add AllZeros type (#427)

* add AllZeros type

* fix 1.6 syntax error

* avoid error

Author: jverzani

docs/src/reference.md

@@ -184,6 +184,13 @@ A useful  strategy  is   to  begin with a non-bracketing  method and switch to a
 Roots.Order0
 ```
 
+## All zeros
+
+The `find_zeros` function heuristically scans an interval for all zeros using a combination of bracketing and non-bracketing methods. The `AllZeros` method may be passed to `solve` to call this.
+
+```@docs
+Roots.AllZeros
+```
 
 ## Rates of convergence
 

src/Roots.jl

@@ -40,7 +40,8 @@ export find_zero,
     Order2,
     Order5,
     Order8,
-    Order16
+    Order16,
+    AllZeros
 
 export Bisection, A42, AlefeldPotraShi, FalsePosition
 

src/find_zeros.jl

@@ -392,3 +392,29 @@ function find_zeros(f, a, b=nothing; no_pts=12, k=8, naive=false, kwargs...)
 
     return zs[inds]
 end
+
+
+# solve interface
+"""
+    AllZeros
+
+Type to indicate to `solve` that `find_zeros` should be used to solve the given  `ZeroProblem`.
+
+## Example
+
+```
+julia> Z = ZeroProblem(cos, (0, 2pi));
+
+julia> solve(Z, AllZeros())
+2-element Vector{Float64}:
+ 1.5707963267948966
+ 4.71238898038469
+```
+
+"""
+struct AllZeros <: AbstractUnivariateZeroMethod
+end
+function solve(𝑭𝑿::ZeroProblem, ::AllZeros; kwargs...)
+    F,x₀ = 𝑭𝑿.F, 𝑭𝑿.x₀
+    find_zeros(F, x₀; kwargs...)
+end

test/test_find_zeros.jl

@@ -124,6 +124,10 @@ end
     # issue #369
     g4(x) = sqrt(abs(x^2 - 1)) / (x * sign(x^2 - 1))
     @test isempty(find_zeros(g4, 1.1, 2))
+
+    # solve interface
+    Z = ZeroProblem(x -> prod(x - i for i in 1:5), (0,6))
+    @test solve(Z, AllZeros()) ≈ 1:5
 end
 
 @testset "find_zeros: not Float64 types" begin