Separate diagonal quasi-Newton types

src/DiagonalHessianApproximation.jl

@@ -1,20 +1,24 @@
-export DiagonalQN, SpectralGradient
+export DiagonalPSB, DiagonalAndrei, SpectralGradient
 
 """
-Implementation of the diagonal quasi-Newton approximations described in
+    DiagonalPSB(d)
+
+Construct a linear operator that represents a diagonal PSB quasi-Newton approximation
+as described in
 
 M. Zhu, J. L. Nazareth and H. Wolkowicz
 The Quasi-Cauchy Relation and Diagonal Updating.
 SIAM Journal on Optimization, vol. 9, number 4, pp. 1192-1204, 1999.
 https://doi.org/10.1137/S1052623498331793.
 
-and
+The approximation satisfies the weak secant equation and is not guaranteed to be
+positive definite.
 
-Andrei, N. 
-A diagonal quasi-Newton updating method for unconstrained optimization. 
-https://doi.org/10.1007/s11075-018-0562-7
+# Arguments
+
+- `d::AbstractVector`: initial diagonal approximation.
 """
-mutable struct DiagonalQN{T <: Real, I <: Integer, V <: AbstractVector{T}, F} <:
+mutable struct DiagonalPSB{T <: Real, I <: Integer, V <: AbstractVector{T}, F} <:
                AbstractDiagonalQuasiNewtonOperator{T}
   d::V # Diagonal of the operator
   nrow::I
@@ -30,32 +34,19 @@ mutable struct DiagonalQN{T <: Real, I <: Integer, V <: AbstractVector{T}, F} <:
   args5::Bool
   use_prod5!::Bool # true for 5-args mul! and for composite operators created with operators that use the 3-args mul!
   allocated5::Bool # true for 5-args mul!, false for 3-args mul! until the vectors are allocated
-  psb::Bool
 end
 
-"""
-    DiagonalQN(d)
-
-Construct a linear operator that represents a diagonal quasi-Newton approximation.
-The approximation satisfies the weak secant equation and is not guaranteed to be
-positive definite.
-
-# Arguments
-
-- `d::AbstractVector`: initial diagonal approximation;
-- `psb::Bool`: whether to use the diagonal PSB update or the Andrei update.
-"""
-function DiagonalQN(d::AbstractVector{T}, psb::Bool = false) where {T <: Real}
+@doc (@doc DiagonalPSB) function DiagonalPSB(d::AbstractVector{T}) where {T <: Real}
   prod = (res, v, α, β) -> mulSquareOpDiagonal!(res, d, v, α, β)
   n = length(d)
-  DiagonalQN(d, n, n, true, true, prod, prod, prod, 0, 0, 0, true, true, true, psb)
+  DiagonalPSB(d, n, n, true, true, prod, prod, prod, 0, 0, 0, true, true, true)
 end
 
 # update function
 # s = x_{k+1} - x_k
 # y = ∇f(x_{k+1}) - ∇f(x_k)
 function push!(
-  B::DiagonalQN{T, I, V, F},
+  B::DiagonalPSB{T, I, V, F},
   s0::V,
   y0::V,
 ) where {T <: Real, I <: Integer, V <: AbstractVector{T}, F}
@@ -71,35 +62,97 @@ function push!(
   sT_y = dot(s, y)
   sT_B_s = dot(s2, B.d)
   q = sT_y - sT_B_s
-  if B.psb
-    q /= trA2
-    B.d .+= q .* s .^ 2
-  else
-    sT_s = dot(s, s)
-    q += sT_s
-    q /= trA2
-    B.d .+= q .* s .^ 2 .- 1
-  end
+  q /= trA2
+  B.d .+= q .* s .^ 2
   return B
 end
 
 """
-    reset!(op::DiagonalQN)
-Resets the DiagonalQN data of the given operator.
+    reset!(op::AbstractDiagonalQuasiNewtonOperator)
+
+Reset the diagonal data of the given operator.
 """
-function reset!(op::DiagonalQN{T}) where {T <: Real}
+function reset!(op::AbstractDiagonalQuasiNewtonOperator{T}) where {T <: Real}
   op.d .= one(T)
   op.nprod = 0
   op.ntprod = 0
   op.nctprod = 0
   return op
 end
 
