notes/Finite difference checks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1e576cd6",
   "metadata": {},
   "source": [
    "# Why compute derivatives approximately instead of exactly?\n",
    "\n",
    "Working out derivatives by hand is a notoriously error-prone procedure for complicated functions.  Even if every individual step is straightforward, there are so many opportunities to make a mistake, either in the derivation or in its implementation on a computer.\n",
    "\n",
    "* Whenever you implement a derivatives, you should **always double-check** for mistakes by comparing it to an independent calculation.  The simplest such check is a *finite-difference approximation*, in which we *estimate* the derivative(s) by comparing $f(x)$ and $f(x + \\delta x)$ for one or more \"finite\" (non-infinitesimal) perturbations $\\delta x$.\n",
    "\n",
    "There are many finite-difference techniques at varying levels of sophistication, as we will discuss below.  They all incur an intrinsic **truncation error** due to the fact that $\\delta x$ is not infinitesimal.  (And we will also see that you can't make $\\delta x$ too small, either, or *roundoff errors* start exploding!)   Moreover, finite differences become expensive for higher-dimensional $x$ (in which you need a separate finite difference for each input dimension to compute the full Jacobian).   This makes them an approach of last resort for computing derivatives accurately.  On the other hand, they are the *first* method you generally employ in order to *check* derivatives: if you have a bug in your analytical derivative calculation, usually the answer is completely wrong, so even a crude finite-difference approximation for a single small $\\delta x$ (chosen at random in higher dimensions) will typically reveal the problem.\n",
    "\n",
    "Another alternative is **automatic differentiation** (AD), software/compilers perform  *analytical* derivatives for you. This is extremely reliable and, with modern AD software, can be very efficient. Unfortunately, there is still lots of code, e.g. code calling external libraries in other languages, that AD tools can't comprehend. And there are other cases where AD is inefficient, typically because it misses some mathematical structure of the problem.  Even in such cases, you can often fix AD by defining the derivative of one small piece of your program by hand, which is much easier than differentiating the whole thing.  In such cases, you still will typically want a finite-difference check to ensure that you have not made a mistake.\n",
    "\n",
    "It turns out that finite-difference approximations are a surprisingly complicated subject, with rich connections to many areas of numerical analysis; in this lecture we will just scratch the surface."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2d90dbc",
   "metadata": {},
   "source": [
    "# Finite-difference approximations: Easy version\n",
    "\n",
    "The simplest way to check a derivative is to recall that the definition of a differential:\n",
    "$$\n",
    "df = f(x+dx) - f(x) = f'(x) dx\n",
    "$$\n",
    "came from dropping higher-order terms from a small but finite difference:\n",
    "$$\n",
    "\\delta f = f(x+\\delta x) - f(x) = f'(x) \\delta x + o(\\Vert \\delta x \\Vert) \\, .\n",
    "$$\n",
    "So, we can just compare the **finite difference** $\\boxed{f(x+\\delta x) - f(x)}$ to our **(directional) derivative operator** $f'(x) \\delta x$ (i.e. the derivative in the direction $\\delta x$).\n",
    "\n",
    "$f(x+\\delta x) - f(x)$ is also called a **forward difference** approximation.  We'll look at other possibilities below.\n",
    "\n",
    "If $x$ is a scalar, we can also divide both sides by $\\delta x$ to get an approximation for $f'(x)$ instead of for $df$:\n",
    "$$\n",
    "f'(x) \\approx \\frac{f(x+\\delta x) - f(x)}{\\delta x} + \\text{(higher-order corrections)} \\, .\n",
    "$$\n",
    "This is a more common way to write the forward-difference approximation, but it only works for scalar $x$, whereas in this class we want to think of $x$ as perhaps belonging to some other vector space.\n",
    "\n",
