test_separableSum.jl

using Random
using LinearAlgebra

Random.seed!(123)

x = randn(10)
X = randn(10,10) .+ im*randn(10,10)
y0 = randn(size(x))
Y0 = randn(size(X)) .+ im*randn(size(X))
y, Y = copy(y0), copy(Y0)

lambdas = (abs.(randn(size(x))), 0.1)
prox_col = (NormL1(lambdas[1]), NormL2(lambdas[2]))

# testing constructors

f = SeparableSum(prox_col)

y, fy = prox(f, (x, X), 1.)
y1, fy1 = prox(prox_col[1], x, 1.)
y2, fy2 = prox(prox_col[2], X, 1.)

@test abs((fy1+fy2)-fy) <= 1e-12
@test norm(y[1]-y1, Inf) <= 1e-12
@test norm(y[2]-y2, Inf) <= 1e-12

y, fy = prox(f, (x, X), (0.5, 1.3))
y1, fy1 = prox(prox_col[1], x, 0.5)
y2, fy2 = prox(prox_col[2], X, 1.3)

@test abs((fy1+fy2)-fy) <= 1e-11
@test norm(y[1]-y1, Inf) <= 1e-11
@test norm(y[2]-y2, Inf) <= 1e-11

gamma1 = 0.5 .+ rand(10)

y, fy = prox(f, (x, X), (gamma1, 1.3))

y1, fy1 = prox(prox_col[1], x, gamma1)
y2, fy2 = prox(prox_col[2], X, 1.3)

@test abs((fy1+fy2)-fy) <= 1e-11
@test norm(y[1]-y1, Inf) <= 1e-11
@test norm(y[2]-y2, Inf) <= 1e-11

# Test two differentiable functions

fs = (SqrNormL2(), LeastSquares(randn(5,10), randn(5)))
f = SeparableSum(fs)
x, y = randn(10), randn(10)

grad_f_x_y, f_x_y = gradient_test(f, (x, y))
grad_f_x, f_x = gradient_test(fs[1], x)
grad_f_y, f_y = gradient_test(fs[2], y)
@test norm(grad_f_x_y .- (grad_f_x, grad_f_y), Inf) <= 1e-12
@test abs((f_x+f_y)-f_x_y) <= 1e-12