{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some notes about recent dolo development"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Toolchain\n",
    "\n",
    "- build tool: `poetry`\n",
    "    - simplifies dependency management\n",
    "    - `setup.py` disappeared\n",
    "    - `pyproject.toml`\n",
    "    - install `poetry` then `pip install .`\n",
    "- tag-based releases:\n",
    "    - automatic release on pypi when tag is pushed to master\n",
    "    - semi-automatic release from pypi to conda\n",
    "- documentation switch to github/actions + mkdocs:\n",
    "    - old: `www.econforge.org/dolo`\n",
    "    - new: `www.econforge.org/dolo.py`\n",
    "    - built and published on tag-release\n",
    "- advertisement: try `mamba` instead of `conda` !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Development choices\n",
    "\n",
    "\n",
    "- semi-object oriented programming:\n",
    "    - type hierarchy\n",
    "    - mostly stateless design\n",
    "        - most objects are simple datastructures with simple internal state\n",
    "- multiple dispatch\n",
    "- use optional typing:\n",
    "    - mostly for documentation\n",
    "    - almost completely useless at runtime\n",
    "- performance\n",
    "    - numba-ification out of reach (no @jitclass) but...\n",
    "    - some objects have a typed numba equivalent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numbaification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<dolo.numeric.grids.UniformCartesianGrid at 0x7fb64c3f92d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "((0.0, 1.0, 10), (0.0, 1.0, 10))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# numba-ification\n",
    "from dolo.numeric.grids import UniformCartesianGrid, NonUniformCartesianGrid\n",
    "grid = UniformCartesianGrid(min=[0.0, 0.0], max=[1.0, 1.0], n=[10, 10])\n",
    "display(grid)\n",
    "display(grid.__numba_repr__())   # fully type inferrable by numba / interpolation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UniTuple(Tuple(float64, float64, int64) x 2)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numba\n",
    "numba.typeof(grid.__numba_repr__())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UniTuple(array(float64, 1d, C) x 2)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "grid = NonUniformCartesianGrid([np.linspace(0,1,10), np.linspace(0,1,10)])\n",
    "numba.typeof( grid.__numba_repr__() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stateless / Statefree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# problem 1\n",
    "\n",
    "class Model:\n",
    "    \n",
    "    def __init__(self, a=1, b=2):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "        \n",
    "    def solve(self):\n",
    "        return self.a + self.b\n",
    "        \n",
    "        \n",
    "d = dict(a=1, b=2.5)\n",
    "model = Model(**d)\n",
    "model.solve() # -> 3.4\n",
    "\n",
    "d['a'] = 1.5 # bad student\n",
    "model.solve() # -> I paid for this school, why don't I get 4.0 ?\n",
    "\n",
    "# solutions:\n",
    "\n",
    "# - terminate student\n",
    "\n",
    "# - promote no reference style of coding:\n",
    "\n",
    "m = Model()\n",
    "m.a = 1\n",
    "m.b = 2\n",
    "\n",
    "# - educate by providing feedback when parameter is set (see below)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model:\n",
    "    \n",
    "    def __init__(self, a=1)\n",
    "        self.a\n",
    "    \n",
    "    def update():\n",
    "        self.b = self.a+1\n",
    "        \n",
    "    def solve():\n",
    "        returb self.a+self.b\n",
    "\n",
    "model = Model()\n",
    "model.update()  # bad design\n",
    "model.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0.0, 1.0, 10), (0.0, 1.0, 10))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# stateless / stateful\n",
    "\n",
    "class Model:\n",
    "    \n",
    "    a = 1\n",
    "    \n",
    "    def update():\n",
    "        self.b = self.a+1\n",
    "        \n",
    "    def solve():\n",
    "        returb self.a+self.b\n",
    "\n",
    "model = Model()\n",
    "model.update()\n",
