LinearOperator compatibility.ipynb

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   "cell_type": "markdown",
   "id": "6e5acf15",
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   "source": [
    "## `LinearOperator` + `svds`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fcf747e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy as sp\n",
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "from tabulate import tabulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ec038da9",
   "metadata": {},
   "outputs": [],
   "source": [
    "class VerboseLinearOperator(sp.sparse.linalg.LinearOperator):\n",
    "    def __init__(self, *args, **kwargs):\n",
    "        super().__init__(*args, **kwargs)\n",
    "        \n",
    "    def __getattribute__(self, attr):\n",
    "        callcounter[attr] += 1\n",
    "        return super().__getattribute__(attr)\n",
    "    \n",
    "    def _matvec(self, x):\n",
    "        return np.zeros((self.shape[0], 1))\n",
    "    \n",
    "    def _matmat(self, X):\n",
    "        return np.zeros((self.shape[0], X.shape[1]))\n",
    "    \n",
    "    def _rmatvec(self, x):\n",
    "        return np.zeros((self.shape[1], 1))\n",
    "    \n",
    "    def _rmatmat(self, X):\n",
    "        return np.zeros((self.shape[1], X.shape[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0b9f1429",
   "metadata": {},
   "outputs": [],
   "source": [
    "vlo = VerboseLinearOperator(dtype=np.float32, shape=(10, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c9ffe1af",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = {}\n",
    "for solver in ['arpack', 'lobpcg', 'propack']:\n",
    "    callcounter = defaultdict(lambda: 0)\n",
    "    U, S, Vt = sp.sparse.linalg.svds(vlo, k=2, solver=solver)\n",
    "    data[solver] = dict(U=U, S=S, Vt=Vt, callcounter=callcounter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8753501e",
   "metadata": {},
   "outputs": [],
   "source": [
    "methods = set()\n",
    "for solver in data:\n",
    "    methods.update(data[solver]['callcounter'].keys())\n",
    "methods = sorted(methods)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "35d2d20f",
   "metadata": {},
   "outputs": [],
   "source": [
    "values = [\n",
    "    [solver, data[solver]['U'].shape, data[solver]['S'].shape, data[solver]['Vt'].shape]\n",
    "    + [data[solver]['callcounter'][method] for method in methods]\n",
    "    for solver in data\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8cb12ab7",
   "metadata": {},
   "outputs": [],
   "source": [
    "rownames = ['attribute'] + \\\n",
    "['shape of ' + name for name in ['U', 'S', 'Vt']] + \\\n",
    "['# calls to ' + name for name in methods]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "953a171f",
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       "<table>\n",
       "<thead>\n",
       "<tr><th>attribute          </th><th>arpack  </th><th>lobpcg  </th><th>propack  </th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td>shape of U         </td><td>(10, 2) </td><td>(10, 2) </td><td>(10, 2)  </td></tr>\n",
       "<tr><td>shape of S         </td><td>(2,)    </td><td>(2,)    </td><td>(2,)     </td></tr>\n",
       "<tr><td>shape of Vt        </td><td>(2, 10) </td><td>(2, 10) </td><td>(2, 10)  </td></tr>\n",
       "<tr><td># calls to _matmat </td><td>0       </td><td>1       </td><td>0        </td></tr>\n",
       "<tr><td># calls to _matvec </td><td>10      </td><td>0       </td><td>11       </td></tr>\n",
       "<tr><td># calls to _rmatmat</td><td>1       </td><td>2       </td><td>0        </td></tr>\n",
       "<tr><td># calls to _rmatvec</td><td>10      </td><td>0       </td><td>12       </td></tr>\n",
       "<tr><td># calls to dtype   </td><td>4       </td><td>4       </td><td>6        </td></tr>\n",
       "<tr><td># calls to matmat  </td><td>1       </td><td>1       </td><td>1        </td></tr>\n",
       "<tr><td># calls to matvec  </td><td>1       </td><td>1       </td><td>12       </td></tr>\n",
       "<tr><td># calls to rmatmat </td><td>1       </td><td>1       </td><td>1        </td></tr>\n",
       "<tr><td># calls to rmatvec </td><td>1       </td><td>1       </td><td>13       </td></tr>\n",
       "<tr><td># calls to shape   </td><td>47      </td><td>12      </td><td>52       </td></tr>\n",
       "</tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "'<table>\\n<thead>\\n<tr><th>attribute          </th><th>arpack  </th><th>lobpcg  </th><th>propack  </th></tr>\\n</thead>\\n<tbody>\\n<tr><td>shape of U         </td><td>(10, 2) </td><td>(10, 2) </td><td>(10, 2)  </td></tr>\\n<tr><td>shape of S         </td><td>(2,)    </td><td>(2,)    </td><td>(2,)     </td></tr>\\n<tr><td>shape of Vt        </td><td>(2, 10) </td><td>(2, 10) </td><td>(2, 10)  </td></tr>\\n<tr><td># calls to _matmat </td><td>0       </td><td>1       </td><td>0        </td></tr>\\n<tr><td># calls to _matvec </td><td>10      </td><td>0       </td><td>11       </td></tr>\\n<tr><td># calls to _rmatmat</td><td>1       </td><td>2       </td><td>0        </td></tr>\\n<tr><td># calls to _rmatvec</td><td>10      </td><td>0       </td><td>12       </td></tr>\\n<tr><td># calls to dtype   </td><td>4       </td><td>4       </td><td>6        </td></tr>\\n<tr><td># calls to matmat  </td><td>1       </td><td>1       </td><td>1        </td></tr>\\n<tr><td># calls to matvec  </td><td>1       </td><td>1       </td><td>12       </td></tr>\\n<tr><td># calls to rmatmat </td><td>1       </td><td>1       </td><td>1        </td></tr>\\n<tr><td># calls to rmatvec </td><td>1       </td><td>1       </td><td>13       </td></tr>\\n<tr><td># calls to shape   </td><td>47      </td><td>12      </td><td>52       </td></tr>\\n</tbody>\\n</table>'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tabulate(list(zip(rownames, *values)), headers='firstrow', tablefmt='html')"
   ]
  }
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