{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Scientific Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A lot of computational algorithms are expressed using Linear Algebra terminology - vectors and matrices. This is thanks to the wide range of methods within Linear Algebra for solving the sort of problems that computers are good at solving!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Within Python, our first thought may be to represent a vector as a list. But there is a downside: lists do not *naturally* behave as vectors. For example:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 2, 3, 4, 9, 16]\n" ] } ], "source": [ "x = [1, 2, 3]\n", "y = [4, 9, 16]\n", "print(x+y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we cannot apply algebraic operations or functions to lists in a straightforward manner that matches our expectations.\n", "\n", "However, there is a Python package - `numpy` - that does give us the behaviour we want." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# numpy" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`numpy` is used so frequently that in a lot of cases and online explanations you will see it abbreviated, using `import numpy as np`. Here we try to avoid that - auto-completion inside spyder means that the additional typing is trivial, and using the full name is clearer." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`numpy` defines a special type, an `array`, which can represent vectors, matrices, and other higher-rank objects. Unlike standard Python lists, an `array` can only contain objects of a single type. The notation to create these objects is straightforward: one easy way is to start with a list:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 5 11 19]\n", "1\n", "[ 9 16]\n" ] } ], "source": [ "x_numpy = numpy.array(x)\n", "y_numpy = numpy.array(y)\n", "print(x_numpy + y_numpy)\n", "print(x_numpy[0])\n", "print(y_numpy[1:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the `array` objects behave as we would expect, and accessing elements is exactly the same as for a list. We can also perform other mathematical operations on the *whole vector*:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3 6 9]\n", "[ 0. 0.69314718 1.09861229]\n", "[ 4 18 48]\n", "[0 1 4]\n" ] } ], "source": [ "print(3*x_numpy)\n", "print(numpy.log(x_numpy))\n", "print(x_numpy*y_numpy)\n", "print((x_numpy-1)**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Think about these carefully. \n", "\n", "1. The first case is straightforward: all elements of the vector are multiplied by a constant. \n", "2. The second case applies a function to each element separately. `numpy` implements a version of most interesting mathematical functions, which are applied directly to each element.\n", "3. The third case is *elementwise* multiplication of the vectors. The first component of the answer is the product of the first component of `x_numpy` with the first component of `y_numpy`. The second component of the answer is the product of the second component of `x_numpy` with the second component of `y_numpy`. We cannot use the `*` operator to represent matrix multiplication, but must use a function (see below; note that there will be an operator in Python `3.5+`, but using it will mean your code is, for now, not widely useable).