Operations on Tables

In this section we describe several of the mathematical operations that can be performed on table data. More specialised topics are described in Chapter 8, "Fitting of Data", and in Chapter 11 Vol B, "Multivariate Analysis Methods".

Arithmetic operations between columns in a table are done with the command

`COMPUTE/TABLE`. The selection flag is reset by this command. Special functions, named according to the FORTRAN
mathematical library, are also available.

Simple statistical descriptors are displayed with the command `STATISTICS/
TABLE`. These descriptors are stored in output keywords for further usage in
a procedure.

A set of histogram-related commands, with qualifier `HISTOGRAM`,
allow the graphic display of the histogram of a column (`PLOT`
and `OVERPLOT` commands), the printout of histogram values
(`READ` and `PRINT` commands), or the generation
of a 1D image with the histogram of a column (command `COMPUTE/HISTOGRAM`).

Linear or polynomial fits in one or two dimensions can be performed on table
columns with the command `REGRESSION`, qualifiers
`LINEAR` and `POLY` respectively. The coefficients and
error estimations are kept in output keywords that can be stored as table
descriptors with the command `SAVE/REGRESSION`. Fitted
values are calculated with `COMPUTE/REGRESSION`.

A topic of special interest is the generation of table data from an image
and vice versa. A transformation was already described in
section 5.4.3,
and consists in copying the data from one format to the other, using the commands
`COPY/IT` and `COPY/TI`. Tabular data can be
converted into 1D or 2D image data with the command `CONVERT/TABLE`. This command works in several modes controlled by a
parameter. In all cases the sampling domain of the result is defined
by a reference image. The modes currently available are : POLY
(polynomial fit to table data), SPLINE (spline approximation),
PLOT (scattergram of the data in the table) and FREQ
(2D histogram of the data in the table).

For more specific resampling and interpolating algorithms, the commands
`REBIN` and `INTERPOLATE` will provide full
conversion between image and table formats (qualifiers `TT, TI, IT`
and `II`).