GradientTest.jl

module GradientTest

import Calculus
import NaNMath

using Test
using ForwardDiff
using ForwardDiff: Dual, Tag
using StaticArrays
using DiffTests

include(joinpath(dirname(@__FILE__), "utils.jl"))

struct TestTag end
struct OuterTestTag end
ForwardDiff.:≺(::Type{TestTag}, ::Type{OuterTestTag}) = true
ForwardDiff.:≺(::Type{OuterTestTag}, ::Type{<:Tag}) = true

##################
# hardcoded test #
##################

f = DiffTests.rosenbrock_1
x = [0.1, 0.2, 0.3]
v = f(x)
g = [-9.4, 15.6, 52.0]

@testset "Rosenbrock, chunk size = $c and tag = $(repr(tag))" for c in (1, 2, 3), tag in (nothing, Tag(f, eltype(x)))
    cfg = ForwardDiff.GradientConfig(f, x, ForwardDiff.Chunk{c}(), tag)

    @test eltype(cfg) == Dual{typeof(tag), eltype(x), c}

    @test isapprox(g, ForwardDiff.gradient(f, x, cfg))
    @test isapprox(g, ForwardDiff.gradient(f, x))

    out = similar(x)
    ForwardDiff.gradient!(out, f, x, cfg)
    @test isapprox(out, g)

    out = similar(x)
    ForwardDiff.gradient!(out, f, x)
    @test isapprox(out, g)

    out = DiffResults.GradientResult(x)
    ForwardDiff.gradient!(out, f, x, cfg)
    @test isapprox(DiffResults.value(out), v)
    @test isapprox(DiffResults.gradient(out), g)

    out = DiffResults.GradientResult(x)
    ForwardDiff.gradient!(out, f, x)
    @test isapprox(DiffResults.value(out), v)
end

cfgx = ForwardDiff.GradientConfig(sin, x)
@test_throws ForwardDiff.InvalidTagException ForwardDiff.gradient(f, x, cfgx)
@test ForwardDiff.gradient(f, x, cfgx, Val{false}()) == ForwardDiff.gradient(f,x)


########################
# test vs. Calculus.jl #
########################

for f in DiffTests.VECTOR_TO_NUMBER_FUNCS
    v = f(X)
    g = ForwardDiff.gradient(f, X)
    @test isapprox(g, Calculus.gradient(f, X), atol=FINITEDIFF_ERROR)
    @testset "... with chunk size = $c and tag = $(repr(tag))" for c in CHUNK_SIZES, tag in (nothing, Tag(f, eltype(x)))
        cfg = ForwardDiff.GradientConfig(f, X, ForwardDiff.Chunk{c}(), tag)

        out = ForwardDiff.gradient(f, X, cfg)
        @test isapprox(out, g)

        out = similar(X)
        ForwardDiff.gradient!(out, f, X, cfg)
        @test isapprox(out, g)

        out = DiffResults.GradientResult(X)
        ForwardDiff.gradient!(out, f, X, cfg)
        @test isapprox(DiffResults.value(out), v)
        @test isapprox(DiffResults.gradient(out), g)
    end
end

##########################################
# test specialized StaticArray codepaths #
##########################################

@testset "Specialized StaticArray codepaths: $T" for T in (StaticArrays.SArray, StaticArrays.MArray)
    x = rand(3, 3)

    sx = T{Tuple{3,3}}(x)

    cfg = ForwardDiff.GradientConfig(nothing, x)
    scfg = ForwardDiff.GradientConfig(nothing, sx)

    actual = ForwardDiff.gradient(prod, x)
    @test ForwardDiff.gradient(prod, sx) == actual
    @test ForwardDiff.gradient(prod, sx, cfg) == actual
    @test ForwardDiff.gradient(prod, sx, scfg) == actual
    @test ForwardDiff.gradient(prod, sx, scfg) isa StaticArray
    @test ForwardDiff.gradient(prod, sx, scfg, Val{false}()) == actual
    @test ForwardDiff.gradient(prod, sx, scfg, Val{false}()) isa StaticArray

    out = similar(x)
    ForwardDiff.gradient!(out, prod, sx)
    @test out == actual

    out = similar(x)
    ForwardDiff.gradient!(out, prod, sx, cfg)
    @test out == actual

    out = similar(x)
    ForwardDiff.gradient!(out, prod, sx, scfg)
    @test out == actual

    result = DiffResults.GradientResult(x)
    result = ForwardDiff.gradient!(result, prod, x)

    result1 = DiffResults.GradientResult(x)
    result2 = DiffResults.GradientResult(x)
    result3 = DiffResults.GradientResult(x)
    result1 = ForwardDiff.gradient!(result1, prod, sx)
    result2 = ForwardDiff.gradient!(result2, prod, sx, cfg)
    result3 = ForwardDiff.gradient!(result3, prod, sx, scfg)
    @test DiffResults.value(result1) == DiffResults.value(result)
    @test DiffResults.value(result2) == DiffResults.value(result)
    @test DiffResults.value(result3) == DiffResults.value(result)
    @test DiffResults.gradient(result1) == DiffResults.gradient(result)
    @test DiffResults.gradient(result2) == DiffResults.gradient(result)
    @test DiffResults.gradient(result3) == DiffResults.gradient(result)

