lecture_4_numerical_python/2_integration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integration\n",
    "\n",
    "Research frequently involves evaluating integrals numerically. The basic idea behind numerical \"quadrature\" is that a definite integral of a function can be approximated by a sum over evaluations of that function multiplied by quadrature \"weights\":\n",
    "\n",
    "\\begin{equation}\n",
    "    \\int_a^b f(x)\\text{d}x \\approx \\sum_n w_n f(x_n), \\hspace{1em} x_n\\in[a,b]\n",
    "\\end{equation}\n",
    "\n",
    "Depending on the function $f$, different choices of weights $w_n$ and grid-points $x_n$ can lead to improvements in accuracy (to floating-point error, in some cases). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the simplest quadratures, known as the trapezoidal rule, approximates a definite integral as the sum of the areas of trapezoids defined by the endpoints of line segments along the curve defined by $f$:\n",
    "\n",
    "\\begin{align}\n",
    "    \\int_a^b f(x)\\text{d}x \n",
    "    &\\approx \\sum_N \\text{[area of trapezoid defined by the four points }(x_n,0),(x_n,f(x_n)),(x_{n+1},0),(x_{n+1},f(x_{n+1}))],\n",
    "\\\\\n",
    "    &=\\sum_{n=0}^{N-2}\\frac{1}{2}(x_{n+1}-x_n)[f(x_n) + f(x_{n+1})]\n",
    "\\end{align}\n",
    "\n",
    "on an interval with $N$ grid-points $x_0,...,x_{N-1}$. For a grid of evenly spaced points with grid-size $\\Delta x$, this simplifies further to\n",
    "\n",
    "\\begin{equation}\n",
    "    \\int_a^b f(x)\\text{d}x \n",
    "    \\approx\\Delta x\n",
    "    \\left[ \n",
    "        \\frac{1}{2}f(x_0) + f(x_1) + ... + f(x_{N-2}) + \\frac{1}{2}f(x_{N-1})\n",
    "    \\right].\n",
    "\\end{equation}\n",
    "\n",
    "Here's an example of a function that applies the trapezoidal rule to integrate a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def trapz_int(f,a,b,tol=1e-10,maxits=100):\n",
    "    '''\n",
    "        uses the trapezoidal rule to compute the definite integral \n",
    "        int_a^b f(x)dx, iteratively increasing the number of grid\n",
    "        points used for quadrature until the solution converges\n",
    "        \n",
    "        Inputs:\n",
    "            f       function to integrate\n",
    "            a       starting point of integration\n",
    "            b       en-point of integration\n",
    "            tol     tolerance for change in subsequent iterations\n",
    "            maxits  maximum number of iterations\n",
    "        Outputs:\n",
    "            I       definite integral int_a^b f(x)dx\n",
    "    '''\n",
    "    # evaluate initial approximation to the integral:\n",
    "    dx= (b-a)                  # coursest possible grid-spacing\n",
    "    I = dx*(f(b)/2. + f(a)/2.) # roughest approximation to integral\n",
    "    N = 2                      # smallest number of grid-pointsS\n",
    "    \n",
    "    # iteratively refine by halving the grid-spacing:\n",
    "    itr= 0\n",
    "    while itr<maxits:\n",
    "        dx_new = dx/2. # decrease grid-spacing\n",
    "        N += 2**itr    # increase number of grid-points\n",
    "        x_eval = np.linspace(a,b,N)[1:-1][::2] # this indexing takes only the grid-points we haven't evaluated yet\n",
    "        I_new = I*dx_new/dx \\\n",
    "              + np.sum(f(x_eval))*dx_new\n",
    "        print(f'iteration {itr} ({N} points): {100*(I_new-I)/I:.4e}% change')\n",
    "        if abs(I_new-I)<tol:\n",
    "            break        \n",
    "        itr+=1\n",
    "        dx = dx_new\n",
    "        I = I_new\n",
    "\n",
    "    if itr==maxits:\n",
    "        print(f'integral did not converge after {itr} refinements')\n",
    "    else:\n",
    "        print('integral converged!')\n",
    "    return I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use this function to calculate the integral $\\int_0^5 dx (x^2 + 3)$, which has the exact answer $5^3 / 3 + 3\\times5\\simeq 56.667$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 0 (3 points): -2.0161e+01% change\n",
