{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sys.version= 3.6.3 |Anaconda, Inc.| (default, Oct  6 2017, 12:04:38) \n",
      "[GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "np.__version__= 1.13.3\n"
     ]
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "import sys\n",
    "\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "print (\"sys.version=\", sys.version)\n",
    "print (\"np.__version__=\", np.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Geophysical Tutorial – coordinated by Matt  Hall\n",
    "\n",
    "# The conjugate gradient method\n",
    "\n",
    "Karl Schleicher, k_schleicher@hotmail.com"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The conjugate gradient method can be used to solve many large linear geophysical problems. For example, least squares parabolic and hyperbolic radon transform, travel time tomography, least squares migration, and full waveform inversion (e.g. Witte et al., 2018). This tutorial revisits the _Linear inversion_ tutorial (Hall, 2016) that estimated reflectivity by deconvolving a known wavelet from a seismic trace using least squares. This tutorial solves the same problem using the conjugate gradient method. This problem is easy to understand and the concepts apply to other applications. The conjugate gradient method is often used to solve large problems because the least squares algorithm is much more expensive — that is, even a large computer may not be able to find a useful solution in a reasonable amount of time.  \n",
    "\n",
    "\n",
    "## Introduction\n",
    "\n",
    "The conjugate gradient method was originally proposed by Hestenes (1952) and extended to handle rectangular matrices by Paige & Saunders (1982). Claerbout (2012) demonstrated its application to geophysical problems. It is an iterative method. Each iteration applies the linear operator and its adjoint. The initial guess is often the zero vector and computation may stop after very few iterations.  \n",
    "\n",
    "The adjoint of the operator $\\mathbf{A}$, denoted as $\\mathbf{A}^\\mathrm{H}$, is defined as the operator that satisfies $\\langle \\mathbf{A} \\mathbf{x}, \\mathbf{y} \\rangle$  = $\\langle \\mathbf{x}, \\mathbf{A}^\\mathrm{H} \\mathbf{y} \\rangle$ for all vectors $\\mathbf{x}$ and $\\mathbf{y}$ (where  $\\langle \\mathbf{u},\\mathbf{v} \\rangle$ represents the inner product between vectors $\\mathbf{u}$ and $\\mathbf{v}$). For a given matrix, the adjoint is simply the complex conjugate of the transpose of the matrix; this is also sometimes known as the Hermitian transpose, and sometimes written as $\\mathbf{A}^\\ast$ or $\\mathbf{A}^\\dagger$. Just to muddy the notation water even further, the complex conjugate transpose is denoted by `A.H` in NumPy and `A'` in MATLAB or Octave. However, we will implement the adjoint operator without forming any matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matrix\n",
      "[[ 2.+0.j  3.+0.j]\n",
      " [ 6.+3.j -7.+0.j]]\n",
      "\n",
      "transpose\n",
      "[[ 2.+0.j  6.+3.j]\n",
      " [ 3.+0.j -7.+0.j]]\n",
      "\n",
      "complex conjugate transpose, aka Hermitian transpose\n",
      "[[ 2.-0.j  6.-3.j]\n",
      " [ 3.-0.j -7.-0.j]]\n"
     ]
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "A  = np.matrix([[2,3], [(6+3j),-7]])\n",
    "\n",
    "print(\"matrix\")\n",
    "print(A)\n",
    "print(\"\\ntranspose\")\n",
    "print(A.T)\n",
    "print(\"\\ncomplex conjugate transpose, aka Hermitian transpose\")\n",
    "print(A.H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many linear operators can be programmed as functions that are more intuitive and efficient than matrix multiplication. The matrices for operators like migration and FWI would be huge, but we avoid this problem because once you have the program for the linear operator, you can write the adjoint operator without computing matrices. Implementing the conjugate gradient algorithm using functions to apply linear operators and their adjoints is practical and efficient. It is wonderful to see programs that implement linear algorithms without matrices and the programming technique is a key theme in Claerbout’s 2012 book.\n",
    "\n",
    "This tutorial provides a quick start to the conjugate gradient method based on Guo’s pseudocode (2002). Those interested in more depth can read Claerbout (2012) and Shewchuk (1994). A Jupyter Notebook with Python code to reproduce the figures in this tutorial is at: https://github.com/seg/tutorials."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "# OMIT SET-UP FROM MANUSCRIPT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SET-UP — Construct the model `m`\n",
