{ "cells": [ { "cell_type": "markdown", "id": "09496c85", "metadata": {}, "source": [ "# Exploring the accuracy of the truncated wavelet transform" ] }, { "cell_type": "code", "execution_count": 1, "id": "32c60123", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "import jax\n", "\n", "import matplotlib.pyplot as plt\n", "from matplotlib import gridspec\n", "import matplotlib.patches as patches\n", "\n", "import WDM" ] }, { "cell_type": "markdown", "id": "613312bf", "metadata": {}, "source": [ "Time series properties." ] }, { "cell_type": "code", "execution_count": 2, "id": "fe639d5e", "metadata": {}, "outputs": [], "source": [ "dt, N, Nt, Nf = 0.5, 512, 64, 8\n", "\n", "assert Nf*Nt==N, \"Incompatible dimensions\"" ] }, { "cell_type": "markdown", "id": "d595d3e9", "metadata": {}, "source": [ "Generate a white noise time series signal with r.m.s. value of 1." ] }, { "cell_type": "code", "execution_count": 3, "id": "12f6ed82", "metadata": {}, "outputs": [], "source": [ "key = jax.random.key(0)\n", "key, subkey = jax.random.split(key)\n", "x = jax.random.normal(subkey, shape=(N,)) # white noise" ] }, { "cell_type": "markdown", "id": "96574d07", "metadata": {}, "source": [ "Perform a bunch of different wavelet transforms with different truncation $q$ parameters.\n", "We quantify the accuracy of the transformation by performing a forward (truncated) and inverse (exact) wavelet transformation and looking at the largest absolute difference between the original and recovered time series." ] }, { "cell_type": "markdown", "id": "e4ba0507", "metadata": {}, "source": [ "Allowed values of $q$. Must be an integer in the range $1\\leq q \\leq N_t/2\\equiv 32$." ] }, { "cell_type": "code", "execution_count": 4, "id": "e8089959", "metadata": {}, "outputs": [], "source": [ "q_vals = [1,2,4,8,10,12,14,16,20,25,32]\n", "\n", "err_vals = np.zeros(len(q_vals))\n", "\n", "for i, q in enumerate(q_vals): \n", " wdm = WDM.WDM.WDM_transform(dt=0.5, \n", " Nf=Nf,\n", " N=N, \n", " q=q,\n", " calc_m0=True)\n", " \n", " w = wdm.forward_transform_truncated(x)\n", "\n", " x_recovered = wdm.inverse_transform(w)\n", "\n", " err_vals[i] = np.max(np.abs(x - x_recovered))" ] }, { "cell_type": "markdown", "id": "1eb0a487", "metadata": {}, "source": [ "We will also compare this with the error when using the exact forward transform. The exact transform should be same as the truncated transform when $q=N_t/2=32$." ] }, { "cell_type": "code", "execution_count": 5, "id": "c62abe02", "metadata": {}, "outputs": [], "source": [ "wdm = WDM.WDM.WDM_transform(dt=0.5, \n", " Nf=Nf,\n", " N=N, \n", " calc_m0=True)\n", "\n", "w = wdm.forward_transform_exact(x)\n", "\n", "x_recovered = wdm.inverse_transform_exact(w)\n", "\n", "err = np.max(np.abs(x - x_recovered))" ] }, { "cell_type": "markdown", "id": "c88007c2", "metadata": {}, "source": [ "Plot the errors in the truncated wavelet transform as a function of the truncation parameter." ] }, { "cell_type": "code", "execution_count": 6, "id": "9e3be8b0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.suptitle(\"Truncated Wavelet Transform Error\")\n", "\n", "ax.plot(q_vals, err_vals, marker='o', label='Truncated')\n", "ax.axhline(err, color='k', lw=3, linestyle=':', label='Exact')\n", "\n", "ax.set_xlabel(r\"$q$\")\n", "ax.set_ylabel(r\"Max error\")\n", "\n", "ax.set_yscale('log')\n", "\n", "ax.grid()\n", "ax.legend(loc='upper right')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4f2b0030", "metadata": {}, "source": [ "The accuracy of the truncated wavelet transformation also depends on the value of $d$.\n", "Wavelets with smaller d are slightly better localised in time leading to a slightly more accurate truncated transformations for small $q$." ] }, { "cell_type": "code", "execution_count": 7, "id": "9a06214a", "metadata": {}, "outputs": [], "source": [ "d_vals = [1, 4, 16]\n", "\n", "q_vals = [1,2,4,8,10,12,14,16,20,25,32]\n", "\n", "err_vals = {}\n", "\n", "for j, d in enumerate(d_vals):\n", "\n", " err_vals[d] = np.zeros(len(q_vals))\n", "\n", " for i, q in enumerate(q_vals): \n", " wdm = WDM.code.discrete_wavelet_transform.WDM.WDM_transform(dt=0.5, \n", " Nf=Nf,\n", " N=N, \n", " q=q,\n", " d=d,\n", " calc_m0=True)\n", " \n", " w = wdm.forward_transform_truncated(x)\n", "\n", " x_recovered = wdm.inverse_transform(w)\n", "\n", " err_vals[d][i] = np.max(np.abs(x - x_recovered))" ] }, { "cell_type": "code", "execution_count": 8, "id": "fc29227f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.suptitle(\"Truncated Wavelet Transform Error\")\n", "\n", "for d in d_vals:\n", " ax.plot(q_vals, err_vals[d], marker='o', label=f'Truncated {d=}')\n", "ax.axhline(err, color='k', lw=3, linestyle=':', label='Exact')\n", "\n", "ax.set_xlabel(r\"$q$\")\n", "ax.set_ylabel(r\"Max error\")\n", "\n", "ax.set_yscale('log')\n", "\n", "ax.grid()\n", "ax.legend(loc='upper right')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "222db2b0", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "WDM", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }