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test_lasso.jl
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test_lasso.jl
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# # tests for lasso: 1/2\|Ax-b\|^2 + λ \|x\|_1
@testset "Lasso ($T)" for T in [Float32, Float64, ComplexF32, ComplexF64]
using Test
using LinearAlgebra
using CIAOAlgorithms
using ProximalOperators
using Base.Iterators: take
using Random
Random.seed!(0)
R = real(T)
# problem definition
N, n = 6, 3 # A in R^{N x n}
p = 2 # nonzeros in the solution
y_star = rand(R, N)
y_star ./= norm(y_star) # y^star
C = rand(R, N, n) .* 2 .- 1
CTy = abs.(C' * y_star)
# indices with decreasing order by abs
perm = sortperm(CTy, rev = true)
rho, λ = R(10), R(1)
alpha = zeros(T, n)
for i = 1:n
if i <= p
alpha[perm[i]] = λ / CTy[perm[i]]
else
alpha[perm[i]] = (CTy[perm[i]] < 0.1 * λ) ? λ : λ * rand() / CTy[perm[i]]
end
end
A = C * diagm(0 => alpha) # scaling the columns of Cin
# generate the solution
x_star = zeros(T, n)
for i = 1:n
if i <= p
x_star[perm[i]] = rand() * rho / sqrt(p) * sign(dot(A[:, perm[i]], y_star))
end
end
b = A * x_star + y_star
# cost function
cost_lasso(x) = norm(A * x - b)^2 / 2 + λ * norm(x, 1)
f_star = cost_lasso(x_star)
# preparations for the solver
F = Vector{LeastSquares}(undef, 0)
L = Vector{R}(undef, 0)
for i = 1:N
tempA = A[i:i, :]
f = LeastSquares(tempA, b[i:i], R(N))
Lf = opnorm(tempA)^2 * N
push!(F, f)
push!(L, Lf)
end
g = NormL1(λ)
x0 = zeros(T, n)
maxit = 1000
tol = 1e-4
@testset "Finito" begin
# sweeping 1, 2, 3 for randomined, cyclic and shuffled sampling strategies, respectively.
## test the solver
# basic finito
@testset "basic Finito" for sweeping in collect(1:3)
solver = CIAOAlgorithms.Finito{R}(maxit = maxit, sweeping = sweeping)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test cost_lasso(x_finito) - f_star < tol
@test eltype(x_finito) == T
end
# limited memory finito
@testset "LFinito" for sweeping in collect(2:3)
# @testset "cyclical" begin
solver =
CIAOAlgorithms.Finito{R}(maxit = maxit, sweeping = sweeping, LFinito = true)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test cost_lasso(x_finito) - f_star < tol
@test eltype(x_finito) == T
end
# # adaptive variant
@testset "adaptive finito" for sweeping in collect(1:3)
solver = CIAOAlgorithms.Finito{R}(
maxit = maxit,
tol = R(1e-5),
sweeping = sweeping,
adaptive = true,
)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test cost_lasso(x_finito) - f_star < tol
@test eltype(x_finito) == T
end
# basic finito with minibatch
vec_ref = [(1, 2), (2, 2), (3, 3)] # different samplings and batch sizes
@testset "Finito_minibatch" for (sweeping, batch) in vec_ref
solver = CIAOAlgorithms.Finito{R}(
maxit = maxit,
sweeping = sweeping,
minibatch = (true, batch),
)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test cost_lasso(x_finito) - f_star < tol
@test eltype(x_finito) == T
end
# limited memory finito with minibatch
vec_ref = [(2, 1), (2, 2), (3, 3)] # different samplings and batch sizes
@testset "LFinito_minibatch" for (sweeping, batch) in vec_ref
solver = CIAOAlgorithms.Finito{R}(
maxit = maxit,
sweeping = sweeping,
LFinito = true,
minibatch = (true, batch),
)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test cost_lasso(x_finito) - f_star < tol
@test eltype(x_finito) == T
end
# test with user defined stepsizes
@testset "γ and L as scalars" begin
@testset "randomized" begin
γ = N / maximum(L)
solver = CIAOAlgorithms.Finito{R}(maxit = maxit, γ = γ)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test cost_lasso(x_finito) - f_star < tol
end
@testset "cyclic" begin
solver = CIAOAlgorithms.Finito{R}(maxit = maxit)