    "model.solve()\n",
    "\n",
    "model.a = 2\n",
    "# model.update()  # bad design\n",
    "model.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "two tools to improve the situation:\n",
    "- user-experience:\n",
    "    - properties\n",
    "- developper experience:\n",
    "    - decorators / annotations\n",
    "    - traits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model:\n",
    "    \n",
    "    @property\n",
    "    def a():\n",
    "        return self._a_\n",
    "    \n",
    "    @a.setter\n",
    "    def a(self, value):\n",
    "        print(f\"Parameter 'a' set to {value}\") # for the bad student\n",
    "        self._a_ = value\n",
    "        self.update()\n",
    "        \n",
    "    def update():\n",
    "        self.b = self.a+1\n",
    "        \n",
    "    def solve():\n",
    "        returb self.a + self.b\n",
    "\n",
    "model = Model()\n",
    "model.a = 2 # triggers update()\n",
    "model.solve() # -> 3\n",
    "\n",
    "## ok but requires lots of recalculations with many parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# better solution with global flag\n",
    "\n",
    "class Model:\n",
    "        \n",
    "    __parameters_reset__ = True\n",
    "    \n",
    "    @property\n",
    "    def a():\n",
    "        return self._a_\n",
    "    \n",
    "    @a.setter\n",
    "    def a(self, value):\n",
    "        print(f\"Parameter 'a' set to {value}\") # for the bad student\n",
    "        self._a_ = value\n",
    "        self.update()\n",
    "        \n",
    "    @property\n",
    "    def b():\n",
    "        return self._b_\n",
    "    \n",
    "    @a.setter\n",
    "    def b(self, value):\n",
    "        print(f\"Parameter 'b' set to {value}\") # for the bad student\n",
    "        self._b_ = value\n",
    "        self.update()\n",
    "        \n",
    "    def update():\n",
    "        if __parameters_reset__:\n",
    "            self.c = self.a+1\n",
    "            __parameters_reset__ = False\n",
    "        \n",
    "    def solve():\n",
    "        returb self.a + self.b\n",
    "\n",
    "model = Model()\n",
    "model.a = 2 # triggers update()\n",
    "model.solve() # -> 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'magiclass' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-7cb212abb298>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m# better solution with global flag\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0;34m@\u001b[0m\u001b[0mmagiclass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0;32mclass\u001b[0m \u001b[0mModel\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'magiclass' is not defined"
     ]
    }
   ],
   "source": [
    "# same code with traits: (many possible syntaxes)\n",
    "\n",
    "# better solution with global flag\n",
    "\n",
    "@magiclass\n",
    "class Model:\n",
    "        \n",
    "    a: Parameter[Float]    \n",
    "    b: Parameter[Float]\n",
    "\n",
    "    @depends(['a', 'b'])\n",
    "    def update():\n",
    "        if __parameters_reset__:\n",
    "            self.c = self.a+1\n",
    "            __parameters_reset__ = False\n",
    "        \n",
    "    @depends(['update'])\n",
    "    def solve():\n",
    "        return self.a + self.b\n",
    "\n",
    "        \n",
    "model = Model()\n",
    "model.a = 2.0  # resets `self.__reset__['update']` and `self.__reset__['solve']` to True\n",
    "model.b = 2.0  # same\n",
    "model.solve()  # will need to recompute update(), which in turn, will take new values of a and b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# other approach\n",
    "\n",
    "class MagicalDict:\n",
    "    \n",
    "    dependencies: Dict[]\n",
    "    def __init__(self, model):\n",
    "        self.model = model\n",
    "    \n",
    "    def __setitem__(self, k, v):\n",
    "        pass #\n",
    "\n",
    "    \n",
    "    \n",
    "\n",
    "class Model\n",
    "\n",
    "    calibration: MagicalDict\n",
    "        \n",
    "model = Model()\n",
    "model.calibration['a'] = 1 # same behaviour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stateless approach in dolo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