    "\n",
    "We start with the slightly odd-seeming number of samples 51. This is because when we calculate the impedance contrasts (reflectivities), we'll lose a sample. Since I'd like 50 samples in the final reflectivity model `m`, we have to start with 50 + 1 samples in the impedance model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "\n",
    "# Impedance, imp     VP    RHO\n",
    "imp = np.ones(51) * 2550 * 2650\n",
    "imp[10:15] =        2700 * 2750\n",
    "imp[15:27] =        2400 * 2450\n",
    "imp[27:35] =        2800 * 3000\n",
    "\n",
    "# Compute reflectivity.\n",
    "m = (imp[1:] - imp[:-1]) / (imp[1:] + imp[:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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9IPDTiDhkN7fbCvwPcDKwDFgInBsRf84t817ghRHxbknnAK+LiDcOtt158+bFokWVN+jr\n38s0ZD0KfOqvXwBQdt7rj5rDD+9cXrP0aub9qb9+AWcdOYc3fjl71Kv0nFA99ruU90g65iP1vA73\nPI3E/R7ofFdzPxrtvI6Ez1SlJN0ZEfOGXK6AIPSriHh5blrAL/Npu7jdY4GPRcSpafpigIj4VG6Z\n+WmZBZLGAE8C02KQgzDcIHTcZbexvKuHd917Awd0L9+ePn5MKwCbt/Y9Zx1JlCtCtdKrmff4Ma0c\nuW8nf165HoDDZnUAcPfjXWW3X4u8H137LABz99qjbnnX49hWM+/hnqeRuN8Dne9q7kejndd65/3w\n5Dl8+YVnAjCns53fXnTic9YZSKVBqIhetO+TdBNwLdk9obOBhaX+5CLiul3c7hzgidz0MuAlAy0T\nEVsldQN7AU/lF5J0AXABwL777jusQgzUm3S5D1TJQDGwWunVzLu0rQnjWivKoxZ5b9zSVza9lnnX\n49hWM+/hnqeRuN8Dne/B8m/281pk3rXqKb+IINQGrAJekabXkA3vfQZZUNrVIKQyaf2PdCXLEBFX\nAldCdiU0nELM7mxneVfP9l8PJXNSL9PLy5zIVom+Mh+KaqVXM+85ne288aIT2a9f+pvSFWA98v5w\nvyqmeuRdj2NbzbyHe55G4n4PdL6ruR+Ndl6LzLtWPeXXfSiHiDh/kNff7MamlwH75Kb3BlYMtEyq\njpsMrNuNPJ/jwlMPpn3szr8+S71MDzTv3JfsU9P0auY9UG/Z9djvIvOux7GtZt7DPVYjcb8H65l9\ntJ7XkfiZ2l1FtI7bH3g/MDeffxUeVl0IHJS2vxw4B3hTv2VuBM4DFgBvAG4b7H7QrijduBusZUm5\nefP2m1LT9GrmXeR+j8RjPlLP63CP1Ujc74FUcz8a7byOtM/U7iqiYcIfga8Bi4FtpfT8c0S7se1X\nA58la6J9VUR8UtKlwKKIuFFSG/At4EiyK6Bz+o/y2t9wGyZY7fVv8WXNzee7MY3khgmbIuKKWmw4\nIm4CbuqX9tHc+01kDSHMzGwEKCIIfU7SJcDNwOZSYkTcVUBZzMysQEUEoRcAbwVOZEd1XKRpMzMb\nRYoIQq8DDnB/cWZmVvcm2sAfgc4C8jUzsxGmiCuhGcADkhay455QRMSZg6xjZmZNqIggdEnuvYCX\nAecWUA4zMytYET0m/BLoBl4DfAM4iWxoBzMzG2XqObz388l6MTiXbCyf75M9LHtCvcpgZmYjSz2r\n4x4Afg2ckRtL6EN1zN/MzEaYelbHvZ5s/J5fSPqKpJMo36u1mZmNEnULQhHxozSK6SHA7cCHgBmS\nvijplHqVw8zMRo4iGiY8GxHfiYjTyYZbuAe4qN7lMDOz4hXxsOp2EbEuIr4cEe6yx8xsFCo0CJmZ\n2ejmIGRmZoVxEDIzs8I4CJmZWWEchMzMrDAOQmZmVhgHITMzK4yDkJmZFcZByMzMCtMUQUjSFEm3\nSHow/d1zgOV+LqlL0k/qXUYzM3uupghCZH3P3RoRBwG3MnBfdJcDb61bqczMbFDNEoTOBK5O768G\nziq3UETcCmyoV6HMbPdcf/dy7n68izseWcdxl93G9XcvL7pIVmXNEoRmRMRKgPR3+u5sTNIFkhZJ\nWrRmzZqqFNDMhuf6u5dz8XWL2dK3DYDlXT1cfN1iB6Im0zBBSNJ/S/pTmdeZ1c4rIq6MiHkRMW/a\ntGnV3ryZVeDy+Uvo6e3bKa2nt4/L5y8pqERWC/Uc3nu3RMQrB5onaZWkWRGxUtIsYHUdi2Z1VKqe\n2dK3jeMuu40LTz2Ys46cU3SxrAZWdPUMK90aU8NcCQ3hRuC89P484IYCy2I14uqZ0WV2Z/uw0q0x\nNUsQugw4WdKDwMlpGknzJH21tJCkXwP/BZwkaZmkUwspre0SV8+MLheeejDtY1t3Smsf28qFpx5c\nUImsFhqmOm4wEbEWOKlM+iLgb3PTf1XPcll1uXpmdClVs14+fwkrunqY3dnu6tcm1BRByEaH2Z3t\nLC8TcFw907zOOnKOg06Ta5bqOBsFXD1j1nx8JWQNw9UzZs1HEVF0GUY0SWuAx3Zx9anAU1UsTqMY\nrfsNo3ffvd+jSyX7vV9EDPmgpYNQDUlaFBHzii5HvY3W/YbRu+/e79Glmvvte0JmZlYYByEzMyuM\ng1BtXVl0AQoyWvcbRu++e79Hl6rtt+8JmZlZYXwlZGZmhXEQMjOzwjgImZlZYRyEzMysMA5CZmZW\nGAchMzMrjIOQmZkVxkHIzMwK4yBkZmaFcRAyM7PCOAiZmVlhHITMzKwwDkJmZlYYByEzMyvMmKIL\nMNJNnTo15s6dW3QxzMwayp133vlUREwbajkHoSHMnTuXRYsWFV0MM7OGIumxSpZzdZyZmRXGV0Jm\no8S9y7p46pnNRRejIrMmt3PorI6ii2F14CBkNgqsfWYzZ37ht0QUXZLKjBvTwuKPncL4Ma1FF8Vq\nzEHIbBRY88xmIuAjpx3CSw/cq+jiDOrWB1Zzxa0Psnr9ZvaZMqHo4liNOQiZjQLdG3sBeOHek3nR\nPp0Fl2ZwT2/cAsDqDZschEYBN0wwGwW6e7IgNLl9bMElGdqMjjYAnuxujPtXtnschMxGga4GCkIz\nUxBatX5TwSWxenAQMhsF1peC0ISRH4Q6J4xl3JgWB6FRwkHIbBTo2thLi2DiuJF/G1gSMzrG86SD\n0KjgIGQ2CnT39NLRPpaWFhVdlIrM7GjzldAo4SBkNgp09/TS2QD3g0qmd7Sxar0bJowGDkJmo0BX\nT29DNEooKV0JRaM8XWu7zEHIbBQoVcc1ihkd49m4pY8Nm7cWXRSrMQchs1FgfU8vnRPGFV2MipWe\nFVrV7ftCza6mQUjShyTdJ+lPkr4nqU3S/pLukPSgpO9LGpeWHZ+ml6b5c3PbuTilL5F0ai79tJS2\nVNJFufRh52HWzLo2bmFy+8hvGVey41kh3xdqdjULQpLmAB8A5kXEXwCtwDnAvwKfiYiDgKeBd6RV\n3gE8HRHPAz6TlkPSYWm9w4HTgP+U1CqpFfgC8CrgMODctCzDzcOsmUUE6zdtbah7Qtt7TXALuaZX\n6+q4MUC7pDHABGAlcCLwgzT/auCs9P7MNE2af5IkpfRrImJzRDwCLAWOTq+lEfFwRGwBrgHOTOsM\nNw+zpvXM5q30bQs62xuwOs5BqOnVLAhFxHLg34HHyYJPN3An0BURpbuNy4A56f0c4Im07ta0/F75\n9H7rDJS+1y7ksRNJF0haJGnRmjVrdmX3zUaMro2N02VPSfu4VjraxjgIjQK1rI7bk+zKY39gNrAH\nWdVZf6U2mOWuSKKK6YPlsXNCxJURMS8i5k2bNuQQ6WYjWqnz0kZqHQcwc3IbT7phQtOrZXXcK4FH\nImJNRPQC1wEvBTpT9RzA3sCK9H4ZsA9Amj8ZWJdP77fOQOlP7UIeZk2r1G9cZwP0G5c3o6ONVRvc\nMKHZ1TIIPQ4cI2lCuu9yEvBn4BfAG9Iy5wE3pPc3pmnS/Nsie1LtRuCc1LJtf+Ag4A/AQuCg1BJu\nHFnjhRvTOsPNw6xpNVIP2nkzOtrcRHsUqFmbzYi4Q9IPgLuArcDdwJXAT4FrJH0ipX0trfI14FuS\nlpJdnZyTtnOfpGvJAthW4O8iog9A0vuA+WQt766KiPvStj4ynDzMmlkjjSWUN7OjjTXPbKZvW9Da\nIH3e2fDV9MGBiLgEuKRf8sNkLdv6L7sJOHuA7XwS+GSZ9JuAm8qkDzsPs2bV3bDVcePp2xasfWYz\n01NrOWs+FVXHSZoh6WuSfpamD5P0jqHWM