fftlogtest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FFTLog\n",
    "\n",
    "This notebook is a translation of `fftlogtest.f` from the Fortran package `FFTLog`, which was presented in Appendix B of Hamilton, 2000, and published at <http://casa.colorado.edu/~ajsh/FFTLog>. It serves as an example for the python package `pyfftlog` (which is a Python version of `FFTLog`), in the same manner as the original file `fftlogtest.f` serves as an example for Fortran package `FFTLog`.\n",
    "\n",
    "\n",
    "### Reference\n",
    "Hamilton, A. J. S., 2000, Uncorrelated modes of the non-linear power spectrum: Monthly Notices of the Royal Astronomical Society, 312, pages 257-284; DOI: <http://dx.doi.org/10.1046/j.1365-8711.2000.03071.x>.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This is fftlogtest.f\n",
    "\n",
    "This is a simple test program to illustrate how `FFTLog` works.\n",
    "The test transform is:\n",
    "\n",
    "$$\n",
    "\\int^\\infty_0 r^{\\mu+1} \\exp\\left(-\\frac{r^2}{2} \\right)\\\n",
    "J_\\mu(k, r)\\ k\\ {\\rm d}r = k^{\\mu+1} \\exp\\left(-\\frac{k^2}{2}\n",
    "\\right) $$\n",
    "\n",
    "\n",
    "**Disclaimer:**  \n",
    "`FFTLog` does NOT claim to provide the most accurate possible\n",
    "solution of the continuous transform (which is the stated aim\n",
    "of some other codes).  Rather, `FFTLog` claims to solve the exact\n",
    "discrete transform of a logarithmically-spaced periodic sequence.\n",
    "If the periodic interval is wide enough, the resolution high\n",
    "enough, and the function well enough behaved outside the periodic\n",
    "interval, then `FFTLog` may yield a satisfactory approximation\n",
    "to the continuous transform.\n",
    "\n",
    "Observe:\n",
    "1.  How the result improves as the periodic interval is enlarged.\n",
    "    With the normal FFT, one is not used to ranges orders of\n",
    "    magnitude wide, but this is how `FFTLog` prefers it.\n",
    "2.  How the result improves as the resolution is increased.\n",
    "    Because the function is rather smooth, modest resolution\n",
    "    actually works quite well here.\n",
    "3.  That the central part of the transform is more reliable\n",
    "    than the outer parts.  Experience suggests that a good general\n",
    "    strategy is to double the periodic interval over which the\n",
    "    input function is defined, and then to discard the outer\n",
    "    half of the transform.\n",
    "4.  That the best bias exponent seems to be $q = 0$.\n",
    "5.  That for the critical index $\\mu = -1$, the result seems to be\n",
    "    offset by a constant from the 'correct' answer.\n",
    "6.  That the result grows progressively worse as mu decreases\n",
    "    below -1.\n",
    "\n",
    "The analytic integral above fails for $\\mu \\le -1$, but `FFTLog`\n",
    "still returns answers.  Namely, `FFTLog` returns the analytic\n",
    "continuation of the discrete transform.  Because of ambiguity\n",
    "in the path of integration around poles, this analytic continuation\n",
    "is liable to differ, for $\\mu \\le -1$, by a constant from the 'correct'\n",
    "continuation given by the above equation.\n",
    "\n",
    "`FFTLog` begins to have serious difficulties with aliasing as\n",
    "$\\mu$ decreases below $-1$, because then $r^{\\mu+1} \\exp(-r^2/2)$ is\n",
    "far from resembling a periodic function.\n",
    "You might have thought that it would help to introduce a bias\n",
    "exponent $q = \\mu$, or perhaps $q = \\mu+1$, or more, to make the\n",
    "function $a(r) = A(r) r^{-q}$ input to `fhtq` more nearly periodic.\n",
    "In practice a nonzero $q$ makes things worse.\n",
    "\n",
    "A symmetry argument lends support to the notion that the best\n",
    "exponent here should be $q = 0,$ as empirically appears to be true.\n",
    "The symmetry argument is that the function $r^{\\mu+1} \\exp(-r^2/2)$\n",
    "happens to be the same as its transform $k^{\\mu+1} \\exp(-k^2/2)$.\n",
    "If the best bias exponent were q in the forward transform, then\n",
    "the best exponent would be $-q$ that in the backward transform;\n",
    "but the two transforms happen to be the same in this case,\n",
    "suggesting $q = -q$, hence $q = 0$.\n",
    "\n",
    "This example illustrates that you cannot always tell just by\n",
    "looking at a function what the best bias exponent $q$ should be.\n",
    "You also have to look at its transform.  The best exponent $q$ is,\n",
    "in a sense, the one that makes both the function and its transform\n",
    "look most nearly periodic.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test-Integral:  $\\int_0^\\infty r^{\\mu+1}\\ \\exp\\left(-\\frac{r^2}{2}\\right)\\ J_\\mu(k,r)\\ k\\ {\\rm d}r = k^{\\mu+1} \\exp\\left(-\\frac{k^2}{2}\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import `pyfftlog` as well as `numpy` and `matplotlib`; some plot settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "4cf9c8a2-cf5f-45cd-b5da-0b1c7fe23108"
    }
   },
   "outputs": [],
   "source": [
    "import pyfftlog\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('ggplot')\n",
