JAX_get_started.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jecampagne/JaxTutos/blob/main/JAX_get_started.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "9s94ihDqcbpb",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import jax\n",
    "\n",
    "import jax.numpy as jnp                       #<----------\n",
    "import numpy as np                            #<----------\n",
    "\n",
    "from jax import grad, jit, vmap\n",
    "from jax import jacfwd, jacrev, hessian\n",
    "jax.config.update(\"jax_enable_x64\", True)\n",
    "\n",
    "from functools import partial\n",
    "\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('image', cmap='jet')\n",
    "mpl.rcParams['font.size'] = 18\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 36
    },
    "id": "TpvHrbzChe-s",
    "outputId": "d9919b83-6dba-4e1d-a51c-5742428c79a4",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.4.33'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.__version__  #<=0.4.26 ok"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "I17OGlHd4c1M",
    "outputId": "7f8976ff-0232-4380-c14a-47de1a8c0099"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[CpuDevice(id=0)]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.devices()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FjflbNJMctqZ"
   },
   "source": [
    "# Theme: get some first flavour of JAX\n",
    "\n",
    "One remark concerns the import: there is 2 ways of naming that you can see in libs:\n",
    "\n",
    "-    either (numpy -> np, jax.numpy -> jnp)\n",
    "-    or (numpy -> onp, jax.numpy -> np)\n",
    "\n",
    "So, when you edit or C&P a JAX code have a look at import to figure out which convention has been adopted by the author(s).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rMnBMT8QXsc8"
   },
   "source": [
    "# JAX Numpy very close to Numpy\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BT1_F0h2Wyea",
    "outputId": "2326ded6-c9c7-49a3-db17-6cfbfa03c7cd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(0.,10.,1)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "A-Gm_bq4W9Ed",
    "outputId": "14927187-cf78-447e-9cf3-3fdd85074c70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.], dtype=float64),\n",
       " jaxlib.xla_extension.ArrayImpl)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Numpy Array -> JAX\n",
    "jx = jnp.array(x)\n",
    "jx, type(jx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "V1vbPBzkXHVV",
    "outputId": "41572fde-e446-49ad-d777-49a794a8a12b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.]), numpy.ndarray)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# JAX Array -> Numpy\n",
    "y = np.asarray(jx)\n",
    "y, type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 440
    },
    "id": "GJPzW9mVZa9h",
    "outputId": "7a2804e8-b4c7-473b-c39d-6f98772058c6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, jx); # no need to convert"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zJhIcI98YL4D"
   },
   "source": [
    "## BUT DeviceArray are immutable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 314
    },
    "id": "aFZ40QZYXfdp",
    "outputId": "da305571-bd06-43ad-81b8-1d485aa993ed"
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'<class 'jaxlib.xla_extension.ArrayImpl'>' object does not support item assignment. JAX arrays are immutable. Instead of ``x[idx] = y``, use ``x = x.at[idx].set(y)`` or another .at[] method: https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.ndarray.at.html",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[8], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m jx \u001b[38;5;241m=\u001b[39m jnp\u001b[38;5;241m.\u001b[39marange(\u001b[38;5;241m0.\u001b[39m,\u001b[38;5;241m10.\u001b[39m,\u001b[38;5;241m1\u001b[39m) \u001b[38;5;66;03m# notice np->jnp\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mjx\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m\n",
      "File \u001b[0;32m/opt/miniconda3/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:587\u001b[0m, in \u001b[0;36m_unimplemented_setitem\u001b[0;34m(self, i, x)\u001b[0m\n\u001b[1;32m    582\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_unimplemented_setitem\u001b[39m(\u001b[38;5;28mself\u001b[39m, i, x):\n\u001b[1;32m    583\u001b[0m   msg \u001b[38;5;241m=\u001b[39m (\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m object does not support item assignment. JAX arrays are \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    584\u001b[0m          \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mimmutable. Instead of ``x[idx] = y``, use ``x = x.at[idx].set(y)`` \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    585\u001b[0m          \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mor another .at[] method: \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    586\u001b[0m          \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mhttps://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.ndarray.at.html\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m--> 587\u001b[0m   \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(msg\u001b[38;5;241m.\u001b[39mformat(\u001b[38;5;28mtype\u001b[39m(\u001b[38;5;28mself\u001b[39m)))\n",
      "\u001b[0;31mTypeError\u001b[0m: '<class 'jaxlib.xla_extension.ArrayImpl'>' object does not support item assignment. JAX arrays are immutable. Instead of ``x[idx] = y``, use ``x = x.at[idx].set(y)`` or another .at[] method: https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.ndarray.at.html"
     ]
    }
   ],
   "source": [
    "jx = jnp.arange(0.,10.,1) # notice np->jnp\n",
    "jx[2]=-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "5vLXj0E4XjA7"
   },
   "outputs": [],
   "source": [
    "jx = jx.at[2].set(-1) # other functions exist, slicing, add"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "M8uCdG_oaXeY"
   },
   "source": [
    "- We can use vectorization in one go (avoid loop even fori_loop see later): see following example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 432
    },
    "id": "jLpYFCdWaWNv",
    "outputId": "1ed13ca2-9d33-4b13-bdf8-68e56be858fa"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ldx = jnp.array([0,1,3]) # \"l\" line indexes\n",
    "cdx = jnp.array([1,3,2]) # \"c\" column indexes\n",
    "val = jnp.array([-1,1,2])# values V_{lc}\n",
    "mtx=jnp.zeros((4,4)).at[ldx,cdx].set(val)\n",
    "plt.matshow(mtx);plt.colorbar();\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 432
    },
    "id": "kmuYwoIdbRaU",
    "outputId": "8489c899-74b5-41fe-be58-ab1ebf1dcf66"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ldx = jnp.array([0,1,3,1])\n",
    "cdx = jnp.array([1,3,2,3])\n",
    "val = jnp.array([-1,1,2,-1])\n",
    "mtx=jnp.zeros((4,4)).at[ldx,cdx].add(val)   #<----- add all V_{lc} in the same (l,c)\n",
    "plt.matshow(mtx);plt.colorbar();\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Udjql7Iddob6"
   },
   "source": [
    "# Automatic differentiation and vectorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "-xwHYxF9cptd"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return jnp.exp(-x*0.5)*jnp.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "lo13524Cdwuh"
   },
   "outputs": [],
   "source": [
    "# Exact f'(x) et f''(x)\n",
    "def fp(x):\n",
    "    return jnp.exp(-x*0.5)*(2.*jnp.cos(x)-jnp.sin(x))/2.\n",
    "def fpp(x):\n",
    "    return -jnp.exp(-x*0.5)*(4.*jnp.cos(x)+3.*jnp.sin(x))/4.\n",
    "\n",
    "# Numerical differenciation via central finite differences  f'(x) et f''(x)\n",
    "def fpnum(x,h=0.1):\n",
    "    return (f(x+h)-f(x-h))/(2*h)\n",
    "def fppnum(x,h=0.1):\n",
    "    return (f(x+h)-2*f(x)+f(x-h))/h**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "wt4TW3x4eA-o"
   },
   "outputs": [],
   "source": [
    "# With JAX gradient (gard)\n",
    "jfp  = grad(f)            #f'\n",
    "jfpp = grad(grad(f))      #f''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EilSP8bFeSkE"
   },
   "source": [
    "Have a look at the code: take a paper and a pencil and check that this code is correct :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "4hhV_BotePKL",
    "outputId": "dac0d4f5-4cd2-4a38-a644-bc56e4a614c5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{ lambda ; a:f64[]. let\n",
       "    b:f64[] = neg a\n",
       "    c:f64[] = mul b 0.5\n",
       "    d:f64[] = exp c\n",
       "    e:f64[] = sin a\n",
       "    f:f64[] = mul d e\n",
       "  in (f,) }"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.make_jaxpr(f)(0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BimEsHwyeZVz",
    "outputId": "6b85180c-6a4a-47b3-e8ec-d2d00650380d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{ lambda ; a:f64[]. let\n",
       "    b:f64[] = neg a\n",
       "    c:f64[] = mul b 0.5\n",
       "    d:f64[] = exp c\n",
       "    e:f64[] = sin a\n",
       "    f:f64[] = cos a\n",
       "    _:f64[] = mul d e\n",
       "    g:f64[] = mul d 1.0\n",
       "    h:f64[] = mul 1.0 e\n",
       "    i:f64[] = mul g f\n",
       "    j:f64[] = mul h d\n",
       "    k:f64[] = mul j 0.5\n",
       "    l:f64[] = neg k\n",
       "    m:f64[] = add_any i l\n",
       "  in (m,) }"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.make_jaxpr(jfp)(0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FoQjtY6We976"
   },
   "source": [
    "vectorization `vmap` is for instance used when we call a function with an array. The result is not like numpy vectorize which is a for-loop.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "bjIUMYOHekcu"
   },
   "outputs": [],
   "source": [
    "jfp  = vmap(grad(f))\n",
    "jfpp = vmap(grad(grad(f)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "w477tQFVfPAh",
    "outputId": "8bf060eb-ebb5-479c-8926-b33936914101"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{ lambda ; a:f64[2]. let\n",
       "    b:f64[2] = neg a\n",
       "    c:f64[2] = mul b 0.5\n",
       "    d:f64[2] = exp c\n",
       "    e:f64[2] = sin a\n",
       "    f:f64[2] = cos a\n",
       "    _:f64[2] = mul d e\n",
       "    g:f64[2] = mul d 1.0\n",
       "    h:f64[2] = mul 1.0 e\n",
       "    i:f64[2] = mul g f\n",
       "    j:f64[2] = mul h d\n",
       "    k:f64[2] = mul j 0.5\n",
       "    l:f64[2] = neg k\n",
       "    m:f64[2] = add_any i l\n",
       "  in (m,) }"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.make_jaxpr(jfp)(jnp.array([0.,1.]))   # notice we create an DeviceArray (JAX) from a list as numpy does"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "iTk8KCYEf4oZ"
   },
   "outputs": [],
   "source": [
    "x=jnp.arange(0,10,0.1)   # as numpy equivalent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 660
    },
    "id": "HtVptzsJgKgo",
    "outputId": "1acb613c-6c63-463a-d4d7-e49825cc3337"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(1, figsize=(8,8))\n",
    "frame1=fig1.add_axes((.1,.30,.8,.5))\n",
    "\n",
    "plt.plot(x,f(x), label=\"$f(x)$\")\n",
    "#plt.scatter(x,fpnum(x), label=\"$f^{\\ \\prime}(x)$ (Num.)\")\n",
    "plt.plot(x,jfp(x), lw=3,label=\"$f^{\\ \\prime}(x)$ (JAX)\")\n",
    "plt.plot(x,fp(x),ls=\"--\",c='k', label=\"$f^{\\ \\prime}(x)$ (True)\")\n",
    "#plt.scatter(x,fppnum(x), label=\"$f^{\\ \\prime\\prime}(x)$ (Num.)\")\n",
    "plt.plot(x,jfpp(x), lw=3,label=\"$f^{\\ \\prime\\prime}(x)$ (JAX)\")\n",
    "plt.plot(x,fpp(x),ls=\"--\", c='purple',label=\"$f^{\\ \\prime\\prime}(x)$ (True)\")\n",
    "plt.grid()\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.legend(loc=\"upper right\");\n",
    "\n",
    "frame1.set_xticklabels([])\n",
    "#frame1.set_xticks([])\n",
    "\n",
    "frame2=fig1.add_axes((.1,.1,.8,.2))\n",
    "plt.plot(x,np.abs(fpnum(x)-fp(x)), c=\"r\", label=\"Num.-True\")\n",
    "plt.plot(x,np.abs(jfp(x)-fp(x)),lw=3,c=\"g\",  label=\"Jax-True\")\n",
    "plt.grid()\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$\\Delta f^{\\prime}(x)$\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend(loc=\"upper right\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "HVh4D4lUhphw",
    "outputId": "fd070893-98f5-4eda-b9a5-4af560f1c492"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(2.22044605e-16, dtype=float64)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=jnp.arange(0,10,0.1)\n",
    "jnp.max(jnp.abs(jfpp(x)-fpp(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eMxEhDI3hKPq"
   },
   "source": [
    "As you see JAX auto-diff precision is at machine precision and finite differences may be difficult to tune (ie. h parameter) to get the same level of accuracy.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1Wjeg-5IX7DI"
   },
   "source": [
    "## Take care: auto-diff means 'diff'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "Hh-Sa3xWYTll"
   },
   "outputs": [],
   "source": [
    "def count(r,X):\n",
    "  return jnp.count_nonzero(X/r<1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "itZ3JLdcYlFK"
   },
   "outputs": [],
   "source": [
    "X = jax.random.uniform(jax.random.PRNGKey(0),(10,),minval=0,maxval=2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "LohvCo9AYrCb",
    "outputId": "2d23c268-3907-4b94-d7da-30744e3eaf1f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(6, dtype=int64)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count(1.,X) # 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 333
    },
    "id": "mO_vpdROYx0S",
    "outputId": "1acdae4a-0e41-484e-ae1b-08db85696578"
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "grad requires real-valued outputs (output dtype that is a sub-dtype of np.floating), but got int64. For differentiation of functions with integer outputs, use jax.vjp directly.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[25], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mjax\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgrad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcount\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1.\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43mX\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;66;03m# 1st crash\u001b[39;00m\n",
      "    \u001b[0;31m[... skipping hidden 6 frame]\u001b[0m\n",
      "File \u001b[0;32m/opt/miniconda3/lib/python3.10/site-packages/jax/_src/api.py:767\u001b[0m, in \u001b[0;36m_check_output_dtype_revderiv\u001b[0;34m(name, holomorphic, x)\u001b[0m\n\u001b[1;32m    761\u001b[0m   \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mname\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m requires real-valued outputs (output dtype that is \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    762\u001b[0m                   \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124ma sub-dtype of np.floating), but got \u001b[39m\u001b[38;5;132;01m{\u001b[39;00maval\u001b[38;5;241m.\u001b[39mdtype\u001b[38;5;241m.\u001b[39mname\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    763\u001b[0m                   \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mFor holomorphic differentiation, pass holomorphic=True. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    764\u001b[0m                   \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mFor differentiation of non-holomorphic functions involving complex \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    765\u001b[0m                   \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124moutputs, use jax.vjp directly.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    766\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m dtypes\u001b[38;5;241m.\u001b[39missubdtype(aval\u001b[38;5;241m.\u001b[39mdtype, np\u001b[38;5;241m.\u001b[39mfloating):\n\u001b[0;32m--> 767\u001b[0m   \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mname\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m requires real-valued outputs (output dtype that is \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    768\u001b[0m                   \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124ma sub-dtype of np.floating), but got \u001b[39m\u001b[38;5;132;01m{\u001b[39;00maval\u001b[38;5;241m.\u001b[39mdtype\u001b[38;5;241m.\u001b[39mname\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    769\u001b[0m                   \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mFor differentiation of functions with integer outputs, use \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    770\u001b[0m                   \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mjax.vjp directly.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mTypeError\u001b[0m: grad requires real-valued outputs (output dtype that is a sub-dtype of np.floating), but got int64. For differentiation of functions with integer outputs, use jax.vjp directly."