7PidW3sZWyraB/bWnRRhsXPCo0Old4T+gZZtdfsNP0/\nwN/XokBmVl3dqfPSRnskbuZk95owGlQahKZGxLXANtj+jE1fzUplZlWzvsF60C7xldDoUGkQelbS\nXqRnaiQdQ/agp5mNcF09WxoyCE2dOJ4WwWoHoaZWacOE/4+sefOBkn4LTGNHE2gzG8G6e3qZNnF8\n0cUYttYWMW3SeD+w2uQqCkIRcZekVwAHk/U6sCQ9gGpmI1x3Ty8HTZ9UdDF2ycyONlfHNblKW8f9\nHTAxIu6LiD8BEyW9t7ZFM7Nq6NrYmPeEILsvtNoNE5papfeE3hkRXaWJiHgaeGdtimRm1dK3Ldiw\naWvD9RtXMsNXQk2v0iDUkh/yII3l0zj9wpuNUhs2pQdVGzQIzZzcRndPL5t63Ri3WVUahOYD10o6\nSdKJwPeAn9euWGZWDY04jEPe9ElZgwoP6dC8Km0d9xHgXcB7yBom3Ax8tVaFMrPqaNR+40pKD6w+\n2b2J/fbao+DSWC1U2jpuG/DF9DKzBtGo/caVzCyNsOohHZpWRUFI0nHAx4D90joCIiIOqF3RzGx3\nNeowDiWljks9pEPzqrQ67mvAh8iG5/YdQitryZMbuP6e5dRyhKYJ41q54OUH0NZgnXEWZXt1XINe\nCXW0jaF9bKvvCTWxSoNQd0T8rKYlsYb36ZuXcMv9qxjbWpuxEiOC3r7gsFkdvPKwGTXJo9msb/Ar\nIUnM6BjvZtpNrNIg9AtJl5MN0b29cjYi7qpJqazh9G0Lfv/wWs4+am/+7Q0vqkkeq9Zv4iX/51ZW\n+gupYl0bt9A2toXxYxr3ynFGR5uvhJpYpUHoJenvvFxaACdWtzjWqO5fuZ71m7by0gOn1iyPqRPH\nM6ZFPNndU7M8mk13Ty+d7Y39SN/MyW3c/XjX0AtaQ6q0ddwJtS6INbbfPfQUAMceuFfN8mhtETM6\n2ljZ5V/Flepu0GEc8kq9JkREw42JZEOreHhvSa8BDge2j7MbEZfWolDWeBY8tJYDpu2xfQyYWpk5\nuY2VbilVsUbuN65kRkcbW7Zuy67qJjT2VZ09V6UdmH4JeCPwfrLm2WeTNdc2o7dvG394ZB3HHlC7\nq6CSWZPdl9hwdPf0NmzLuJIZHVmvCT7vzanSZkwvjYi3AU9HxL8AxwL71K5Y1kgWL+/m2S19Nb0f\nVDJrchsrunqIWrYDbyKNOqpqXumBVY8r1JwqDUKlO8EbJc0GeoH9a1MkazQLHloLwDEHTKl5XjMn\nt7N567btfaLZ4LqaIAiVqng9pENzqjQI/URSJ3A5cBfwKHBNrQpljWXBQ2s5ZOYk9qrD6J2zUl9i\nvi80tN6+bWzc0tewPWiXTHd1XFOrKAhFxMcjoisifkh2L+iQiPjn2hbNGsHmrX0semwdx9ThfhDs\nCEJPrncz7aE0em8JJePHtDJlj3EOQk1q0NZxkv56kHlExHXVL5I1knse72JT7zZeWsOm2XmzJrcD\nsMLNtIfU6MM45E2fNJ7VDkJNaagm2mekv9OBlwK3pekTgNvJelCwUWzBw2uR4CX71ycITZs0ntYW\n+SZ1BRp9GIe8mW4V2bQGrY6LiPMj4nyy3hEOi4jXR8TryZ4XGpSkgyXdk3utl/T3kqZIukXSg+nv\nnml5SbpC0lJJ90p6cW5b56XlH5R0Xi79KEmL0zpXlEZ/3ZU8bNf87qG1HD67o25VPq0tYvqk8b4n\nVIFG7zcub2ZHG6vcMKEpVdowYW5ErMxNrwKeP9gKEbEkIo6IiCOAo4CNwI+Ai4BbI+Ig4NY0DfAq\n4KD0uoA0dpGkKcAlZF0HHQ1cUgoqaZkLcuudltKHlYftmp4tfdzzeFddmmbnzZrcxkp33TOkrp4t\nQHMEoekdbTz1zGZ6+7YVXRSrskqD0O2S5kt6e7oS+Snwi2HkcxLwUEQ8BpwJXJ3SrwbOSu/PBL4Z\nmd8DnZJmAacCt0TEuoh4GrgFOC3N64iIBZE9NPLNftsaTh62C+587Gm29G2ry0OqebMmt7s6rgLd\nG0sD2jV+LwMzO9qIgDUe3K7pVNo67n3Al4AXAUcAV0bE+4eRzznA99L7GaWrqvR3ekqfAzyRW2dZ\nShssfVmZ9F3JYyeSLpC0SNKiNWvWDGM3R5cFDz9Fa4v4y/1r/3xQXqnrHj+wOrjSgHYdbRX3zjVi\nlXpNcG/azWc4A7/cBfw0Ij4EzJc0qZKVJI0DXgv811CLlkmLXUjflTx2Toi4MiLmRcS8adOmDbHJ\n0et3D63lhXtPZuL4+n7JzZrcRk9vH+t7ttY130bT3dPLxPFjGFOj8Z3qqfTAqoNQ86m077h3Aj8A\nvpyS5gDXV5jHq4C7ImJVml5VqgJLf1en9GXs3BXQ3sCKIdL3LpO+K3nYMD2zeSv3LuuuW9PsvO3N\ntH1faFDN0IN2yczJpSDk6rgQ7K/tAAANu0lEQVRmU+lPpL8DjgPWA0TEg+yo4hrKueyoigO4ESi1\ncDsPuCGX/rbUgu0YstFcVwLzgVMk7ZkaJJwCzE/zNkg6JrWKe1u/bQ0nDxumhY+so29bcOwB9W2U\nADu+kHxfaHDdTdCDdsmUCeMY2yo3025CldajbI6ILaWxPCSNYeiqLyRNAE4G3pVLvgy4VtI7gMfJ\neuQGuAl4NbCUrCXd+QARsU7Sx4GFablLI2Jdev8e4BtAO/Cz9Bp2HjZ8Cx5ey7jWFo7ab8+hF64y\nd91TmWa6EmppEdMntbHK57zpVBqEfinpn4B2SScD7wV+PNRKEbER2Ktf2lqy1nL9lw2yK65y27kK\nuKpM+iLgL8qkDzsPG54FD63liH07aR9X/2Gjp08aT4vwCKtD6O7p5XnTJxZdjKqZ3jGeVRschJpN\npdVxFwFrgMVkVzU3Af+7VoWyka17Yy9/WlHM/SCAMa0tTJ/Uxgr/Kh5UM/SgnTezo81VsE2o0uG9\nt0m6GriDrBpuSbh97Kh1xyNriaDuzwflzZzsL6ShNFN1HGQt5H7z4FNFF8OqrKIglIb2/hLwEFkz\n5/0lvSsifjb4mqPXT+5dwTV/eGLoBRvQE09vpG1sC0fs21lYGWZ3trHkyQ2F5T/SbertY8vWbQ3f\ng3bejI42Nmzeypu/+ntU9mkLq7bzj5vLSYfOqGkeld4T+jRwQkQsBZB0IFmvCQ5CA9jaF/T09hVd\njJqYOnE8rztyDuPH1P9+UMnMjnZuX7KGiKDUYMZ2aKYetEuOP3gaty9ZzaZed91TL719ta/wqjQI\nrS4FoORhdjx7Y2WcdeQczjryOZ0xWJXMmtzGxi19rN+0tam+aKulmXrQLjl0Vgfff9exRRfDqqzS\nIHSfpJuAa8nuCZ0NLCyNN+Rxhaze8s8KNdMXbbWUglBne+P3G2fNrdLWcW1kPWe/AjierKXcFLLx\nhk6vScnMBjG7s/SskJtpl9O1sXl60LbmVmnrOD/UaSPKzNR1jx9YLa8Zq+OsOVXaOm5/4P3A3Pw6\nEfHa2hTLbHDTJ41HchAayPYg1ESt46w5VXpP6Hrga2S9JLhpihVubGsL0yaOd68JA+ju6UWCSXXu\n4dxsuCr9hG6KiCtqWhKzYZrV2e4roQF09/TS0TaWlhY3X7eRrdIg9DlJlwA3A9v7Uo+Iu2pSKrMK\nzOpoY+maZ4ouxojU3dNLp6virAFUGoReALwVOJEd1XGRps0KMXNyG79Z6m5cyulqomEcrLlVGoRe\nBxwQEVtqWRiz4Zjd2cYzm7eyYVMvk9r8hZvXbP3GWfOq9DmhPwLFdRRmVoabaQ9svYOQNYhKr4Rm\nAA9IWsjO94TcRNsKkx/c7vkzJhVcmpGl2YZxsOZVaRC6pKalMNsFMztKXfe4mXZeRLg6zhpGpT0m\n/LLWBTEbrhkdbUiwosvVcXnPbumjb1u4dZw1hEGDkKQNZK3gnjOLbLTsjpqUyqwC48a0MHXieA9u\n14/7jbNGMmgQighXtNuINmtyGyvXOwjlud84aySVto4zG5FmTW7zPaF+dgQhD+NgI5+DkDW0WZPb\nWel7QjvpbsJRVa15OQhZQ5s5uY0N6YFVy2wf0M4NE6wBOAhZQys9K7TK94W28z0hayQOQtbQZrnX\nhOfo6ullTIuYMK616KKYDclByBra9l4TfF9ou1IP2pKHcbCRz0HIGtr0jvGAr4Tyunt66XBVnDWI\nmgYhSZ2SfiDpAUn3SzpW0hRJt0h6MP3dMy0rSVdIWirpXkkvzm3nvLT8g5LOy6UfJWlxWucKpZ9+\nu5KHNabxY1qzB1bXu5l2SbeHcbAGUusroc8BP4+IQ4AXAfcDFwG3RsRBwK1pGuBVwEHpdQHwRcgC\nClnfdS8BjgYuKQWVtMwFufVOS+nDysMa26zJbe66J6e7p5dOByFrEDULQpI6gJcDXwOIiC0R0QWc\nCVydFrsaOCu9PxP4ZmR+D3RKmgWcCtwSEesi4mngFuC0NK8jIhZERADf7Let4eRhDWzm5DZ33ZPj\nzkutkdTySugAYA3wdUl3S/qqpD2AGRGxEiD9nZ6WnwM8kVt/WUobLH1ZmXR2IY+dSLpA0iJJi9as\nWTO8vba6mzW5jZXuNWG7ro1bHISsYdQyCI0BXgx8