Introduce Signal Measurement Demo

src/stage1/forward.jl

@@ -203,6 +203,7 @@ function (::∂☆{N})(::ZeroBundle{N, typeof(map)}, f::ATB{N}, args::ATB{N, <:A
     rebundle(map(FwdMap(f), map(unbundle, args)...))
 end
 
+
 function (::∂☆{N})(::ZeroBundle{N, typeof(map)}, f::ATB{N}, args::ATB{N}...) where {N}
     ∂☆recurse{N}()(ZeroBundle{N, typeof(map)}(map), f, args...)
 end

test/runtests.jl

@@ -20,7 +20,8 @@ const bwd = Diffractor.PrimeDerivativeBack
     "forward.jl",
     "reverse.jl",
     "regression.jl",
-    "AbstractDifferentiationTests.jl"
+    "AbstractDifferentiationTests.jl",
+    "signal_measurement.jl",
     #"pinn.jl",  # Higher order control flow not yet supported (https://github.com/JuliaDiff/Diffractor.jl/issues/24)
 )
     include(file)

test/signal_measurement.jl

@@ -0,0 +1,64 @@
+"""
+This is a demo of using Diffractor for Very basic signal processing.
+Where you have a signal that is represented as a series of sampled readings.
+Not even something as sophistricated as FFT, just time domain edge detection stuff.
+Its an important use case so we test it directly.
+"""
+module SignalMeasurement
+
+using Diffractor
+using Diffractor: ∂☆, ZeroBundle, TaylorBundle
+using Diffractor: bundle, first_partial, TaylorTangentIndex
+
+
+function make_soft_square_pulse(width, hardness=100)
+    function soft_square(t)
+        1/(1+exp(-hardness*(t-0.25))) - 1/(1+exp(-hardness*(t-0.25-width)))
+    end
+end
+#soft_square = make_soft_square_pulse(0.5, 8)
+#signal = soft_square.(0:0.001:1)
+#scatter(signal)
+
+function determine_width(xs, ts)
+    # vs real signal processing functions this is not very robust, but for sake of demonstration it is fine.
+    @assert eachindex(xs) == eachindex(ts)
+
+    start_idx = nothing
+    end_idx = nothing
+    for ii in eachindex(xs)
+        x = xs[ii]
+        if isnothing(start_idx)
+            if x > 0.5
+                start_idx = ii
+            end
+        else
+            if x < 0.5
+                end_idx = ii
+                break
+            end
+        end
+    end
+
+    (isnothing(start_idx) || isnothing(end_idx)) && throw(DomainError("no pulse found"))
+    return ts[end_idx] - ts[start_idx]
+end
+
+#ts = 0:0.001:1
+#determine_width(make_soft_square_pulse(0.5, 5).(ts), ts)
+
+
+function signal_problem(width)
+    func = make_soft_square_pulse(width, 8)
+    ts = 0.0:0.001:1.0
+    signal = func.(ts)
+    return determine_width(signal, ts)
+end
+
+
+
+🐰 = ∂☆{1}()(ZeroBundle{1}(signal_problem), TaylorBundle{1}(0.5, (1.0,)))
+@test primal(🐰) ≈ signal_problem(0.5)
+@test first_partial(🐰) ≈ 1.0
+
+end  # module