Merge pull request #214 from jhlegarreta/AddCovModelNotebook

ENH: Add dMRI covariance model notebook

docs/notebooks/dmri_covariance.ipynb

@@ -0,0 +1,88 @@
+{
+ "cells": [
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Plot the exponential and spherical covariance models.",
+   "id": "68526eb57440fb0e"
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Compute the exponential and the spherical covariance function matrix values for angles between 0 and $\\pi/2$. The length scale parameters are set to $a=1.23$ and $a=0.5$ for the spherical and the exponential functions respectively.",
+   "id": "a124686bde634d64"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "from eddymotion.model.dmri_covariance import (\n",
+    "    compute_exponential_covariance,\n",
+    "    compute_spherical_covariance,\n",
+    ")\n",
+    "\n",
+    "theta_lin = np.linspace(0, np.pi/2, num=1000)\n",
+    "\n",
+    "a_exp = 0.5\n",
+    "cov_exp = compute_exponential_covariance(theta_lin, a_exp)\n",
+    "\n",
+    "a_sph = 1.23\n",
+    "cov_sph = compute_spherical_covariance(theta_lin, a_sph)"
+   ],
+   "id": "457b781088e1cae2",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Plot the exponential and spherical covariance functions.",
+   "id": "1c5f9da8b3a9394e"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# Plot the exponential and spherical model covariances\n",
+    "plt.plot(theta_lin, cov_exp, label=\"Exponential cov\")\n",
+    "plt.plot(theta_lin, cov_sph, label=\"Spherical cov\")\n",
+    "\n",
+    "plt.xticks([0.0, np.pi/8, np.pi/4, 3*np.pi/8, np.pi/2], [\"0\", \"pi/8\", \"pi/4\", \"3pi/8\", \"pi/2\"])\n",
+    "\n",
+    "plt.xlabel(\"Angular distance\")\n",
+    "plt.ylabel(\"Covariance (arbitrary scaling)\")\n",
+    "\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ],
+   "id": "9f8abf14503066e0",
+   "outputs": [],
+   "execution_count": null
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}