reduce unnecessary warnings

Author: lkdvos

src/pullbacks/eig.jl

@@ -43,7 +43,7 @@ function eig_pullback!(
 
         mask = abs.(transpose(D) .- D) .< degeneracy_atol
         Δgauge = norm(view(VᴴΔV, mask), Inf)
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`eig` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         VᴴΔV .*= conj.(inv_safe.(transpose(D) .- D, degeneracy_atol))
@@ -121,7 +121,7 @@ function eig_trunc_pullback!(
         VᴴΔV = V' * ΔV
         mask = abs.(transpose(D) .- D) .< degeneracy_atol
         Δgauge = norm(view(VᴴΔV, mask), Inf)
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`eig` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         ΔVperp = ΔV - V * inv(G) * VᴴΔV

src/pullbacks/eigh.jl

@@ -44,7 +44,7 @@ function eigh_pullback!(
 
         mask = abs.(D' .- D) .< degeneracy_atol
         Δgauge = norm(view(aVᴴΔV, mask))
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`eigh` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         aVᴴΔV .*= inv_safe.(D' .- D, degeneracy_atol)
@@ -112,7 +112,7 @@ function eigh_trunc_pullback!(
 
         mask = abs.(D' .- D) .< degeneracy_atol
         Δgauge = norm(view(aVᴴΔV, mask))
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`eigh` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         aVᴴΔV .*= inv_safe.(D' .- D, degeneracy_atol)

src/pullbacks/lq.jl

@@ -50,7 +50,7 @@ function lq_pullback!(
             ΔL22 = view(ΔL, (p + 1):m, (p + 1):minmn)
             Δgauge = max(Δgauge, norm(ΔL22, Inf))
         end
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`lq` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
     end
 
@@ -70,7 +70,7 @@ function lq_pullback!(
             # Q2' * ΔQ2 as a gauge dependent quantity.
             ΔQ2Q1ᴴ = ΔQ2 * Q1'
             Δgauge = norm(mul!(copy(ΔQ2), ΔQ2Q1ᴴ, Q1, -1, 1), Inf)
-            Δgauge < gauge_atol ||
+            Δgauge ≤ gauge_atol ||
                 @warn "`lq` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
             ΔQ̃ = mul!(ΔQ̃, ΔQ2Q1ᴴ', Q2, -1, 1)
         end
@@ -120,7 +120,7 @@ function lq_null_pullback!(
     if !iszerotangent(ΔNᴴ) && size(Nᴴ, 1) > 0
         aNᴴΔN = project_antihermitian!(Nᴴ * ΔNᴴ')
         Δgauge = norm(aNᴴΔN)
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`lq_null` cotangent sensitive to gauge choice: (|Δgauge| = $Δgauge)"
         L, Q = lq_compact(A; positive = true) # should we be able to provide algorithm here?
         X = ldiv!(LowerTriangular(L)', Q * ΔNᴴ')

src/pullbacks/qr.jl

@@ -51,7 +51,7 @@ function qr_pullback!(
             ΔR22 = view(ΔR, (p + 1):minmn, (p + 1):n)
             Δgauge = max(Δgauge, norm(ΔR22, Inf))
         end
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`qr` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
     end
 
@@ -70,7 +70,7 @@ function qr_pullback!(
             # Q2' * ΔQ2 as a gauge dependent quantity.
             Q1dΔQ2 = Q1' * ΔQ2
             Δgauge = norm(mul!(copy(ΔQ2), Q1, Q1dΔQ2, -1, 1), Inf)
-            Δgauge < gauge_atol ||
+            Δgauge ≤ gauge_atol ||
                 @warn "`qr` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
             ΔQ̃ = mul!(ΔQ̃, Q2, Q1dΔQ2', -1, 1)
         end
@@ -120,7 +120,7 @@ function qr_null_pullback!(
     if !iszerotangent(ΔN) && size(N, 2) > 0
         aNᴴΔN = project_antihermitian!(N' * ΔN)
         Δgauge = norm(aNᴴΔN)
-        Δgauge < gauge_atol ||
+        Δgauge ≤ gauge_atol ||
             @warn "`qr_null` cotangent sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         Q, R = qr_compact(A; positive = true)

src/pullbacks/svd.jl

@@ -72,7 +72,7 @@ function svd_pullback!(
     # check whether cotangents arise from gauge-invariance objective function
     mask = abs.(Sr' .- Sr) .< degeneracy_atol
     Δgauge = norm(view(aUΔU, mask) + view(aVΔV, mask), Inf)
-    Δgauge < gauge_atol ||
+    Δgauge ≤ gauge_atol ||
         @warn "`svd` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
     UdΔAV = (aUΔU .+ aVΔV) .* inv_safe.(Sr' .- Sr, degeneracy_atol) .+
@@ -160,7 +160,7 @@ function svd_trunc_pullback!(
     # check whether cotangents arise from gauge-invariance objective function
     mask = abs.(S' .- S) .< degeneracy_atol
     Δgauge = norm(view(aUΔU, mask) + view(aVΔV, mask), Inf)
-    Δgauge < gauge_atol ||
+    Δgauge ≤ gauge_atol ||
         @warn "`svd` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
     UdΔAV = (aUΔU .+ aVΔV) .* inv_safe.(S' .- S, degeneracy_atol) .+