x_finito, it_finito = solver(x0, F = F, g = g, L = maximum(L), N = N)
@test cost_lasso(x_finito) - f_star < tol
end
end
## test the iterator
vec_ref = [(1, false, false), (2, false, false), (3, false, true), (3, true, false)]
@testset "the iterator" for (sweeping, LFinito, adaptive) in vec_ref
solver = CIAOAlgorithms.Finito{R}(
sweeping = sweeping,
LFinito = LFinito,
adaptive = adaptive,
)
iter = CIAOAlgorithms.iterator(solver, x0, F = F, g = g, L = L, N = N)
@test iter.x0 === x0
for state in take(iter, 2)
@test solution(state) === state.z
@test eltype(solution(state)) == T
end
end
end
@testset "SVRG" begin
## test the solver
γ = 1 / (7 * maximum(L))
@testset "SVRG-Base" begin
solver = CIAOAlgorithms.SVRG{R}(maxit = maxit, γ = γ)
x_SVRG, it_SVRG = solver(x0, F = F, g = g, N = N)
@test cost_lasso(x_SVRG) - f_star < tol
@test eltype(x_SVRG) == T
end
@testset "SVRG++" begin
solver = CIAOAlgorithms.SVRG{R}(maxit = 16, γ = γ, m = 1, plus = true)
x_SVRG, it_SVRG = solver(x0, F = F, g = g, N = N)
@test cost_lasso(x_SVRG) - f_star < tol
@test eltype(x_SVRG) == T
end
# test the iterator
@testset "the iterator" begin
solver = CIAOAlgorithms.SVRG{R}(γ = γ)
iter = CIAOAlgorithms.iterator(solver, x0, F = F, g = g, N = N)
@test iter.x0 === x0
for state in take(iter, 2)
@test solution(state) === state.z_full
@test eltype(solution(state)) == T
end
next = iterate(iter) # next = (state, state)
# one iteration with the solver
solver = CIAOAlgorithms.SVRG{R}(γ = γ, maxit = 1)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test solution(next[2]) == x_finito
end
end
@testset "SAGA" begin
## test the solver
@testset "SAGA-Base" begin
solver = CIAOAlgorithms.SAGA{R}(maxit = maxit)
x_SAGA, it_SAGA = solver(x0, F = F, g = g, N = N, L = L)
@test cost_lasso(x_SAGA) - f_star < tol
@test eltype(x_SAGA) == T
end
@testset "SAGA-stepsize" begin
γ = 1 / (3 * maximum(L))
solver = CIAOAlgorithms.SAGA{R}(maxit = maxit, γ = γ)
x_SAGA, it_SAGA = solver(x0, F = F, g = g, N = N)
@test cost_lasso(x_SAGA) - f_star < tol
@test eltype(x_SAGA) == T
end
# test the iterator
@testset "the iterator" begin
γ = 1 / (3 * maximum(L))
solver = CIAOAlgorithms.SAGA{R}(γ = γ)
iter = CIAOAlgorithms.iterator(solver, x0, F = F, g = g, N = N)
@test iter.x0 === x0
for state in take(iter, 2)
@test solution(state) === state.z
@test eltype(solution(state)) == T
end
next = iterate(iter) # next = (state, state)
# one iteration with the solver
solver = CIAOAlgorithms.SAGA{R}(γ = γ, maxit = 1)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test solution(next[2]) == x_finito
end
end
@testset "SAG" begin
# note that proximal SAG may not be theoretically convergent
maxit = 10000
## test the solver
@testset "SAG-Base" begin
solver = CIAOAlgorithms.SAG(R, maxit = maxit)
x_SAG, it_SAG = solver(x0, F = F, g = g, N = N, L = L)
@test cost_lasso(x_SAG) - f_star < tol
@test eltype(x_SAG) == T
end
@testset "SAG" begin
γ = 1 / (16 * maximum(L))
solver = CIAOAlgorithms.SAG(R, maxit = maxit, γ = γ)
x_SAG, it_SAG = solver(x0, F = F, g = g, N = N)
@test cost_lasso(x_SAG) - f_star < tol
@test eltype(x_SAG) == T
end
# test the iterator
@testset "the iterator" begin
γ = 1 / (16 * maximum(L))
solver = CIAOAlgorithms.SAG(R, γ = γ)
iter = CIAOAlgorithms.iterator(solver, x0, F = F, g = g, N = N)
@test iter.x0 === x0
for state in take(iter, 2)
@test solution(state) === state.z
@test eltype(solution(state)) == T
end
next = iterate(iter) # next = (state, state)
# one iteration with the solver
solver = CIAOAlgorithms.SAG(R, γ = γ, maxit = 1)
x_finito, it_finito = solver(x0, F = F, g = g, L = L, N = N)
@test solution(next[2]) == x_finito
end
end
end