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#!/usr/bin/lua
-- ----------------------------------------------------------------- --
--      This Lua5 script is Copyright (c) 2010, Peter J Billam       --
--                        www.pjb.com.au                             --
--                                                                   --
--   This script is free software; you can redistribute it and/or    --
--          modify it under the same terms as Lua5 itself.           --
-- ----------------------------------------------------------------- --
local Version = '1.0  for Lua5'
local VersionDate  = '31jul2010';
local Synopsis = [[
program_name [options] [filenames]
]]

local RK = require 'RungeKutta'
--------------------------- infrastructure -----------------------
local eps = .000000001
function equal(x, y)  -- unused here
    if #x ~= #y then return false end
    local i; for i in pairs(x) do
        if math.abs(x[i]-y[i]) > eps then return false end
    end
    return true
end
-- use Test::Simple tests => 6;
local Test = 12 ; local i_test = 0; local Failed = 0;
function ok(b,s)
    i_test = i_test + 1
    if b then
        io.write('ok '..i_test..' - '..s.."\n")
    else
        io.write('not ok '..i_test..' - '..s.."\n")
        Failed = Failed + 1
    end
end
------------------------------------------------------------------

local func_evals = 0
local i_test     = 0
local n_failed   = 0
local n_passed   = 0
function dydt(t, y)
	local dydt_f = {}
	dydt_f[1] = y[2]
	dydt_f[2] = 0.0 - y[1]
	func_evals = func_evals + 1
	return dydt_f
end
function dydt_hash(t, ya)
	local i
	local dydt_f = {}
	dydt_f["x"] = 0.0 + ya["y"]
	dydt_f["y"] = 0.0 - ya["x"]
	func_evals = func_evals + 1
	return dydt_f
end

twopi = 2.0 * 3.141592653589
algorithms = {RK.rk2, RK.rk4, RK.rk4_classical, RK.rk4_ralston, epsilon, errors}
algnames = {'rk2', 'rk4', 'rk4_classical', 'rk4_ralston'}
passmark0 = { 0.2,   .0004,  .0015,               .0015, .0001, .0003 }
passmark1 = { 0.04,  .00004, .0006,               .0006, .00001, .00001 }
for i=1,4 do
	algorithm = algorithms[i]
	i_test = i_test + 1
	n = 16
	dt= twopi / n

	y = {0,1}; t=0
	for j=1, n do t, y = algorithm(y, dydt, t, dt) end
	local err0 = math.abs(y[1]);
	local err1 = math.abs(y[2]-1.0)
	ok(err0 < passmark0[i] and err1 < passmark1[i], algnames[i]..' with array')

	y = {x=0, y=1}; t=0