unicode subscripts

Author: lkdvos

src/pullbacks/lq.jl

@@ -59,48 +59,48 @@ function lq_pullback!(
 
     ΔL, ΔQ = ΔLQ
 
-    Q1 = view(Q, 1:p, :)
-    L11 = LowerTriangular(view(L, 1:p, 1:p))
-    ΔA1 = view(ΔA, 1:p, :)
-    ΔA2 = view(ΔA, (p + 1):m, :)
+    Q₁ = view(Q, 1:p, :)
+    L₁₁ = LowerTriangular(view(L, 1:p, 1:p))
+    ΔA₁ = view(ΔA, 1:p, :)
+    ΔA₂ = view(ΔA, (p + 1):m, :)
 
     check_lq_cotangents(L, Q, ΔL, ΔQ, p; gauge_atol)
 
     ΔQ̃ = zero!(similar(Q, (p, n)))
     if !iszerotangent(ΔQ)
-        ΔQ1 = view(ΔQ, 1:p, :)
-        copy!(ΔQ̃, ΔQ1)
+        ΔQ₁ = view(ΔQ, 1:p, :)
+        copy!(ΔQ̃, ΔQ₁)
         if minmn < size(Q, 1)
-            ΔQ3 = view(ΔQ, (minmn + 1):size(ΔQ, 1), :)
-            Q3 = view(Q, (minmn + 1):size(Q, 1), :)
-            ΔQ3Q1ᴴ = ΔQ3 * Q1'
-            ΔQ̃ = mul!(ΔQ̃, ΔQ3Q1ᴴ', Q3, -1, 1)
+            ΔQ₃ = view(ΔQ, (minmn + 1):size(ΔQ, 1), :)
+            Q₃ = view(Q, (minmn + 1):size(Q, 1), :)
+            ΔQ₃Q₁ᴴ = ΔQ₃ * Q₁'
+            ΔQ̃ = mul!(ΔQ̃, ΔQ₃Q₁ᴴ', Q₃, -1, 1)
         end
     end
     if !iszerotangent(ΔL) && m > p
-        L21 = view(L, (p + 1):m, 1:p)
-        ΔL21 = view(ΔL, (p + 1):m, 1:p)
-        ΔQ̃ = mul!(ΔQ̃, L21' * ΔL21, Q1, -1, 1)
-        # Adding ΔA2 contribution
-        ΔA2 = mul!(ΔA2, ΔL21, Q1, 1, 1)
+        L₂₁ = view(L, (p + 1):m, 1:p)
+        ΔL₂₁ = view(ΔL, (p + 1):m, 1:p)
+        ΔQ̃ = mul!(ΔQ̃, L₂₁' * ΔL₂₁, Q₁, -1, 1)
+        # Adding ΔA₂ contribution
+        ΔA₂ = mul!(ΔA₂, ΔL₂₁, Q₁, 1, 1)
     end
 
     # construct M
     M = zero!(similar(L, (p, p)))
     if !iszerotangent(ΔL)
-        ΔL11 = LowerTriangular(view(ΔL, 1:p, 1:p))
-        M = mul!(M, L11', ΔL11, 1, 1)
+        ΔL₁₁ = LowerTriangular(view(ΔL, 1:p, 1:p))
+        M = mul!(M, L₁₁', ΔL₁₁, 1, 1)
     end
-    M = mul!(M, ΔQ̃, Q1', -1, 1)
+    M = mul!(M, ΔQ̃, Q₁', -1, 1)
     view(M, uppertriangularind(M)) .= conj.(view(M, lowertriangularind(M)))
     if eltype(M) <: Complex
         Md = diagview(M)
         Md .= real.(Md)
     end
-    ldiv!(L11', M)
-    ldiv!(L11', ΔQ̃)
-    ΔA1 = mul!(ΔA1, M, Q1, +1, 1)
-    ΔA1 .+= ΔQ̃
+    ldiv!(L₁₁', M)
+    ldiv!(L₁₁', ΔQ̃)
+    ΔA₁ = mul!(ΔA₁, M, Q₁, +1, 1)
+    ΔA₁ .+= ΔQ̃
     return ΔA
 end
 

src/pullbacks/qr.jl

@@ -61,10 +61,10 @@ function qr_pullback!(
 
     ΔQ, ΔR = ΔQR
 
-    Q1 = view(Q, :, 1:p)
-    R11 = UpperTriangular(view(R, 1:p, 1:p))
-    ΔA1 = view(ΔA, :, 1:p)
-    ΔA2 = view(ΔA, :, (p + 1):n)
+    Q₁ = view(Q, :, 1:p)
+    R₁₁ = UpperTriangular(view(R, 1:p, 1:p))
+    ΔA₁ = view(ΔA, :, 1:p)
+    ΔA₂ = view(ΔA, :, (p + 1):n)
 
     check_qr_cotangents(Q, R, ΔQ, ΔR, p; gauge_atol)
 