      "iteration 1 (5 points): -6.3131e+00% change\n",
      "iteration 2 (9 points): -1.6846e+00% change\n",
      "iteration 3 (17 points): -4.2838e-01% change\n",
      "iteration 4 (33 points): -1.0755e-01% change\n",
      "iteration 5 (65 points): -2.6918e-02% change\n",
      "iteration 6 (129 points): -6.7312e-03% change\n",
      "iteration 7 (257 points): -1.6829e-03% change\n",
      "iteration 8 (513 points): -4.2074e-04% change\n",
      "iteration 9 (1025 points): -1.0518e-04% change\n",
      "iteration 10 (2049 points): -2.6296e-05% change\n",
      "iteration 11 (4097 points): -6.5740e-06% change\n",
      "iteration 12 (8193 points): -1.6435e-06% change\n",
      "iteration 13 (16385 points): -4.1088e-07% change\n",
      "iteration 14 (32769 points): -1.0272e-07% change\n",
      "iteration 15 (65537 points): -2.5680e-08% change\n",
      "iteration 16 (131073 points): -6.4200e-09% change\n",
      "iteration 17 (262145 points): -1.6050e-09% change\n",
      "iteration 18 (524289 points): -4.0125e-10% change\n",
      "iteration 19 (1048577 points): -1.0031e-10% change\n",
      "integral converged!\n",
      "56.66666666674246\n",
      "error of -1.3375e-10% \n",
      "CPU times: user 9.2 ms, sys: 12.9 ms, total: 22.1 ms\n",
      "Wall time: 21.1 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "ans = 5.**3 / 3 + 3 * 5.\n",
    "tst = trapz_int(f=lambda x: x**2 + 3,a=0,b=5,tol=1e-10)\n",
    "print(tst)\n",
    "print(f'error of {(ans - tst)/ans*100:.4e}% ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This converged reasonably well, but it required evaluating our function at a lot of points. Scipy includes a wrapper for a Fortran routine that uses a much more accurate, and also efficient quadrature (see https://en.wikipedia.org/wiki/Gaussian_quadrature):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "\u001b[0;34m\u001b[0m    \u001b[0mcomplex_func\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Compute a definite integral.\n",
       "\n",
       "Integrate func from `a` to `b` (possibly infinite interval) using a\n",
       "technique from the Fortran library QUADPACK.\n",
       "\n",
       "Parameters\n",
       "----------\n",
       "func : {function, scipy.LowLevelCallable}\n",
       "    A Python function or method to integrate. If `func` takes many\n",
       "    arguments, it is integrated along the axis corresponding to the\n",
       "    first argument.\n",
       "\n",
       "    If the user desires improved integration performance, then `f` may\n",
       "    be a `scipy.LowLevelCallable` with one of the signatures::\n",
       "\n",
       "        double func(double x)\n",
       "        double func(double x, void *user_data)\n",
       "        double func(int n, double *xx)\n",
       "        double func(int n, double *xx, void *user_data)\n",
       "\n",
       "    The ``user_data`` is the data contained in the `scipy.LowLevelCallable`.\n",
       "    In the call forms with ``xx``,  ``n`` is the length of the ``xx``\n",
       "    array which contains ``xx[0] == x`` and the rest of the items are\n",
       "    numbers contained in the ``args`` argument of quad.\n",
       "\n",
       "    In addition, certain ctypes call signatures are supported for\n",
       "    backward compatibility, but those should not be used in new code.\n",
       "a : float\n",
       "    Lower limit of integration (use -numpy.inf for -infinity).\n",
       "b : float\n",
       "    Upper limit of integration (use numpy.inf for +infinity).\n",
       "args : tuple, optional\n",
       "    Extra arguments to pass to `func`.\n",
       "full_output : int, optional\n",
       "    Non-zero to return a dictionary of integration information.\n",
       "    If non-zero, warning messages are also suppressed and the\n",
       "    message is appended to the output tuple.\n",
       "complex_func : bool, optional\n",
       "    Indicate if the function's (`func`) return type is real\n",