    "mpl.rcParams.update({'font.size': 16})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the parameters you wish to use\n",
    "\n",
    "The presets are the *Reasonable choices of parameters* from `fftlogtest.f`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Range of periodic interval\n",
    "logrmin = -4\n",
    "logrmax = 4\n",
    "\n",
    "# Number of points (Max 4096)\n",
    "n = 64\n",
    "\n",
    "# Order mu of Bessel function\n",
    "mu = 0\n",
    "\n",
    "# Bias exponent: q = 0 is unbiased\n",
    "q = 0\n",
    "\n",
    "# Sensible approximate choice of k_c r_c\n",
    "kr = 1\n",
    "\n",
    "# Tell fhti to change kr to low-ringing value\n",
    "# WARNING: kropt = 3 will fail, as interaction is not supported\n",
    "kropt = 1\n",
    "\n",
    "# Forward transform (changed from dir to tdir, as dir is a python fct)\n",
    "tdir = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculation related to the logarithmic spacing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Central point of periodic interval at log10(r_c) =  0.0\n"
     ]
    }
   ],
   "source": [
    "# Central point log10(r_c) of periodic interval\n",
    "logrc = (logrmin + logrmax)/2\n",
    "\n",
    "print('Central point of periodic interval at log10(r_c) = ', logrc)\n",
    "\n",
    "# Central index (1/2 integral if n is even)\n",
    "nc = (n + 1)/2.0\n",
    "\n",
    "# Log-spacing of points\n",
    "dlogr = (logrmax - logrmin)/n\n",
    "dlnr = dlogr*np.log(10.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate input function: $r^{\\mu+1}\\exp\\left(-\\frac{r^2}{2}\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r = 10**(logrc + (np.arange(1, n+1) - nc)*dlogr)\n",
    "ar = r**(mu + 1)*np.exp(-r**2/2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize FFTLog transform - note fhti resets `kr`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyfftlog.fhti: new kr =  0.953538967579\n"
     ]
    }
   ],
   "source": [
    "kr, xsave = pyfftlog.fhti(n, mu, dlnr, q, kr, kropt)\n",
    "print('pyfftlog.fhti: new kr = ', kr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Call `pyfftlog.fht` (or `pyfftlog.fhtl`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Central point in k-space at log10(k_c) =  -0.0206615542605\n"
     ]
    }
   ],
   "source": [
    "logkc = np.log10(kr) - logrc\n",
    "print('Central point in k-space at log10(k_c) = ', logkc)\n",
    "\n",
    "# rk = r_c/k_c\n",
    "rk = 10**(logrc - logkc)\n",
    "\n",
    "# Transform\n",
    "#ak = pyfftlog.fftl(ar.copy(), xsave, rk, tdir)\n",
    "ak = pyfftlog.fht(ar.copy(), xsave, tdir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate Output function: $k^{\\mu+1}\\exp\\left(-\\frac{k^2}{2}\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "k = 10**(logkc + (np.arange(1, n+1) - nc)*dlogr)\n",
    "theo = k**(mu + 1)*np.exp(-k**2/2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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7c1z2woUL2d44//z58xg+fDh++uknDBo0CGPGjEFmZiZeffVV3Lp1S7V4Hz58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m5QAEAoc7tc+u6GG3Tbtm36XNJlERGaP3++unbtajoaENQc4eFqJylBUtW+fabjAAgwFEERUPLz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\nga1VGoAwIAQFAAAAAABxJ3AkqC8lpdnXO5cvl62iQpJUfdFFU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83a563d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "\n",
    "# Transformed result\n",
    "ax2 = plt.subplot(1, 2, 2)\n",
    "plt.plot(k, theo, 'k', lw=2, label='Theoretical')\n",
    "plt.plot(k, ak, 'r--', lw=2, label='FFTLog')\n",
    "plt.xlabel('k')\n",
    "plt.title(r'$k^{\\mu+1} \\exp(-k^2/2)$', fontsize=20)\n",
    "plt.legend(loc='best')\n",
    "plt.xscale('log')\n",
    "plt.yscale('symlog', basey=10, linthreshy=1e-5)\n",
    "ax2ylim = plt.ylim()\n",
    "\n",
    "# Input\n",
    "ax1 = plt.subplot(1, 2, 1)\n",
    "plt.plot(r, ar, 'k', lw=2)\n",
    "plt.xlabel('r')\n",
    "plt.title(r'$r^{\\mu+1}\\ \\exp(-r^2/2)$', fontsize=20)\n",
    "plt.xscale('log')\n",
    "plt.yscale('symlog', basey=10, linthreshy=1e-5)\n",
    "plt.ylim(ax2ylim)\n",
    "\n",
    "# Main title\n",
    "plt.suptitle(r'$\\int_0^\\infty r^{\\mu+1}\\ \\exp(-r^2/2)\\ J_\\mu(k,r)\\ k\\ {\\rm d}r = k^{\\mu+1} \\exp(-k^2/2)$',\n",
    "             fontsize=24, y=1.08)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Print values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           k                 a(k)       k^(mu+1) exp(-k^2/2)\n",
      "----------------------------------------------------------------\n",
      "      1.101130e-04       6.332603e-05       1.101130e-04\n",
      "      1.468380e-04       9.168618e-05       1.468380e-04\n",
      "      1.958116e-04       1.374282e-04       1.958116e-04\n",
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      "      8.257307e+03       4.510046e-05       0.000000e+00\n"
     ]
    }
   ],
   "source": [
    "print('           k                 a(k)       k^(mu+1) exp(-k^2/2)')\n",
    "print('----------------------------------------------------------------')\n",
    "for i in range(n):\n",
    "    print(\"%18.6e %18.6e %18.6e\"% (k[i], ak[i], theo[i]))"
   ]
  }
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