{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive PDE discretizations on Cartesian grids\n",
    "## Volume : Algorithmic tools\n",
    "## Part : Automatic differentiation\n",
    "## Chapter : Known bugs and incompatibilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The techniques of automatic differentiation technique play an essential role in the notebooks presented in this repository. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[**Summary**](Summary.ipynb) of volume Algorithmic tools, this series of notebooks.\n",
    "\n",
    "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n",
    "\tbook of notebooks, including the other volumes.\n",
    "\n",
    "# Table of contents\n",
    "  * [1 Matrix multiplication and inversion](#1-Matrix-multiplication-and-inversion)\n",
    "  * [2. In place modifications and aliasing](#2.-In-place-modifications-and-aliasing)\n",
    "    * [2.1 Aliasing of the AD information](#2.1-Aliasing-of-the-AD-information)\n",
    "    * [2.2 Non writeable AD information](#2.2-Non-writeable-AD-information)\n",
    "  * [3. CPU/GPU generic programming](#3.-CPU/GPU-generic-programming)\n",
    "\n",
    "\n",
    "\n",
    "**Acknowledgement.** Some of the experiments presented in these notebooks are part of \n",
    "ongoing research with Ludovic Métivier and Da Chen.\n",
    "\n",
    "Copyright Jean-Marie Mirebeau, Centre Borelli, ENS Paris-Saclay, CNRS, University Paris-Saclay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Importing the required libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.182340Z",
     "iopub.status.busy": "2024-04-30T08:46:36.182051Z",
     "iopub.status.idle": "2024-04-30T08:46:36.190784Z",
     "shell.execute_reply": "2024-04-30T08:46:36.190361Z"
    }
   },
   "outputs": [],
   "source": [
    "import sys; sys.path.insert(0,\"..\") # Allow importing agd from parent directory\n",
    "#from Miscellaneous import TocTools; TocTools.displayTOC('ADBugs','Algo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.193434Z",
     "iopub.status.busy": "2024-04-30T08:46:36.193218Z",
     "iopub.status.idle": "2024-04-30T08:46:36.458728Z",
     "shell.execute_reply": "2024-04-30T08:46:36.458308Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse.linalg\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.460542Z",
     "iopub.status.busy": "2024-04-30T08:46:36.460390Z",
     "iopub.status.idle": "2024-04-30T08:46:36.464876Z",
     "shell.execute_reply": "2024-04-30T08:46:36.464573Z"
    }
   },
   "outputs": [],
   "source": [
    "import agd.AutomaticDifferentiation as ad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.466315Z",
     "iopub.status.busy": "2024-04-30T08:46:36.466231Z",
     "iopub.status.idle": "2024-04-30T08:46:36.468015Z",
     "shell.execute_reply": "2024-04-30T08:46:36.467783Z"
    }
   },
   "outputs": [],
   "source": [
    "def reload_packages():\n",
    "    from Miscellaneous.rreload import rreload\n",
    "    global ad\n",
    "    ad, = rreload([ad],rootdir='..',verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Matrix multiplication and inversion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please use the `ad.apply_linear_mapping` and `ad.apply_linear_inverse` functions in combination with `np.dot`, or scipy solve functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.469414Z",
     "iopub.status.busy": "2024-04-30T08:46:36.469335Z",
     "iopub.status.idle": "2024-04-30T08:46:36.471577Z",
     "shell.execute_reply": "2024-04-30T08:46:36.471352Z"
    }
   },
   "outputs": [],
   "source": [
    "v = ad.Dense.denseAD( np.random.standard_normal((4,)),np.random.standard_normal((4,4)))\n",
    "m0 = np.random.standard_normal((4,4))\n",
    "m1 = scipy.sparse.coo_matrix( ([1.,2.,3.,4.,5.],([0,2,1,2,3],[0,1,2,2,3]))).tocsr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.472888Z",
     "iopub.status.busy": "2024-04-30T08:46:36.472806Z",
