Don't use the macro @.

src/bilq.jl

@@ -329,19 +329,19 @@ kwargs_bilq = (:c, :transfer_to_bicg, :M, :N, :ldiv, :atol, :rtol, :itmax, :time
       # Compute d̅ₖ.
       if iter == 1
         # d̅₁ = v₁
-        @. d̅ = vₖ
+        @kcopy!(n, d̅, vₖ)
       else
         # d̅ₖ = s̄ₖ * d̅ₖ₋₁ - cₖ * vₖ
         @kaxpby!(n, -cₖ, vₖ, conj(sₖ), d̅)
       end
 
       # Compute vₖ₊₁ and uₖ₊₁.
-      @. vₖ₋₁ = vₖ # vₖ₋₁ ← vₖ
-      @. uₖ₋₁ = uₖ # uₖ₋₁ ← uₖ
+      @kcopy!(n, vₖ₋₁, vₖ)  # vₖ₋₁ ← vₖ
+      @kcopy!(n, uₖ₋₁, uₖ)  # uₖ₋₁ ← uₖ
 
       if pᴴq ≠ 0
-        @. vₖ = q / βₖ₊₁        # βₖ₊₁vₖ₊₁ = q
-        @. uₖ = p / conj(γₖ₊₁)  # γ̄ₖ₊₁uₖ₊₁ = p
+        vₖ .= q ./ βₖ₊₁        # βₖ₊₁vₖ₊₁ = q
+        uₖ .= p ./ conj(γₖ₊₁)  # γ̄ₖ₊₁uₖ₊₁ = p
       end
 
       # Compute ⟨vₖ,vₖ₊₁⟩ and ‖vₖ₊₁‖

src/bilqr.jl

@@ -316,7 +316,7 @@ kwargs_bilqr = (:transfer_to_bicg, :atol, :rtol, :itmax, :timemax, :verbose, :hi
         # Compute d̅ₖ.
         if iter == 1
           # d̅₁ = v₁
-          @. d̅ = vₖ
+          @kcopy!(n, d̅, vₖ)
         else
           # d̅ₖ = s̄ₖ * d̅ₖ₋₁ - cₖ * vₖ
           @kaxpby!(n, -cₖ, vₖ, conj(sₖ), d̅)
@@ -375,22 +375,22 @@ kwargs_bilqr = (:transfer_to_bicg, :atol, :rtol, :itmax, :timemax, :verbose, :hi
         if iter == 2
           wₖ₋₁ = wₖ₋₂
           @kaxpy!(n, one(FC), uₖ₋₁, wₖ₋₁)
-          @. wₖ₋₁ = uₖ₋₁ / conj(δₖ₋₁)
+          wₖ₋₁ .= uₖ₋₁ ./ conj(δₖ₋₁)
         end
         # w₂ = (u₂ - λ̄₁w₁) / δ̄₂
         if iter == 3
           wₖ₋₁ = wₖ₋₃
           @kaxpy!(n, one(FC), uₖ₋₁, wₖ₋₁)
           @kaxpy!(n, -conj(λₖ₋₂), wₖ₋₂, wₖ₋₁)
-          @. wₖ₋₁ = wₖ₋₁ / conj(δₖ₋₁)
+          wₖ₋₁ .= wₖ₋₁ ./ conj(δₖ₋₁)
         end
         # wₖ₋₁ = (uₖ₋₁ - λ̄ₖ₋₂wₖ₋₂ - ϵ̄ₖ₋₃wₖ₋₃) / δ̄ₖ₋₁
         if iter ≥ 4
           @kscal!(n, -conj(ϵₖ₋₃), wₖ₋₃)
           wₖ₋₁ = wₖ₋₃
           @kaxpy!(n, one(FC), uₖ₋₁, wₖ₋₁)
           @kaxpy!(n, -conj(λₖ₋₂), wₖ₋₂, wₖ₋₁)
-          @. wₖ₋₁ = wₖ₋₁ / conj(δₖ₋₁)
+          wₖ₋₁ .= wₖ₋₁ ./ conj(δₖ₋₁)
         end
 
         if iter ≥ 3
@@ -421,12 +421,12 @@ kwargs_bilqr = (:transfer_to_bicg, :atol, :rtol, :itmax, :timemax, :verbose, :hi
       end
 
