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Fix LU factorization in-place operations #22774

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merged 4 commits into from
Aug 24, 2017
Merged

Fix LU factorization in-place operations #22774

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8775d66
Add tests for in-place operations of A_ldiv_B!(y, LU, x) for LU facto…
haampie Jul 12, 2017
d08467c
Do Ax_ldiv_B! for LU factorizations in-place
haampie Jul 12, 2017
5f2350a
Remove incorrect condition in LU test. The transpose should be tested…
haampie Jul 12, 2017
944f02a
Get rid of allocations, apply the (inverse) permutation in-place
haampie Aug 22, 2017
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Add tests for in-place operations of A_ldiv_B!(y, LU, x) for LU facto… 
…rizations
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@haampie
haampie committed Aug 23, 2017
commit 8775d66a0aa372d155d50a9e4110986b54470cbb
21 changes: 21 additions & 0 deletions test/linalg/lu.jl
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Expand Up @@ -89,6 +89,27 @@ dimg = randn(n)/2
@test norm(a.'*(lua.'\c) - c,1) < ε*κ*n
end
end

# Test whether Ax_ldiv_B!(y, LU, x) indeed overwrites y
resultT = typeof(oneunit(eltyb) / oneunit(eltya))

b_dest = similar(b, resultT)
c_dest = similar(c, resultT)

A_ldiv_B!(b_dest, lua, b)
A_ldiv_B!(c_dest, lua, c)
@test norm(b_dest - lua \ b, 1) < ε*κ*2n
@test norm(c_dest - lua \ c, 1) < ε*κ*n

At_ldiv_B!(b_dest, lua, b)
At_ldiv_B!(c_dest, lua, c)
@test norm(b_dest - lua.' \ b, 1) < ε*κ*2n
@test norm(c_dest - lua.' \ c, 1) < ε*κ*n

Ac_ldiv_B!(b_dest, lua, b)
Ac_ldiv_B!(c_dest, lua, c)
@test norm(b_dest - lua' \ b, 1) < ε*κ*2n
@test norm(c_dest - lua' \ c, 1) < ε*κ*n
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@Sacha0 Sacha0 Jul 15, 2017 •
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Perhaps DRY out these tests? For example, something along the lines of

for (Aq_ldiv_B!, q) in (
        (A_ldiv_B!, identity),
        (At_ldiv_B!, transpose),
        (Ac_ldiv_B!, ctranspose) )
    Aq_ldiv_B!(b_dest, lua, b)
    Aq_ldiv_B!(c_dest, lua, c)
    @test norm(b_dest - q(lua) \ b, 1) < ε*κ*2n
    @test norm(c_dest - q(lua) \ c, 1) < ε*κ*n
end

might serve? (Edit: Missed the secondary op the first time around! :) )

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I've tried it, but it doesn't seem to work :(

> transpose(lufact(rand(3, 3))) \ rand(3)
ERROR: transpose not implemented for Base.LinAlg.LU{Float64,Array{Float64,2}}

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It is because A.' \ B becomes At_ldiv_B(A, B) (not transpose(A) \ B). Perhaps this will do?

for (Aq_ldiv_B!, f) in (
        (A_ldiv_B!, \),
        (At_ldiv_B!, At_ldiv_B),
        (Ac_ldiv_B!, Ac_ldiv_B) )
    Aq_ldiv_B!(b_dest, lua, b)
    Aq_ldiv_B!(c_dest, lua, c)
    @test norm(b_dest - f(lua, b), 1) < ε*κ*2n
    @test norm(c_dest - f(lua, c), 1) < ε*κ*n
end

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Thx, so is .' \ parsed as a single operator or something?

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@fredrikekre fredrikekre Aug 23, 2017 •
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Yes,

julia> expand(Main, :(A.'\B))
:(At_ldiv_B(A, B))

and similarly for * as well.

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@StefanKarpinski StefanKarpinski Aug 23, 2017 •
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This is definitely a hack and we want to get rid of it, but we're not quite there yet.

end
if eltya <: BlasFloat && eltyb <: BlasFloat
e = rand(eltyb,n,n)
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