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@leftaroundabout
Created September 16, 2017 17:36
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{
"cells": [
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"{-# LANGUAGE TypeFamilies #-}\n",
"import Graphics.Rendering.Chart.Easy\n",
"import Data.Default.Class\n",
"import Control.Lens\n",
"import Control.Monad\n",
"import Control.Arrow\n",
"import Data.VectorSpace"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"type ℝ = Double\n",
"type Time = Double\n",
"\n",
"s :: Time -> ℝ\n",
"s t = fromIntegral (round t) - t"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"signalPlot :: String -> [(Time,ℝ)] -> EC (Layout ℝ ℝ) ()\n",
"signalPlot capt sig = do\n",
" layout_x_axis . laxis_title .= \"t\"\n",
" plot (line capt [takeWhile ((<3).fst) sig])"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"toRenderable $ signalPlot \"s(t)\" [(t,s t) | t <- [0,0.01..]]"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"rk₄ :: (VectorSpace y, Scalar y ~ ℝ)\n",
" => (Time -> y -> y) -- the function r_t(t,r)\n",
" -> Time -- time-step for the solver\n",
" -> [(Time, y)] -- sequence of solution snapshots [r(t)]\n",
"rk₄ f h = go 0 zeroV\n",
" where go t y = (t,y) : go (t+h) (y ^+^ (h/6)*^(k₁ ^+^ 2*^k₂ ^+^ 2*^k₃ ^+^ k₄))\n",
" where k₁ = f t y\n",
" k₂ = f (t + h/2) (y ^+^ (h/2)*^k₁)\n",
" k₃ = f (t + h/2) (y ^+^ (h/2)*^k₂)\n",
" k₄ = f (t + h) (y ^+^ h*^k₃)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"toRenderable $ forM [0 .. 8] $ \\η -> signalPlot (\"η = \"++show η)\n",
" $ rk₄ (\\t r -> η * (s t - r)) 0.01"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"toRenderable $ forM [0, 5 .. 30] $ \\η -> signalPlot (\"η = \"++show η) $ second fst\n",
" <$> rk₄ (\\t (r,u) -> (u, η^2 * (s t - r) - η*u)) 0.005"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Haskell",
"language": "haskell",
"name": "haskell"
},
"language_info": {
"codemirror_mode": "ihaskell",
"file_extension": ".hs",
"name": "haskell",
"version": "7.10.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@leftaroundabout
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