Gri: contour plots

Chapters: 1: Introduction 2: Simple example 3: Invocation 4: Finer Control 5: X-Y Plots 6: Contour Plots 7: Image Plots 8: Examples 9: Gri Commands 10: Programming 11: Environment 12: Emacs Mode 13: History 14: Installation 15: Gri Bugs 16: Test Suite 17: Gri in Press 18: Acknowledgments 19: License Indices: Concepts Commands Variables | # 6: Contour Plots Contour plots can be done with either pregridded data or randomly distributed (ie, ungridded) data. Pre-gridded Data: Contouring f(x1, y1, x2, y2, ...) Ungridded Data: Contouring f(x, y) where (x,y) are not on a grid ## 6.1: Pre-gridded Data This section presents two examples of contouring pre-gridded data, the first example illustrating a boilerplate program to contour data stored in a simple matrix form in a file, the second example illustrating a case with more control of the details (e.g., a nonuniform grid). ### 6.1.1: Simple example This example was hardwired to know the size of the grid, etc. Here's an example which is more general, in that it determines the dimensions of the grid data from using unix system commands. Note that the grid is set to run from 0 to 1 in both x and y; you'll most likely want to change that after you see the initial plot, but this should get you started.
    \file = "somefile.dat"
    \rows = system wc \file      | awk '{print $1}'
    \cols = system head -1 \file | awk '{print NF}'
    set x grid 0 1 /\cols
    set y grid 0 1 /\rows
    open \file
    read grid data \rows \cols
    close
    draw contour
### 6.1.2: Complicated example To get a simple contour graph based on pre-gridded data, with full control of axes, etc, do something like this: The command-file. Here several new things have been introduced. First, you've got to define a grid in xy space. This example uses a non-uniform x-grid, and reads it in from the commandfile. In this form, the blank line is essential; it tells Gri that the end of data has been located; if you like, you can specify the number of lines to read, as in ``read grid x 3`'. The y-grid for this example is uniform, however, so it may be specified with the ``set y grid`' command. It obtains values (10, 12.5, 15, 17.5, 20). The ``set x|y grid`' commands accept negative increments. Furthermore, it is possible to specify the number of steps, rather than the increment size, by putting ``/`' before the third number; thus ``set x grid 0 1 /5`' and ``set x grid 0 1 0.2`' are equivalent. Having defined a grid, it is time to read in the gridded data. Here this is done with the ``read grid data`' command. Since Gri already knows the grid dimensions, it will read the data appropriately. You could also have told it (``read grid data 3 5`'). The first dataline is the top of the y-grid. In other words, the data appear in the file just as they would on the graph, assuming that the x-grid and y-grid both increase. Sometimes you want to read in the transpose of a matrix. Gri lets you do that. If the ``bycolumns`' keyword is present at the end of the ``read grid`' command, the first dataline will contain the first column, of the data. If you have an extraneous column of data to the left of your data matrix, do ``read grid data * 2 3`' Now Gri has the grid in its head. We tell it to draw some contours with the ``draw contour`' command. As the comments in the example show, the contour values will be selected automatically, but you can alter that. ## 6.2: Ungridded data When you have f=f(x,y) points at random x and y, you must cast them onto a grid to contour them. This is a difficult problem. There are many ways to grid data, and all have both good and bad features. You should try various methods, and various settings of the parameters of the methods. If you have a favorite gridding method that you prefer, you should probably pre-grid the data yourself. If not, Gri can do it for you. Gri has two methods for doing this, the ``boxcar'' method and the ``objective analysis'' method. Each method puts holes in the grid wherever there are too few data to map to grid points, unless you specifically ask to fill in the whole grid. The next two sections show first an example, then a discussion of the methods and how to use them. ### 6.2.1: Example This example uses data taken from Figure 5 of S. E. Koch and M. DesJardins and P. J. Kocin, 1983. ``An interactive Barnes objective map anlaysis scheme for use with satellite and conventional data,'', J. Climate Appl. Met., vol 22, p. 1487-1503. Readers should compare Figures 5 and 6 of that paper to the results shown here. The command-file. ### 6.2.2: Discussion of Methods The various commands for converting columns to a grid are given in (see Convert Columns To Grid). Generally, the Barnes method is best.