MSKOBJ5lR7VYOeWa8sQupA+monUi4sqImBcR\n86ZNmzbEJq1osya3s37TVp7dvLXoohRu27Zgw+atTJ7gLnusMdQyCC0DlkXEHWn6B2RBaVWpCiz9\nXZ1bfp/c+nsDK4ZI37tMOruQhzWw/OB2o92GTVuJ8IOq1jgqHdRu2CLiSUlPSDo4IpYAJwF/Tq/z\ngMvS3xvSKjcC75N0DVkjhO6IWClpPvB/co0RTgEujoh1kjZIOga4A3gb8H9z26o4j1odA6uPmSkI\nfXPBo+w7ZUKxhSmYe0uwRlOzIJS8H/iOpHHAw8D5ZFdf10p6B/A4cHZa9ibg1cBSYGNalhRsPg4s\nTMtdGhHr0vv3AN8A2oGfpRdkwafiPKyxPW/6RNrHtvLNBY8VXZQRobVFHDhtj6KLYVYRZQ3LbCDz\n5s2LRYsWFV0MG8Km3j629G0ruhgjwtiWFtrdZY8VTNKdETFvqOVqfSVkVhdtY1tpG+svXrNG4257\nzMysMA5CZmZWGN8TGoKkNcCu3vGeCjxVxeI0Au/z6OB9Hh12Z5/3i4ghH7R0EKohSYsquTHXTLzP\no4P3eXSoxz67Os7MzArjIGRmZoVxEKqtK4suQAG8z6OD93l0qPk++56QmZkVxldCZmZWGAchMzMr\njINQjUg6TdISSUslDTaOUsOSdJWk1ZL+lEubIukWSQ+mv3sOto1GImkfSb+QdL+k+yR9MKU38z63\nSfqDpD+mff6XlL6/pDvSPn8/dVLcVCS1pgE5f5Kmm3qfJT0qabGkeyQtSmk1/2w7CNWApFbgC8Cr\ngMOAcyUdVmypauIbwGn90i4Cbo2Ig4BbGXwgw0azFfiHiDgUOAb4u3Rem3mfNwMnRsSLgCOA09Lw\nKf8KfCbt89PAOwosY618ELg/Nz0a9vmEiDgi92xQzT/bDkK1cTSwNCIejogtwDXAmQWXqeoi4lfA\nun7JZwJXp/dXA2fVtVA1FBErI+Ku9H4D2RfUHJp7nyMinkmTY9MrgBPJBqqEJttnAEl7A68Bvpqm\nRZPv8wBq/tl2EKqNOcATuellKW00mFEaKDD9nV5weWpC0lzgSLIBFZt6n1O11D1kIxTfAjwEdEVE\naTz1Zvx8fxb4MFAaH2Qvmn+fA7hZ0p2SLkhpNf9seyiH2lCZNLeFbxKSJgI/BP4+ItZnP5KbV0T0\nAUdI6gR+BBxabrH6lqp2JJ0OrI6IOyUdX0ous2jT7HNyXESskDQduEXSA/XI1FdCtbEM2Cc3vTew\noqCy1NsqSbMA0t/VBZenqiSNJQtA34mI61JyU+9zSUR0AbeT3Q/rlFT6Edtsn+/jgNdKepSsKv1E\nsiujZt5nImJF+rua7MfG0dThs+0gVBsLgYNSa5pxwDnAjQWXqV5uBM5L788DbiiwLFWV7gt8Dbg/\nIv4jN6uZ93laugJCUjvwSrJ7Yb8A3pAWa6p9joiLI2LviJhL9r97W0S8mSbeZ0l7SJpUeg+cAvyJ\nOny23WNCjUh6Ndmvp1bgqoj4ZMFFqjpJ3wOOJ+vufRVwCXA9cC2wL/A4cHZE9G+80JAkvQz4NbCY\nHfcK/onsvlCz7vMLyW5It5L9aL02Ii6VdADZVcIU4G7gLRGxubiS1kaqjvvHiDi9mfc57duP0uQY\n4LsR8UlJe1Hjz7aDkJmZFcbVcWZmVhgHITMzK4yDkJmZFcZByMzMCuMgZGZmhXGPCWa7KDVfvTVN\nzgT6gDVpemNEvLSQglWJpGciYmLR5bDm5ibaZlUg6WPAMxHx70WXpVochKweXB1nVgOSnkl/j5f0\nS0nXSvofSZdJenMao2expAPTctMk/VDSwvQ6rsw2D0/r3SPpXkkHpfTrU6eT9+U6nkTSM5L+Nc37\nb0lHS7pd0sOSXpuWebukGyT9XNn4V5cMsD8XpnLdWxpTyKwaHITMau9FZGPTvAB4K/D8iDiabJiA\n96dlPkc2Vs1fAq9P8/p7N/C5iDgCmEfWRyHA30TEUSntA6maEGAP4PY0bwPwCeBk4HXApbntHg28\nmWy8oLMlzcvNQ9IpwEFpuSOAoyS9fFcOhFl/vidkVnsLS93hS3oIuDmlLwZOSO9fCRyW65G7Q9Kk\nNG5RyQLg/09j3VwXEQ+m9A9Iel16vw9ZwFgLbAF+nstrc0T0SloMzM1t95aIWJvKdx3wMmBRbv4p\n6XV3mp6Y8vjVsI6CWRkOQma1l+9fbFtuehs7/gdbgGMjomegjUTEdyXdQTbY2nxJf5u28cq07kZJ\ntwNtaZXe2HHTd3u+EbEt1xs0PHdIgv7TAj4VEV8efDfNhs/VcWYjw83A+0oTko7ov0DqZPLhiLiC\nrHfjFwKTgadTADqEbJiF4TpZ0pTUS/ZZwG/7zZ8P/E0aRwlJc9KYM2a7zVdCZiPDB4AvSLqX7P/y\nV2T3gPLeCLxFUi/wJNl9nWeBd6f1lgC/34W8fwN8C3geWe/J+ao4IuJmSYcCC1J14TPAW2jScZOs\nvtxE22wUk/R2YF5EvG+oZc1qwdVxZmZWGF8JmZlZYXwlZGZmhXEQMjOzwjgImZlZYRyEzMysMA5C\nZmZWmP8HjhErwEyM27oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d9d860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "fig, axs = plt.subplots(nrows=2)\n",
    "\n",
    "ax = axs[0]\n",
    "ax.set_title('Acoustic impedence and reflectivity')\n",
    "ax.set_ylabel('Amplitude')\n",
    "ax.set_xticklabels([])\n",
    "ax.stem(m)\n",
    "\n",
    "ax = axs[1]\n",
    "ax.plot(imp)\n",
    "ax.set_xlabel('Time sample')\n",
    "ax.set_ylabel('Impedance')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We lost a sample, leaving 50. This is exactly we wanted.\n",
    "\n",
    "## SET-UP — Make a wavelet\n",
    "\n",
    "Now we make a Ricker wavelet to convolve on the reflectivity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "from scipy.signal import ricker\n",
    "\n",
    "# Use an odd number so we get a centered peak.\n",
    "wavelet = ricker(points=21, a=2)\n",
    "\n",
    "# Normalize the wavelet amplitude to 1 so that the amplitude\n",
    "# relates directly to the reflectivity.\n",
    "wavelet /= np.amax(wavelet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+NXgEPCKI8x3A43G2cWKfiOAREE60TUr0MDApgdTkBFKTEkhJSiA12UNqknPf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\nGGNM0CxpGGOMCZolDWOMMUH7/wFQXt36hKlxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b1224ae48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Ricker Wavelet')\n",
    "ax.set_xlabel('Time Sample')\n",
    "ax.set_ylabel('Amplitude')\n",
