Implement hcubature_count and hcubature_print

src/HCubature.jl

@@ -20,7 +20,7 @@ module HCubature
 using StaticArrays, LinearAlgebra
 import Combinatorics, DataStructures, QuadGK
 
-export hcubature, hquadrature, hcubature_buffer
+export hcubature, hquadrature, hcubature_buffer, hcubature_count, hcubature_print
 
 include("genz-malik.jl")
 include("gauss-kronrod.jl")
@@ -236,6 +236,51 @@ hcubature(f, a, b; norm=norm, rtol::Real=0, atol::Real=0,
     hcubature_(f, a, b, norm, rtol, atol, maxevals, initdiv, buffer)
 
 
+"""
+    hcubature_count(f, a, b; kws...)
+
+Identical to [`hcubature`](@ref) but returns a triple `(I, E, count)`
+of the estimated integral `I`, the estimated error bound `E`, and a `count`
+of the number of times the integrand `f` was evaluated.
+
+The count of integrand evaluations is a useful performance metric: a large
+number typically indicates a badly behaved integrand (with singularities,
+discontinuities, sharp peaks, and/or rapid oscillations), in which case
+it may be possible to mathematically transform the problem in some way
+to improve the convergence rate.
+"""
+function hcubature_count(f, a, b; kws...)
+    count = Ref(0)
+    I, E = hcubature(a, b; kws...) do x
+        count[] += 1
+        f(x)
+    end
+    return (I, E, count[])
+end
+
+"""
+    hcubature_print([io], f, a, b; kws...)
+
+Identical to [`hcubature`](@ref), but **prints** each integrand
+evaluation to the stream `io` (defaults to `stdout`) in the form:
+```
+f(x1) = y1
+f(x2) = y2
+...
+```
+which is useful for pedagogy and debugging.
+
+Also, like [`hcubature_count`](@ref), it returns a triple `(I, E, count)`
+of the estimated integral `I`, the estimated error bound `E`, and a `count`
+of the number of times the integrand `f` was evaluated.
+"""
+hcubature_print(io::IO, f, a, b; kws...) = hcubature_count(a, b; kws...) do x
+    y = f(x)
+    println(io, "f($x) = $y")
+    y
+end
+hcubature_print(f, a, b; kws...) = hcubature_print(stdout, f, a, b; kws...)
+
 """
     hquadrature(f, a, b; norm=norm, rtol=sqrt(eps), atol=0, maxevals=typemax(Int), initdiv=1)
 

test/runtests.jl

@@ -17,6 +17,29 @@ using Test
       end
 end
 
+@testset "count" begin
+      (i, e, count) = hcubature_count(x -> 2, (0,0), (2pi, pi))
+      @test i ≈ 4pi^2
+      @test count == HCubature.countevals(HCubature.GenzMalik(Val(2)))
+end
+
+@testset "print" begin
+      # Capture println's in a buffer, ensure one printed line per integrand eval
+      let io = IOBuffer()
+            (i, e, count) = hcubature_print(io, x -> 2, (0,0), (2pi, pi))
+            regex = r"f\((?<x>.+?)\) = (?<y>.+?)"
+            io_lines = collect(eachmatch(regex, String(take!(io))))
+            @test i ≈ 4pi^2
+            @test length(io_lines) == count
+      end
+
+      # Test hcubature_print(f, a, b) without io arg specified
+      # Suppress output of internal printing to stdout
+      f() = hcubature_print(x -> 2, (0,0), (2pi, pi))
+      (i, e, count) = redirect_stdout(f, devnull);
+      @test i ≈ 4pi^2
+end
+
 # function wrapper for counting evaluations
 const gcnt = Ref(0)
 cnt(f) = x -> begin