     ]
    }
   ],
   "source": [
    "jax.grad(count)(1.,X) # 1st crash"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "bJchp_mVY_X3"
   },
   "outputs": [],
   "source": [
    "def count_modif1(r,X):\n",
    "  return jnp.count_nonzero(X/r<1.0)*1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BOB9fNpMZEhM",
    "outputId": "70877c52-3aa6-42a7-9936-7f216bc88a6c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0., dtype=float64, weak_type=True)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.grad(count_modif1)(1.,X) # no crash but silent problem if you ant a gradient descent optim!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 440
    },
    "id": "wQyskT26aZo7",
    "outputId": "23435fbe-2236-4414-8d48-c6140b2b180d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e2ZbySoNFG/abXY6Iz3I6INntdtauXcvcuXMZO3YsXbp0wWKxYLFYmD17dqP6KCwsZPbs2SQkJBAWFkZkZCQDBgxg0aJFlJWVOVvaZcnNzWXx4sVcd911dO/e3SPbFBG5lOmjq44ivfdlHntyz5lcjYhv8ne24bZt2xgzZozTG87Ozubmm28mKysLgJCQEEpLS8nIyCAjI4Nly5aRnp5OVFTUBW0Nw6C0tHEXMFqtVgICAi66zG63c9ddd1FaWsorr7zi9HcREXGl+E6R3NE/htU783h63de8ef91Zpck4nOadIotKiqK5ORkUlNTWb58OdHR0Y1qV1FRwe23305WVhYdO3YkLS2N4uJi7HY7K1asIDw8nB07djBp0qSLts/OziY4OLhRr2uuueaifZSVlTF27Fi++OILli1bRr9+/Zz+PYiIuNq0kb2w+VnYdPAUnxw8ZXY5Ij7H6SNIQ4YMueCur+nTpzeq7ZIlS9i9ezcAq1atYtCgQUDV0Z7x48fjcDiYOHEia9asIT09neTk5Drt27Zty+LFixu1rYsdgSovL+fuu+9mw4YNLF68mLFjxzaqLxERT7miTQj3XNeFNz7L4n/X7WN19xuxWi1mlyXiM5wOSH5+fk5vdMmSJQAMGzasJhzVNmHCBGbOnElmZiZLly69ICCFhYVx3333ObXtyspKJk6cyPvvv89LL71ESkqKU/2IiLjbIz+4kne2f8Oe3AI+2JXHD6/uZHZJIj7D43ex2e12Pv30UwBGjx590XUsFgujRo0CYMOGDS7btsPhICUlhXfeeYdnnnmGX/ziFy7rW0TE1dqEBfLg0G4ALNywn7IKh8kVifgOp48gOWvfvn04HFU7eXx8fIPrVS87duwY+fn5tG7dusnbTk1NZdmyZQwaNIi2bdvy1ltv1Vl+ww030K1btyZvR0TEVe4f0pWlW7LJyT/Psq3Z/GRwV7NLEvEJHg9I1XMOAXTq1PDh4trL8vLyXBKQtm/fDsDmzZvZvHnzBcsXL17cYEAqLS2tc+dcQUEBUHU9U3m56x4sWd2XK/sUz9IYer/mNIY2CzwyrBuzVu/j/6Uf5If9ogkP8vifbq/SnMZPnOPOMWxsnx7fywoLC2veh4SENLhe7WW12zTFRx995HTbefPmMWfOnAs+37BhwyW/h7PS0tJc3qd4lsbQ+zWXMQwzoH2QHyfs5Ux/40NuvUKn2hqjuYyfOM8dY2i3N26Gev1nSCPNmDGDqVOn1vxcUFBAbGwsI0eOJCIiwmXbKS8vJy0tjREjRmCz2VzWr3iOxtD7NccxDIg7zpQVO9l0wp/H7xlC+/BAs0tqtprj+MnlcecYVp8B+j4eD0jh4eE17y+V4movq93GLIGBgQQGXvgHyWazuWUHdFe/4jkaQ+/XnMbw1v6deP2zbHYcPcsLH2fy1F0JZpfU7DWn8RPnuGMMG9ufx+9ii4mJqXmfm5vb4Hq1l9VuIyLiiywWC9NHVT2C5O3Pczh8ssjkikRaNo8HpD59+mC1Vm12z549Da5XvSw6OtolF2iLiHi767q1Ibl3eyodBgvW6UG2Iu7k8YAUEhLC4MGDAVi3bt1F1zEMg/Xr1wMwcuRIj9UmItLc/XZUb6wWWPfVMb44esbsckRaLI8HJKBm9uqNGzeydevWC5avXLmSI0eOADB58mSP1iYi0pz1ig5n3DWdAfjfNV9jGIbJFYm0TE0KSGfOnOHUqVM1r+oJIO12e53Pi4rqnitPSUkhISEBwzAYN24c6enpQNVM1ytXruSBBx4Aqmbarv+YERERXzd1ZE8C/a1sy8pnw97jZpcj0iI1KSAlJibSrl27mldOTg4ACxYsqPP5lClT6rTz9/dn9erVxMXFkZuby/DhwwkNDSU0NJS7776bgoICEhMTWbZsWVPKExFpkTpGBvOzIVUzas9bs0+PIBFxA1NOsQHExcWxa9cuZs2aRXx8PBaLBZvNRlJSEgsXLmTLli1ERUWZVZ6ISLP20M1X0jYsgKzTdt7akm12OSItTpPmQcrKymrSxsPDw5kzZ85FZ6gWEZGGhQX6M3VEL37/7m6eTT/I2Gs60SokwOyyRFoM044giYhI09x9bWd6dgjj3Plynvv3IbPLEWlRFJBERLyUv5+Vmbf2BWDp5iyyThWbXJFIy6GAJCLixW7q2Y6hPdtRXmnw9LqvzS5HpMVQQBIR8XIzx/TBaoG1e46xLTPf7HJEWgQFJBERL9crOpzxA64A4Ml/7cXh0OSRIk2lgCQi0gJMHdGT0AA/dn5zjg925ZldjojXU0ASEWkB2oUH8sthVwLw9NqvKSmvNLkiEe+mgCQi0kLcf2NXYiKDyDtXwuufZJpdjohXU0ASEWkhgmx+pI7qBcCLGw9xsrDU5IpEvJcCkohIC/LD/p3o1zmS4rJKnvnwgNnliHgtBSQRkRbEarXwh+8mj1yx7SgHjheaXJGId1JAEhFpYQZ2bc2oq6JxGPDkv/aZXY6IV1JAEhFpgaaP7o3Nz8LHB07y0f4TZpcj4nUUkEREWqC4tqGkDIoD4E//3Et5pcPcgkS8jAKSiEgL9UhyD9qEBnD4ZDFLN2ebXY6IV1FAEhFpoSKDbaTeUnXb/18+PMDpIt32L9JYCkgiIi3Y/1wby1UxERSWVLAoTbf9izSWApKISAvmZ7Xw+O1XAbB821G+yjtnckUi3kEBSUSkhRvYtTW39euIYcCcD/ZiGIbZJYk0ewpIIiI+YMaYPgTZrGzLzGfN7mNmlyPS7CkgiYj4gE6tgvnFTd0BeGrNPkrKK02uSKR5U0ASEfERDw7tTkxkELlnz/PKf46YXY5Is6aAJCLiI4ID/Jgxpg8AL350iLyz502uSKT5UkASEfEht/XryIC4KErKHTy97muzyxFpthSQRER8iMVSddu/xQLvf5lHRla+2SWJNEsKSCIiPia+UyQTBsQCMPuDr3A4dNu/SH0KSCIiPug3I3sRHujPntwC3tn+jdnliDQ7CkgiIj6obVggjw7vAcD89V9TWFJuckUizYsCkoiIj5o8KI5u7UI5VVTGsx8eNLsckWZFAUlExEcF+FuZdVtfABZ/lsWB44UmVyTSfCggiYj4sJt7tWdk3w5UOgxmvb9Hz2kT+Y4CkoiIj/vjbX0J9Ley5Ug+H+z61uxyRJoFBSQRER8X2zqEh4ddCcCT/9pLUWmFyRWJmE8BSURE+PnQbnRpE8LxglKeS9cF2yIKSCIiQpDNj8dvr7pg+/VPMjmoC7bFxykgiYgIAD/o3YHhfdpT4TB4fPVXumBbfJoCkoiI1Jh121UE+Fv57PBp/rVbF2yL71JAEhGRGle0CeGhm7oDMPef+yjWBdvioxSQRESkjodu7k5s62COFZTw3L8PmV2OiCkUkEREpI4gmx+zbrsKgNc/OcLhk0UmVyTieQpIIiJygeF92jOsVzvKKw1m64Jt8UEKSCIicgGLxcLsO6ou2N508BTr9hwzuyQRj1JAEhGRi+rSJpRfDO0GwJ/+uRd7mS7YFt+hgCQiIg166OYr6dQqmLxzJTyvC7bFhyggiYhIg4ID/jvD9qubjmiGbfEZCkgiInJJI/pWzbBdXmkw8709umBbfIICkoiIXFL1BdvBNj+2Zeaz6otcs0sScTsFJBER+V6do0J4dHgPAJ5as48zxWUmVyTiXgpIIiLSKPff2JWeHcLILy7j6XVfm12OiFspIImISKPY/Kw8eVcCACs+zyEjK9/kikTcx2cD0tdff01gYCAWi4V169aZXY6IiFcYENea8dfGAjDz3T2UVzpMrkjEPXw2ID300EPYbDazyxAR8TrTR/cmKsTG/uOF/O2TTLPLEXELnwxIb775Jlu3bmXatGlmlyIi4nWiQgP4/Zg+APzlw4N8c8ZuckUirudzAens2bNMmzaN6dOnExcXZ3Y5IiJe6UdJnRnYtTXnyyuZvXqv2eWIuJzPBaTp06cTFhbGb3/7W7NLERHxWhaLhSfvjMffauHDfcfZ8JUeZisti1MByW63s3btWubOncvYsWPp0qULFoulajKx2bMb1UdhYSGzZ88mISGBsLAwIiMjGTBgAIsWLaKszD3za2zdupVXX32VZ599lqCgILdsQ0TEV/ToEM7Pv3uY7ezVX1FcqofZSsvh70yjbdu2MWbMGKc3mp2dzc0330xWVhYAISEhlJaWkpGRQUZGBsuWLSM9PZ2oqKgL2hqGQWlpaaO2Y7VaCQgIAKCyspKHHnqIMWPGcNtttzldu4iI/NcjP+jB6p15fHPmPM+mH6y5NknE2zl9ii0qKork5GRSU1NZvnw50dHRjWpXUVHB7bffTlZWFh07diQtLY3i4mLsdjsrVqwgPDycHTt2MGnSpIu2z87OJjg4uFGva665pqbd888/z759+3j22Wed/coiIlJPcIAfT/zwKgBe/ySTfd8WmFyRiGs4dQRpyJAh5OfXnSBs+vTpjWq7ZMkSdu/eDcCqVasYNGgQUHW0Z/z48TgcDiZOnMiaNWtIT08nOTm5Tvu2bduyePHiRm2r+gjUuXPn+OMf/8jkyZOxWq01R65OnToFwPHjx8nKyiI2NhY/P79G9S0iIlV+0LsDo66KZt1Xx/j9u7tZ9YsbsFotZpcl0iROBaSmhIglS5YAMGzYsJpwVNuECROYOXMmmZmZLF269IKAFBYWxn333XdZ2zxz5gyFhYW88sorvPLKKxcsr+4vJyeHzp07X1bfIiICj9/Rl08OnWLH0bO8tTWbyYPizC5JpEmcCkjOstvtfPrppwCMHj36outYLBZGjRrFSy+9xIYNG1yy3fbt2/Puu+9e8Pm///1vnnvuOWbNmkViYiJt27Z1yfZERHxNx8hgUm/pxeOrv2L+uv2M6NuBjpHBZpcl4jSPBqR9+/bhcFRNSx8fH9/getXLjh07Rn5+Pq1bt27SdkNCQrjzzjsv+Pzs2bMADBo0iFGjRjVpGyIivm7S9V1478tcdhw9yx/f+4pXJydhsehUm3gnjwakvLy8mvedOnVqcL3ay/Ly8pockFyhtLS0zt1zBQVVFyKWl5dTXl7usu1U9+XKPsWzNIbeT2PovLl39OHOl7bw4b7j/HNnLqOu6uDxGjR+3s+dY9jYPj0akAoLC2veh4SENLhe7WW127jafffd1+jrmebNm8ecOXMu+HzDhg2X/C7OSktLc3mf4lkaQ++nMXTOsGgrG3KtzFz1JUWHKwnx6L80/6Xx837uGEO7vXGPxjHp/7beZ8aMGUydOrXm54KCAmJjYxk5ciQREREu2055eTlpaWmMGDFCD9P1UhpD76cxbJrk8kpuf2EzmaftfGnEMXdMX49uX+Pn/dw5htVngL6PRwNSeHh4zftLJbjay2q3MVNgYCCBgYEXfG6z2dyyA7qrX/EcjaH30xg6x2azMW9cPya8soW3M75hXFIsA7t6/lIJjZ/3c8cYNrY/jz6LLSYmpuZ9bm5ug+vVXla7jYiIeIfru7VhwoBYAGb8YxelFZUmVyRyeTwakPr06YPVWrXJPXv2NLhe9bLo6OhmcYG2iIhcvhmj+9A2LJDDJ4t5YeNhs8sRuSweDUghISEMHjwYgHXr1l10HcMwWL9+PQAjR470WG0iIuJakSE25txR9RiSlz46xIHj7rvpRsTVPBqQAFJSUgDYuHEjW7duvWD5ypUrOXLkCACTJ0/2aG0iIuJaYxKiGd6nPeWVBjP+sRuHwzC7JJFGcTognTlzhlOnTtW8qieAtNvtdT4vKiqq0y4lJYWEhAQMw2DcuHGkp6cD4HA4WLlyJQ888ABQNdN2/ceMiIiId7FYLDzxw3hCA/zYnn2GZduOml2SSKM4HZASExNp165dzSsnJweABQsW1Pl8ypQpddr5+/uzevVq4uLiyM3NZfjw4YSGhhIaGsrdd99NQUEBiYmJLFu2rGnfTEREmoWYVlWPIQF4eu3XHDtXYnJFIt/P46fYAOLi4ti1axezZs0iPj4ei8WCzWYjKSmJhQsXsmXLFqKioswoTURE3ODeQXFcHduKotIKZr2/B8PQqTZp3pyeBykrK6tJGw4PD2fOnDkXnZ1aRERaFj+rhafH9ePW/7eJDXuPs2b3MW7t19HsskQaZMoRJBER8T29osP55bArAZj1/h7yi8tMrkikYQpIIiLiMVOGXUmvDuGcLi7jiQ++MrsckQYpIImIiMcE+FuZ/6N+WC3w3pd5fLj3uNkliVyUApKIiHhU/9hWPDCkGwAz39vNufPlJlckciEFJBER8bhfj+hJ17ahHC8oZd6afWaXI3IBBSQREfG4IJsf83/UD4sFVnyew6aDJ80uSaQOBSQRETHFgLjWTL6+CwDTV+2muLTC5IpE/ksBSURETPPbUb3p1CqY3LPnmb/ua7PLEamhgCQiIqYJDfTn6XH9AFiyOZttmfkmVyRSRQFJRERMdWOPtoy/NhaA363aRUl5pckViSggiYhIM/D7W/vQISKQzFPFPJN2wOxyRBSQRETEfJHBNp66KwGAVzcdYWfOWXMLEp+ngCQiIs1Ccp8O/PDqGBwGpL6zk9IKnWoT8yggiYhIs/H47VfRJjSAA8eLeC79kNnliA9TQBIRkWajdWgAc++MB+Cljw/rVJuYRgFJRESaldEJHbmjfwyVDoPfrNypu9rEFApIIiLS7My54yrahQdy6ESR7moTUyggiYhIsxMVGlBzV9srm46wPVsTSIpnKSCJiEizNKJvB8Ze0wnDgGkrd3G+TKfaxHMUkEREpNl6/LaraiaQXLB+v9nliA9RQBIRkWYrMsTG/373rLbFn2Wy9chpkysSX6GAJCIizdqwXu0Zf20shgGp7+yiuLTC7JLEByggiYhIs/eH2/oQExnE0Xw7/7v2a7PLER+ggCQiIs1eeJCN+T/qD8CbW7L59NApkyuSlk4BSUREvMKNPdoy6forAPjtO7soLCk3uSJpyRSQRETEa8wY3YfY1sHknj3PU2v2mV2OtGAKSCIi4jVCA/1Z8N2ptuXbcti4/4TJFUlLpYAkIiJe5fpubbjvhjig6lTbmeIycwuSFkkBSUREvM7vRvWme7tQThaW8of39mAYhtklSQujgCQiIl4nOMCPZ8Zfjb/Vwr92f8v7X+aZXZK0MApIIiLilfp1bsWvknsA8Mf395B39rzJFUlLooAkIiJe65c3d+fq2FYUllQwbeVOHA6dahPXUEASERGv5e9n5c939yfIZuWzw6d547Mss0uSFkIBSUREvFq3dmHMvLUvAE+v+5pDJ4pMrkhaAgUkERHxepOuu4KberajtMLBtFW7qXCYXZF4OwUkERHxehaLhfk/6kerEBtf5RWy/hv98yZNo/8HiYhIi9AhIogn70wAIC3Xwo6cs+YWJF5NAUlERFqMW/t15I5+HTGwkPrOHuxlFWaXJF5KAUlERFqUx2/rTasAg+x8O0/+Sw+0FecoIImISIsSEWxj4pVVV2kv23pUD7QVpyggiYhIi9Mr0iBl0BUApK7cxamiUpMrEm+jgCQiIi1S6oge9OoQzqmiUn73zi490FYuiwKSiIi0SIE2P5798dUE+FtJ//oEb209anZJ4kUUkEREpMXqHR3B9FG9AZj7z70cPF5ockXiLRSQRESkRfvJ4LiaWbZ/teJLSisqzS5JvIACkoiItGgWi4UF/9OP1qEB7Pu2gIXr95tdkngBBSQREWnx2ocHMX9cPwBe3ZTJJwdPmVyRNHcKSCIi4hOG9+3ApOurbv2f+vcvyS8uM7kiac4UkERExGfMHNOXK9uHcaKwlN+t0q3/0jAFJBER8RnBAX48O+FqbH4W0vYeZ8XnOWaXJM2UApKIiPiUq2Ii+e0tVbf+P/HBXg6fLDK5ImmOfC4gnThxgilTptClSxcCAwPp2LEjt956K4cPHza7NBER8ZD7b+zKjVe25Xx5JY+u2EFZhcPskqSZ8Te7AE86fPgwQ4cOxWaz8dOf/pTY2FhOnz7Ntm3byM/Pp3v37maXKCIiHmC1Wlh0d39u+ct/2JNbwKK0/cwY3cfssqQZ8amAdM8999C+fXv+85//EB4ebnY5IiJiog4RQTw9rh8Pvrmdlz8+wo1XtmVIj3ZmlyXNhM+cYtu4cSNbt27liSeeIDw8nJKSEkpL9XRnERFfdstV0dxzXdWt/79+eycnC/XvglTxmYC0bt06AFq1asVNN91ESEgIwcHBDBw4kE2bNplcnYiImOWPt/WlV4dwThWV8puVO3E4dOu/OBmQ7HY7a9euZe7cuYwdO5YuXbpgsViwWCzMnj27UX0UFhYye/ZsEhISCAsLIzIykgEDBrBo0SLKylw/edeBAwcAGDduHBEREaxYsYIXX3yRb7/9luHDh7N9+3aXb1NERJq/IJsfz01MJMhm5T8HTvLaJ0fMLkmaAaeuQdq2bRtjxoxxeqPZ2dncfPPNZGVlARASEkJpaSkZGRlkZGSwbNky0tPTiYqKuqCtYRiNPjVmtVoJCAgAqgIZQO/evVm9ejUWiwWA5ORk+vbty5w5c1i9erXT30lERLxXzw7hzLrtKn7/7m7mr9vPdV3b0D+2ldlliYmcPsUWFRVFcnIyqampLF++nOjo6Ea1q6io4PbbbycrK4uOHTuSlpZGcXExdrudFStWEB4ezo4dO5g0adJF22dnZxMcHNyo1zXXXFPTLjg4GIDJkyfXhCOAHj16cMMNN/Dxxx87+6sQEZEW4McDY7k1oSMVDoNHlu+gsKTc7JLERE4dQRoyZAj5+fl1Pps+fXqj2i5ZsoTdu3cDsGrVKgYNGgRUHe0ZP348DoeDiRMnsmbNGtLT00lOTq7Tvm3btixevLhR26p9BKpTp04AFw1yHTt25D//+Q+VlZX4+fk1qm8REWlZLBYLT41N4MucsxzNtzPz3T08O+HqOv9RLb7DqYDUlBCxZMkSAIYNG1YTjmqbMGECM2fOJDMzk6VLl14QkMLCwrjvvvsue7sDBgzg5Zdf5ptvvrlgWU5ODm3atFE4EhHxcZHBNv7fjxO5++XNrN6Zx4092nL3tbFmlyUm8OhdbHa7nU8//RSA0aNHX3Qdi8XCqFGjANiwYYPLtv3DH/6QkJAQXnnlFcrL/3vYdMeOHWzevLlmmyIi4tuSukQxdURPAB5//ysOndCjSHyRRwPSvn37cDiqpnOPj49vcL3qZceOHbvgVJ6z2rZty1NPPcWOHTsYOnQozz33HLNnzyY5OZmoqCieeOIJl2xHRES83y9u6s4N3dtwvrySR5bvoKS80uySxMM8OpN2Xl5ezfvqa4IupvayvLw8Wrdu7ZLtP/roo7Rt25ZFixaRmppKcHAwycnJzJs3j27dul2ybWlpaZ275woKCgAoLy+vc0Sqqar7cmWf4lkaQ++nMfRurhq/+WOv4vYXNrPv2wKe/NdeZt3a2xXlSSO4cx9sbJ8eDUjVt9pD1a39Dam9rHYbV7jnnnu45557LrvdvHnzmDNnzgWfb9iw4ZLfxVlpaWku71M8S2Po/TSG3s0V4/c/V1h45Ws/3txylMAzmSS01iSSnuSOfdButzdqPZ96FltTzJgxg6lTp9b8XFBQQGxsLCNHjiQiIsJl2ykvLyctLY0RI0Zgs9lc1q94jsbQ+2kMvZsrx28MUL52P4s/y+ado0FMvn0QHSODXFOoNMid+2D1GaDv49GAVPsBsZdKcLWXNZeHygYGBhIYGHjB5zabzS1/QN3Vr3iOxtD7aQy9m6vGb8aYvmRkn2V37jl+vXI3K35+PTY/n3lSl6ncsQ82tj+PjnBMTEzN+9zc3AbXq72sdhsRERFPC/C38sLEawgP9Gd79hkWbthvdkniAR4NSH369MFqrdrknj17Glyvell0dLTLLtAWERFx1hVtQpj/o34AvPzxEf799XGTKxJ382hACgkJYfDgwQCsW7fuousYhsH69esBGDlypMdqExERuZTRCR2574Y4AKb+fSd5Z8+bW5C4lcdPoqakpACwceNGtm7desHylStXcuRI1ZOUJ0+e7NHaRERELmXGmN4kdIrkrL2cR5bvoLzSYXZJ4iZOB6QzZ85w6tSpmlf1BJB2u73O50VFdWcgTUlJISEhAcMwGDduHOnp6QA4HA5WrlzJAw88AFTNtF3/MSMiIiJmCvT30/VIPsLpgJSYmEi7du1qXjk5OQAsWLCgzudTpkyp087f35/Vq1cTFxdHbm4uw4cPJzQ0lNDQUO6++24KCgpITExk2bJlTftmIiIibqDrkXyDKfcpxsXFsWvXLmbNmkV8fDwWiwWbzUZSUhILFy5ky5YtREVFmVGaiIjI99L1SC2f0/MgZWVlNWnD4eHhzJkz56KzU4uIiDR3M8b0Znv2GXbnnuOR5Ts0P1ILo5EUERFxgq5HatkUkERERJyk65FaLgUkERGRJqh/PVKurkdqERSQREREmqj2/EgPL/uCsgrNj+TtFJBERESaKNDfjxfvuYbIYBtf5pzlyX/tNbskaSIFJBEREReIbR3CM+P7A7Bkczard+aZXJE0hQKSiIiIi/ygdwceHtYdgOmrdnHweKHJFYmzFJBERERc6NfDezKoWxvsZZU8tOwLiksrzC5JnKCAJCIi4kL+flb+348TaR8eyKETRcz4x24MwzC7LLlMCkgiIiIu1i48kBfuuQY/q4XVO/N4c0u22SXJZVJAEhERcYMBca2ZMbo3AH/65152HD1jckVyORSQRERE3OT+G7syOj6a8kqDh5d9QX5xmdklSSMpIImIiLiJxWJh/o/60bVtKHnnSnjs7S9xOHQ9kjdQQBIREXGj8CAbL026hiCblf8cOMlz/z5kdknSCApIIiIibtY7OoIn70wA4C/pB/j4wEmTK5Lvo4AkIiLiAeOSOvPjgVdgGPDoih3k5NvNLkkuQQFJRETEQ2bf0Zf+naseavuLt7ZTUl5pdknSAAUkERERDwn09+OlSUm0CQ3gq7wCfv+uJpFsrhSQREREPCimVTDPTUzEaoF/fJHLW5pEsllSQBIREfGwG7q3ZcboPgA88c+9bM/ON7kiqU8BSURExAQ/G9KVW/t1pLzS4KG3vuBEYYnZJUktCkgiIiImsFgszB/Xjx7twzhRWMrDy76gvNJhdlnyHQUkERERk4QG+vPyvUmEB/rzedYZnvzXPrNLku8oIImIiJioW7sw/jz+agDe+CyL93bkmluQAApIIiIiphvRtwOP/OBKAKb/Yxd78wpMrkgUkERERJqBx4b35Kae7Sgpd/CLt7Zzzl5udkk+TQFJRESkGfCzWnh2wtXEtg7maL6dX63YQaVDk0iaRQFJRESkmWgVEsBfJyURZLPy8YGTLFi/3+ySfJYCkoiISDNyVUwk83/UH4C/fnyYD3bmmVyRb1JAEhERaWbu6B/Dgzd1AyD1nZ18lXfO5Ip8jwKSiIhIM/TbW3oz9LuLtn++dDv5xWVml+RTFJBERESaIT+rhecmJBLXJoTcs+c107aHKSCJiIg0U5EhNl6ZfC2hAX5sPnKap9Zopm1PUUASERFpxnp2CGfR3VcDsPjTLN7Z/o25BfkIBSQREZFmblR8NL9K7gHA79/dzZc5Z80tyAcoIImIiHiBx5J7MLxPB8oqHPzize2cKCwxu6QWTQFJRETEC1itFp4Z358r24dxrKCEh976grIKXbTtLgpIIiIiXiI8yMYr9yYRHuTP9uwzPL56D4ahx5G4gwKSiIiIF+nWLoz/NyERiwWWb8th6eZss0tqkRSQREREvMyw3u2ZPqo3AE/8cy+fHDxlckUtjwKSiIiIF/r50G6MTexEpcPgl8u2k3mq2OySWhQFJBERES9ksVh4amwCiVe0oqCkgvuXfM658+Vml9ViKCCJiIh4qSCbHy/fm0THyCCOnCzmV8t3UOnQRduuoIAkIiLixdqHB/Hq5GsJsln5+MBJ5ulxJC6hgCQiIuLl4jtFsuh/rgbgtU8y+XtGjrkFtQAKSCIiIi3Arf068uh3jyOZ+e5uMrLyTa7IuykgiYiItBCPJvdgdHw05ZUGv3hrO9+csZtdktdSQBIREWkhrFYLi+7uT9+OEZwqKuOBpdspLq0wuyyvpIAkIiLSgoQE+PNqyrW0DQtg37cF/ObvO3HozrbLpoAkIiLSwnRqFczL9yYR4Gdl3VfHWJS23+ySvI5PBaTc3FwefPBBunfvTnBwMF26dOGee+5h3z7dEikiIi1LUpfWzBubAMALGw/zzvZvTK7Iu/ibXYCnnDp1igEDBlBSUsJDDz1Et27dOHz4MC+99BIffPABO3fupGvXrmaXKSIi4jLjkjqTeaqY5zceYsY/dnFF6xAGdm1tdllewWcC0vLly/n22295//33ueOOO2o+v+6667jzzjt5++23mT59uokVioiIuN7UET05cqqINbuP8eCbGbz38GC6tAk1u6xmz2dOsZ07dw6Ajh071vk8JiYGgJCQEI/XJCIi4m5Wq4VF/3M1/TtHcsZezk/f0DPbGsNnAtIPfvADAKZMmcKmTZvIzc1l06ZNPPzww3Tt2pVJkyaZXKGIiIh7BAf48erka+kYGcThk8U8vOwLyisdZpfVrDkVkOx2O2vXrmXu3LmMHTuWLl26YLFYsFgszJ49u1F9FBYWMnv2bBISEggLCyMyMpIBAwawaNEiysrKnCnrkm644Qaef/55Dhw4wNChQ+ncuTNDhw7FZrOxefNmWrfWOVkREWm52kcE8VrKtYQE+PHJoVM8vvorDEO3/zfEqWuQtm3bxpgxY5zeaHZ2NjfffDNZWVlA1emt0tJSMjIyyMjIYNmyZaSnpxMVFXVBW8MwKC0tbdR2rFYrAQEBNT9fccUVDBw4kBEjRtCzZ0/279/P/PnzGT16NB9++KFCkoiItGhXxUTy7IREfv5mBv+39Sjd24Vx/426QelinD7FFhUVRXJyMqmpqSxfvpzo6OhGtauoqOD2228nKyuLjh07kpaWRnFxMXa7nRUrVhAeHs6OHTsaPOWVnZ1NcHBwo17XXHNNTbv333+fu+66i6effppp06Zxxx13kJqayrp169i5cydz58519lchIiLiNUb07cDvR/cBYO6/9pK+77jJFTVPTh1BGjJkCPn5dR+C19g7wJYsWcLu3bsBWLVqFYMGDQKqjvaMHz8eh8PBxIkTWbNmDenp6SQnJ9dp37ZtWxYvXtyobdU+AvWXv/yFbt26cfXVV9dZJykpiW7durFx48ZG9SkiIuLtfjakK0dOFbF8Ww6/Wr6Ddx66gT4dI8wuq1lxKiD5+fk5vcElS5YAMGzYsJpwVNuECROYOXMmmZmZLF269IKAFBYWxn333XfZ283Ly6OysvKiyyoqKqio0LNqRETEN1gsFp74YTzZp+18dvg097/xOe89PJj2EUFml9ZsePQuNrvdzqeffgrA6NGjL7qOxWJh1KhRAGzYsMFl2+7Tpw+ZmZls2rSpzucfffQRWVlZXHvttS7bloiISHNn87Py0j1JdGsbSt65Eu5fkoG9TAcLqnk0IO3btw+Ho+q2wvj4+AbXq1527NixC07lOWv69OnYbDZGjx7NtGnTeOWVV5g2bRq33norERERmiRSRER8TmSIjb/dN4DWoQHszj3Hr5Z/SaUebAt4eCbtvLy8mvedOnVqcL3ay/Ly8lxyd9n111/P9u3b+dOf/sSqVavIzc2lVatW3HrrrcyZM4devXpdsn1paWmdu+cKCgoAKC8vp7zcdRNuVfflyj7FszSG3k9j6N00fpenU2QAL028mnsXZ/DhvuM88cEe/jCmt6k1uXMMG9unRwNSYWFhzftLzVxde1ntNk0VHx/P22+/7VTbefPmMWfOnAs+37Bhg1tm4U5LS3N5n+JZGkPvpzH0bhq/yzOxq4U3DvqxZPNRir7NZGhH848kuWMM7XZ7o9bzmWexNdWMGTOYOnVqzc8FBQXExsYycuRIIiJcd+V/eXk5aWlpjBgxApvN5rJ+xXM0ht5PY+jdNH7OGQO0/U8mC9MO8m62HyMGX01y7/am1OLOMaw+A/R9PBqQwsPDa95fKsHVXla7jZkCAwMJDAy84HObzeaWHdBd/YrnaAy9n8bQu2n8Lt/DP+jBN2dLWPF5Dr/++27+/uAgEjpHmlaPO8awsf159CLt6gfDAuTm5ja4Xu1ltduIiIiI+1gsFv50ZzxDerTlfHklP13yOblnz5tdlik8GpD69OmD1Vq1yT179jS4XvWy6OhoPf5DRETEg2x+Vl645xp6dQjnZGEpP138OQUlvnfBu0cDUkhICIMHDwZg3bp1F13HMAzWr18PwMiRIz1Wm4iIiFSJCLLxt58MoF14IPuPF/Lwsi8or3SYXZZHeTQgAaSkpACwceNGtm7desHylStXcuTIEQAmT57s0dpERESkSqdWwfwtZQDBNj82HTzFH9/bg2GYf2ebpzgdkM6cOcOpU6dqXtUTQNrt9jqfFxUV1WmXkpJCQkIChmEwbtw40tPTAXA4HKxcuZIHHngAqJppu/5jRkRERMRzEjpH8tyPE7FaYMXnObyw8ZDZJXmM0wEpMTGRdu3a1bxycnIAWLBgQZ3Pp0yZUqedv78/q1evJi4ujtzcXIYPH05oaCihoaHcfffdFBQUkJiYyLJly5r2zURERKTJhvftwOO3XwXAwg0HWLX9G5Mr8gyPn2IDiIuLY9euXcyaNYv4+HgsFgs2m42kpCQWLlzIli1biIqKMqM0ERERqSflhjgeHNoNgN+t2sWmgydNrsj9nJ4HKSsrq0kbDg8PZ86cORednVpERESal9+N6k3euRI+2JnHQ299wd8fHETfGNdNlNzcmHIESURERLyL1Wph4f/047qurSkqreAnb2xr0XMkKSCJiIhIowT6+/HK5Gvp2SGM4wWl3Pe3bZyzt8w5khSQREREpNEig20s/slAOkQEcvBEET9/M4PSikqzy3I5BSQRERG5LJ1aBbP4voGEBfqzNTOfaSt34XC0rDmSFJBERETksvWNieCvk5Lwt1r4YGceT6/72uySXEoBSURERJxyY4+2zP9RPwBe/s8R3vg00+SKXEcBSURERJw29prOpN7SC4A5/9zLuj3fmlyRayggiYiISJP88ubuTLzuCgwDfrXiS7YeOW12SU2mgCQiIiJNYrFYeOKOqxjRtwNlFQ5+tjSDr48VmF1WkyggiYiISJP5+1l57seJXNslisKSClL+5t0TSSogiYiIiEsE2fx4LeVaerSvmkhy8utbOVNcZnZZTlFAEhEREZdpFRLAkp8OpGNkEIdPFvPTJZ9zvsz7JpJUQBIRERGXimkVzNKfDiQy2MaOo2eZ8n9fUFHpMLusy6KAJCIiIi7Xo0M4f7vvWgL9raR/fYLfv7sbw/Ce2bYVkERERMQtkrq05vmJ12C1wN8zvmHRhgNml9RoCkgiIiLiNiP6duCpuxIAeH7jIZZ8lmVuQY2kgCQiIiJuNWHgFUwd0ROA2R98xb92Nf/ZthWQRERExO0e+cGV3Ht9FwwDfv32l3xy8JTZJV2SApKIiIi4ncViYfYdVzEmIZqySgc/fzODnTlnzS6rQQpIIiIi4hF+VgvPjL+aG69si72skvsWb+PQiSKzy7ooBSQRERHxmEB/P16+N4n+nSM5Yy/n3te3NstHkiggiYiIiEeFBvqz+CcD6d4ulG/PlXDv61vJb2aPJFFAEhEREY9rHRrAm/dfR0xkEEdOFvOTxdsoKq0wu6waCkgiIiJiiphWwSy9/zqiQmzs/OYcD76ZQWlF83humwKSiIiImObK9mG88ZOBhAb48emh0zy24ksqHeY/kkQBSUREREzVP7YVr0y+lgA/K2v3HOPxD/Zh9mPbFJBERETEdIOvbMuzE67GaoG3M77hXznmRhQFJBEREWkWRid05MnvntuWlmvli6NnTavF37Qti4iIiNTz44FXcLqwhMMHv+aaK1qZVoeOIImIiEiz8uDQrtzc0dyLkBSQREREROpRQBIRERGpRwFJREREpB4FJBEREZF6FJBERERE6lFAEhEREalHAUlERESkHgUkERERkXoUkERERETqUUASERERqUcBSURERKQeBSQRERGRehSQREREROrxN7sAb2UYVU8ZLigocGm/5eXl2O12CgoKsNlsLu1bPENj6P00ht5N4+f93DmG1f9uV/873hAFJCcVFhYCEBsba3IlIiIicrkKCwuJjIxscLnF+L4IJRflcDjIy8sjPDwci8Xisn4LCgqIjY0lJyeHiIgIl/UrnqMx9H4aQ++m8fN+7hxDwzAoLCwkJiYGq7XhK410BMlJVquVzp07u63/iIgI7dheTmPo/TSG3k3j5/3cNYaXOnJUTRdpi4iIiNSjgCQiIiJSjwJSMxMYGMjjjz9OYGCg2aWIkzSG3k9j6N00ft6vOYyhLtIWERERqUdHkERERETqUUASERERqUcBSURERKQeBSQRERGRehSQ3KSwsJDZs2eTkJBAWFgYkZGRDBgwgEWLFlFWVtakvo8fP85vfvMbevXqRXBwMK1bt2bIkCG89tpr3/tsGWk8d4zh7NmzsVgs3/s6dOiQi7+N77Db7axdu5a5c+cyduxYunTpUvN7nT17tku2oX3Qvdw5htoHPeP06dMsXryYSZMm0bdvX0JDQwkMDKRz587ceeedvPvuu03ehjv/nQXAEJfLysoy4uLiDMAAjJCQECMwMLDm58TERCM/P9+pvjMyMow2bdrU9BUWFmb4+/vX/HzLLbcYpaWlLv5GvsddY/j4448bgGGz2YwOHTo0+MrMzHT9l/IRGzdurBmn+q/HH3+8yf1rH3Q/d46h9kHPqL1PAEZQUJARGhpa57PRo0cbxcXFTvXvzn9nq+kIkotVVFRw++23k5WVRceOHUlLS6O4uBi73c6KFSsIDw9nx44dTJo06bL7PnfuHLfddhunT5+md+/efP755xQWFlJcXMzzzz+PzWZj/fr1PPbYY67/Yj7EnWNY7YYbbuDYsWMNvuLi4lz3hXxQVFQUycnJpKamsnz5cqKjo13Sr/ZBz3HXGFbTPuheFRUVDBw4kBdffJHDhw9z/vx5ioqKyMzM5P777wdg7dq1PPjgg0717e6/0YCOILnaa6+9VpNgP/vsswuW/9///V/N8g8//PCy+v7DH/5gAEZwcLBx5MiRC5Y/9dRTBmD4+fkZ+/fvd/o7+Dp3jmH1f73edNNNLqpW6quoqLjgsy5durjk6IP2Qc9w5xhqH/SMf//735dc/uCDD9b8HT169Ohl9e3Ov9G16QiSiy1ZsgSAYcOGMWjQoAuWT5gwga5duwKwdOnSy+q7ev3afdT2yCOPEBYWRmVlJcuWLbvc0uU77hxDcT8/Pz+39a190DPcOYbiGcOGDbvk8uqjSAAZGRmX1ben/kYrILmQ3W7n008/BWD06NEXXcdisTBq1CgANmzY0Oi+9+/fz9GjRy/Zd1hYGEOGDLnsvuW/3DmG4t20D4q4TlBQUM37ysrKRrfz5N9oBSQX2rdvHw6HA4D4+PgG16teduzYMfLz8xvV9549ey5of6m+9+7d26h+pS53jmFtX331FfHx8YSEhBAWFkavXr144IEH2LFjh3OFi9tpH2xZtA+a66OPPqp5n5CQ0Oh2nvobDQpILpWXl1fzvlOnTg2uV3tZ7Tau7LugoICioqJG9S3/5c4xrO3UqVPs27eP4OBgSktLOXDgAK+99hpJSUn84Q9/uOz+xP20D7Ys2gfNc/bsWebNmwfAkCFD6NWrV6PbeupvNCgguVRhYWHN+5CQkAbXq72sdhuz+pb/cvfvuUePHsyfP5/9+/dTUlLC6dOnKS4uZv369SQlJWEYBk8++SSLFi1y7guI22gfbBm0D5rL4XBw77338u233xIUFMTzzz9/We09uR8qIIl40D333ENqaio9e/bEZrMBEBAQwMiRI/nkk08YMGAAUDWZ3blz58wsVaRF0j5orkcffZR//vOfALzwwgv069fP5IoapoDkQuHh4TXv7XZ7g+vVXla7jVl9y3+Z+XsOCgriqaeeAqCoqIj09HSX9CuuoX2w5dM+6F7Tpk2rOWL0zDPP8NOf/vSy+/DkfqiA5EIxMTE173Nzcxtcr/ay2m1c2XdERARhYWGN6lv+y51j2Bi1b1k9cuSIy/qVptM+6Bu0D7rHb3/725rTlgsXLnR6MlVP/o1WQHKhPn36YLVW/Upr3/FSX/Wy6OhoWrdu3ai+a1+t35i++/bt26h+pS53jqF4N+2DIs5JTU1lwYIFAMyfP5/f/OY3Tvflyb/RCkguFBISwuDBgwFYt27dRdcxDIP169cDMHLkyEb33bNnT6644opL9l1cXMymTZsuu2/5L3eOYWNs2bKl5v3FJiIU82gf9A3aB11r2rRpLFy4EKgKR6mpqU3qz5N/oxWQXCwlJQWAjRs3snXr1guWr1y5suaw7eTJkxvdr8ViqVl/xYoVZGVlXbDOCy+8QFFREX5+ftxzzz1OVC/gvjE0vucp76WlpcycOROA0NBQkpOTG923uJ/2Qe+nfdCzpk2bVue0WlPDUTV3/Y2+gNMPKZGLKi8vNxISEgzA6NSpU81zYCorK42///3vRkRERM1TjOurfkYQcNEnSZ89e9aIjo42AKNv375GRkaGYRiGUVpaarz44otGQECAARgPPfSQW79jS+euMfzoo4+M5ORkY+nSpUZOTk7N52VlZcaHH35oDBgwoKbt008/7dbv2NLl5+cbJ0+erHnFxsYagJGamlrn88LCwjrttA82H+4YQ+2DnpOamlrzu/zzn/98WW0XL15c03bjxo0XLG/K3+jLoYDkBpmZmUZcXFzNAIeEhBhBQUE1PycmJhr5+fkXtPu+P86GYRgZGRlGmzZtatYLDw83bDZbzc8jR440SkpK3PwNWz53jOHGjRtrlvHdA0/btm1bZ/ysVqvx+9//3kPfsuWqfrDp971SUlLqtNM+2Hy4Ywy1D3pGdnZ2nd9nhw4dLvlasGBBnfbfF5AMw/m/0ZdDp9jcIC4ujl27djFr1izi4+OxWCzYbDaSkpJYuHAhW7ZsISoqyqm+k5KS+Oqrr/j1r39Njx49KC8vJzQ0lBtvvJFXX32VtWvXEhgY6OJv5HvcMYYJCQksXLiQcePG0bNnT4KDgzl79izBwcH079+fKVOm8OWXX/Lkk0+66VuJK2gf9F7aBz2j+lEg1e+PHz9+yZczM86789/ZahbD+J6TsiIiIiI+RkeQREREROpRQBIRERGpRwFJREREpB4FJBEREZF6FJBERERE6lFAEhEREalHAUlERESkHgUkERERkXoUkERERETqUUASERERqUcBSURERKQeBSQRERGRehSQREREROpRQBIRERGp5/8DDq2EsdcMkk0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=30\n",
    "xval = jnp.linspace(0.,2.)\n",
    "yval = 1./jnp.sqrt(1 + xval**(2.*n))\n",
    "plt.plot(xval,yval)\n",
    "plt.yscale('log')\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "RrbcCaMUZU5c"
   },
   "outputs": [],
   "source": [
    "def count_modif2(r,X,n=30):\n",
    "  u = X/r\n",
    "  return jnp.sum(1./jnp.sqrt(1 + u**(2.*n)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "YTj5P9RuZ8bp",
    "outputId": "67989a0b-7dfe-48e8-f612-44976106392d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(5.90886867, dtype=float64)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_modif2(1.,X)  # approx 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8tgQtEtsaN2i",
    "outputId": "6435b21f-f9c4-4b5a-a3ef-a82dbfef39be"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(4.81316697, dtype=float64, weak_type=True)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.grad(count_modif2)(1.,X)  # gradient =/= 0 !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ICMbzJPajq-O"
   },
   "source": [
    "## Non-scalar function : Jacobian (See Hessian after)\n",
    "For non-scalar functions, the jacfwd or jacrev compute the Jacobian, as well as you can compute the hessian.\n",
    "\n",
    "$$\n",
    "f(W,x) = y = W x \\quad \\mathrm{with} \\quad  W=\\begin{pmatrix}\n",
    "1 & 2 \\\\\n",
    "3 & 5\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "We can write the result as\n",
    "$$\n",
    "\\begin{cases}\n",
    "y_1 &= W_{11} \\times x_1 + W_{12} \\times x_2 + W_{21}\\times 0 + W_{22}\\times 0 \\\\\n",
    "y_2 &=W_{11}\\times 0 + W_{12}\\times 0 + W_{21}\\times x1 + W_{22}\\times x2\n",
    "\\end{cases}\n",
    "$$\n",
    "So, we have 4 parameters ($n$) for 2 outputs ($m$), We expect a matrix of rank $m \\times n$. With $x=(x_1,x_2)$\n",
    "$$\n",
    "\\begin{pmatrix}\n",
    "\\frac{\\partial y_1}{\\partial W_{11}}=x_1 & \\frac{\\partial y_1}{\\partial W_{12}}= x_2 & \\frac{\\partial y_1}{\\partial W_{21}}=0 & \\frac{\\partial y_1}{\\partial W_{12}}=0 \\\\\n",
    "\\frac{\\partial y_2}{\\partial W_{11}}=0 & \\frac{\\partial y_2}{\\partial W_{12}}= 0 & \\frac{\\partial y_2}{\\partial W_{21}}=x_1 & \\frac{\\partial y_2}{\\partial W_{12}}=x_2 \\\\\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "In fact, the output keep track of the parameter shape:\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\begin{pmatrix}\n",
    "\\frac{\\partial y_1}{\\partial W_{11}}=x_1 & \\frac{\\partial y_1}{\\partial W_{12}}= x_2 \\\\ \\frac{\\partial y_1}{\\partial W_{21}}=0 & \\frac{\\partial y_1}{\\partial W_{12}}=0\n",
    "\\end{pmatrix}\n",
    "\\\\\n",
    "\\begin{pmatrix}\n",
    "\\frac{\\partial y_2}{\\partial W_{11}}=0 & \\frac{\\partial y_2}{\\partial W_{12}}= 0 \\\\ \\frac{\\partial y_2}{\\partial W_{21}}=x_1 & \\frac{\\partial y_2}{\\partial W_{12}}=x_2\n",
    "\\end{pmatrix}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "So a tensor rank that I write as $(2,(2,2))$ which is\"shape\" of $(2,2,2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "2PwSSiZDhmDo"
   },
   "outputs": [],
   "source": [
    "def fvec(W,x):\n",
    "  return W @ x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Tgp0RG7WkUIb",
    "outputId": "e7195183-c765-4718-e2b0-87681b189deb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([[1., 2.],\n",
       "        [3., 5.]], dtype=float64),\n",
       " Array([-1.,  1.], dtype=float64))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = jnp.array([[1., 2.],[3.,5.]])\n",
    "x = jnp.array([-1.,1.])\n",
    "W,x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "d-V-Qhnkkjse",
    "outputId": "9ed21736-1c6d-453f-9f76-489925871a18"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([1., 2.], dtype=float64)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fvec(W,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "MDwcPL6DlCAl",
    "outputId": "cb1f6c15-2426-4dea-9f19-ae93454fadd8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2, 2) \n",
      " [[[-1.  1.]\n",
      "  [ 0.  0.]]\n",
      "\n",
      " [[ 0.  0.]\n",
      "  [-1.  1.]]]\n"
     ]
    }
   ],
   "source": [
    "Jfwd =jacfwd(fvec)(W,x)   # W is the parameter\n",
    "print(Jfwd.shape,\"\\n\",Jfwd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "elLfguiT_Yvc",
    "outputId": "4d124850-0982-44fe-872c-066696860eae"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2, 2) \n",
      " [[[-1.  1.]\n",
      "  [-0.  0.]]\n",
      "\n",
      " [[-0.  0.]\n",
      "  [-1.  1.]]]\n"
     ]
    }
   ],
   "source": [
    "Jrev =jacrev(fvec)(W,x)\n",
    "print(Jrev.shape,\"\\n\",Jrev)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uCnR2SMnDy9K"
   },
   "source": [
    "**Warning**: (if we flatten the parameter matrix/tensor)\n",
    "\n",
    "- `jacfwd` is designed for $\\mathbb{R}^n \\rightarrow \\mathbb{R}^m$ with $n\\ll m$ (*tall matrix*)\n",
    "\n",
    "- `jacrev` is designed for $\\mathbb{R}^n \\rightarrow \\mathbb{R}^m$ with $m\\ll n$ (*wide matrix*)\n",
    "\n",
    "The last case is particularly adapted when we have a lot of parameters ($n$) with a few outputs ($m$). But this will imply restriction for the coding (`fori_loop` and `while` loop) see [doc](https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html#summary)\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MRFghTaZjtBE"
   },
   "source": [
    "## Auto-diff on multi-args function\n",
    "\n",
    "The differentiation is by default on the 1st argument of the function but this is not exclusive\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "pL-rGxAbjtbe",
    "outputId": "d8e1e3a9-2dc8-46a3-bd70-f471de01db8e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.0\n",
      "8.0\n",
      "6.0\n",
      "(Array(8., dtype=float64, weak_type=True), Array(6., dtype=float64, weak_type=True))\n"
     ]
    }
   ],
   "source": [
    "def func(x, y):\n",
    "    return 2 * x * y\n",
    "\n",
    "print(grad(func)(3., 4.))  # 8.                 # function evaluated @ (3,4)\n",
    "print(grad(func, argnums=0)(3., 4.))  # 8.      # df/dx    evaluated @  (3,4)\n",
    "print(grad(func, argnums=1)(3., 4.))  # 6       # df/dy    evaluated @  (3,4)\n",
    "print(grad(func, argnums=(0, 1))(3., 4.))  # (8., 6.)  # both firs derivatives evaluated at once"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YVC13eJ1pFSb"
   },
   "source": [
    "# Example via the minimization of the Mean Squared Error (MSE)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lXR0D_RzsoUV"
   },
   "source": [
    "## Model, loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "p8JhzQxoo4ZY"
   },
   "outputs": [],
   "source": [
    "def model(p, x):\n",
    "    return jnp.exp(-x*p[0])*jnp.sin(x*p[1])\n",
    "\n",
    "def loss_fun(p, xi, yi):\n",
    "    yhat = model(p, xi)\n",
    "    return jnp.mean( (yhat - yi)**2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kxWzkFTXqLI7"
   },
   "source": [
    "In passing: jnp.exp, jnp.sin ... are vectorized so  `model` and ``loss_fun` do not need vmap.\n",
    "\n",
    "## Dataset\n",
    "Let us now generate a dataset. Look at random number generation\n",
    "\n",
    "pseudo-random number generation uses cryptoghy algorithm\n",
    "[see](https://github.com/google/jax/blob/main/docs/jep/263-prng.md)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "6eUtBDLWpJ_x"
   },
   "outputs": [],
   "source": [
    "# dataset\n",
    "ptrue = jnp.array([0.5,1])\n",
    "\n",
    "xin = jnp.arange(0,10,1.)\n",
    "yerr = 0.05\n",
    "key, subskey = jax.random.split(jax.random.PRNGKey(42),2) #simple way to give a key to the RNG\n",
    "#key can be used here after if necessary\n",
    "y_true =  model(ptrue, xin)\n",
    "yin = y_true + yerr*jax.random.normal(jax.random.PRNGKey(42),shape=xin.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 446
    },
    "id": "LOrHq5NQr61L",
    "outputId": "b5a0ce1c-971f-4fb6-b333-e390ce1c1e9e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(xin,yin,yerr=yerr, fmt='o', linewidth=2, capsize=0, c='k', label=\"data\");\n",
    "plt.plot(xin,y_true, label='True (noiseless)')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Qikc3aalr9WJ"
   },
   "source": [
    "notice: most of matplotlib accept JAX Device array asis as they have a numpy representation. If not use np.asarray(JAX-device-array)\n",
    "\n",
    "## Gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "id": "XpTXHZlUssVI"
   },
   "outputs": [],
   "source": [
    "@jit  # we will see what it is later\n",
    "def gradient_descent_step(p, xi, yi, lr=0.1):\n",
    "    return p - lr * jax.grad(loss_fun)(p, xi, yi)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yeShvARPs5EP"
   },
   "source": [
    "Below is a simple minimizer from scratch with a for loop. We will use a more JAXy version later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "id": "3aEBYFKCs29S"
   },
   "outputs": [],
   "source": [
    "def minimzer(loss_fun, x_data, y_data, par_init, method, verbose=True):\n",
    "    p_cur = par_init\n",
    "    new_loss=jnp.inf\n",
    "\n",
    "    for t in range(5000):\n",
    "\n",
    "        if (t % 100 == 0) and verbose:\n",
    "            print(t, p_cur,new_loss)\n",
    "\n",
    "        old_loss = new_loss\n",
    "        new_p = method(p_cur, x_data,y_data)\n",
    "        new_loss = loss_fun(new_p, x_data,y_data)\n",
    "\n",
    "        if jnp.abs(new_loss-old_loss) < 1e-9:\n",
    "            print(f\"Converged after {t} epochs: p = {new_p}, loss = {new_loss}\")\n",
    "            break\n",
    "\n",
    "        p_cur = new_p\n",
    "\n",
    "    return p_cur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "xTT1UzARtMrV",
    "outputId": "60490c3e-b00e-4f8d-b14b-ea03b56846f1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 [0.  0.5] inf\n",
      "100 [2.15953273 0.56389911] 0.033247239677726276\n",
      "200 [1.59564364 0.98068681] 0.023004943889561494\n",
      "300 [0.59298792 1.08997104] 0.0019512935874766468\n",
      "Converged after 370 epochs: p = [0.52381757 1.10343296], loss = 0.0015533005412891193\n"
     ]
    }
   ],
   "source": [
