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Jul 29, 2020
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Don't create a reshaped array when compute a Jacobian of a StaticVector #113

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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -19,8 +19,8 @@ julia = "1.2"
BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[targets]
test = ["Test", "BlockBandedMatrices", "BandedMatrices", "Pkg", "SafeTestsets"]
4 changes: 4 additions & 0 deletions src/FiniteDiff.jl
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Expand Up @@ -8,6 +8,10 @@ import Base: resize!
_vec(x) = vec(x)
_vec(x::Number) = x

_mat(x::AbstractMatrix) = x
_mat(x::StaticVector) = reshape(x, (axes(x, 1), SOneTo(1)))
_mat(x::AbstractVector) = reshape(x, (axes(x, 1), OneTo(1)))

include("iteration_utils.jl")
include("epsilons.jl")
include("derivatives.jl")
Expand Down
36 changes: 15 additions & 21 deletions src/jacobians.jl
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Expand Up @@ -121,7 +121,7 @@ end

function _make_Ji(::AbstractArray, xtype, dx, color_i, nrows, ncols)
Ji = mapreduce(i -> i==color_i ? dx : zero(dx), hcat, 1:ncols)
size(Ji)!=(nrows, ncols) ? reshape(Ji,(nrows,ncols)) : Ji #branch when size(dx) == (1,) => size(Ji) == (1,) while size(J) == (1,1)
size(Ji) != (nrows, ncols) ? reshape(Ji, (nrows, ncols)) : Ji #branch when size(dx) == (1,) => size(Ji) == (1,) while size(J) == (1,1)
end

function finite_difference_jacobian(f, x,
Expand Down Expand Up @@ -186,17 +186,15 @@ function finite_difference_jacobian(
x_save = ArrayInterface.allowed_getindex(vecx, i)
epsilon = compute_epsilon(Val{:forward}, x_save, relstep, absstep, dir)
_vecx1 = Base.setindex(vecx, x_save+epsilon, i)
_x1 = reshape(_vecx1,size(x))
_x1 = reshape(_vecx1, axes(x))
vecfx1 = _vec(f(_x1))
dx = (vecfx1-vecfx) / epsilon
return dx
end

if jac_prototype isa Nothing && sparsity isa Nothing
J = mapreduce(calculate_Ji_forward, hcat, 1:maximum(colorvec))
if maximum(colorvec) == 1
J = reshape(J, 1, 1)
end
J = _mat(J)
else
@inbounds for color_i ∈ 1:maximum(colorvec)
if sparsity isa Nothing
Expand All @@ -206,7 +204,7 @@ function finite_difference_jacobian(
tmp = norm(vecx .* (colorvec .== color_i))
epsilon = compute_epsilon(Val{:forward}, sqrt(tmp), relstep, absstep, dir)
_vecx = @. vecx + epsilon * (colorvec == color_i)
_x = reshape(_vecx,size(x))
_x = reshape(_vecx, axes(x))
vecfx1 = _vec(f(_x))
dx = (vecfx1-vecfx)/epsilon
Ji = _make_Ji(J,rows_index,cols_index,dx,colorvec,color_i,nrows,ncols)
Expand All @@ -222,8 +220,8 @@ function finite_difference_jacobian(
epsilon = compute_epsilon(Val{:forward}, x1_save, relstep, absstep, dir)
_vecx1 = Base.setindex(vecx1,x1_save+epsilon,i)
_vecx = Base.setindex(vecx,x_save-epsilon,i)
_x1 = reshape(_vecx1,size(x))
_x = reshape(_vecx,size(x))
_x1 = reshape(_vecx1, axes(x))
_x = reshape(_vecx, axes(x))
vecfx1 = _vec(f(_x1))
vecfx = _vec(f(_x))
dx = (vecfx1-vecfx)/(2epsilon)
Expand All @@ -232,9 +230,7 @@ function finite_difference_jacobian(

if jac_prototype isa Nothing && sparsity isa Nothing
J = mapreduce(calculate_Ji_central, hcat, 1:maximum(colorvec))
if maximum(colorvec) == 1
J = reshape(J, 1, 1)
end
J = _mat(J)
else
@inbounds for color_i ∈ 1:maximum(colorvec)
if sparsity isa Nothing
Expand All @@ -245,8 +241,8 @@ function finite_difference_jacobian(
epsilon = compute_epsilon(Val{:forward}, sqrt(tmp), relstep, absstep, dir)
_vecx1 = @. vecx1 + epsilon * (colorvec == color_i)
_vecx = @. vecx - epsilon * (colorvec == color_i)
_x1 = reshape(_vecx1,size(x))
_x = reshape(_vecx, size(x))
_x1 = reshape(_vecx1, axes(x))
_x = reshape(_vecx, axes(x))
vecfx1 = _vec(f(_x1))
vecfx = _vec(f(_x))
dx = (vecfx1-vecfx)/(2epsilon)
Expand All @@ -257,29 +253,27 @@ function finite_difference_jacobian(
end
elseif fdtype == Val{:complex} && returntype <: Real
epsilon = eps(eltype(x))

