{ "cells": [ { "cell_type": "markdown", "id": "f569a665-f294-4842-9ff6-d602efc63e40", "metadata": {}, "source": [ "# Log Gaussian 2D" ] }, { "cell_type": "markdown", "id": "6b9201df-6507-46df-96e2-a6580f9bf43b", "metadata": {}, "source": [ "`lamatrix` provides a log Gaussian to fit to data in 2D. You should read through the `lnGaussian` example before reading this one to see some of the caveats. This model expands to two dimensions, but has the same caveats. Keep in mind for now this does not implement the $\\rho$ correlation term in this 2D Gaussian. Below is a derivation of the 2D case of a log Gaussian.\n", "\n", "$$\n", "G(x, y) = A \\frac{1}{2 \\pi \\sigma_x \\sigma_y} \\exp ^{\\left( -\\frac{(x - \\mu_x)^2}{2\\sigma_x^2} - \\frac{(y - \\mu_y)^2}{2\\sigma_y^2} \\right)}\n", "$$\n", "\n", "$$\n", "\\ln G(x, y) = \\ln(A) -\\ln(2 \\pi \\sigma_x \\sigma_y) - \\frac{x^2}{2\\sigma_x^2} + \\frac{x\\mu_x}{\\sigma_x^2} - \\frac{\\mu_x^2}{2\\sigma_x^2} - \\frac{y^2}{2\\sigma_y^2} + \\frac{y\\mu_y}{\\sigma_y^2} - \\frac{\\mu_y^2}{2\\sigma_y^2}\n", "$$\n", "\n", "\n", "$$\n", "a_x = - \\frac{1}{2\\sigma_x^2}\n", "$$\n", "$$\n", "b_x = \\frac{\\mu_x}{\\sigma_x^2}\n", "$$\n", "\n", "$$\n", "a_y = - \\frac{1}{2\\sigma_y^2}\n", "$$\n", "$$\n", "b_y = \\frac{\\mu_y}{\\sigma_y^2}\n", "$$\n", "$$\n", "c = \\ln(A) - \\ln(2\\pi\\sigma_x\\sigma_y) - \\frac{\\mu_x^2}{2\\sigma_x^2} - \\frac{\\mu_y^2}{2\\sigma_y^2}\n", "$$\n", "\n", "$$\n", "\\ln(G(x)) = a_x x^2 + b_x x + a_y y^2 + b_y y + c\n", "$$\n" ] }, { "cell_type": "markdown", "id": "bfba5521-cf4f-4b81-9733-945b3e0e2250", "metadata": {}, "source": [ "Let's look at the equation for this model" ] }, { "cell_type": "code", "execution_count": 1, "id": "47e00fe5-dd14-4dbb-ab90-4df8c172f663", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "X, Y = np.mgrid[-10:10:200j,-9:9:180j]\n", "\n", "\n", "from lamatrix import lnGaussian2D" ] }, { "cell_type": "code", "execution_count": 2, "id": "8e91b1f7-8ca2-46d5-8690-da889d0e683f", "metadata": {}, "outputs": [], "source": [ "model = lnGaussian2D()" ] }, { "cell_type": "code", "execution_count": 3, "id": "4502adb7-bf7c-4ce8-a299-4e2d0f61f843", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\\[f(\\mathbf{y}, \\mathbf{x}) = w_{0} x^2 + w_{1} x + w_{2} y^2 + w_{3} y + w_{4} \\]
" ], "text/plain": [ "'\\\\[f(\\\\mathbf{y}, \\\\mathbf{x}) = w_{0} x^2 + w_{1} x + w_{2} y^2 + w_{3} y + w_{4} \\\\]'" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.equation" ] }, { "cell_type": "markdown", "id": "d40503aa-0388-4ab4-a7d6-f66f26201bd6", "metadata": {}, "source": [ "Just like in the case of the 1D log Gaussian, you are able to add priors to this object." ] }, { "cell_type": "code", "execution_count": 4, "id": "ce2f1ad2-11e7-4487-ab21-e5b2fdd60efb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "lnGaussian2D(y, x)[n, 5]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lnGaussian2D(prior_A=(10, 0.1), prior_mu_x=(0, 0.1), prior_sigma_x=(1, 0.1), prior_mu_y=(0, 0.1), prior_sigma_y=(2, 0.1))" ] }, { "cell_type": "markdown", "id": "9ae40e6c-0a4a-4c27-b66e-4b6b95e57ef3", "metadata": {}, "source": [ "Let's create some fake data to fit" ] }, { "cell_type": "code", "execution_count": 5, "id": "5754b728-f063-4f56-9857-1f51e9d3e2bd", "metadata": {}, "outputs": [], "source": [ "from lamatrix import Gaussian2D\n", "\n", "X, Y = np.mgrid[-10:10:100j,-9:9:99j]\n", "A, mu_x, sigma_x, mu_y, sigma_y = 10, -0.5, 1.5, 2, 1\n", "truth = Gaussian2D(sigma_x=sigma_x, mu_x=mu_x, sigma_y=sigma_y, mu_y=mu_y)(x=X, y=Y).dot([A]) \n", "data = truth + np.random.normal(0, 0.01, size=X.shape)\n", "errors = np.ones_like(X) * 0.01" ] }, { "cell_type": "markdown", "id": "c7288b80-3e57-4a37-b648-78a981e38723", "metadata": {}, "source": [ "Below we fit the data. As in the 1D example, we clip out any data points that are within errors of being 0." ] }, { "cell_type": "code", "execution_count": 6, "id": "98282dd6-087b-4c25-b7b7-cad5c47bad77", "metadata": {}, "outputs": [], "source": [ "model = lnGaussian2D()\n", "k = data > 5*errors\n", "model.fit(x=X[k], y=Y[k], data=np.log(data[k]), errors=errors[k]/data[k])" ] }, { "cell_type": "markdown", "id": "d1fabe53-1947-4152-a0cc-df0b76fe05ae", "metadata": {}, "source": [ "Below we plot the best fit" ] }, { "cell_type": "code", "execution_count": 7, "id": "f9718c7f-ad32-473a-851f-a89f95809ab1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 0, '$x$'), Text(0.5, 1.0, 'Best Fit')]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 3, figsize=(10, 5), sharex=True, sharey=True)\n", "ax[0].imshow(truth, cmap='Greys', vmin=0, vmax=0.3)\n", "ax[1].imshow(data, cmap='Greys', vmin=0, vmax=0.3)\n", "ax[2].imshow(np.exp(model.evaluate(x=X, y=Y)), cmap='Greys', vmin=0, vmax=0.3)\n", "ax[0].set(xlabel='$x$', ylabel='$y$', title='Truth')\n", "ax[1].set(xlabel='$x$', title='Data')\n", "ax[2].set(xlabel='$x$', title='Best Fit')" ] }, { "cell_type": "markdown", "id": "ca845164-b987-43a9-8a42-b0942ccc2f21", "metadata": {}, "source": [ "And we can show the best fit parameters" ] }, { "cell_type": "code", "execution_count": 8, "id": "a9382ba8-2cfb-4c68-8abc-46800a9574ba", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DistributionContainer\n", "\t[(10.04, 0.16), (-0.4993, 0.0025), (1.5032, 0.0018), (2.0001, 0.007), (1.0045, 0.0012)]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.coefficients_to_gaussian_parameters(model.posteriors)" ] }, { "cell_type": "markdown", "id": "147c12d3-19c7-4bf4-aa68-295e20f70d7b", "metadata": {}, "source": [ "These are within errors of our inputs!" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }