{ "cells": [ { "cell_type": "code", "execution_count": 32, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", "plt.style.use(\"https://github.com/mlefkir/beauxgraphs/raw/main/beautifulgraphs_colblind.mplstyle\")" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian process method\n", "\n", "Here, we describe how to generate a random time series using the Gaussian process method. \n", "\n", "## Description\n", "\n", "### Basic idea\n", "Given a random process described with either a Power Spectral Density (PSD) or an autocovariance function (ACVF), the Gaussian Process method allows drawing a realisation of this process. The main idea is to draw the time series from a multivariate normal distribution (Eq. {math:numref}`eq:multigauss`) with a covariance matrix $\\Sigma$ that is given by the PSD or ACVF.\n", "\n", "\n", "```{eval-rst}\n", ".. math::\n", " :name: eq:multigauss\n", " \n", " p(\\boldsymbol{y}| \\boldsymbol{m},\\Sigma) =\\dfrac{1}{(2\\pi)^{n/2} | \\Sigma |^{1/2}} \\exp{ \\left( -\\dfrac{1}{2} \\left(\\boldsymbol{y}-\\boldsymbol{m} \\right)^{\\rm T} {\\Sigma}^{-1} \\left(\\boldsymbol{y}-\\boldsymbol{m} \\right) \\right) }\n", "```\n", "\n", "\n", "If the PSD is given, the ACVF is computed as the inverse Fourier transform of the PSD. To reduce distortions due to aliasing and leakage, the range of frequencies in the PSD is extended, see more details in the Notebook [on the FFT](../references/On_the_fft.ipynb). The discretised ACVF is then interpolated to the desired time lags. \n", "\n", "### Drawing samples from a multivariate normal distribution\n", "\n", "To easily draw samples, we compute the Cholesky decomposition of the covariance matrix $\\Sigma$ decomposition with the function {func}`jax.numpy.linalg.cholesky`. The Cholesky decomposition is a lower triangular matrix $L$ such that $\\Sigma = L L^{\\rm T}$. Random numbers from a multivariate normal distribution can then be drawn by multiplying a vector of independent standard normal random variables with $L$.\n", "\n", "\n", "\n", "### Implementation in `pioran`\n", "\n", "This method is implemented in the class {class}`~pioran.simulate.Simulations` via the method {meth}`~pioran.simulate.Simulations.GP_method`. The method takes as input the PSD or ACVF, the number of samples and the sampling frequency. The output is a time series of the same length as the PSD or ACVF.\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Usage\n", "\n", "The first thing to do is to define the parameters of the time series, duration, sampling and model. If the model is a PSD then $S_\\mathrm{low}$ and $S_\\mathrm{high}$ must be given.\n", "All of these are given to the initialisation of a {class}`~pioran.simulate.Simulations` object." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "from pioran import Simulations\n", "from pioran.acvf import Exponential\n", "from pioran.psd import Lorentzian\n", "\n", "acv_model = Exponential([1,1e-2])\n", "psd_model = Lorentzian([0.00,1,1e-2])\n", "\n", "duration = 400\n", "dt = 1.5\n", "Sim = Simulations(T=duration,dt=dt,model=acv_model)\n", "Sim_psd = Simulations(T=duration,dt=dt,model=psd_model,S_high=20,S_low=20)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the autocovariance function of the model:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax = Sim.plot_acvf(figsize=(7,4))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "To generate a random time series we use the {meth}`~pioran.simulate.Simulations.simulate` method. We specify the method to use with `method='GP'`. By default, the values of the time series are randomised with a normal distribution. This can be changed with the `randomise_fluxes` argument. The errors are assumed to be Gaussian.\n", "\n", "By default, the mean of the time series is shifted to twice the minimum of the time series to get a positive-valued time series. This can be changed with the `mean` argument." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculating the autocovariance function\n", "Interpolating the autocovariance function\n" ] } ], "source": [ "t, ts, ts_err = Sim.simulate(method='GP',seed=342)\n", "t_psd, ts_psd, ts_psd_err = Sim_psd.simulate(method='GP',seed=342)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the time series obtained using a PSD and an ACVF are identical." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,4))\n", "ax.errorbar(t_psd,ts_psd,yerr=ts_psd_err,fmt='o',color='C3')\n", "ax.errorbar(t,ts,yerr=ts_err,fmt='s')\n", "ax.set_xlabel('Time (d)')\n", "ax.set_ylabel('Simulated time series')\n", "ax.legend(['ACV','PSD'])\n", "fig.tight_layout()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "tags": [ "hide-input" ] }, "source": [ "## References\n", "\n", "Rasmussen, C. E., & Williams, C. K. I. Gaussian processes for machine learning. (2006) MIT press. " ] } ], "metadata": { "kernelspec": { "display_name": "pioran", "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": "3.10.9" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }