initial

CwJ/differentiable_vector_calculus/data/hearts.mmd

@@ -0,0 +1,29 @@
+From [bennedich](https://discourse.julialang.org/t/love-in-245-characters-code-golf/20771)
+
+```
+   0:2e-3:2π    .|>d->(P=
+ fill(5<<11,64 ,25);z=8cis(
+d)sin(.46d);P[ 64,:].=10;for
+r=0:98,c=0 :5^3 x,y=@.mod(2-
+$reim((.016c-r/49im-1-im)z),
+ 4)-2;4-x^2>√2(y+.5-√√x^2)^
+  2&&(P[c÷2+1,r÷4+1]|=Int(
+    ")*,h08H¨"[4&4c+1+r&
+      3])-40)end;print(
+       "\e[H\e[1;31m",
+         join(Char.(
+            P)))
+             );
+```
+
+
+
+[New York Times](https://www.nytimes.com/2019/02/14/science/math-algorithm-valentine.html)
+
+Süss — German for “sweet” — is an interactive widget that allows you to tweak the algebra and customize the heart to your souls’s delight. It was created for Valentine’s Day by Imaginary, a nonprofit organization in Berlin that designs open-source mathematics programs and exhibitions.
+
+You can stretch and squeeze the heart by moving the two left-most sliders, which change the “a” and “b” parameters; the right-most slider zooms in and out. Better yet, canoodle directly with Süss’s equation and engage in the dialectical interplay between algebra and geometry. (Change that final z³ to a z² to see the heart in its underwear.)
+
+```
+(x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3
+```

CwJ/differentiable_vector_calculus/data/lenape.csv

@@ -0,0 +1,72 @@
+"","elevation","elev_units","longitude","latitude"
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+"70",84.49,"meters",-74.2924236,40.755502
+"71",84.36,"meters",-74.2923562,40.7554961

