From ce86cc5d5ca85ca76f3cee11e4e98e945e0cf22b Mon Sep 17 00:00:00 2001
From: CarloLucibello <carlo.lucibello@gmail.com>
Date: Tue, 20 Feb 2018 10:51:30 -0500
Subject: [PATCH 1/2] cholesky

---
 src/linalg/dense.jl | 18 ++++++++++++++++++
 test/primitives.jl  |  2 ++
 2 files changed, 20 insertions(+)

diff --git a/src/linalg/dense.jl b/src/linalg/dense.jl
index cd6f4f3..a863034 100644
--- a/src/linalg/dense.jl
+++ b/src/linalg/dense.jl
@@ -37,3 +37,21 @@ dense2arg = Dict{Symbol,Any}(
 # cond
 # sylvester
 # lyap
+
+@primitive chol(x),dy,y   chol_back(y, dy)
+
+chol_ϕ(A) = tril(A) - 0.5diagm(diag(A))
+
+# ref: Iain Murray's https://arxiv.org/pdf/1602.07527.pdf
+# difference with the paper with respect to the paper:
+# julia L is upper triangular and we do not need the
+# final simmetrization of S
+function chol_back(L, dL)
+    dL = triu(dL)
+    iL = inv(L)
+    S = iL * chol_ϕ(L*dL') * iL'
+    #  S + S' - diagm(diag(S))
+    S
+end
+
+
diff --git a/test/primitives.jl b/test/primitives.jl
index 0f74da4..38171e8 100644
--- a/test/primitives.jl
+++ b/test/primitives.jl
@@ -1,6 +1,8 @@
 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]...)

From dbef75680df916787ba56b88ba5cc96cf4d04742 Mon Sep 17 00:00:00 2001
From: CarloLucibello <carlo.lucibello@gmail.com>
Date: Tue, 20 Feb 2018 17:17:08 -0500
Subject: [PATCH 2/2] add lq and qr

---
 src/linalg/dense.jl | 41 +++++++++++++++++++++++++++++++++--------
 test/primitives.jl  | 10 ++++++++++
 2 files changed, 43 insertions(+), 8 deletions(-)

diff --git a/src/linalg/dense.jl b/src/linalg/dense.jl
index a863034..4f6dc30 100644
--- a/src/linalg/dense.jl
+++ b/src/linalg/dense.jl
@@ -40,18 +40,43 @@ dense2arg = Dict{Symbol,Any}(
 
 @primitive chol(x),dy,y   chol_back(y, dy)
 
-chol_ϕ(A) = tril(A) - 0.5diagm(diag(A))
-
-# ref: Iain Murray's https://arxiv.org/pdf/1602.07527.pdf
-# difference with the paper with respect to the paper:
-# julia L is upper triangular and we do not need the
-# final simmetrization of S
+# 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 * chol_ϕ(L*dL') * iL'
-    #  S + S' - diagm(diag(S))
+    S = iL * Symmetric(L*dL',:L) * iL'
+    S/2
+end
+
+@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
+
+
 
diff --git a/test/primitives.jl b/test/primitives.jl
index 38171e8..3214efb 100644
--- a/test/primitives.jl
+++ b/test/primitives.jl
@@ -7,6 +7,16 @@ include("header.jl")
         #@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