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‎posts/02082023-numpy-latex/index.quarto_ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"---\n",
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"title: Convert a NumPy array to LaTeX\n",
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"description: LaTeX matrices and determinants from NumPy arrays\n",
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"author: 'Enrique Pérez Herrero'\n",
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"date: '08-02-2023'\n",
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"editor: source\n",
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"image: 'theta3x3matrix.png'\n",
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"draft: false\n",
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"categories:\n",
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" - Python\n",
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" - Numpy\n",
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" - Latex\n",
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" - Determinant\n",
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"---\n",
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"\n",
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"\n",
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"![Sierra de las Nieves (Málaga)](20180104_134329.jpg)\n",
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"\n",
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"# Convert Numpy array to $LaTeX$\n",
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"\n",
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"Sometimes, when you are writing a statistics or a math article, you must go\n",
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"through a tedious process of typing and testing numerous lines of text until\n",
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"your code works. This can be especially boring when dealing with long matrices.\n",
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"If you want to improve your productivity, automating this process comes in very\n",
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"handy, and [Python](https://www.python.org/) is particularly useful for that.\n",
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"\n",
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"\n",
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"## Functions for matrices and determinants\n",
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"\n",
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"The functions `matrix2latex` and `det2latex` generate an indented $LaTeX$ string\n",
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"that can be copied or directly rendered in your math article.\n",
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"\n",
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"The `INDENT_SPACES` parameter specifies the number of spaces used for\n",
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"indentation.\n"
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],
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"id": "127a872b"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| label: latex_functions\n",
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"import numpy as np\n",
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"\n",
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"INDENT_SPACES = 3\n",
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"\n",
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"def indent(num_indent=1):\n",
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" \"\"\"\n",
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" Number of spaces for indentation\n",
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" \"\"\"\n",
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" return num_indent * INDENT_SPACES * \" \"\n",
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"\n",
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"def matrix2latex(matrix):\n",
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" \"\"\"\n",
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" Convert a NumPy array to LaTeX code as a matrix\n",
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" \"\"\"\n",
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" left_latex = r\"\\left(\" + \"\\n\" + indent(1) + r\"\\begin{array}\"\n",
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" right_latex = indent(1) + r\"\\end{array}\" + \"\\n\" + r\"\\right)\"\n",
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" m_cols = matrix.shape[1]\n",
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" array_cols = \"{\" + \"r\" * m_cols + \"}\\n\"\n",
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" elements_latex = \"\"\n",
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" for row in matrix:\n",
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" elements_latex = \\\n",
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" elements_latex + indent(2) + \" & \".join([str(x) for x in row]) + \\\n",
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" r\" \\\\ \" + \"\\n\"\n",
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" latex = left_latex + array_cols + elements_latex + right_latex\n",
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" return f\"$$\\n{latex}\\n$$\"\n",
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"\n",
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"def det2latex(matrix):\n",
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" \"\"\"\n",
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" Convert a NumPy array to LaTeX code as a determinant\n",
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" \"\"\"\n",
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" left_latex = r\"\\begin{vmatrix}\" + \"\\n\"\n",
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" right_latex = r\"\\end{vmatrix}\"\n",
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" m_cols = matrix.shape[1]\n",
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" elements_latex = \"\"\n",
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" for row in matrix:\n",
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" elements_latex = \\\n",
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" elements_latex + indent(1) + \" & \".join([str(x) for x in row]) + \\\n",
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" r\" \\\\ \" + \"\\n\"\n",
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" latex = left_latex + elements_latex + right_latex\n",
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" return f\"$$\\n{latex}\\n$$\""
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],
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"id": "latex_functions",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Output string\n",
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"\n",
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"Using the [NumPy](https://numpy.org/) function `np.eye`, we can create an\n",
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"identity matrix of the desired dimensions, making it a convenient tool for\n",
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"testing our functions.\n"
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],
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"id": "b0e17845"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"print(matrix2latex(np.eye(3, dtype=int)))"
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],
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"id": "bf31123b",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Rendering output in a document\n",
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"\n",
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"If you are working in a [Jupyter](https://jupyter.org/) notebook, you can render\n",
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"a $LaTeX$ string using the `Math` function from the `IPython` library, which can\n",
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"be imported as follows:\n"
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],
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"id": "27e76398"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| eval: false\n",
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"from IPython.display import Math"
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],