CwJ/differentiable_vector_calculus/data/xy_ys.jl

@@ -0,0 +1,294 @@
+## container of points into vectors n vectors of length N
+## N points, each of size n
+
+## Lesson learned -- this is a very bad idea!
+## better to handle the T a different way
+evec(T,n) =  Tuple(T[] for _ in 1:n)
+evec(T, N, n) =  Tuple(Vector{T}(undef, N) for _ in 1:n)
+
+
+## julia> @btime xs_ys1(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   83.308 μs (1013 allocations: 172.67 KiB)
+
+## julia> @btime xs_ys2(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   222.371 μs (2016 allocations: 180.72 KiB)
+
+## julia> @btime xs_ys3(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   1.003 ms (1019 allocations: 165.20 KiB)
+
+## julia> @btime xs_ys4(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   1.115 ms (5474 allocations: 210.95 KiB)
+
+## julia> @btime xs_ys5(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   1.120 ms (5474 allocations: 210.95 KiB)
+
+## julia> @btime xs_ys6(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   76.604 μs (1008 allocations: 164.63 KiB)
+
+## julia> @btime xs_ys7(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   74.306 μs (1008 allocations: 164.63 KiB)
+
+## julia> @btime xs_ys8(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   36.098 μs (2006 allocations: 94.25 KiB)
+
+## julia> @btime xs_ys9(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   85.732 μs (3006 allocations: 203.63 KiB)
+
+## ....
+
+    ## THE WINNER, but we would use one with keywords
+## julia> @btime xs_ys13a(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   62.768 μs (1003 allocations: 117.28 KiB)
+
+## julia> @btime xs_ys13akw(vs) setup=(vs=[randn(1000) for i in 1:3]);
+##   65.905 μs (1003 allocations: 117.28 KiB)
+
+
+## make a matrix n x N, then go down 1:n
+function xs_ys1(vs)
+    A=hcat(vs...)
+    Tuple([A[i,:] for i in eachindex(first(vs))])
+end
+
+## broadcast push!
+function xs_ys2(vs)
+    u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    v0 = evec(T,n)
+    for v in vs
+        push!.(v0, v)
+    end
+    v0
+end
+
+
+## broadcast push!
+function xs_ys2a(vs)
+    u = first(vs); N = length(vs)
+    n = length(u)
+    v0 = Tuple(eltype(u)[] for _ in eachindex(u))
+    for v in vs
+        push!.(v0, v)
+    end
+    v0
+end
+
+## broadcast setindex!
+function xs_ys3(vs)
+  u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    v0 = evec(T,N,n)
+    for (i,v) in enumerate(vs)
+        setindex!.(v0, v, i)
+    end
+
+    v0
+end
+
+## 10 times faster ~77mus avoiding passing T
+function xs_ys3a(vs)
+  u = first(vs); N = length(vs)
+    n = length(u)
+    v0 = Tuple(Vector{eltype(u)}(undef, N) for _ in eachindex(u))
+    for (i,v) in enumerate(vs)
+        setindex!.(v0, v, i)
+    end
+
+    v0
+end
+
+
+function xs_ys3b(vs)
+  u = first(vs); N = length(vs)
+    n = length(u)
+    v0 = ntuple(_ -> Vector{eltype(u)}(undef, N), n)
+    for (i,v) in enumerate(vs)
+        setindex!.(v0, v, i)
+    end
+
+    v0
+end
+
+## loop N n
+function xs_ys4(vs)
+    u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    v0 = evec(T,N,n)
+
+    for i in 1:N
+        for j in 1:n
+            v0[j][i] = vs[i][j]
+        end
+    end
+    v0
+end
+
+
+## loop N n
+function xs_ys4a(vs)
+    u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    v0 = evec(T,N,n)
+
+    for (i,v) in enumerate(vs)
+        for j in 1:n
+            v0[j][i] = v[j]
+        end
+    end
+    v0
+end
+
+## fast 67mus
+function xs_ys4b(vs)
+    u = first(vs); N = length(vs)
+    n = length(u)
+    v0 = Tuple(Vector{eltype(u)}(undef, N) for _ in eachindex(u))
+
+    for (i,v) in enumerate(vs)
+        for j in 1:n
+            v0[j][i] = v[j]
+        end
+    end
+    v0
+end
+
+## loop n N
+function xs_ys5(vs)
+    u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    v0 = evec(T,N,n)
+
+    for j in 1:n
+        for i in 1:N
+            v0[j][i] = vs[i][j]
+        end
+    end
+    v0
+end
+
+function xs_ys6(vs)
+    u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    A = Matrix{T}(undef, (N,n))
+    for (i,v) in enumerate(vs)
+        A[i,:] = v
+    end
+    Tuple(A[:,i] for i in 1:n)
+end
+
+function xs_ys7(vs)
+    u = first(vs); N = length(vs)
+    T = eltype(u); n = length(u)
+    A = Matrix{T}(undef, (n, N))
+    for (i,v) in enumerate(vs)
+        A[:,i] = v
+    end
+    Tuple(A[i, :] for i in 1:n)
+end
+
+# faster but doesn't wotk with plot recipes
+# and may be slower once realized
+function xs_ys8(vs)
+    N = length(vs)
+    u = first(vs); T = eltype(u); n = length(u)
+    Tuple((vs[j][i] for j in 1:N) for i in 1:n)
+end
+
+function xs_ys9(vs)
+    N = length(vs)
+    u = first(vs); T = eltype(u); n = length(u)
+    Tuple(collect(vs[j][i] for j in 1:N) for i in 1:n)
+end
+
+function xs_ys10(vs)
+    N = length(vs)
+    u = first(vs); T = eltype(u); n = length(u)
+    v0 = evec(T,N, n)
+    for j in 1:n
+        v0[j][:] .= (v[j] for v in vs)
+    end
+    v0
+end
+
+# mauro3 https://github.com/JuliaDiffEq/ODE.jl/issues/80
+_pluck(y,i) =  eltype(first(y))[el[i] for el in y]
+xs_ys11(vs) = Tuple(_pluck(vs, i) for i in eachindex(first(vs)))
+
+# slower
+xs_ys11a(vs) = ntuple(i->_pluck(vs, i), length(first(vs)))
+
+# one liner
+xs_ys11b(vs) = Tuple(eltype(first(vs))[el[i] for el in vs]  for i in eachindex(first(vs)))
+
+
+function xs_ys11c(vs)
+    u = first(vs)
+    Tuple(eltype(u)[el[i] for el in vs] for i in eachindex(u))
+end
+xs_ys11d(vs) = (u=first(vs);  Tuple(eltype(u)[el[i] for el in vs] for i in eachindex(u)))
+xs_ys11e(vs) = (u=first(vs);  ntuple(i->eltype(u)[v[i] for v in vs], length(u)))
+xs_ys11f(vs) = (u=first(vs);n::Int=length(u);T::DataType=eltype(u);ntuple(i->eltype(u)[v[i] for v in vs], n))
+xs_ys11g(vs::Vector{Vector{T}}) where {T} = (u=first(vs);n::Int=length(u);ntuple(i->T[v[i] for v in vs], n))
+
+
+@inline _pluck(T, y, i) =  T[el[i] for el in y]
+function xs_ys11b(vs)
+    T = eltype(first(vs))
+    Tuple(_pluck(T, vs, i) for i in eachindex(first(vs)))
+end
+
+function xs_ys12(vs)
+    N = length(vs)
+    u = first(vs); T = eltype(u); n = length(u)
+    Tuple(T[el[i] for el in vs] for i in eachindex(first(vs)))
+    end
+
+function xs_ys12a(vs)
+    N = length(vs)
+    u = first(vs); T = eltype(u); n = length(u)
+    ntuple( i -> T[el[i] for el in vs], n)
+end
+
+
+
+function xs_ys11h(vs)
+    u = first(vs)
+    T = eltype(u)
+    Tuple(T[el[i] for el in vs] for i in eachindex(u))
+    end
+
+function xs_ys11i(vs)
+    u = first(vs)
+    Tuple(eltype(u)[el[i] for el in vs] for i in eachindex(u))
+end
+
+
+function _xs_ys12(vs, u::Vector{T}) where {T}
+    Tuple(T[el[i] for el in vs] for i in eachindex(u))
+end
+
+xs_ys13(vs, u::Vector{T}=first(vs)) where {T} = Tuple(T[el[i] for el in vs] for i in eachindex(u))
+
+xs_ys13a(vs, u::Vector{T}=first(vs), n::Val{N}=Val(length(u))) where {T,N} = ntuple(i -> T[el[i] for el in vs], n)
+
+
+## cleaned up
+function xs_ys13a(vs, u::Vector{T}=first(vs), n::Val{N}=Val(length(u))) where {T,N}
+   plucki = i -> T[el[i] for el in vs]
+   ntuple(plucki, n)
+end
+
+
+function xs_ys13akw(vs; u::Vector{T}=first(vs), n::Val{N}=Val(length(u))) where {T,N}
+   plucki = i -> T[el[i] for el in vs]
+   ntuple(plucki, n)
+end
+
+function xs_ys13b(vs, u::Vector{T}=first(vs), n::Val{N}=Val(length(u))) where {T,N}
+    Tuple(T[el[i] for el in vs] for i in eachindex(u))
+end
+
+
+xs_ys14(vs) = Tuple(eltype(vs[1])[vs[i][j] for i in 1:length(vs)] for j in 1:length(vs[1]))
+
+xs_ys14a(vs) = Tuple([vs[i][j] for i in 1:length(vs)] for j in 1:length(first(vs)))