Re: Question About Variable Limits of Integration

[Steve Hankin <hankin@xxxxxxxxxxxxx>]

Hi Ben,

If you perform a definite integral (@DIN) in 3 dimensions (X,Y & Z), Ferret
will perform this as a true 3-dimensional integral. Limits on an axis, which
are themselves dependent on the orthogonal axes, can be represented in the way
the variable is masked (where missing values are placed.

==> Your solution: mask the data with a mask built of your integration limits

The following example illustrates a volume integral over highly irregular
limits. Notice that the output is documented as "XYZ integ." -- indicating the
multi-dimensional integration used.

    - steve

yes? use levitus_climatology
yes? let temp_gt_15 = if temp gt 15 then temp

yes? shade/k=1 temp_gt_15
yes? shade/y=0 temp_gt_15

yes? list temp_gt_15[x=@din,y=@din,z=0:1000@din]
             IF TEMP GT 15 THEN TEMP
             LONGITUDE: 20E to 20E(380) (XYZ integ.)
             LATITUDE: 90S to 90N (XYZ integ.)
             DEPTH (m): 0 to 1000 (XYZ integ.)
             DATA SET: /home/r3/tmap/fer_dsets/descr/levitus_climatology.des
          1.028E+18

=================================================

blintner@socrates.berkeley.edu wrote:

> Ferret Developers,
>
>   I have a question concerning limits of integration of one coordinate
> that vary with other coordinates.  What I would like to do is perform
> an integration of a field over x, y, and z, where the limits of
> integration of the y coordinate depend on x, z, and t.  The lower limit
> of integration of the y coordinate is derived by maximizing another field,
> and the values of y limits of integration obtained depend on the
> remaining coordinates.  For example, for i=1, k=1, l=1, the lower limit
> is y(i=1,k=1,l=1)=2S, for i=2, k=1, l=1, the lower limit is
> y(i=2,k=1,l=1)=4N, and so on and so forth.  Do you have any suggestions
> how I might accomplish this integration?  Thanks you.
>
> Ben Lintner

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