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tabint - integrate a sorted table, optionally higher order moments
tabint [parameter=value]
tabint integrates a function
Y=F(X) that is defined by a set of (X,Y) points selected from two columns
from an ASCII table. The function can either be resampled using a spline
interpolation, or directly summed using the trapezoid rule. X values need
to sorted increasing or decreasing.
See also tabhist(1NEMO)
with cumul=t
for a visual display, though the cumulative option here can also produce
a table for display to check the convergence of the integral.
An optional
scale factor can be applied, which folds in any X or Y scaling that might
need to be applied. This is particularly useful if you integrate the points
themselves (i.e. without giving a step=) but still want to scale the X coordinate.
Optionally higher order moments (1 through 4) can be also computed (step=,
normalize= and cumulative= are then ignored).
0: integrated sum 1: mean X value 2: dispersion in X 3: skewness (0=symmetric)
4: kurtosis (0 means normal)
The following parameters are
recognized in order; they may be given in any order if the keyword is also
given. Use --help to confirm this man page is up to date.
- in=
- Input table
file.
No default.
- xcol=
- Column with sorted X coordinates. If the X coordinates
are not increasing, the array will be reversed.
[Default: 1]
- ycol=
- Column with Y coordinate of the function
[Default: 2]
- xmin=
- If given, value below which data to be discarded
By default it uses the smallest datapoint from the table.
- xmax=
- If given,
value above which data to be discarded
By default it uses the largest datapoint from the table.
- step=
- Integration
step if resampling used.
By default the datapoints themselves are used, but by setting an integration
step here, the function is resampled using a spline and numerically integrated
that way. See also scale=.
- normalize=t|f
- Normalize integral. If set, the integral
is normalized by the integration interval. An output table contains the
cumulative function.
[Default: f]
- cumulative=t|f
- If set, it will show the invidual cumulative
integrations instead. Only implemented for native steps.
[Default: f]
- scale=
- scale factor to apply to the integral. This is also
to use a different step size if integrating the individual points.
[Default: 1]
- mom=0|1|2|3|4
- The moment along the profile. mom=0 is the flux,
mom=1 the first moment along the X axis, and mom=2 the dispersion.
[Default: 0]
Integrating the square function from 0 to 1 to get
1/3:
% nemoinp 0:1:0.1 | tabmath - - ’%1*%1’ | tabint -
0.335
% nemoinp 0:1:0.1 | tabmath - - ’%1*%1’ | tabint - step=0.01
0.33335
Here is an example to compute the line integral of a spectrum where
the frequency axis is in GHz, and intensity in Kelvin. We want to get an
answer in K.km/s instead. We know the line is (redshifted) around 110.5 GHz,
and we take a window of 0.3 GHz around the line:
% tabint rsr.33551.driver.sum.txt
xmin=110.5-0.3 xmax=110.5+0.3 scale=c/110.5/1000
8.05
% tabint rsr.33551.driver.sum.txt xmin=110.5-0.3 xmax=110.5+0.3 scale=c/110.5/1000
|\
tabplot - 1 2 line=1,1 point=2,0.1 ycoord=0
Recall that c is in m/s and the requested line integral was requested
in km/s.
The table needs to be (reverse) sorted in X. A future option
might sort, though sort(1)
might already work. Here’s an example where the
3rd column is an unsorted X coordinate. The 6th column is the data value:
% sort -n +2 my.tab | tabint - 3 6
perhaps easier
% tabcols my.tab 3,6 | sort -n | tabint -
All moments, expecially the higher order ones, are susceptible to the
correct window if the shape of a line feature is to be determined accurately.
tabfilter(1NEMO)
, tabhist(1NEMO)
, tabmath(1NEMO)
, tabnllsqfit(1NEMO)
ΒΈ
tabpeak(1NEMO)
, table(5NEMO)
src/kernel/tab
Peter Teuben
13-May-05 V0.1 Created PJT
10-sep-2022 V0.5 added cumulative= PJT
22-feb-2022 V0.6 added xmin=, xmax=, scale= PJT
31-jul-2023 V0.7 poor man’s implementation of mom= PJT
6-apr-2024 V0.9 clarifications PJT
17-jan-2025 V1.0 added mom=3,4 options PJT
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