    "* The antonym of a forward diffence is a **backward difference** approximation $f(x) - f(x - \\delta x) \\approx f'(x) \\delta x$ … if you just want to compute a derivative, there is not much practical distinction between forward and backward differences.  The distinction becomes more important when discretizing (approximating) differential equations.\n",
    "\n",
    "* Finite-difference approximations come in many forms, but they are generally a **last resort** in cases where it's too much effort to work out an analytical derivative and AD fails.  But they are also useful to **check** your analytical derivatives and to quickly **explore**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a4818b6",
   "metadata": {},
   "source": [
    "## example: f(A)=A²\n",
    "\n",
    "Let's try it for $f(A) = A^2$ (a matrix-valued function of a square matrix $A \\in \\mathbb{R}^{m\\times m}$).\n",
    "\n",
    "First, we'll do it by hand via the product rule:\n",
    "\n",
    "$$\n",
    "df = A dA + dA A\n",
    "$$\n",
    "i.e. $f'(A)$ is the **linear operator** $\\boxed{f'(A)[\\delta A] = A \\delta A + \\delta A A}$.  This is **≠ 2AδA** because because **A and δA do not commute** in general.\n",
    "\n",
    "Let's check it against a finite difference.   We'll try it for a *random* input A and a *random small* perturbation $\\delta A$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9d0e4943",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       "  0.586497   0.834277  -0.0256691  2.40974\n",
       "  0.380476  -0.346487   0.379867   1.03513\n",
       " -0.36028    0.478118   0.124059   0.205695\n",
       " -0.176444  -0.771825   1.11523    0.799608"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(A) = A^2\n",
    "\n",
    "A = randn(4,4) # 4×4 matrix with Gaussian random (bell curve) entries of magnitude ~ 1 (std. dev = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3daece4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       " -4.83097e-9   2.21459e-9   1.4161e-8    1.76983e-8\n",
       " -2.20995e-10  1.45181e-10  1.51685e-8  -1.06988e-8\n",
       "  8.50876e-9   8.46833e-9   5.69589e-9   1.53053e-8\n",
       " -2.37132e-9   2.86742e-9   1.68817e-8  -2.33579e-8"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dA = randn(4,4) * 1e-8 # a small random perturbation ~ 10⁻⁸"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "542cc00d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       " -1.91658e-8  -3.57472e-9   8.39542e-8  -4.75095e-8\n",
       " -4.63548e-9   2.22526e-8   9.78165e-9  -1.37407e-8\n",
       "  5.66239e-9  -4.01326e-9   2.71034e-8   2.82821e-8\n",
       "  6.35546e-9   3.43619e-8  -1.716e-8    -1.44242e-8"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx = f(A + dA) - f(A) # finite difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e955820e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       " -1.91658e-8  -3.57472e-9   8.39542e-8  -4.75095e-8\n",
       " -4.63548e-9   2.22526e-8   9.78165e-9  -1.37407e-8\n",
       "  5.66239e-9  -4.01326e-9   2.71034e-8   2.82821e-8\n",
       "  6.35546e-9   3.43619e-8  -1.716e-8    -1.44242e-8"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exact = A*dA + dA*A # exact directional \"differential\" (linearization)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "43cb4db7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       " -1.79008e-8  1.62247e-8  1.22989e-7  -1.1045e-7\n",
       " -1.96785e-9  1.39546e-8  3.95414e-8  -1.58474e-8\n",
       "  4.40532e-9  1.82385e-9  1.26591e-8  -2.87949e-8\n",
       "  1.72321e-8  2.24683e-8  1.12898e-8   7.0532e-9"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2A*dA # wrong! matrices don't commute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "20818794",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       "  9.43443e-17   7.22749e-18   2.47258e-16  -3.95619e-16\n",
       "  1.34871e-16   1.21774e-16  -1.27327e-16   6.66362e-16\n",
       " -6.94601e-17   2.19421e-16   5.2911e-16   -3.42296e-16\n",
       "  2.68437e-16  -3.23023e-17  -4.74263e-16   7.51032e-16"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx - exact"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "630c56ec",
