{
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   "cell_type": "code",
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   "metadata": {
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   "source": [
    "{-# LANGUAGE ScopedTypeVariables, TypeOperators #-}\n",
    "import Data.Manifold\n",
    "import Data.Manifold.TreeCover\n",
    "import Data.Manifold.Web\n",
    "import Data.Manifold.Shade\n",
    "import Data.Manifold.Types\n",
    "import Data.Function.Affine\n",
    "import Math.LinearMap.Category\n",
    "import Math.LinearMap.Category.Derivatives\n",
    "import Data.VectorSpace\n",
    "import Linear (V2(..), _x, _y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test x = x`seq`putStrLn \"Ok\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ok"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Ok"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import Graphics.Dynamic.Plot.R2\n",
    "import Data.Colour.Names\n",
    "import Data.Colour.Manifold\n",
    "\n",
    "colourscheme :: Shade' ℝ -> Shade (Colour ℝ)\n",
    "colourscheme = f `seq` \\(Shade' y e) -> f (Shade y $ dualNorm e)\n",
    " where Just (f :: Shade ℝ -> Shade (Colour ℝ))\n",
    "          = rangeWithinVertices (1, maxc)\n",
    "                              [ (0, black) ]\n",
    "       Just maxc = toInterior (grey :: Colour ℝ)\n",
    "test colourscheme\n",
    "\n",
    "colourscheme_nabla :: Shade' (V2 ℝ+>ℝ) -> Shade (Colour ℝ)\n",
    "colourscheme_nabla = f `seq` \\(Shade' y e) -> f (Shade y $ dualNorm e)\n",
    " where Just (f :: Shade (V2 ℝ+>ℝ) -> Shade (Colour ℝ))\n",
    "          = rangeWithinVertices (zeroV, neutral)\n",
    "                              [ (V2 2 0-+|>1, red)\n",
    "                              , (V2 0 2-+|>1, green) ]\n",
    "       Just neutral = toInterior (grey :: Colour ℝ)\n",
    "test colourscheme_nabla"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gaußianPeak :: [ℝ²] -> ℝ -> PointsWeb ℝ² (Shade' ℝ)\n",
    "gaußianPeak ps δy = fromWebNodes euclideanMetric\n",
    "       [ (xy, exp (-2*magnitudeSq xy) |±|[δy]) | xy <- ps ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GraphWindowSpecR2{lBound=-2.666666666666667, rBound=2.666666666666666, bBound=-1.4999999999999998, tBound=2.4999999999999987, xResolution=640, yResolution=480}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "GraphWindowSpecR2{lBound=-2.666666666666666, rBound=2.6666666666666656, bBound=-1.4999999999999998, tBound=2.499999999999999, xResolution=640, yResolution=480}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "GraphWindowSpecR2{lBound=-2.666666666666666, rBound=2.6666666666666656, bBound=-1.4999999999999993, tBound=2.4999999999999987, xResolution=640, yResolution=480}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "GraphWindowSpecR2{lBound=-2.666666666666666, rBound=2.666666666666665, bBound=-1.4999999999999996, tBound=2.499999999999999, xResolution=640, yResolution=480}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "δ = 0.01\n",
    "grid = [V2 x y | x<-[-2,-1.8..2], y<-[-1,-0.8..2]]\n",
    "\n",
    "plotWindow [plot . fmap colourscheme $ gaußianPeak grid δ ]\n",
    "plotWindow [plot . fmap colourscheme_nabla . differentiateUncertainWebFunction\n",
    "              $ gaußianPeak grid δ ]\n",
    "plotWindow [plot . fmap (colourscheme_nabla . projectShade (lensEmbedding (1*∂id/∂_x)))\n",
    "   . differentiateUncertainWebFunction . differentiateUncertainWebFunction\n",
    "       $ gaußianPeak grid δ ]\n",
    "plotWindow [plot . fmap (colourscheme_nabla . projectShade (lensEmbedding ((1*∂id/∂_x)/∂id)))\n",
    "   . differentiateUncertainWebFunction . differentiateUncertainWebFunction\n",
    "       $ gaußianPeak grid δ ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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