make gauge tolerances relative

Author: lkdvos

src/common/defaults.jl

@@ -10,12 +10,13 @@ quantity needs to be computed.
 defaulttol(x::Any) = eps(real(float(one(eltype(x)))))^(2 / 3)
 
 """
-    default_pullback_gauge_atol(A)
+    default_pullback_gauge_atol(ΔA...)
 
 Default tolerance for deciding to warn if incoming adjoints of a pullback rule
 has components that are not gauge-invariant.
 """
-default_pullback_gauge_atol(A) = eps(real(eltype(A)))^(3 / 4)
+default_pullback_gauge_atol(A) = eps(norm(A, Inf))^(3 / 4)
+default_pullback_gauge_atol(A, As...) = maximum(default_pullback_gauge_atol, (A, As...))
 
 """
     default_pullback_degeneracy_atol(A)

src/pullbacks/eig.jl

@@ -2,7 +2,7 @@
     eig_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV, [ind];
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
 Adds the pullback from the full eigenvalue decomposition of `A` to `ΔA`, given the output
@@ -22,7 +22,7 @@ not small compared to `gauge_atol`.
 function eig_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV, ind = Colon();
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
     # Basic size checks and determination
@@ -83,7 +83,7 @@ end
     eig_trunc_pullback!(
         ΔA::AbstractMatrix, ΔDV, A, DV;
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
 Adds the pullback from the truncated eigenvalue decomposition of `A` to `ΔA`, given the
@@ -104,7 +104,7 @@ not small compared to `gauge_atol`.
 function eig_trunc_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV;
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
     # Basic size checks and determination

src/pullbacks/eigh.jl

@@ -2,7 +2,7 @@
     eigh_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV, [ind];
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
 Adds the pullback from the Hermitian eigenvalue decomposition of `A` to `ΔA`, given the
@@ -22,7 +22,7 @@ anti-hermitian part of `V' * ΔV`, restricted to rows `i` and columns `j` for wh
 function eigh_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV, ind = Colon();
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
     # Basic size checks and determination
@@ -73,7 +73,7 @@ end
     eigh_trunc_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV;
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
 Adds the pullback from the truncated Hermitian eigenvalue decomposition of `A` to `ΔA`,
@@ -94,7 +94,7 @@ not small compared to `gauge_atol`.
 function eigh_trunc_pullback!(
         ΔA::AbstractMatrix, A, DV, ΔDV;
         degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(DV[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
     )
 
     # Basic size checks and determination

src/pullbacks/lq.jl

@@ -2,7 +2,7 @@
     lq_pullback!(
         ΔA, A, LQ, ΔLQ;
         rank_atol::Real = default_pullback_rank_atol(LQ[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(LQ[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔLQ[2])
     )
 
 Adds the pullback from the LQ decomposition of `A` to `ΔA` given the output `LQ` and
@@ -18,7 +18,7 @@ or rows exceed `gauge_atol`, a warning will be printed.
 function lq_pullback!(
         ΔA::AbstractMatrix, A, LQ, ΔLQ;
         rank_atol::Real = default_pullback_rank_atol(LQ[1]),
-        gauge_atol::Real = default_pullback_gauge_atol(LQ[1])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔLQ[2])
     )
     # process
     L, Q = LQ
@@ -105,7 +105,7 @@ end
 """
     lq_null_pullback!(
         ΔA::AbstractMatrix, A, Nᴴ, ΔNᴴ;
-        gauge_atol::Real = default_pullback_gauge_atol(A)
+        gauge_atol::Real = default_pullback_gauge_atol(ΔNᴴ)
     )
 