   "metadata": {},
   "source": [
    "To be more quantitative, we might compute the \"norm\" $\\Vert \\text{approx} - \\text{exact} \\Vert$, which we want to be small.   But small **compared to what?**   The natural answer is **small compared to the correct answer**.  This is called the [relative error](https://en.wikipedia.org/wiki/Approximation_error) (or \"fractional\" error):\n",
    "$$\n",
    "\\text{relative error} = \\frac{\\Vert \\text{approx} - \\text{exact} \\Vert}{\\Vert \\text{exact}\\Vert}\n",
    "$$\n",
    "Here, $\\Vert \\cdot \\Vert$ is a [norm](https://en.wikipedia.org/wiki/Norm_(mathematics)), like the length of a vector. In Julia, the `LinearAlgebra` package provides a `norm` function, and we can use that to define a relative error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "45931cc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "relative_error (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "\n",
    "relative_error(approx, exact) = norm(approx - exact) / norm(exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7dc766e",
   "metadata": {},
   "source": [
    "Let's try it on our case above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1fb85dc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2137715275736226e-8"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_error(approx, exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa60621b",
   "metadata": {},
   "source": [
    "Pretty good — we are matching to **about eight significant digits**!\n",
    "\n",
    "Getting a good match for a random input and a random small displacement isn't a proof of correctness, but it is always a good thing to check.   This kind of randomized comparison will almost always **catch major bugs** where you have calculated the symbolic derivative incorrectly, like our $2AdA$ example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c4ed374c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6100609198300581"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_error(approx, 2A*dA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a234dc8e",
   "metadata": {},
   "source": [
    "Here, for our buggy derivative, the relative error was **close to 100%**.  We would notice immediately that something is wrong."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "117f334b",
   "metadata": {},
   "source": [
    "### aside: norm of a matrix?\n",
    "\n",
    "Wait, what do we mean by the norm $\\Vert A \\Vert$ of a matrix $A$?\n",
    "\n",
    "The ordinary Euclidean (\"L2\") norm of a column vector $x \\in \\mathbb{R}^n$ is $\\Vert x \\Vert = \\sqrt{x^T x} = \\sqrt{\\sum_i x_i^2}$.\n",
    "\n",
    "For a matrix, the natural analogue is the **sqrt of the sum of the squares of the entries**.  This is called the [Frobenius norm](https://mathworld.wolfram.com/FrobeniusNorm.html), and is what `norm(A)` does in Julia by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a34d0cb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ \\begin{equation}\n",
       "\\left[\n",
       "\\begin{array}{ccc}\n",
       "m_{1}ˏ_1 & m_{1}ˏ_2 & m_{1}ˏ_3 \\\\\n",
       "m_{2}ˏ_1 & m_{2}ˏ_2 & m_{2}ˏ_3 \\\\\n",
       "\\end{array}\n",
       "\\right]\n",
       "\\end{equation}\n",
       " $$"
      ],
      "text/plain": [
       "2×3 Matrix{Num}:\n",
       " m[1, 1]  m[1, 2]  m[1, 3]\n",
       " m[2, 1]  m[2, 2]  m[2, 3]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Symbolics\n",
    "\n",
    "@variables m[1:2, 1:3]\n",
    "M = collect(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f8846473",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ \\begin{equation}\n",
       "\\sqrt{\\left|m_{1}ˏ_2\\right|^{2} + \\left|m_{1}ˏ_1\\right|^{2} + \\left|m_{2}ˏ_1\\right|^{2} + \\left|m_{2}ˏ_3\\right|^{2} + \\left|m_{1}ˏ_3\\right|^{2} + \\left|m_{2}ˏ_2\\right|^{2}}\n",
       "\\end{equation}\n",
       " $$"
      ],
      "text/plain": [
       "sqrt(abs2(m[1, 2]) + abs2(m[1, 1]) + abs2(m[2, 1]) + abs2(m[2, 3]) + abs2(m[1, 3]) + abs2(m[2, 2]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8981b83",
   "metadata": {},
   "source": [
    "But we can write this in linear algebra notation!\n",
    "\n",