function calculate_Ji_complex(i)
x_save = ArrayInterface.allowed_getindex(vecx,i)
_vecx = Base.setindex(complex.(vecx),x_save+im*epsilon,i)
_x = reshape(_vecx,size(x))
_x = reshape(_vecx, axes(x))
vecfx = _vec(f(_x))
dx = imag(vecfx)/epsilon
return dx
end

if jac_prototype isa Nothing && sparsity isa Nothing
J = mapreduce(calculate_Ji_complex, hcat, 1:maximum(colorvec))
if maximum(colorvec) == 1
J = reshape(J, 1, 1)
end
J = _mat(J)
else
@inbounds for color_i ∈ 1:maximum(colorvec)
if sparsity isa Nothing
dx = calculate_Ji_complex(color_i)
J = J + _make_Ji(J, eltype(x), dx, color_i, nrows, ncols)
else
_vecx = @. vecx + im * epsilon * (colorvec == color_i)
_x = reshape(_vecx,size(x))
_x = reshape(_vecx, axes(x))
vecfx = _vec(f(_x))
dx = imag(vecfx)/epsilon
Ji = _make_Ji(J,rows_index,cols_index,dx,colorvec,color_i,nrows,ncols)
Expand Down Expand Up @@ -332,7 +326,7 @@ function finite_difference_jacobian!(
dir = true) where {T1,T2,T3,cType,sType,fdtype,returntype}

m, n = size(J)
_color = reshape(colorvec,size(x)...)
_color = reshape(colorvec, axes(x)...)

x1, fx, fx1 = cache.x1, cache.fx, cache.fx1
copyto!(x1, x)
Expand Down
33 changes: 25 additions & 8 deletions test/out_of_place_tests.jl
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Expand Up @@ -16,28 +16,45 @@ function second_derivative_stencil(N)
end

x = @SVector ones(30)
J = FiniteDiff.finite_difference_jacobian(f,x, Val{:forward}, eltype(x))
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:forward}, eltype(x))
@test J ≈ second_derivative_stencil(30)

J = FiniteDiff.finite_difference_jacobian(f,x, Val{:central}, eltype(x))
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:central}, eltype(x))
@test J ≈ second_derivative_stencil(30)

J = FiniteDiff.finite_difference_jacobian(f,x, Val{:complex}, eltype(x))
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:complex}, eltype(x))
@test J ≈ second_derivative_stencil(30)

spJ = sparse(second_derivative_stencil(30))
J = FiniteDiff.finite_difference_jacobian(f,x, Val{:forward}, eltype(x),jac_prototype=spJ)
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:forward}, eltype(x), jac_prototype=spJ)
@test J ≈ second_derivative_stencil(30)
@test typeof(J) == typeof(spJ)
J = FiniteDiff.finite_difference_jacobian(f,x, Val{:forward}, eltype(x),colorvec=repeat(1:3,10),sparsity=spJ,jac_prototype=spJ)
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:forward}, eltype(x),
colorvec=SVector{30}(repeat(1:3, 10)), sparsity=spJ, jac_prototype=spJ)
@test J ≈ second_derivative_stencil(30)
@test typeof(J) == typeof(spJ)

#1x1 SVector test
x = SVector{1}([1.])
f(x) = x
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:forward}, eltype(x))
@test J ≈ SMatrix{1,1}([1.])
@test J[1, 1] ≈ 1.0
@test J isa SMatrix{1,1}
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:central}, eltype(x))
@test J[1, 1] ≈ 1.0
@test J isa SMatrix{1,1}
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:complex}, eltype(x))
@test J[1, 1] ≈ 1.0
@test J isa SMatrix{1,1}

x = SVector{1}([1.])
f(x) = vcat(x, x)
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:forward}, eltype(x))
@test J ≈ fill(1.0, 2, 1)
@test J isa SMatrix{2,1}
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:central}, eltype(x))
@test J ≈ SMatrix{1,1}([1.])
@test J ≈ fill(1.0, 2, 1)
@test J isa SMatrix{2,1}
J = FiniteDiff.finite_difference_jacobian(f, x, Val{:complex}, eltype(x))
@test J ≈ SMatrix{1,1}([1.])
@test J ≈ fill(1.0, 2, 1)
@test J isa SMatrix{2,1}