Nothing
p <- 4
f <- function(th) drop(-sin(th / 2) * sin(th)^(p - 2))
I <- integrate(f, lower = 0, upper = pi, rel.tol = 1e-12)$value
test_that("Gauss_Legen for N = 5, 10, 20, ..., 2560, 5120", {
expect_equal(sum(Gauss_Legen_weights(a = 0, b = pi, N = 5) *
f(Gauss_Legen_nodes(a = 0, b = pi, N = 5))), I,
tolerance = 1e-3)
expect_equal(sum(Gauss_Legen_weights(a = 0, b = pi, N = 10) *
f(Gauss_Legen_nodes(a = 0, b = pi, N = 10))), I,
tolerance = 1e-12)
for (N in c(10 * 2^(1:9))) {
expect_equal(sum(Gauss_Legen_weights(a = 0, b = pi, N = N) *
f(Gauss_Legen_nodes(a = 0, b = pi, N = N))), I,
tolerance = 3e-14)
}
})
test_that("Gauss_Legen edge cases", {
expect_error(Gauss_Legen_weights(a = 0, b = pi, N = 19))
expect_error(Gauss_Legen_nodes(a = 0, b = pi, N = 19))
})
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