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chol, qr, lq gradients #55

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Mar 18, 2018
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chol, qr, lq gradients #55

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ce86cc5
cholesky
CarloLucibello Feb 20, 2018
dbef756
add lq and qr
CarloLucibello Feb 20, 2018
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43 changes: 43 additions & 0 deletions src/linalg/dense.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -37,3 +37,46 @@ dense2arg = Dict{Symbol,Any}(
# cond
# sylvester
# lyap

@primitive chol(x),dy,y chol_back(y, dy)

# ref: formulua in https://arxiv.org/pdf/1602.07527.pdf
# as described in https://arxiv.org/pdf/1710.08717.pdf
# In julia L is upper triangular
function chol_back(L, dL)
dL = triu(dL)
iL = inv(L)
S = iL * Symmetric(L*dL',:L) * iL'
S/2
end

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@CarloLucibello let's not break the AutoGrad's regular testing pipeline. Could you pls. add

  1. addtest(:chol, rand(3,3))
  2. I think we need to find a way to write similar tests for qr and lq and remove them from the test/primitives.jl

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I'd like to keep tests this way. It is kind of atypical in the julia ecosystem to add tests into the src/ folder, and I don't want to scratch my head to figure out how to add tests for qr in the non-standard way while the easy way is also the standard way

@primitive lq(x),dy,y lq_back(y, dy)


# ref: https://arxiv.org/pdf/1710.08717.pdf
function lq_back(y, dy)
L, Q = y
dL, dQ = dy
dL == nothing && (dL = zeros(L))
dQ == nothing && (dQ = zeros(Q))
dL = tril(dL)
M = Symmetric(L'dL - dQ*Q', :L)
S = inv(L)' *(dQ + M*Q)
S
end

@primitive qr(x),dy,y qr_back(y, dy)

function qr_back(y, dy)
Q, R = y
dQ, dR = dy
dR == nothing && (dR = zeros(R))
dQ == nothing && (dQ = zeros(Q))
dR = triu(dR)
M = Symmetric(R*dR' - dQ'*Q, :L)
S = (dQ + Q*M)*inv(R)'
S
end



12 changes: 12 additions & 0 deletions test/primitives.jl
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@@ -1,10 +1,22 @@
include("header.jl")

@testset "primitives" begin
@test gradcheck(x->chol(x'x), rand(3,3))

for t in AutoGrad.alltests()
#@show t
@test gradcheck(eval(AutoGrad,t[1]), t[2:end]...)
end

@test gradcheck(x->chol(x'x), rand(3,3))

@test gradcheck(x->qr(x)[1], rand(3,3))
@test gradcheck(x->qr(x)[2], rand(3,3))
@test gradcheck(x->(y=qr(x); sum(y[1]+y[2])), rand(3,3))

@test gradcheck(x->lq(x)[1], rand(3,3))
@test gradcheck(x->lq(x)[2], rand(3,3))
@test gradcheck(x->(y=lq(x); sum(y[1]+y[2])), rand(3,3))
end

nothing