 Adds the pullback from the left nullspace of `A` to `ΔA`, given the nullspace basis
@@ -115,7 +115,7 @@ See also [`lq_pullback!`](@ref).
 """
 function lq_null_pullback!(
         ΔA::AbstractMatrix, A, Nᴴ, ΔNᴴ;
-        gauge_atol::Real = default_pullback_gauge_atol(A)
+        gauge_atol::Real = default_pullback_gauge_atol(ΔNᴴ)
     )
     if !iszerotangent(ΔNᴴ) && size(Nᴴ, 1) > 0
         aNᴴΔN = project_antihermitian!(Nᴴ * ΔNᴴ')

src/pullbacks/qr.jl

@@ -3,7 +3,7 @@
         ΔA, A, QR, ΔQR;
         tol::Real = default_pullback_gaugetol(QR[2]),
         rank_atol::Real = default_pullback_rank_atol(QR[2]),
-        gauge_atol::Real = default_pullback_gauge_atol(QR[2])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔQR[1])
     )
 
 Adds the pullback from the QR decomposition of `A` to `ΔA` given the output `QR` and
@@ -19,7 +19,7 @@ and also the adjoint variables `ΔQ` and `ΔR` should have nonzero values only i
 function qr_pullback!(
         ΔA::AbstractMatrix, A, QR, ΔQR;
         rank_atol::Real = default_pullback_rank_atol(QR[2]),
-        gauge_atol::Real = default_pullback_gauge_atol(QR[2])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔQR[1])
     )
     # process
     Q, R = QR
@@ -105,7 +105,7 @@ end
 """
     qr_null_pullback!(
         ΔA::AbstractMatrix, A, N, ΔN;
-        gauge_atol::Real = default_pullback_gauge_atol(A)
+        gauge_atol::Real = default_pullback_gauge_atol(ΔN)
     )
 
 Adds the pullback from the right nullspace of `A` to `ΔA`, given the nullspace basis
@@ -115,7 +115,7 @@ See also [`qr_pullback!`](@ref).
 """
 function qr_null_pullback!(
         ΔA::AbstractMatrix, A, N, ΔN;
-        gauge_atol::Real = default_pullback_gauge_atol(A)
+        gauge_atol::Real = default_pullback_gauge_atol(ΔN)
     )
     if !iszerotangent(ΔN) && size(N, 2) > 0
         aNᴴΔN = project_antihermitian!(N' * ΔN)

src/pullbacks/svd.jl

@@ -3,7 +3,7 @@
         ΔA, A, USVᴴ, ΔUSVᴴ, [ind];
         rank_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
         degeneracy_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
-        gauge_atol::Real = default_pullback_gauge_atol(USVᴴ[2])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔUSVᴴ[1], ΔUSVᴴ[3])
     )
 
 Adds the pullback from the SVD of `A` to `ΔA` given the output USVᴴ of `svd_compact` or
@@ -24,7 +24,7 @@ function svd_pullback!(
         ΔA::AbstractMatrix, A, USVᴴ, ΔUSVᴴ, ind = Colon();
         rank_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
         degeneracy_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
-        gauge_atol::Real = default_pullback_gauge_atol(USVᴴ[2])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔUSVᴴ[1], ΔUSVᴴ[3])
     )
 
     # Extract the SVD components
@@ -106,7 +106,7 @@ end
         ΔA, A, USVᴴ, ΔUSVᴴ;
         rank_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
         degeneracy_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
-        gauge_atol::Real = default_pullback_gauge_atol(USVᴴ[2])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔUSVᴴ[1], ΔUSVᴴ[3])
     )
 
 Adds the pullback from the truncated SVD of `A` to `ΔA`, given the output `USVᴴ` and the
@@ -127,7 +127,7 @@ function svd_trunc_pullback!(
         ΔA::AbstractMatrix, A, USVᴴ, ΔUSVᴴ;
         rank_atol::Real = 0,
         degeneracy_atol::Real = default_pullback_rank_atol(USVᴴ[2]),
-        gauge_atol::Real = default_pullback_gauge_atol(USVᴴ[2])
+        gauge_atol::Real = default_pullback_gauge_atol(ΔUSVᴴ[1], ΔUSVᴴ[3])
     )
 
     # Extract the SVD components