       # Compute vₖ₊₁ and uₖ₊₁.
-      @. vₖ₋₁ = vₖ  # vₖ₋₁ ← vₖ
-      @. uₖ₋₁ = uₖ  # uₖ₋₁ ← uₖ
+      @kcopy!(n, vₖ₋₁, vₖ)  # vₖ₋₁ ← vₖ
+      @kcopy!(n, uₖ₋₁, uₖ)  # uₖ₋₁ ← uₖ
 
       if pᴴq ≠ zero(FC)
-        @. vₖ = q / βₖ₊₁        # βₖ₊₁vₖ₊₁ = q
-        @. uₖ = p / conj(γₖ₊₁)  # γ̄ₖ₊₁uₖ₊₁ = p
+        vₖ .= q ./ βₖ₊₁        # βₖ₊₁vₖ₊₁ = q
+        uₖ .= p ./ conj(γₖ₊₁)  # γ̄ₖ₊₁uₖ₊₁ = p
       end
 
       # Update ϵₖ₋₃, λₖ₋₂, δbarₖ₋₁, cₖ₋₁, sₖ₋₁, γₖ and βₖ.

src/cg_lanczos.jl

@@ -218,9 +218,9 @@ kwargs_cg_lanczos = (:M, :ldiv, :check_curvature, :atol, :rtol, :itmax, :timemax
       @kaxpy!(n, -δ, Mv, Mv_next)        # Mvₖ₊₁ ← Mvₖ₊₁ - δₖMvₖ
       if iter > 0
         @kaxpy!(n, -β, Mv_prev, Mv_next) # Mvₖ₊₁ ← Mvₖ₊₁ - βₖMvₖ₋₁
-        @. Mv_prev = Mv                  # Mvₖ₋₁ ← Mvₖ
+        @kcopy!(n, Mv_prev, Mv)          # Mvₖ₋₁ ← Mvₖ
       end
-      @. Mv = Mv_next                      # Mvₖ ← Mvₖ₊₁
+      @kcopy!(n, Mv, Mv_next)              # Mvₖ ← Mvₖ₊₁
       MisI || mulorldiv!(v, M, Mv, ldiv)   # vₖ₊₁ = M⁻¹ * Mvₖ₊₁
       β = sqrt(@kdotr(n, v, Mv))           # βₖ₊₁ = vₖ₊₁ᴴ M vₖ₊₁
       @kscal!(n, one(FC) / β, v)           # vₖ₊₁  ←  vₖ₊₁ / βₖ₊₁

src/cg_lanczos_shift.jl

@@ -211,9 +211,9 @@ kwargs_cg_lanczos_shift = (:M, :ldiv, :check_curvature, :atol, :rtol, :itmax, :t
       @kaxpy!(n, -δ, Mv, Mv_next)          # Mvₖ₊₁ ← Mvₖ₊₁ - δₖMvₖ
       if iter > 0
         @kaxpy!(n, -β, Mv_prev, Mv_next)   # Mvₖ₊₁ ← Mvₖ₊₁ - βₖMvₖ₋₁
-        @. Mv_prev = Mv                    # Mvₖ₋₁ ← Mvₖ
+        kcopy!(n, Mv_prev, Mv)             # Mvₖ₋₁ ← Mvₖ
       end
-      @. Mv = Mv_next                      # Mvₖ ← Mvₖ₊₁
+      kcopy!(n, Mv, Mv_next)               # Mvₖ ← Mvₖ₊₁
       MisI || mulorldiv!(v, M, Mv, ldiv)   # vₖ₊₁ = M⁻¹ * Mvₖ₊₁
       β = sqrt(@kdotr(n, v, Mv))           # βₖ₊₁ = vₖ₊₁ᴴ M vₖ₊₁
       @kscal!(n, one(FC) / β, v)           # vₖ₊₁  ←  vₖ₊₁ / βₖ₊₁

src/fgmres.jl

@@ -241,7 +241,7 @@ kwargs_fgmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rtol, :i
       # Initial ζ₁ and V₁
       β = @knrm2(n, r₀)
       z[1] = β
-      @. V[1] = r₀ / rNorm
+      V[1] .= r₀ ./ rNorm
 