    "par_mini_GD = minimzer(loss_fun, x_data=xin, y_data=yin, par_init=jnp.array([0., 0.5]),\n",
    "                    method=partial(gradient_descent_step, lr=0.5), verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 446
    },
    "id": "gXnTSFUktTy6",
    "outputId": "3006a2e0-86cf-459b-b971-a9b7d70b157d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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25YYbbuD++++v9pqVn1VeXp7dO+2qqto7VpvG/h188MEH3HTTTezdu5cXX3yRF198EQ8PDwYOHMj48eO55557CA4OtjqnIe/fkWToTTSOycSqF6YQd+2DjP60iNtWFTNycRFxbxaw6qc/4L1hkLDK0VEKIRpIq22+Xi2j0QjAFVdcgaqqdXq4g8DAQH766Se2bt3KU089xZAhQ9DpdOzatYt//vOfdOrUqdpQXuVn9e6779bpc/r444/rFEtj/w7atWvHn3/+ydq1a3nssccYMGAAJpOJbdu28dRTT9GxY0d++umnRr9/R5JESTRcRSmr/m8Mk/65nFN51v950vJUJi0vZtXeLFh5F3w7E8ob9tugEMJ5VfbIlJSU2D2mcjjIVnh4ONDwIbXmVLUn7dSpU3aPq9yn0+mq9ZxcylVXXcW//vUvfvnlF3Jycvj666/p1asXxcXF3H333VY9PM31WTXFdTUaDddeey1vvvkmO3fuJCsriyVLltCuXTuys7O57bbbaqzvVJ/370iSKImGKc7B+MkEZrz/U41TtyvbZq4twWhSYddH8MFoOHe0JaMUQtionHzbVL0zQUFBAKSmpto95rfffquxvXL+U3p6Ojt37mySeJpK//79LZ/Vxo0b7R63YcMGAPr06dOoNd0q71xbtcrcA19SUsIvv/xi2V/5WX333XcNfo2aNMffgb+/P7fddptlAnpGRgb79++v9ZxLvX9HkkRJ1F/uKfjoOrZu2VytJ6kqFUjNU9maYu7aJSMB3h8Be5e2SJhCiOoCAgIA811dTaFPnz6A+W6owsLCavt/+uknfv311xrPHTlypGWS9axZsy5ZVTorK6uR0dZdYGAg115rvjng9ddfr3HOz969e/nyyy8BuPXWW+t03YqKCkwmk9393t7elueViRpguW0/ISGBd999t9bXKCwsrHOF7sb8HVzq2JreS0PfvyM5RxTCdaQnwAfXwNmDnMmv22+kVseVF8JXD8Dqv0FZ9R+qQojm1bNnTwDWrFlDWlpao693yy23oNFoOH/+PLfeeqtlKKq4uJjFixfzl7/8xe6QlE6n47333kOn0/HLL78wbNgwNm7caDWp+uTJk7z33nsMHDiQd955p9Hx1sdLL72EXq/n+PHjXHvttZZeEZPJxJo1a7j++uupqKigQ4cOPPDAA3W65qlTp+jUqRMvvfQSu3fvpqKiwrJv3759TJs2DQBfX1+GDx9u2Td8+HDuuusuAB5++GFmzZrFyZMnLftLS0vZsWMHTz31FLGxsVaT0WvTmL+D7du307t3b9544w0OHTpkSYBUVWX79u089NBDgHnCe+/evRv1/h2qzrW+RY1a1RImJzap6svRqvpCgKq+EKBumu5jVabe3mPTjG6Wc6we7w1V1ZKalw0QoipZwqTpHD16VPXy8lIBVaPRqGFhYWpsbKwaGxurpqamWo6z/P/dtOmS13z++eet/s8bDAZVp9OpgHrzzTerzz77bK1LmHz11VeWpVG4sAxGmzZtrJbGANSXXnqpXu+16hIm9tS21Iiqmpd+8fDwsFoypPLzowFLmFRt58LyHcHBwVav4eHhoa5YsaLaNUtLS9V7773X6nw/Pz81KCjIakkWQD116pTVuZdawqQhfwebNm2y2ld5TuXffeXntWXLliZ5/7WRJUyE4x38Bj6bBKUXb0sd2k5LdKDeaoHMqhRFISYmhqGv/g79p1c/4Mxe2P6f5opYCFGDTp06sWnTJm666Sbatm3L+fPnSU5OJjk52eq3+/qYO3cun376KYMGDcLX1xej0Ujfvn157733WLVq1SXvnLv55ps5fvw4L7zwApdffjl+fn7k5OTg6elJnz59uPfee/nqq6948sknGxRfY0yZMoUDBw7wwAMP0KFDB0pLS9HpdPTt25e5c+eSkJBAt27d6ny9qKgovvnmG2bNmsWgQYOIiIigoKAAnU5H9+7defjhh0lISGDSpEnVzvXw8GDRokVs376dO++8kw4dOmA0GikoKCA0NJQRI0bw/PPPs2/fvnrfXt+Qv4OBAweyfPlyHnroIQYMGEBISAh5eXl4eXnRt29fnnrqKQ4dOsTQoUOb5P07iqKqbnK/pYPk5eVhMBjIzc21jP27neIcWNgbSm3uXIkZxCqf25h0u7k7uKZ/Sh1ufZ5OV4wmxM+Da4xbmZI+H09TlbF+TwPM3Afegc0Xv3B5JSUlJCYmEh8fj5eXl6PDEUI4mYb8jKjr97f0KIlLO/Rt9SSp201wx9dMuHU6K1eurPbbi9Y/hLY3/4OKdpdz6EweW49l8vzJbkwofsb6OqW58Nt/m/kNCCGEEA0jZWzFpe1fbr3d4WqYvBgu3JEwYcIEKqIH8NjCz6nIP49yeAMpCX+QW2Iks6CUzIJSzheUmf8sbM/ug+voV/DzxevteBsGPQhehhZ8U0IIIcSlSaIkapd3BhK3Wrf1n25JkgCOny1gzneH8GrXm5ytn+FXnIm3px5vTz3hhhq6QAe8Au8Ovrhdkgu/vQ/DW37+gRBCCFEbGXoTtTuwiovlIwEPf+h8ceHRknIjj3z+J0VlRkxnDpP76/Lq17AV1gO16zirJtOvb0HJpdcvEkIIIVqSJEqidvtsEp/uN4H+YkGwF787yOH0fEL8PDBt/xBU+4XEqlJG/J/VtqYkB+OO9xobrRBCCNGkJFES9mUegzN7rNt6Xbxl87t9p1nyWwqKAm9M6QvF9egRCu8FXW+0aird+h8ozW94vEIIIUQTk0RJ2Ld/pfW2byjEDQMg+XwhT39prlL7txEdGNqpbf2vP9y6V8nHmMfBr+c1KFQhhBCiOUiiJGqmqtXvdus5EbQ6SiuMPPL5bvJLK7gsNohZozs37DUiekOXG6ybDnzIoeTTDQxaCCGEaFqSKImanf4Tsk5at/WaDMC/fjjC/rRcAn30/PvWfui0jfhnNPwpq80gJZ/Nn75MdmHdFnQUQgghmpMkSqJmtsNuQfEQ1Z/1BzP437ZEAOZN6kNkoHcNJ9dDZF/ofJ1V0y3lq3liyXYqjHWbGC6EEEI0F0mURHUmIyR8ad3W+xbSckt4YsVeAO69Kp7R3cOa5vVs7oBro+TTMXkpr/94pGmuL4QQQjSQJEqiusQtUJBh1WTqMZEZX+wmt7icPtEGnhrbteleL7IfdB5r1XSf7ns+2XKQtQlnmu51hBBCiHqSRElUt3+F9XZEH/4sasvO5Gx8PLT859b+eOia+J+OzR1wIUoe07QbeO3HIxhNsm6zEEIIx5BESVgrL4aD31i39bqFNfvTAbi2Rzjt2vg0/etG9YdOY6yaHtR/z+lzWaw/mN70ryeEEELUgSRKwtqxdVBWteijgqn7X/jhwhDYdT3Dm++1h//darMNudyu3cC7P59EVaVXSQghRMuTRElYs12yJO4q9uT5cCa3BF8PLcM6N6CwZF1FD4COo62aHtR9x5HUDHaczGq+1xVCCCHskERJXFScY+5Rqqr3Lfyw39ybNKpbGF56bfPGYNOr1FbJZYp2M+/9fKJ5X1cI4RJSUlK46667aNeuHR4eHiiKQmBgIABJSUkoioKiKCQlJTk0TuE+dI4OQDiRQ9+CsUqhR60HatdxrFm3G4Dre0U0fwwxA6HDKDix0dI0UbuVm45ey4HTufSINDR/DEK0EiaTia+//ppvv/2WHTt2kJGRQV5eHn5+fkRFRdGvXz/Gjh3LuHHjCAgIqHb+5s2bGTlyZLV2b29vAgICCAsLo0+fPlx55ZVMmTKF4ODgRsWbm5vLkCFDOHXqFAAGgwEvLy8Mhkv/XEhKSuLjjz8GYM6cOY2KQ7Qu0qMkLrJdsqTTGPadV0jLKcbHQ8uILs047FbVlQ9bbfbWnCRWSee/P5+0c4IQor5+++03unfvzoQJE/joo484dOgQubm5BAQEUFxczIEDB/jss8+YNm0aMTExvPHGG7VeLygoiLCwMMLCwvDx8eH8+fPs27ePTz/9lL/97W9ERkby2GOPUVhY2OCYv/jiC06dOkVQUBCHDh0iJyeH9PR0jhwx11zT6/V06dKFLl26oNfrrc5NSkpi7ty5zJ07t8GvL1onSZSEWd4ZSNxq3dZrMmsuDLtd3TX0ksNus2fP5oUXXmD27NmNiyV+OPiEWDXdoNnBd/tOk3K+qHHXFkKwevVqhg0bxpEjR2jTpg0vvvgiCQkJlJeXc/78eUpKSsjIyGDlypWMHz+egoICli1bVus1V61aRXp6Ounp6WRmZlJeXk5iYiKffvopgwcPprS0lP/85z9cccUVZGdnNyju/fvNC3FfffXVdO1avZZbVFQUhw8f5vDhw0RFRTXoNYSwJYmSMDuwCqhyZ5mHP2qnMay5cLdbXYbdZs+ezZw5cxqfKGl10H28VdNUnz8wqbBoq/QqCdEYhw8fZtq0aZSVldG7d2/27dvHs88+S48ePVAUxXJcaGgoEydOZPXq1ezbt48rr7yy3q8VFxfHtGnT2LZtGwsWLADgwIEDTJ06tUGxFxWZf1Hy8/Nr0PlCNIQkSsLM9m63buNIOFtOalYx3notI7uEtmw8PSdYbbYrT6SjcorlO1PJLCht2ViEcCPPPvsshYWF+Pr68tVXXxEZGXnJc3r06HHJobdLmTVrFg8/bB5WX7duHRs3brzEGReNGDECRVEsc4wWL15smbRdtd3eZO64uDiruVRVz1UUhTvvvLNR7024N0mUBGQegzN7rNt6T7b0Jo3s2hZvj2a+281WuyvB37oX697A3ZRWmFi8PallYxHCTZw5c4ZVq1YB8Ne//pX27du36Os/88wzlrlDixcvrvN5wcHBhIWF4eXlBYCXl5dlPlRYWBje3rUvzt22bVuCgoIs21XPDQsLq9NkcNF6yV1vAvavtN72DUWNG8qaVb8ALXS3my2NFrrfDL+9a2m6UbeDv3Mjn/yazAPDO+DnKf98xQUmExS7aa0t72DQNM3vtJs2bbIUb73pppua5Jr1ERERQb9+/fj999/5+eef63xeZXJ35513snjxYqZMmWLpRaqLP/74w+oOvfR0qfYv6k6+aVo7Va1+t1vPCRzMKCL5fBGeOk3LD7tZ4pholSj55ScyOugcG7JDWfp7CvcObdnfhoUTK86C1zs4Oorm8eQJ8A259HF1cPDgQcvzvn37Nsk166tPnz78/vvvpKSkUFFRgU4nX0PCucnQW2t3Zg9k2UyQ7nWL5W63kV1C8XVUz030ZWBoZ9U0O8J818sHWxMpqzA5IiohXNb58+ctz+3VNDp+/Djh4eE1PrZv397oGKq+blaWm/YCCrciiVJrl/Kb9XZQHGpkP8siuNf1asa13S5FUaDnX6yaumVtINTPg/S8Er7ek+agwIRwXxUVFWRkZNT4KCsru/QFhHAzkii1draTuGOHcORsAYmZhXjoNIzqFuaQsCx6WN/9puQk8/c+5luE3/v5BCaTLJYrRF21adPG8txeb07Xrl1RVdXySExMbNIYqr5uYyt1C9ESZHC4tTu9x3o7oi9r9pmH3YZ3buv4CdMRfSC4A2RdXOvtRs2vvOA1khPnCtlwKIMxPRzY6yWcg3eweS6PO/JuumSie/fulud79uwhIqLlb9TYu3cvALGxsTI/SbgE+VfampUVQeYR67bIvqzZZh52u8ERd7vZUhRzTaUtr1uaPA5/zV+vuIN3fk7k3Z9PcE33MKtCeaIV0miabMKzOxs5ciSKoqCqKt988w3XXXddi77+mTNn2L3bvHbkiBEjWvS1hWgoGXprzTISQK0yIVrRcEyJ4/jZAjy0Gq7u5qC73WzZDL+Rf5r74s7hodOwOyWH3xNlQqgQdREREcGECeb/T59++mmTD6tdyv/7f/+P8vJygBYv8qipUmKhskSCEHUhiVJrZjvsFtKF7w/nADCscwgBXvpqpzhEWHdo282qKSjxOyYNiAbg/S2yrIkQdfXSSy/h6+tLYWEhN998M6dPn26R1124cCFvv/02AGPHjm3xHqWAgADL85ycnBZ9beHaJFFqzc7std6O6GMpC3BdTycYdqvKZkkTDqzmnsHm0gGbj57jXL4sayJEXXTt2pXPPvsMDw8P9u3bR+/evXnppZc4cOCAVU9LXl4ea9eu5dFHH23wa6WkpLBkyRKuuuoqZs2aBUCvXr344osvGv0+6qtz5854eHgA8MEHH0ivkqgzSZRaM5s73s75d+VoRgF6rcLo7g6+282W7fBb4Vk6FO6hb0wgRpPKt3tb5rdiIdzBzTffzM8//0yXLl04f/48zz33HD179kSv1xMSEoLBYMBgMHDdddfx3Xff4e/vz4svvsigQYPsXnPChAmWekshISF4eHgQGxtrWRTX09OTGTNmsGPHDgIDA1vuzV7g4+PDX//6VwCeeuop/Pz8iI2NJS4ujieeeKLF4xGuQyZzt1blxXD2kFXT5nzzUNZVHUMweDvJsFulkI4Q3hvS911sS/iSv/SbzZ7UHFbvSePuq+IdF58QLmbQoEEcPHiQ1atX8+2337Jjxw4yMjLIzc3Fz8+Pbt260b9/f8aMGcPEiRPx9fWt9XrZ2dmW515eXgQFBREeHk6fPn0YPHgwU6ZMsVpvzRHefvttYmJi+PLLLzlx4gQpKSkAZGZmOjQu4dwUVfofGyUvLw+DwUBubq7VGLjTO7ULPri6SoPCzYZl7Mmo4LVJvbnlshiHhWbXLwthwwsXt72DOP9gAlf8awsVJpUNs4fTMdTPYeGJ5lNSUkJiYiLx8fGWhVGFEKJSQ35G1PX7W4beWqszu602y4I6sCejAp1GYYyzDbtV6mFdpZvibNqc/ZXhndsCsHq3VOoWQgjRtCRRaq1s7nhL1HcCYHDHEAJ9PBwQUB0ExUL0QOu2hFXc3C8KgK92p0mlbiGEEE1KEqXWyuaOty35kQDc4Mi13erCdlL34e+4pnMgfp460nKK2ZmcXfN5QgghRANIotQaVZRWm8i9IScSrUbhmu7OnijdDFSpwl2ah1fyJq7raY77Kxl+E0II0YQkUWqNzh4EU7lV0wE1lstigwj2ddJht0oBkRA72LotYRV/uTD89v2+05SUGx0QmBBCCHckiVJrZDM/KdMjmgJ86Nsu0CHh1JvtpO4jPzAoxpsIgxd5JRVsPnLWMXEJIYRwO5IotUY2hSYP0h6A3lGBLR9LQ3S/GZQq/3TLC9EcX8dNfc3zrGT4TQghRFNxukQpPz+fOXPm0KtXL/z8/DAYDAwcOJD58+dTVlbWpK/14IMPoigKiqIQFxfXpNd2ajYTubcXm2sm9Y42OCKa+vNrC/HDrNsSvrQMv/10+Cw5RU37b0UIIUTr5FSJUnJyMr1792bu3LkkJCSgqiqlpaXs3LmTJ554gkGDBllVf22MTZs28f777zfJtVxKRRlkHLBq2muMI9BHT3SQt4OCaoCeE623T2yia4gX3SICKDeqfH9hzTohhBCiMZwmUaqoqGDcuHEkJSURERHB+vXrKSwspKioiKVLl+Lv78/u3buZNm1ao1+rqKiI++67D51Ox2WXXdYE0buQc4fAaN3bcsAUR68oA4qi2DnJCXW+znq7rABSfuUv/czDb1J8UgghRFNwmkRp8eLF7N+/H4Avv/yS0aNHA6DRaJgyZQr//e9/AVizZg0bN25s1Gs988wznDhxgqeeeooePXo0LnBXYzPslukRRR6+rjPsVsmvLUT2s247vp6b+kShKPBHUjapWUWOiU0IIYTbcKpECWDkyJFceeWV1fZPnTqV+HjzoqeffPJJg19nx44d/Pvf/6Zz5848++yzDb6Oy7K54+2Qav5Me7nKRO6qOl5jvX1sA+EGL4Z0CAGkV0kIIUTjOUWiVFRUxLZt2wC47rrrajxGURTGjh0LwLp16xr0OqWlpdx9992oqsr777/fOhfXtLnj7VdXm8hdVSebROncIcg9dXFJkz1pyJrPQgghGsMpEqVDhw5hMpkA6Nmzp93jKvelp6eTlZVV79f55z//yaFDh7jnnnsYPnx4w4J1ZcZySE+watpriiPEz5MIgwsmjVEDwDvIuu3Yesb2DMdLr+HkuUL2ncp1TGxCCCHcglMkSqdPn7Y8j4qKsntc1X1Vz6mL3bt389prrxEWFsbrr79e/yAvKC0tJS8vz+rhMs4dAWOpVdMBUxy9o11sIncljRY6XG3ddmw9fp46xnSXJU1E81iwYAFz5sxhwYIFjg5FCNECnCJRys/Ptzz38fGxe1zVfVXPuZSKigruvvtuKioq+Pe//01gYGCD4gR45ZVXMBgMlkdMTEyDr9XibIbdzuvDycGfXlEuOOxWyXaeUuLPUFFmqan07d7TlBtNDghMuKsFCxYwd+5cSZSEaCWcIlFqbq+++ip79uzhxhtv5JZbbmnUtZ5++mlyc3Mtj9TU1CaKsgXY3PF2UL1QkdsV5ydV6jjaevtCmYChnUJo4+vB+cIyfjmW6ZjYhBBCuDynSJT8/f0tz4uK7N/SXXVf1XNqc/DgQV588UX8/Px45513Gh7kBZ6engQEBFg9XIbNHW+/lUQDuHaPkp0yATqthnF9ZEkTIRrqzjvvRFEU7rzzTkeHIoRDOUWiFBkZaXmelmb/S63qvqrn1Obhhx+mrKyMZ555hqCgIAoKCqweFRUVAKiqamkrLy9v4DtxYsYKSN9v1bTPFE94gBehAS44kbuqGsoEAJbht3UH0ykorWjpqIQQNlavXs2cOXNYvXq1o0MRos6cIlHq1q0bGo05lISEBLvHVe4LDw8nODi4TtdOTEwEzENm/v7+1R5LliwBICUlxdL29ttvN+btOKfzx6Ci2KopwRRPL1cedqtkp0xA72gD7dv6UlJuYm1CumNiE0JYrF69mrlz50qiJFyKUyRKPj4+DBkyBIC1a9fWeIyqqvz4448AjBkzpsVicxs2w27ZulCyCKC3Kw+7VbJTJkBRFP7S19yrJMUnhRBCNIRTJEoA06dPB8yL1f7222/V9q9YsYKTJ08CcMcdd9T5uklJSaiqavdR+bqxsbGWtpkzZzb+DTkbm4ncB7hQkdsdepRqKhNw3Dz8Vll8ctuJTDILSm3PFKJejEYjpaXmf0elpaUYjUYHRySEaG5OlSj16tULVVWZOHGiZT03k8nEihUruO+++wBz5e5Ro0ZZnTtnzhwURUFRFJKSklo6dNdgUxpgR3E7wMUncldlO0/p5GaoKCMm2IdeUQZUFTYczHBIaMI9rFq1iri4ODIzzXdRZmZmEhcXx6pVqxwcWcMtWbKEIUOG4O/vj8Fg4IorruD999+vtaJ9eno6//nPfxg/fjzdunXDYDDg7e1Nx44duffeezlw4EC1czZv3oyiKJalqhYvXmz5mV352Lx5c6NeQ4jmonN0AJV0Oh3ffPMNI0eOJCkpidGjR+Pj44PJZKKkpASAfv36WeYUiXowGeHMPqumBDWOqEBv2vh5OiioJtbROnmmrABSd0D8MMb2DGd/Wi5rD6Qz9fJ2jolPuLRVq1YxadKkaglEWloakyZNYuXKlUyYMMFB0dWfqqrcc889fPTRR4B5iajAwEB27tzJ77//zqZNm/D0rPlnw9///ndLwqPT6QgICKCoqIgTJ05w4sQJPvvsM5YsWcLEiRMt53h4eBAWFkZubi4lJSV4eXlhMFj/kubh4dGo1xCiuThNjxJAXFwc+/bt4/nnn6dnz54oioJer2fAgAHMmzePHTt2EBQUdOkLCWvnT0B5oVVTgqm9a9dPsuUXChF9rduOrQfg2h5hAGw/fp78Eje8o1E0K6PRyIwZM2rsZalsmzlzpksNw/3nP/+xJEmPPPIIZ8+eJSsri6ysLObMmcOyZcv4+uuvazy3Y8eOvP766+zfv5/i4mLOnz9PaWkpCQkJ3H777ZSWljJ9+nSr1RMGDx5Meno6U6ZMAWDKlCmkp6dbPQYPHtyo1xCi2aiiUXJzc1VAzc3NdXQo9u1dpqovBFgeWS+2V2P/7zv17U3HHB1Z09r4otX7VN8eZNk1ct4mNfb/vlO/3pNmdcr8+fPVF154QZ0/f35LRyvqobi4WD148KBaXFzc4q+9adMmFbjkY9OmTS0eW0MUFxerwcHBKqD+9a9/rfGYv//975b3NX369Hpd/4YbblAB9cUXX6y2b/r06Q26Zn1eQ7RODfkZUdfvb6fqURLNxOaOt4OqeSJ376jAlo+lOdnOUzp7EHJPAXBtD/Pabz8esC4TIMtRiEs5c+ZMkx7naOvWrbMsKv7888/XeMzf//53vLwaVl/thhtuAOCXX35pWIBO8hpCVJJEqTWwuePt9xI3m8hdKfoy8Aq0brMMv5kTpc2Hz1JS7jpDJMLxIiIimvQ4R9u5cycAMTExdOzYscZjDAYDAwYMsHuNvXv38re//Y3evXsTEBCARqOxTMr+29/+BsCpU6caFWdLvIYQdeE0k7lFMzGZqiVK+9V4Ytv4YPDROyioZlJZJuBAlbuQjm+Ay+6id5SB8AAv0vNK2HY8k1HdwhwXp3ApQ4cOJTo6mrS0tBrnKSmKQnR0NEOHDnVAdPV39uxZAKKiomo9Ljo6usb2t956ixkzZmAymRebVhQFg8FgmfxdXFxMXl4ehYWFNZ5fFy3xGkLUlfQoubusk1CWb9WUYIp3v96kSrZVui+UCdBoFMukbtvhNyFqo9VqefPNNwHzF3ZVldsLFy5Eq9W2eGwt7dChQ8ycOROTycTkyZP5/fffKSkpITs72zIpu3IYu6ak0lleQ4j6kETJ3dnUT8rVBnOWIPe6462qjqOttyvLBHBx+G3DobNUGE0tHZlwYRMmTGDlypXVemGio6NdrjRAaGgoUPu6mvb2r1y5EqPRSLdu3Vi6dCkDBw60uq0fzDWQGqMlXkOI+pBEyd3ZJEoJFyZy93K3idyV/EIhoo9124V5SpfHBxPooyersIydydkOCE64sgkTJpCUlERISAgAISEhJCYmulSSBHDZZZcBkJqayokTJ2o8Ji8vj127dlVrT01NBaBPnz6W9Tltbdiwwe5rV55TW09QY19DiKYmiZK7s7njbWeZeSJ3z6gABwTTQmzvfruwnIlOq2FUVxl+Ew2n1Wot82Q8PT1dcrjtmmuusdSje/HFF2s85rXXXqO4uLhae2WRyP3799eY7Pzwww9WFbZtBQSYf+7k5OTYPaaxryFEU5NEyZ2pavWK3KZ42rf1xd/LzSZyV2U7T8mqTIA5UVp3IEPmN4hWydvbm+eeew4wLyUyc+ZMzp8/D5h7kl588UVefvllAgMDq507duxYAA4cOMDDDz9sKTNQWFjIf//7XyZNmkSbNm3svnbPnj0B2Lp1K4cPH67xmMa+hhBNTRIld5adCKW5Vk37TfH0dteJ3JWiLgMvm/d4oVdpWOe2eOu1pOUUk5CW54DghHC8GTNm8Ne//hWAN998k9DQUIKDgwkODub5559nypQpjB8/vtp5o0aNYurUqQC8++67tGnThqCgIAwGAw8++CDdunVjzpw5dl934sSJtG3bluzsbLp160bbtm2Ji4sjLi6OHTt2NMlrCNHUJFFyZzbDbnmaQNIJpld0oEPCaTFaHXSwWfvtwjwlL72WEV3aAjL8JlovjUbDJ598wieffMKgQYPw9vamoqKC/v3789577/H555/bPXfJkiUsXLiQ3r174+npidFopFevXrzyyits27YNPz8/u+cGBQWxZcsWpk6dSlRUFLm5uSQnJ5OcnGxZ07OxryFEU1NUGX9olLy8PAwGA7m5uZbxd6ex8Z+wdb5lc7vSj9uKn2TFg1cyMC7YgYG1gD2fw+qHLm57+MNTJ0HnwerdacxctodOoX4cWnA7aWlpREVFSfE6J1ZSUkJiYiLx8fENrhjdVCprKsm/GSGcR0N+RtT1+1t6lNxZ1kmrzYTySDQK9Ih0soSuOVQrE5APqb8BMLJrKDqNwrGzBRAghSeFEELYJ4mSO8tOstpMUUPpFOqPj0crKMheU5mA4+bhN4O3nis7mCeDKjF9WzgwIYQQrqQVfGO2YjaJUrIaRi93LTRZk47XWC/fcmwDXPNPwFx8cuuxTDQx/RwUnHBVs2fPJi8vz/mG2oUQzUISJXdVnAPF1kUVU9RQrmlNiVKna2DrvIvbZw9A3hkIiGBM9zCe+zoBQuLR+smtxqLuZs+e7egQhBAtSIbe3JVNb5IRDafVEPdd460mUZeBp81v/Yk/AxAa4EX/duaie96dBrV0ZEIIIVyEJEruyiZROm1qg6rR0y2iFQ0XaHUQZ7Oi+8mfLU8ri0/6dL6yJaMSQgjhQiRRclfZiVabKWooncP88dK73pILjdJ+hPX2yc3miuXA6K5tKUnZh7Ewm1KjgtFobPHwhBBCODdJlNxVDXe89W5N85Mq2SZK+ach8xirVq1i+IAeZHzxD85/N5/M9FPExcWxatUqh4QphBDCOUmi5K6qJUqt7I63SiGdwD/SqmnVhwuYNGlStWKBaWlpTJo0SZIlJyb1cYUQNWnOnw2SKLmrrOpDb72jAh0TiyMpilWvktGkMuP1T2r8T1XZNnPmTBmGczIajflHlfy9CCFqUvmzofJnRVOSRMkdGcsh17q35IwmjM7hrXR9pCqJ0tYUI6eyiu0eqqoqqampbN26tQUCE3Wl1+vR6/UUFBQ4OhQhhBPKz8+3/JxoapIouaPcU6Ba/+btFdoBT10rm8hdKX6Y5emZ/Lp1z545c6a5ohENoCgK/v7+5ObmUlxsP9EVQrQ+xcXF5OXl4e/vj6IoTX59KTjpjmzueMtVfYiNjnZQME4gIALadoVzh4nwr9t/ooiIiGYOStRXSEgIxcXFpKSkEBAQgL+/P1qttll+MAohnJuqqhiNRvLz88nLy8PT05OQkJBmeS1JlNxRDXe8dWjr65hYnEX7EXDuMEPbaYkOUEjLU6mxb0lRiImOZujQoTXtFQ6k1WqJiYkhMzOT/Px8cnJyHB2SEMLB9Ho9gYGBhISEoNU2z6iJJEruqIZEKT5EEiV+ew+tRuHNsV5MWl6MoijVJ3WrsHDhwmb7DycaR6vVEhYWRmhoKOXl5ZhMJkeHJIRwEI1Gg16vb/ZeZUmU3FG1O97CuKZNK0+UYoeAogXVyIRuelbeAjO2+HIqPdNyiNY/hE7jH+Evf/mLAwMVdaEoCh4eHo4OQwjRCshkbndk06OUqobSLtjHMbE4C68AiL7Msjmhm56k/91nGdMOCQ0n/pGPKI66jKMZcmeVEEIIM0mU3I2qVkuUivxi8NDJX7VtlW5t8hY8PT0B8NRruapTKAAbDmW0dGRCCCGclHx7upvibCjNs2rSBMc7KBgnY7ucSfp+gr0uznEZ1c28SK4kSkIIISpJouRubEoDVKgaAsLiHBOLs4m6DPTWc7UGR1ysNzWqm7lHaU9qDpkFpS0amhBCCOckiZK7sRl2S1NDiAlphWu81UTnAbGDrZqGRl1MlCIM3vSMCkBV4afDZ1s6OiGEEE5IEiV3Y5MoJathxIe08oncVdkMv10VWWG1Paqrefhtowy/CSGEQBIl92NTGiBVDSWutZcGqMomUYoNUIkPvFiDY/SFeUpbjmZSUi4LsAohRGsniZK7selROkUoMa29NEBVod3Bt61V0+j2F8uJ9YwKICzAk+JyI7+ePN/S0QkhhHAykii5m+xkq80C3xj0WvlrttBoIH64VVPVRElRFMvdbzL8JoQQQr5B3UlFGeSdsm4LktIA1dgMv10dr0WpsvLb6At3v/106Gz1JU6EEEK0KpIouZPcVFCt177yDm3voGCcmE2iFOKjoXubi5/b4A4heOk1nM4t4eCZPIQQQrRekii5E5saSlmqHxFhYQ4KxokFxkBwB6umoZEXJ2576bUM7WSex7ThoJQJEEKI1kwSJXdSbTHcUOJC5I63GrW3nqd0VZR1mYDK4beNh2WekhBCtGaSKLmTGhbDjZfSADWzGX67ItwI5SWW7ZFdzYnSvlO5ZOSVIIQQonWSRMmd2CZKhBMd5O2YWJxd3FDgYv0kbx1w6nfLdqi/F31iAgGp0i2EEK2ZJEruxCZRKvSJRielAWrmEwyRfa3bTm622hx9oVdJygQIIUTrJd+i7kJVqyVKxsBYx8TiKmyG36olSt3NE+G3HsukuEyqdAshRGskiZK7KDoPZQVWTZ5tO9g5WADVE6XTu6E4x7LZNdyfqEBvSitMbDue2aKhCSGEcA6SKLkLmzveylQtbSLiHBOLq4gZRAUXq3KjmiDpF8umuUq33P0mhBCtmSRK7sJ2jTe1LbFtAxwTi6vQe6Frf5V1m83w28XlTM5iMkmVbiGEaG0kUXIXNolSihompQHqwmbdN9tEaVD7YHw9tJzNLyXhdG7LxSWEEMIpSKLkLmyqcp8ilMhALwcF40Js5ymdPwa5F9fL89RpGda5skq3DL8JIURrI4mSu7DpUcr3ltIAdRLRB7wCrdtO/my1WTn8tuGQ1FMSQojWRr5J3YVNolRhiHNIGC5Ho4X4YdZtidaJ0sgubVEUOHgmj9M5xS0YnBBCCEeTRMkdlJdA3mmrJn1IewcF44JqqqekXpy43cbPkwHtggDYKFW6hRCiVZFEyR3kpADWd2QZIqWGUp3ZJkoFGXDusFXTxbvfZJ6SEEK0JpIouQObYbdMNYDo8FDHxOKKgtuDIca6zbZK94V6StuPn6ewtKKFAhNCCOFokii5A5s73lLUUOKkNEDdKQq0ty0TYD1PqWOoH+2CfSgzmth6TKp0CyFEayGJkjuwLTZJGJGB3o6JxVXFj7DeTvoFjOWWTUVRGC3Db0II0epIouQObBKlXK8otBrFMbG4KtsepbJ8SPvTqml0d/Pw20+Hz2KUKt1CCNEqSKLkDmzWeSsPiHVQIC7MLxRCe1i32ZQJGBgXjL+XjvOFZexJzW7B4IQQQjiKJEquTlWr9Sjp2sQ7JhZXV22e0marTb1Ww8gu5l4lKT4phBCtgyRKrq7gLFRYF0H0i+jooGBcnG2ZgNTfobTAqml09wtVumU5EyGEaBUkUXJ1Nne8lap6QiOlR6lBYgeDRndx21QOKb9aHTK8c1t0GoVjZwtIyixs4QCFEEK0NEmUXJ3NsFuq2pa4tn6OicXVefpD9EDrNpvhN4O3nsvjgwHYIHe/CSGE25NEydXVVBrAIKUBGiy+9npKQJUyATJPSQgh3J0kSq7O5o63bK8oNFIaoOFs5yll7IeCc1ZNlYnS70lZ5BaVI4QQwn1JouTqbHqUSv3bOSYOdxF9GXjYDF0mbbHabNfGh85hfhhNKpuPSq+SEEK4M0mUXJ1NoqQJinNIGG5DqzdP6q7KZp4SXOxVWi93vwkhhFuTRMmVlRVBQbpVk0+4lAZoNNvhtxObzfWqqqgsE/Dz0XOUVZhaJi4hhBAtThIlV5aTXK0pJLqzAwJxM7aJUm5KtTIMfaMDCfHzIL+kgj+SslouNiGEEC1KEiVXZjPsdlYNpF14iGNicSeh3cG3rXWbzd1vGo3C1V3NVbpl+E0IIdyXJEquzOaOt1TCCA/wclAwbkRRaigTsLnaYZYyAYczUFVZJFcIIdyRJEquzKZHKdsjUkoDNBXb4bfEn8FkPRfpqk4heOo0pGYVczTDeqkTIYQQ7kESJVdmkygV+8Y4Jg53ZJsoFWdD+j6rJh8PHVd1NA91SpVuIYRwT06XKOXn5zNnzhx69eqFn58fBoOBgQMHMn/+fMrKyhp0zbS0NN555x0mT55Mx44d8fb2xtvbm/j4eG699VZ++umnJn4XLcRmgjHBssZbkwmMgeD21m2J1at0j5IyAUII4dZ0lz6k5SQnJzNixAiSkpIA8PHxobS0lJ07d7Jz506WLFnCxo0bCQoKqvM1U1NTiY2NtZpD4uPjg6qqJCUlkZSUxNKlS7n77rt5//330Wq1Tf22mofJBNnWd715hXZwUDBuqv0IyDp5cfvkZhgyw+qQUd1C4SvYeyqHs/klhPrLHDEhhHAnTtOjVFFRwbhx40hKSiIiIoL169dTWFhIUVERS5cuxd/fn927dzNt2rR6XddoNKKqKqNGjWLx4sWkpaVRWFhIQUEBBw4cYPz48QD873//Y86cOc3wzppJQToYS62agqKkNECTsh1+S/4VKqw/87AAL/pEG1BV2HRYqnQLIYS7cZpEafHixezfvx+AL7/8ktGjRwOg0WiYMmUK//3vfwFYs2YNGzdurPN1g4KC2LVrFxs2bOCOO+4gMjLSct3u3bvz1VdfMXbsWAAWLlxISUlJU76t5mM7P0n1IDomziGhuK24oUCVyfEVxZD6e7XDLlbplkRJCCHcjVMlSgAjR47kyiuvrLZ/6tSpxMeb5+B88skndb6uwWCgf//+dvcrisLdd98NQEFBAYcOHapP2I5TrTRAKKFSGqBp+QRDRB/rthrKBFTOU/rl+DlKyo0tEJgQQoiW4hSJUlFREdu2bQPguuuuq/EYRVEsPT/r1q1r0tf38rqYYBiNLvJFZ9OjlKWX0gDNwnb4rYZEqVuEP1GB3pSUm9h2PLNFwhJCCNEynCJROnToEKYLNWp69uxp97jKfenp6WRlNd2yEZs3bwbAw8ODzp1dZJ6PTaJUKKUBmkd7m8KTp/+E4hyrJkVRGN3NXKVbygQIIYR7cYpE6fTp05bnUVFRdo+ruq/qOY2RmJjIe++9B8CUKVMICAio9fjS0lLy8vKsHg6Rm2q1aQqMdUwc7q7dlaD1vLitmiB5W7XDKoffNhw6i8kkVbqFEMJdOEWilJ+fb3nu4+Nj97iq+6qe01DFxcVMnjyZoqIiQkJCePXVVy95ziuvvILBYLA8YmIc1JOTf8Zq07uN9Cg1C703tLvCuq2G4bcr2gfj56njXH4p+9NyWyY2IYQQzc4pEiVHqKio4LbbbmPXrl3o9XqWLFliuSOuNk8//TS5ubmWR2pq6iXPaXKqCvnpVk1BYZIoNZs6zFPy1GkZ3tm8kK4MvwkhhPtwikTJ39/f8ryoqMjucVX3VT2nvoxGI7fffjurV69Gp9Px+eefM2bMmDqd6+npSUBAgNWjxZXkQIV1GYPQqLiWj6O1iB9hvZ15FPKqD/2O7m6epyRVuoUQwn04RaJUtScnLS3N7nFV99Wl96cmRqORadOmsXz5crRaLZ999hmTJk1q0LUcxqY3CSBEepSaT2Rf8DRYt9XQqzSicygaBQ6n53Mq237CL4QQwnU4RaLUrVs3NBpzKAkJCXaPq9wXHh5OcHBwvV+nsidp6dKlliRpypQpDQvakWzmJ+UqASh6qaHUbDRaiB9q3Xa8etHTIF8PLosz/7vcIL1KQgjhFpwiUfLx8WHIkCEArF27tsZjVFXlxx9/BKjzMFlVRqOR2267jWXLllmSpKlTpzY8aEfKt/4SzteHOCiQVqTjKOvtEz+BqXrNrWsqq3TLPCUhhHALTpEoAUyfPh2ATZs28dtvv1Xbv2LFCk6eNC9Qescdd9Tr2pU9ScuXL0en07FkyRLXTZKgWo9SmXeogwJpRTrYJErFWXBmT7XDru0RDsCOk1lkF5a1QGBCCCGak1MlSr169UJVVSZOnGhZz81kMrFixQruu+8+wFy5e9Qo6y+tOXPmoCgKiqKQlJRkta9yTtKyZcssE7ddcritKts5Sv7hjomjNQmKhTadrNuO/1TtsHZtfOgeEYDRpEqvkhBCuAGnSZR0Oh3ffPMNcXFxpKWlMXr0aHx9ffH19eWWW24hLy+Pfv36sWTJknpdd9u2bSxduhQwV1B+9NFHCQ8Pt/tYtmxZc7y9pmXTo6QzNGxiu6gn2+G34xtqPGxsT3Pi+mNC9Un3QgghXIvTJEoAcXFx7Nu3j+eff56ePXuiKAp6vZ4BAwYwb948duzYQVBQUL2uWbk0CkB5eTkZGRm1PoqLi5v6bTU9mx4lrzb2q5mLJtRxtPX2qT+qLWcCFxOlrccyKSitaIHAhBBCNBdFVVVZb6ER8vLyMBgM5ObmtlxNpYW9ICfFslk88RO8e41vmdduzcqK4F9xYCy92HbLJ9Dd+rNXVZVR83/mZGYh/7m1H+P6SI+fEEI4m7p+fztVj5KogxqqcnsHSY9Si/DwgdjB1m01DL8pisK1F3qV1h6Q4TchhHBlkii5muJsMNrcTSWTuVuO7fDb8Z/MyauNsRfuftt0+Cwl5dXLCAghhHANkii5GpuJ3AD4hbV8HK2V7YTuvFNw7ki1w3pHG4gweFFUZuSXY5ktFJwQQoimJomSq7FJlPJ1QaDVOyiYVqhtVwiwGeo8Ub1Kt6IolppKMvwmhBCuSxIlV2MzP6nYs62DAmmlFKXeZQI2HMqg3Giq8RghhBDOTRIlV2OTKBl9ZNitxdlW6U7aZr4jzsbAuGDa+HqQU1TO74lZLRScEEKIpiSJkquxrcodIBO5W1z7EaBoL24bSyF5e7XDtBqFa7qbE9m1UnxSCCFckiRKrsZmjpJHoNToaXHegRB9mXXbpap0H0jHZJKSZUII4WokUXI1Nj1KviExDgqklbMtE1DDhG6AwR1C8PfUcTa/lN2pOc0flxBCiCYliZKrsV2+RIpNOobthO7Mo1bV0it56DSM6hYKmHuVhBBCuBZJlFyJyQQFNivS+8tkboeI6AvewdZtx2vuVaocflubkI6sGCSEEK5FEiVXUpwFpnLrNv8Ix8TS2mm00OFq6zY785SGdW6Ll15DSlYRh87kt0BwQgghmookSq7EZiK3CQV8Qx0UjKg2/HbyZzCWVzvMx0PH8M7meldSfFIIIVyLJEquxLbYpD4YtDoHBSOq9SiV5cOpP2o81HL3m5QJEEIIlyKJkiux6VEq9ZbeJIfyD4fwXtZtdobfru4ahk6jcCQjn5PnClogOCGEEE1BEiVXYtOjpPpJsUmHs63SbWdCt8Fbz+COIYAMvwkhhCuRRMmV2CRKWoNM5HY423pKZ/ZAwbkaDx3bQ4bfhBDC1Uii5EpsEiXvYKmh5HAxV4CHn3XbyU01HnpN9zAUBfaeyiUtp7gFghNCCNFYkii5Eps5Sp5SbNLxdB4QP8y6zc48pbb+ngyMNddeWifDb6KZLFiwgDlz5rBgwQJHhyKEW5BEyZXYLogrNZScg22ZgOMbzcVBa3BtleKTQjSHBQsWMHfuXEmUhGgikii5CpOxhqrcMpnbKdhO6C7KhPR9NR56bQ9zJfU/krLILCht7siEEEI0kiRKrqLoPKhG6zZJlJxDcDwEd7BuszP8Fh3kQ68oAyYVNhzMqPEYIYQQzkMSJVdRrSq3BnzbOigYUY3t8NuJn+weWll88gcZfhNCCKcniZKrsJmfVOIZYl5vTDgH2zIBqb9BSV6Nh153IVH65Xgm52X4TQghnJokSq7CpkepwjfMQYGIGsVdBVqPi9umCkjcUuOh7dv60SvKgNGksmb/mRqPEUII4RwkUXIVNj1KSoDc8eZUPHyh3ZXWbcfW2T18fN9IAL7ec7o5oxJCCNFIkii5CpseJY9ASZScju3w29G1dssEjOsTiaLAzuRsUrOKWiA4IYQQDSGJkqvIt75DyiMw0kGBCLu63mC9XZABabtqPDQswIsr27cB4Ju90qskhBDOShIlV2HTo6RIsUnn06YDtO1q3Xb4O7uH39zXXFn9Gxl+E0IIpyWJkquQqtyuocv11tuHv7d76LU9w/HQajiSkc+hMzXfISeEEMKxJFFyBcYKKDxr3SbFJp1T1xutt88fg3NHazzU4K3n6q6hgEzqFkIIZyWJkisoPAeqzaRgSZScU2S/6r19R+z3KlXe/fbNnjRMJrU5IxNCCNEAkii5ggLrYTeTogWfEAcFI2ql0UCX66zbahl+G9k1FH9PHadzS9iZnN3MwQkhhKgvSZRcgc38pDKvtuYvZOGcbO9+O7Wz+hyzC7z0WsuSJl/vSWvuyIQQQtSTfNu6Aps73lQZdnNuccPAM6BKgwpHfrB7+PgLd799v/8MZRU1110SQgjhGJIouQKb3gidQWooOTWdR/Xik7UMv13ZoQ1t/T3JKSpn67FzzRycEEKI+pBEyRXY9CjpDFIawOnZDr8l/gyl+TUeqtUojOstS5qIxjMajZSWmhdaLi0txWg0OjgiIVyfJEquwHadN6mh5Pw6XQMa/cVtYxkc32D38Mq739YfzKCwtKK5oxNuaNWqVcTFxZGZmQlAZmYmcXFxrFq1ysGRCeHaJFFyBdWKTcocJafnZYD4YdZttQy/9Y42ENfGh+JyI+sPZtg9ToiarFq1ikmTJnHq1Cmr9rS0NCZNmiTJkhCNIImSK5Cq3K6pq02V7qPrwFhe46GKolgmda+Wu99EPRiNRmbMmIGqVq/DVdk2c+ZMGYYTooEkUXJ2xnJzwcmqpEfJNdguZ1KaC0m/2D28cvht67FMzheUNmdkwo1s3bq1Wk9SVaqqkpqaytatW1swKiHchyRKzq7gLGDzm6IkSq4hIBKiBli31TL81r6tH72jDRhNKmv2n7F7nBBVnTlTt38rdT1OCGFNEiVnZzPsZtLowTvYQcGIeqtpkdwahkgq3dTH3Ku0Wu5+E3UUEVG3ofi6HieEsCaJkrOzWb6kwidUqnK7EttFcvNPw+nddg8f1ycSRYFdydmkZhU1c3DCHQwdOpTo6GgURalxv6IoxMTEMHTo0BaOTAj3IN+4zs6mhpJGJnK7lrZdILiDdduRNXYPDwvwYnCHNgB8s1d6lcSlabVa3nzzTYBqyVLl9sKFC9FqtS0emxDuQBIlZ2cz9KYNlETJpShK9bvfapmnBDC+z4W733an1XgnkxC2JkyYwMqVK4mKirJqj46OZuXKlUyYMMFBkQnh+iRRcnY2PUqKn0zkdjm2w29nD0LWSbuHX9szHA+thmNnCzicXnM1b9EyFixYwJw5c1iwYIGjQ7mkCRMmkJSUREhICAAhISEkJiZKkiREI0mi5Oyk2KTrix4Ivm2t2w7bH34zeOu5umsoIDWVHG3BggXMnTvXJRIlMA/DeXp6AuDp6SnDbUI0AUmUnJ0Um3R9Gi10Hmvddqnhtws1lb7dcxqjSYbfhBDCUSRRcnbSo+QebIffUndAwbmajwVGdg0lwEvH6dwSthyzf5wQQojmJYmSM6sog6JM6zbpUXJN7YeD3vfitmqCo2vtHu6l1zJpQAwAn/+W0tzRCSGEsEMSJWdWUMPiqNKj5Jr03tBxlHVbLWUCAG67wpwobTyUwZnc4uaKTAghRC0kUXJm1apye4B3kIOCEY3W9Qbr7RM/QVmh3cM7hvpzRXwwJhWW/p7azMEJIdydK93F6UwkUXJmNqUBVP9wc10e4Zo6jQGlyl1IFSXmZKkWtw+KBWDpHylUGE3NGZ0Qws252l2czkISJWdmM/SmCZD5SS7NJxjihli3XeLut2t7hNHG14OMvFI2Hj7bjMEJIYSoiSRKzsy22KTMT3J9XWyG3w5/D+X25x956rRMvkwmdQshhKNIouTMbEsDSFVu19dtHFBl+LQ0D478UOspt15uTpS2HDtHynlZKFe4H5k7I5yZJErOzKZHSe54cwOGKIi3WcV979JaT4lt48vQTiGoKnzxh/QqCfcjc2eEM5NEyZlJVW731OdW6+3jG2otPglw+xXmSd3L/0ilrEImdQshREuRRMmZSY+Se+o2DnTeF7dVIySsrPWUUd1CCQvw5HxhGT8eSK/1WCFE85PhwtZDEiVnVVEKxdnWbdKj5B48/S/MVariEsNveq2GKQPbAbDkt+TmikwIUUcyXNh6SKLkrGyH3UB6lNxJnynW22f2wNnDtZ4ydWAMGgV2nMxi5vOvyg9oIYRoAZIoOSubREnVeYGXwUHBiCYXPwL8wqzb9tXeqxQZ6M3VXUMB+GTbCUmUhBCiBegcHYCwo6b5SVKV231oddBrMvz61sW2fcvh6udBY//3l9uviGXDobP49hyFenxDCwQqXM3s2bPJy8sjICDA0aEI4RYkUXJWNj1KisxPcj99plonSnlpkLQV2g+3e8qwzm1RCzLR+oVgbDegBYJsvYxGI6WlpQCUlpZiNBrRarWXOMvxZs+e7egQhHArkig5qwLb0gAyP8nthPeCsJ6QkXCxbd+yWhMlrUbBdPwXtH1vRtN5WAsE2TqtWrWKGTNmkJmZCUBmZiZxcXG8+eabTJgwwcHROUhpAeQkQ+4pKCuA8hKoKLb+s7zY/LyiFDRa0PuChy94+ICHH+h9Lmz7mp97B0JAFKA6+t0JYZckSs5Kaii1Dr2nwPoqidLBr+H6eeYvFjvUE9tQe92I0rYDh87k0S1Chlia0qpVq5g0aRKqav3lnZaWxqRJk1i5cqV7JkuqCnmnITvJ5pFo/rOw9lpfjXH8TjiV50dmaRF8ea/5511AFAREQEA0tGkP3kHN9vpC1EYSJWdlO0fJduKvcA+9JsOGF0C9UESyrMC8/lvvyfbPKc6j6NgOfLtexee/pfDizT1bJtZWwGg0MmPGjGpJEoCqqiiKwsyZMxk/frxLDMPVymSCswcgaRskb4Pk7VCU6ZBQvHTQMVhDR4ywf0XNB/mEQEgnaNPxwp8XngfHg1bfsgGLVkUSJWclPUqtQ0AEtB8BJ3662LZvae2JElCw5wd8u17FV7vT+Pt1XfH1lP/KTWHr1q2cOnXK7n5VVUlNTWXr1q2MGDGi5QJrCsYKSN9rToiStkHKdijJdXRUdVeUCSmZkPKrVbMJLbleUZz37UCWXydy/DuR49+ZIt8YtDodOo2CVqOg0yj4eeoI8NYT4KXH4KMnwEuHr4cOjUZulBH2yU9XZyVVuVuPPrdaJ0onfjInyrX8nZck70PNy6AgIIxv9p7m1svbtUCg7u/MmTOXPqgexzlceTEcWQP7V0LiVijLb/w1/cLMw2A6L9B7X/xT722uOK/3MreZKqCs0PwoL7r4/MK2WlYAxTkojZyfpMFIUEkKQSUpcH6Tpb1Q9eSoGsMhUwwJajsOm9pxSI0lH+thbY0C/l56DN56Arx1BPt6EubvSWiAJ2EBXoT6exJ64c+2/p546ly8J1HUmyRKzqi8uPpvetKj5L663mCe9FpeaN5WTeYvtsGP1HKSiunYVrQDJrHkt2RJlJpIRETd/p/V9TiHMJnMvS57vzDPeSvNq9/5Om8Iiqv5Ediu1vlz9pQbTRzLKCDhdC4H0nJJOJ3Hwaw8ystLCSWHcCXrwiO7yvMsIsgiQjmPTqn/+oa+Sin9lOP00xy3aj+thHGIePZWxLLP2I4DpjjOFQeRW1xep+sG+egJN3ijGf4QQRkpKJSwNiGd6CBvooO8MXjrUZywlIur3sXpDCRRckZSlbt18fCF7jeZv9gq7V16iUQJ1JPb8bj8FhLS8tiVnMWA2OBmDtT9DR06lOjoaNLS0mqcp6QoCtHR0QwdOtQB0V1C5nHzsO3eZZCbUvfzguIgdsiFx2DzdiO+6E0mlYNn8tiTmsOB07kkpOVxJD2fMmP1ZEer0aMExLDraA5FmSV4qxpe+sfLeBu88TF44RfojdYT8912mcfg/LELfx43/9mAOVWRagaRZDBKuwMu5AkV3m0pDO5OTkA3Tnt34oSuA8fL2pCeX87Z/BIy8ko5l19KmdFEdlE52UXlaGL6EhDTF4AHP9tlub6fp86SNLUL9iUuxId2wT7EtfElKsgbvbbl6zzLXZyNo6g1/TRwoPz8fObPn8+XX35JYmIiWq2Wzp07M3XqVB599FE8PDwafO2MjAxee+01vvvuO1JSUvD29qZHjx5Mnz6de+65p0G/BeTl5WEwGMjNzW26Am/Jv8JHYy2bqt4H5R+npeCkOzu5GT4Zb9320HYI61Ht0Mov8qioKG5b+D3Ld55iRJe2fHzX5S0Tq5urvOsNsEqWKn8+ONVdb6UF5uRozxeQtrNu54R0NidEsVeZ/zRENTqMzIJSth47x89HzrHlWCZZhWXVjvH30tEjMoCekQZ6RhnoGRVAXBtfdFqN1b/p2uaIVVOcDedPwNlDcPagudRGegIUZzX6PeHhD+E9Ibw3RPRGDe9Fjm8HMopMnMkt4Y4HZ1KgeuIfHkv/oddwKruYzILSWi+p1ShEBnoR18bXkjzFtvEhPsSXmGAfvPRN38Nj7y5Op/z33MLq+v3tVIlScnIyI0aMICkpCQAfHx+r7sJ+/fqxceNGgoLqf5vorl27uPbaazl//jwAfn5+lJSUUFFRAcC1117LN998U+9ErFkSpYRVsPKui9vB7eGx3U1zbeGcTEZ4oyfkn77YNvgxGPNitUOrfqn8sucIV8/fjEmFbx+5il7RssxNU6j8Dbzql3ZMTAwLFy50ji+Vkjz4YxFsf6sOSYEC8cPMBU47jga/0Ea/fIXRxO7UHH4+co6fj55jf5r1VAE/Tx39Y4PoGRlgTooiDcQEe9v9ZbTBiVJNVBUKMsxJU8ZByDhgfpw7DKa6Da/ZpdFDaDcI780L765gy9EsMjWh7D9h/n9bUm4kLaeYU9nFpGQVkXK+kOTzRaRkFZF0vpCScvtDiIoCkQZv4kLMCVR8iC9xbXyJC/ElJti7QXOjjEYjcXFxdj/Tyh7Syk6J1sblEqWKigr69+/P/v37iYiI4JNPPmH06NGYTCZWrFjBfffdR35+Ptdffz3ff/99va6dm5tL165dSU9Pp2vXrnz66adcdtlllJWVsWjRImbNmkV5eTkPPfQQ77zzTr2u3SyJ0q/vwI9PX9yOHQJ3rWmaawvntf4F2Lbw4rZ/BMw6YC7cV4Xtl8qsZXv4ancaY7qH8f4dl7VszG7MaDQSHh5OZmYmISEhpKenO/7LpDgHfvsv7HgHSnJqP7ZtV3Ny1OuWJuk1Kqsw8dPhDL7Ze5qtxzLJL6mw2t8jMoDhndsyvHNb+scG1XmIqcU+54oyOHcIzuyD9H3mPzMSzCU5Gss/wtz7G9bDXEQ2rIe5fIHu4i/eqqpyLr+UpPNFJF9IoJLOF5ofmUUUlFbYvbxGMa/1WNkDZfkzxNwzZa8navPmzYwcOfKS4W/atMn17uJsAnX9/naaOUqLFy9m//79AHz55ZdceeWVAGg0GqZMmYLJZOK2225jzZo1bNy4kVGjRtX52vPmzSM9PR1vb2/WrFlDfHw8AB4eHjz88MPk5eXxj3/8g/fff5+ZM2fSuXPnpn+D9SF3vLVOfaZaJ0r5ZyDxZ+hwda2nPTyyA6v3pLHuYIYUoGxCWq0WT09PADw9PR2bJBVlwa9vw+/v1z4527etuTZX7ykQ0afRw/WqqrLvVC5f/nmKb/aeJqfoYo9MkI+eoZ3MidHQziGE+nvV+/otOndG52H+TCL6XGwzmSDrpLlsQtUEqr5zn/LPmB9V11/U6CC4A7TtDCFdUNp2ITSkM6FRnbg83no+oaqqnC8sIymzkMTMi8lTYmYhyecLKSwzcirb3FP1y3GqiTB40S7Y5+KjjQ8xwT4cTazbXDWXuYvTQZwqUQIYOXKkJUmqaurUqTzzzDMkJibyySef1CtR+uSTTyzXqEySqnr00Ud5+eWXKSgoYMmSJcydO7eB76KJFGRYb8sdb61DaDfzD/Ezey+27V16yUSpY6g/1/eM4Pv9Z3hr03Hevq1/MwcqWkzBOfj1P/DHh7X3fHQeC5fdAx1GNknxxYy8Er7ancaXu05x7OzF1w0L8OTmflFc1zOCXlEGtI2oP+QUFdA1GgjpaH70nGhuU1Vz0nNmH6Tvv5hE5STX79qmCsg8Yn7wrfU+QztLAkWb9ihBcYQExRMS047L4qonUZkFZSSfL7yQOJl7opLPF5GUWUh+aQVncks4k1vCb4nWw7AlKWl1CtWp7+J0Ak6RKBUVFbFt2zYArrvuuhqPURSFsWPH8u6777Ju3bo6X/vIkSOkpKTUem0/Pz+GDh3KDz/8wLp16xyfKElV7tar91TrROnQt+YJu55+tZ72yNUd+X7/GdbsP8Pxs/l0DPVv5kBFsyorgl8WmOcgVRTbP67bOBj2pHUvSQOVVhj58UAGK3ed4pdj5zBdyF88dRqu7RHOxAHRXNUxpFHJUSWnroCuKBAQaX50uXhTDcU5FxKnfRhP7+fjzz5Dh5FYg4ah7bT1+1xyU8yPqj1QAIoWDNHmauNB8RAcjxIUR1tDDG3bRHFZuyhzcneBqqpkF5WTmFlIapZ5LlRKVhGpFx6nY3qg9Q/BmG+/h0wXEMLcP4x8eOI3ogK9iQz0JuxCDanKR5CPc5Y8aClOkSgdOnQIk8k8ya1nT/vLMVTuS09PJysri+DgS98OnZBwcR2tS137hx9+4ODBg3UNu/lIVe7Wq9ckWPcsqEbzdnmROVnqe2utp3WLCOCa7mGsP5jB25tO8MaUvs0fq2geR3+ENU9Ajr1hEwV6/AWGPVHjXZH1lVtczue/pfC/bYmcy79419bAuCAm9o/m+t4RBHg17RIhLlkB3TsQ4oeyavc5Zsx8lVOnCi27osPa8OaD1zChs2qeOF6f8gxVqUZzz1VOMrC5+n6N/sI6eOZETgmIJDggiuCASAYEh0FMCPjEgFcgaDSUVhj5X9eF/O2ev15Yd7h6Yhp09f0kni8h8XyJ3bA8tBpLAc6wAE9C/b0I8fOgjZ8nbXyr/umBn6fO7ZIqp0iUTp++eKdPVJT9SYdV950+fbpOiVJ9r52Xl0dBQQF+fjX/Bl9aWmq5C6/y+CZXLVGSOUqthl8odBwFx6r0mu5bakmUaisa99jVnVh/MIOv96Qxc3QnYtv4tnj4ohFyUmHt3+HwdzXvVzTQc5I5QWrbpdEvdya3mI+2JfH5bymWicThAV7cMjCGif2jmvXfj6tWQLc7XHg2i0n/XGYeLpw1wdz7lHkUzh0x321X+TwnhZqSlTozlV/sjaqNogWfYDx9QnjIpw1hs4YxY/EuTp2/OIwaE9aGef94gGEjriajVEdakY7UIh0p+RpOFxhJzy8nI6+ErMIyyowmyxypS/HQaQjx9SDYz4NAb48LFc/NVc8N3nrLI+BCNXR/Lx2+njp8PLT4eOise+ZUFYzlYCw1/3khAWxpTpEo5edfLKvv42O/6mvVfVXPaY5r20uUXnnlleYdmistqD5ZU3qUWpfeU6wTpZM/Q+YxVm3ZX+vE117RBkZ0acvmI+d4Z9MJ/jWpt4PegKgXY7l5ovbP/zL3INpStOaJ/kMfhzYdGv1yRzPyeX/LSb7ek0a50fyl3SXMnweGt2dcn8gWKYjoihXQ6zVc6B0IMZebH1WVFV0olnkhcTp/DLISITuxadfdU41QeM78ACb4w/i/KWxN8eFMvkqEv8LQdmVos96CVW8RDlQbvNXoQeeJGuyJUeOBUdFThgdl6ChRdZQbocx04WE0P8pNoKKgFimYihQ0qGgwocWEVjFZnldtL8dIIRWUKxUUU4EHFeiVC39icyfg40cc0nHgFImSK3n66aeZPXu2ZTsvL4+YmJimewFTBVzxEN9+sYggXQkxgXpi/WWOUqvS9QbwMlT5wamyav4sJv1rzSUnvj56dSc2HznHl3+e4tFRHYkOqv9yE6IFJW2D72ebex1q0m4w3DAfwro36mVUVeWPpGz++/MJNh4+a2kf1D6YB4Z3YETnti06XOKKFdCbZLjQwwcizAUsqynKMidM2UkXk6esJPN2/pmLw/ENpNUojIirx1e+qRzKylHKCtBhThY8aztewVLpvNkYqxcybQlOkSj5+1+ceFpUVMNvVDXsq3pOfa5tr1ZCXa/t6elpuWW4WXgHwnWv8tB9n5GWlmWulbNAJua2KnpvuOxu+OUNAIwmlRnv/FCn32QHxAYxpGMbth0/z3s/n+Clm3u1dPSiLgrOwfrnrJetqconBMa8ZO5JamQC82dKNq/+cJjfL9wRpSgwtkc49w9rT7929S/e2xS0Wi1vvvkmkyZNQlGUGiugL1y40PF1q6po9uFCn2DzI2pA9X0mIxScNRekzat8pFk/L8xsmppQzqyiFSdKkZGRludpaWn07l3zkEFa2sVbHaueU59r20uUKq8dEBBgd9hNiBZz+QPmO55M5WxNMXIqz35FX9vfZB8Z2Yltx8+z/I9TPDKyE+GG+te3Ec3o8Pfw9SN2KmorcNldcPVz5i/NRjh5roDXfzzCDwnmOY8eOg2TBkRz39D2xIc4fv7ahAkTWLlyZbUK6NHR0c5TAb0Khw4XarQQEGF+1JRIVSovgaLz5jpQhZnmXirL80y+WfEZemMJbfw9ubx3VyjNh7J8c6X3RvZYtYjW3KPUrVs3NBoNJpOJhIQEu7fxV97BFh4eXqeJ3GB9p1tCQgLdunWr9drduzeui1uIJhEQAb1vgT1LOJNft8mflb/JDmofzMC4IPNQy5YTvDCu8XdGiSZQVgTrnoGd/6t5f3hvuPENiG5cdfVz+aX8e+MxPv89BaNJRaPApAHRzLqmMxEG70Zdu6lNmDCB8ePHW1XmdtblNFxiuFDvZa7CbqcS+98e+vLCSEUQp97bfnGHqkJFyYXEqcDcc2MshYoqD2Op+ZjKfarJfF7ln1Q+r/JQNOY5dhrtheeaC8+1F59rdKDzBK2HuQaYtspzS/uFh0+blvkcbThFouTj48OQIUPYunUra9eu5cknn6x2jKqq/PjjjwCMGTOmztfu3Lkz7dq1IyUlhbVr1zJ58uRqxxQWFrJ169Z6X1uIZnXlI7BnCRH+dRt6qfxNVlEUHr26E3f873e++D2Fv43oSFv/ZhwuFpeWvh9W3nOh+KANzwBzD9LAe6otV1MfhaUVLNp6kkVbTlJYZu4duLprKP83titdwp13+N6pKqDXwhWHC+tMUcxD/npvoPFrAbqblr/Pzo7p06cD5jVnfvvtt2r7V6xYwcmTJwG444476nxdRVEsxy9dutSy4G5Vb7/9NgUFBWi1Wm6//fYGRC9EMwjrDh1HM7SdlugABXvpkqIoxMTEWP0mO7RTCH1iAikpN/HBLydbJl5RnarCjndh0dU1J0ndxsEjf8AV9zc4SSo3mvh0RzLDX9/Mwg3HKCwz0ifawBf3DeJ/dw506iTJ1VQOF9qWmomOjm6ZSuLCIZwqUerVqxeqqjJx4kQ2btwIYLUoLpira9suXzJnzhwURUFRlBoToSeeeILw8HCKioq44YYb2LVrFwBlZWW8++67PPfccwDcf//9jl/nTYiqBj+GVqPw5ljzPCPbZMneb7KKovDY1R0B+PTXZLILHTO236oVnIUlk821kWznVuh9YNy/4ZZPG3W78/YTmYxduIXnVieQWVBKbBsf3rqtH6sfHsKVHRwzTOHuJkyYQFJSEiEhIQCW4UJJktyXUwy9Aeh0Or755htGjhxJUlISo0ePxsfHB5PJREmJuWJov379WLJkSb2vbTAY+O6777j22ms5ePAgl112Gf7+/pSUlFBebl7kccyYMbzxxhtN+p6EaLT4YRDemwnsY+UtMGNtCafyLnb51zbx9equoXSPCODgmTz+ty2Rx8c0vkihqKNjG2D1g5Y6NlbCe8PED81rfTXQufxSXl5ziK92m29CCfb14LGrO3LbFbF46Jzm91+35SrDhaJpONX/qLi4OPbt28fzzz9Pz549URQFvV7PgAEDmDdvHjt27CAoqGG3sw4YMIADBw4wa9YsOnXqRHl5Ob6+vlx11VUsWrSIH374oXlv+xeiIRQFBj8GwIRuepJm+LFpug+dgpVL/iZrnqtk7lX6eFsSucXlNR4nmlBFGax9GpZMrDlJuvIRuHdDg5Mkk0nlsx3JjJq/ma92p6EoMG1QOzY9PoI7h8RLkiREM1DUmqbvizrLy8vDYDCQm5trt/RAQ1TeXREVFVVrkTPRChjL4c2+kHfx38GXB8uZsT34kv82TCaVsW9u4WhGAfcPa88/rq/5rk9Rs3r9P8zPgOV3QOqO6vv8wuAv70GHqxscS0JaLs+sTmBvag4APSID+H9/6UXfmMAGX9NZuOLPO4nZ9dX1+1t+/XBCNa3nJVoxrR4GPWTV9JduOuID7NdWqqTRKPz9uq4AfPhLIofTm2FtQgGndsL7w2tOkjqPhYe2NzhJKiit4J/fHuSmt35hb2oOfp46XhjXna8fHuIWSZIQzk4SJSezatUq4uLiqq3ntWrVKgdHJhyq/x3m28gv0CgK9/as2wTtq7uGMbZHOEaTyj9W7cdkkk7kupo9ezYvvPCC1bJF1fz5KXx0nXmZiaq0nnD9PLh1KfiG1Pu1VVVlzf4zjJq/mf9tS8Skwg29I9j4+HDuGhKPrgXWZBNCONFkblHLytQ263mJVsgrAAbcCdv/bWma0rncXHG3Dl/CL9zUna3HzvFnSg7LdqZy6+XtmjFY91FrglRRBj8+DX98UH2foR1M/Qwiqi01Wifn8kt5bnUCaw+Yq2rHtvHhxfE9Gda5bYOuJ4RoOPmVxElcamVqgJkzZ8owXGt2xYPmKrYXeOmAPz6s06kRBm9mX7jr7dUfDpNZUNocEbYeBWfhk5tqTpLih8H9mxuUJKmqyjd7TzPmjZ9ZeyAdncZc5uHHmcMkSRLCQSRRchL1WZlatFKGKOg5ybrt9/ehvLhOp0+/MpbuEQHkFpfz8veHmiHAVuLULvjvcEj5tfq+QQ/DtK/At/41jM7ll/LgZ7t47IvdZBeV0z0igG8euYrZY7rgpZfbz4VwFEmUnESzr0wt3MPgR6y3izJh79I6narTanh5Qi8UBVbtTmP7icxmCNDN7f7swnyk09btOi+YsAjGvgza+s1oUFWVr/ekcc0bP/PjgQx0GoWZozvx9SND6B7ZdHfSCiEaRhIlJ+HQlamF6wjvxc+nbHoXfn0LTJe+Aw6gb0wg066IBeDZ1QmUVshQbp2YjLD2H/D1w+YFQasyxMDdP5oXMa6nyl6kGUv3kFOlF2nm6M7oZbK2EE5BJnM7CZdYmVo4hff2ezA8uspw2/njcHQtdL2+Tuc/cW0XfkhI5+S5Qv7780keG9WpmSJ1E6UF8OU95s/YVtxQmPxxve9qq5yL9MI3B8gpKkenMS9k/LeRHSRBEs1m9uzZ5OXlNWnNv9ZAEiUn4dYrU4smtTVNy950I33Cq/xb2P6fOidKBm89z93YjRlL9/DWpuPc1CeSuBDfZorWxeWmwRdTIH1/9X2D/gbXvFjvobaswjKeXb2fNfvNd7T1iAzg9Ul9ZJhNNLta7+IUdsmvLk5EVqYWdaMw71ebGkop283ri9XRTX0