Creating new Op.ipynb

{
 "cells": [
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "1404f35a",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97799c52",
   "metadata": {},
   "source": [
    "## Op’s basic methods\n",
    " - make_node() - method creates an Apply node representing the application of the Op on the inputs provided.\n",
    " - perform()   - method defines the Python implementation of an Op. \n",
    "               - It takes several arguments:\n",
    "                   - node is a reference to an Apply node which was previously obtained via the make_node()\n",
    "                   - inputs is a list of references to data which can be operated\n",
    "                   - output_storage is a list of storage cells where the output is to be stored\n",
    "                   \n",
    " - The __props__ attribute lists the properties that influence how the computation is performed\n",
    " - __props__ enables the automatic generation of appropriate __eq__() and __hash__()\n",
    " - The infer_shape() method allows an Op to infer the shape of its output variables without actually computing them.\n",
    " - The grad() method is required if you want to differentiate some cost whose expression includes your Op. \n",
    " - The R_op() method is needed if you want aesara.gradient.Rop to work with your Op"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ac55d70",
   "metadata": {},
   "source": [
    "## Example: Op definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "937935bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "from aesara import tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6316acc5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARN: Could not locate executable g77\n",
      "WARN: Could not locate executable f77\n",
      "WARN: Could not locate executable ifort\n",
      "WARN: Could not locate executable ifl\n",
      "WARN: Could not locate executable f90\n",
      "WARN: Could not locate executable DF\n",
      "WARN: Could not locate executable efl\n"
     ]
    }
   ],
   "source": [
    "import aesara\n",
    "from aesara.graph.op import Op\n",
    "from aesara.graph.basic import Apply\n",
    "\n",
    "\n",
    "class DoubleOp1(Op):\n",
    "    __props__ = ()\n",
    "\n",
    "    def make_node(self, x):\n",
    "        x = aesara.tensor.as_tensor_variable(x)\n",
    "        # Note: using x_.type() is dangerous, as it copies x's broadcasting\n",
    "        # behaviour\n",
    "        return Apply(self, [x], [x.type()])\n",
    "\n",
    "    def perform(self, node, inputs, output_storage):\n",
    "        x = inputs[0]\n",
    "        z = output_storage[0]\n",
    "        z[0] = x * 2\n",
    "\n",
    "    def infer_shape(self, fgraph, node, i0_shapes):\n",
    "        return i0_shapes\n",
    "\n",
    "    def grad(self, inputs, output_grads):\n",
    "        return [output_grads[0] * 2]\n",
    "\n",
    "    def R_op(self, inputs, eval_points):\n",
    "        # R_op can receive None as eval_points.\n",
    "        # That mean there is no diferientiable path through that input\n",
    "        # If this imply that you cannot compute some outputs,\n",
    "        # return None for those.\n",
    "        if eval_points[0] is None:\n",
    "            return eval_points\n",
    "        return self.grad(inputs, eval_points)\n",
    "\n",
    "doubleOp1 = DoubleOp1()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0401b8ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DoubleOp1.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "doubleOp1(tensor.vector())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f5f23eca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TensorType(float64, (None, None))>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import aesara\n",
    "\n",
    "x = aesara.tensor.matrix()\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bb9eef2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = aesara.function([x], DoubleOp1()(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a8e3c369",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = np.arange(2*3).reshape(2,3)\n",
    "inp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e44c46fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  2.,  4.],\n",
       "       [ 6.,  8., 10.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = f(inp)\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8e877624",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[12, 13, 14, 15],\n",
       "        [16, 17, 18, 19],\n",
       "        [20, 21, 22, 23]]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = np.arange(2*3*4).reshape(2,3,4)\n",
