histogram: Fix bug with the -N normal curve for reverse cumulative histograms (-Qr) - #9218
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Two separate mistakes made the -N overlay unusable together with -Qr, while -Q was fine: - pshistogram_plot_boxes derived "area" (the grand total, used to scale the -N curve) by picking up the last bin, on the grounds that it "has the entire sum". That holds for -Q, where the bars count up, but under -Qr they count down and the last bin is ~0. On a 6521-point sample the reported area came out as 21 instead of 6521, so the curve was drawn roughly 300x too small -- flat against the axis. With -S (stairs) the last bin is exactly 0, so the curve vanished altogether. Use F->sum_w, which is the same value the last bin gives under -Q and is correct either way, and hoist it out of the bar loop since it no longer depends on the bin. - The reverse curve was computed as f - yp, but f is only half the grand total (it is set to 0.5 and later multiplied by area), while the forward curve yp spans 0 to 2f. Subtracting f therefore started the curve at half height and drove it negative past the mean instead of running from the total down to zero. Use 2f - yp. With both fixed, the -Qr curve is the mirror image of the -Q one and tracks the bars, for every -Z mode and not just counts. Adds a test asserting that the reported area equals the number of input points for both -Q and -Qr; it fails on the previous code for -Qr. No baseline image changes: no existing test plots -Qr, and the -Q value is unchanged, so all eight pshistogram baselines still compare at RMS 0.0000, including distributions.sh which combines -Q with -N. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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This fails:
gmt histogram @v3206_06.txt -T-7000/0/250 -Z0 -JX12c/8c -Baf -Ggray -W0.5p -N0+p2p,red -Qr -png lixoOutput with bug:
Output with this fix:
Done with Claude Sonnet 5 and review by Opus 5.
This PR also adds a test asserting that the reported area equals the number of input points for both -Q and -Qr; it fails on the previous code for -Qr.