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Re: Function Maximum [message #35474 is a reply to message #35470]

Thu, 19 June 2003 14:06

Paul Van Delst[1]
Messages: 1157
Registered: April 2002

Senior Member

Kate wrote:
>
> If I have a function definition, say it is
>
> FUNCTION MYGAMMA, X, P
> RETURN, P[0]*(X^P[1])*EXP(-1*X/P[2])
> END
>
> Where P holds my fit parameters that are already determined.
>
> If I want to find a local maximum in a certain range is it possible to
> do this with an existing written IDL function?

How about something like:

maxY = MAX( mygamma(X,P) )

?

You already have your P's and your X's define the range in which the maximum is sought. If
you need the X-value of the maximum, then

maxY = MAX( mygamma(X,P), maxXLoc )
maxX = X[maxXLoc]

If you don't want to carry around a bunch of X-vectors, then why not do something like:

FUNCTION FINDMAX, Xr, P, UserFunction
X1 = DOUBLE(Xr[0]) ; The beginning of the range
X2 = DOUBLE(Xr[1]) ; The end of the range
dX = DOUBLE(Xr[2]) ; The resolution within the range

; Compute the ordinate vector
nX = LONG( (X2-X1)/dX ) + 1.5d0 )
X = ( DINDGEN( nX ) / DOUBLE( nX-1 ) ) * ( X2-X1 ) + X1

; Find the maximum value of your user function
Y = CALL_FUNCTION( UserFunction, X, DOUBLE(P) )
maxY = MAX( Y, maxXLoc )
maxX = X[ maxXLoc ]

; Return the coordinate of the local max
RETURN, [ maxX, maxY ]

END

where the Xr input defines the function range [x1,x2] and the resolution at which the
function is calculated (Sort of like a loop triplet.)

Otherwise maybe you could use something like the FX_ROOT function to find the roots of the
first derivative of your function (via DERIV or your own calculated derivative) and use
the second derivative to determine if it's a max or min.

paulv

--
Paul van Delst
CIMSS @ NOAA/NCEP/EMC
Ph: (301)763-8000 x7748
Fax:(301)763-8545

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[Message index]

		Re: Function Maximum By: faeriepunk on Fri, 20 June 2003 06:25
		Re: Function Maximum By: Paul Van Delst[1] on Thu, 19 June 2003 14:06
		Re: Function Maximum By: R.Bauer on Thu, 19 June 2003 12:55
		Re: Function Maximum By: Haje Korth on Thu, 19 June 2003 11:48
		Re: Function Maximum By: James Kuyper on Thu, 19 June 2003 10:10
		Re: Function Maximum By: Craig Markwardt on Thu, 19 June 2003 09:50
		Re: Function Maximum By: James Kuyper on Thu, 19 June 2003 09:27
		Re: Function Maximum By: Benjamin Panter on Thu, 19 June 2003 08:02
		Re: Function Maximum By: Craig Markwardt on Thu, 19 June 2003 07:45
		Re: Function Maximum By: R.Bauer on Thu, 19 June 2003 07:44

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