+"""
+    DiagonalAndrei(d)
+
+Construct a linear operator that represents a diagonal quasi-Newton approximation
+as described in
+
+Andrei, N.
+A diagonal quasi-Newton updating method for unconstrained optimization.
+https://doi.org/10.1007/s11075-018-0562-7
+
+The approximation satisfies the weak secant equation and is not guaranteed to be
+positive definite.
+
+# Arguments
+
+- `d::AbstractVector`: initial diagonal approximation.
+"""
+mutable struct DiagonalAndrei{T <: Real, I <: Integer, V <: AbstractVector{T}, F} <:
+               AbstractDiagonalQuasiNewtonOperator{T}
+  d::V # Diagonal of the operator
+  nrow::I
+  ncol::I
+  symmetric::Bool
+  hermitian::Bool
+  prod!::F
+  tprod!::F
+  ctprod!::F
+  nprod::I
+  ntprod::I
+  nctprod::I
+  args5::Bool
+  use_prod5!::Bool # true for 5-args mul! and for composite operators created with operators that use the 3-args mul!
+  allocated5::Bool # true for 5-args mul!, false for 3-args mul! until the vectors are allocated
+end
+
+@doc (@doc DiagonalAndrei) function DiagonalAndrei(d::AbstractVector{T}) where {T <: Real}
+  prod = (res, v, α, β) -> mulSquareOpDiagonal!(res, d, v, α, β)
+  n = length(d)
+  DiagonalAndrei(d, n, n, true, true, prod, prod, prod, 0, 0, 0, true, true, true)
+end
+
+# update function
+# s = x_{k+1} - x_k
+# y = ∇f(x_{k+1}) - ∇f(x_k)
+function push!(
+  B::DiagonalAndrei{T, I, V, F},
+  s0::V,
+  y0::V,
+) where {T <: Real, I <: Integer, V <: AbstractVector{T}, F}
+  s0Norm = norm(s0, 2)
+  if s0Norm == 0
+    error("Cannot update DiagonalQN operator with s=0")
+  end
+  # sᵀBs = sᵀy can be scaled by ||s||² without changing the update
+  s = (si / s0Norm for si ∈ s0)
+  s2 = (si^2 for si ∈ s)
+  y = (yi / s0Norm for yi ∈ y0)
+  trA2 = dot(s2, s2)
+  sT_y = dot(s, y)
+  sT_B_s = dot(s2, B.d)
+  q = sT_y - sT_B_s
+  sT_s = dot(s, s)
+  q += sT_s
+  q /= trA2
+  B.d .+= q .* s .^ 2 .- 1
+  return B
+end
+
 """
 Implementation of a spectral gradient quasi-Newton approximation described in
 
-Birgin, E. G., Martínez, J. M., & Raydan, M. 
-Spectral Projected Gradient Methods: Review and Perspectives. 
+Birgin, E. G., Martínez, J. M., & Raydan, M.
+Spectral Projected Gradient Methods: Review and Perspectives.
 https://doi.org/10.18637/jss.v060.i03
 """
 mutable struct SpectralGradient{T <: Real, I <: Integer, F} <:
@@ -152,15 +205,3 @@ function push!(
   B.d[1] = dot(s, y) / dot(s, s)
   return B
 end
-
-"""
-    reset!(op::SpectralGradient)
-Resets the SpectralGradient data of the given operator.
-"""
-function reset!(op::SpectralGradient{T}) where {T <: Real}
-  op.d[1] = one(T)
-  op.nprod = 0
-  op.ntprod = 0
-  op.nctprod = 0
-  return op
-end

src/LinearOperators.jl

@@ -16,7 +16,7 @@ include("kron.jl")
 # quasi-Newton operators
 include("qn.jl")
 
-# Hessian diagonal approximations
+# diagonal Hessian approximations
 include("DiagonalHessianApproximation.jl")
 
