GaussianRMT.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simplest Example of a Gaussian Random Matrix\n",
    "\n",
    "\n",
    "#### Gaussian Random Matrices, $W$, which are $N\\times M$, $Q=N/M$\n",
    "\n",
    "\n",
    "\n",
    "$$P(W_{i,j})\\sim N(0,1)$$\n",
    "\n",
    "#### Corelation Matrix\n",
    "$$\\mathbf{X}=\\mathbf{W}^{T}\\mathbf{W}$$\n",
    "\n",
    "#### Eigenvalues\n",
    "\n",
    "$$\\mathbf{X}\\mathbf{v}=\\lambda\\mathbf{v}$$\n",
    "\n",
    "#### Empirical Spectral Density (ESD)\n",
    "A histogram of the Eigenvalues\n",
    "$$\\rho(\\lambda)=\\dfrac{1}{N}\\sum_{i=1}^{M}\\left(\\lambda-\\lambda_{i}\\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-11T18:39:32.388709Z",
     "start_time": "2018-09-11T18:39:29.781373Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charlesmartin14/anaconda3/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: compiletime version 3.5 of module 'tensorflow.python.framework.fast_tensor_util' does not match runtime version 3.6\n",
      "  return f(*args, **kwds)\n",
      "/Users/charlesmartin14/.local/lib/python3.6/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.19.1\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import pickle, time\n",
    "from copy import deepcopy\n",
    "from shutil import copy\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import sklearn\n",
    "from sklearn.random_projection import sparse_random_matrix\n",
    "print(sklearn.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-11T19:13:35.571649Z",
     "start_time": "2018-09-11T19:13:35.564601Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [10, 10]\n",
    "matplotlib.rcParams.update({'font.size': 16})\n",
    "plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-11T19:17:38.500783Z",
     "start_time": "2018-09-11T19:17:33.903631Z"
    }
   },
   "outputs": [
    {
     "data": {
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NsnXnzmEDcJIkSetXlzlgP5PkNsBpwA3A05bKX1VPnvf280lOA74OHA/cf5FyW4AtAJs3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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(2,2)\n",
    "\n",
    "for idx in range(4):\n",
    "    \n",
    "    Q=1+idx*2\n",
    "    iay = idx % 2\n",
    "    iax = int(idx / 2)\n",
    "    subplot = axes[iax,iay]\n",
    "    \n",
    "    M = 1000\n",
    "    N = int(Q*M)\n",
    "    W = np.random.normal(0,1,size=(N,M))\n",
    "    X = (1/N)*np.dot(W.T,W)\n",
    "    evals = np.linalg.eigvals(X)\n",
    "    subplot.hist(evals, bins=100,density=True);\n",
    "    subplot.set_title(r\"$\\rho(\\lambda)$, Q={}\".format(Q))\n",
    "    #subplot.set_xlabel(\"Eigenvalues of $X=W^{T}.W$\")\n",
    "plt.savefig(\"img/gaussian_random_mats.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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