    "Recall that the (Euclidean) \"inner product\" of two matrices is $B \\cdot A = \\text{tr}(B^T A)$.   Then we can define the Frobenius norm of a matrix as the sqrt of the dot product with itself!\n",
    "\n",
    "$$\n",
    "\\Vert A \\Vert_F = \\sqrt{\\text{trace}(A^T A)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "625bb0ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3547225362168174"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b1dba485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3547225362168174"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(tr(A'A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e61e275b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3547225362168174"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(sum(abs2, A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e2440768",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3547225362168174"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(sum(A[i,j]^2 for i = 1:4, j = 1:4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ada58d4",
   "metadata": {},
   "source": [
    "(There are also other ways to define a norm of matrix, most famously by \"induced norms\", but we will stick with the Frobenius norm here.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f6347b0",
   "metadata": {},
   "source": [
    "# Accuracy of finite differences\n",
    "\n",
    "How accurate is our finite-difference approximation above?  How should we choose the size of δx?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd265557",
   "metadata": {},
   "source": [
    "Let's try our example $f(A) = A^2$ above, and plot the relative error as a function of $\\Vert \\delta A \\Vert$ as we scale $\\delta A$ by a factor $s$, making it larger or smaller."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "675c58b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots # load a plotting package; there are several to choose from in Julia; this is a popular one\n",
    "using LaTeXStrings # makes it easy to put LaTeX equations in L\"...\" strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0dc9de16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = 10 .^ range(-8,8,50) # 50 points from 10⁻⁸ to 10⁸\n",
    "errors = [relative_error(f(A+s*dA)-f(A), exact*s) for s in s]\n",
    "scatter(s * norm(dA) / norm(A), errors, xaxis=:log, yaxis=:log, markershape=:circle,markercolor=:blue,\n",
    "     title = L\"forward-difference accuracy for $f(A)=A^2$\", xlabel=L\"input perturbation $\\Vert \\delta A\\Vert / \\Vert A \\Vert$\", ylabel=L\"relative error  in $\\delta f$\",\n",
    "     label = \"error\", fmt=:png, xticks = [1, 10^-4, 10^-8, 10^-12, 10^-16], xlim=[10^-17, 10^1], ylim = [10^-10, 10^1], legend=:top)\n",
    "plot!(10 .^ range(-10,8,50), 10 .^ range(-10,8,50), linecolor=:blue, label=L\"1st-order $ \\sim \\Vert \\delta A\\Vert$ reference\")\n",
    "# savefig(\"fig1.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77479cce",
   "metadata": {},
   "source": [
    "We observe two main features:\n",
    "\n",
    "* The relative error decreases *linearly* with $\\Vert \\delta A \\Vert$.  This is called **first-order accuracy**.  Why?\n",
    "* When δA gets too small, the error *increases*.  Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "860ad8bb",
   "metadata": {},
   "source": [
    "## Order of accuracy\n",
    "\n",
    "If the relative error scales with $\\Vert \\delta A \\Vert^n$, we call the approximation **n-th order accurate**.  For forward differences, here, the order is **n=1**.  Why?\n",
    "\n",
    "For any $f(x)$ with a nonzero second derivative (think of the Taylor series), we have\n",
    "$$\n",
    "    f(x + \\delta x) = f(x) + f'(x) \\delta x + (\\text{terms proportional to }\\Vert \\delta x \\Vert^2) + \\underbrace{o(\\Vert \\delta x \\Vert^2)}_\\text{i.e. higher-order terms}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1675f2b3",
   "metadata": {},
   "source": [
    "That is, the terms we *dropped* in our forward-difference approximations are proportional to $\\Vert \\delta x\\Vert^2$.  But that means that the **relative error is linear**:\n",
    "$$\n",
    "\\begin{align}\n",
