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if not modules then modules = { } end modules ['meta-imp-functions'] = {
version = 1.001,
comment = "companion to meta-imp-functions.mkxl",
author = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
copyright = "PRAGMA ADE / ConTeXt Development Team",
license = "see context related readme files",
}
local formatters = string.formatters
local sequenced = table.sequenced
local noffunctions = 0
local version = 1
local function preparecache(p)
noffunctions = noffunctions + 1
local action = p.action
p.action = nil
local hash = md5.HEX(sequenced(p))
local name = formatters["mkiv-%s-m-f-%03i.lua"](tex.jobname,noffunctions)
p.action = action
return name, hash
end
local function getcache(p)
local cache = p.cache
if cache then
local name, hash = preparecache(p)
local data = table.load(name)
if data and data.hash == hash and data.version == version and data.data then
return hash, name, data.data
else
return hash, name, false
end
else
return false, false, false
end
end
local function setcache(hash,name,data)
local result = {
version = version,
hash = hash,
data = data,
}
table.save(name,result)
end
local injectpath = mp.inject.path
local getparameterset = metapost.getparameterset
local report = logs.reporter("metapost","functions")
local functions = { }
local actions = { }
function mp.registerfunction(specification)
local name = specification.name
functions[name] = specification
end
function mp.registeraction(specification)
local name = specification.name
actions[name] = specification
end
metapost.registerscript("processfunction", function()
local specification = getparameterset("function")
local name = specification.name
local lua = specification.lua
local fnction = functions[name]
local action = lua and actions[lua]
if fnction then
if action then
specification.action = action.action
end
-- statistics.starttiming(functions)
fnction.action(specification)
-- statistics.stoptiming(functions)
end
end)
-- statistics.register("mp function time", function()
-- return statistics.elapsedseconds(functions,"including feedback to metapost")
-- end)
-- Here comes the fancy stuff:
local math = math
local sqrt = math.sqrt
local mathfunctions = math.functions or { }
math.functions = mathfunctions
-- Todo : reference where we got the factors from because those from
--
-- This is Runge-Kutta-Merson 4("5")
-- See Table 4.1. Merson 4("5") of Hairer, Nørsett, Wanner - Solving Ordinary Differential Equations I (Springer, 2008)
--
-- function mathfunctions.rungekutta(specification)
-- local f = specification.action or function(t,x,y) return x, y end
-- local x = specification.x or 0
-- local y = specification.y or 0
-- local t = 0
-- local tmax = specification.tmax or 1
-- local dt = specification.dt or tmax/10
-- local eps = specification.eps or dt/10
-- local r = 1
-- -- local result = { { x, y, x, y, x, y } }
-- local result = { { x, y } }
-- while t < tmax do
-- local k1x, k1y = f(t, x,
-- y)
-- k1x = dt * k1x
-- k1y = dt * k1y
-- local k2x, k2y = f(t + (1/3) * dt, x + (1/3) * k1x,
-- y + (1/3) * k1y)
-- k2x = dt * k2x
-- k2y = dt * k2y
-- local k3x, k3y = f(t + (1/3) * dt, x + (1/6) * k1x + (1/6) * k2x,
-- y + (1/6) * k1y + (1/6) * k2y)
-- k3x = dt * k3x
-- k3y = dt * k3y
-- local k4x, k4y = f(t + (1/2) * dt, x + (1/8) * k1x + (3/8) * k3x,
-- y + (1/8) * k1y + (3/8) * k3y)