iGdophLIKE899nVBjL2ard3o3LLq6epKk0cPN78LYV+qdJP10OINrF25hzX7zHW2zRndm9cMyF0kIZyY9Sk5mwoQJjB8/nvDwcDIzMy3reUlPkqhqWUI5r43xIcK3SoLzw5MQ9yvovS55vqIovDi+J2MWbmHrsUy+3XeGm/pENmPELubQt/DlfVBhc0ehdxBMWQJxQ+p1ucLSCl76/hBf/J4CQKdQP96Y0peeUYamitilyZCQcGaSKDkhWZlaXEq5Cebt8mT+sJKLjVknzQUphz9Vp2vEhfjyyMiOLFh/lBe/O8jwzm0xeOubKWIXoarmz3D9C4BNL1ubjnDbcmjToV6X3JmUxezle0nJKkJR4J4h8TxxrdzyX5UMCQlnJkNvQrio5Ud1EH25dePW+ZCdVOdrPDC8Pe1DfDmXX8q8H480bYCupqIMvnkU1j9PtSQpbijcu6FeSVJphZF/rT3MLf/9lZSsIqICvfn83kE8e2N3SZKEcCGSKAnholQUuGE+KFX+G1eUwA//V+dreOq0vPSXngB89lsyu1OymzpM11CcDUsmwu5Pq+/r91eYtso87FZHh9PzGP/WNt7dfAKTChP7R/PDzKFc2aH+hSiFEI4lQ29CuLKI3nD5/fDbexfbjq6Fw2vqfBfc4A4hTOgXxardaTzy+W5WPzyEtv6ezRSwEzp/Aj6fAuePVd83ei4MmQEX7jy9FKNJ5YOtJ5m/7ihlRhPBvh68/JdejO0Z3sRBC0eTeVWthyRKQri6kf+AA19BQcbFth/+D9qPAA+fOl3i+XHd2Z2aQ2JmIQ98upPP7xvUOoaHkrfD0tuhOMu6XecNE96H7jfV+VJJmYU8vmIvu5LNvXKju4XyyoTerSvpbEVkXlXrIYmSEC6m2m+yXgYY8xKsuu/iQbkp5vlKo56r0zUDfTz4cPpl/OWd7fyZksP/fbmPhVP6Wmp4uaW9y+CbR8BoU2rBLxxu/QKi+tfpMiaTyme/JfPKmsMUlxvx89Tx/I3dmXxZtHt/fkK0EooqBVQaJS8vD4PBQG5ubpN2wVZW6Y6Kiqp1sVwhAPPdWovHQVKVRZO1HvDQrxDSsc6X2X48kzv+9zsVJpXZ13R2z6rdqgqbXoYtr1XfF9YLblsKhug6Xep0TjFPrdzHL8fN6+Zd2b4Nr0/uTXRQ3XryhBCOU9fvb5nMLYQ7UBS4fh5oqnQSG8tgzRPmxKCOBncM4cWbzZO7F6w/yrd7T1/iDBdTXgwr7645Sep0Ldz9Q52SJFVVWbnrFNe+sYVfjmfipdcwZ1x3ltx7hSRJQrgZSZSEcBehXc3LalR1chMcXF2vy9x6eTvuvSoegCdW7GVPak7TxOdoBWfNvW4HVlXfN+hv5uE2T/9LXuZsfgn3fbKLJ1bsJb+0gn7tAlnz2FDuHBKPRiNDbUK4G5mjJIQ7Gf5/kPAl5KVdbFv7D+g4uk5JQKWnr+9GYmYhGw+f5d7FO/n6kSFEBXo3KrQFCxZY5la1+ETYs4dgyS3muVtVKVq47l9w+X01n1eFqqp8t+8Mz3+dQHZROR5aDbOu6cz9w9qjlQRJCLclc5QaSeYoCadzYDWsmG7dNvhR84TveigorWDSu9s5nJ5P13B/Vj40GD/Phv9u5bB/08c3wIq7oDTPut3DHyZ/DJ1GX/ISp7KLeG51ApuOnAOge0QAC6b0oWu43BouhKuSOUpCtFbdx0OHq63bdrxr7lWpBz9PHR9Mv4wQP08Op+czc+lujCYX+r1KVeGXN2DJ5OpJkqEd3LPukklShdHEoi0nuWbBFjYdOYeHVsPM0Z1Y/fAQSZKEaCUkURLC3VRO7NZ6XGwzVcD3j9drYjdAdJAPi+4YgIdOw4ZDZ3n1h/olWw5Tmm/uVdswB1ST9b6oy+C+jRDWvdZL7D+Vy/i3t/H/1hyiuNzI5fHBrJkxlJmjO+Ohkx+dQrQW8r9dCHfUpoO5onRVydvMt8XXU792Qcyb3AeARVsT+eTXpCYIsBllHocPRsPBr6vv634z3Pkd+IXaPb2wtIJ/fnuQ8W//woHTeRi89fxrYi+W3jeIjqF+zRe3EMIpyWRuIdzVVbNh3zLIqTKBectr4B8GA++t16Vu6hPJyXMFLNxwjOe/PsDRjHyeu7E7njonq959ZK258KbtUBsKXP0MXPU4aOz/frjhYAbPf53A6dwSwPy+n7uxu1TXFqIVk0RJCHfl4QM3LoQlk6yHn75/AnxD67U8B8CMC8Un39x4jM92pLA/LY93b+9PZCPvhmsSJhP8/C/4+dXq+7wMMPFD6HSN3dNPnCvgtbWH+fGAeRmYmGBvXhzfkxFd7Pc8CSFaB0mUnJQsuCiaRMdRcMN8+G5WlUYVvrwXfFdD7OA6X0pRFGaO7kyfmEBmLt3D3tQcbvzPL/zn1n4M6RjS5KHXWXEOfPWAeTFgW6E9YOpnENy+xlPP5Bbz5oZjrNh1CqNJRatRuHdoPDNHdcbbw8l6y4QQDiHlARqpucoDCNGkNr1SvbfFywB3rb3kpOaapGYV8eBnuzhwOg+NAk9e25UHh7evdW2zZikPcPaQeVHbrBPV9/WcBDf9Gzx8q+3KLizj3Z9P8PH2JMoqzL1to7uF8uS1XekSXvd6U0II1yXlAYQQF434O/S3qa1UkgufTYSc1HpfLibYhy8fGszkAdGYVPjX2sM8+Nku8krKmyjgSzCZzCUP3h9ZPUlStHDtyzDxg2pJUlFZBW/9dIxhr23i/S0nKaswMTAuiJUPXskH0wdKkiSEqEaG3oRoDRQFblgAhefgyJqL7fmnzcnS3WvBJ7hel/TSa3ltUm/6xwbxwtcH+PFABkcztvHetAHNm3CcPwFfPwwpv1bf59PGXEQyfphVc1mFiWV/pPDmxuNkFpQC0DXcn/8b25URXdrW2hMmhGjdZOitkWToTbiUsiL49GZI/c26PeYKuONr0DdsYvbe1Bwe+mwXp3NL8NZreWFcdyb0j7aqN9TooTeTCX7/L2yYCxXF1fdH9oNbPoXAGEvT6Zxivtx1iqV/pJKWYz6nXbAPj4/pzLjekbI2mxCtWF2/vyVRaiRJlITLKcqC/42FzCPW7V2uNyca2oZ1NGcVljFj6W62HssEIMTPgykDY7j18nZEB/k0LlGqrRcJ4PL74ZoXQe9FSbmRdQczWLEzlV+OZ1pqbIb4eTJjVEemDGwnBSOFEJIotRRJlIRLykmFD8eYh96q6n8H3PhmrbWGamM0qSzaepKPtiWSkWce4tIocHXXUH58+1lO/bGeqKjIuidKl+pFCoyF8W+jxl3FvlO5rNiVyjd7TpNXUmE55Ir4YG65LIbre0XInWxCCAtJlFqIJErCZWUchI/Gmid1VxV1Gdz4BkT0bvCly40mNhzM4LPfktl2/PzF9uwzaBK3s/er9wj29ajlClyyF6m0/70kdJvJrjNlfLkrjSMZ+RffQqA3E/tHMWlADO3a+DT4fQgh3JckSi1EEiXh0pK3wyc3g7HUul3RwBUPwsh/gGfjJmafOFfAkh0pfLjpAIqHOWnx0GkY3rkt0UHehPh50tb/wsPPk4jyVIL2vIdm/zIwllW73lltOHOUv7GmoKNVu6dOw9ie4UweEMPgDm1k/pEQolaSKLUQSZSEyzv0LSy/o/risQD+ETD2FfMaaY28Myw6Np4cQyfaXHEzSpvYavv7Ksd5UPctYzQ70Sg1/1j6uGIMr1VMpQgvwNxz1DnMj1HdwhjXJxKDt75RMQohWg9JlFqIJErCLSRuhW9n1Fy4EaDjaLj+dbsVruui6mTu739N4I+kLDLzS2lzZgtXnV1Ct9K9ds89RSgfhTyBsd1VdAn3p3OYP53C/AjwksRICNEwkii1EEmUhNsoL4Ftb8LW+dWH4gB0XjD0cRgyA3T1WyTWaDQSHh5OZmYmISEhpKedQnv4G/PrZey3e55J40Fpv7vwHvM8ePrV9x0JIYRdkii1EEmUhNs5fwLWPAEnfqp5v38ERF9mXkct7MIjKN7unXKrVq5gxmOPcupMhqUt2qDlzWs9mNDNTo+QpwEG3mOeJ+Uf1th3JIQQ1Uii1EIkURJuSVXhwFew9mkoSL/08XpfCO12MXFSTZCewKq1m5j030PY/pCpnO208hZv62TJLxyu/BsMuAu85P+TEKL5SKLUQiRREm6tJA82vWyuZVTTZO9aGE0qcW8WcCqv5h8xChAdoJA4ww9t284w5DHoPaXew3pCCNEQsiiuEKLxvALgulfhvk3m+kr1sDXFaDdJAlCB1DyVrR3+Dg//bi52KUmSEMLJyKK4QohLi+wL926AjAQ4sxcyDpifZxyAovM1nnImv26d1Wc87M9vEkIIR5NESQhRN4oC4b3Mj0qqCgVnLyZNGQfg3GFQFCJ0gbDq60teNiIiovliFkKIRpI5So0kc5SEqJnRaCQuLo60tDRq+jGjKArR0dEkJiai1coabEKIliVzlIQQDqXVannzzTcBc1JUVeX2woULJUkSQjg1SZSEEM1mwoQJrFy5kqioKKv26OhoVq5cyYQJExwUmRBC1I0MvTWSDL0JcWnVKnOnp0tPkhDCoWToTQjhNLRaLZ6e5lv/PT09JUkSQrgMSZSEEEIIIeyQREkIIYQQwg5JlIQQQggh7JBESQghhBDCDkmUhBBCCCHskERJCCGEEMIOSZSEEEIIIeyQREkIIYQQwg5JlIQQQggh7JBESQghhBDCDkmUhBBCCCHskERJCCGEEMIOSZSEEEIIIeyQREkIIYQQwg5JlIQQQggh7NA5OgAhROswe/Zs8vLyCAgIcHQoQghRZ5IoCSFaxOzZsx0dghBC1JsMvQkhhBBC2CGJkhBCCCGEHZIoCSGEEELYIYmSEEIIIYQdkigJIYQQQtjhVIlSfn4+c+bMoVevXvj5+WEwGBg4cCDz58+nrKyswddNS0vjnXfeYfLkyXTs2BFvb2+8vb2Jj4/n1ltv5aeffmrCdyGEEEIId6Goqqo6OgiA5ORkRowYQVJSEgA+Pj4YjUZKS0sB6NevHxs3biQoKKhe101NTSU2Npaqb9PHxwdVVSkuLra03X333bz//vtotdp6XT8vLw+DwUBubq7UhxFCCCFcRF2/v52iR6miooJx48aRlJREREQE69evp7CwkKKiIpYuXYq/vz+7d+9m2rRp9b620WhEVVVGjRrF4sWLSUtLo7CwkIKCAg4cOMD48eMB+N///secOXOa+J0JIYQQwpU5RY/Shx9+yL333gvA9u3bufLKK632f/HFF9x2220AbNiwgVGjRtX52rm5uZw4cYL+/fvXuF9VVa6//nrWrl2Ln58f586dw8vLq87Xlx4lIYQQwvW4VI/S4sWLARg5cmS1JAlg6tSpxMfHA/DJJ5/U69oGg8FukgSgKAp33303AAUFBRw6dKhe1xdCCCGE+3J4olRUVMS2bdsAuO6662o8RlEUxo4dC8C6deuaPIaqPUhGo7HJry+EEEII1+TwROnQoUOYTCYAevbsafe4yn3p6elkZWU1aQybN28GwMPDg86dOzfptYUQQgjhuhy+KO7p06ctz6OiouweV3Xf6dOnCQ4ObpLXT0xM5L333gNgypQpl5xnVFpaarkTD8xjnEIIIYRwTw7vUcrPz7c89/HxsXtc1X1Vz2mM4uJiJk+eTFFRESEhIbz66quXPOeVV17BYDBYHjExMU0SixBCCCGcT4N6lD7++GPuuuuuBr/oDz/8YJlz5CgVFRXcdttt7Nq1C71ez5IlS4iMjLzkeU8//TSzZ8+2bOfm5tKuXTvpWRJCCCFcSOX39qVu/nf40Ju/v7/leVFRkd3jqu6rek5DGI1Gbr/9dlavXo1Op+Pzzz9nzJgxdTrX09MTT09Py3blBy09S0IIIYTryc/Px2Aw2N3foETp1ltv5cYbb2xwUFUDqtqLk5aWRu/evWs8Jy0trcZz6stoNDJt2jSWL1+OVqvls88+Y9KkSQ2+XmRkJKmpqfj7+6MoSoOvYysvL4+YmBhSU1OlPlMzks+55chn3TLkc24Z8jm3jOb8nFVVJT8//5I5RYMSJdtelcbo1q0bGo0Gk8lEQkKC3RIBCQkJAISHhzd4IndlT9KyZcssSdKUKVMaHDuARqMhOjq6UdeoTUBAgPwnbAHyObcc+axbhnzOLUM+55bRXJ9zbT1JlRw+mdvHx4chQ4YAsHbt2hqPUVWVH3/8EaDOQ2S2jEYjt912m1WSNHXq1IYFLYQQQohWweGJEsD06dMB2LRpE7/99lu1/StWrODkyZMA3HHHHfW+fmVP0vLly9HpdCxZskSSJCGEEEJcktMkSr169UJVVSZOnMjGjRsBMJlMrFixgvvuuw8wV+6uaZ23OXPmoCgKiqKQlJRkta9yTtKyZcssE7cbO9zWEjw9PXnhhReabIhT1Ew+55Yjn3XLkM+5Zcjn3DKc4XN2ikVxAZKSkhg5cqQl0fHx8cFkMlFSUgJAv3792LhxI0FBQdXOnTNnDnPnzgXMBSTj4uIs+7Zs2cLw4cMB0Ov1l5zf9Oabb7pEIiWEEEKI5ufw8gCV4uLi2LdvH/PmzWPVqlUkJiai1+vp0aMHt956K48++igeHh71vm7l8igA5eXlZGRk1Hp8cXFxvV9DCCGEEO7JaXqUhBBCCCGcjVPMURJCCCGEcEaSKAkhhBBC2CGJkhBCCCGEHZIoOZn8/HzmzJlDr1698PPzw2AwMHDgQObPn09ZWZmjw3N558+f56OPPmLatGl0794dX19fPD09iY6O5uabb+arr75ydIhu7dVXX7WU8mjKJX+EeamHf/3rXwwePJi2bdta/l2PHDmSOXPmkJOT4+gQ3cL69eu55ZZbiI2NxcvLC29vb9q3b8/tt9/Ozz//7OjwnF5RURE//PADL730EhMmTCA2Ntby82DOnDl1ukZGRgaPP/44Xbp0wdvbm+DgYIYOHcoHH3xwyQVuG0QVTiMpKUmNi4tTARVQfXx8VE9PT8t2v3791KysLEeH6dJ0Op3l8wRULy8v1dfX16rtuuuuUwsLCx0dqts5fPiw6uXlZfVZi6bx008/qWFhYZbP1cPDQw0MDLT6rHfv3u3oMF2ayWRSH3jgAavP1NvbW/X29rZqmzVrlqNDdWqbNm2y+ryqPl544YVLnr9z5061TZs2lnP8/Pysfq5fe+21amlpaZPGLD1KTqKiooJx48aRlJREREQE69evp7CwkKKiIpYuXYq/vz+7d+9m2rRpjg7VpVVUVHD55ZfzzjvvcOLECYqLiykoKCAxMZF77rkHgB9++IEHHnjAwZG6F5PJxN13301JSQlXXnmlo8NxK9u2beOGG24gIyODCRMm8Mcff1BSUkJ2djaFhYX8/vvvPPPMM3Va00rY9/HHH/Pf//4XgEmTJnH06FGKioooKiri8OHDjB8/HoA33nhDeqYvISgoiFGjRvHkk0/yxRdfEB4eXqfzcnNzufHGGzl//jxdu3bljz/+ID8/n8LCQt566y30ej0//vgjM2fObNqAmzTtEg32wQcfWDLi7du3V9v/+eefW/Zv2LDBARG6h59++qnW/VV/Y0xJSWmhqNzfwoULVUC9/fbb1RdeeEF6lJpIYWGh2r59exVQH330UUeH49ZGjBihAmrHjh3V8vLyavvLysosfxdTp051QISuoaKiolpbbGxsnXqUnn32WUtP3smTJ6vtf/nll1VA1Wq16pEjR5oqZOlRchaLFy8GYOTIkTX+xj116lTi4+MB+OSTT1o0NncycuTIWvdX9ioB7Ny5s7nDaRUSExN55plnaNOmDW+88Yajw3Ern376KSdPniQ8PJzXXnvN0eG4tTNnzgDQp08fdLrqtZr1ej19+/YFoKCgoCVDcylarbbB51Z+91X9Pqzq0Ucfxc/PD6PRyJIlSxr8OrYkUXICRUVFbNu2DTCvZ1cTRVEYO3YsAOvWrWux2FobLy8vy3Oj0ejASNzHfffdR2FhIQsWLKBt27aODsetVH5xTJ482erfrmh67du3B2Dv3r1UVFRU219eXs6ePXsAuOyyy1oytFbhyJEjpKSkAPa/J/38/Bg6dCjQtN+Tkig5gUOHDlmWWunZs6fd4yr3paenk5WV1SKxtTabN2+2PO/Vq5fjAnETixYtYuPGjYwePZo77rjD0eG4ldLSUkuv54ABA0hJSeH+++8nJiYGDw8PwsLCGDduHN9//72DI3UPDz30EADHjx/n1ltv5fjx45Z9R44c4ZZbbuHkyZN06NCBWbNmOSpMt5WQkGB5XpfvyYMHDzbZa0ui5AROnz5teR4VFWX3uKr7qp4jmkZOTg6vvPIKAEOHDqVLly4Ojsi1paWl8eSTT+Lt7W2ZBCuaTlJSkqVkyMmTJ+nZsyeLFi3i7Nmz+Pr6cvbsWb777jtuvPFG7rvvvua5bboVGTduHG+88QYeHh6sXLmSTp064ePjg4+PD127dmXz5s089NBD/P777wQEBDg6XLdT3+/JvLy8JhsClUTJCeTn51ue+/j42D2u6r6q54jGM5lM/PWvf+XMmTN4eXnx1ltvOTokl/fAAw+Qm5vLnDlzLMMWoulkZ2dbnr/00kvo9XpWrFhBQUEB2dnZJCcnM3nyZAA++OADmR/WBGbOnMmqVasIDQ0FzIuoVy6kXlZWRkFBAbm5uY4M0W058ntSEiUhgBkzZvDdd98B8Pbbb9O7d28HR+TaPvvsM77//nv69u3L7NmzHR2OW6ocrq98/uGHHzJp0iT0ej0A7dq1Y+nSpfTp0weAl19+uca5NaJuioqKmDJlCjfeeCPt2rVj3bp1nDt3jnPnzrFu3Tq6d+/Op59+yuWXX86+ffscHa5oQpIoOQF/f3/L86KiIrvHVd1X9RzROE888YSlB+mNN97g7rvvdnBEri0jI4OZM2ei1WpZtGhRjXcIicar+jOgU6dO3HzzzdWO0Wg0PPHEE4C5Kv2uXbtaKjy38+STT7J8+XK6dOnC1q1bueaaawgJCSEkJIRrrrmGLVu20LlzZzIzM3n44YcdHa7bceT3pCRKTiAyMtLyPC0tze5xVfdVPUc03FNPPcX8+fMBmDdvXtMXKmuF/v73v3P+/Hnuv/9+unbtSkFBgdWj6lI8NbWJuqk6T6Nr1652j+vevbvleXJycrPG5K7y8/N5//33AXj44YdrvMPQ29ubRx55BIBffvmFs2fPtmiM7q6+35MBAQH4+fk1yWtLouQEunXrhkZj/quoOrPfVuW+8PBwgoODWyQ2d/bkk0/y+uuvA/Daa6/x+OOPOzgi95CYmAjAu+++i7+/f7VH5YR5wNL21FNPOSpclxUcHFzrpNZKVSdxy/p6DXP06FHLsGWHDh3sHtepUyfL88r/B6JpVL3TrS7fk1V/QWgsSZScgI+PD0OGDAFg7dq1NR6jqio//vgjAGPGjGmx2NzVE088wbx58wBzkvTkk086OCIh6q/yZ8GhQ4fsHlP1NumaivSJS6v8RRZq75XLyMiwPJfpEU2rc+fOtGvXDrD/PVlYWMjWrVuBJv6ebLIa36JRKpcwURRF3bFjR7X9y5YtkyVMmsjjjz9u+SznzZvn6HBaHVnCpOls2bLF8ll+9dVX1fYbjUa1d+/eKqBGRUWpRqOx5YN0A0VFRZbFb/v371/jEiYVFRXq4MGDVUANCgqqcakOUbP6LmHi4+OjJiYmVtv/r3/9q1mWMJGfVE6ivLxc7dWrl+UHWmUyZDQa1eXLl6sBAQGWle1Fwz355JOWL5YFCxY4OpxWSRKlpjVp0iQVUNu0aaOuXLnS8iWenJys3nLLLZbP+uOPP3ZwpK7t0UcftXyWY8eOVfft26cajUbVaDSqe/fuVceMGWPZP3fuXEeH69SysrLUc+fOWR4xMTEqoD755JNW7fn5+Vbn5eTkqOHh4Sqgdu/eXd25c6eqqqpaWlqqvvPOO6qHh4cKqA899FCTxis/qZxIYmKiGhcXZ/nP5uPjo3p5eVm2+/Xrp2ZlZTk6TJeVnJxs+Sw1Go0aFhZW6+P11193dMhuSRKlplVQUKAOGzbM8pl6enqqQUFBlu26/KYuLq2oqEgdO3as1efq6empenp6WrXdeuut0pt0CZU9SJd6TJ8+vdq5O3fuVNu0aWM5xt/fX9Xr9ZbtMWPGqCUlJU0ar8xRciJxcXHs27eP559/np49e6IoCnq9ngEDBjBv3jx27NhBUFCQo8N0WbZ1ZzIyMmp9yMKWwhX4+vqyadMmFi1axLBhw/D19aWgoICoqCimTp3Ktm3bmDNnjqPDdHne3t6sWbOGFStWMH78eKKjoy0T5WNiYpg4cSLfffcdn3/+eaMWfhW1GzBgAAcOHGDWrFl06tSJ8vJyfH19ueqqq1i0aBE//PADnp6eTfqaiqpKXXshhBBCiJpIj5IQQgghhB2SKAkhhBBC2CGJkhBCCCGEHZIoCSGEEELYIYmSEEIIIYQdkigJIYQQQtghiZIQQgghhB2SKAkhhBBC2CGJkhBCCCGEHZIoCSGEEELYIYmSEEIIIYQdkigJIYQQQtghiZIQQgghhB3/H4fIzt6ETyaJAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(xin,yin,yerr=yerr, fmt='o', linewidth=2, capsize=0, c='k', label=\"data\")\n",
    "x_val = jnp.linspace(0.,10,50)\n",
    "plt.plot(x_val,model(ptrue, x_val),label=\"true noiseless\")\n",
    "plt.plot(x_val,model(par_mini_GD, x_val) ,lw=3,label=\"GD fit\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zMQjon_ctd8l"
   },
   "source": [
    "## Use 2nd order method : Hessian\n",
    "\n",
    "By default the implementation is `jax.hessian(f)=jacfwd(jacrev(f))`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "LQ7VRWAlJsz7",
    "outputId": "ed136ac9-695a-43ad-95b6-d3b733e1cacc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[1.11422423, 0.82477425, 0.97932333],\n",
       "       [0.82477425, 0.7279259 , 0.96683766],\n",
       "       [0.97932333, 0.96683766, 1.35939096]], dtype=float64)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = jax.random.uniform(jax.random.PRNGKey(10),(3, 3))\n",
    "C = jnp.dot(A, A.transpose())\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "id": "bjEuJPjOK9Kb"
   },
   "outputs": [],
   "source": [
    "def f(x,C):  #x parameter, C is fixed\n",
    "  return 0.5 * x.T @ C @ x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zY4DENeyLOby",
    "outputId": "0b1ccf11-0042-4dcb-f7bc-52f86ade289d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[1.11422423, 0.82477425, 0.97932333],\n",
       "       [0.82477425, 0.7279259 , 0.96683766],\n",
       "       [0.97932333, 0.96683766, 1.35939096]], dtype=float64)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=jnp.array([0.,0.,0.])\n",
    "jax.hessian(f)(x,C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "id": "gVvtCVs0tche"
   },
   "outputs": [],
   "source": [
    "gLoss = lambda p,xi,yi: jacfwd(loss_fun)(p,xi,yi)\n",
    "hLoss = lambda p,xi,yi: jax.hessian(loss_fun)(p,xi,yi)\n",
    "\n",
    "@jit\n",
    "def oneStepNewton(p,xi,yi,lr=1.0):\n",
    "    return p - lr * jnp.linalg.inv(hLoss(p,xi,yi)) @ gLoss(p,xi,yi)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Nxvlpz-UtnRU",
    "outputId": "1ae4aec6-ce90-4147-e8b0-d8c9343d4175"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 [0.  0.5] inf\n",
      "100 [0.07535074 0.00358029] 0.039375743499862684\n",
      "Converged after 183 epochs: p = [0.52373613 1.10348083], loss = 0.001553297865019117\n"
     ]
    }
   ],
   "source": [
    "par_mini_Newton = minimzer(loss_fun, x_data=xin, y_data=yin, par_init=jnp.array([0., 0.5]),\n",
    "                    method=partial(oneStepNewton, lr=0.1), verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 446
    },
    "id": "5GLh_eaqtuXP",
    "outputId": "14414c46-d5c4-4408-f195-6f7d1953a6da"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(xin,yin,yerr=yerr, fmt='o', linewidth=2, capsize=0, c='k', label=\"data\")\n",
    "x_val = jnp.linspace(0.,10,50)\n",
    "plt.plot(x_val,model(ptrue, x_val),label=\"true noiseless\")\n",
    "plt.plot(x_val,model(par_mini_GD, x_val) ,lw=3,label=\"GD fit\")\n",
    "plt.plot(x_val,model(par_mini_Newton, x_val),ls='--',lw=3,label=\"Newton fit\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Oe5mG6YCiuc7"
   },
   "source": [
    "We will envisage to draw \"error\" bands later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LrruiqWzt34T"
   },
   "source": [
    "# Gradient/Vmap...wrt  tuples, lists, and dicts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "id": "1RgdvwK3t_tH"
   },
   "outputs": [],
   "source": [
    "def f(p:dict,x):\n",
    "    return p[\"a\"]**2 + p[\"b\"]*x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Dtw2LB4guNdq"
   },
   "source": [
    "$$\n",
    "∂ f/\\partial p(a) = 2 p(a), \\qquad ∂ f/\\partial p(b) = x\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Y1B_rHVsuDMQ",
    "outputId": "18d69477-61be-4a33-865a-fcfd5115d395"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': Array(6., dtype=float64, weak_type=True), 'b': Array(10., dtype=float64, weak_type=True)}\n"
     ]
    }
   ],
   "source": [
    "p= {\"a\":3.,\"b\":1.}\n",
    "x = 10.\n",
    "print(grad(f)(p,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "C4Q1R_UAvLt1"
   },
   "source": [
    "$$\\partial f / \\partial x = p(b)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "WXhW0Q7EvF6d",
    "outputId": "f4ecbb42-12d5-41d2-bc1f-85401458cfed"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(grad(f, argnums=1)(p,x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "id": "QcipjzVcveGX"
   },
   "outputs": [],
   "source": [
    "def f(p:tuple,x):\n",
    "    return p[0]**2 + p[1]*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EF1zEPoavoYV",
    "outputId": "ec984721-d5d4-4342-9259-85f99e6b4952"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(Array(6., dtype=float64, weak_type=True), Array(10., dtype=float64, weak_type=True))\n"
     ]
    }
   ],
   "source": [
    "p= (3.,1.)\n",
    "x = 10.\n",
    "print(grad(f)(p,x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "id": "LOwRLi7fvyDY"
   },
   "outputs": [],
   "source": [
    "def f(p:list,x):\n",
    "    return p[0]**2 + p[1]*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "T-7LdS92v428",