    "  \\text{relative error} &= \\frac{\\Vert f(x+\\delta x) - f(x) - f'(x) \\delta x \\Vert}{\\Vert f'(x) \\delta x \\Vert} \\\\\n",
    "   &= \\frac{(\\text{terms proportional to }\\Vert \\delta x \\Vert^2) + o(\\Vert \\delta x \\Vert^2)}{\\text{proportional to }\\Vert \\delta x \\Vert} = (\\text{terms proportional to }\\Vert \\delta x \\Vert) + o(\\Vert \\delta x \\Vert)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "466a440e",
   "metadata": {},
   "source": [
    "This source of error in a finite-difference approximation, due to **inherent** error in the formula for **non-infinitesimal** $\\delta x$, is called **truncation error**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc1ef94d",
   "metadata": {},
   "source": [
    "## Roundoff error\n",
    "\n",
    "The reason why the error *increased* for very small $\\delta A$ was due to **roundoff errors**.  The computer only stores a **finite number of significant digits** (about 15 decimal digits) for each real number and rounds off the rest on each operation — this is called [floating-point arithmetic](https://en.wikipedia.org/wiki/Floating-point_arithmetic).\n",
    "\n",
    "If δx is too small, then the difference $f(x+\\delta x) - f(x)$ gets rounded off to zero (some or all of the *significant digits cancel*).  This is called [catastrophic cancellation](https://en.wikipedia.org/wiki/Catastrophic_cancellation).\n",
    "\n",
    "Let's compute the derivative of $\\sin(x)$ at $x=1$ with finite differences.   For a scalar $f(x)$, we have $f(x+\\delta x) - f(x) \\approx f'(x) \\delta x$, or equivalently:\n",
    "\n",
    "$$\n",
    "f'(x) = \\frac{f(x+\\delta x) - f(x)}{\\delta x} + \\underbrace{O(\\delta x)}_{\\text{terms proportional to }|\\delta x|\\text{ or smaller}}\n",
    "$$\n",
    "\n",
    "(This is the usual way you see a forward difference approximation written, but it only works when $\\delta x$ is a scalar.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "60dd9d6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5402980985058647"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = 1e-5\n",
    "(sin(1 + dx) - sin(1))/dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2d2587ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5403023058681398"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos(1) # correct answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4fc600b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.787052228587771e-6"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_error((sin(1 + dx) - sin(1))/dx, cos(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f9e44dc",
   "metadata": {},
   "source": [
    "So far, so good.  For $\\delta x = 10^{-5}$, we got about 5–6 significant digits correct.  Now let's make $\\delta x$ much smaller, $\\delta x = 10^{-100}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "504d0d5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = 1e-100\n",
    "(sin(1 + dx) - sin(1))/dx"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35440ed2",
   "metadata": {},
   "source": [
    "What happened?   The computer can represent small numbers just fine, because floating-point corresponds to \"scientific notation\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "173b2d27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0e-100"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e-100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a7d8a53",
   "metadata": {},
   "source": [
    "But look at this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c8093692",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + 1e-100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a5fdedb",
   "metadata": {},
   "source": [
    "The correct answer would be\n",
    "$$\n",
    "1 + 10^{-100} = 1.\\underbrace{000000\\cdots000000}_{\\text{99 zeros}}1\n",
    "$$\n",
    "but the computer only stores about 15 decimal digits (by default … you can ask for more, at the expense of speed), so it rounds this to $1.0$.\n",
    "\n",
    "Hence, our finite difference gave zero.\n",
    "\n",
