From 281a7701b5eac489e95bcbc98072dbe6cf0b69c1 Mon Sep 17 00:00:00 2001
From: stla <laurent_step@yahoo.fr>
Date: Thu, 9 Nov 2023 10:19:57 +0100
Subject: [PATCH] nome

---
 NAMESPACE                  |  1 +
 R/nome.R                   | 20 ++++++++++++++++++++
 man/nome.Rd                | 20 ++++++++++++++++++++
 tests/testthat/test-nome.R |  5 +++++
 4 files changed, 46 insertions(+)
 create mode 100644 R/nome.R
 create mode 100644 man/nome.Rd
 create mode 100644 tests/testthat/test-nome.R

diff --git a/NAMESPACE b/NAMESPACE
index d86569c..6cdabec 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -30,6 +30,7 @@ export(ljtheta1)
 export(ljtheta2)
 export(ljtheta3)
 export(ljtheta4)
+export(nome)
 export(sl)
 export(slh)
 export(sm)
diff --git a/R/nome.R b/R/nome.R
new file mode 100644
index 0000000..7e3a5a6
--- /dev/null
+++ b/R/nome.R
@@ -0,0 +1,20 @@
+#' @title Nome
+#' @description The nome in function of the parameter \eqn{m}.
+#'
+#' @param m the parameter, square of elliptic modulus
+#'
+#' @return A complex number.
+#' @export
+#' @importFrom Carlson elliptic_F
+#'
+#' @examples
+#' nome(-2)
+nome <- function(m) {
+  if(m == 0) {
+    return(as.complex(0))
+  }
+  if(m == 1) {
+    return(as.complex(1))
+  }
+  exp(-pi * elliptic_F(pi/2, 1-m) / elliptic_F(pi/2, m))
+}
\ No newline at end of file
diff --git a/man/nome.Rd b/man/nome.Rd
new file mode 100644
index 0000000..ec37df8
--- /dev/null
+++ b/man/nome.Rd
@@ -0,0 +1,20 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/nome.R
+\name{nome}
+\alias{nome}
+\title{Nome}
+\usage{
+nome(m)
+}
+\arguments{
+\item{m}{the parameter, square of elliptic modulus}
+}
+\value{
+A complex number.
+}
+\description{
+The nome in function of the parameter \eqn{m}.
+}
+\examples{
+nome(-2)
+}
diff --git a/tests/testthat/test-nome.R b/tests/testthat/test-nome.R
new file mode 100644
index 0000000..bec2b25
--- /dev/null
+++ b/tests/testthat/test-nome.R
@@ -0,0 +1,5 @@
+test_that("Some value of the nome", {
+  expect_equal(nome(-2), as.complex(-0.06823783), tolerance = 1e-6)
+  expect_equal(nome(0.5), as.complex(exp(-pi)))
+  expect_equal(nome(5/16), as.complex(0.02340125), tolerance = 1e-6)
+})
\ No newline at end of file