    "ax.plot(wavelet)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# END OF SET-UP\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The forward and adjoint operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting with a known reflectivity model $\\mathbf{m}$, we create synthetic seismic data  $\\mathbf{d} = \\mathbf{F} \\mathbf{m}$, where $\\mathbf{F}$ is the linear operator that performs the function \"convolve with a Ricker wavelet\".  Given such a trace and the operator, the conjugate gradient method can be used to estimate the original reflectivity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Hall (2016) called the operator $\\mathbf{G}$ instead of $\\mathbf{F}$, and he created a matrix by shifting the wavelet and padding with zeros. In contrast, I implement the operator using the NumPy function `convolve()`. This is advantageous because it allows us to solve the linear equation $\\hat{\\mathbf{m}} = \\mathbf{F}^{-1}\\mathbf{d}$ without ever having to construct (or invert) this matrix, which can become very large. This matrix-free approach is faster and uses less memory than the matrix implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can add one more feature to the operator and implement it with its adjoint. A convenient way to combine the two operations is to use a so-called 'object-oriented programming' approach and define a Python class. Then we can have two methods (i.e. functions) defined on the class: `forward`, implementing the forward operator, and `adjoint` for the adjoint operator, which in this case is correlation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Operator(object):\n",
    "    \"\"\"A linear operator.\n",
    "    \"\"\"\n",
    "    def __init__(self, wavelet):\n",
    "        self.wavelet = wavelet\n",
    "\n",
    "    def forward(self, v):\n",
    "        \"\"\"Defines the forward operator.\n",
    "        \"\"\"\n",
    "        return np.convolve(v, self.wavelet, mode='same')\n",
    "    \n",
    "    def adjoint(self, v):\n",
    "        \"\"\"Defines the adjoint operator.\n",
    "        \"\"\"\n",
    "        return np.correlate(v, self.wavelet, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<Fx, y>  = -6.43451315371\n",
      "<x, F*y> = -6.43451315371\n",
      "diff     = 0.0\n"
     ]
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "# Dot product test.\n",
    "w = np.array([1.0, -2.0, 0.5, 0, 0])\n",
    "x = np.random.rand(50)\n",
    "y = np.random.rand(50)\n",
    "\n",
    "F = Operator(w)\n",
    "\n",
    "convx = F.forward(x)\n",
    "cadjy = F.adjoint(y)\n",
    "\n",
    "print('<Fx, y>  =', np.dot(convx, y))\n",
    "print('<x, F*y> =', np.dot(x, cadjy))\n",
    "print('diff     =', np.dot(convx, y) - np.dot(x, cadjy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Claerbout (2012) teaches how to write this kind of symmetrical code, and provides many examples of geophysical operators with adjoints (e.g. derivative vs negative derivative, causal integration vs anticausal integration, stretch vs squeeze, truncate vs zero pad). Writing functions to apply operators is more efficient then computing matrices.\n",
    "\n",
    "Now that we have the operator, we can instantiate the class with a wavelet. This wavelet will be 'built in' to the instance `F`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "F = Operator(wavelet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute $\\mathbf{d} = \\mathbf{F}\\,\\mathbf{m}$ simply by passing the model `m` to the method `F.forward()`, which already has the wavelet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d = F.forward(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This results in the synthetic seismogram shown in Figure 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UlEgLXgBprSkpKWHXrl20bdvWq3PJUihCCOFvWju3tDUmuNv6Um1aJlUIP2nR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\nlqUfSr3jAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106b0240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "\n",
    "plt.stem(m, label=\"Model $\\mathbf{m}$\", basefmt='none', linefmt='k', markerfmt='ko')\n",
    "plt.axhline(c='k', lw=1)\n",
    "ax.plot(d, color='orange', lw=4, zorder=1, label=\"Data $\\mathbf{d}$\")\n",
    "ax.text(-1, 0.16, 'A model and synthetic trace', size=15)\n",
    "ax.set_xlabel('Time sample', size=14)\n",
    "ax.set_ylabel('Amplitude', size=14)\n",
    "ax.legend(fontsize=12)\n",
    "ax.grid(color='k', alpha=0.2)\n",
    "\n",
    "plt.savefig('figure1_model_data.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Figure 1__: A plot of reflectivity model $\\mathbf{m}$ (black) and the synthetic seismic data $\\mathbf{d}$ (orange)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "## The conjugate gradient method\n",
    "\n",
    "Now that we have a synthetic, we wish to solve the linear inverse problem and estimate the model $\\mathbf{m}$ from the data $\\mathbf{d}$. The model can not be completely recovered because the Ricker wavelet is bandlimited, so some information is lost.\n",
    "\n",
