3. Axes

Residuals fall over decades: a linear axis shows the first iterations and flattens the rest. A log axis shows the whole convergence.

call fig%set_logscale('y')                     ! residuals span decades
call fig%set_grid                              ! grid lines at the major ticks
call fig%set_xrange(min=0.0_R8P, max=120.0_R8P)
call fig%set_xtics(step=20.0_R8P)              ! a tick every 20 iterations
call fig%set_format('%.0e', axes='y')          ! 1e-03 instead of 10^-3

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• set_logscale('y') is gnuplot's set logscale y: base 10; non-positive values become gaps. 'x', 'xy', 'y2' name other axes; without argument, all.
• set_grid draws grid lines at the major ticks (g toggles them in the page).
• set_xrange(min, max): an absent end is autoscaled; min > max reverses the axis.
• set_xtics(step=20): a tick every 20; start and end limit them. On a log axis the step is a factor.
• set_format('%.0e', axes='y'): the printf format of the tick labels, %f, %e, %g, and gnuplot's %h.

Autoscaling, as gnuplot

An autoscaled end extends outward to the next tick: the x axis above runs to 120, a multiple of the step, not to the last iteration. A fixed end does not move. Tick labels are exact decimals — 0.3, never 0.30000000000000004 — because they are built from integers, in Fortran and in the page alike.

What you learned

Log axes, grid, ranges, tick steps and label formats. Reference: gnuplot Subset.

Next: 4. From the log, with a script.