context("Herz's relations")

test_that("Herz's relation for 1F1", {
  X <- toeplitz(c(3, 2, 1)) / 100
  o1 <- hypergeomPFQ(m = 15, a = 2, b = 3, x = X)
  o2 <- exp(sum(diag(X))) * hypergeomPFQ(m = 15, a = 3 - 2, b = 3, x = -X)
  expect_equal(o1, o2)
  #
  X <- toeplitz(c(3i, 2, 1)) / 100
  o1 <- hypergeomPFQ(m = 15, a = 2i, b = 3, x = X)
  o2 <- exp(sum(diag(X))) * hypergeomPFQ(m = 15, a = 3 - 2i, b = 3, x = -X)
  expect_equal(o1, o2)
})

test_that("Herz's relation for 2F1", {
  X <- toeplitz(c(3, 2, 1)) / 100
  o1 <- hypergeomPFQ(m = 15, a = c(1, 2i), b = 3, x = X)
  o2 <- det(diag(3) - X)^(-2i) *
    hypergeomPFQ(15, a = c(3 - 1, 2i), b = 3, -X %*% solve(diag(3) - X))
  expect_equal(o1, o2)
  #
  X <- toeplitz(c(3, 2, 1)) / 100
  o1 <- hypergeomPFQ(m = 15, a = c(1, 2), b = 3, x = X)
  o2 <- det(diag(3) - X)^(-2) *
    hypergeomPFQ(15, a = c(3 - 1, 2), b = 3, -X %*% solve(diag(3) - X))
  expect_equal(o1, o2)
  #
  X <- toeplitz(c(3i, 2, 1)) / 100
  o1 <- hypergeomPFQ(m = 15, a = c(1, 2i), b = 3, x = X)
  o2 <- EigenR::Eigen_det(diag(3) - X)^(-2i) *
    hypergeomPFQ(15, a = c(3 - 1, 2i), b = 3, -X %*% solve(diag(3) - X))
  expect_equal(o1, o2)
  #
  X <- toeplitz(c(3i, 2, 1)) / 100
  o1 <- hypergeomPFQ(m = 15, a = c(1, 2), b = 3, x = X)
  o2 <- EigenR::Eigen_det(diag(3) - X)^(-2) *
    hypergeomPFQ(15, a = c(3 - 1, 2), b = 3, -X %*% solve(diag(3) - X))
  expect_equal(o1, o2)
})