    "One way to solve linear problems is to start with an initial guess and iteratively improve the solution. The next few paragraphs derive an iterative method. You do not need to understand all the derivation, so you might want to lightly read it and move to the section about the pseudo code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with an initial estimate for the model, $\\hat{\\mathbf{m}}_0 = \\mathbf{0}$ (the zero vector) and compute the residual $\\mathbf{r}_0 = \\mathbf{d} - \\mathbf{F}\\, \\hat{\\mathbf{m}}_0$ (i.e. the difference between the data and the action of the forward operator on the model estimate). A good measure of the error in the initial solution is the inner product $\\langle \\mathbf{r}_0, \\mathbf{r}_0 \\rangle$ or `np.dot(r0, r0)` in code. This is equivalent to the squared norm (length) of the residual vector $\\mathbf{r}_0$, and constitutes our cost function. If the cost is 0, or within some small tolerance, then we have a solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can improve the estimate, $\\hat{\\mathbf{m}}_0$ by selecting a direction $\\mathbf{s}_0$ and a scale $\\alpha_0$ to move $\\hat{\\mathbf{m}}_0$ to a new guess, $\\hat{\\mathbf{m}}_1 = \\hat{\\mathbf{m}}_0 + \\alpha_0\\,\\mathbf{s}_0$. You can compute the direction in model space that most rapidly decreases the error.  This is the gradient of $ \\langle \\mathbf{d} - \\mathbf{F} \\hat{\\mathbf{m}} \\ , \\mathbf{d} - \\mathbf{F} \\hat{\\mathbf{m}} \\ \\rangle$ or $\\langle \\mathbf{r}_0, \\mathbf{r}_0 \\rangle$.  If you grind through the mathematics, the gradient $\\mathbf{g}$ turns out to be given by the action of the adjoint operator on the residual: $\\mathbf{F}^\\mathrm{H} \\mathbf{r}_0$.\n",
    "\n",
    "The scalar $\\alpha_0$ is computed to minimize the residual, $\\mathbf{r}_1 = \\mathbf{d} - \\mathbf{F}\\,\\hat{\\mathbf{m}}_1 = \\mathbf{d} - \\mathbf{F} (\\hat{\\mathbf{m}}_0 + \\alpha_0 \\mathbf{s}_0) = \\mathbf{r}_0  - \\alpha_0 \\mathbf{F}\\,\\mathbf{s}_0$. We can them compute $\\alpha_0$ by taking the derivative of $\\langle \\mathbf{r}_1, \\mathbf{r}_1\\rangle$ with respect to $\\alpha_0$, setting the derivative to 0, and solving for $\\alpha_0$. The result is:\n",
    "\n",
    "$$\\alpha_0 = \\langle \\mathbf{g}_0, \\mathbf{g}_0\\rangle\\ /\\ \\langle \\mathbf{F}\\mathbf{s}_0, \\mathbf{F}\\mathbf{s}_0\\rangle $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These equations define a reasonable approach to iteratively improve an estimated solution and it is called “the steepest descent method”. The conjugate gradient algorithm builds on this. It is not much harder to implement, has similar cost per iteration, and faster convergence.\n",
    "\n",
    "The first iteration of the conjugate gradient method is the same as the steepest descent method. The second (and later) iterations compute the gradient $\\mathbf{g}_1$ and $\\mathbf{F}\\,\\mathbf{g}_1$. With $\\mathbf{s}_0$ and $\\mathbf{F}\\,\\mathbf{s}_0$ from the previous iteration we can then compute the step direction. Scalars $\\alpha$ and $\\beta$ are computed to minimize\n",
    "\n",
    "$$\\mathbf{r}_2 = \\mathbf{d} - \\mathbf{F} (\\hat{\\mathbf{m}}_1 + \\alpha\\, \\mathbf{s}_0 + \\beta\\, \\mathbf{g}_1).$$\n",
    "\n",
    "Some mathematical manipulations determine the best direction is $\\mathbf{s}_1 = \\mathbf{g}_1 + \\beta\\,\\mathbf{s}_0$ where $\\beta = \\langle \\mathbf{g}_1, \\mathbf{g}_1 \\rangle\\ /\\ \\langle \\mathbf{g}_0, \\mathbf{g}_0 \\rangle$.  The conjugate gradient algorithm is guaranteed to converge when the number of iterations is equal to the dimension of $\\hat{\\mathbf{m}}$, but only a few iterations often give sufficient accuracy. For our implementation, we'll start with a simplifed version of the pseudo-code provided by Guo (2002), with its implementation in Python:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\mathbf{\\hat{m}} = \\mathbf{0}$<br>\n",
    "$\\mathbf{r} = \\mathbf{d} - \\mathbf{F}\\,\\mathbf{\\hat{m}}$<br>\n",
    "$\\mathbf{s} = \\mathbf{0}$<br>\n",
    "$\\beta = 0$<br>\n",
    "\n",
    "$\\mathrm{iterate}\\ n\\ \\mathrm{times}:$<br>\n",
    "$\\qquad \\mathbf{g} = \\mathbf{F}^\\mathrm{H} \\mathbf{r}$<br>\n",
    "$\\qquad \\mathrm{if}\\ \\mathrm{not}\\ \\mathrm{first}\\ \\mathrm{iteration}:$<br>\n",
    "$\\qquad \\qquad \\beta = \\langle \\mathbf{g}, \\mathbf{g} \\rangle \\ /\\ \\gamma$<br>\n",
    "$\\qquad \\gamma = \\langle \\mathbf{g}, \\mathbf{g} \\rangle$<br>\n",
    "$\\qquad \\mathbf{s} = \\mathbf{g} + \\beta\\, \\mathbf{s}$<br>\n",
    "$\\qquad \\Delta \\mathbf{r} = \\mathbf{F}\\, \\mathbf{s}$<br>\n",
    "$\\qquad \\alpha = \\langle \\mathbf{g}, \\mathbf{g} \\rangle\\ /\\ \\langle \\Delta \\mathbf{r}, \\Delta \\mathbf{r} \\rangle$<br>\n",
    "$\\qquad \\mathbf{\\hat{m}} = \\mathbf{\\hat{m}} + \\alpha\\, \\mathbf{s}$<br>\n",