     "iopub.status.idle": "2024-04-30T08:46:36.474387Z",
     "shell.execute_reply": "2024-04-30T08:46:36.474144Z"
    }
   },
   "outputs": [],
   "source": [
    "# Fails\n",
    "#print(\"np.dot looses AD:\",np.dot(m0,v))\n",
    "#print(\"scipy '*' looses AD:\",m1*v) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.475749Z",
     "iopub.status.busy": "2024-04-30T08:46:36.475668Z",
     "iopub.status.idle": "2024-04-30T08:46:36.478026Z",
     "shell.execute_reply": "2024-04-30T08:46:36.477752Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "np.dot with AD:\n",
      " denseAD([-3.04188743 -1.81059366 -4.60168428 -0.402255  ],\n",
      "[[-2.18883126 -1.92773839  3.22406318  3.43328336]\n",
      " [-1.16890347 -0.462756    1.82295919  2.66970312]\n",
      " [-2.75635892 -3.19868113  1.28256549  3.17149694]\n",
      " [-0.1224066   0.03960797 -0.308438    0.39619431]])\n",
      "scipy '*' with AD:\n",
      " denseAD([ 0.7291558   5.45572649  9.19406824 -2.45149384],\n",
      "[[ 0.60006067  0.66252011  0.93092156 -0.2395021 ]\n",
      " [ 2.49177526  5.05030758 -0.55925942 -0.93759285]\n",
      " [ 5.41915601  7.88410999 -3.17199694 -4.56263608]\n",
      " [-3.14881496 -5.70942489 -0.69430255 -1.26786441]])\n"
     ]
    }
   ],
   "source": [
    "print(\"np.dot with AD:\\n\",ad.apply_linear_mapping(m0,v))\n",
    "print(\"scipy '*' with AD:\\n\",ad.apply_linear_mapping(m1,v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.479385Z",
     "iopub.status.busy": "2024-04-30T08:46:36.479301Z",
     "iopub.status.idle": "2024-04-30T08:46:36.481425Z",
     "shell.execute_reply": "2024-04-30T08:46:36.481192Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scipy solve with AD :\n",
      " denseAD([ 0.7291558   0.26936566  0.31996104 -0.09805975],\n",
      "[[ 0.60006067  0.66252011  0.93092156 -0.2395021 ]\n",
      " [-0.28363379  0.45826241  0.71556267  0.94790528]\n",
      " [ 0.34946483  0.19172776 -0.40438629 -0.55208538]\n",
      " [-0.1259526  -0.228377   -0.0277721  -0.05071458]])\n"
     ]
    }
   ],
   "source": [
    "print(\"scipy solve with AD :\\n\",ad.apply_linear_inverse(scipy.sparse.linalg.spsolve,m1,v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. In place modifications and aliasing\n",
    "\n",
    "The AD information often consists of very large arrays. In order to save time and memory, this information is not systematically copied and/or stored fully. It can take the form of a broadcasted array, or of an alias to another array. In that case a copy is necessary to enable modifications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Aliasing of the AD information\n",
    "\n",
    "When an operation leaves the AD information untouched, an alias is used. This can lead to bugs if in place modifications are used afterward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.482798Z",
     "iopub.status.busy": "2024-04-30T08:46:36.482717Z",
     "iopub.status.idle": "2024-04-30T08:46:36.484337Z",
     "shell.execute_reply": "2024-04-30T08:46:36.484107Z"
    }
   },
   "outputs": [],
   "source": [
    "x=ad.Dense.identity(constant=np.array([1.,2.]))\n",
    "y=x+1 # Only affects the value, not the AD information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.485590Z",
     "iopub.status.busy": "2024-04-30T08:46:36.485512Z",
     "iopub.status.idle": "2024-04-30T08:46:36.487207Z",
     "shell.execute_reply": "2024-04-30T08:46:36.486981Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Values are distinct : False\n",
      "AD information is shared : True\n"
     ]
    }
   ],
   "source": [
    "print(\"Values are distinct :\", x.value is y.value)\n",
    "print(\"AD information is shared :\", y.coef is x.coef)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A modification of the aliased variable will impact the original one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.488573Z",