    "inp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9c3ddc81",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "Bad input argument to aesara function with name \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\4237001567.py:1\" at index 0 (0-based).  \nBacktrace when that variable is created:\n\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\ipykernel\\zmqshell.py\", line 528, in run_cell\n    return super().run_cell(*args, **kwargs)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2881, in run_cell\n    result = self._run_cell(\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2936, in _run_cell\n    return runner(coro)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\async_helpers.py\", line 129, in _pseudo_sync_runner\n    coro.send(None)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3135, in run_cell_async\n    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3338, in run_ast_nodes\n    if await self.run_code(code, result, async_=asy):\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3398, in run_code\n    exec(code_obj, self.user_global_ns, self.user_ns)\n  File \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\3645586177.py\", line 4, in <cell line: 4>\n    x = aesara.tensor.matrix()\nWrong number of dimensions: expected 2, got 3 with shape (2, 3, 4).",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[1;32mIn [17]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[0m out \u001b[38;5;241m=\u001b[39m \u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[43minp\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m      2\u001b[0m out\n",
      "File \u001b[1;32mD:\\OpenSource\\aesara\\aesara\\compile\\function\\types.py:863\u001b[0m, in \u001b[0;36mFunction.__call__\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    861\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m    862\u001b[0m     \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m--> 863\u001b[0m         s\u001b[38;5;241m.\u001b[39mstorage[\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtype\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfilter\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m    864\u001b[0m \u001b[43m            \u001b[49m\u001b[43marg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstrict\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstrict\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mallow_downcast\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mallow_downcast\u001b[49m\n\u001b[0;32m    865\u001b[0m \u001b[43m        \u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m    867\u001b[0m     \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[0;32m    868\u001b[0m         function_name \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124maesara function\u001b[39m\u001b[38;5;124m\"\u001b[39m\n",
      "File \u001b[1;32mD:\\OpenSource\\aesara\\aesara\\tensor\\type.py:227\u001b[0m, in \u001b[0;36mTensorType.filter\u001b[1;34m(self, data, strict, allow_downcast)\u001b[0m\n\u001b[0;32m    224\u001b[0m                 \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(err_msg)\n\u001b[0;32m    226\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mndim \u001b[38;5;241m!=\u001b[39m data\u001b[38;5;241m.\u001b[39mndim:\n\u001b[1;32m--> 227\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[0;32m    228\u001b[0m         \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mWrong number of dimensions: expected \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mndim\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m,\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    229\u001b[0m         \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m got \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mdata\u001b[38;5;241m.\u001b[39mndim\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m with shape \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mdata\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    230\u001b[0m     )\n\u001b[0;32m    231\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m data\u001b[38;5;241m.\u001b[39mflags\u001b[38;5;241m.\u001b[39maligned:\n\u001b[0;32m    232\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[0;32m    233\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe numpy.ndarray object is not aligned.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    234\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m Aesara C code does not support that.\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[0;32m    235\u001b[0m     )\n",
      "\u001b[1;31mTypeError\u001b[0m: Bad input argument to aesara function with name \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\4237001567.py:1\" at index 0 (0-based).  \nBacktrace when that variable is created:\n\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\ipykernel\\zmqshell.py\", line 528, in run_cell\n    return super().run_cell(*args, **kwargs)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2881, in run_cell\n    result = self._run_cell(\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2936, in _run_cell\n    return runner(coro)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\async_helpers.py\", line 129, in _pseudo_sync_runner\n    coro.send(None)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3135, in run_cell_async\n    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3338, in run_ast_nodes\n    if await self.run_code(code, result, async_=asy):\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3398, in run_code\n    exec(code_obj, self.user_global_ns, self.user_ns)\n  File \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\3645586177.py\", line 4, in <cell line: 4>\n    x = aesara.tensor.matrix()\nWrong number of dimensions: expected 2, got 3 with shape (2, 3, 4)."