    "outputId": "a8831c57-a76a-4f79-f048-8817bc4b346c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Array(6., dtype=float64, weak_type=True), Array(10., dtype=float64, weak_type=True)]\n"
     ]
    }
   ],
   "source": [
    "p= [3.,1.]\n",
    "x = 10.\n",
    "print(grad(f)(p,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J77xygjPjESS"
   },
   "source": [
    "We will see later an other kind of structure that allow differentiation.\n",
    "\n",
    "There are also special functions for Jacobian and vector product.\n",
    "$f: \\mathbb{R}^n → \\mathbb{R}^m$ then the Jacobian is $∂f \\in \\mathbb{R}^{m\\times n}$. But, at $x$ we can define a tangent space to the manyfold where $x$ lives, and similarly at $f(x)$ we can define a tangent space to the manyfold where $f(x)$ lives. The Jacobian is the mapping between these two spaces.\n",
    "So if then\n",
    "\n",
    "- `jvp` for Jacobian vector product (aka forward mode) $v\\in \\mathbb{R}^n$ (ie. a vector tangent at $x$ in $\\mathbb{R}^n$)  : $(x,v)→(f(x),∂f . v)$\n",
    "- `vjp` for vector Jacobian product (aka backward mode) $v\\in \\mathbb{R}^m$ (ie. a vector tangent at $f(x)$ in $\\mathbb{R}^m$)  : $(x,v)→(f(x),v^T . ∂f)$\n",
    "\n",
    "There is the possibility to code user `jax.custom_jvp()` and `jax.custom_vjp()` to define custom differentiation rules for Python functions that are already JAX-transformable...\n",
    "\n",
    "\n",
    "More info [here](https://jax.readthedocs.io/en/latest/_tutorials/advanced-autodiff.html#hessian-vector-products-with-jax-grad-of-jax-grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AhRJDjERvW-I"
   },
   "source": [
    "# Vectorization partielle: in-axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "id": "sji3Deq4wI2w"
   },
   "outputs": [],
   "source": [
    "def f(p:dict,x):\n",
    "    return p[\"a\"]**2 + p[\"b\"]*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "djIVP9zNwyUa",
    "outputId": "473c785a-89ac-441b-ca60-fca7527d53ed"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11. 21. 31.]\n"
     ]
    }
   ],
   "source": [
    "# We vectorize on the \"b\" values of the dictionnary as array of (1,2,3)\n",
    "# p(a)=1, x=10\n",
    "print(vmap(f, in_axes=({\"a\": None, \"b\": 0},None))({\"a\":1.,\"b\":jnp.array([1.,2.,3.])},10.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jdVASvWvwzch",
    "outputId": "64cd7be9-a13a-4c80-c565-3a4b16d222b0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([21., 24., 29.], dtype=float64)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make p(b)=2, x=10 and vectorize upon p(a)\n",
    "vmap(f, in_axes=({\"a\":0, \"b\": None},None))({\"a\":jnp.array([1.,2.,3.]),\"b\":2.0},10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fodoECFlxHBd"
   },
   "source": [
    "A bit more in_axis manipulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "id": "gcfecWTdxNwS"
   },
   "outputs": [],
   "source": [
    "def func(a,b,x):\n",
    "    return a**2 + b*x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "id": "1c7btsNvxRZa"
   },
   "outputs": [],
   "source": [
    "vfunc = vmap(func, in_axes=(0,None,None))  # vectorize on \"a\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kwh8qJumxY70",
    "outputId": "0e98b348-d56b-48cf-8db8-6cf61353d26c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([11., 14., 19.], dtype=float64)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vfunc(jnp.array([1.,2.,3.]), 1.,10.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "id": "M3ltXgWmxe-Y"
   },
   "outputs": [],
   "source": [
    "# map over 2 axis : \"a\" and \"b\"\n",
    "vvfunc = vmap(vmap(func, in_axes=(0,None,None)),in_axes=(None,0,None))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SKrJrRSKxtHC",
    "outputId": "aa9124c0-05eb-4328-b18c-0047e4230737"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[ 1.,  4.,  9.],\n",
       "       [11., 14., 19.],\n",
       "       [41., 44., 49.],\n",
       "       [51., 54., 59.]], dtype=float64)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vvfunc(jnp.array([1.,2.,3.]),jnp.array([0.,1.,4.,5.]),10.)\n",
    "# x= 10\n",
    "# a:(1,2,3) b: 0\n",
    "# a:(1,2,3) b: 1\n",
    "# a:(1,2,3) b: 4\n",
    "# a:(1,2,3) b: 5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1Cbq9OCGx3UQ",
    "outputId": "2b5c3575-da6d-4f7d-e5b2-addede8d3874"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1.0, 4.0, 9.0], [11.0, 14.0, 19.0], [41.0, 44.0, 49.0], [51.0, 54.0, 59.0]]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Python list comprehension equiv.\n",
    "[[func(ai,bj,x=10.) for ai in [1,2,3]] for bj in [0.,1.,4.,5.]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yHBHjNBTyDmi",
    "outputId": "130ee747-2ae5-4aac-f4ee-0e8e31312168"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([ 1., 14., 49.], dtype=float64)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vmap(func,in_axes=(0,0,None))(jnp.array([1.,2.,3.]),jnp.array([0.,1.,4.]),10.)\n",
    "# here map a,b at the same times : requires than arrays have the same sizes\n",
    "#x=10\n",
    "# a:1 b:0\n",
    "# a:2 b:1\n",
    "# a:3 b:4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SlXiPQdgyXzl",
    "outputId": "fe7c3f0e-5ab5-45cc-b622-3fb68c42bf30"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 14.0, 49.0]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Python list comprehension equiv.\n",
    "[func(ai,bj,x=10.) for ai,bj in zip([1,2,3],[0.,1.,4.,5.])]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "t6J58uO-zX-a"
   },
   "source": [
    "Now, \"0\" in the above in_axes means the first dimension of each \"a\" and \"b\" args.\n",
    "\n",
    "What about if \"b\" is a matrix, and \"a\" a vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "id": "daMxMxTCzXNa"
   },
   "outputs": [],
   "source": [
    "a = np.array([1.,2.,3.])\n",
    "b = np.array([[0.,1.,4.],\n",
    "               [1.,2.,8.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "e3P7SV6fz39G",
    "outputId": "a8057da9-42d3-4107-f42d-1467e944bf0d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1. 11.]\n",
      "[14. 24.]\n",
      "[49. 89.]\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(a)):\n",
    "  print(func(a[i],b[:,i],10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qobEwTZny2zH",
    "outputId": "5d4e6969-edfa-4c1e-bafa-dbd5ace0d9a5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[ 1., 11.],\n",
       "       [14., 24.],\n",
       "       [49., 89.]], dtype=float64)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# here is the vmap equivalent\n",
    "vmap(func,in_axes=(0,1,None))(a,b,10.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bgix1V1gN9PQ"
   },
   "source": [
    "# Ploting a 2D scalar function and its gradient flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 426
    },
    "id": "R7BUoLQiN7o0",
    "outputId": "dab6feb6-7f8e-433d-8b17-4da6f01bc016"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7faf289d75e0>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(p):\n",
    "  x,y=p[0],p[1]\n",
    "  return jnp.sin(x)*jnp.cos(y)\n",
    "fig,ax = plt.subplots(1,1,figsize=(5,5))\n",
    "\n",
    "xmin,xmax,ymin,ymax,Npix = -jnp.pi,jnp.pi,-jnp.pi,jnp.pi,101\n",
    "grid = x0,y0 = jnp.mgrid[xmin:xmax:Npix*1j,ymin:ymax:Npix*1j]\n",
    "pts = jnp.swapaxes(grid,0,-1).reshape(-1,2)\n",
    "vfunc = vmap(f)\n",
    "v = vfunc(pts)\n",
    "v = jnp.swapaxes(v.reshape(Npix,Npix),0,-1)\n",
    "\n",
    "g0=ax.contourf(x0,y0,v, levels = 100)\n",
    "img = ax.contour(x0,y0,v, levels = 10, colors = 'w')\n",
    "\n",
    "xmin,xmax,ymin,ymax,Npix = -jnp.pi,jnp.pi,-jnp.pi,jnp.pi,20\n",
    "grid = x0,y0 = jnp.mgrid[xmin:xmax:Npix*1j,ymin:ymax:Npix*1j]\n",
    "pts = jnp.swapaxes(grid,0,-1).reshape(-1,2)\n",
    "\n",
    "gradients = vmap(grad(f))(pts)\n",
    "scale = 1\n",
    "ax.quiver(\n",
    "        pts[:,0],\n",
    "        pts[:,1],\n",
    "        gradients[:,0],\n",
    "        gradients[:,1],\n",
    "        color=\"white\",\n",
    "        angles = 'xy',\n",
    "        scale_units='xy',\n",
    "        scale = scale\n",
    "    )\n",
    "ax.set_aspect(\"equal\")\n",
    "fig.colorbar(g0,ax=ax,shrink=0.95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ya2AenXz1uPG"
   },
   "source": [
    "# PyTree: a user structure adapted to JAX (vmap,grad,jit)\n",
    "\n",
    "\n",
    "\n",
    "> A pytree is a container-like structure built out of container-like Python objects — “leaf” pytrees and/or more pytrees. A pytree can include lists, tuples, and dicts. A leaf is anything that’s not a pytree, such as an array, but a single leaf is also a pytree.\n",
    "\n",
    "It can be **list, tuples, dictionaries, namedtuple, OrderedDict, and None (!)** But you can \"register\" your **own strcture**.\n",
    "\n",
    "\n",
    "\n",
    "Here a simple example with a class with 2 fields (a, b).\n",
    "\n",
    "Notice that one can implement in different way (eg. NamedTuple) and may use library (eg. Equinox)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "r8EBfEGU18GG"
   },
   "outputs": [],
   "source": [
    "from jax.tree_util import register_pytree_node_class\n",
    "\n",
    "@register_pytree_node_class\n",
    "class Params:\n",
    "    def __init__(self, a, b):\n",
    "        self._a = a\n",
    "        self._b = b\n",
    "\n",
    "    def __repr__(self):\n",
    "        return f\"Params(a={self._a}, b={self._b})\"\n",
    "\n",
    "    @property\n",
    "    def a(self):\n",
    "        return self._a\n",
    "\n",
    "    @property\n",
    "    def b(self):\n",
    "        return self._b\n",
    "\n",
    "    def tree_flatten(self):\n",
    "        children = (self._a, self._b)\n",
    "        aux_data = None\n",
    "        return (children, aux_data)\n",
    "\n",
    "    @classmethod\n",
    "    def tree_unflatten(cls, aux_data, children):\n",
    "        return cls(*children)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "MSZ3lfeT2aZ6",
    "outputId": "b5c5f73e-fd11-4eba-d246-0a4919cbd137"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Params(a=3.0, b=1.0)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_params = Params(3.,1.)\n",
    "my_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "GPe2eOQm2etD"
   },
   "outputs": [],
   "source": [
    "def g(p: Params,x):\n",
    "    return (p.a)**2 + (p.b)*x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "G_zmzrxY2mnl",
    "outputId": "04c90102-f39d-44b7-a9d7-2ee95edc5b4f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Params(a=6.0, b=10.0)\n"
     ]
    }
   ],
   "source": [
    "print(grad(g)(my_params,10)) # as easy as arrays, dicts, lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zoS3wKLJ2z0U",
    "outputId": "3654f5c5-89df-4957-8274-2d8773f07a9e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[19. 29. 39.]\n"
     ]
    }
   ],
   "source": [
    "# vmaping to the \"b\" parameter (2nd field) of Params class\n",
    "print(vmap(g, in_axes=(Params(None, 0), None))(Params(3., jnp.array([1.,2.,3.])), 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6n8JDhdm3EZ2"
   },
   "outputs": [],
   "source": [
    "# A way to see the structure\n",
    "from jax.tree_util import tree_flatten, tree_unflatten\n",
    "def show_example(structured):\n",
    "    flat, tree = tree_flatten(structured)\n",
    "    unflattened = tree_unflatten(tree, flat)\n",
    "    print(\"structured={}\\n  flat={}\\n  tree={}\\n  unflattened={}\".format(\n",
    "          structured, flat, tree, unflattened))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "iyu41J7L3d_k",
    "outputId": "051b3417-5bef-4c9c-ae07-f906f35edace"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "structured=Params(a=3.0, b=1.0)\n",
      "  flat=[3.0, 1.0]\n",
      "  tree=PyTreeDef(CustomNode(Params[None], [*, *]))\n",
      "  unflattened=Params(a=3.0, b=1.0)\n"
     ]
    }
   ],
   "source": [
    "show_example(my_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o_jA6sA-38jD"
   },
   "source": [
    "# Use of Equinox data structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "B6yE9TJR362B",
    "outputId": "8d5e835c-1f0a-45e4-ef38-987dc11d7751"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m175.2/175.2 kB\u001b[0m \u001b[31m1.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
      "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m41.2/41.2 kB\u001b[0m \u001b[31m4.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
      "\u001b[?25h"
     ]
    }
   ],
   "source": [
    "! pip install -q equinox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "3MPQc2Rk4KN5"
   },
   "outputs": [],
   "source": [
    "import equinox as eqx\n",
    "\n",
    "#like a layer in a NN\n",
    "class Model(eqx.Module):\n",
    "  a : float                 # the params\n",
    "  b : float\n",
    "\n",
    "  def __init__(self, a,b):  # the init\n",
    "    self.a = a\n",
    "    self.b = b\n",
    "\n",
    "  def __call__(self, x):    # the forward call\n",
    "    return self.a + x *  self.b**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "fXlKXTob7lUZ"
   },
   "outputs": [],
   "source": [
    "def f(model, x):\n",
    "  return vmap(model)(x)   # in the presnt use case vmap is not necessary\n",
    "\n",
    "model = Model(a=0.,b=1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "PblktoTV7gm2",
    "outputId": "3f153cb3-8198-4ae8-da89-aa337a3b966e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([ 0.        ,  1.11111111,  2.22222222,  3.33333333,  4.44444444,\n",
       "        5.55555556,  6.66666667,  7.77777778,  8.88888889, 10.        ],      dtype=float64)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(model,jnp.linspace(0.,10.,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "XMCHwSJ38ydV"
   },
   "outputs": [],
   "source": [
    "grads = jacfwd(f)(model,jnp.linspace(0.,10.,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ULbiJxaF82K2",
    "outputId": "1975b348-790f-4924-d94a-536d274b462d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.], dtype=float64),\n",
       " Array([ 0.        ,  2.22222222,  4.44444444,  6.66666667,  8.88888889,\n",
       "        11.11111111, 13.33333333, 15.55555556, 17.77777778, 20.        ],      dtype=float64))"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grads.a, grads.b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d1XHoeUWWcva"
   },
   "source": [
    "# Slices & JIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-WeplqO3Wcvc",
    "outputId": "ade20b4a-08f0-481f-f15d-b00b0ea12302"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int64)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.clear_caches() # clean compilation caches\n",
    "x = jnp.arange(0,10,1)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zkGSpvoDWcvd",
    "outputId": "e7442489-601a-449f-e4a6-6daef059c876"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([2, 3, 4, 5, 6], dtype=int64)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2:7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "1eLxMj2qWcvi"
   },
   "outputs": [],
   "source": [
    "def f(x,i,j):\n",
    "  return x[i:j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jylJFRjxWcvk",
    "outputId": "7e76f73b-7a08-46d3-d9eb-4bc63fca2696"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([2, 3, 4, 5, 6], dtype=int64)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x,2,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 449
    },
    "id": "oqVS1ElYWcvl",
    "outputId": "324c6f27-c4fc-40d2-b7bb-4ca6a3b1e344"
