897.0,35089.0,35377.0,35665.0]
>> Y=[0.3002,1.3849,1.3004,1.226,1.3118]
>> A=[1.25,-1.0,-0.1]
>
> Problem 2. Your initial value of "B" of -1 is not a good choice.
> When the fitter tries to evaluate EXP(-1.0*30185.) the result is zero.
> A better choice would be about -1./30000.
>
> Problem 3. Your data don't look very exponential to me! There is
> just one low point. You are going to have to live with some very
> large confidence intervals...
>
>> weight=[1.0,1.0,1.0,1.0,1.0]
>> yfit=CURVEFIT[X,Y,weights,A,SIGMA,FUNCTION_NAME='decayfunc', /DOUBLE]
>
> Suggestion. It might be worth trying MPCURVEFIT or MPFITFUN from my
> web page. The fitting routines appear to be much more robust than the
> stock CURVEFIT.
>
> Good luck,
> Craig
>
> http://cow.physics.wisc.edu/~craigm/idl/idl.html (under curve fitting)
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