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[BUG] heatmap output shifts relative to axis when using logarithmic xscale and setting xlims on GR #4908

Description

@LordCMonkey

Details

When plotting with heatmap(x, y, z::matrix) and a logarithmic xscale, setting xlims causes the heatmap output to shift to an incorrect position on the x axis.
The same happens when first plotting using heatmap(x, y, z::matrix) and then plotting 2D data, even without explicitly setting xlims, The 2D data is plotted in the correct location.
This also occurs when using :ln or :log2 and scatter instead of plot.

The expected output can be observed when using plotly or pyplot (for :log10).

Minimal working example:

using Plots

function test_bug()
    x = [10.0^x for x in 0:1]
    A = zeros(2, 2)

    heatmap(x, 1:2, A, xscale=:log10,
            xlims=[10.0^-1, 10.0^2]
    )
    #plot!(x, x -> 1.8, label="")
end

function demonstrate()
    gr()
    gui(test_bug())
    
    plotly()
    gui(test_bug())
    
    pyplot()
    gui(test_bug())
end

When commenting the xlims=.. line and uncommenting the plot! call, the same behaviour occurs.

Backends

This bug occurs on ( insert x below )

Backend yes no untested
gr (default) x
pythonplot x
plotlyjs x
pgfplotsx x
unicodeplots x
inspectdr x
gaston x

Versions

Plots.jl version: 1.40.2
Backend version: GR: 0.73.3, PlotlyBase 0.8.19 & PlotlyKaleide 2.2.4, PyPlot 2.11.2
Output of versioninfo():

Julia Version 1.10.2
Commit bd47eca2c8 (2024-03-01 10:14 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: 4 × Intel(R) Core(TM) i5-7400 CPU @ 3.00GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
Threads: 4 default, 0 interactive, 2 GC (on 4 virtual cores)
Environment:
JULIA_NUM_THREADS = auto

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