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       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt, dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><div class='xr-wrap'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>T</span>: 40</li><li><span class='xr-has-index'>N</span>: 10</li><li><span class='xr-has-index'>V</span>: 9</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-7f9eed56-112d-48d1-91d4-b649e0f33e7a' class='xr-array-in' type='checkbox' ><label for='section-7f9eed56-112d-48d1-91d4-b649e0f33e7a' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.0 0.0 9.355 0.3296 0.2329 ... 0.2355 0.9913 0.7559 0.03638 1.982</span></div><pre class='xr-array-data'>array([[[ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 2.16900189e-02,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        ...,\n",
       "        [ 2.16900189e-02,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00]],\n",
       "\n",
       "       [[-2.16900189e-02,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00],\n",
       "        [ 2.16900189e-02,  2.16900189e-02,  9.35400230e+00, ...,\n",
       "          7.62822957e-01,  3.60682624e-02,  2.05898938e+00],\n",
       "        [ 2.16900189e-02,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00,  2.16900189e-02,  9.35400230e+00, ...,\n",
       "          7.62822957e-01,  3.60682624e-02,  2.05898938e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00]],\n",
       "\n",
       "       [[ 0.00000000e+00, -2.16900189e-02,  9.35306089e+00, ...,\n",
       "          7.59958581e-01,  3.41148441e-02,  1.98356112e+00],\n",
       "        [-2.16900189e-02,  3.90420340e-02,  9.37970083e+00, ...,\n",
       "          7.64374529e-01,  3.67820030e-02,  2.09271518e+00],\n",
       "        [ 0.00000000e+00,  2.16900189e-02,  9.35306089e+00, ...,\n",
       "          7.62809192e-01,  3.60717286e-02,  2.05889192e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00,  1.73520151e-02,  9.37970083e+00, ...,\n",
       "          7.62909791e-01,  3.57742049e-02,  2.05396620e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35306089e+00, ...,\n",
       "          7.61370512e-01,  3.50810677e-02,  2.02083514e+00],\n",
       "        [-2.16900189e-02,  0.00000000e+00,  9.35306089e+00, ...,\n",
       "          7.61370512e-01,  3.50810677e-02,  2.02083514e+00]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[-2.16900189e-02, -1.07439022e-03,  9.61420916e+00, ...,\n",
       "          7.65100181e-01,  3.41202851e-02,  2.04538252e+00],\n",
       "        [-2.16900189e-02,  1.40518882e-02,  9.34551078e+00, ...,\n",
       "          7.62189721e-01,  3.57475889e-02,  2.04462352e+00],\n",
       "        [-2.16900189e-02, -2.45856318e-02,  9.27466543e+00, ...,\n",
       "          7.58599962e-01,  3.42649707e-02,  1.97074028e+00],\n",
       "        ...,\n",
       "        [-2.16900189e-02, -3.32566969e-03,  9.07518640e+00, ...,\n",
       "          7.56987961e-01,  3.59598257e-02,  1.98647444e+00],\n",
       "        [ 2.16900189e-02, -4.46909134e-03,  9.14991498e+00, ...,\n",
       "          7.58044345e-01,  3.56244995e-02,  1.99225926e+00],\n",
       "        [ 0.00000000e+00, -3.56943011e-02,  9.04737363e+00, ...,\n",
       "          7.54422827e-01,  3.45998302e-02,  1.92907212e+00]],\n",
       "\n",
       "       [[-2.16900189e-02, -2.25495311e-02,  9.60281302e+00, ...,\n",
       "          7.63568665e-01,  3.32232268e-02,  2.00702789e+00],\n",
       "        [ 0.00000000e+00, -1.04485083e-02,  9.36204534e+00, ...,\n",
       "          7.60820733e-01,  3.45806083e-02,  2.00369527e+00],\n",
       "        [ 0.00000000e+00, -4.13585243e-02,  9.24721744e+00, ...,\n",
       "          7.57116396e-01,  3.36272937e-02,  1.93988298e+00],\n",
       "        ...,\n",
       "        [-2.16900189e-02, -2.43505546e-02,  9.08023430e+00, ...,\n",
       "          7.55667124e-01,  3.49847249e-02,  1.95134965e+00],\n",
       "        [ 0.00000000e+00,  1.81147458e-02,  9.15088379e+00, ...,\n",
       "          7.59578184e-01,  3.66655795e-02,  2.03152971e+00],\n",