       "    (``complex_func=False``: default) or complex (``complex_func=True``).\n",
       "    In both cases, the function's argument is real.\n",
       "    If full_output is also non-zero, the `infodict`, `message`, and\n",
       "    `explain` for the real and complex components are returned in\n",
       "    a dictionary with keys \"real output\" and \"imag output\".\n",
       "\n",
       "Returns\n",
       "-------\n",
       "y : float\n",
       "    The integral of func from `a` to `b`.\n",
       "abserr : float\n",
       "    An estimate of the absolute error in the result.\n",
       "infodict : dict\n",
       "    A dictionary containing additional information.\n",
       "message\n",
       "    A convergence message.\n",
       "explain\n",
       "    Appended only with 'cos' or 'sin' weighting and infinite\n",
       "    integration limits, it contains an explanation of the codes in\n",
       "    infodict['ierlst']\n",
       "\n",
       "Other Parameters\n",
       "----------------\n",
       "epsabs : float or int, optional\n",
       "    Absolute error tolerance. Default is 1.49e-8. `quad` tries to obtain\n",
       "    an accuracy of ``abs(i-result) <= max(epsabs, epsrel*abs(i))``\n",
       "    where ``i`` = integral of `func` from `a` to `b`, and ``result`` is the\n",
       "    numerical approximation. See `epsrel` below.\n",
       "epsrel : float or int, optional\n",
       "    Relative error tolerance. Default is 1.49e-8.\n",
       "    If ``epsabs <= 0``, `epsrel` must be greater than both 5e-29\n",
       "    and ``50 * (machine epsilon)``. See `epsabs` above.\n",
       "limit : float or int, optional\n",
       "    An upper bound on the number of subintervals used in the adaptive\n",
       "    algorithm.\n",
       "points : (sequence of floats,ints), optional\n",
       "    A sequence of break points in the bounded integration interval\n",
       "    where local difficulties of the integrand may occur (e.g.,\n",
       "    singularities, discontinuities). The sequence does not have\n",
       "    to be sorted. Note that this option cannot be used in conjunction\n",
       "    with ``weight``.\n",
       "weight : float or int, optional\n",
       "    String indicating weighting function. Full explanation for this\n",
       "    and the remaining arguments can be found below.\n",
       "wvar : optional\n",
       "    Variables for use with weighting functions.\n",
       "wopts : optional\n",
       "    Optional input for reusing Chebyshev moments.\n",
       "maxp1 : float or int, optional\n",
       "    An upper bound on the number of Chebyshev moments.\n",
       "limlst : int, optional\n",
       "    Upper bound on the number of cycles (>=3) for use with a sinusoidal\n",
       "    weighting and an infinite end-point.\n",
       "\n",
       "See Also\n",
       "--------\n",
       "dblquad : double integral\n",
       "tplquad : triple integral\n",
       "nquad : n-dimensional integrals (uses `quad` recursively)\n",
       "fixed_quad : fixed-order Gaussian quadrature\n",
       "quadrature : adaptive Gaussian quadrature\n",
       "odeint : ODE integrator\n",
       "ode : ODE integrator\n",
       "simpson : integrator for sampled data\n",
       "romb : integrator for sampled data\n",
       "scipy.special : for coefficients and roots of orthogonal polynomials\n",
       "\n",
       "Notes\n",
       "-----\n",
       "For valid results, the integral must converge; behavior for divergent\n",
       "integrals is not guaranteed.\n",
       "\n",
       "**Extra information for quad() inputs and outputs**\n",
       "\n",
       "If full_output is non-zero, then the third output argument\n",
       "(infodict) is a dictionary with entries as tabulated below. For\n",
       "infinite limits, the range is transformed to (0,1) and the\n",
       "optional outputs are given with respect to this transformed range.\n",
       "Let M be the input argument limit and let K be infodict['last'].\n",