 # Special operators

test/test_diag.jl

@@ -17,7 +17,7 @@ x1 = x0 + [1.0, 0.0, 1.0]
     grad = eval(grad_fun)
     s = x1 - x0
     y = grad(x1) - grad(x0)
-    B = DiagonalQN([1.0, -1.0, 1.0])
+    B = DiagonalAndrei([1.0, -1.0, 1.0])
     push!(B, s, y)
     @test abs(dot(s, B * s) - dot(s, y)) <= 1e-10
   end
@@ -28,53 +28,53 @@ end
     grad = eval(grad_fun)
     s = x1 - x0
     y = grad(x1) - grad(x0)
-    B = DiagonalQN([1.0, -1.0, 1.0], true)
+    B = DiagonalPSB([1.0, -1.0, 1.0])
     push!(B, s, y)
     @test abs(dot(s, B * s) - dot(s, y)) <= 1e-10
   end
 end
 
 @testset "Hard coded test" begin
+  Bref = Dict{Symbol, Dict{Any, Any}}()
+  Bref[:∇f] = Dict{Any, Any}()
+  Bref[:∇g] = Dict{Any, Any}()
+  Bref[:∇h] = Dict{Any, Any}()
+  Bref[:∇f][DiagonalPSB] = [2, -1, 2]
+  Bref[:∇f][DiagonalAndrei] = [2, -2, 2]
+  Bref[:∇g][DiagonalPSB] = [1 + (sin(-1) - exp(-1) - 1) / 2, -1, 1 + (sin(-1) - exp(-1) - 1) / 2]
+  Bref[:∇g][DiagonalAndrei] = [(1 + sin(-1) - exp(-1)) / 2, -2, (1 + sin(-1) - exp(-1)) / 2]
+  Bref[:∇h][DiagonalPSB] = [-5 / 2, -1, -5 / 2]
+  Bref[:∇h][DiagonalAndrei] = [-5 / 2, -2, -5 / 2]
+
+  Bref_spg = Dict{Any, Any}()
+  Bref_spg[:∇f] = 2
+  Bref_spg[:∇g] = (1 - exp(-1) + sin(-1)) / 2
+  Bref_spg[:∇h] = -5 / 2
+
   for grad_fun in (:∇f, :∇g, :∇h)
     grad = eval(grad_fun)
     s = x1 - x0
     y = grad(x1) - grad(x0)
-    for psb ∈ (false, true)
-      B = DiagonalQN([1.0, -1.0, 1.0], psb)
-      if grad_fun == :∇f
-        Bref = psb ? [2, -1, 2] : [2, -2, 2]
-      elseif grad_fun == :∇g
-        Bref =
-          psb ? [1 + (sin(-1) - exp(-1) - 1) / 2, -1, 1 + (sin(-1) - exp(-1) - 1) / 2] :
-          [(1 + sin(-1) - exp(-1)) / 2, -2, (1 + sin(-1) - exp(-1)) / 2]
-      else
-        Bref = psb ? [-5 / 2, -1, -5 / 2] : [-5 / 2, -2, -5 / 2]
-      end
+    for DQN ∈ (DiagonalPSB, DiagonalAndrei)
+      B = DQN([1.0, -1.0, 1.0])
       push!(B, s, y)
-      @test norm(B.d - Bref) <= 1e-10
+      @test norm(B.d - Bref[grad_fun][DQN]) <= 1e-10
     end
 
     B = SpectralGradient(1.0, 3)
-    if grad_fun == :∇f
-      Bref = 2
-    elseif grad_fun == :∇g
-      Bref = (1 - exp(-1) + sin(-1)) / 2
-    else
-      Bref = -5 / 2
-    end
     push!(B, s, y)
-    @test abs(B.d[1] - Bref) <= 1e-10
+    @test abs(B.d[1] - Bref_spg[grad_fun]) <= 1e-10
   end
 end
 
 @testset "Allocations test" begin
   d = rand(5)
-  A = DiagonalQN(d)
+  A = DiagonalAndrei(d)
   v = rand(5)
   u = similar(v)
   mul!(u, A, v)
   @test (@allocated mul!(u, A, v)) == 0
-  B = DiagonalQN(d, true)
+  B = DiagonalPSB(d)
   mul!(u, B, v)
   @test (@allocated mul!(u, B, v)) == 0
   C = SpectralGradient(rand(), 5)
@@ -83,7 +83,7 @@ end
 end
 
 @testset "reset" begin
-  B = DiagonalQN([1.0, -1.0, 1.0], false)
+  B = DiagonalAndrei([1.0, -1.0, 1.0])
   s = x1 - x0
   y = ∇f(x1) - ∇f(x0)
   push!(B, s, y)