     "iopub.status.busy": "2024-04-30T08:46:36.488478Z",
     "iopub.status.idle": "2024-04-30T08:46:36.490467Z",
     "shell.execute_reply": "2024-04-30T08:46:36.490206Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "denseAD(1.0,[1. 0.])\n",
      "Caution ! Shared AD information is affected : denseAD(1.0,[2. 0.])\n"
     ]
    }
   ],
   "source": [
    "print(x[0])\n",
    "y[0]*=2\n",
    "print(\"Caution ! Shared AD information is affected :\", x[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avoid this effect by making a copy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.491861Z",
     "iopub.status.busy": "2024-04-30T08:46:36.491761Z",
     "iopub.status.idle": "2024-04-30T08:46:36.493678Z",
     "shell.execute_reply": "2024-04-30T08:46:36.493459Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AD information is distinct : False\n"
     ]
    }
   ],
   "source": [
    "x=ad.Dense.identity(constant=np.array([1.,2.]))\n",
    "y=(x+1).copy()\n",
    "print(\"AD information is distinct :\", y.coef is x.coef)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that a similar effect arises with the `-` binary operator, but not with `*`or `/`. That is because the latter modify the AD information, which therefore must be copied anyway."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.495201Z",
     "iopub.status.busy": "2024-04-30T08:46:36.495101Z",
     "iopub.status.idle": "2024-04-30T08:46:36.497174Z",
     "shell.execute_reply": "2024-04-30T08:46:36.496946Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AD information is shared : True\n",
      "AD information is distinct : False\n",
      "AD information is distinct : False\n"
     ]
    }
   ],
   "source": [
    "x=ad.Dense.identity(constant=np.array([1.,2.]))\n",
    "print(\"AD information is shared :\", (x-1).coef is x.coef)\n",
    "print(\"AD information is distinct :\", (x*2).coef is x.coef)\n",
    "print(\"AD information is distinct :\", (x/2).coef is x.coef)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Non writeable AD information\n",
    "\n",
    "When creating an dense AD variable, the coefficients may be non writeable (e.g. broadcasted) arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.498500Z",
     "iopub.status.busy": "2024-04-30T08:46:36.498402Z",
     "iopub.status.idle": "2024-04-30T08:46:36.500226Z",
     "shell.execute_reply": "2024-04-30T08:46:36.500019Z"
    }
   },
   "outputs": [],
   "source": [
    "x=ad.Dense.identity(constant=np.array([[1.,2.],[3.,4.]]),shape_bound=(2,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.501541Z",
     "iopub.status.busy": "2024-04-30T08:46:36.501438Z",
     "iopub.status.idle": "2024-04-30T08:46:36.504376Z",
     "shell.execute_reply": "2024-04-30T08:46:36.504113Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.coef.flags.writeable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.505750Z",
     "iopub.status.busy": "2024-04-30T08:46:36.505656Z",
     "iopub.status.idle": "2024-04-30T08:46:36.507180Z",
     "shell.execute_reply": "2024-04-30T08:46:36.506921Z"
    }
   },
   "outputs": [],
   "source": [
    "# x+=1 # Fails because non-writeable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a copy to solve the issue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.508566Z",
     "iopub.status.busy": "2024-04-30T08:46:36.508483Z",
     "iopub.status.idle": "2024-04-30T08:46:36.510098Z",
     "shell.execute_reply": "2024-04-30T08:46:36.509877Z"
    }
   },
   "outputs": [],
   "source": [
    "y=x.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.511379Z",
     "iopub.status.busy": "2024-04-30T08:46:36.511299Z",
     "iopub.status.idle": "2024-04-30T08:46:36.513249Z",
     "shell.execute_reply": "2024-04-30T08:46:36.513010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.coef.flags.writeable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.514568Z",
