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Oct 6, 2019
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Correction for nonsquare jacobian #66

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a26c079
correction for nonsquare jacobian
Oct 6, 2019
b314d45
del fx
Oct 6, 2019
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11 changes: 9 additions & 2 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -73,10 +73,17 @@ In addition, a faster forward-mode autodiff call can be utilized as well:

```julia
forwarddiff_color_jacobian!(jac, f, x, colorvec = colors)
jacout = forwarddiff_color_jacobian(g, x, colorvec = colors, sparsity = similar(jac), jac_prototype = similar(jac))
#OR
jacout = forwarddiff_color_jacobian(g, x, dx = similar(x),colorvec = colors, sparsity = similar(jac), jac_prototype = similar(jac))
```
One can specify the type of the output jacobian by giving an additional `jac_prototype` to
One can specify the type and shape of the output jacobian by giving an additional `jac_prototype` to
the out-of place `forwarddiff_color_jacobian` function, otherwise it will become a dense matrix.
If `jac_prototype` and `sparsity` is not specified (both default to `nothing`), the oop jacobian will
assume that the function has a *square* jacobian matrix. If it is not the case, please specify
the shape of output by giving `dx` or giving `dx = nothing` where the shape is determined
automatically at the cost of a function evaluation `f(x)`.
If not necessary (e.g `StaticArrays` involved), please turn to the inplace jacobian function
`forwarddiff_color_jacobian!` which is faster in general cases.

If one only need to compute products, one can use the operators. For example,

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36 changes: 22 additions & 14 deletions src/differentiation/compute_jacobian_ad.jl
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Expand Up @@ -24,7 +24,7 @@ function ForwardColorJacCache(f,x,_chunksize = nothing;
colorvec=1:length(x),
sparsity::Union{AbstractArray,Nothing}=nothing)

if _chunksize === nothing
if _chunksize isa Nothing
chunksize = default_chunk_size(maximum(colorvec))
else
chunksize = _chunksize
Expand All @@ -33,11 +33,17 @@ function ForwardColorJacCache(f,x,_chunksize = nothing;
p = adapt.(typeof(x),generate_chunked_partials(x,colorvec,chunksize))
t = reshape(Dual{typeof(f)}.(vec(x),first(p)),size(x)...)

if dx === nothing
if dx isa Nothing
fx = similar(t)
_dx = similar(x)
else
fx = reshape(Dual{typeof(f)}.(vec(dx),first(p)),size(x)...)
pi = first(p) #perform trim (length(dx)<length(x)) or padding (length(dx)>length(x)) to first(p)
if length(dx)>length(x)
pi = vcat(pi,reshape(mapslices(Tuple,zeros(Bool,length(first(pi)),length(dx)-length(x)),dims=1),:))
else
pi = pi[1:length(dx)]
end
fx = reshape(Dual{typeof(f)}.(vec(dx),pi),size(dx)...)
_dx = dx
end

Expand All @@ -60,16 +66,18 @@ end

function forwarddiff_color_jacobian(f,
x::AbstractArray{<:Number};
dx = nothing,
dx = similar(x), #if dx is nothing, we will estimate dx at the cost of a function call
colorvec = 1:length(x),
sparsity = nothing,
jac_prototype = nothing)
if dx isa Nothing
dx = f(x)
end
forwarddiff_color_jacobian(f,x,ForwardColorJacCache(f,x,dx=dx,colorvec=colorvec,sparsity=sparsity),jac_prototype)
end

function forwarddiff_color_jacobian(f,x::AbstractArray{<:Number},jac_cache::ForwardColorJacCache,jac_prototype=nothing)
t = jac_cache.t
fx = jac_cache.fx
dx = jac_cache.dx
p = jac_cache.p
colorvec = jac_cache.colorvec
Expand All @@ -80,8 +88,8 @@ function forwarddiff_color_jacobian(f,x::AbstractArray{<:Number},jac_cache::Forw

vecx = vec(x)

ncols=length(x)
J = jac_prototype isa Nothing ? false .* x .* x' : zero(jac_prototype)
J = jac_prototype isa Nothing ? (sparsity isa Nothing ? false .* dx .* x' : zeros(eltype(x),size(sparsity))) : zero(jac_prototype)
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zeros gives an Array

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I think when jac_prototype is not specified, J should be an Array.

