illustrating np.linalg.inv issue in autograd

gistfile1.txt

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python 3.5.1\r\n"
     ]
    }
   ],
   "source": [
    "!python --version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "autograd==1.1.3\r\n",
      "bokeh==0.11.0\r\n",
      "cycler==0.9.0\r\n",
      "decorator==4.0.6\r\n",
      "future==0.15.2\r\n",
      "holoviews==1.4.1\r\n",
      "ipykernel==4.2.2\r\n",
      "ipython==4.0.2\r\n",
      "ipython-genutils==0.1.0\r\n",
      "ipywidgets==4.1.1\r\n",
      "Jinja2==2.8\r\n",
      "jsonschema==2.5.1\r\n",
      "jupyter==1.0.0\r\n",
      "jupyter-client==4.1.1\r\n",
      "jupyter-console==4.1.0\r\n",
      "jupyter-core==4.0.6\r\n",
      "lancet-ioam==0.9.0\r\n",
      "MarkupSafe==0.23\r\n",
      "matplotlib==1.5.1\r\n",
      "mistune==0.7.1\r\n",
      "mpld3==0.2\r\n",
      "nbconvert==4.1.0\r\n",
      "nbformat==4.0.1\r\n",
      "notebook==4.1.0\r\n",
      "numpy==1.10.4\r\n",
      "pandas==0.17.1\r\n",
      "param==1.3.2\r\n",
      "path.py==8.1.2\r\n",
      "pexpect==4.0.1\r\n",
      "pickleshare==0.5\r\n",
      "ptyprocess==0.5\r\n",
      "py==1.4.31\r\n",
      "Pygments==2.0.2\r\n",
      "pyparsing==2.0.7\r\n",
      "pytest==2.8.5\r\n",
      "python-dateutil==2.4.2\r\n",
      "pytz==2015.7\r\n",
      "PyYAML==3.11\r\n",
      "pyzmq==15.2.0\r\n",
      "qtconsole==4.1.1\r\n",
      "requests==2.9.1\r\n",
      "scipy==0.16.1\r\n",
      "seaborn==0.6.0\r\n",
      "simplegeneric==0.8.1\r\n",
      "six==1.10.0\r\n",
      "terminado==0.6\r\n",
      "tornado==4.3\r\n",
      "tqdm==3.7.1\r\n",
      "traitlets==4.0.0\r\n"
     ]
    }
   ],
   "source": [
    "!pip freeze | grep -v instr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from autograd import grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "X = rng.randn(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def invert_and_sum(x):\n",
    "    return np.sum(np.linalg.inv(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.12651573809571348"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "invert_and_sum(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grad_invsum = grad(invert_and_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "No loop matching the specified signature and casting\nwas found for ufunc inv",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mforward_pass\u001b[1;34m(fun, args, kwargs, argnum)\u001b[0m\n\u001b[0;32m     29\u001b[0m     \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0margnum\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmerge_tapes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstart_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marg_wrt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 30\u001b[1;33m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mend_node\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     31\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0madd_extra_error_message\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-5-8223705fb99d>\u001b[0m in \u001b[0;36minvert_and_sum\u001b[1;34m(x)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0minvert_and_sum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36minv\u001b[1;34m(a)\u001b[0m\n\u001b[0;32m    525\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 526\u001b[1;33m     \u001b[0mainv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_umath_linalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    527\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mainv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: No loop matching the specified signature and casting\nwas found for ufunc inv",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-8-2f7f04034344>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mgrad_invsum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mgradfun\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m     19\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mattach_name_and_doc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margnum\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'Gradient'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     20\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mgradfun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 21\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mbackward_pass\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mforward_pass\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margnum\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     22\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mgradfun\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mforward_pass\u001b[1;34m(fun, args, kwargs, argnum)\u001b[0m\n\u001b[0;32m     29\u001b[0m     \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0margnum\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmerge_tapes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstart_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marg_wrt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     30\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mend_node\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 31\u001b[1;33m     \u001b[1;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0madd_extra_error_message\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     32\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mstart_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mend_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     33\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/autograd/core.py\u001b[0m in \u001b[0;36madd_extra_error_message\u001b[1;34m(e)\u001b[0m\n\u001b[0;32m    358\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    359\u001b[0m             \u001b[0mraise_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mAutogradHint\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mextra_message\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0metype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtraceback\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 360\u001b[1;33m     \u001b[0mraise_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0metype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtraceback\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/future/utils/__init__.py\u001b[0m in \u001b[0;36mraise_\u001b[1;34m(tp, value, tb)\u001b[0m\n\u001b[0;32m    412\u001b[0m             \u001b[0mexc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtp\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    413\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mexc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__traceback__\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mtb\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 414\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mexc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    415\u001b[0m         \u001b[1;32mraise\u001b[0m \u001b[0mexc\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    416\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mforward_pass\u001b[1;34m(fun, args, kwargs, argnum)\u001b[0m\n\u001b[0;32m     28\u001b[0m     \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m     \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0margnum\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmerge_tapes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstart_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marg_wrt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 30\u001b[1;33m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mend_node\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     31\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0madd_extra_error_message\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     32\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mstart_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mend_node\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-5-8223705fb99d>\u001b[0m in \u001b[0;36minvert_and_sum\u001b[1;34m(x)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0minvert_and_sum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m/home/gavin/venvs/value/lib/python3.5/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36minv\u001b[1;34m(a)\u001b[0m\n\u001b[0;32m    524\u001b[0m     \u001b[0msignature\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m'D->D'\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32melse\u001b[0m \u001b[1;34m'd->d'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    525\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 526\u001b[1;33m     \u001b[0mainv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_umath_linalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    527\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mainv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    528\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: No loop matching the specified signature and casting\nwas found for ufunc inv"
     ]
    }
   ],
   "source": [
    "grad_invsum(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from autograd.util import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.96653074,  0.76412611,  0.337624  ],\n",
       "       [-0.17531486,  0.13860155,  0.06124017],\n",
       "       [ 1.2562561 , -0.99317905, -0.43882951]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_invsum(X)"
   ]
  }
 ],
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