# -*- tcl -*-
# eliptic.test --
# Test cases for the ::math::special package (Elliptic integrals)
#
# This file contains a collection of tests for one or more of the Tcllib
# procedures. Sourcing this file into Tcl runs the tests and
# generates output for errors. No output means no errors were found.
#
# Copyright (c) 2004 by Arjen Markus. All rights reserved.
#
# RCS: @(#) $Id: elliptic.test,v 1.12 2007/08/21 17:33:00 andreas_kupries Exp $
# -------------------------------------------------------------------------
source [file join \
[file dirname [file dirname [file join [pwd] [info script]]]] \
devtools testutilities.tcl]
testsNeedTcl 8.5;# statistics,linalg!
testsNeedTcltest 2.1
support {
useLocal math.tcl math
useLocal constants.tcl math::constants
useLocal linalg.tcl math::linearalgebra ;# for statistics
useLocal statistics.tcl math::statistics
useLocal polynomials.tcl math::polynomials
}
testing {
useLocal special.tcl math::special
}
# -------------------------------------------------------------------------
# As the values were given with four digits, an absolute
# error is most appropriate
proc matchNumbers {expected actual} {
set match 1
foreach a $actual e $expected {
#puts "abs($a-$e) = [expr {abs($a-$e)}]"
if {abs($a-$e) > 0.1e-5} {
set match 0
break
}
}
return $match
}
::tcltest::customMatch numbers matchNumbers
# -------------------------------------------------------------------------
test "Elliptic-1.0" "Complete elliptic integral of the first kind" \
-match numbers -body {
set result {}
foreach k2 {0.0 0.1 0.2 0.4 0.5 0.7 0.8 0.95} {
set k [expr {sqrt($k2)}]
lappend result [::math::special::elliptic_K $k]
}
set result
} -result {1.570796 1.612441 1.659624 1.777519 1.854075
2.075363 2.257205 2.908337}
test "Elliptic-2.0" "Complete elliptic integral of the second kind" \
-match numbers -body {
set result {}
foreach k2 {0.0 0.1 0.2 0.4 0.5 0.7 0.8 0.95} {
set k [expr {sqrt($k2)}]
lappend result [::math::special::elliptic_E $k]
}
set result
} -result {1.570796 1.530758 1.489035 1.399392 1.350644
1.241671 1.17849 1.060474}
# Jacobi elliptic functions: cn, sn and dn
set um_pairs {
0 0
0 0.1
0 0.8
0.1 0.1
0.1 0.2
0.1 0.5
0.1 0.7
0.1 0.8
0.2 0.01
0.2 0.1
0.2 0.5
0.3 0.01
0.3 0.1
0.3 0.5
0.4 0.01
0.5 0.01
0.5 0.1
0.6 0.1
0.7 0.1
0.8 0.1
0.8 0.5
0.9 0.01
0.9 0.1
0.9 0.5
0.99 0.5
}
test "Elliptic-3.1" "Jacobi elliptic cn function" \
-match numbers -body {
set result {}
foreach {u m} $um_pairs {
set k [expr {sqrt($m)}]
lappend result [::math::special::cn $u $k]
}
set result
} -result {1.000000 1.000000 1.000000 0.995006 0.995007 0.995012 0.995016 0.995017 0.980069 0.980093 0.980198 0.955350 0.955467
0.955986 0.921101 0.877678 0.878530 0.827220 0.768165 0.702062 0.722917 0.622418 0.629653 0.660895 0.602576}
test "Elliptic-3.2" "Jacobi elliptic sn function" \
-match numbers -body {
set result {}
foreach {u m} $um_pairs {
set k [expr {sqrt($m)}]
lappend result [::math::special::sn $u $k]
}
set result
} -result {0.000000 0.000000 0.000000 0.0998169 0.0998003 0.0997507 0.0997176 0.0997011 0.198656 0.198540 0.198022 0.295478 0.295098
0.293413 0.389323 0.479252 0.477687 0.561878 0.640252 0.712115 0.690935 0.782685 0.776876 0.750478 0.798062}
test "Elliptic-3.3" "Jacobi elliptic dn function" \
-match numbers -body {
set result {}
foreach {u m} $um_pairs {
set k [expr {sqrt($m)}]
lappend result [::math::special::dn $u $k]
}
set result
} -result {1.000000 1.000000 1.000000 0.999502 0.999003 0.997509 0.996514 0.996016 0.999803 0.998027 0.990148 0.999563 0.995636
0.978241 0.999242 0.998851 0.988525 0.984088 0.979289 0.974315 0.872528 0.996932 0.969354 0.847580 0.825560}
# End of test cases
testsuiteCleanup