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "Array slice indices must have static start/stop/step to be used with NumPy indexing syntax. Found slice(Traced<ShapedArray(int64[], weak_type=True)>with<DynamicJaxprTrace(level=1/0)>, Traced<ShapedArray(int64[], weak_type=True)>with<DynamicJaxprTrace(level=1/0)>, None). To index a statically sized array at a dynamic position, try lax.dynamic_slice/dynamic_update_slice (JAX does not support dynamically sized arrays within JIT compiled functions).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-68-f534c3969d65>\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mjf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mjit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mjf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "    \u001b[0;31m[... skipping hidden 11 frame]\u001b[0m\n",
      "\u001b[0;32m<ipython-input-66-245d7e5eac86>\u001b[0m in \u001b[0;36mf\u001b[0;34m(x, i, j)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py\u001b[0m in \u001b[0;36mop\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    734\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_forward_operator_to_aval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    735\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 736\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34mf\"_{name}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    737\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    738\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py\u001b[0m in \u001b[0;36m_getitem\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m    347\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    348\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_getitem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 349\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0mlax_numpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_rewriting_take\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    350\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    351\u001b[0m \u001b[0;31m# Syntactic sugar for scatter operations.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_rewriting_take\u001b[0;34m(arr, idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m   4602\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4603\u001b[0m   \u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatic_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic_idx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_split_index_for_jit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0midx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4604\u001b[0;31m   return _gather(arr, treedef, static_idx, dynamic_idx, indices_are_sorted,\n\u001b[0m\u001b[1;32m   4605\u001b[0m                  unique_indices, mode, fill_value)\n\u001b[1;32m   4606\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_gather\u001b[0;34m(arr, treedef, static_idx, dynamic_idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m   4611\u001b[0m             unique_indices, mode, fill_value):\n\u001b[1;32m   4612\u001b[0m   \u001b[0midx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_merge_static_and_dynamic_indices\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatic_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic_idx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4613\u001b[0;31m   \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_index_to_gather\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0midx\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# shared with _scatter_update\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4614\u001b[0m   \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4615\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_index_to_gather\u001b[0;34m(x_shape, idx, normalize_indices)\u001b[0m\n\u001b[1;32m   4854\u001b[0m                \u001b[0;34m\"dynamic_update_slice (JAX does not support dynamically sized \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4855\u001b[0m                \"arrays within JIT compiled functions).\")\n\u001b[0;32m-> 4856\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4857\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4858\u001b[0m       \u001b[0mstart\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mslice_size\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_preprocess_slice\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_shape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx_axis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: Array slice indices must have static start/stop/step to be used with NumPy indexing syntax. Found slice(Traced<ShapedArray(int64[], weak_type=True)>with<DynamicJaxprTrace(level=1/0)>, Traced<ShapedArray(int64[], weak_type=True)>with<DynamicJaxprTrace(level=1/0)>, None). To index a statically sized array at a dynamic position, try lax.dynamic_slice/dynamic_update_slice (JAX does not support dynamically sized arrays within JIT compiled functions)."
     ]
    }
   ],
   "source": [
    "jf = jit(f)\n",
    "jf(x,2,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-o10IxpTWcvn",
    "outputId": "e3c0c0a8-2e86-4f10-9873-03ff13c8e867"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([2, 3, 4, 5, 6], dtype=int64)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# possible solution\n",
    "jf = partial(jit, static_argnames=(\"i\",\"j\"))(f) # or static_argnums=(1,2) ie. position index\n",
    "jf(x,2,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "igwMJqnaWcvo"
   },
   "outputs": [],
   "source": [
    "# lets try with a fix width\n",
    "@partial(jit, static_argnames=(\"i\"))\n",
    "def f(x, i):\n",
    "  print(\"i:\",i)\n",
    "  jax.debug.print(\"i: {}\",i)\n",
    "  return x[i:i + 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9y4RDlDMWcvo",
    "outputId": "d2ba81e7-3235-4518-cd14-87e2a4b1084f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: 2\n",
      "i: 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([2, 3, 4, 5, 6], dtype=int64)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 505
    },
    "id": "OkPiJ1yhWcvo",
    "outputId": "e44a3966-76ed-4668-9015-1c0806b63752"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: Traced<ShapedArray(int64[])>with<BatchTrace(level=1/0)> with\n",
      "  val = Array([2, 3], dtype=int64)\n",
      "  batch_dim = 0\n"
     ]
    },
    {
     "ename": "IndexError",
     "evalue": "Array slice indices must have static start/stop/step to be used with NumPy indexing syntax. Found slice(Traced<ShapedArray(int64[])>with<BatchTrace(level=1/0)> with\n  val = Array([2, 3], dtype=int64)\n  batch_dim = 0, Traced<ShapedArray(int64[])>with<DynamicJaxprTrace(level=2/0)>, None). To index a statically sized array at a dynamic position, try lax.dynamic_slice/dynamic_update_slice (JAX does not support dynamically sized arrays within JIT compiled functions).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-72-70cf5040af8d>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mvmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpartial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "    \u001b[0;31m[... skipping hidden 14 frame]\u001b[0m\n",
      "\u001b[0;32m<ipython-input-70-c4db7f371fd1>\u001b[0m in \u001b[0;36mf\u001b[0;34m(x, i)\u001b[0m\n\u001b[1;32m      4\u001b[0m   \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"i:\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m   \u001b[0mjax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdebug\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"i: {}\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py\u001b[0m in \u001b[0;36mop\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    734\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_forward_operator_to_aval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    735\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 736\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34mf\"_{name}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    737\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    738\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py\u001b[0m in \u001b[0;36m_getitem\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m    347\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    348\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_getitem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 349\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0mlax_numpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_rewriting_take\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    350\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    351\u001b[0m \u001b[0;31m# Syntactic sugar for scatter operations.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_rewriting_take\u001b[0;34m(arr, idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m   4602\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4603\u001b[0m   \u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatic_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic_idx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_split_index_for_jit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0midx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4604\u001b[0;31m   return _gather(arr, treedef, static_idx, dynamic_idx, indices_are_sorted,\n\u001b[0m\u001b[1;32m   4605\u001b[0m                  unique_indices, mode, fill_value)\n\u001b[1;32m   4606\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_gather\u001b[0;34m(arr, treedef, static_idx, dynamic_idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m   4611\u001b[0m             unique_indices, mode, fill_value):\n\u001b[1;32m   4612\u001b[0m   \u001b[0midx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_merge_static_and_dynamic_indices\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatic_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic_idx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4613\u001b[0;31m   \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_index_to_gather\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0midx\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# shared with _scatter_update\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4614\u001b[0m   \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4615\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_index_to_gather\u001b[0;34m(x_shape, idx, normalize_indices)\u001b[0m\n\u001b[1;32m   4854\u001b[0m                \u001b[0;34m\"dynamic_update_slice (JAX does not support dynamically sized \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4855\u001b[0m                \"arrays within JIT compiled functions).\")\n\u001b[0;32m-> 4856\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4857\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4858\u001b[0m       \u001b[0mstart\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mslice_size\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_preprocess_slice\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_shape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx_axis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: Array slice indices must have static start/stop/step to be used with NumPy indexing syntax. Found slice(Traced<ShapedArray(int64[])>with<BatchTrace(level=1/0)> with\n  val = Array([2, 3], dtype=int64)\n  batch_dim = 0, Traced<ShapedArray(int64[])>with<DynamicJaxprTrace(level=2/0)>, None). To index a statically sized array at a dynamic position, try lax.dynamic_slice/dynamic_update_slice (JAX does not support dynamically sized arrays within JIT compiled functions)."
     ]
    }
   ],
   "source": [
    "vmap(partial(f,x))(jnp.array([2,3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "FQ3GF1JMWcvs",
    "outputId": "251c0e00-3663-40fe-8b14-2fb28c2644f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: Traced<ShapedArray(int64[], weak_type=True)>with<DynamicJaxprTrace(level=1/0)> width: 5\n",
      "i: 2, width: 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([2, 3, 4, 5, 6], dtype=int64)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# possible alternative in case the width is known\n",
    "@partial(jit, static_argnames=(\"width\"))  #<---- \"i\" is dynamic & width remains static\n",
    "def g(x,i, width):\n",
    "  print(\"i:\",i, \"width:\",width)\n",
    "  jax.debug.print(\"i: {}, width: {}\",i,width)\n",
    "  return jax.lax.dynamic_slice(x, (i,), (width,))\n",
    "g(x,2,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "R9jBRFA_Wcvu",
    "outputId": "b8427f50-6d96-42fb-c512-b7991a27b431"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: Traced<ShapedArray(int64[])>with<DynamicJaxprTrace(level=2/0)> width: 5\n",
      "i: 2, width: 5\n",
      "i: 3, width: 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([[2, 3, 4, 5, 6],\n",
       "       [3, 4, 5, 6, 7]], dtype=int64)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vmap(partial(g,x,width=5))(jnp.array([2,3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "3xLxdtaKWcvu",
    "outputId": "94da0891-1218-4177-f660-2eaf878e4366"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([8, 9], dtype=int64)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_1UkCe-mWcvw",
    "outputId": "acbc6de0-89a4-48b3-8234-850785cac3ca"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: 8, width: 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([5, 6, 7, 8, 9], dtype=int64)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(x,8,5) # take care !!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Gz91RwqDWcvy"
   },
   "source": [
    "# Device\n",
    "\n",
    "By default, JAX arrays are placed uncommitted on the default device (jax.devices()[0]), which is the first GPU or TPU by default. If no GPU or TPU is present, jax.devices()[0] is the CPU.\n",
    "\n",
    "So most of the cases you do not care about contrary to Pytorch for instance with the `to_device` and the `detach`...\n",
    "\n",
    "But we can \"put\" into a particular device..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "tLrJGpfLWcvy",
    "outputId": "3783decb-dc73-4b86-a16b-77363998c283"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SingleDeviceSharding(device=cuda(id=0))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jx.sharding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Jt530KbyWcv1",
    "outputId": "76c2ad4d-5e3c-4092-a1f4-9e5cdb307b9a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SingleDeviceSharding(device=CpuDevice(id=0))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tmp = jax.device_put(jx,device=jax.devices(\"cpu\")[0])\n",
    "tmp.sharding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MLTuwhCc__4Y"
   },
   "source": [
    "# Takeaway message\n",
    "\n",
    "- JAX rather easy to be on board in you know Python. After sometimes you will discover that you need to think differently (ie. pure-functions)\n",
    "- jax.numpy as API close to Numpy. Now, DeviceArray are immutable objects so there are some adaptation\n",
    "- auto-diff is easy and exact\n",
    "- vmap is really amazing, there are other kinds of paralellization (eg. pmap for multi-devices)\n",
    "- You can use JAX optimization on jnp.array, dict and User structures using PyTree\n",
    "\n",
    "Other nbs use JAX fucntions to use JIT (Just-In-Time compilation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2dgQ4ENJrhii"
   },
   "source": [
    "# Docs\n",
    "\n",
    "- JAX https://jax.readthedocs.io/en/latest/index.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "J7mhz0MdrsDl"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Diaporama",
  "colab": {
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