       npass = npass + 1
       solver.inner_iter = 0
@@ -332,7 +332,7 @@ kwargs_fgmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rtol, :i
             push!(V, S(undef, n))
             push!(z, zero(FC))
           end
-          @. V[inner_iter+1] = q / Hbis  # hₖ₊₁.ₖvₖ₊₁ = q
+          V[inner_iter+1] .= q ./ Hbis  # hₖ₊₁.ₖvₖ₊₁ = q
           z[inner_iter+1] = ζₖ₊₁
         end
       end

src/fom.jl

@@ -233,7 +233,7 @@ kwargs_fom = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rtol, :itma
       # Initial ζ₁ and V₁
       β = @knrm2(n, r₀)
       z[1] = β
-      @. V[1] = r₀ / rNorm
+      V[1] .= r₀ ./ rNorm
 
       npass = npass + 1
       inner_iter = 0
@@ -314,7 +314,7 @@ kwargs_fom = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rtol, :itma
           if !restart && (inner_iter ≥ mem)
             push!(V, S(undef, n))
           end
-          @. V[inner_iter+1] = q / Hbis  # hₖ₊₁.ₖvₖ₊₁ = q
+          V[inner_iter+1] .= q ./ Hbis  # hₖ₊₁.ₖvₖ₊₁ = q
         end
       end
 

src/gmres.jl

@@ -235,7 +235,7 @@ kwargs_gmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rtol, :it
       # Initial ζ₁ and V₁
       β = @knrm2(n, r₀)
       z[1] = β
-      @. V[1] = r₀ / rNorm
+      V[1] .= r₀ ./ rNorm
 
       npass = npass + 1
       solver.inner_iter = 0
@@ -325,7 +325,7 @@ kwargs_gmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rtol, :it
             push!(V, S(undef, n))
             push!(z, zero(FC))
           end
-          @. V[inner_iter+1] = q / Hbis  # hₖ₊₁.ₖvₖ₊₁ = q
+          V[inner_iter+1] .= q ./ Hbis  # hₖ₊₁.ₖvₖ₊₁ = q
           z[inner_iter+1] = ζₖ₊₁
         end
       end

src/gpmr.jl

@@ -261,12 +261,12 @@ kwargs_gpmr = (:C, :D, :E, :F, :ldiv, :gsp, :λ, :μ, :reorthogonalization, :ato
     # βv₁ = Cb
     β = @knrm2(m, b₀)
     β ≠ 0 || error("b must be nonzero")
-    @. V[1] = b₀ / β
+    V[1] .= b₀ ./ β
 
     # γu₁ = Dc
     γ = @knrm2(n, c₀)
     γ ≠ 0 || error("c must be nonzero")
-    @. U[1] = c₀ / γ
+    U[1] .= c₀ ./ γ
 
     # Compute ‖r₀‖² = γ² + β²
     rNorm = sqrt(γ^2 + β^2)
@@ -479,15 +479,15 @@ kwargs_gpmr = (:C, :D, :E, :F, :ldiv, :gsp, :λ, :μ, :reorthogonalization, :ato
 
         # hₖ₊₁.ₖ ≠ 0
         if Haux > btol
-          @. V[k+1] = q / Haux  # hₖ₊₁.ₖvₖ₊₁ = q
+          V[k+1] .= q ./ Haux  # hₖ₊₁.ₖvₖ₊₁ = q
         else
           # Breakdown -- hₖ₊₁.ₖ = ‖q‖₂ = 0 and Auₖ ∈ Span{v₁, ..., vₖ}
           V[k+1] .= zero(FC)  # vₖ₊₁ = 0 such that vₖ₊₁ ⊥ Span{v₁, ..., vₖ}
         end
 
