test_that("group norms are correct", {
  asparse <- .05
  gr <- c(1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3)
  x <- c(-5):5
  expect_equal(grouped_one_norm(x, gr), c(14, 1, 15))
  expect_equal(
    grouped_two_norm(x, gr),
    c(two_norm(x[1:4]), two_norm(x[5:6]), two_norm(x[7:11]))
  )
  expect_equal(
    sp_group_norm(x, gr, asparse),
    asparse * one_norm(x) + (1 - asparse) * gr_two_norm(x, gr)
  )
  asparse <- .3
  expect_equal(
    sp_group_norm(x, gr, asparse),
    asparse * one_norm(x) + (1 - asparse) * gr_two_norm(x, gr)
  )
  expect_error(sp_group_norm(x, 1, 0.05))
  expect_error(sp_group_norm(x, gr, 3))
  expect_error(sp_group_norm(x, gr, -1))
})