     ]
    }
   ],
   "source": [
    "out = f(inp)\n",
    "out"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa4fcaf9",
   "metadata": {},
   "source": [
    "# 1. Op returns x * y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3eca9452",
   "metadata": {},
   "outputs": [],
   "source": [
    "from aesara import tensor as at\n",
    "from aesara.tensor.type import TensorType\n",
    "\n",
    "class ProdOp(Op):\n",
    "    def make_node(self, x, y):\n",
    "        x = at.as_tensor_variable(x)\n",
    "        y = at.as_tensor_variable(y)\n",
    "        outdim = x.ndim\n",
    "        output = TensorType(\n",
    "            dtype=aesara.scalar.upcast(x.dtype, y.dtype), shape=[False] * outdim\n",
    "        )()\n",
    "        return Apply(self, inputs=[x, y], outputs=[output])\n",
    "\n",
    "    def perform(self, node, inputs, output_storage):\n",
    "        x, y = inputs\n",
    "        z = output_storage[0]\n",
    "        z[0] = x * y\n",
    "\n",
    "    def infer_shape(self, fgraph, node, i0_shapes):\n",
    "        return [i0_shapes[0]]\n",
    "\n",
    "    def grad(self, inputs, output_grads):\n",
    "        return [output_grads[0] * inputs[1], output_grads[0] * inputs[0]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "639963d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(43)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "aa3ca9a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from aesara.tensor.type import dmatrix, matrix\n",
    "\n",
    "x = matrix()\n",
    "y = matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "482b2d15",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = aesara.function([x, y], ProdOp()(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "e764404c",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_val = rng.random((5, 4))\n",
    "y_val = rng.random((5, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a10d0267",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5, 4), (5, 4))"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "e43c1052",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.16683821e-01, 4.13732263e-02, 1.18810339e-02, 7.91266621e-01],\n",
       "       [5.85899328e-01, 7.58709442e-03, 8.91329444e-02, 2.00722194e-01],\n",
       "       [5.29749506e-02, 1.54181857e-01, 2.86612802e-01, 4.91478036e-01],\n",
       "       [1.41043375e-02, 1.25610718e-01, 2.34385553e-01, 4.85944625e-04],\n",
       "       [1.05474324e-01, 4.80209154e-01, 2.54785008e-01, 2.23596030e-01]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = f(x_val, y_val)\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "bea91aa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 4)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "66360e2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_val = rng.random((5, 4, 3))\n",
    "y_val = rng.random((5, 4, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "82354f81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5, 4, 3), (5, 4, 3))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "a9ed0451",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "Bad input argument to aesara function with name \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\570262654.py:1\" at index 0 (0-based).  \nBacktrace when that variable is created:\n\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\ipykernel\\zmqshell.py\", line 528, in run_cell\n    return super().run_cell(*args, **kwargs)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2881, in run_cell\n    result = self._run_cell(\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2936, in _run_cell\n    return runner(coro)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\async_helpers.py\", line 129, in _pseudo_sync_runner\n    coro.send(None)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3135, in run_cell_async\n    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3338, in run_ast_nodes\n    if await self.run_code(code, result, async_=asy):\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3398, in run_code\n    exec(code_obj, self.user_global_ns, self.user_ns)\n  File \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\2681715491.py\", line 3, in <cell line: 3>\n    x = matrix()\nWrong number of dimensions: expected 2, got 3 with shape (5, 4, 3).",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[1;32mIn [44]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[0m out \u001b[38;5;241m=\u001b[39m \u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx_val\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my_val\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m      2\u001b[0m out\n",
      "File \u001b[1;32mD:\\OpenSource\\aesara\\aesara\\compile\\function\\types.py:863\u001b[0m, in \u001b[0;36mFunction.__call__\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    861\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m    862\u001b[0m     \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m--> 863\u001b[0m         s\u001b[38;5;241m.\u001b[39mstorage[\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtype\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfilter\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m    864\u001b[0m \u001b[43m            \u001b[49m\u001b[43marg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstrict\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstrict\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mallow_downcast\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mallow_downcast\u001b[49m\n\u001b[0;32m    865\u001b[0m \u001b[43m        \u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m    867\u001b[0m     \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[0;32m    868\u001b[0m         function_name \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124maesara function\u001b[39m\u001b[38;5;124m\"\u001b[39m\n",
