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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,106 @@ | ||
| ###### | ||
| ###### `inv` | ||
| ###### | ||
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| function frule((_, Δx), ::typeof(inv), x::AbstractArray) | ||
| Ω = inv(x) | ||
| return Ω, -Ω * Δx * Ω | ||
| end | ||
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| function rrule(::typeof(inv), x::AbstractArray) | ||
| Ω = inv(x) | ||
| function inv_pullback(ΔΩ) | ||
| return NO_FIELDS, -Ω' * ΔΩ * Ω' | ||
| end | ||
| return Ω, inv_pullback | ||
| end | ||
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| ##### | ||
| ##### `*` | ||
| ##### | ||
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| function rrule(::typeof(*), A::AbstractMatrix{<:Real}, B::AbstractMatrix{<:Real}) | ||
| function times_pullback(Ȳ) | ||
| return (NO_FIELDS, @thunk(Ȳ * B'), @thunk(A' * Ȳ)) | ||
| end | ||
| return A * B, times_pullback | ||
| end | ||
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| function rrule(::typeof(*), A::Real, B::AbstractArray{<:Real}) | ||
| function times_pullback(Ȳ) | ||
| return (NO_FIELDS, @thunk(dot(Ȳ, B)), @thunk(A * Ȳ)) | ||
| end | ||
| return A * B, times_pullback | ||
| end | ||
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| function rrule(::typeof(*), B::AbstractArray{<:Real}, A::Real) | ||
| function times_pullback(Ȳ) | ||
| return (NO_FIELDS, @thunk(A * Ȳ), @thunk(dot(Ȳ, B))) | ||
| end | ||
| return A * B, times_pullback | ||
| end | ||
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| ##### | ||
| ##### `/` | ||
| ##### | ||
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| function rrule(::typeof(/), A::AbstractVecOrMat{<:Real}, B::AbstractVecOrMat{<:Real}) | ||
| Aᵀ, dA_pb = rrule(adjoint, A) | ||
| Bᵀ, dB_pb = rrule(adjoint, B) | ||
| Cᵀ, dS_pb = rrule(\, Bᵀ, Aᵀ) | ||
| C, dC_pb = rrule(adjoint, Cᵀ) | ||
| function slash_pullback(Ȳ) | ||
| # Optimization note: dAᵀ, dBᵀ, dC are calculated no matter which partial you want | ||
| _, dC = dC_pb(Ȳ) | ||
| _, dBᵀ, dAᵀ = dS_pb(unthunk(dC)) | ||
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| ∂A = last(dA_pb(unthunk(dAᵀ))) | ||
| ∂B = last(dA_pb(unthunk(dBᵀ))) | ||
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| (NO_FIELDS, ∂A, ∂B) | ||
| end | ||
| return C, slash_pullback | ||
| end | ||
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| ##### | ||
| ##### `\` | ||
| ##### | ||
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| function rrule(::typeof(\), A::AbstractVecOrMat{<:Real}, B::AbstractVecOrMat{<:Real}) | ||
| Y = A \ B | ||
| function backslash_pullback(Ȳ) | ||
| ∂A = @thunk begin | ||
| B̄ = A' \ Ȳ | ||
| Ā = -B̄ * Y' | ||
| _add!(Ā, (B - A * Y) * B̄' / A') | ||
| _add!(Ā, A' \ Y * (Ȳ' - B̄'A)) | ||
| Ā | ||
| end | ||
| ∂B = @thunk A' \ Ȳ | ||
| return NO_FIELDS, ∂A, ∂B | ||
| end | ||
| return Y, backslash_pullback | ||
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| end | ||
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| ##### | ||
| ##### `\`, `/` matrix-scalar_rule | ||
| ##### | ||
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| function rrule(::typeof(/), A::AbstractArray{<:Real}, b::Real) | ||
| Y = A/b | ||
| function slash_pullback(Ȳ) | ||
| return (NO_FIELDS, @thunk(Ȳ/b), @thunk(-dot(Ȳ, Y)/b)) | ||
| end | ||
| return Y, slash_pullback | ||
| end | ||
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| function rrule(::typeof(\), b::Real, A::AbstractArray{<:Real}) | ||
| Y = b\A | ||
| function backslash_pullback(Ȳ) | ||
| return (NO_FIELDS, @thunk(-dot(Ȳ, Y)/b), @thunk(Ȳ/b)) | ||
| end | ||
| return Y, backslash_pullback | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,66 @@ | ||
| @testset "arraymath" begin | ||
| @testset "inv(::Matrix{$T})" for T in (Float64, ComplexF64) | ||
| N = 3 | ||
| B = generate_well_conditioned_matrix(T, N) | ||
| frule_test(inv, (B, randn(T, N, N))) | ||
| rrule_test(inv, randn(T, N, N), (B, randn(T, N, N))) | ||
| end | ||
|
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| @testset "*" begin | ||
| @testset "Matrix-Matrix" begin | ||
| dims = [3,4,5] | ||
| for n in dims, m in dims, p in dims | ||
| # don't need to test square case multiple times | ||
| n > 3 && n == m == p && continue | ||
| A = randn(m, n) | ||
| B = randn(n, p) | ||
| Ȳ = randn(m, p) | ||
| rrule_test(*, Ȳ, (A, randn(m, n)), (B, randn(n, p))) | ||
| end | ||
| end | ||
| @testset "Scalar-AbstractArray" begin | ||
| for dims in ((3,), (5,4), (10,10), (2,3,4), (2,3,4,5)) | ||
| rrule_test(*, randn(dims), (1.5, 4.2), (randn(dims), randn(dims))) | ||
| rrule_test(*, randn(dims), (randn(dims), randn(dims)), (1.5, 4.2)) | ||
| end | ||
| end | ||
| end | ||
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| @testset "$f" for f in (/, \) | ||
| @testset "Matrix" begin | ||
| for n in 3:5, m in 3:5 | ||
| A = randn(m, n) | ||
| B = randn(m, n) | ||
| Ȳ = randn(size(f(A, B))) | ||
| rrule_test(f, Ȳ, (A, randn(m, n)), (B, randn(m, n))) | ||
| end | ||
| end | ||
| @testset "Vector" begin | ||
| x = randn(10) | ||
| y = randn(10) | ||
| ȳ = randn(size(f(x, y))...) | ||
| rrule_test(f, ȳ, (x, randn(10)), (y, randn(10))) | ||
| end | ||
| if f == (\) | ||
| @testset "Matrix $f Vector" begin | ||
| X = randn(10, 4) | ||
| y = randn(10) | ||
| ȳ = randn(size(f(X, y))...) | ||
| rrule_test(f, ȳ, (X, randn(size(X))), (y, randn(10))) | ||
| end | ||
| @testset "Vector $f Matrix" begin | ||
| x = randn(10) | ||
| Y = randn(10, 4) | ||
| ȳ = randn(size(f(x, Y))...) | ||
| rrule_test(f, ȳ, (x, randn(size(x))), (Y, randn(size(Y)))) | ||
| end | ||
| end | ||
| end | ||
| @testset "/ and \\ Scalar-AbstractArray" begin | ||
| A = randn(3, 4, 5) | ||
| Ā = randn(3, 4, 5) | ||
| Ȳ = randn(3, 4, 5) | ||
| rrule_test(/, Ȳ, (A, Ā), (7.2, 2.3)) | ||
| rrule_test(\, Ȳ, (7.2, 2.3), (A, Ā)) | ||
| end | ||
| end |
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