| Re: IDL fitting of piecewise continuous function [message #76112] |
Tue, 17 May 2011 19:35 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On May 17, 3:53 pm, Jeremy Bailin <astroco...@gmail.com> wrote:
> If you define your function analogously to the example in the MPFIT code, it might look like:
>
> FUNCTION MYFUNCT, p, X=x, Y=y, ERR=err
> ; p[0] is A
> x_m = SOME_CONSTANT_VALUE
>
> ; x lt x_m is 1 if x<x_m and 0 otherwise
> ; x ge x_m is 1 if x >= x_m and 0 otherwise
> model = (x lt x_m) * p[0] * x^(0.5) + (x ge x_m) * p[0] * x_m^(1.5) / x
>
> return, (y-model)/err
> END
>
> Of course, that assumes that x_m is a constant, not a parameter - but if it's a parameter, you would just use p[1] instead of a constant value, for example.
Yep, what he said.
Craig
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| Re: IDL fitting of piecewise continuous function [message #76114 is a reply to message #76112] |
Tue, 17 May 2011 12:53  |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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If you define your function analogously to the example in the MPFIT code, it might look like:
FUNCTION MYFUNCT, p, X=x, Y=y, ERR=err
; p[0] is A
x_m = SOME_CONSTANT_VALUE
; x lt x_m is 1 if x<x_m and 0 otherwise
; x ge x_m is 1 if x >= x_m and 0 otherwise
model = (x lt x_m) * p[0] * x^(0.5) + (x ge x_m) * p[0] * x_m^(1.5) / x
return, (y-model)/err
END
Of course, that assumes that x_m is a constant, not a parameter - but if it's a parameter, you would just use p[1] instead of a constant value, for example.
-Jeremy.
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| Re: IDL fitting of piecewise continuous function [message #76115 is a reply to message #76114] |
Tue, 17 May 2011 12:26 |
Sasha Singh
Messages: 13
Registered: November 2010
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Junior Member |
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Thanks Jeremy,
I did look look at MPFIT. I am confused as to how do I define the
constraints x<x_m and x > x_m in the function. Sorry I am quite new to
IDL.
Sasha
On May 17, 3:21 pm, Jeremy Bailin <astroco...@gmail.com> wrote:
> Craigh Markwardt's MPFIT (and its varients) is most people's preferred fitting routine:
>
> http://www.physics.wisc.edu/~craigm/idl/fitting.html
>
> You define your own function to feed in, so it can have whatever behaviour you want. To ensure continuity, I would recommend re-parametrizing the functional form so that it is continuous by definition. In this, case, A and B aren't actually independent, so calculate B in terms of A by setting them equal at x=x_m, which gives
> B = A x_m^(3/2)
>
> So you're actually fitting:
>
> f(x) = A x_m^(1/2) x^(1/2) x < x_m
> A x_m^(3/2) x^(-1) x > x_m
>
> -Jeremy.
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| Re: IDL fitting of piecewise continuous function [message #76117 is a reply to message #76116] |
Tue, 17 May 2011 12:21 |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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Craigh Markwardt's MPFIT (and its varients) is most people's preferred fitting routine:
http://www.physics.wisc.edu/~craigm/idl/fitting.html
You define your own function to feed in, so it can have whatever behaviour you want. To ensure continuity, I would recommend re-parametrizing the functional form so that it is continuous by definition. In this, case, A and B aren't actually independent, so calculate B in terms of A by setting them equal at x=x_m, which gives
B = A x_m^(3/2)
So you're actually fitting:
f(x) = A x_m^(1/2) x^(1/2) x < x_m
A x_m^(3/2) x^(-1) x > x_m
-Jeremy.
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