@@ -73,36 +73,36 @@ function qr_pullback!(
         ΔQ₁ = view(ΔQ, :, 1:p)
         copy!(ΔQ̃, ΔQ₁)
         if minmn < size(Q, 2)
-            ΔQ3 = view(ΔQ, :, (minmn + 1):size(ΔQ, 2)) # extra columns in the case of qr_full
-            Q3 = view(Q, :, (minmn + 1):size(Q, 2))
-            Q1ᴴΔQ3 = Q1' * ΔQ3
-            ΔQ̃ = mul!(ΔQ̃, Q3, Q1ᴴΔQ3', -1, 1)
+            ΔQ₃ = view(ΔQ, :, (minmn + 1):size(ΔQ, 2)) # extra columns in the case of qr_full
+            Q₃ = view(Q, :, (minmn + 1):size(Q, 2))
+            Q₁ᴴΔQ₃ = Q₁' * ΔQ₃
+            ΔQ̃ = mul!(ΔQ̃, Q₃, Q₁ᴴΔQ₃', -1, 1)
         end
     end
     if !iszerotangent(ΔR) && n > p
-        R12 = view(R, 1:p, (p + 1):n)
-        ΔR12 = view(ΔR, 1:p, (p + 1):n)
-        ΔQ̃ = mul!(ΔQ̃, Q1, ΔR12 * R12', -1, 1)
-        # Adding ΔA2 contribution
-        ΔA2 = mul!(ΔA2, Q1, ΔR12, 1, 1)
+        R₁₂ = view(R, 1:p, (p + 1):n)
+        ΔR₁₂ = view(ΔR, 1:p, (p + 1):n)
+        ΔQ̃ = mul!(ΔQ̃, Q₁, ΔR₁₂ * R₁₂', -1, 1)
+        # Adding ΔA₂ contribution
+        ΔA₂ = mul!(ΔA₂, Q₁, ΔR₁₂, 1, 1)
     end
 
     # construct M
     M = zero!(similar(R, (p, p)))
     if !iszerotangent(ΔR)
-        ΔR11 = UpperTriangular(view(ΔR, 1:p, 1:p))
-        M = mul!(M, ΔR11, R11', 1, 1)
+        ΔR₁₁ = UpperTriangular(view(ΔR, 1:p, 1:p))
+        M = mul!(M, ΔR₁₁, R₁₁', 1, 1)
     end
-    M = mul!(M, Q1', ΔQ̃, -1, 1)
+    M = mul!(M, Q₁', ΔQ̃, -1, 1)
     view(M, lowertriangularind(M)) .= conj.(view(M, uppertriangularind(M)))
     if eltype(M) <: Complex
         Md = diagview(M)
         Md .= real.(Md)
     end
-    rdiv!(M, R11') # R11 is upper triangular
-    rdiv!(ΔQ̃, R11')
-    ΔA1 = mul!(ΔA1, Q1, M, +1, 1)
-    ΔA1 .+= ΔQ̃
+    rdiv!(M, R₁₁') # R₁₁ is upper triangular
+    rdiv!(ΔQ̃, R₁₁')
+    ΔA₁ = mul!(ΔA₁, Q₁, M, +1, 1)
+    ΔA₁ .+= ΔQ̃
     return ΔA
 end
 

test/testsuite/ad_utils.jl

@@ -85,9 +85,9 @@ function remove_qr_gauge_dependence!(ΔQ, ΔR, A, Q, R; rank_atol = MatrixAlgebr
     ΔQ₃ = view(ΔQ, :, (minmn + 1):size(ΔQ, 2)) # extra columns in the case of qr_full
     Q₁ᴴΔQ₃ = Q₁' * ΔQ₃
     mul!(ΔQ₃, Q₁, Q₁ᴴΔQ₃)
-    ΔR22 = view(ΔR, (r + 1):minmn, (r + 1):size(R, 2))
-    MatrixAlgebraKit.diagview(ΔR22) .= 0
-    view(ΔR22, MatrixAlgebraKit.uppertriangularind(ΔR22)) .= 0
+    ΔR₂₂ = view(ΔR, (r + 1):minmn, (r + 1):size(R, 2))
+    MatrixAlgebraKit.diagview(ΔR₂₂) .= 0
+    view(ΔR₂₂, MatrixAlgebraKit.uppertriangularind(ΔR₂₂)) .= 0
     return ΔQ, ΔR
 end
 
@@ -120,9 +120,9 @@ function remove_lq_gauge_dependence!(ΔL, ΔQ, A, L, Q; rank_atol = MatrixAlgebr
     ΔQ₃ = view(ΔQ, (minmn + 1):size(ΔQ, 1), :) # extra rows in the case of lq_full
     ΔQ₃Q₁ᴴ = ΔQ₃ * Q₁'
     mul!(ΔQ₃, ΔQ₃Q₁ᴴ, Q₁)
-    ΔL22 = view(ΔL, (r + 1):size(ΔL, 1), (r + 1):minmn)
-    MatrixAlgebraKit.diagview(ΔL22) .= 0
-    view(ΔL22, MatrixAlgebraKit.lowertriangularind(ΔL22)) .= 0
+    ΔL₂₂ = view(ΔL, (r + 1):size(ΔL, 1), (r + 1):minmn)
+    MatrixAlgebraKit.diagview(ΔL₂₂) .= 0
+    view(ΔL₂₂, MatrixAlgebraKit.lowertriangularind(ΔL₂₂)) .= 0
     return ΔL, ΔQ
 end