       "The entries are:\n",
       "\n",
       "'neval'\n",
       "    The number of function evaluations.\n",
       "'last'\n",
       "    The number, K, of subintervals produced in the subdivision process.\n",
       "'alist'\n",
       "    A rank-1 array of length M, the first K elements of which are the\n",
       "    left end points of the subintervals in the partition of the\n",
       "    integration range.\n",
       "'blist'\n",
       "    A rank-1 array of length M, the first K elements of which are the\n",
       "    right end points of the subintervals.\n",
       "'rlist'\n",
       "    A rank-1 array of length M, the first K elements of which are the\n",
       "    integral approximations on the subintervals.\n",
       "'elist'\n",
       "    A rank-1 array of length M, the first K elements of which are the\n",
       "    moduli of the absolute error estimates on the subintervals.\n",
       "'iord'\n",
       "    A rank-1 integer array of length M, the first L elements of\n",
       "    which are pointers to the error estimates over the subintervals\n",
       "    with ``L=K`` if ``K<=M/2+2`` or ``L=M+1-K`` otherwise. Let I be the\n",
       "    sequence ``infodict['iord']`` and let E be the sequence\n",
       "    ``infodict['elist']``.  Then ``E[I[1]], ..., E[I[L]]`` forms a\n",
       "    decreasing sequence.\n",
       "\n",
       "If the input argument points is provided (i.e., it is not None),\n",
       "the following additional outputs are placed in the output\n",
       "dictionary. Assume the points sequence is of length P.\n",
       "\n",
       "'pts'\n",
       "    A rank-1 array of length P+2 containing the integration limits\n",
       "    and the break points of the intervals in ascending order.\n",
       "    This is an array giving the subintervals over which integration\n",
       "    will occur.\n",
       "'level'\n",
       "    A rank-1 integer array of length M (=limit), containing the\n",
       "    subdivision levels of the subintervals, i.e., if (aa,bb) is a\n",
       "    subinterval of ``(pts[1], pts[2])`` where ``pts[0]`` and ``pts[2]``\n",
       "    are adjacent elements of ``infodict['pts']``, then (aa,bb) has level l\n",
       "    if ``|bb-aa| = |pts[2]-pts[1]| * 2**(-l)``.\n",
       "'ndin'\n",
       "    A rank-1 integer array of length P+2. After the first integration\n",
       "    over the intervals (pts[1], pts[2]), the error estimates over some\n",
       "    of the intervals may have been increased artificially in order to\n",
       "    put their subdivision forward. This array has ones in slots\n",
       "    corresponding to the subintervals for which this happens.\n",
       "\n",
       "**Weighting the integrand**\n",
       "\n",
       "The input variables, *weight* and *wvar*, are used to weight the\n",
       "integrand by a select list of functions. Different integration\n",
       "methods are used to compute the integral with these weighting\n",
       "functions, and these do not support specifying break points. The\n",
       "possible values of weight and the corresponding weighting functions are.\n",
       "\n",
       "==========  ===================================   =====================\n",
       "``weight``  Weight function used                  ``wvar``\n",
       "==========  ===================================   =====================\n",
       "'cos'       cos(w*x)                              wvar = w\n",
       "'sin'       sin(w*x)                              wvar = w\n",
       "'alg'       g(x) = ((x-a)**alpha)*((b-x)**beta)   wvar = (alpha, beta)\n",
       "'alg-loga'  g(x)*log(x-a)                         wvar = (alpha, beta)\n",
       "'alg-logb'  g(x)*log(b-x)                         wvar = (alpha, beta)\n",
       "'alg-log'   g(x)*log(x-a)*log(b-x)                wvar = (alpha, beta)\n",
       "'cauchy'    1/(x-c)                               wvar = c\n",
