{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Phase Axis Formatters & Locators\n", "\n", "One-stop guide to format Matplotlib axes in multiples of π for phase/radian data using `PiFormatter`, `PiLocator`, and `setup_phase_axis`.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What & Why\n", "Phase data (e.g., wrapped interferometric phase) is naturally expressed in radians.\n", "Displaying ticks as clean multiples/fractions of π improves readability over raw decimal radians.\n", "This tutorial shows how to format axes in π units for clearer phase plots.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quick Start\n", "3 steps: import, plot, apply π-based formatter/locator.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from faninsar.plots.formatters import PiFormatter, PiLocator, setup_phase_axis\n", "\n", "x = np.linspace(-np.pi, np.pi, 200)\n", "fig, ax = plt.subplots(figsize=(5, 3))\n", "ax.plot(x, np.sin(x), label=\"sin(x)\")\n", "\n", "# Option A: manual control\n", "ax.xaxis.set_major_locator(PiLocator(base=0.5)) # π/2\n", "ax.xaxis.set_major_formatter(PiFormatter(denominator=4))\n", "\n", "# Option B: convenience helper (uncomment to try)\n", "# setup_phase_axis(ax.xaxis, base=0.5, denominator=4)\n", "\n", "ax.set_xlabel(\"Phase (radians)\")\n", "ax.set_ylabel(\"sin(x)\")\n", "ax.legend()\n", "fig.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expected: x-axis ticks like −π, −π/2, 0, π/2, π.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Core Concepts\n", "- [PiFormatter](#faninsar.plots.formatters.PiFormatter) converts radians into multiples of π; supports plain text and LaTeX mathtext.\n", "- [PiLocator](#faninsar.plots.formatters.PiLocator) places ticks at base×π intervals (e.g., 0.25 → π/4).\n", "- [setup_phase_axis](#faninsar.plots.formatters.setup_phase_axis) applies both to a given axis (e.g., `ax.xaxis` or `ax.yaxis`).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parameters & Options\n", "PiFormatter\n", "- `denominator` (int, default 4): max fraction denominator (e.g., 3π/4). Larger → finer fractions.\n", "- `symbol` (str | None): override π symbol (e.g., `\"pi\"`). If `latex=True` and None → `\\pi`.\n", "- `use_unicode` (bool, default True): use `π` vs `pi` when `latex=False`.\n", "- `latex` (bool, default False): render labels with mathtext (e.g., `$\\frac{\\pi}{2}$`).\n", "\n", "PiLocator\n", "- `base` (float, default 0.5): spacing in multiples of π; common values: 1.0 (π), 0.5 (π/2), 0.25 (π/4).\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Default (π symbol): π/2\n", "ASCII symbol: pi\n", "LaTeX: $-\\pi$\n", "Finer fraction: 3π/8\n" ] } ], "source": [ "# Micro-examples for PiFormatter\n", "from faninsar.plots.formatters import PiFormatter\n", "\n", "print(\"Default (π symbol):\", PiFormatter()(np.pi/2)) # 'π/2'\n", "print(\"ASCII symbol:\", PiFormatter(symbol=\"pi\")(np.pi)) # 'pi'\n", "print(\"LaTeX:\", PiFormatter(latex=True)(-np.pi)) # '$-\\pi$'\n", "print(\"Finer fraction:\", PiFormatter(denominator=8)(3*np.pi/8)) # '3π/8'\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extended Examples (3)\n", "### 1) Y-axis as phase (LaTeX labels)\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-np.pi, np.pi, 200)\n", "y = 0.5 * x # linear ramp in radians\n", "\n", "fig, ax = plt.subplots(figsize=(5, 3))\n", "ax.plot(x, y, color=\"tab:orange\", label=\"0.5*x\")\n", "setup_phase_axis(ax.yaxis, base=0.25, denominator=4, latex=True)\n", "ax.set_xlabel(\"x (radians)\")\n", "ax.set_ylabel(\"phase (π units)\")\n", "ax.legend()\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2) Custom symbol and fine fractions\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-np.pi, np.pi, 200)\n", "fig, ax = plt.subplots(figsize=(5, 3))\n", "ax.plot(x, np.cos(x), color=\"tab:green\", label=\"cos(x)\")\n", "ax.xaxis.set_major_locator(PiLocator(base=0.25)) # π/4\n", "ax.xaxis.set_major_formatter(PiFormatter(denominator=8, symbol=\"pi\"))\n", "ax.set_title(\"Custom 'pi' symbol and 1/8 fractions\")\n", "ax.legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3) Both axes as phase\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-np.pi, np.pi, 200)\n", "y = np.linspace(-np.pi, np.pi, 200)\n", "X, Y = np.meshgrid(x, y)\n", "Z = np.sin(X) * np.cos(Y)\n", "\n", "fig, ax = plt.subplots(figsize=(5, 4))\n", "im = ax.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()], origin=\"lower\")\n", "setup_phase_axis(ax.xaxis, base=0.5, denominator=4, latex=False)\n", "setup_phase_axis(ax.yaxis, base=0.5, denominator=4, latex=False)\n", "ax.set_xlabel(\"x (phase)\")\n", "ax.set_ylabel(\"y (phase)\")\n", "fig.hist_colorbar(Z, im, ax=ax, extend=\"both\", label=\"sin(x)*cos(y)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Best Practices\n", "- Choose `base` to balance readability and density; `0.25` (π/4) is a good starting point.\n", "- Use `latex=True` in publication-quality figures for better typography.\n", "- Keep `denominator` modest (4–8) to avoid overly complex labels.\n", "- Apply formatters to the correct axis object (`ax.xaxis` vs `ax.yaxis`).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Troubleshooting & FAQs\n", "- Labels show decimals like `1.1π` instead of fractions → increase `denominator`; decimals are used when a clean fraction is not close.\n", "- Tiny values display as `0` → values with |x/π| < 1e-10 are treated as zero to reduce noise.\n", "- Ticks not as expected → ensure axis limits include multiples of π and that the locator/formatter are set on the intended axis.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## API Cheat Sheet\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "from faninsar.plots import PiFormatter, PiLocator, setup_phase_axis\n", "import matplotlib.pyplot as plt\n", "\n", "# X-axis: π/2 spacing, plain text\n", "ax = plt.subplots(figsize=(4, 2))[1]\n", "ax.xaxis.set_major_locator(PiLocator(base=0.5))\n", "ax.xaxis.set_major_formatter(PiFormatter(denominator=4, latex=False))\n", "plt.close()\n", "\n", "# Y-axis: π/4 spacing, LaTeX labels\n", "ax = plt.subplots(figsize=(4, 2))[1]\n", "setup_phase_axis(ax.yaxis, base=0.25, denominator=8, latex=True)\n", "plt.close()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Reading\n", "- Matplotlib TickLocators/Formatters: https://matplotlib.org/stable/api/ticker_api.html\n", "- NumPy: https://numpy.org/doc/stable/\n" ] } ], "metadata": { "kernelspec": { "display_name": "faninsar_dev", "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": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 5 }