       "        [ 2.16900189e-02, -2.85554409e-02,  9.01536523e+00, ...,\n",
       "          7.54392233e-01,  3.50390162e-02,  1.93766096e+00]],\n",
       "\n",
       "       [[ 4.57115202e-02, -3.97296437e-02,  9.56595110e+00, ...,\n",
       "          7.61963572e-01,  3.26114858e-02,  1.97420672e+00],\n",
       "        [ 0.00000000e+00, -8.35880664e-03,  9.34821961e+00, ...,\n",
       "          7.60752155e-01,  3.47230841e-02,  2.00588815e+00],\n",
       "        [ 0.00000000e+00, -3.30868194e-02,  9.20122029e+00, ...,\n",
       "          7.56944271e-01,  3.41533438e-02,  1.94902275e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00, -4.11704626e-02,  9.06019616e+00, ...,\n",
       "          7.54268583e-01,  3.43090827e-02,  1.92133853e+00],\n",
       "        [ 0.00000000e+00,  1.44917966e-02,  9.17926823e+00, ...,\n",
       "          7.59757658e-01,  3.63878793e-02,  2.02815454e+00],\n",
       "        [ 0.00000000e+00, -1.15433383e-03,  8.99282986e+00, ...,\n",
       "          7.55875214e-01,  3.63784208e-02,  1.98159464e+00]]])</pre></div></li><li class='xr-section-item'><input id='section-47825f40-8a31-4e3d-a5d2-6aa60854d308' class='xr-section-summary-in' type='checkbox'  checked><label for='section-47825f40-8a31-4e3d-a5d2-6aa60854d308' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>T</span></div><div class='xr-var-dims'>(T)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 ... 34 35 36 37 38 39</div><input id='attrs-eb05eefc-28cb-4e25-970f-084e1c28ad04' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-eb05eefc-28cb-4e25-970f-084e1c28ad04' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2854b0fa-f9f0-44a2-890a-3a6a92f5cbe9' class='xr-var-data-in' type='checkbox'><label for='data-2854b0fa-f9f0-44a2-890a-3a6a92f5cbe9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><pre class='xr-var-data'>array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
       "       18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,\n",
       "       36, 37, 38, 39])</pre></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>N</span></div><div class='xr-var-dims'>(N)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 7 8 9</div><input id='attrs-853d420c-2c5e-40c6-87bd-23045532a658' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-853d420c-2c5e-40c6-87bd-23045532a658' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bbc0d8c6-3fbd-4cca-9856-b1dad5b7b10c' class='xr-var-data-in' type='checkbox'><label for='data-bbc0d8c6-3fbd-4cca-9856-b1dad5b7b10c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><pre class='xr-var-data'>array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])</pre></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>V</span></div><div class='xr-var-dims'>(V)</div><div class='xr-var-dtype'>&lt;U3</div><div class='xr-var-preview xr-preview'>&#x27;e_z&#x27; &#x27;z&#x27; &#x27;k&#x27; &#x27;n&#x27; ... &#x27;c&#x27; &#x27;rk&#x27; &#x27;w&#x27;</div><input id='attrs-adac2717-f460-4296-ad48-ac595a3a0154' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-adac2717-f460-4296-ad48-ac595a3a0154' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a102b5dc-6e98-4843-9ef6-3221e0fe5b9e' class='xr-var-data-in' type='checkbox'><label for='data-a102b5dc-6e98-4843-9ef6-3221e0fe5b9e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><pre class='xr-var-data'>array([&#x27;e_z&#x27;, &#x27;z&#x27;, &#x27;k&#x27;, &#x27;n&#x27;, &#x27;i&#x27;, &#x27;y&#x27;, &#x27;c&#x27;, &#x27;rk&#x27;, &#x27;w&#x27;], dtype=&#x27;&lt;U3&#x27;)</pre></li></ul></div></li><li class='xr-section-item'><input id='section-6606eac1-67bf-476c-a29f-ea9283c20d57' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-6606eac1-67bf-476c-a29f-ea9283c20d57' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (T: 40, N: 10, V: 9)>\n",
       "array([[[ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 2.16900189e-02,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        ...,\n",
       "        [ 2.16900189e-02,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35497829e+00, ...,\n",
       "          7.61398778e-01,  3.50741693e-02,  2.02103089e+00]],\n",