         # fₖ₊₁.ₖ ≠ 0
         if Faux > btol
-          @. U[k+1] = p / Faux  # fₖ₊₁.ₖuₖ₊₁ = p
+          U[k+1] .= p ./ Faux  # fₖ₊₁.ₖuₖ₊₁ = p
         else
           # Breakdown -- fₖ₊₁.ₖ = ‖p‖₂ = 0 and Bvₖ ∈ Span{u₁, ..., uₖ}
           U[k+1] .= zero(FC)  # uₖ₊₁ = 0 such that uₖ₊₁ ⊥ Span{u₁, ..., uₖ}

src/minres.jl

@@ -276,8 +276,8 @@ kwargs_minres = (:M, :ldiv, :λ, :atol, :rtol, :etol, :conlim, :itmax, :timemax,
       end
       @kaxpy!(n, one(FC) / β, v, w)
 
-      @. r1 = r2
-      @. r2 = y
+      @kcopy!(n, r1, r2)
+      @kcopy!(n, r2, y)
       MisI || mulorldiv!(v, M, r2, ldiv)
       oldβ = β
       β = @kdotr(n, r2, v)

src/minres_qlp.jl

@@ -369,12 +369,12 @@ kwargs_minres_qlp = (:M, :ldiv, :λ, :atol, :rtol, :Artol, :itmax, :timemax, :ve
       # Compute directions wₖ₋₂, ẘₖ₋₁ and w̄ₖ, last columns of Wₖ = Vₖ(Pₖ)ᴴ
       if iter == 1
         # w̅₁ = v₁
-        @. wₖ = vₖ
+        @kcopy!(n, wₖ, vₖ)
       elseif iter == 2
         # [w̅ₖ₋₁ vₖ] [cpₖ  spₖ] = [ẘₖ₋₁ w̅ₖ] ⟷ ẘₖ₋₁ = cpₖ * w̅ₖ₋₁ + spₖ * vₖ
         #           [spₖ -cpₖ]             ⟷ w̅ₖ   = spₖ * w̅ₖ₋₁ - cpₖ * vₖ
         @kswap(wₖ₋₁, wₖ)
-        @. wₖ = spₖ * wₖ₋₁ - cpₖ * vₖ
+        wₖ .= spₖ .* wₖ₋₁ .- cpₖ .* vₖ
         @kaxpby!(n, spₖ, vₖ, cpₖ, wₖ₋₁)
       else
         # [ẘₖ₋₂ w̄ₖ₋₁ vₖ] [cpₖ  0   spₖ] [1   0    0 ] = [wₖ₋₂ ẘₖ₋₁ w̄ₖ] ⟷ wₖ₋₂ = cpₖ * ẘₖ₋₂ + spₖ * vₖ

src/qmr.jl

@@ -326,35 +326,35 @@ kwargs_qmr = (:c, :M, :N, :ldiv, :atol, :rtol, :itmax, :timemax, :verbose, :hist
       if iter == 1
         wₖ = wₖ₋₁
         @kaxpy!(n, one(FC), vₖ, wₖ)
-        @. wₖ = wₖ / δₖ
+        wₖ .= wₖ ./ δₖ
       end
       # w₂ = (v₂ - λ₁w₁) / δ₂
       if iter == 2
         wₖ = wₖ₋₂
         @kaxpy!(n, -λₖ₋₁, wₖ₋₁, wₖ)
         @kaxpy!(n, one(FC), vₖ, wₖ)
-        @. wₖ = wₖ / δₖ
+        wₖ .= wₖ ./ δₖ
       end
       # wₖ = (vₖ - λₖ₋₁wₖ₋₁ - ϵₖ₋₂wₖ₋₂) / δₖ
       if iter ≥ 3
         @kscal!(n, -ϵₖ₋₂, wₖ₋₂)
         wₖ = wₖ₋₂
         @kaxpy!(n, -λₖ₋₁, wₖ₋₁, wₖ)
         @kaxpy!(n, one(FC), vₖ, wₖ)
-        @. wₖ = wₖ / δₖ
+        wₖ .= wₖ ./ δₖ
       end
 
