Log Plots

log_plot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = linspace(0.1,10,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = log(x)\n",
    "y2 = log2(x)\n",
    "y10 = log10(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c86bdd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, y, label='ln')\n",
    "plot(x, y2, label='2')\n",
    "plot(x, y10, label='10')\n",
    "plot(x, log1p(x), label='1p')\n",
    "legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[0;31mType:            \u001b[0mufunc\n",
      "\u001b[0;31mString form:     \u001b[0m<ufunc 'log1p'>\n",
      "\u001b[0;31mFile:            \u001b[0m/Users/bgranger/anaconda/lib/python2.7/site-packages/numpy/__init__.py\n",
      "\u001b[0;31mDocstring:\u001b[0m\n",
      "log1p(x[, out])\n",
      "\n",
      "Return the natural logarithm of one plus the input array, element-wise.\n",
      "\n",
      "Calculates ``log(1 + x)``.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "x : array_like\n",
      "    Input values.\n",
      "\n",
      "Returns\n",
      "-------\n",
      "y : ndarray\n",
      "    Natural logarithm of `1 + x`, element-wise.\n",
      "\n",
      "See Also\n",
      "--------\n",
      "expm1 : ``exp(x) - 1``, the inverse of `log1p`.\n",
      "\n",
      "Notes\n",
      "-----\n",
      "For real-valued input, `log1p` is accurate also for `x` so small\n",
      "that `1 + x == 1` in floating-point accuracy.\n",
      "\n",
      "Logarithm is a multivalued function: for each `x` there is an infinite\n",
      "number of `z` such that `exp(z) = 1 + x`. The convention is to return\n",
      "the `z` whose imaginary part lies in `[-pi, pi]`.\n",
      "\n",
      "For real-valued input data types, `log1p` always returns real output.\n",
      "For each value that cannot be expressed as a real number or infinity,\n",
      "it yields ``nan`` and sets the `invalid` floating point error flag.\n",
      "\n",
      "For complex-valued input, `log1p` is a complex analytical function that\n",
      "has a branch cut `[-inf, -1]` and is continuous from above on it.\n",
      "`log1p` handles the floating-point negative zero as an infinitesimal\n",
      "negative number, conforming to the C99 standard.\n",
      "\n",
      "References\n",
      "----------\n",
      ".. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n",
      "       10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/\n",
      ".. [2] Wikipedia, \"Logarithm\". http://en.wikipedia.org/wiki/Logarithm\n",
      "\n",
      "Examples\n",
      "--------\n",
      ">>> np.log1p(1e-99)\n",
      "1e-99\n",
      ">>> np.log(1 + 1e-99)\n",
      "0.0\n",
      "\u001b[0;31mClass docstring:\u001b[0m\n",
      "Functions that operate element by element on whole arrays.\n",
      "\n",
      "To see the documentation for a specific ufunc, use np.info().  For\n",
      "example, np.info(np.sin).  Because ufuncs are written in C\n",
      "(for speed) and linked into Python with NumPy's ufunc facility,\n",
      "Python's help() function finds this page whenever help() is called\n",
      "on a ufunc.\n",
      "\n",
      "A detailed explanation of ufuncs can be found in the \"ufuncs.rst\"\n",
      "file in the NumPy reference guide.\n",
      "\n",
      "Unary ufuncs:\n",
      "=============\n",
      "\n",
      "op(X, out=None)\n",
      "Apply op to X elementwise\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "X : array_like\n",
      "    Input array.\n",
      "out : array_like\n",
      "    An array to store the output. Must be the same shape as `X`.\n",
      "\n",
      "Returns\n",
      "-------\n",
      "r : array_like\n",
      "    `r` will have the same shape as `X`; if out is provided, `r`\n",
      "    will be equal to out.\n",
      "\n",
      "Binary ufuncs:\n",
      "==============\n",
      "\n",
      "op(X, Y, out=None)\n",
      "Apply `op` to `X` and `Y` elementwise. May \"broadcast\" to make\n",
      "the shapes of `X` and `Y` congruent.\n",
      "\n",
      "The broadcasting rules are:\n",
      "\n",
      "* Dimensions of length 1 may be prepended to either array.\n",
      "* Arrays may be repeated along dimensions of length 1.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "X : array_like\n",
      "    First input array.\n",
      "Y : array_like\n",
      "    Second input array.\n",
      "out : array_like\n",
      "    An array to store the output. Must be the same shape as the\n",
      "    output would have.\n",
      "\n",
      "Returns\n",
      "-------\n",
      "r : array_like\n",
      "    The return value; if out is provided, `r` will be equal to out.\n"
     ]
    }
   ],
   "source": [
    "np.log1p?"
   ]
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