using_uv/Files/intro_to_gennaker.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "49493b25-32ca-4f4e-a0cf-948e3d957505",
   "metadata": {},
   "outputs": [],
   "source": [
    "from symbolic_math import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e78aac2a-9ecf-4384-8ca8-ad6926f91908",
   "metadata": {},
   "source": [
    "# Introduction to Gennaker "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1522ef7c-4285-4a20-8c20-f05e9114ee10",
   "metadata": {},
   "source": [
    "Gennaker is an app that lets you read or write a type of document called a booklet. The characteristic feature of a booklet is that it can conveys ideas that are codified in three complementary ways:\n",
    "\n",
    "- natural language \n",
    "- mathematics\n",
    "- computer code"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "517e5455-1e48-4c31-82b9-10e784e0df1d",
   "metadata": {},
   "source": [
    "## Python and Notebooks\n",
    "\n",
    "Python is the default code dialect because it is programming language that is closest to a universal second language. \n",
    "\n",
    "Gennaker relies heavily on JupyterLab (henceforth JL) and its notebooks. A JL notebook is essentially a text file with code like any other but better comments. \n",
    "\n",
    "Neither Gennaker nor JupyterLab try to be an integrated developoment environment (IDE) for writing code. JupyterLab is a toolkit. Gennaker is a collection of tools that make it easy for authors can use to create and distribute technical documents and equally easy for readers to read and experiment with such documents. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91372beb-4cd8-40ef-bd17-2541eb46ca2c",
   "metadata": {},
   "source": [
    "## The Role for Gennaker\n",
    "\n",
    "In contrast to the familiar tools for creating and read PDFs, Gennaker is committed to equal treatment for authors and readers. \n",
    "\n",
    "It is also intended as a set of “training wheels” that make it easy for someone to started using Python and JupyterLab to read and write documents that are like PDFs with working code. Like JupyterLab, Gennaker is open source. The people who are developing Gennaker have zero incentive to lock you into using it. Like training wheels for bicycles, Gennaker succeeds when people stop using it. \n",
    "\n",
    "If you are working on macOS or Windows and aren't familiar with Python and JupyterLab, Gennaker makes it trivial to get up and running. All you have to do is download and install an app. (If you are working on Linux, you don't need training wheels.)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2f4a448-ea61-4fa3-90b3-2721869da6be",
   "metadata": {},
   "source": [
    "## Booklets\n",
    "Gennaker is organizes its documents as booklets. In many ways, a booklet is like a software project that will eventually be published as a library. Booklets should also be published, and might even be published on sites such as [`http://pypi.org`](https://pypi.org) that distributes code libraries, but a more natural channel might be a reasearch paper repository analogous to [`https://arxiv.org`](https://arxiv.org) or [`https://nber.org`](https://nber.org). \n",
    "\n",
    "Booklets will often (but not always) include a JupyterLab notebook. Frequently they will include other files too. If you look in the browser bar to the right, you'll see that this booklet includes both this notebook, with the characteristic suffix, `.ipynb` and a comma-separated-value file `data.csv` that the code in the notebook reads from.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2db5ad7-c267-481b-ba5d-7fc4d233dc87",
   "metadata": {},
   "source": [
    "## Clean and Classic Notebook Interfaces\n",
    "When you open a notebook that was authored inside Gennaker, the default is to display a decluttered version of the classic user interface of JupyterLab. The file format for a notebook is unchanged, so there are many possibilities:  \n",
    "\n",
    "- An author can publish a booklet with notebooks that by default using either the clean interface or JupyterLab's classic, full-featured interface.\n",
    "\n",
    "- No matter what the author decided, a reader can choose which interface to use to display a notebook. \n",
    "\n",
    "If you want to see a side by side comparision of the two interfaces, use the main Gennaker page to open the “Classic JupyterLab” booklet. It has a copy of this notebook. Open it and compare it to this version of the notebook to see the difference in the interfaces. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fb874ca-68d9-42e8-ba21-27baf45ab194",
   "metadata": {},
   "source": [
    "## What You Can Do With a Gennaker Booklet"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21550cd0-10ab-40d9-9fba-b857c68dae09",
   "metadata": {},
   "source": [
    "### Latex Math and Symbolic Calculations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7372ef42-1920-4467-b9d9-e2c6b7125705",
   "metadata": {},
   "source": [
    "You can display typeset mathematics using markup from Latex that you type in by hand:\n",
    "$$V = \\sum_{t = 0}^{\\infty} \\beta^t x_t$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4565cef2-2b60-447d-995e-b3c478835bbc",
   "metadata": {},
   "source": [
    "You sometimes it is easier to build up complex Latex expressions by composing functions. For example, to specify a time dependent desity function you can define some functions and compose them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "afc66e23-7f0c-40bf-9149-6a0fb1f37c75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( x \\mapsto e^{- \\frac{1}{x^{2}}} \\right)$"