       "\n",
       "       [[-2.16900189e-02,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00],\n",
       "        [ 2.16900189e-02,  2.16900189e-02,  9.35400230e+00, ...,\n",
       "          7.62822957e-01,  3.60682624e-02,  2.05898938e+00],\n",
       "        [ 2.16900189e-02,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00,  2.16900189e-02,  9.35400230e+00, ...,\n",
       "          7.62822957e-01,  3.60682624e-02,  2.05898938e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35400230e+00, ...,\n",
       "          7.61384391e-01,  3.50776803e-02,  2.02093125e+00]],\n",
       "\n",
       "       [[ 0.00000000e+00, -2.16900189e-02,  9.35306089e+00, ...,\n",
       "          7.59958581e-01,  3.41148441e-02,  1.98356112e+00],\n",
       "        [-2.16900189e-02,  3.90420340e-02,  9.37970083e+00, ...,\n",
       "          7.64374529e-01,  3.67820030e-02,  2.09271518e+00],\n",
       "        [ 0.00000000e+00,  2.16900189e-02,  9.35306089e+00, ...,\n",
       "          7.62809192e-01,  3.60717286e-02,  2.05889192e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00,  1.73520151e-02,  9.37970083e+00, ...,\n",
       "          7.62909791e-01,  3.57742049e-02,  2.05396620e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  9.35306089e+00, ...,\n",
       "          7.61370512e-01,  3.50810677e-02,  2.02083514e+00],\n",
       "        [-2.16900189e-02,  0.00000000e+00,  9.35306089e+00, ...,\n",
       "          7.61370512e-01,  3.50810677e-02,  2.02083514e+00]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[-2.16900189e-02, -1.07439022e-03,  9.61420916e+00, ...,\n",
       "          7.65100181e-01,  3.41202851e-02,  2.04538252e+00],\n",
       "        [-2.16900189e-02,  1.40518882e-02,  9.34551078e+00, ...,\n",
       "          7.62189721e-01,  3.57475889e-02,  2.04462352e+00],\n",
       "        [-2.16900189e-02, -2.45856318e-02,  9.27466543e+00, ...,\n",
       "          7.58599962e-01,  3.42649707e-02,  1.97074028e+00],\n",
       "        ...,\n",
       "        [-2.16900189e-02, -3.32566969e-03,  9.07518640e+00, ...,\n",
       "          7.56987961e-01,  3.59598257e-02,  1.98647444e+00],\n",
       "        [ 2.16900189e-02, -4.46909134e-03,  9.14991498e+00, ...,\n",
       "          7.58044345e-01,  3.56244995e-02,  1.99225926e+00],\n",
       "        [ 0.00000000e+00, -3.56943011e-02,  9.04737363e+00, ...,\n",
       "          7.54422827e-01,  3.45998302e-02,  1.92907212e+00]],\n",
       "\n",
       "       [[-2.16900189e-02, -2.25495311e-02,  9.60281302e+00, ...,\n",
       "          7.63568665e-01,  3.32232268e-02,  2.00702789e+00],\n",
       "        [ 0.00000000e+00, -1.04485083e-02,  9.36204534e+00, ...,\n",
       "          7.60820733e-01,  3.45806083e-02,  2.00369527e+00],\n",
       "        [ 0.00000000e+00, -4.13585243e-02,  9.24721744e+00, ...,\n",
       "          7.57116396e-01,  3.36272937e-02,  1.93988298e+00],\n",
       "        ...,\n",
       "        [-2.16900189e-02, -2.43505546e-02,  9.08023430e+00, ...,\n",
       "          7.55667124e-01,  3.49847249e-02,  1.95134965e+00],\n",
       "        [ 0.00000000e+00,  1.81147458e-02,  9.15088379e+00, ...,\n",
       "          7.59578184e-01,  3.66655795e-02,  2.03152971e+00],\n",
       "        [ 2.16900189e-02, -2.85554409e-02,  9.01536523e+00, ...,\n",
       "          7.54392233e-01,  3.50390162e-02,  1.93766096e+00]],\n",
       "\n",
       "       [[ 4.57115202e-02, -3.97296437e-02,  9.56595110e+00, ...,\n",
       "          7.61963572e-01,  3.26114858e-02,  1.97420672e+00],\n",
       "        [ 0.00000000e+00, -8.35880664e-03,  9.34821961e+00, ...,\n",
       "          7.60752155e-01,  3.47230841e-02,  2.00588815e+00],\n",
       "        [ 0.00000000e+00, -3.30868194e-02,  9.20122029e+00, ...,\n",
       "          7.56944271e-01,  3.41533438e-02,  1.94902275e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00, -4.11704626e-02,  9.06019616e+00, ...,\n",
       "          7.54268583e-01,  3.43090827e-02,  1.92133853e+00],\n",
       "        [ 0.00000000e+00,  1.44917966e-02,  9.17926823e+00, ...,\n",
