Added dgrid3d function
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Giorgio Calderone
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@ -198,7 +198,7 @@ saveas("advanced013b") # hide
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```
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The [`hist()`](@ref) function compute also 2D histograms by passing two vectors (with the same lengths), e.g.:
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The [`hist()`](@ref) function compute also 2D histograms by passing two vectors (with the same lengths), e.g.:
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```@example abc
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x = randn(10_000)
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y = randn(10_000)
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@ -272,6 +272,53 @@ saveas("advanced014f") # hide
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## Interpolation of 2D scattered data
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The `dgrid3d()` function allows to interpolate 2D scattered data onto a 2D regular grid, e.g.:
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```@example abc
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x = (rand(200) .- 0.5) .* 3;
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y = (rand(200) .- 0.5) .* 3;
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z = exp.(-(x.^2 .+ y.^2));
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# Interpolate on a 20x30 regular grid with splines
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gx, gy, gz = dgrid3d(x, y, z, "20,30 splines")
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@gsp "set size ratio -1" "set xyplane at 0" xlab="X" ylab="Y" :-
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@gsp :- x y z "w p t 'Scattered data' lc pal"
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@gsp :- gx gy gz "w l t 'Interpolation on a grid' lc pal"
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saveas("advanced015a") # hide
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```
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!!! warn
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The `splines` algorithm may be very slow on large datasets. An alternative option is to use a smoothing kernel, such as `gauss`.
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The interpolated data in scarcely sampled regions are poorly constrained, i.e. they are actually *extrapolated values*. By using the `extra=false` keyword all extrapolated values are set to `NaN`:
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```@example abc
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x = randn(2000) .* 0.5;
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y = randn(2000) .* 0.5;
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rsq = x.^2 + y.^2;
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z = exp.(-rsq) .* sin.(y) .* cos.(2 * rsq);
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@gsp "set size ratio -1" palette(:balance, smooth=true) "set view map" "set pm3d" :-
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@gsp :- "set multiplot layout 1,3" xr=[-2,2] yr=[-2,2] :-
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@gsp :- 1 tit="Scattered data" x y z "w p notit lc pal"
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# Show extrapolated values
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gx, gy, gz = dgrid3d(x, y, z, "40,40 gauss 0.1,0.1")
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@gsp :- 2 tit="Interpolation on a grid\\n(extrapolated values are shown)" gx gy gz "w l notit lc pal"
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# Hide exrapolated values
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gx, gy, gz = dgrid3d(x, y, z, "40,40 gauss 0.1,0.1", extra=false)
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@gsp :- 3 tit="Interpolation on a grid\\n(extrapolated values are hidden)" gx gy gz "w l notit lc pal"
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save(term="pngcairo size 1000,400 fontscale 1.0", output="assets/advanced015b.png") # hide
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```
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## Animations
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The [Multiplot](@ref) capabilities can also be used to stack plots one above the other in order to create an animation, as in the following example:
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@ -13,6 +13,7 @@ The list of **Gnuplot.jl** exported symbols is as follows:
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boxxy
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contourlines
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dataset_names
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dgrid3d
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gpexec
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gpmargins
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gpranges
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@ -21,6 +21,8 @@ The **Gnuplot.jl** package allows easy and fast use of [gnuplot](http://gnuplot.
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- enhanced support for contour plots;
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- 2D interpolation of scattered data on a regular grid;
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- export to a huge number of formats such as `pdf`, `png`, `gif`, ``\LaTeX``, `svg`, etc. (actually all those supported by gnuplot);
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- compatibility with Jupyter and Juno;
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101
src/Gnuplot.jl
101
src/Gnuplot.jl
@ -10,7 +10,7 @@ import Base.show
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export session_names, dataset_names, palette_names, linetypes, palette,
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terminal, terminals, test_terminal,
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stats, @gp, @gsp, save, gpexec,
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boxxy, contourlines, hist, recipe, gpvars, gpmargins, gpranges
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boxxy, contourlines, dgrid3d, hist, recipe, gpvars, gpmargins, gpranges
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# ╭───────────────────────────────────────────────────────────────────╮
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@ -2094,6 +2094,105 @@ function contourlines(x::AbstractVector{Float64}, y::AbstractVector{Float64}, z:
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end
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# --------------------------------------------------------------------
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"""
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dgrid3d(x, y, z, opts=""; extra=true)
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Interpolate non-uniformly spaced 2D data onto a regular grid.
