vizIR.ipynb

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      "text/plain": [
       "Stochaskell, version 0.1.0\n",
       "Copyright (C) 2015-2020 David A Roberts\n",
       "This program comes with ABSOLUTELY NO WARRANTY.\n",
       "This is free software, and you are welcome to redistribute it\n",
       "under certain conditions; see the LICENSE for details.\n",
       "\n",
       "Using installation directory at \n",
       "  /home/jovyan/stochaskell"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "{-# LANGUAGE FlexibleContexts, MonadComprehensions, NoImplicitPrelude, RebindableSyntax, TypeFamilies #-}\n",
    "import Language.Stochaskell\n",
    "stochaskell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import IHaskell.Display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "let v_0_0 = sin a :: R\n",
       "    v_0_1 = 4.2 + v_0_0 :: R\n",
       " in v_0_1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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   ],
   "source": [
    "let z = 4.2 + sin (symbol \"a\")\n",
    "print z\n",
    "svg <$> vizIR (return z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Language.Graphviz"
   ]
  },
  {
   "cell_type": "code",
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   },
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       "/*\n",
       "let v_0_0 = \n",
       "      [ let v_1_0 = 2 * i_1_1 :: Z\n",
       "            v_1_1 = 1 + v_1_0 :: Z\n",
       "         in v_1_1\n",
       "      | i_1_1 <- 1...n ] :: ZVec\n",
       "    v_0_1 = \n",
       "      [ let v_1_0 = i_1_1 - i_1_2 :: Z\n",
       "            v_1_1 = v_1_0 * v_1_0 :: Z\n",
       "         in v_1_1\n",
       "      | i_1_1 <- 1...n, i_1_2 <- 1...k ] :: ZMat\n",
       "    v_0_2 = getExternal x_ns_0_0 :: Array 1...n R\n",
       " in do x_ns_0_0 <- \n",
       "         [ normal i_1_1 1.0 :: P R\n",
       "         | i_1_1 <- 1...n ] :: Array 1...n R\n",
       "       return [v_0_0,v_0_1,x_ns_0_0]\n",
       "*/\n",
       "\n",
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       "    \n",
       "    \n",
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     "metadata": {},
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   ],
   "source": [
    "p :: P (ZVec,ZMat,RMat)\n",
    "p = do\n",
    "  let n = symbol \"n\"\n",
    "      k = symbol \"k\"\n",
    "      v = vector [ 2*i + 1 | i <- 1...n ]\n",
    "      m = matrix [ (i-j)^2 | i <- 1...n, j <- 1...k ]\n",
    "  z <- joint matrix [ normal (cast i) 1 | i <- 1...n ]\n",
    "  return (v,m,z)\n",
    "putStrLn $ graphviz p\n",
    "svg <$> vizIR p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior :: P (Z,RVec,RVec)\n",
    "prior = do\n",
    "  n <- poisson 5\n",
    "  let base = uniform 0 5\n",
    "  x <- orderedSample n base\n",
    "  let mu = vector [ 0 | i <- 1...n ]\n",
    "      kernel a b = exp (-(a - b)^2 / 2) + if a == b then 1e-6 else 0\n",
    "      cov = matrix [ kernel (x!i) (x!j) | i <- 1...n, j <- 1...n ]\n",
    "  y <- normal mu cov\n",
    "  return (n,x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "let posterior = [ y | (n,x,y) <- prior, n == 5, x == list [0.5,1.5,2.5,3.5,4.5] ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "/*\n",
       "let v_0_0 = getExternal x_ns_0_0 :: Z\n",
       "    v_0_1 = \n",
       "      [ 0.0\n",
       "      | i_1_1 <- 1...x_ns_0_0 ] :: RVec\n",
       "    v_0_2 = getExternal x_ns_0_1 :: Array 1...x_ns_0_0 R\n",
       "    v_0_3 = \n",
       "      [ let v_1_0 = id x_ns_0_1!i_1_1 :: R\n",
       "            v_1_1 = id x_ns_0_1!i_1_2 :: R\n",
       "            v_1_2 = v_1_0 - v_1_1 :: R\n",
       "            v_1_3 = v_1_2 * v_1_2 :: R\n",
       "            v_1_4 = v_1_3 / 2.0 :: R\n",
       "            v_1_5 = negate v_1_4 :: R\n",
       "            v_1_6 = exp v_1_5 :: R\n",
       "            v_1_7 = v_1_0 == v_1_1 :: B\n",
       "            v_1_8 = ifThenElse v_1_7 1.0e-6 0.0 :: R\n",
       "            v_1_9 = v_1_6 + v_1_8 :: R\n",
       "         in v_1_9\n",
       "      | i_1_1 <- 1...x_ns_0_0, i_1_2 <- 1...x_ns_0_0 ] :: RMat\n",
       "    v_0_4 = getExternal x_ns_0_2 :: RVec\n",
       " in do x_ns_0_0 <- poisson 5.0 :: P Z\n",
       "       x_ns_0_1 <- orderedSample (uniform 0.0 5.0 :: P R) x_ns_0_0 :: P Array 1...x_ns_0_0 R\n",
       "       x_ns_0_2 <- multi_normal v_0_1 v_0_3 :: P RVec\n",
       "       return [x_ns_0_2]\n",
       "*/\n",
       "\n",
       "digraph {\n",
       "  compound=\"true\"\n",
       "  \n",
       "  \n",
       "  subgraph cluster_array__v_0_1 {\n",
       "    label=\"array\"\n",
       "    _v_0_1_i_1_1 [shape=\"record\" label=\"index 1|1|<f2>\"]\n",
       "    \n",
       "    \n",
       "    _v_0_1 [label=\"0\" style=\"bold\"]\n",
       "  }\n",
       "  \n",
       "  \n",
       "  \n",
       "  subgraph cluster_array__v_0_3 {\n",
       "    label=\"array\"\n",
       "    _v_0_3_i_1_1 [shape=\"record\" label=\"index 1|1|<f2>\"]\n",
       "    _v_0_3_i_1_2 [shape=\"record\" label=\"index 2|1|<f2>\"]\n",
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       "    _v_0_3 [shape=\"record\" label=\"<f1>|+|<f2>\"]\n",
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