       "          7.59757658e-01,  3.63878793e-02,  2.02815454e+00],\n",
       "        [ 0.00000000e+00, -1.15433383e-03,  8.99282986e+00, ...,\n",
       "          7.55875214e-01,  3.63784208e-02,  1.98159464e+00]]])\n",
       "Coordinates:\n",
       "  * T        (T) int64 0 1 2 3 4 5 6 7 8 9 10 ... 30 31 32 33 34 35 36 37 38 39\n",
       "  * N        (N) int64 0 1 2 3 4 5 6 7 8 9\n",
       "  * V        (V) <U3 'e_z' 'z' 'k' 'n' 'i' 'y' 'c' 'rk' 'w'"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mostly stateless\n",
    "\n",
    "from dolo import *\n",
    "model = yaml_import(\"examples/models/rbc_iid.yaml\")\n",
    "dr = time_iteration(model, details=False, verbose=False)\n",
    "simulate(model, dr, N=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# with some exceptions\n",
    "model.set_calibration(beta=0.96)  # (sets global flag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TimeIterationResult(dr=<dolo.numeric.decision_rule.DecisionRule object at 0x7fb649ecfc90>, iterations=126, complementarities=True, dprocess=FiniteDistribution(points=array([[-0.04571152],\n",
       "       [-0.02169002],\n",
       "       [ 0.        ],\n",
       "       [ 0.02169002],\n",
       "       [ 0.04571152]]), weights=array([0.01125741, 0.22207592, 0.53333333, 0.22207592, 0.01125741]), origin=Normal(Μ=[0.],Σ=[[0.000256]])), x_converged=True, x_tol=1e-06, err=9.689385253586202e-07, log=None, trace=None)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = time_iteration(model, details=True, verbose=False)\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'FiniteDistribution' object has no attribute 'model'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-62-e22c1fc6dbfd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiscretize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'FiniteDistribution' object has no attribute 'model'"
     ]
    }
   ],
   "source": [
    "model.discretize()[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FiniteDistribution(points=array([[-0.04571152],\n",
       "       [-0.02169002],\n",
       "       [ 0.        ],\n",
       "       [ 0.02169002],\n",
       "       [ 0.04571152]]), weights=array([0.01125741, 0.22207592, 0.53333333, 0.22207592, 0.01125741]), origin=Normal(Μ=[0.],Σ=[[0.000256]]))"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol.dprocess"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Towards more separatation between pure objects and discretized ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'z': array([-0.05333333,  0.05333333]),\n",
       " 'k': array([ 4.67748915, 14.03246744])}"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.domain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<dolo.numeric.grids.EmptyGrid object at 0x7fb64b5c4210> × <dolo.numeric.grids.UniformCartesianGrid object at 0x7fb64b5c48d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "FiniteDistribution(points=array([[-0.04571152],\n",
       "       [-0.02169002],\n",
       "       [ 0.        ],\n",
       "       [ 0.02169002],\n",
       "       [ 0.04571152]]), weights=array([0.01125741, 0.22207592, 0.53333333, 0.22207592, 0.01125741]), origin=Normal(Μ=[0.],Σ=[[0.000256]]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid, dprocess = model.discretize()\n",
    "display( grid )\n",
    "display( dprocess  )\n",
    "# model.grid will disappear but there might be a DiscretizedModel object with a pointer to its parent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Processes and Distributions\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Three separate concepts:\n",
    "    \n",
    "- distribution ($\\epsilon$):\n",
    "\n",
    "    - does `dist.draw(N: int)`, `dist.integrate(f)`\n",
    "\n",
    "- processes $(\\epsilon_t)_{t}$:\n",
    "\n",
    "    - does `dist.simulate()`\n",
    "\n",
    "- discretized process:\n",
    "\n",
    "    - does `dist.node(i)`, `dist.inode(i,j)`, `dist.iweight(i,j)`\n",
    "    - used to solve models\n",
    "\n",
    "With multiple inheritances, it is possible to belong to several classes: \n",
    "\n",
    "- a distribution is a process\n",