       "==========  ===================================   =====================\n",
       "\n",
       "wvar holds the parameter w, (alpha, beta), or c depending on the weight\n",
       "selected. In these expressions, a and b are the integration limits.\n",
       "\n",
       "For the 'cos' and 'sin' weighting, additional inputs and outputs are\n",
       "available.\n",
       "\n",
       "For finite integration limits, the integration is performed using a\n",
       "Clenshaw-Curtis method which uses Chebyshev moments. For repeated\n",
       "calculations, these moments are saved in the output dictionary:\n",
       "\n",
       "'momcom'\n",
       "    The maximum level of Chebyshev moments that have been computed,\n",
       "    i.e., if ``M_c`` is ``infodict['momcom']`` then the moments have been\n",
       "    computed for intervals of length ``|b-a| * 2**(-l)``,\n",
       "    ``l=0,1,...,M_c``.\n",
       "'nnlog'\n",
       "    A rank-1 integer array of length M(=limit), containing the\n",
       "    subdivision levels of the subintervals, i.e., an element of this\n",
       "    array is equal to l if the corresponding subinterval is\n",
       "    ``|b-a|* 2**(-l)``.\n",
       "'chebmo'\n",
       "    A rank-2 array of shape (25, maxp1) containing the computed\n",
       "    Chebyshev moments. These can be passed on to an integration\n",
       "    over the same interval by passing this array as the second\n",
       "    element of the sequence wopts and passing infodict['momcom'] as\n",
       "    the first element.\n",
       "\n",
       "If one of the integration limits is infinite, then a Fourier integral is\n",
       "computed (assuming w neq 0). If full_output is 1 and a numerical error\n",
       "is encountered, besides the error message attached to the output tuple,\n",
       "a dictionary is also appended to the output tuple which translates the\n",
       "error codes in the array ``info['ierlst']`` to English messages. The\n",
       "output information dictionary contains the following entries instead of\n",
       "'last', 'alist', 'blist', 'rlist', and 'elist':\n",
       "\n",
       "'lst'\n",
       "    The number of subintervals needed for the integration (call it ``K_f``).\n",
       "'rslst'\n",
       "    A rank-1 array of length M_f=limlst, whose first ``K_f`` elements\n",
       "    contain the integral contribution over the interval\n",
       "    ``(a+(k-1)c, a+kc)`` where ``c = (2*floor(|w|) + 1) * pi / |w|``\n",
       "    and ``k=1,2,...,K_f``.\n",
       "'erlst'\n",
       "    A rank-1 array of length ``M_f`` containing the error estimate\n",
       "    corresponding to the interval in the same position in\n",
       "    ``infodict['rslist']``.\n",
       "'ierlst'\n",
       "    A rank-1 integer array of length ``M_f`` containing an error flag\n",
       "    corresponding to the interval in the same position in\n",
       "    ``infodict['rslist']``.  See the explanation dictionary (last entry\n",
       "    in the output tuple) for the meaning of the codes.\n",
       "\n",
       "\n",
       "**Details of QUADPACK level routines**\n",
       "\n",
       "`quad` calls routines from the FORTRAN library QUADPACK. This section\n",
       "provides details on the conditions for each routine to be called and a\n",
       "short description of each routine. The routine called depends on\n",
       "`weight`, `points` and the integration limits `a` and `b`.\n",
       "\n",
       "================  ==============  ==========  =====================\n",
       "QUADPACK routine  `weight`        `points`    infinite bounds\n",
       "================  ==============  ==========  =====================\n",
       "qagse             None            No          No\n",
       "qagie             None            No          Yes\n",
       "qagpe             None            Yes         No\n",
       "qawoe             'sin', 'cos'    No          No\n",
       "qawfe             'sin', 'cos'    No          either `a` or `b`\n",