    "Even if we do something less extreme, we have problems.   This looks okay:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "bdb27010",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000000000001"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = 1e-13\n",
    "1 + dx"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2510c60",
   "metadata": {},
   "source": [
    "because the computer has enough digits, right?  But compare:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ee8e581d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8414709848079505"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(1 + dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "173807c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8414709848078965"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9852d20f",
   "metadata": {},
   "source": [
    "They only differ in the **last 4 significant digits stored**.  So when you subtract them, you only have **4 digits** left:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6bbe34e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001358343083756518"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_error((sin(1 + dx) - sin(1))/dx, cos(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a4220af",
   "metadata": {},
   "source": [
    "and the error for $\\delta x = 10^{-13}$ is now $10^{-3}$!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5487bb0",
   "metadata": {},
   "source": [
    "### Machine precision and a rule of thumb for finite differences\n",
    "\n",
    "The number of significant digits stored by the computer is expressed by the [machine epsilon](https://en.wikipedia.org/wiki/Machine_epsilon) $\\epsilon$.  Essentially, for a number $x$, the number $\\epsilon |x|$ is the size of the *last significant digit* of $x$, so that the *next* floating-point nubmer is $\\approx x (1+\\epsilon)$. \n",
    "\n",
    "$\\epsilon$ is returned by the [`eps()` function in Julia](https://docs.julialang.org/en/v1/base/base/#Base.eps-Tuple{Type{%3C:AbstractFloat}})."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e5e375b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-16"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ϵ = eps()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11e0ea89",
   "metadata": {},
   "source": [
    "This tells us that the computer stores about 15–16 decimal digits (in the default [\"double precision\"](https://en.wikipedia.org/wiki/Double-precision_floating-point_format)).  It's not an exact number of *decimal* digits because it's actually 52 **binary digits** $1.\\underbrace{ddd\\cdots ddd}_{52} \\times 2^\\mathrm{exponent}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2b917fb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-16"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2^-52"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "625d10d6",
   "metadata": {},
   "source": [
    "A **very crude** rule of thumb for finite differences is to choose $\\delta x$ to correspond to about **half the significant digits** of $x$, i.e.\n",
    "$$\n",
    "\\Vert \\delta x \\Vert \\approx \\sqrt{\\varepsilon} \\Vert x \\Vert\n",
    "$$\n",
    "That is, if $x$ is of order $\\sim 1$, then $\\delta x$ should be of order $\\sqrt{\\epsilon} \\approx 10^{-8}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "31d46e84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4901161193847656e-8"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "√ϵ"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1e8542b",
   "metadata": {},
   "source": [
    "Indeed we saw above with $f(A) = A^2$ that this was about where we saw a minimum error from the finite difference — it \"balanced\" the truncation and roundoff errors.  We can see something similar for the derivative of $\\sin x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5a028dc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = 10 .^ range(-16,0,50)\n",
    "errors = [relative_error((sin(1+s)-sin(1))/s, cos(1)) for s in s]\n",
    "scatter(s, errors, xaxis=:log, yaxis=:log, markershape=:circle,markercolor=:blue,\n",
    "     title = L\"forward-difference accuracy for $\\sin(x)$ at $x=1$\", xlabel=L\"\\Vert \\delta x\\Vert / \\Vert x \\Vert\", ylabel=\"relative error\",\n",
    "     label = \"error\", fmt=:png, legend=:bottomright)\n",