      "File \u001b[1;32mD:\\OpenSource\\aesara\\aesara\\tensor\\type.py:227\u001b[0m, in \u001b[0;36mTensorType.filter\u001b[1;34m(self, data, strict, allow_downcast)\u001b[0m\n\u001b[0;32m    224\u001b[0m                 \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(err_msg)\n\u001b[0;32m    226\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mndim \u001b[38;5;241m!=\u001b[39m data\u001b[38;5;241m.\u001b[39mndim:\n\u001b[1;32m--> 227\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[0;32m    228\u001b[0m         \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mWrong number of dimensions: expected \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mndim\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m,\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    229\u001b[0m         \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m got \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mdata\u001b[38;5;241m.\u001b[39mndim\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m with shape \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mdata\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    230\u001b[0m     )\n\u001b[0;32m    231\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m data\u001b[38;5;241m.\u001b[39mflags\u001b[38;5;241m.\u001b[39maligned:\n\u001b[0;32m    232\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[0;32m    233\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe numpy.ndarray object is not aligned.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    234\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m Aesara C code does not support that.\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[0;32m    235\u001b[0m     )\n",
      "\u001b[1;31mTypeError\u001b[0m: Bad input argument to aesara function with name \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\570262654.py:1\" at index 0 (0-based).  \nBacktrace when that variable is created:\n\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\ipykernel\\zmqshell.py\", line 528, in run_cell\n    return super().run_cell(*args, **kwargs)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2881, in run_cell\n    result = self._run_cell(\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2936, in _run_cell\n    return runner(coro)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\async_helpers.py\", line 129, in _pseudo_sync_runner\n    coro.send(None)\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3135, in run_cell_async\n    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3338, in run_ast_nodes\n    if await self.run_code(code, result, async_=asy):\n  File \"C:\\Users\\Purna\\anaconda3\\envs\\aesara-dev\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 3398, in run_code\n    exec(code_obj, self.user_global_ns, self.user_ns)\n  File \"C:\\Users\\Purna\\AppData\\Local\\Temp\\ipykernel_6756\\2681715491.py\", line 3, in <cell line: 3>\n    x = matrix()\nWrong number of dimensions: expected 2, got 3 with shape (5, 4, 3)."
     ]
    }
   ],
   "source": [
    "out = f(x_val, y_val)\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "2406d64d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = rng.random((5, 4))\n",
    "y = rng.random((5, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "bcd00c90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08497896, 0.25256654, 0.98439382, 0.79617129],\n",
       "       [0.90860337, 0.80361407, 0.41776704, 0.52551226],\n",
       "       [0.70324975, 0.70184239, 0.56080873, 0.0074693 ],\n",
       "       [0.96903872, 0.34545331, 0.05316001, 0.63817275],\n",
       "       [0.55293487, 0.6066848 , 0.7885123 , 0.10156737]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "609bd74b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "2ec8ab6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "296eff23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "11847d36",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = y.astype('int8')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "49db40fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 0],\n",
       "       [0, 0, 0, 0],\n",
       "       [0, 0, 0, 0],\n",
       "       [0, 0, 0, 0],\n",
       "       [0, 0, 0, 0]], dtype=int8)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5523d5ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dtype('float64'), dtype('float64'))"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dtype, y.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "93050b6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'float64'"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aesara.scalar.upcast(x.dtype, y.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "329b579a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[False, False]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outdim = x.ndim\n",
    "shape=[False] * outdim\n",
    "\n",
    "shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "dd97eac8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[False, False, False]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[False] * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "22e205f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "output = [TensorType(dtype=\"int64\", shape=(False,))() for i in range(x.ndim)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "29ed6159",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<TensorType(int64, (None,))>, <TensorType(int64, (None,))>]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "948fc001",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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