       "qawse             'alg*'          No          No\n",
       "qawce             'cauchy'        No          No\n",
       "================  ==============  ==========  =====================\n",
       "\n",
       "The following provides a short desciption from [1]_ for each\n",
       "routine.\n",
       "\n",
       "qagse\n",
       "    is an integrator based on globally adaptive interval\n",
       "    subdivision in connection with extrapolation, which will\n",
       "    eliminate the effects of integrand singularities of\n",
       "    several types.\n",
       "qagie\n",
       "    handles integration over infinite intervals. The infinite range is\n",
       "    mapped onto a finite interval and subsequently the same strategy as\n",
       "    in ``QAGS`` is applied.\n",
       "qagpe\n",
       "    serves the same purposes as QAGS, but also allows the\n",
       "    user to provide explicit information about the location\n",
       "    and type of trouble-spots i.e. the abscissae of internal\n",
       "    singularities, discontinuities and other difficulties of\n",
       "    the integrand function.\n",
       "qawoe\n",
       "    is an integrator for the evaluation of\n",
       "    :math:`\\int^b_a \\cos(\\omega x)f(x)dx` or\n",
       "    :math:`\\int^b_a \\sin(\\omega x)f(x)dx`\n",
       "    over a finite interval [a,b], where :math:`\\omega` and :math:`f`\n",
       "    are specified by the user. The rule evaluation component is based\n",
       "    on the modified Clenshaw-Curtis technique\n",
       "\n",
       "    An adaptive subdivision scheme is used in connection\n",
       "    with an extrapolation procedure, which is a modification\n",
       "    of that in ``QAGS`` and allows the algorithm to deal with\n",
       "    singularities in :math:`f(x)`.\n",
       "qawfe\n",
       "    calculates the Fourier transform\n",
       "    :math:`\\int^\\infty_a \\cos(\\omega x)f(x)dx` or\n",
       "    :math:`\\int^\\infty_a \\sin(\\omega x)f(x)dx`\n",
       "    for user-provided :math:`\\omega` and :math:`f`. The procedure of\n",
       "    ``QAWO`` is applied on successive finite intervals, and convergence\n",
       "    acceleration by means of the :math:`\\varepsilon`-algorithm is applied\n",
       "    to the series of integral approximations.\n",
       "qawse\n",
       "    approximate :math:`\\int^b_a w(x)f(x)dx`, with :math:`a < b` where\n",
       "    :math:`w(x) = (x-a)^{\\alpha}(b-x)^{\\beta}v(x)` with\n",
       "    :math:`\\alpha,\\beta > -1`, where :math:`v(x)` may be one of the\n",
       "    following functions: :math:`1`, :math:`\\log(x-a)`, :math:`\\log(b-x)`,\n",
       "    :math:`\\log(x-a)\\log(b-x)`.\n",
       "\n",
       "    The user specifies :math:`\\alpha`, :math:`\\beta` and the type of the\n",
       "    function :math:`v`. A globally adaptive subdivision strategy is\n",
       "    applied, with modified Clenshaw-Curtis integration on those\n",
       "    subintervals which contain `a` or `b`.\n",
       "qawce\n",
       "    compute :math:`\\int^b_a f(x) / (x-c)dx` where the integral must be\n",
       "    interpreted as a Cauchy principal value integral, for user specified\n",
       "    :math:`c` and :math:`f`. The strategy is globally adaptive. Modified\n",
       "    Clenshaw-Curtis integration is used on those intervals containing the\n",
       "    point :math:`x = c`.\n",
       "\n",
       "**Integration of Complex Function of a Real Variable**\n",
       "\n",
       "A complex valued function, :math:`f`, of a real variable can be written as\n",
       ":math:`f = g + ih`.  Similarly, the integral of :math:`f` can be\n",
       "written as\n",
       "\n",
       ".. math::\n",
       "    \\int_a^b f(x) dx = \\int_a^b g(x) dx + i\\int_a^b h(x) dx\n",
       "\n",
       "assuming that the integrals of :math:`g` and :math:`h` exist\n",
       "over the inteval :math:`[a,b]` [2]_. Therefore, ``quad`` integrates\n",