    sresult1 = DiffResults.GradientResult(sx)
    sresult2 = DiffResults.GradientResult(sx)
    sresult3 = DiffResults.GradientResult(sx)
    sresult1 = ForwardDiff.gradient!(sresult1, prod, sx)
    sresult2 = ForwardDiff.gradient!(sresult2, prod, sx, cfg)
    sresult3 = ForwardDiff.gradient!(sresult3, prod, sx, scfg)
    @test DiffResults.value(sresult1) == DiffResults.value(result)
    @test DiffResults.value(sresult2) == DiffResults.value(result)
    @test DiffResults.value(sresult3) == DiffResults.value(result)
    @test DiffResults.gradient(sresult1) == DiffResults.gradient(result)
    @test DiffResults.gradient(sresult2) == DiffResults.gradient(result)
    @test DiffResults.gradient(sresult3) == DiffResults.gradient(result)

    # make sure this is not a source of type instability
    @inferred ForwardDiff.GradientConfig(f, sx)
end

@testset "exponential function at base zero" begin
    @test isequal(ForwardDiff.gradient(t -> t[1]^t[2], [0.0, -0.5]), [NaN, NaN])
    @test isequal(ForwardDiff.gradient(t -> t[1]^t[2], [0.0,  0.0]), [NaN, NaN])
    @test isequal(ForwardDiff.gradient(t -> t[1]^t[2], [0.0,  0.5]), [Inf, NaN])
    @test isequal(ForwardDiff.gradient(t -> t[1]^t[2], [0.0,  1.5]), [0.0, 0.0])
end

# Issue 399
@testset "chunk size zero" begin
    f_const(x) = 1.0
    g_grad_const = x -> ForwardDiff.gradient(f_const, x)
    @test g_grad_const([1.0]) == [0.0]
    @test isempty(g_grad_const(zeros(Float64, 0)))
end

@testset "dimension errors for gradient" begin
    @test_throws DimensionMismatch ForwardDiff.gradient(identity, 2pi) # input
    @test_throws DimensionMismatch ForwardDiff.gradient(identity, fill(2pi, 2)) # vector_mode_gradient
    @test_throws DimensionMismatch ForwardDiff.gradient(identity, fill(2pi, 10^6)) # chunk_mode_gradient
end

@testset "ArithmeticStyle" begin
    function f(p)
        sum(collect(0.0:p[1]:p[2]))
    end
    @test ForwardDiff.gradient(f, [0.3, 25.0]) == [3486.0, 0.0]
end

@testset "gradient for exponential with NaNMath" begin
    @test isnan(ForwardDiff.gradient(x -> NaNMath.pow(x[1],x[1]), [NaN, 1.0])[1])
    @test ForwardDiff.gradient(x -> NaNMath.pow(x[1], x[2]), [1.0, 1.0]) == [1.0, 0.0]
    @test isnan(ForwardDiff.gradient((x) -> NaNMath.pow(x[1], x[2]), [-1.0, 0.5])[1])

    @test isnan(ForwardDiff.gradient(x -> x[1]^x[2], [NaN, 1.0])[1])
    @test ForwardDiff.gradient(x -> x[1]^x[2], [1.0, 1.0]) == [1.0, 0.0]
    @test_throws DomainError ForwardDiff.gradient(x -> x[1]^x[2], [-1.0, 0.5])
end

# issue #769
@testset "functions with `Dual` output" begin
    x = [Dual{OuterTestTag}(Dual{TestTag}(1.3, 2.1), Dual{TestTag}(0.3, -2.4))]
    f(x) = sum(ForwardDiff.value, x)
    der = ForwardDiff.derivative(ForwardDiff.value, first(x))

    # Vector mode
    grad = ForwardDiff.gradient(f, x)
    @test grad isa Vector{typeof(der)}
    @test grad == [der]
    grad = ForwardDiff.gradient(f, SVector{1}(x))
    @test grad isa SVector{1,typeof(der)}
    @test grad == SVector{1}(der)

    # Chunk mode
    y = repeat(x, 3)
    cfg = ForwardDiff.GradientConfig(f, y, ForwardDiff.Chunk{2}())
    grad = ForwardDiff.gradient(f, y, cfg)
    @test grad isa Vector{typeof(der)}
    @test grad == [der, der, der]
    cfg = ForwardDiff.GradientConfig(f, SVector{3}(y), ForwardDiff.Chunk{2}())
    grad = ForwardDiff.gradient(f, SVector{3}(y), cfg)
    @test grad isa SVector{3,typeof(der)}
    @test grad == SVector{3}(der, der, der)
end

end # module