Re: [ferret_users] zaxreplace and integrals

[Ansley Manke <ansley.b.manke@xxxxxxxx>]

Hi Jimmy,
Applying an integral to the result of a ZAXREPLACE function should not 
pose any problems. You don't say what problems you're running into, but 
I did a few tests, and I wonder if you're might be running into the fact 
that any indefinite integral computation stops when it encounters 
missing data. Here is a simple example, I'll do a ZAXREPLACE example below.

  yes? def axis/z=1:5:1 zax
  yes? let a = reshape({1,2,3,,5},z[gz=zax])
  yes? list a,a[z=@iin]
               Z: 0.5 to 5.5
   Column  1: A is RESHAPE({1,2,3,,5},Z[GZ=ZAX])
   Column  2: A[Z=@IIN] is RESHAPE({1,2,3,,5},Z[GZ=ZAX]) (indef. integ. 
on Z)
               A     A
  1   / 1:  1.000  1.000
  2   / 2:  2.000  3.000
  3   / 3:  3.000  6.000
  4   / 4:   ....   ....
  5   / 5:  5.000   ....
 
  yes? let b =  reshape({,2,3,4,5},z[gz=zax])
  yes? list b, b[z=@iin]
               Z: 0.5 to 5.5
   Column  1: B is RESHAPE({,2,3,4,5},Z[GZ=ZAX])
   Column  2: B[Z=@IIN] is RESHAPE({,2,3,4,5},Z[GZ=ZAX]) (indef. integ. 
on Z)
               B    B
  1   / 1:   ....  ....
  2   / 2:  2.000  ....
  3   / 3:  3.000  ....
  4   / 4:  4.000  ....
  5   / 5:  5.000  ....


When integrating the variable in z, if the start of the column of data 
is missing, then the entire result is missing. (This is true integrating 
in any direction, not just z).

Taking the example from the ZAXREPLACE section of the Users Guide,

  yes? use levitus_climatology

  yes? let sigma = rho_un(salt, temp, 0)-1000
  yes? def axis/z=21:28:0.05 axden
  yes? let saltonsigma = zaxreplace(salt, sigma, z[gz=a
  yes? set view left; fill/y=0/x=120e:75w/vlim=28:21:-1 saltonsigmaxden])

       ! notice that saltonsigma always starts with a
       ! missing value at z=21, so the integral is all missing:

  yes? set view right; fill/y=0/x=120e:75w/vlim=28:21:-1 
saltonsigma[z=@iin]

       ! try @iin over a range of z where there is data at the start of
       ! the range of integration. Now there are results where there
       ! is valid data at z=23, and no result where saltonsigma is
       ! missing at z=23