       # Compute solution xₖ.
       # xₖ ← xₖ₋₁ + ζₖ * wₖ
       @kaxpy!(n, ζₖ, wₖ, x)
 
       # Compute vₖ₊₁ and uₖ₊₁.
-      @. vₖ₋₁ = vₖ  # vₖ₋₁ ← vₖ
-      @. uₖ₋₁ = uₖ  # uₖ₋₁ ← uₖ
+      @kcopy!(n, vₖ₋₁, vₖ)  # vₖ₋₁ ← vₖ
+      @kcopy!(n, uₖ₋₁, uₖ)  # uₖ₋₁ ← uₖ
 
       if pᴴq ≠ zero(FC)
-        @. vₖ = q / βₖ₊₁        # βₖ₊₁vₖ₊₁ = q
-        @. uₖ = p / conj(γₖ₊₁)  # γ̄ₖ₊₁uₖ₊₁ = p
+        vₖ .= q ./ βₖ₊₁        # βₖ₊₁vₖ₊₁ = q
+        uₖ .= p ./ conj(γₖ₊₁)  # γ̄ₖ₊₁uₖ₊₁ = p
       end
 
       # Compute τₖ₊₁ = τₖ + ‖vₖ₊₁‖²

src/symmlq.jl

@@ -303,9 +303,9 @@ kwargs_symmlq = (:M, :ldiv, :transfer_to_cg, :λ, :λest, :atol, :rtol, :etol, :
       mul!(Mv_next, A, v)
       α = @kdotr(m, v, Mv_next) + λ
       @kaxpy!(m, -oldβ, Mvold, Mv_next)
-      @. Mvold = Mv
+      @kcopy!(m, Mvold, Mv)
       @kaxpy!(m, -α, Mv, Mv_next)
-      @. Mv = Mv_next
+      @kcopy!(m, Mv, Mv_next)
       MisI || mulorldiv!(v, M, Mv, ldiv)
       β = @kdotr(m, v, Mv)
       β < 0 && error("Preconditioner is not positive definite")

src/tricg.jl

@@ -369,22 +369,22 @@ kwargs_tricg = (:M, :N, :ldiv, :spd, :snd, :flip, :τ, :ν, :atol, :rtol, :itmax
       if iter == 1
         # [ 1  0 ] [ gx₁ gy₁ ] = [ v₁ 0  ]
         # [ δ̄₁ 1 ] [ gx₂ gy₂ ]   [ 0  u₁ ]
-        @. gx₂ₖ₋₁ = vₖ
-        @. gx₂ₖ   = - conj(δₖ) * gx₂ₖ₋₁
-        @. gy₂ₖ   = uₖ
+        @kcopy!(m, gx₂ₖ₋₁, vₖ)
+        gx₂ₖ .= -conj(δₖ) .* gx₂ₖ₋₁
+        @kcopy!(n, gy₂ₖ, uₖ)
       else
         # [ 0  σ̄ₖ 1  0 ] [ gx₂ₖ₋₃ gy₂ₖ₋₃ ] = [ vₖ 0  ]
         # [ η̄ₖ λ̄ₖ δ̄ₖ 1 ] [ gx₂ₖ₋₂ gy₂ₖ₋₂ ]   [ 0  uₖ ]
         #                [ gx₂ₖ₋₁ gy₂ₖ₋₁ ]
         #                [ gx₂ₖ   gy₂ₖ   ]
-        @. gx₂ₖ₋₁ = conj(ηₖ) * gx₂ₖ₋₁ + conj(λₖ) * gx₂ₖ
-        @. gy₂ₖ₋₁ = conj(ηₖ) * gy₂ₖ₋₁ + conj(λₖ) * gy₂ₖ
+        gx₂ₖ₋₁ .= conj(ηₖ) .* gx₂ₖ₋₁ .+ conj(λₖ) .* gx₂ₖ
+        gy₂ₖ₋₁ .= conj(ηₖ) .* gy₂ₖ₋₁ .+ conj(λₖ) .* gy₂ₖ
 
-        @. gx₂ₖ = vₖ - conj(σₖ) * gx₂ₖ
-        @. gy₂ₖ =    - conj(σₖ) * gy₂ₖ
+        gx₂ₖ .= vₖ .- conj(σₖ) .* gx₂ₖ
+        gy₂ₖ .=    .- conj(σₖ) .* gy₂ₖ
 
-        @. gx₂ₖ₋₁ =    - gx₂ₖ₋₁ - conj(δₖ) * gx₂ₖ
-        @. gy₂ₖ₋₁ = uₖ - gy₂ₖ₋₁ - conj(δₖ) * gy₂ₖ
+        gx₂ₖ₋₁ .=    .- gx₂ₖ₋₁ .- conj(δₖ) .* gx₂ₖ
+        gy₂ₖ₋₁ .= uₖ .- gy₂ₖ₋₁ .- conj(δₖ) .* gy₂ₖ
 