     "iopub.status.busy": "2024-04-30T08:46:36.514488Z",
     "iopub.status.idle": "2024-04-30T08:46:36.516018Z",
     "shell.execute_reply": "2024-04-30T08:46:36.515793Z"
    }
   },
   "outputs": [],
   "source": [
    "y+=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. CPU/GPU generic programming\n",
    "\n",
    "The agd library allows CPU/GPU generic programming to some extent. Here are the guidelines to make this approach work.\n",
    "\n",
    "*Make a copy of the numpy array module*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.517324Z",
     "iopub.status.busy": "2024-04-30T08:46:36.517245Z",
     "iopub.status.idle": "2024-04-30T08:46:36.518907Z",
     "shell.execute_reply": "2024-04-30T08:46:36.518597Z"
    }
   },
   "outputs": [],
   "source": [
    "xp = np "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Activate GPU acceleration.*\n",
    "If uncommented, the following line will replace the module xp with np, and modify its other arguments in a custom manner intended for easy interaction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.520245Z",
     "iopub.status.busy": "2024-04-30T08:46:36.520168Z",
     "iopub.status.idle": "2024-04-30T08:46:36.521646Z",
     "shell.execute_reply": "2024-04-30T08:46:36.521422Z"
    },
    "tags": [
     "GPU_config"
    ]
   },
   "outputs": [],
   "source": [
    "#xp,plt = map(ad.cupy_friendly,[xp,plt])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Create basic arrays using `xp`.* Basic arrays are arrays of zeros, of ones, arange, linspace, etc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.522941Z",
     "iopub.status.busy": "2024-04-30T08:46:36.522843Z",
     "iopub.status.idle": "2024-04-30T08:46:36.524465Z",
     "shell.execute_reply": "2024-04-30T08:46:36.524247Z"
    }
   },
   "outputs": [],
   "source": [
    "x = xp.linspace(0,2*np.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Use numpy's overloading mechanisms.* These mechanisms will dispatch the function calls to cupy, or to the AutomaticDifferentiation module of the agd library, depending on the data type (array from numpy, cupy, or ad)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.525814Z",
     "iopub.status.busy": "2024-04-30T08:46:36.525730Z",
     "iopub.status.idle": "2024-04-30T08:46:36.527323Z",
     "shell.execute_reply": "2024-04-30T08:46:36.527105Z"
    }
   },
   "outputs": [],
   "source": [
    "y = np.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Use `ad.asarray` and `ad.array`.* Stacking arrays using np.array will not work for AD or cupy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.528630Z",
     "iopub.status.busy": "2024-04-30T08:46:36.528556Z",
     "iopub.status.idle": "2024-04-30T08:46:36.530162Z",
     "shell.execute_reply": "2024-04-30T08:46:36.529945Z"
    }
   },
   "outputs": [],
   "source": [
    "xy = ad.array([x,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Use functions that accept both numpy and cupy arrays.* Or modify them for that purpose, as we did for the member functions of the pyplot module using the `ad.cupy_friendly` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.531509Z",
     "iopub.status.busy": "2024-04-30T08:46:36.531436Z",
     "iopub.status.idle": "2024-04-30T08:46:36.593579Z",
     "shell.execute_reply": "2024-04-30T08:46:36.593308Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(*xy);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*If needed, convert cupy array's to numpy arrays.* Using the `get` member function of the `cupy.ndarray` class, or using `ad.cupy_generic.cupy_get` (which leaves non-cupy variables unchanged)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:36.595141Z",
     "iopub.status.busy": "2024-04-30T08:46:36.595035Z",
     "iopub.status.idle": "2024-04-30T08:46:36.597328Z",
     "shell.execute_reply": "2024-04-30T08:46:36.597059Z"
    }
   },
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