From ae37cc25c3bc517e52705135278a8955ed467e53 Mon Sep 17 00:00:00 2001
From: Avraham Adler <avraham.adler@gmail.com>
Date: Wed, 30 Aug 2023 10:34:26 -0400
Subject: [PATCH] Write documentation and unit tests, and update other
 documentation to reference minimaxErr. Also remove Pade mention.

---
 inst/tinytest/test_MiniMaxApprox.R | 28 ++++++++++++++--------
 man/MiniMaxApprox.Rd               |  6 +----
 man/minimaxErr.Rd                  | 38 ++++++++++++++++++++++++++++++
 man/minimaxEval.Rd                 |  4 ++--
 4 files changed, 59 insertions(+), 17 deletions(-)
 create mode 100644 man/minimaxErr.Rd

diff --git a/inst/tinytest/test_MiniMaxApprox.R b/inst/tinytest/test_MiniMaxApprox.R
index 532605d..45dbc83 100644
--- a/inst/tinytest/test_MiniMaxApprox.R
+++ b/inst/tinytest/test_MiniMaxApprox.R
@@ -144,16 +144,6 @@ expect_error(minimaxApprox(fn, -1, 1, c(3L, 3L), xi = xi), errMess)
 expect_error(minimaxApprox(sin,  0.75 * pi, 1.25 * pi, c(2L, 3L)),
              "The 3 degree polynomial in the denominator has a zero at 2.80961")
 
-# Test evaluation function
-x <- seq(0.1, 0.4, 0.025)
-mmA <- minimaxApprox(exp, 0, 0.5, 5L)
-expect_true(all(exp(x) - minimaxEval(x, mmA) <= mmA$EE))
-mmA <- minimaxApprox(exp, 0, 0.5, c(2L, 3L))
-expect_true(all(exp(x) - minimaxEval(x, mmA) <= mmA$EE))
-## Check error trap
-errMess <- "This function only works with 'minimaxApprox' objects."
-expect_error(minimaxEval(x, sin), errMess)
-
 # Test HW Borchers request of returning n degree if n fails but n + 1 works with
 # uppermost effectively 0 with Runge function between -1 and 1 and degree 10.
 ## Test successful restart
@@ -213,3 +203,21 @@ if (Sys.info()["nodename"] == "HOME") {
 
 # This should test RATIONAL failover to QR
 expect_error(minimaxApprox(sin, 0, pi / 2, c(13L, 0L)))
+
+# Test evaluation function
+x <- seq(0.1, 0.4, 0.025)
+mmA <- minimaxApprox(exp, 0, 0.5, 5L)
+expect_true(all(exp(x) - minimaxEval(x, mmA) <= mmA$EE))
+mmA <- minimaxApprox(exp, 0, 0.5, c(2L, 3L))
+expect_true(all(exp(x) - minimaxEval(x, mmA) <= mmA$EE))
+## Check error trap
+errMess <- "This function only works with 'minimaxApprox' objects."
+expect_error(minimaxEval(x, sin), errMess)
+
+# Test error function
+x <- seq(0.1, 0.4, 0.025)
+mmA <- minimaxApprox(exp, 0, 0.5, 5L)
+expect_identical(minimaxEval(x, mmA) - exp(x), minimaxErr(x, mmA))
+## Check error trap
+errMess <- "This function only works with 'minimaxApprox' objects."
+expect_error(minimaxErr(x, sin), errMess)
diff --git a/man/MiniMaxApprox.Rd b/man/MiniMaxApprox.Rd
index 42b9ae6..6246ce0 100644
--- a/man/MiniMaxApprox.Rd
+++ b/man/MiniMaxApprox.Rd
@@ -186,11 +186,7 @@ using barycentric representations instead of monomials.
 }
 }
 
-\seealso{
-\code{\link{minimaxEval}} for a convenience function to calculate approximation
-values and \code{\link[Pade:Pade]{Pade}} for a function to calculate
-\enc{Padé}{Pade} coefficients given suitable Taylor series coefficients.
-}
+\seealso{\code{\link{minimaxEval}}, \code{\link{minimaxErr}}}
 
 \examples{
 minimaxApprox(exp, 0, 1, 5)                              # Built-in & polynomial
diff --git a/man/minimaxErr.Rd b/man/minimaxErr.Rd
new file mode 100644
index 0000000..06deb22
--- /dev/null
+++ b/man/minimaxErr.Rd
@@ -0,0 +1,38 @@
+\name{minimaxErr}
+\alias{minimaxErr}
+\title{
+Evaluate the Minimax Approximation Error
+}
+\description{
+Evaluates the difference between the function and the minimax approximation at
+\code{x}.
+}
+\usage{
+minimaxErr(x, mmA)
+}
+\arguments{
+  \item{x}{a numeric vector}
+  \item{mmA}{a \code{"minimaxApprox"} return object}
+}
+\details{
+This is a convenience function to evaluate the approximation error at \code{x}.
+}
+\value{
+A vector of the same length as \code{x} containing the approximation error
+values.
+}
+\author{Avraham Adler \email{Avraham.Adler@gmail.com}}
+\seealso{\code{\link{minimaxApprox}}, \code{\link{minimaxEval}}}
+\examples{
+# Show results
+x <- seq(0, 0.5, length.out = 11L)
+mmA <- minimaxApprox(exp, 0, 0.5, 5L)
+err <- minimaxEval(x, mmA) - exp(x)
+all.equal(err,  minimaxErr(x, mmA))
+
+# Plot results
+x <- seq(0, 0.5, length.out = 1001L)
+plot(x, minimaxErr(x, mmA), type = "l")
+}
+
+\keyword{NumericalMathematics}
diff --git a/man/minimaxEval.Rd b/man/minimaxEval.Rd
index c1e658b..da5c7e4 100644
--- a/man/minimaxEval.Rd
+++ b/man/minimaxEval.Rd
@@ -24,13 +24,13 @@ This is a convenience function to evaluate the approximation at \code{x}.
 A vector of the same length as \code{x} containing the approximated values.
 }
 \author{Avraham Adler \email{Avraham.Adler@gmail.com}}
-\seealso{\code{\link{minimaxApprox}}}
+\seealso{\code{\link{minimaxApprox}}, \code{\link{minimaxErr}}}
 \examples{
 # Show results
 x <- seq(0, 0.5, length.out = 11L)
 mmA <- minimaxApprox(exp, 0, 0.5, 5L)
 apErr <- abs(exp(x) - minimaxEval(x, mmA))
-all.equal(max(apErr),  mmA$EE)
+all.equal(max(apErr), mmA$EE)
 
 # Plot results
 curve(exp, 0.0, 0.5)