    "$\\qquad \\mathbf{r} = \\mathbf{r} - \\alpha \\Delta\\mathbf{r}$<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "n = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "# This version has the cache, which is just a convenient\n",
    "# way to store the results of the iterations.\n",
    "m_est = np.zeros_like(d)\n",
    "r = d - F.forward(m_est)\n",
    "s = np.zeros_like(d)\n",
    "beta = 0\n",
    "\n",
    "cache = [m_est]\n",
    "for i in range(n):\n",
    "    g = F.adjoint(r)\n",
    "    if i != 0:\n",
    "        beta = np.dot(g, g) / gamma\n",
    "    gamma = np.dot(g, g)\n",
    "    s = g + beta * s\n",
    "    deltar = F.forward(s)\n",
    "    alpha = np.dot(g, g) / np.dot(deltar, deltar)\n",
    "    m_est = m_est + alpha * s\n",
    "    r = r - alpha * deltar\n",
    "    cache.append(m_est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_est = np.zeros_like(d)\n",
    "r = d - F.forward(m_est)\n",
    "s = np.zeros_like(d)\n",
    "beta = 0\n",
    "\n",
    "for i in range(n):\n",
    "    g = F.adjoint(r)\n",
    "    if i != 0:\n",
    "        beta = np.dot(g, g) / gamma\n",
    "    gamma = np.dot(g, g)\n",
    "    s = g + beta * s\n",
    "    deltar = F.forward(s)\n",
    "    alpha = np.dot(g, g) / np.dot(deltar, deltar)\n",
    "    m_est = m_est + alpha * s\n",
    "    r = r - alpha * deltar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "The Python code in the previous section was used to invert for the reflectivity. Figure 2 shows the five iterations of the conjugate gradient method. The conjugate gradient method converged in only four iterations; the results of the fourth and fifth iteration almost exactly overlay on the plot. Fast convergence is important for a practical algorithm. Convergence is guaranteed in 50 iterations (the dimension of the model).\n",
    "\n",
    "Figure 3 compares the original model, the data, and the model estimated using conjugate gradient inversion. Conjugate gradient inversion does not completely recover the model because the Ricker wavelet is bandlimitted, but sidelobes are reduced (for example samples 17 through 23).\n",
    "\n",
    "Finally, we compute the predicted data from the estimated model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d_pred = F.forward(m_est)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 4 compares the predicted data with the original data to show that we have done a good job of the estimation. This demonstrates there is more than one reflectivity sequence that when convolved with the Ricker wavelet that will fit the data, in particular the original model and the model estimated by the conjugate gradient method. It may be interesting to explore preconditioning operators that promote a sparse solution.\n",
    "\n",
    "The Jupyter notebook provided with this tutorial further explores finding least-squares solutions using the conjugate gradient method. The notebook demonstrates how preconditioning can be used to promote a sparse solution. It also provides examples using sparse solvers provided in the SciPy package. You can find the notebooks at https://github.com/seg/tutorials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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btm1Da01sbGy98j799FN3WVOnTmXHjh307duX++67j08//fS03dxNsVqt7hY/cE3Z79q1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\n3OcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c136ae208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "\n",
    "#plt.stem(m, label=r'Model $\\mathbf{m}$', basefmt='none', linefmt='k', markerfmt='ko')\n",
    "#plt.axhline(color='k', lw=1)\n",
    "idx = np.linspace(0, 1, len(cache)+1)\n",
    "for c, (i, m_est) in zip(idx, enumerate(cache)):\n",
    "    label = 'iter {}'.format(i) if i else \"initial\" \n",
    "    plt.plot(m_est, color=plt.cm.plasma_r(c), label=label, lw=2)\n",
    "plt.legend(fontsize=12)\n",
    "plt.grid(color='k', alpha=0.15)\n",
    "ax.text(-1, 0.07, 'Conjugate gradient estimates', size=14)\n",
    "ax.text(-1, 0.06, 'Initial plus {} iterations'.format(n), size=12)\n",
    "ax.set_xlabel('Time sample', size=14)\n",
    "ax.set_ylabel('Amplitude', size=14)\n",
    "\n",
    "plt.savefig('figure2_cg_est_iter.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 2** Model estimated by the first five iterations of conjugate gradient plotted with the original model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TpnTYOk8CvBaUkZHRqPXNNX78eE6dOkVqairV1dW89957zJ49277dbDYzbdo0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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c13737208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "\n",
