{ "cells": [ { "cell_type": "markdown", "id": "d48e3acb-8020-486a-aa85-d9f32f9113de", "metadata": {}, "source": [ "# Introduction to `lamatrix`: Sparse Spline Models\n", "\n", "Some models that we make are inherrently sparse. An example might be a spline model with a high number of knots; many of the components in such a model are full of zeros. Because of this, it can be helpful to use the `sparse` library from `scipy`, which enables us to use linear algebra without storing zeros in memory. `lamatrix` has some support for sparse models, which we will show briefly here." ] }, { "cell_type": "code", "execution_count": 1, "id": "c67d414b-f4d6-4f66-8f61-5a7aa85de15c", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from astropy.io import fits\n", "import matplotlib.pyplot as plt\n", "import sys" ] }, { "cell_type": "code", "execution_count": 3, "id": "12d8a3c6-a6f7-4300-b9cb-1488422cf452", "metadata": {}, "outputs": [], "source": [ "x = np.arange(-5, 5, 0.001)\n", "y = np.random.normal(size=len(x))\n", "y = np.convolve(y, np.ones(1000), mode='same') + np.random.normal(0, 0.3, size=len(x))\n", "ye = np.ones(len(x)) * 0.3" ] }, { "cell_type": "code", "execution_count": 4, "id": "8ff5cf3a-e729-4f4a-a88f-29f3aee351a5", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.errorbar(x, y, ye, ls='', c='k')\n", "ax.set(xlabel='$x$', ylabel='$y$', title='Randomly Generated Data');" ] }, { "cell_type": "markdown", "id": "18fbcd96-01e5-4f81-9cf1-bc902bc2ef4f", "metadata": {}, "source": [ "Here we have created a simple dataset with correlated noise in it. We want to fit this with a spline. We can use the `Spline` model" ] }, { "cell_type": "code", "execution_count": 5, "id": "bf821785-9231-4d37-bf9e-da30b2e3131d", "metadata": {}, "outputs": [], "source": [ "from lamatrix import Spline" ] }, { "cell_type": "markdown", "id": "361e9952-85fe-435a-ac9d-cd3d656536de", "metadata": {}, "source": [ "We know we need a small knot spacing (i.e. a large number of knots) to fit this trend" ] }, { "cell_type": "code", "execution_count": 7, "id": "6b16236c-49fa-48db-92d5-8f7422fc579c", "metadata": {}, "outputs": [], "source": [ "knot_spacing = 0.05\n", "order = 3\n", "knots = np.arange(-5 - knot_spacing * (order - 1), 5 + (knot_spacing * (order - 1)) + knot_spacing, knot_spacing)" ] }, { "cell_type": "code", "execution_count": 8, "id": "cb70cb0d-187d-471f-b755-8f2b2a21c4e2", "metadata": {}, "outputs": [], "source": [ "model = Spline('x', knots=knots, order=order)" ] }, { "cell_type": "code", "execution_count": 9, "id": "2028a20a-00ae-4770-8a48-4415886c99ac", "metadata": {}, "outputs": [], "source": [ "model.fit(x=x, data=y)" ] }, { "cell_type": "code", "execution_count": 10, "id": "4c9dd159-2741-48f2-9fcc-9a1af77e0ca2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.errorbar(x, y, ye, ls='', c='k')\n", "ax.plot(x, model.evaluate(x=x))\n", "ax.set(xlabel='$x$', ylabel='$y$', title='Randomly Generated Data');" ] }, { "cell_type": "markdown", "id": "de10fc68-1a63-408f-bf2d-1f79d5bddb82", "metadata": {}, "source": [ "This fits nicely, however when we look at the size of the design matrix we see" ] }, { "cell_type": "code", "execution_count": 11, "id": "aba7ab57-2482-4489-a33b-fc4d5388a159", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16160000" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.design_matrix(x=x).nbytes" ] }, { "cell_type": "markdown", "id": "17c51b81-31f6-4ae6-bbd1-6feaca86c5e5", "metadata": {}, "source": [ "This is large in memory, taking up megabytes of memory currently. If we sum up the number of zeros in the design matrix we see that it's almost all zeros." ] }, { "cell_type": "code", "execution_count": 12, "id": "567e8a08-e255-40c7-85ab-c7d93565f136", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9851490099009901" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(model.design_matrix(x=x) == 0).sum()/(model.width * len(x))" ] }, { "cell_type": "markdown", "id": "7b3be0ef-c6fd-4149-8465-d15e2c911f3d", "metadata": {}, "source": [ "If we were to try to fit more data points or use more knots, this might become too large to fit in memory. We can use the `SparseSpline` in stead" ] }, { "cell_type": "code", "execution_count": 13, "id": "2f3e3258-9064-4705-b0e0-838084ab0c69", "metadata": {}, "outputs": [], "source": [ "from lamatrix import SparseSpline" ] }, { "cell_type": "code", "execution_count": 14, "id": "f909c5bb-057f-4393-bca4-18de29699aed", "metadata": {}, "outputs": [], "source": [ "model_sparse = SparseSpline('x', knots=knots, order=order)" ] }, { "cell_type": "code", "execution_count": 15, "id": "0f7ea942-f53e-4666-9870-5c3dc8e0f4b4", "metadata": {}, "outputs": [], "source": [ "model_sparse.fit(x=x, data=y)" ] }, { "cell_type": "code", "execution_count": 16, "id": "a790f4c9-c8be-4236-9f14-407229dae3b9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.errorbar(x, y, ye, ls='', c='k')\n", "ax.plot(x, model.evaluate(x=x))\n", "ax.set(xlabel='$x$', ylabel='$y$', title='Randomly Generated Data');" ] }, { "cell_type": "markdown", "id": "56f44711-871a-49a2-a730-89dd962c81b8", "metadata": {}, "source": [ "This provides as good of a fit to our data but when we look at the design matrix we see this is much smaller in memory" ] }, { "cell_type": "code", "execution_count": 17, "id": "0cae8c15-2ba7-4cb4-aa8a-49ae6037d911", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "239992" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model_sparse.design_matrix(x=x).data.nbytes" ] }, { "cell_type": "code", "execution_count": 18, "id": "9b9b306c-a053-4d7d-a505-3280225df1b2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0148509900990099" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "239992/16160000" ] }, { "cell_type": "markdown", "id": "cac30f55-5a54-45c6-86c4-1248b146dbdc", "metadata": {}, "source": [ "This model is 1% of the size in memory of the non sparse model!" ] }, { "cell_type": "markdown", "id": "21c9448e-5d8a-4164-acb9-15fb535232ee", "metadata": {}, "source": [ "Currently only `Spline`s are implemented with a `sparse` version (as most other models within `lamatrix` are not well suited to being sparse). It is not possible to combine the `SparseSpline` with other model types currently, but this may be updated in the future." ] } ], "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 }