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"id": "29c0bda7",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"If you are writing a `Python` chunk in a `Quarto` file in\n",
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"[RStudio](https://posit.co/download/rstudio-desktop/), you need to include the\n",
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"option `#| output: asis` at the top of the code chunk. This option determines\n",
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"how the output is rendered in the final document.\n"
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],
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"id": "22e95356"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| label: identity_det\n",
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"#| output: asis\n",
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"print(det2latex(np.eye(3, dtype=int)))"
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],
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"id": "identity_det",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| label: identity_matrix\n",
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"#| output: asis\n",
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"# Identity 4x4 matrix\n",
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"identity_4 = np.eye(4, dtype=int)\n",
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"identity_4_latex = r\"$$I_4 = \" + f\"{matrix2latex(identity_4)}\"[2:]\n",
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"print(identity_4_latex)"
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],
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"id": "identity_matrix",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Rendering the output to a file\n",
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"\n",
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"The $LaTeX$ string can be rendered and saved to a file using the\n",
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"following function, which is based on the `SymPy` library.\n"
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],
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"id": "c767ecf6"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| eval: false\n",
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"from sympy import preview\n",
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"\n",
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"def latex2png(latex, filename, fontsize=300):\n",
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" \"\"\"\n",
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" Render LaTeX code to a PNG image\n",
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" \"\"\"\n",
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" return preview(latex,\n",
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" viewer='file',\n",
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" filename=filename,\n",
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" euler=False,\n",
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" dvioptions=['-D', f'{str(fontsize)}'])"
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],
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"id": "1d678be2",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Other types of automated matrices\n",
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"\n",
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"### Matrices with numbered elements\n"
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],
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"id": "2109eb16"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"def element_matrix(n, notation=r\"x\"):\n",
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" \"\"\"\n",
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" Matrix with elements in algebraic notation \n",
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" \"\"\"\n",
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" vec_function = \\\n",
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" np.vectorize(lambda i, j: notation + \"_{\" + f\"{i + 1}{j + 1}\" + \"}\")\n",
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" return np.fromfunction(vec_function,\n",
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" shape=(n, n),\n",
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" dtype=int)"
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],
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"id": "e113a4fb",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| label: element_matrix_example\n",
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"#| output: asis\n",
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"print(matrix2latex(element_matrix(5, notation=r\"\\theta\")))"
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],
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"id": "element_matrix_example",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Triangular matrices\n",
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"\n",
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"* _Upper Triangular Matrix_: In an upper triangular matrix, all elements below the\n",
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"main diagonal are zero.\n"
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],
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"id": "23a78e28"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"def up_triangular_matrix(n):\n",
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" \"\"\"\n",
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" Upper Triangular matrix filled with ones and zeros\n",
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" \"\"\"\n",
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" return np.fromfunction(lambda i, j: 1 * np.less_equal(i , j),\n",
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" shape=(n, n),\n",
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" dtype=int)"
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],
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"id": "82e86e4b",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* _Lower Triangular Matrix_: In a lower triangular matrix, all elements above the main diagonal are zero.\n"
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],
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"id": "9b7fa372"
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"def lw_triangular_matrix(n):\n",
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" \"\"\"\n",
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" Lower Triangular matrix filled with ones and zeros\n",
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" \"\"\"\n",
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" return np.fromfunction(lambda i, j: 1 * np.greater_equal(i , j),\n",
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" shape=(n, n),\n",
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" dtype=int)"
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],
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"id": "bac1687e",
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {},
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"source": [
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"#| label: upper_matrix_example\n",
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"#| output: asis\n",
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"print(matrix2latex(up_triangular_matrix(5)))"
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],
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"id": "upper_matrix_example",
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"execution_count": null,
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"outputs": []
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}
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],
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"metadata": {
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"kernelspec": {
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"name": "shiny-test",
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"language": "python",
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"display_name": "Shiny Test",
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"path": "/home/eph/.local/share/jupyter/kernels/shiny-test"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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