       "complex-valued functions by integrating the real and imaginary components\n",
       "separately.\n",
       "\n",
       "\n",
       "References\n",
       "----------\n",
       "\n",
       ".. [1] Piessens, Robert; de Doncker-Kapenga, Elise;\n",
       "       Überhuber, Christoph W.; Kahaner, David (1983).\n",
       "       QUADPACK: A subroutine package for automatic integration.\n",
       "       Springer-Verlag.\n",
       "       ISBN 978-3-540-12553-2.\n",
       "\n",
       ".. [2] McCullough, Thomas; Phillips, Keith (1973).\n",
       "       Foundations of Analysis in the Complex Plane.\n",
       "       Holt Rinehart Winston.\n",
       "       ISBN 0-03-086370-8\n",
       "\n",
       "Examples\n",
       "--------\n",
       "Calculate :math:`\\int^4_0 x^2 dx` and compare with an analytic result\n",
       "\n",
       ">>> from scipy import integrate\n",
       ">>> import numpy as np\n",
       ">>> x2 = lambda x: x**2\n",
       ">>> integrate.quad(x2, 0, 4)\n",
       "(21.333333333333332, 2.3684757858670003e-13)\n",
       ">>> print(4**3 / 3.)  # analytical result\n",
       "21.3333333333\n",
       "\n",
       "Calculate :math:`\\int^\\infty_0 e^{-x} dx`\n",
       "\n",
       ">>> invexp = lambda x: np.exp(-x)\n",
       ">>> integrate.quad(invexp, 0, np.inf)\n",
       "(1.0, 5.842605999138044e-11)\n",
       "\n",
       "Calculate :math:`\\int^1_0 a x \\,dx` for :math:`a = 1, 3`\n",
       "\n",
       ">>> f = lambda x, a: a*x\n",
       ">>> y, err = integrate.quad(f, 0, 1, args=(1,))\n",
       ">>> y\n",
       "0.5\n",
       ">>> y, err = integrate.quad(f, 0, 1, args=(3,))\n",
       ">>> y\n",
       "1.5\n",
       "\n",
       "Calculate :math:`\\int^1_0 x^2 + y^2 dx` with ctypes, holding\n",
       "y parameter as 1::\n",
       "\n",
       "    testlib.c =>\n",
       "        double func(int n, double args[n]){\n",
       "            return args[0]*args[0] + args[1]*args[1];}\n",
       "    compile to library testlib.*\n",
       "\n",
       "::\n",
       "\n",
       "   from scipy import integrate\n",
       "   import ctypes\n",
       "   lib = ctypes.CDLL('/home/.../testlib.*') #use absolute path\n",
       "   lib.func.restype = ctypes.c_double\n",
       "   lib.func.argtypes = (ctypes.c_int,ctypes.c_double)\n",
       "   integrate.quad(lib.func,0,1,(1))\n",
       "   #(1.3333333333333333, 1.4802973661668752e-14)\n",
       "   print((1.0**3/3.0 + 1.0) - (0.0**3/3.0 + 0.0)) #Analytic result\n",
       "   # 1.3333333333333333\n",
       "\n",
       "Be aware that pulse shapes and other sharp features as compared to the\n",
       "size of the integration interval may not be integrated correctly using\n",
       "this method. A simplified example of this limitation is integrating a\n",
       "y-axis reflected step function with many zero values within the integrals\n",
       "bounds.\n",
       "\n",
       ">>> y = lambda x: 1 if x<=0 else 0\n",
       ">>> integrate.quad(y, -1, 1)\n",
       "(1.0, 1.1102230246251565e-14)\n",
       ">>> integrate.quad(y, -1, 100)\n",
       "(1.0000000002199108, 1.0189464580163188e-08)\n",
       ">>> integrate.quad(y, -1, 10000)\n",
       "(0.0, 0.0)\n",
       "\u001b[0;31mFile:\u001b[0m      ~/anaconda3/lib/python3.11/site-packages/scipy/integrate/_quadpack_py.py\n",
       "\u001b[0;31mType:\u001b[0m      function"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "quad?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56.66666666666666 6.29126380620922e-13\n",
      "CPU times: user 91 µs, sys: 23 µs, total: 114 µs\n",
      "Wall time: 118 µs\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "I, err = quad(func=lambda x: x**2 + 3, a=0, b=5, epsabs=1.e-15)\n",
    "print (I, err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration of a pre-sampled function\n",
    "\n",
    "Often we need to calculate the area under the curve of a function pre-sampled at fixed points. The approach to integrating over a pre-sampled function isn't any different in principle, but we no longer have the option of iteratively refining our answer until the solution converges. \n",