\n", "4. The fourth case shows a combination of cases above. The answer is given by elementwise subtraction of 1, then squaring (elementwise) that result." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Defining a matrix can be done by applying the `array` function to a list of lists:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 4 9]\n", " [16 25 36]\n", " [49 64 0]]\n" ] } ], "source": [ "A_numpy = numpy.array([ [1, 2, 3], [4, 5, 6], [7, 8, 0]])\n", "print(A_numpy**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that for higher rank objects such as matrices, the operations are still performed *elementwise*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To multiply a matrix by a vector, or a vector by a vector, in the standard linear algebra sense, we use the `numpy.dot` function:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14\n", "[14 32 23]\n" ] } ], "source": [ "x_squared = numpy.dot(x_numpy, x_numpy)\n", "A_times_x = numpy.dot(A_numpy, x_numpy)\n", "print(x_squared)\n", "print(A_times_x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we have appeared to multiply a matrix by a row vector, and get a row vector back. This is because `numpy` does not distinguish between row and column vectors, so everything appears as a row vector. (You could define a $n \\times 1$ `array` instead, but there is no advantage)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To actually check the *shape* and *size* of `numpy` arrays, you can directly check their attributes:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3\n", "(3,)\n", "9\n", "(3, 3)\n" ] } ], "source": [ "print(x_numpy.size)\n", "print(x_numpy.shape)\n", "print(A_numpy.size)\n", "print(A_numpy.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`numpy` contains a number of very efficient functions for working with arrays, for finding extreme values, and performing linear algebra tasks. Particular functions that are worth knowing, or starting from, are\n", "\n", "* `arange`: constructs an array containing increasing integers\n", "* `linspace`: constructs a linearly spaced array\n", "* `zeros` and `ones`: constructs arrays containing just ones or zeros\n", "* `diag`: extracts the diagonal of a matrix, or build a matrix with just diagonal entries\n", "* `mgrid`: constructs matrices from vectors for 3d plots\n", "* `random.rand`: constructs an array of random numbers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear algebra" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`numpy` also defines a number of linear algebra functions. However, a more comprehensive set of functions, which is better maintained and often more efficient, is given by `scipy`:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy import linalg" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.33333333 0.66666667 0. ]\n", "27.0\n" ] } ], "source": [ "print(linalg.solve(A_numpy, x_numpy))\n", "print(linalg.det(A_numpy))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to solving linear systems and computing determinants, you can also factorize matrices and generally do most linear algebra operations that you need. The [scipy documentation](http://docs.scipy.org/doc/scipy/reference/) is comprehensive, and has a [specific section on Linear Algebra](http://docs.scipy.org/doc/scipy/reference/linalg.html), as well as a [section in the tutorial](http://docs.scipy.org/doc/scipy/reference/tutorial/linalg.html). Johansson [also has a tutorial on scipy in general](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-3-Scipy.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Working with files" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Often we will want to work with data - constants, parameters, initial conditions, measurements, and so on. `numpy` provides ways to work with data stored in files - either reading them in or writing them out. A list of \"[File I/O routines](http://docs.scipy.org/doc/numpy/reference/routines.io.html)\" is available, but the two key routines are [`loadtxt`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html#numpy.loadtxt) and [`savetxt`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.savetxt.html#numpy.savetxt).\n", "\n", "As a simple example we take our matrix `A_numpy` above and save it to a file:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "numpy.savetxt('A_numpy.txt', A_numpy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then check the contents of that file (you should open the file on your machine to check):" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.000000000000000000e+00 2.000000000000000000e+00 3.000000000000000000e+00\r\n", "4.000000000000000000e+00 5.000000000000000000e+00 6.000000000000000000e+00\r\n", "7.000000000000000000e+00 8.000000000000000000e+00 0.000000000000000000e+00\r\n" ] } ], "source": [ "!cat A_numpy.txt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can read the contents of that file into a new variable and check that it matches:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ True True True]\n", " [ True True True]\n", " [ True True True]]\n" ] } ], "source": [ "A_from_file = numpy.loadtxt('A_numpy.txt')\n", "print(A_from_file == A_numpy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many Python plotting libraries depending on your purpose. However, the standard general-purpose library is `matplotlib`. This is often used through its `pyplot` interface.\n", "\n", "This is a quick recap of the basic plotting commands, but using `numpy` as well." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from matplotlib import pyplot" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true, "nbconvert": { "hide_code": true } }, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import rcParams\n", "rcParams['figure.figsize']=(12,9)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bNv61EslGQcYbMF6RHswhA+Fh/jg9GLNIBwoy3oCCnB7MIQPhYf44PSjI6UBB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\nJ84DtAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = numpy.linspace(0, 2.0)\n", "y = numpy.sin(numpy.pi*x)**2\n", "pyplot.plot(x, y)\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plotting interface is straightforward, but the results are not particularly nice. The following commands illustrate some of the ways of improving the plot:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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//QZPPAEjRlgXl8GDQ0ckIpI8li6FtWuhZcvQkUisJXoNdjvgF+/9fO/9ZmAo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\nX36x7kJBoRpshypWVHItIlZL2LOnneJ8/HHX0QTT6tXwySc2mEdEJOz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = numpy.linspace(0, 