    "plt.stem(m, label='Model $\\mathbf{m}$', basefmt='none', linefmt='k', markerfmt='ko')\n",
    "plt.axhline(color='k', lw=1)\n",
    "ax.plot(d, 'o-', color='orange', lw=3, label='Data $\\mathbf{d}$')\n",
    "ax.plot(m_est, 'o-', color='darkorchid', lw=3, label='Estimated model $\\mathbf{\\hat{m}}$')\n",
    "ax.legend(fontsize=12)\n",
    "ax.set_xlabel('Time sample', size=14)\n",
    "ax.set_ylabel('Amplitude', size=14)\n",
    "ax.text(-1, 0.16, 'The estimated model', color='k', size=16)\n",
    "ax.grid(color='k', alpha=0.2)\n",
    "\n",
    "plt.savefig('figure3_data_model_estmodel.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Figure 3__: Comparison of the model (black) and the model estimated using conjugate gradient inversion (purple), along with the data (orange) for comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00073174262505606665"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "\n",
    "# Check the norm\n",
    "difference = d - d_pred\n",
    "misfit = np.linalg.norm(difference)**2\n",
    "misfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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erosgP7PRoQkhvI8kd0II4WbZx3/imJ8vAL4oekf3vqjjDE0YYbR/DvDHcnKT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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c15e6f940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NOT FOR MANUSCRIPT\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "\n",
    "ax.plot(d, label='d', color='C1', lw=3)\n",
    "ax.plot(d_pred, label=\"d_pred\", color='C2', lw=3)\n",
    "ax.text(-1, 0.16, 'Data d and prediction d_pred', color='k', size=15)\n",
    "ax.text(-1, 0.14, 'Misfit = {:.3f}'.format(misfit), color='k', size=12)\n",
    "ax.text(48, -0.025, 'd', ha='right', color='C1', size=16)\n",
    "ax.text(48, 0.02, 'd_pred', ha='right', color='C2', size=16)\n",
    "ax.set_xlabel('Time sample', size=14)\n",
    "ax.set_ylabel('Amplitude', size=14)\n",
    "ax.grid(color='k', alpha=0.2)\n",
    "\n",
    "plt.savefig('figure4_data_cg_pred.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Figure 4__: Comparison of the predicted data `d_pred` (green) from the conjugate gradient inversion with the original data `d` (orange). It overplots the data almost exactly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions\n",
    "\n",
    "I described the conjugate gradient algorithm and presented an implementation. This is an iterative method that requires functions to apply the linear operator and its adjoint. Many linear operators that are familiar geophysical operations like convolution are more efficiently implemented without matrices. The reflectivity estimation problem described in Hall’s _Linear inversion_ tutorial was solved using the conjugate gradient method.  Convergence only took four iterations. The conjugate gradient method is often used to solve large problems because well known solvers like least squares are much more expensive.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acknowledgments\n",
    "The SEG Seismic Working Workshop on Reproducible Tutorials held August 9 to 13 in Houston inspired this tutorial.  For more information visit: http://ahay.org/wiki/Houston_2017\n",
    "\n",
    "\n",
    "## References\n",
    "Claerbout, J., Fomel, S., 2012, Image Estimation by Example,\n",
    "http://sepwww.stanford.edu/sep/prof/gee1-2012.pdf\n",
    "\n",
    "Guo, J., Hongbo, Z., Young, J., Gray, S., 2002, Merits and challenges for accurate velocity model building by 3D gridded tomography, Geophysics. https://doi.org/10.1190/1.1817395 \n",
    "\n",
    "Hall, M., 2016, Linear Inversion, The Leading Edge, pages 1085-1087. https://doi.org/10.1190/tle35121085.1\n",
    "\n",
    "Hestenes, Magnus R.; Stiefel, Eduard, 1952, \"Methods of Conjugate Gradients for Solving Linear Systems\". Journal of Research of the National Bureau of Standards. 49 (6). doi:10.6028/jres.049.044\n",
    "\n",
    "Paige, C. C., Saunders, M. A., 1982, LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares, ACM Transactions on Mathematical Software,\n",
    "http://web.stanford.edu/class/cme324/paige-saunders2.pdf\n",
    "\n",
    "Shewchuk, J. R., 1994, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, \n",
    "http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf\n",
    "\n",
    "\t\n",
    "Witte, P, Mathias Louboutin, Keegan Lensink, Michael Lange, Navjot Kukreja, Fabio Luporini, Gerard Gorman, Felix J. Herrman, 2018, Full-waveform inversion, Part 3: Optimization. The Leading Edge 37, 2(2018); pp. 142-145.\n",
    "https://doi.org/10.1190/tle37020142.1"
   ]
  }
 ],
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