-- k4x = dt * k4x
-- k4y = dt * k4y
-- local k5x, k5y = f(t + dt, x + (1/2) * k1x - (3/2) * k3x - (2) * k4x,
-- y + (1/2) * k1y - (3/2) * k3y - (2) * k4y)
-- k5x = dt * k5x
-- k5y = dt * k5y
-- --
-- local teps = sqrt(((1/10-1/6) * k1x + (3/10) * k3x + (2/5-2/3) * k4x + (1/5 -1/6) * k5x)^2 +
-- ((1/10-1/6) * k1y + (3/10) * k3y + (2/5-2/3) * k4y + (1/5 -1/6) * k5y)^2 )
-- if teps < eps then
-- dt = 0.9 * dt * (eps/teps)^(1/4)
-- x = x + (1/10) * k1x + (3/10) * k3x + (2/5) * k4x + (1/5) * k5x
-- y = y + (1/10) * k1y + (3/10) * k3y + (2/5) * k4y + (1/5) * k5y
-- r = r + 1
-- -- result[r] = { x, y, x, y, x, y }
-- result[r] = { x, y }
-- t = t + dt
-- else
-- dt = 0.9 * dt * (eps/teps)^(1/3)
-- end
-- end
-- return result
-- end
local function rungekutta(specification)
local f = specification.action or function(t,x,y) return x, y end
local x = specification.x or 0
local y = specification.y or 0
local tmin = specification.tmin or 0
local tmax = specification.tmax or 1
local t = tmin
local rmax = specification.maxpath or 0
local stepsize = specification.stepsize or "adaptive"
local dt = specification.dt or (tmax-tmin)/10
local eps = specification.eps or dt/10
local kind = specification.kind or specification.type -- xy x y
local adaptive = stepsize == "adaptive"
local r = 1
local result
if kind ~= "tx" and kind ~= "ty" then
kind = "xy"
end
if kind == "xy" then
-- result = { { x, y, x, y, x, y } }
result = { { x, y } }
elseif kind == "tx" then
-- result = { { x, x, t, x, t, x } }
result = { { t, x } }
else
-- result = { { x, y, t, y, t, y } }
result = { { t, y } }
end
local hash, name, data = getcache(specification)
if data then
-- print(hash,name,"REUSING")
return data
else
-- print(hash,name,"GENERATING")
end
if rmax == 0 then
rmax = 0xFFFF
end
while t < tmax do
local k1x, k1y = f(t, x,
y)
k1x = dt * k1x
k1y = dt * k1y
local k2x, k2y = f(t + (1/3) * dt, x + (1/3) * k1x,
y + (1/3) * k1y)
k2x = dt * k2x
k2y = dt * k2y
local k3x, k3y = f(t + (1/3) * dt, x + (1/6) * k1x + (1/6) * k2x,
y + (1/6) * k1y + (1/6) * k2y)
k3x = dt * k3x
k3y = dt * k3y
local k4x, k4y = f(t + (1/2) * dt, x + (1/8) * k1x + (3/8) * k3x,
y + (1/8) * k1y + (3/8) * k3y)
k4x = dt * k4x
k4y = dt * k4y
local k5x, k5y = f(t + dt, x + (1/2) * k1x - (3/2) * k3x - (2) * k4x,
y + (1/2) * k1y - (3/2) * k3y - (2) * k4y)
k5x = dt * k5x
k5y = dt * k5y
--
if adaptive then
local teps = sqrt(((1/10-1/6) * k1x + (3/10) * k3x + (2/5-2/3) * k4x + (1/5 -1/6) * k5x)^2 +
((1/10-1/6) * k1y + (3/10) * k3y + (2/5-2/3) * k4y + (1/5 -1/6) * k5y)^2 )
local step = eps/teps
if teps < eps then
step = step^(1/4)
dt = 0.9 * dt * step
else
step = step^(1/3)
dt = 0.9 * dt * step
goto again
end
end
::append::
t = t + dt
x = x + (1/10) * k1x + (3/10) * k3x + (2/5) * k4x + (1/5) * k5x
y = y + (1/10) * k1y + (3/10) * k3y + (2/5) * k4y + (1/5) * k5y
r = r + 1
if kind == "xy" then
result[r] = { x, y }
elseif kind == "tx" then
result[r] = { t, x }
else
result[r] = { t, y }
end
if r >= rmax then
-- report("pathmax is set to %i, quiting",rmax)
break
end
::again::
end
if name and hash then
setcache(hash,name,result)
end
return result
end
mathfunctions.rungekutta = rungekutta
mp.registerfunction {
name = "rungekutta",
action = function(specification)
local result = rungekutta(specification)
if result then
injectpath(result)
else
injectpath { { 0, 0 } }
end
end
}
|
