Derivator.ipynb

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   "source": [
    "## Exercise for the course [Python for MATLAB users](http://sese.nu/python-for-matlab-users-ht15/), by Olivier Verdier"
   ]
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      "Using matplotlib backend: MacOSX\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
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    "%pylab\n",
    "%matplotlib inline"
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    "A numerical derivative of a function $f$ is a formula of the type\n",
    "\\\\[\n",
    "f'(x_0) \\simeq \\frac{f(x_0+h/2) - f(x_0-h/2)}{h}\n",
    "\\\\]"
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   "source": [
    "Implement a function `derivator` which returns the derivative *function*."
   ]
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    "collapsed": false
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   "source": [
    "def derivator(f, h):\n",
    "    def df(x):\n",
    "        return (f(x+h/2) - f(x - h/2))/h\n",
    "    return df"
   ]
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   "cell_type": "code",
   "execution_count": 3,
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   "source": [
    "msin_ = derivator(cos, 1e-10)"
   ]
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   "execution_count": 4,
   "metadata": {
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   "source": [
    "assert(allclose(msin_(0), 0))\n",
    "assert(allclose(msin_(pi), 0))\n",
    "assert(allclose(msin_(pi/2), -1.))"
   ]
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   "cell_type": "code",
   "execution_count": null,
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