    "\n",
    "### Exercise 3\n",
    "Write a function, called trapz_fixed_int(f,x), that takes as input an array of samples $f$ of a function $f$ at an array of grid-points $x$, and uses the trapezoidal rule to compute the definite integral $\\int_a^bf\\text{d}x$, where $a$ and $b$ are the end-points $x[0]$ and $x[-1]$. Use the same number of grid-points used in the final iteration of trapz_int above, and compare with the analytical answer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "xx = np.linspace(0,5,1048577) # the largest number of grid-points used in trapz_int before\n",
    "ans = 5.**3 / 3 + 3 * 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scipy also includes some ready-to-use functions for integrating over pre-sampled points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import trapezoid,simpson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56.666666666685714\n",
      "error of -3.3617e-11% \n",
      "CPU times: user 16.9 ms, sys: 0 ns, total: 16.9 ms\n",
      "Wall time: 15.4 ms\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "# this should give a similar answer to result from exercise\n",
    "tst= trapezoid(y=xx**2 + 3,x=xx)\n",
    "print(tst)\n",
    "print(f'error of {(ans - tst)/ans*100:.4e}% ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56.66666666666664\n",
      "error of 3.7617e-14% \n",
      "CPU times: user 21.5 ms, sys: 20.1 ms, total: 41.6 ms\n",
      "Wall time: 39.3 ms\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "tst= simpson(y=xx**2 + 3,x=xx)\n",
    "print(tst)\n",
    "print(f'error of {(ans - tst)/ans*100:.4e}% ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interpolation\n",
    "\n",
    "We often have data sampled at a relatively small number of points, and so we need to interpolate between them. In other cases, we may need to downsample from high to lower resolution. There are a number of different ways to interpolate functions. Scipy has a few built-in options:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d,CubicSpline,splrep,splev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try interpolating the function $f(x) = e^{-x}  \\sin(2  \\pi  x)$ using only a small number of points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define and sample the function at a small number of points\n",
    "def myf(x):\n",
    "    return (np.exp(-x)) * np.sin(2 * np.pi * x)\n",
    "x_coarse = np.linspace(0,2,8)\n",
    "data = myf(x_coarse)\n",
    "\n",
    "# construct interpolation functions:\n",
    "linterp = interp1d(x=x_coarse,y=data,kind='linear')\n",
    "splterp = splrep(x=x_coarse,y=data)\n",
    "csplterp= CubicSpline(x=x_coarse,y=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above calls to scipy's interpolation functions return new functions that we can then evaluate at our desired grid-points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# evaluate and plot the interpolation functions\n",
    "x_fine = np.linspace(0,2,1000) \n",
    "truth = myf(x_fine)\n",
    "\n",
    "f,ax = plt.subplots(2,1,figsize=(10,8),sharex=True)\n",
    "ax[0].plot(x_coarse,data,'ko')\n",
    "ax[0].plot(x_fine,linterp(x_fine),label='linear')\n",
    "ax[0].plot(x_fine,csplterp(x_fine),label='Spline #1')\n",
    "ax[0].plot(x_fine,splev(x_fine,splterp),label='Spline #2')\n",
    "ax[0].plot(x_fine,truth,'k',label='Truth')\n",
    "ax[0].legend(fontsize=12)\n",
    "ax[0].set_ylabel('$f(x)$')\n",
    "\n",
    "# now plot residuals from the function evaluation:\n",
    "for terp in [linterp(x_fine),csplterp(x_fine),splev(x_fine,splterp)]:\n",
    "    ax[1].plot(x_fine,terp - truth)\n",
    "ax[1].set_ylabel('Residual')\n",
    "ax[1].set_xlabel('$x$')\n",
    "plt.subplots_adjust(hspace=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "None of these are perfect, so be careful not to trust interpolation too much! "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}