    "plot!(s, s, linecolor=:blue, label=L\"1st-order $\\sim \\Vert \\delta x\\Vert$ reference\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0b9b6ba",
   "metadata": {},
   "source": [
    "Yup, the minimum is around $\\approx 10^{-8}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ad6e6b8",
   "metadata": {},
   "source": [
    "## Higher-order finite-difference approximations\n",
    "\n",
    "Of course, there are other finite-difference formulas.  For example, the most famous is the **centered-difference** formula:\n",
    "\n",
    "$$\n",
    "f'(x) \\delta x \\approx \\frac{f(x+\\delta x) - f(x - \\delta x)}{2} + O(\\Vert \\delta \\Vert^3)\n",
    "$$\n",
    "\n",
    "which for scalar $\\delta x$ can be written in the more familiar form\n",
    "\n",
    "\n",
    "$$\n",
    "f'(x) \\approx \\frac{f(x+\\delta x) - f(x - \\delta x)}{2\\delta x} + O(\\Vert \\delta \\Vert^2)\n",
    "$$\n",
    "\n",
    "This formula is **second-order accurate**: the error in the derivative is proportional to $\\Vert \\delta \\Vert^2$ (assuming a thrice-differentiable function).   You can show this by plugging the Taylor series for $f(x\\pm \\delta x)$ into the difference formula.\n",
    "\n",
    "We can try it for $\\sin(x)$ as above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "72add7bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = 10 .^ range(-16,0,50)\n",
    "errors = [relative_error((sin(1+s)-sin(1))/s, cos(1)) for s in s]\n",
    "scatter(s, errors, xaxis=:log, yaxis=:log, markershape=:circle, markercolor=:blue,\n",
    "     title = L\"finite-difference accuracies for $\\sin(x)$ at $x=1$\", xlabel=L\"\\Vert \\delta x\\Vert / \\Vert x\\Vert\", ylabel=\"relative error\",\n",
    "     legend=:bottomright,\n",
    "     label = \"forward-difference error\", fmt=:png)\n",
    "\n",
    "errors2 = [relative_error((sin(1+s)-sin(1-s))/2s, cos(1)) for s in s]\n",
    "scatter!(s, errors2, xaxis=:log, yaxis=:log, markershape=:square, markercolor=:red,\n",
    "     label = \"center-difference error\")\n",
    "plot!(s, s, linecolor=:blue, label=L\"1st-order $\\sim \\Vert \\delta x\\Vert$ reference\")\n",
    "plot!(s, s.^2, linecolor=:red, label=L\"2nd-order $\\sim \\Vert \\delta x\\Vert^2$ reference\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0cae23c",
   "metadata": {},
   "source": [
    "Indeed, the error goes down faster than before, so it turns out that our crude rule of thumb from before is not quite so good — the minimum error occurs around $10^{-5}$, not $10^{-8}$.  (But $10^{-8}$ is still not a terrible choice.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91f1f090",
   "metadata": {},
   "source": [
    "It's also instructive (though initially mystifying) to apply center-difference approximations to $f(X)=A^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d4bbabff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = 10 .^ range(-8,8,50)\n",
    "errors = [relative_error(f(A+s*dA)-f(A-s*dA), exact*2s) for s in s]\n",
    "plot(s * norm(dA), errors, xaxis=:log, yaxis=:log, markershape=:square, markercolor=:red,\n",
    "     title = L\"center-difference accuracy for $f(A)=A^2$\", xlabel=L\"\\Vert \\delta A\\Vert\", ylabel=\"relative error\",\n",
    "     label = \"error\", fmt=:png, legend=:top, ylim=[10^-16, 10])\n",
    "plot!(s, s.^2, linecolor=:red, label=L\"2nd-order $\\sim\\Vert \\delta A\\Vert$ reference\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "988a65f4",
   "metadata": {},
   "source": [
    "Here, the error gets **worse monotonically** as you decrease $\\delta A$!?!\n",
    "\n",
    "The reason for this is that a center-difference formula is *exact* for quadratic functions, since\n",
    "$$\n",
    "(A+\\delta A)^2 - (A-\\delta A)^2 = 2[A \\delta A + \\delta A\\, A]\n",
    "$$\n",
    "*exactly*.   So, the *only* error is the roundoff error, which increases with smaller $\\delta A$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc211ad5",
   "metadata": {},
   "source": [
    "### Even higher order:\n",
    "\n",
    "\n",
    "One can go even further than this:\n",
    "\n",