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!!! note
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This feature is not available in *dry* mode and will raise an error if used.
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# Arguments:
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- `x`, `y`, `z` (as `AbstractVector{Float64}`): coordinates and values of the function to interpolate;
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- `opts`: interpolation settings (see gnuplot documentation for `dgrid3d`);
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- `extra`: if `true` (default) compute inerpolated values in all regions, even those which are poorly constrained by input data (namely, extrapolated values). If `false` set these values to `NaN`.
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# Return values:
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A tuple with `x` and `y` coordinates on the regular grid (as `Vector{Float64}`), and `z` containing interpolated values (as `Matrix{Float64}`).
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# Example
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```julia
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x = (rand(200) .- 0.5) .* 3;
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y = (rand(200) .- 0.5) .* 3;
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z = exp.(-(x.^2 .+ y.^2));
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# Interpolate on a 20x30 regular grid with splines
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gx, gy, gz = dgrid3d(x, y, z, "20,30 splines")
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@gsp "set size ratio -1" "set xyplane at 0" xlab="X" ylab="Y" :-
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@gsp :- x y z "w p t 'Scattered data' lc pal"
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@gsp :- gx gy gz "w l t 'Interpolation on a grid' lc pal"
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```
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!!! warn
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The `splines` algorithm may be very slow on large datasets. An alternative option is to use a smoothing kernel, such as `gauss`:
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```julia
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x = randn(2000) .* 0.5;
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y = randn(2000) .* 0.5;
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rsq = x.^2 + y.^2;
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z = exp.(-rsq) .* sin.(y) .* cos.(2 * rsq);
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@gsp "set size ratio -1" palette(:balance, smooth=true) "set view map" "set pm3d" :-
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@gsp :- "set multiplot layout 1,3" xr=[-2,2] yr=[-2,2] :-
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@gsp :- 1 tit="Scattered data" x y z "w p notit lc pal"
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# Show extrapolated values
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gx, gy, gz = dgrid3d(x, y, z, "40,40 gauss 0.1,0.1")
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@gsp :- 2 tit="Interpolation on a grid\\\\n(extrapolated values are shown)" gx gy gz "w l notit lc pal"
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# Hide exrapolated values
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gx, gy, gz = dgrid3d(x, y, z, "40,40 gauss 0.1,0.1", extra=false)
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@gsp :- 3 tit="Interpolation on a grid\\\\n(extrapolated values are hidden)" gx gy gz "w l notit lc pal"
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```
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"""
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function dgrid3d(x::AbstractVector{Float64},
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y::AbstractVector{Float64},
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z::AbstractVector{Float64},
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opts::String="";
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extra=true)
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c = Gnuplot.gp_write_table("set dgrid3d $opts", x, y, z, is3d=true)
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gx = Vector{Float64}()
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gy = Vector{Float64}()
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gz = Vector{Float64}()
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ix = 0
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iy = 0
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for l in c
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l = string(strip(l))
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if l == "# x y z type"
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ix += 1
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iy = 1
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else
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(l == "" ) && continue
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(l[1] == '#') && continue
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n = Meta.parse.(split(l)[1:3])
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(iy == 1) && push!(gx, n[1])
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(ix == 1) && push!(gy, n[2])
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if n[3] == :NaN
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push!(gz, NaN)
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else
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push!(gz, n[3])
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end
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iy += 1
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end
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end
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gz = collect(reshape(gz, length(gy), length(gx))')
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if !extra
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dx = abs(gx[2]-gx[1]) / 2
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dy = abs(gy[2]-gy[1]) / 2
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for ix in 1:length(gx)
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for iy in 1:length(gy)
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n = length(findall(((gx[ix] - dx) .< x .< (gx[ix] + dx)) .&
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((gy[iy] - dy) .< y .< (gy[iy] + dy))))
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(n == 0) && (gz[ix, iy] = NaN)
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end
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end
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end
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return (gx, gy, gz)
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end
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# ╭───────────────────────────────────────────────────────────────────╮
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# │ GNUPLOT REPL │
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# ╰───────────────────────────────────────────────────────────────────╯
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