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true, makes sense.

nrows,ncols = size(J)

if !(sparsity isa Nothing)
rows_index, cols_index = ArrayInterface.findstructralnz(sparsity)
Expand All @@ -100,19 +108,19 @@ function forwarddiff_color_jacobian(f,x::AbstractArray{<:Number},jac_cache::Forw
rows_index_c = rows_index[pick_inds]
cols_index_c = cols_index[pick_inds]
len_rows = length(pick_inds)
unused_rows = setdiff(1:ncols,rows_index_c)
unused_rows = setdiff(1:nrows,rows_index_c)
perm_rows = sortperm(vcat(rows_index_c,unused_rows))
cols_index_c = vcat(cols_index_c,zeros(Int,ncols-len_rows))[perm_rows]
Ji = [j==cols_index_c[i] ? dx[i] : false for i in 1:ncols, j in 1:ncols]
cols_index_c = vcat(cols_index_c,zeros(Int,nrows-len_rows))[perm_rows]
Ji = [j==cols_index_c[i] ? dx[i] : false for i in 1:nrows, j in 1:ncols]
J = J + Ji
color_i += 1
(color_i > maxcolor) && return J
end
else
for j in 1:chunksize
col_index = (i-1)*chunksize + j
(col_index > maxcolor) && return J
J = J + mapreduce(i -> i==col_index ? partials.(vec(fx), j) : zeros(ncols), hcat, 1:ncols)
(col_index > ncols) && return J
J = J + mapreduce(i -> i==col_index ? partials.(vec(fx), j) : zeros(nrows), hcat, 1:ncols)
end
end
end
Expand All @@ -122,7 +130,7 @@ end
function forwarddiff_color_jacobian!(J::AbstractMatrix{<:Number},
f,
x::AbstractArray{<:Number};
dx = nothing,
dx = Array{eltype(x)}(undef,size(J,1)),
colorvec = 1:length(x),
sparsity = ArrayInterface.has_sparsestruct(J) ? J : nothing)
forwarddiff_color_jacobian!(J,f,x,ForwardColorJacCache(f,x,dx=dx,colorvec=colorvec,sparsity=sparsity))
Expand Down Expand Up @@ -187,7 +195,7 @@ function forwarddiff_color_jacobian!(J::AbstractMatrix{<:Number},
else
for j in 1:chunksize
col_index = (i-1)*chunksize + j
(col_index > maxcolor) && return
(col_index > ncols) && return
J[:, col_index] .= partials.(vecfx, j)
end
end
Expand Down
91 changes: 89 additions & 2 deletions test/test_ad.jl
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Expand Up @@ -27,11 +27,53 @@ function oopf(x)
dx
end

function nsqf(x)#length(dx)<length(x)
global fcalls +=1
dx = zero(x)[1:div(length(x),2)]
for i in 2:length(dx)
dx[i] = x[i-1] - 2x[i] + x[i+1]
end
dx[1] = -2x[1] + x[2]
dx
end

function nsqf2(x)#length(dx)>length(x)
global fcalls +=1
dx = zeros(eltype(x),length(x)*2)
for i in 2:length(x)-1
dx[i] = x[i-1] - 2x[i] + x[i+1]
end
dx[1] = -2x[1] + x[2]
dx
end

function nsqf!(dx,x)
global fcalls +=1
for i in 2:length(dx)
dx[i] = x[i-1] - 2x[i] + x[i+1]
end
dx[1] = -2x[1] + x[2]
nothing
end