    "- a markov chain is both a discretized process and a process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What matters most to me:\n",
    "\n",
    "- establish stable user-facing conventions in yaml file (***)\n",
    "    - processes names must match distributions\n",
    "    - documented here: http://www.econforge.org/dolo.py/processes/\n",
    "    - solution:  align with distiributions.jl/R/rvlib for conventions\n",
    "    - a wrapper is almost certainly needed\n",
    "- define clean language API allowing for more flexibility (**) (truncations, conditional, etc.)\n",
    "- simplify development process (*)\n",
    "    - transaprent API\n",
    "    - synchronize Python API, with Dolang API\n",
    "    - less code duplication within projects (language_element decoretor @language)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distributions\n",
    "\n",
    "- all distributions are multi-dimensional\n",
    "    - 1d distribution is a special class\n",
    "        - with `pdf`, `cdf` function\n",
    "        - automatic equiprobable discretization\n",
    "    - they carry variable names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dolo.numeric.distribution import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "dist = UNormal(μ=0, σ=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: x**2\n",
    "scip = dist.integrate(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "discr = [dist.discretize(N=n).integrate(f) for n in range(1,10)]\n",
    "discr_gh = [dist.discretize(N=n, method=\"gauss-hermite\").integrate(f) for n in range(1,10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7fb649513450>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(discr)\n",
    "plt.plot(discr_gh)\n",
    "plt.hlines(scip,*plt.xlim())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "trunc = Truncation[UNormal](dist=dist, lb=0, ub=np.Inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "dtrunc = trunc.discretize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb649a44250>]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dtrunc.points.ravel(), dtrunc.weights, 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = ProductDistribution([dist, trunc])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp = p.discretize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb648fd4450>]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pp.points[:,0], pp.points[:,1],'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "index = Bernouilli(π=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "mix = Mixture(index=index, distributions={0: dist, 1: trunc})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00789516])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mix.discretize().integrate(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m\n",
       "\u001b[0mUNormal\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msimulate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mN\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mint\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mT\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mint\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mi0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mm0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mstochastic\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mxarray\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdataarray\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataArray\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m <no docstring>\n",
       "\u001b[0;31mFile:\u001b[0m      ~/Mobilhome/econforge/dolo/dolo/numeric/processes.py\n",
       "\u001b[0;31mType:\u001b[0m      function\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "UNormal.simulate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dolo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = yaml_import(\"examples/models/rbc.yaml\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<dolo.numeric.distribution.UNormal at 0x7fb64992d110>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.exogenous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}