      ],
      "text/plain": [
       "Lambda(x, exp(-1/x**2))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = Lambda(x, exp(-x**(-2))) \n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "836c65c4-8914-4d9c-bd3b-76de0dad993b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( x \\mapsto \\alpha + \\beta \\left(1 - e^{- \\frac{1}{x^{2}}}\\right) \\right)$"
      ],
      "text/plain": [
       "Lambda(x, alpha + beta*(1 - exp(-1/x**2)))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = Lambda(x, a + b*(1-g(x)))\n",
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5b95ab3d-245c-47ec-b06d-026deadf22f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( x \\mapsto \\frac{\\alpha}{\\alpha + \\beta \\left(1 - e^{- \\frac{1}{x^{2}}}\\right)} \\right)$"
      ],
      "text/plain": [
       "Lambda(x, alpha/(alpha + beta*(1 - exp(-1/x**2))))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = Lambda(x, (a / h(x)))\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "03daf02c-7bb5-4119-8f47-56ec7891fe48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left( x, \\  t\\right) \\mapsto \\frac{1}{\\frac{\\alpha}{\\alpha + \\beta \\left(1 - e^{- \\frac{1}{x^{2}}}\\right)} + \\left(- \\frac{\\alpha}{\\alpha + \\beta \\left(1 - e^{- \\frac{1}{x^{2}}}\\right)} + 1\\right) e^{t \\left(\\alpha + \\beta \\left(1 - e^{- \\frac{1}{x^{2}}}\\right)\\right)}} \\right)$"
      ],
      "text/plain": [
       "Lambda((x, t), 1/(alpha/(alpha + beta*(1 - exp(-1/x**2))) + (-alpha/(alpha + beta*(1 - exp(-1/x**2))) + 1)*exp(t*(alpha + beta*(1 - exp(-1/x**2))))))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F = Lambda((x, t), (exp(h(x) * t) * (1 - r(x)) + r(x))**(-1))\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae22df78-c867-4ecd-964f-30299ad04259",
   "metadata": {},
   "source": [
    "This type of distribtuion function has a time varying proabitatiy mass at zero. Sympy will calculate the limit for you. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dcb6ee7e-5bac-4a4d-90dc-8d430198b2b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( t \\mapsto \\frac{\\alpha + \\beta}{\\alpha + \\beta e^{\\alpha t + \\beta t}} \\right)$"
      ],
      "text/plain": [
       "Lambda(t, (alpha + beta)/(alpha + beta*exp(alpha*t + beta*t)))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F0 = Lambda(t, limit(F(x, t), x, 0))\n",
    "F0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db98aeb9-717d-4351-8b81-8cb0d7f53e16",
   "metadata": {},
   "source": [
    "### Graphing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc011088-4e40-40ef-9769-a688f6b692f1",
   "metadata": {},
   "source": [
    "The Python workhorses for scientific visualization and data analysis have long been `matplotlib` and `pandas`. The default package manager was `pip`.\n",
    "\n",
    "These are widely used and well tested, so of course, Gennaker supports them. But there are newer possibilities you can try. \n",
    "\n",
    "The `uv` library can speed things up dramatically, especially on Windows. If you are familiar with `ggplot` from `R`. you might want to try the `plotnine` library. Here, we'll use `polars` to turn a `csv` file into the type of dataframe that `ggplot` expects. \n",
    "\n",
    "If we wanted to hide these details from the reader, we could put some of what follows into a `.py` and import from it, just as we did for SymPy. Instead, we can do the `uv` version of a `pip install` on the fly by using the `!` operator to have JupyterLab pass a command onto the operating system shell instead of giving it to the Python interpreter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "08ed7171-dad7-4eaf-8df5-8cd60419d6cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !uv pip install plotnine polars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "83c6d770-6e7e-4a6c-9373-437fc0d51b79",
   "metadata": {},
   "outputs": [],
   "source": [
    "# from plotnine import ggplot, aes, geom_point, geom_smooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bc1fb547-2603-4c38-8c25-7c9489fed5b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# from polars import read_csv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8c7283b-4b24-48a0-87b5-97c300e0fb16",
   "metadata": {},
   "source": [
    "We can define a Python dictionary `dtypes` to override the default assumptions that Polars would otherwise make when it reads the data from the `csv` file. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "27d3e23e-f5dc-41d7-aba2-60d6aa791a63",
   "metadata": {},
   "outputs": [],
   "source": [
    "dtypes = {\"x\": float, \"y\": float}\n",
    "\n",
    "df = read_csv(\n",
    "    \"data.csv\",\n",
    "    schema_overrides=dtypes\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e102aa0-2c13-4057-a7bb-9cc24b62bd73",
   "metadata": {},
   "source": [
    "Finally, we use the layered approach of `ggplot` to define the look of the plot and add some geometric objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ccc7ef57-e467-4b8c-bfde-57fe32c06d16",
   "metadata": {},
   "outputs": [
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"
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 640
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(\n",
    "    ggplot(data=df, mapping=aes(x=\"x\", y=\"y\"))\n",
    "    + geom_point()\n",
    "    + geom_smooth(method=\"lm\", color=\"blue\")\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd8389f-85b4-4845-b5c7-a35cf2e71f1a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.13.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}