function nsqf2!(dx,x)
global fcalls +=1
for i in 2:length(x)-1
dx[i] = x[i-1] - 2x[i] + x[i+1]
end
dx[1] = -2x[1] + x[2]
nothing
end

function staticf(x,N=length(x))
global fcalls += 1
SVector{N}([i == 1 ? -2x[1]+x[2] : (i == N ? x[N-1]-2x[N] : x[i-1]-2x[i]+x[i+1]) for i in 1:N])
end


function staticnsqf(x,N=div(length(x),2))
global fcalls += 1
SVector{N}(vcat([-2x[1]+x[2]],[x[i-1]-2x[i]+x[i+1] for i in 2:N]))
end

function second_derivative_stencil(N)
A = zeros(N,N)
Expand Down Expand Up @@ -73,11 +115,56 @@ _J1 = forwarddiff_color_jacobian(staticf, SVector{30}(x), colorvec = repeat(1:3,

_J1 = forwarddiff_color_jacobian(staticf, SVector{30}(x), jac_prototype = SMatrix{30,30}(_J))
@test _J1 ≈ J
_J1 = forwarddiff_color_jacobian(oopf, x, jac_prototype = _J)
_J1 = forwarddiff_color_jacobian(oopf, x, jac_prototype = similar(_J))
@test _J1 ≈ J
_J1 = forwarddiff_color_jacobian(oopf, x)
@test _J1 ≈ J

#Non-square Jacobian
#length(dx)<length(x)
nsqJ = jacobian(nsqf,x)
spnsqJ = sparse(nsqJ)
_nsqJ = forwarddiff_color_jacobian(nsqf, x, dx = nothing)
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf, x, colorvec = repeat(1:3,10), sparsity = spnsqJ)
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf, x, jac_prototype = similar(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf, x, colorvec = repeat(1:3,10), sparsity = spnsqJ, jac_prototype = similar(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf, x, jac_prototype = SMatrix{15,30}(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(staticnsqf, SVector{30}(x), jac_prototype = SMatrix{15,30}(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(staticnsqf, SVector{30}(x), jac_prototype = SMatrix{15,30}(nsqJ), colorvec = repeat(1:3,10), sparsity = spnsqJ)
@test _nsqJ ≈ nsqJ
_nsqJ = similar(nsqJ)
forwarddiff_color_jacobian!(_nsqJ, nsqf!, x)
@test _nsqJ ≈ nsqJ
_nsqJ = similar(nsqJ)
forwarddiff_color_jacobian!(_nsqJ, nsqf!, x, colorvec = repeat(1:3,10), sparsity = spnsqJ )
@test _nsqJ ≈ nsqJ

#length(dx)>length(x)
nsqJ = jacobian(nsqf2,x)
spnsqJ = sparse(nsqJ)
_nsqJ = forwarddiff_color_jacobian(nsqf2, x, dx = nothing)
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf2, x, colorvec = repeat(1:3,10), sparsity = spnsqJ)
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf2, x, jac_prototype = similar(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf2, x, colorvec = repeat(1:3,10), sparsity = spnsqJ, jac_prototype = similar(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = forwarddiff_color_jacobian(nsqf2, x, jac_prototype = SMatrix{60,30}(nsqJ))
@test _nsqJ ≈ nsqJ
_nsqJ = similar(nsqJ)
forwarddiff_color_jacobian!(_nsqJ, nsqf2!, x)
@test _nsqJ ≈ nsqJ
_nsqJ = similar(nsqJ)
forwarddiff_color_jacobian!(_nsqJ, nsqf2!, x, colorvec = repeat(1:3,10), sparsity = spnsqJ )
@test _nsqJ ≈ nsqJ

fcalls = 0
_J1 = similar(_J)
jac_cache = ForwardColorJacCache(f,x,colorvec = repeat(1:3,10), sparsity = _J1)
Expand Down