GNU set heatmap axis limits around a dynamically computed point

Question

I'm plotting a heatmap in gnuplot from a text file that is in matrix format:

z11 z12 z13
z21 z22 z23
z31 z32 z33

and so forth, using the following command (not including axis labelling, etc, for brevity):

plot '~/some_text_file.txt' matrix notitle with image

The matrix is quite large, in excess of 50 000 elements in the majority of cases, and it's mostly due to the size of my y-dimension (#rows). I would like to know if there's a way to change the limits in the y-dimension for a set number of values around a maximum, while keeping the x and z dimensions the same. E.g. if a maximum in the matrix is at [4000, 33], I want my y range to be centred at 4000 +- let's say 20% of length of the y-dimension.

Thanks.

Answer 1

---

Edit:

The solution below is basically the correct idea, however it works in my example but not in general because a bug in how gnuplot uses the stats command with matrix files. See the comments after the answer for further info.

---

You can do this using stats to get the indices that correspond to the maximum value dynamically.

Consider the following file which I named data:

0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
0 1 5 3 4
0 1 2 3 4

If I run statsI get:

gnuplot> stats "data" matrix

* FILE: 
  Records:      25
  Out of range:  0
  Invalid:       0
  Blank:         0
  Data Blocks:   1

* MATRIX: [5 X 5] 
  Mean:          2.1200
  Std Dev:       1.5315
  Sum:          53.0000
  Sum Sq.:     171.0000

  Minimum:       0.0000 [ 0 0 ]
  Maximum:       5.0000 [ 3 2 ]
  COG:           2.9434      2.0566

The maximum value is in position [ 3 2 ] meaning row 3+1 and column 2+1 (in gnuplot the first row/column would be number 0). After running stats some variables are created automatically (help stats for more info), with STATS_index_max_x and STATS_index_max_y among them, which store the position of the maximum:

gnuplot> print STATS_index_max_x
3.0
gnuplot> print STATS_index_max_y
2.0

Which you can use to automatically set the ranges. Now, because STATS_index_max_x actually gives you the y (instead of x) position, you'll need to be careful. The total number of rows to obtain the range can be obtained with a system call (there might be a better built-in function, which I do not know):

gnuplot> range = system("awk 'END{print NR}' data")
gnuplot> print range
5

So basically you'll do:

stats "data" matrix
range = system("awk 'END{print NR}' data")
range_center = STATS_index_max_x
d = 0.2 * range
set yrange [range_center - d : range_center + d]

which will center the yrange at the position of your maximum value and will stretch it by +-20% of its total range.

The result of plot "data" matrix w image is now

instead of