{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "00866294",
   "metadata": {},
   "source": [
    "# R Kernel Spec Demonstration\n",
    "\n",
    "JupyterLab is not restricted to Python alone. Architecturally, the Jupyter framework natively supports a wide variety of programming languages through language-specific kernel specifications and runtimes.\n",
    "\n",
    "By extending this language-agnostic execution model to the [Jupyter MCP capability](https://github.com/datalayer/jupyter-mcp-server/pull/292), JupyDeep enables seamless multi-language workflows. Users can now harness the full power of JupyDeep for data science with unparalleled flexibility, efficiency, and intelligence across diverse runtime environments.\n",
    "\n",
    "In this section, we demonstrate how to leverage this capability to run an R kernel in JupyterLab using JupyDeep.\n",
    "\n",
    "To get started, we need to set up the appropriate environment. We will use [Pixi](https://pixi.prefix.dev/latest/) as our environment manager—please make sure it is installed on your system before proceeding. Afterward, you can clone the example repository - Misc_RKernel - from the [JupyDeep Gallery](https://github.com/yezhenqing/jupydeep-gallery/tree/main/Misc_RKernel).\n",
    "\n",
    "Next, navigate into the cloned directory and start the environment by running:\n",
    "\n",
    "```bash\n",
    "git clone https://github.com/yezhenqing/jupydeep-gallery.git\n",
    "cd ./jupydeep-gallery/Misc_RKernel\n",
    "pixi install\n",
    "pixi run jupyter lab --ip=0.0.0.0\n",
    "```\n",
    "\n",
    "Once executed, you will have a ready-to-go JupyterLab environment with both the **R kernel** and **JupyDeep** pre-installed.\n",
    "If you don't see Agents appear, please try refreshing the web page or restarting the Jupyter server. \n",
    "\n",
    "> *Create a new R Notebook plotting sine and cosine curves with tidyverse (do not overwrite existing notebooks).*\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "Paste the prompt above into the chat input box. The content below demonstrates the subsequent output generated by JupyDeep via WuKong agent with z-ai/glm-5.2 LLM model. For the complete example and additional files, please refer to this case in the [JupyDeep Gallery](https://github.com/yezhenqing/jupydeep-gallery/tree/main/Misc_RKernel).\n",
    "\n",
    "Brilliant! Enjoy your data science journey with both R and Python in JupyDeep!\n",
    "\n",
    "<iframe \n",
    "    width=\"600\" \n",
    "    height=\"400\" \n",
    "    src=\"https://www.youtube.com/embed/qu2vch54JP8\" \n",
    "    title=\"YouTube video player\" \n",
    "    frameborder=\"0\" \n",
    "    allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" \n",
    "    allowfullscreen></iframe>\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bff6939c",
   "metadata": {},
   "source": [
    "## Sine and Cosine Curves in R\n",
    "\n",
    "This notebook plots **sine** and **cosine** curves using the `tidyverse` ecosystem in R, leveraging `tibble`, `dplyr`, and `ggplot2`.\n",
    "\n",
    "The mathematical functions plotted are:\n",
    "\n",
    "$$\\sin(x) = \\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n+1)!} x^{2n+1}$$\n",
    "\n",
    "$$\\cos(x) = \\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n)!} x^{2n}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8d1f453e",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "── Attaching core tidyverse packages ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 2.0.0 ──\n",
      "✔ dplyr     1.2.1     ✔ readr     2.2.0\n",
      "✔ forcats   1.0.1     ✔ stringr   1.6.0\n",
      "✔ ggplot2   4.0.3     ✔ tibble    3.3.1\n",
      "✔ lubridate 1.9.5     ✔ tidyr     1.3.2\n",
      "✔ purrr     1.2.2     \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "── Conflicts ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "✖ dplyr::filter() masks stats::filter()\n",
      "✖ dplyr::lag()    masks stats::lag()\n",
      "ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tidyverse loaded successfully.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R version: R version 4.5.3 (2026-03-11) \n"
     ]
    }
   ],
   "source": [
    "# Install tidyverse if not already installed\n",
    "if (!requireNamespace(\"tidyverse\", quietly = TRUE)) {\n",
    "  install.packages(\"tidyverse\", repos = \"https://cloud.r-project.org\")\n",