         # g₂ₖ₋₃ == g₂ₖ and g₂ₖ₋₂ == g₂ₖ₋₁
         @kswap(gx₂ₖ₋₁, gx₂ₖ)

src/trilqr.jl

@@ -300,7 +300,7 @@ kwargs_trilqr = (:transfer_to_usymcg, :atol, :rtol, :itmax, :timemax, :verbose,
         # Compute d̅ₖ.
         if iter == 1
           # d̅₁ = u₁
-          @. d̅ = uₖ
+          @kcopy!(n, d̅, uₖ)
         else
           # d̅ₖ = s̄ₖ * d̅ₖ₋₁ - cₖ * uₖ
           @kaxpby!(n, -cₖ, uₖ, conj(sₖ), d̅)
@@ -351,22 +351,22 @@ kwargs_trilqr = (:transfer_to_usymcg, :atol, :rtol, :itmax, :timemax, :verbose,
         if iter == 2
           wₖ₋₁ = wₖ₋₂
           @kaxpy!(m, one(FC), vₖ₋₁, wₖ₋₁)
-          @. wₖ₋₁ = vₖ₋₁ / conj(δₖ₋₁)
+          wₖ₋₁ .= vₖ₋₁ ./ conj(δₖ₋₁)
         end
         # w₂ = (v₂ - λ̄₁w₁) / δ̄₂
         if iter == 3
           wₖ₋₁ = wₖ₋₃
           @kaxpy!(m, one(FC), vₖ₋₁, wₖ₋₁)
           @kaxpy!(m, -conj(λₖ₋₂), wₖ₋₂, wₖ₋₁)
-          @. wₖ₋₁ = wₖ₋₁ / conj(δₖ₋₁)
+          wₖ₋₁ .= wₖ₋₁ ./ conj(δₖ₋₁)
         end
         # wₖ₋₁ = (vₖ₋₁ - λ̄ₖ₋₂wₖ₋₂ - ϵ̄ₖ₋₃wₖ₋₃) / δ̄ₖ₋₁
         if iter ≥ 4
           @kscal!(m, -conj(ϵₖ₋₃), wₖ₋₃)
           wₖ₋₁ = wₖ₋₃
           @kaxpy!(m, one(FC), vₖ₋₁, wₖ₋₁)
           @kaxpy!(m, -conj(λₖ₋₂), wₖ₋₂, wₖ₋₁)
-          @. wₖ₋₁ = wₖ₋₁ / conj(δₖ₋₁)
+          wₖ₋₁ .= wₖ₋₁ ./ conj(δₖ₋₁)
         end
 
         if iter ≥ 3
@@ -399,14 +399,14 @@ kwargs_trilqr = (:transfer_to_usymcg, :atol, :rtol, :itmax, :timemax, :verbose,
       end
 
       # Compute uₖ₊₁ and uₖ₊₁.
-      @. vₖ₋₁ = vₖ  # vₖ₋₁ ← vₖ
-      @. uₖ₋₁ = uₖ  # uₖ₋₁ ← uₖ
+      @kcopy!(m, vₖ₋₁, vₖ)  # vₖ₋₁ ← vₖ
+      @kcopy!(n, uₖ₋₁, uₖ)  # uₖ₋₁ ← uₖ
 
       if βₖ₊₁ ≠ zero(T)
-        @. vₖ = q / βₖ₊₁  # βₖ₊₁vₖ₊₁ = q
+        vₖ .= q ./ βₖ₊₁  # βₖ₊₁vₖ₊₁ = q
       end
       if γₖ₊₁ ≠ zero(T)
-        @. uₖ = p / γₖ₊₁  # γₖ₊₁uₖ₊₁ = p
+        uₖ .= p ./ γₖ₊₁  # γₖ₊₁uₖ₊₁ = p
       end
 
       # Update ϵₖ₋₃, λₖ₋₂, δbarₖ₋₁, cₖ₋₁, sₖ₋₁, γₖ and βₖ.