    "* You can derive higher-order finite-difference \"stencil\" formulas whose truncation error goes down even faster, at the expense of more function evaluations.   A simple four-line function to generate finite-difference stencils in Julia is given [here](https://discourse.julialang.org/t/generating-finite-difference-stencils/85876/5?u=stevengj). It defineds a function `stencil`, which takes a vector $x$ of $n$ points $x[i]$ and returns a vector of weights $w[i]$ to compute the $m$-th derivative ($m < n$) of a function at given $x_0$ (usually $x_0 = 0$) at a maximum order ($\\ge n - m$) of accuracy, via the formula $f^{(m)}(x_0) \\approx \\sum_i w[i] f(x[i])$:\n",
    "\n",
    "```jl\n",
    "function stencil(x::AbstractVector{<:Real}, x₀::Real, m::Integer)\n",
    "    ℓ = 0:length(x)-1\n",
    "    m in ℓ || throw(ArgumentError(\"order $m ∉ $ℓ\"))\n",
    "    A = @. (x' - x₀)^ℓ / factorial(ℓ)\n",
    "    return A \\ (ℓ .== m) # vector of weights w\n",
    "end\n",
    "```\n",
    "\n",
    "Given this stencil, we can then compute $f^{(m)}(y)$ at any point $y + h x_0$, with a step size scaled by $h$, via $f^{(m)}(y + h x_0) \\approx \\frac{1}{h^m} \\sum_i w[i] f(y+hx[i])$.   So, for example, we will get the ordinary centered-difference approximation from `stencil([-1,0,1], 0//1, 1)`, which returns weights $[-1/2, 0, +1/2]$.\n",
    "\n",
    "* You can evaluate $f(x+\\delta x)$ for smaller and smaller $\\delta x$, fit to polynomials of higher and higher degree in $\\delta x$, and *extrapolate* to $\\delta x \\to 0$.  You can even do this *adaptively* in order to determine when to stop shrinking $\\delta x$ because roundoff errors are dominating.  A sophisticated version of this process is called [Richardson extrapolation](https://github.com/JuliaMath/Richardson.jl).\n",
    "\n",
    "The [Julia FiniteDifferences.jl package](https://github.com/JuliaDiff/FiniteDifferences.jl) provides a large number of these techniques (both higher-order formulas and Richardson extrapolation techniques)."
   ]
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   "id": "816983bb",
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   "source": [
    "## Finite differences in higher dimensions\n",
    "\n",
    "Higher-dimensional *inputs* $x$ pose a fundamental computational challenge for finite-difference techniques, because if you want to know what happens for **every possible direction δx** then we need **many finite differences** — one for **each dimension of δx**.\n",
    "\n",
    "For example, suppose $x \\in \\mathbb{R}^n$ ($n$-component column vector) and $f(x)$ is a scalar.  Then $f'(x) = (\\nabla f)^T$ has **n components** $\\partial f/\\partial x_k$, and if you want to know the *whole gradient* then you need **n finite differences**.\n",
    "\n",
    "Generally, you need one finite difference for \"each column\" of the Jacobian (i.e. each input dimension).\n",
    "\n",
    "The net result is that **finite differences in higher dimensions are expensive**: you have to evaluate $f(x)$ around $\\sim n$ times in $n$ input dimensions.   This makes finite differences **impractical** for high-dimensional optimization (e.g. neural networks) where $n$ might be thousands or millions or (even billions).   \n",
    "\n",
    "On the other hand, if you are just using finite differences as a *check*, it is usually sufficient to compute $f'(x) \\delta x$ in a few **random directions**, i.e. for random small $\\delta x$."
   ]
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  {
   "cell_type": "markdown",
   "id": "02c548df",
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   "source": [
    "## Prefer analytical derivatives, with finite differences as a check\n",
    "\n",
    "The upshot of all this is that you should **use analytical derivatives if at all possible**.  However, derivative computation is tricky, so finite differences are still incredibly useful as a check.\n",
    "\n",
    "(Automatic differentiation is much less tricky and should generally give correct results.  But there are still many cases where AD fails or is inefficient, and has to be supplemented by hand-formulated derivatives for at least *part* of your calculation.)"
   ]
  }
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