    "}\n",
    "\n",
    "# Load tidyverse\n",
    "library(tidyverse)\n",
    "\n",
    "cat(\"tidyverse loaded successfully.\\n\")\n",
    "cat(\"R version:\", R.version.string, \"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "249facc1",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wide format:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# A tibble: 6 × 3\n",
      "        x   sin_x cos_x\n",
      "    <dbl>   <dbl> <dbl>\n",
      "1 0       0       1    \n",
      "2 0.00629 0.00629 1.000\n",
      "3 0.0126  0.0126  1.000\n",
      "4 0.0189  0.0189  1.000\n",
      "5 0.0252  0.0252  1.000\n",
      "6 0.0314  0.0314  1.000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Long format:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# A tibble: 6 × 3\n",
      "        x `function`       y\n",
      "    <dbl> <chr>        <dbl>\n",
      "1 0       sin(x)     0      \n",
      "2 0       cos(x)     1      \n",
      "3 0.00629 sin(x)     0.00629\n",
      "4 0.00629 cos(x)     1.000  \n",
      "5 0.0126  sin(x)     0.0126 \n",
      "6 0.0126  cos(x)     1.000  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Summary ranges:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# A tibble: 1 × 4\n",
      "  x_min x_max sin_range cos_range\n",
      "  <dbl> <dbl> <chr>     <chr>    \n",
      "1     0  6.28 -1 to 1   -1 to 1  \n"
     ]
    }
   ],
   "source": [
    "# Generate x values from 0 to 2*pi (1000 points for smooth curves)\n",
    "# Use tibble and dplyr to build a tidy dataset\n",
    "data <- tibble(\n",
    "  x = seq(0, 2 * pi, length.out = 1000)\n",
    ") |>\n",
    "  mutate(\n",
    "    sin_x = sin(x),\n",
    "    cos_x = cos(x)\n",
    "  )\n",
    "\n",
    "# Pivot into long format for easy ggplotting with color aesthetics\n",
    "data_long <- data |>\n",
    "  pivot_longer(\n",
    "    cols = c(sin_x, cos_x),\n",
    "    names_to = \"function\",\n",
    "    values_to = \"y\"\n",
    "  ) |>\n",
    "  mutate(`function` = recode(`function`,\n",
    "    sin_x = \"sin(x)\",\n",
    "    cos_x = \"cos(x)\"\n",
    "  ))\n",
    "\n",
    "# Preview the data\n",
    "cat(\"Wide format:\\n\")\n",
    "print(head(data))\n",
    "\n",
    "cat(\"\\nLong format:\\n\")\n",
    "print(head(data_long))\n",
    "\n",
    "cat(\"\\nSummary ranges:\\n\")\n",
    "data |>\n",
    "  summarise(\n",
    "    x_min = min(x), x_max = max(x),\n",
    "    sin_range = paste(round(min(sin_x), 4), \"to\", round(max(sin_x), 4)),\n",
    "    cos_range = paste(round(min(cos_x), 4), \"to\", round(max(cos_x), 4))\n",
    "  ) |>\n",
    "  print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9a22a529",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define nice pi-based break labels\n",
    "pi_breaks <- c(0, pi / 2, pi, 3 * pi / 2, 2 * pi)\n",
    "pi_labels <- c(\"0\", \"π/2\", \"π\", \"3π/2\", \"2π\")\n",
    "\n",
    "# Plot sine and cosine curves with ggplot2\n",
    "ggplot(data_long, aes(x = x, y = y, color = `function`)) +\n",
    "  geom_line(linewidth = 1.1) +\n",
    "  # Highlight intersection points (sin(x) == cos(x) at π/4 and 5π/4)\n",
    "  geom_point(\n",
    "    data = tibble(\n",
    "      x = c(pi / 4, 5 * pi / 4),\n",
    "      y = c(sin(pi / 4), sin(5 * pi / 4)),\n",
    "      `function` = \"intersection\"\n",
    "    ),\n",
    "    aes(color = NULL),\n",
    "    color = \"green\",\n",
    "    size = 3,\n",
    "    shape = 19\n",
    "  ) +\n",
    "  scale_color_manual(\n",
    "    name = \"Function\",\n",
    "    values = c(\"sin(x)\" = \"blue\", \"cos(x)\" = \"red\")\n",
    "  ) +\n",
    "  scale_x_continuous(breaks = pi_breaks, labels = pi_labels) +\n",
    "  scale_y_continuous(limits = c(-1.2, 1.2)) +\n",
    "  labs(\n",
    "    title = \"Sine and Cosine Curves\",\n",
    "    x = \"x (radians)\",\n",
    "    y = \"y\"\n",
    "  ) +\n",
    "  geom_hline(yintercept = 0, color = \"black\", linewidth = 0.4) +\n",
    "  theme_minimal(base_size = 13) +\n",
    "  theme(\n",
    "    plot.title = element_text(face = \"bold\", hjust = 0.5),\n",
    "    panel.grid.minor = element_line(linetype = \"dotted\", color = \"grey80\")\n",
    "  )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de90894c-384b-4b34-9147-c022cbe0e10e",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}