2.0)\n", "y = numpy.sin(numpy.pi*x)**2\n", "pyplot.plot(x, y, marker='x', markersize=10, linestyle=':', linewidth=3, \n", " color='b', label=r'$\\sin^2(\\pi x)$')\n", "pyplot.legend(loc='lower right')\n", "pyplot.xlabel(r'$x$')\n", "pyplot.ylabel(r'$y$')\n", "pyplot.title('A basic plot')\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Whilst most of the commands are self-explanatory, a brief note should be made of the strings line `r'$x$'`. These strings are in LaTeX format, which is *the* standard typesetting method for professional-level mathematics. The `$` symbols surround mathematics. The `r` before the definition of the string says that the following string will be \"raw\": that backslash characters should be left alone. Then, special LaTeX commands have a backslash in front of them: here we use `\\pi` and `\\sin`. We can also use `^` to denote superscripts (used here), `_` to denote subscripts, and use `{}` to group terms." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By combining these basic commands with other plotting types (`semilogx` and `loglog`, for example), most simple plots can be produced quickly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Saving figures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you want to save the figure to a file, instead of printing it to the screen, use the [`savefig`](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.savefig) command instead of the `show` command. For example, try:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vbX/9a74cys9Fjiq4uXNh6VLYcsvcSbQ6jY2wxRYwb176+pVXYM8982aSKtF7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\niERJQV/jnJyexe6PRJIC2fe44HhEIjoeIhIsKrAraM4cb95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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = numpy.linspace(0, 2.0)\n", "y = numpy.sin(numpy.pi*x)**2\n", "pyplot.plot(x, y, marker='^', markersize=10, linestyle='-.', linewidth=3, \n", " color='b', label=r'$\\sin^2(\\pi x)$')\n", "pyplot.legend(loc='lower right')\n", "pyplot.xlabel(r'$x$')\n", "pyplot.ylabel(r'$y$')\n", "pyplot.title('A basic plot')\n", "pyplot.savefig('simple_plot.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then check the file on disk (you should open the file on your machine to check):" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OE5u2bJGeeMKsPjlnju00AKpj8WKzef1ZZ5n9/OCtBg3MKpR33y2tWMFG2MCJ\noIXvgW3btqljx46Hv+7QoYNycnKOes9tt92mK6+8Uu3bt1dhYaFeeeUVr2MiAjRrZjtBbHr/fenT\nT6UbbpAuv9x2GgDVcf/90v/9n5SbK3XtajtN7ImLk/78Z9spAH+iAIsQoVBI/fr105IlS7Rx40Zd\nfvnlWr16tZo2bWo7GhD1xo83LwD+UqeO1K+f7RQAcGIowDwQHx+vLVu2HP5669atio+PP+o9c+bM\n0X333SdJOvPMM9WlSxetX79eCQkJx/2+Bx988PDxkCFDNGTIEFdyAwAAIHYsXbpUS5cutR0j6rEP\nmAdKS0vVo0cPLV68WO3atdPAgQM1f/589erV6/B7Jk6cqDZt2mjy5MnasWOHEhISlJubq5YtWx71\nu9iPIbqkpEgFBWYSczAo1a9vOxEAACdu927z5zHNFvgc7U53sAiHB+Li4jRz5kwNGzZMvXv31pgx\nY9SrVy/Nnj1bTz31lCTp/vvv17Jly3TOOefo8ssv17Rp044rvhB9Zs2SHnxQuvhiKTvbdhqU27fP\n0aRJ07jpABFo5UpHl1wyTatWOay8FwHmz5f695dOO0165hnbaQB/YATMZ+iJiB6bN0tnnGGOGzeW\n9uxhBMy2xx6T0tKkjIx0NW4c0nPPDdeoUewNAESSkSPT9cYbIUnD9ZvfJGn6dNuJYtuzz0o33WSO\nk5Kk9HS7eVC7aHe6gxEwwJKWLaWXXpJuvlkaO5biKxK895700UeOHCekAwdSNH16OjceIII4jqP3\n3gtJSpGUrosu4vy07bLLzJ9xcVJJCfuBAdVBAQZY0qyZKbyeflr6xz9sp4Fk9gGTTM+6FFBeXpLS\n0hbZDQXgsIULQyorM+enlKSCAs5P2zp3lkIhMwfsX/9iPzCgOijAAOA/Ro50dOaZIUnDJEnhcBKj\nYECEcBxHf/lLSEVFw/7zN0l64gnOz0gwbJjUvLntFIB/UIABwH8sXx5Sfn5577rEKBgQOVJTQ8rL\n4/wE4H8UYIAFdNhGHsdxNGNGSOHwsKP+nlEwwD7OTwDRhAIMsOAXv5CGDJGmTJG2bbOdBlJlvevl\n6GUHbOP89Ifdu81KsmvX2k4CRDYKMMCCv/9duucead8+KRy2nQZV9a6Xo5cdsIfz0x+mTTMLcjz1\nlLRrl+00QGRjHzCfYT8GoPYtXJiu8eMDCoer3vOrceN0zZsXYF8wwGOcn/6wZ4/UpAlbqkQb2p3u\nqGs7AAAQTYZXAAAgAElEQVTYlpmZp4SEQgUCWZKkAwekhg3NvjblHMdRRkZTGniAx449PyvD+Wlf\nixa2EwD+wQiYz9ATAQAAAC/Q7nQHc8AAD5WUSN99ZzsFAAAAbKEAAzy0fLnUurXUr580fbrtNADg\nD2VlthOgurZskebMMQtNAagcc8AADy1ZYvYAW7VKSkiwnQY/ZudO6aOPpLZtpQsvtJ0GiF2DBkn1\n6kkXXSTdfbfUqpXtRKjMwYNS9+7SoUPm6+Rk6fTT7WYCIhEjYICHdu6sWNjh0kvtZsEPe/ZZU3iN\nHi09+aTtNEDs2rtXysmRMjKkqVNZZS+SNWokJSZWfP3++/ayAJGMETDAQzNnSn/6k/Thh0ffpBB5\nzj234vijj8zIZeDYPWABuG7FCnP+Sebx7WbN7ObBD7viCqlBA9PJOHCg7TRAZGIVRJ9hNRrAGyUl\nUrt2Us+e5rGnBx+k5x2wZccOMwJWp4501VW20wCxg3anOyjAfIYTAfBOSYlUl+cEAAAxinanO5gD\nBgBVoPgCAAC1jQIM8MD+/VJqqrR7t+0kAAAAsIkCDPDAt99K//iHdMYZ0vXX204DAP6wZYsUDttO\ngRN16JD03HPmfpeQULGICgCDAgzwwJlnSu++K+3aJT38sO00OBE7dkivvirddpv0r3/ZTgPElhkz\nzOb1gwaZ/RPhD3FxZt/LwYOl+fNtpwEiD4tw+AyTIQFvTZtmVl+7+GLpZz+Tuna1nQiILQcOSNnZ\nZmsINmAGvEW70x0UYD7DiQAAAAAv0O50B48gAgAAAIBHWGQZcNkzz0iBgHTZZVLnzrbTAADgrZIS\nszBH48a2kwCRgREwwGWPPCLddJNZATE723YaAIh8ZWVSWpq0c6ftJDgZoZB05ZVm7t7MmbbTAJGD\nAgxw0VdfOdq0aZokR02aSP362U6Emti3T/r736Vx46Srr7adBoh+n30mjRoltW0rXXKJ7TSoqe3b\npTfflPbvd/S3v01jLhHwHzyCCLjo/fdDatAgXz17LlK3bkmqX992ItTEoUPShAnmuF496eBBqVEj\nu5mAaPbhhxXHrVvby4GTc+ml5Uchbd6cr9TURRo9OslmJCAiMAIGuMRxHD39dEhFRSlq2DBdCxbQ\n8+dXrVtLPXua4+JiHiUF3NaqlXThhVL9+tJFF9lOg5rq3FmaM8fRueeG5DgpmjEjnVEwQCxD7zss\nB+ofCxema/z4gMLhJDVunK558wIaNYqeP7+aPduMfF10kdmPqC7PDwCu+/57s4BD06a2k6CmuBf6\nG+1Od1CA+Qwngj84jqPExGRlZ6dICkhyFAwmKysrRYFAwHY8AABcx73Q/2h3uoNHEAEXpKaGlJc3\nXOaGI0kB5eUlKS1tkc1YAAB4hnshUDkKMKCWOY6jGTNCCoeHHfX34XCSpk/n+XcAQPTjXghUjQIM\nqGXH9/iVo+cvWjiOVFhoOwUQnR58UHr1VSk/33YSnAzuhUDVKMCAWlRVj185ev78be1a6dprpfh4\n6bbbbKcBok9ZmVlw44UXpIQEswUE/Id7IfDDWITDZ5gMGdmOXO2pKqwC5V9bt0qLF5uVELt0kZhD\nDrjHcTjH/Ip7YfSg3ekOFlIGalFmZp4SEgoVCGRV+R7HcZSR0ZSbjg916CCNH287BRAbKL78i3sh\n8MMYAfMZeiL8gZ5bAADgd7Q73cEcMKCWFRdLZ5wh/b//J/3pT1Jpqe1EAADYV1goLVkihUK2kwB2\nMQLmM/RERL4VK8zkcUnq1EnavNluHrijuFjKzZUGDGC0E6gN778vPf20dPHF0n/9l9Stm+1EqE0Z\nGdIll5iFVgYMkD75xHYiVAftTncwAgbUsuzsiuNBg+zlgHtGj5ZatJDOP1/6979tpwGiQ3q6NH++\nNGGCNGuW7TSobX36mOJLklatkg4csJsHsIlFOIBaNmGCdNll0rJlZgQM0aewsKLx8NFHZkVEACfn\no48qji+6yF4OuOPUU6W+fc0TA4MGmWtokya2UwF2UIABtSwQkHr0MC9Ep4svNnMYOnVinyKgtsyc\nKX3wgSnELrzQdhq4YcUKqV492ykA+5gD5jM8iwvYt2OHVFTECCcAILrR7nQHBZjPcCIAAADAC7Q7\n3cEiHEAt2rGDZecBAABQNQowoBZNnCi1aiUlJUkbNthOAwCRz3HMC7Fh3z6z4uUDD5g/gVhEAQbU\nooULpS+/NIVY69a208Bthw5JWVnSs8/aTgL41yefSPHx0rXXSi++aDsN3Pbcc9K0aWZJ+nbtbKcB\n7GAOmM/wLC4QGb7/3jQezjhDGjJESklhQ2agJhxH2rTJrH5YXCzdfLPtRADK0e50BwWYz3AiAJGj\nsFBq2tR2CgAA3EG70x0UYD7DiQAAAAAv0O50B3PAgFrgOGYD0QMHbCcBAABAJGMEzGfoiYhMX3wh\n9eghxcVJl14qLVpkOxEARL5du6RTTpHq1bOdBF4qKJDeeENatkwqKZFmz7adCFWh3ekORsCAWrBs\nmfmztFSqX99uFnhr717p7belSZOklSttpwH85fbbpRYtpGHDpOxs22nglX37pF/8Qpo1S3rhBbP4\nChBLKMCAWhAXJ/XubY4HD7abBd66917piiukqVNNIQagehzHrHx44ID03nuMgsWSDh2kTp3McTgs\nrV5tNw/gNR5B9BmGgiPb3r1mb5OWLW0ngVdeeEG67jpJctS583Rt2vRbBViPHvhRu3Y56tp1ugoK\nfqtmzQLas8d0ZiE2/PnPUlGRNGiQ6bhs3Nh2IlSGdqc76toOAESTU0+1nQBeu/hiKSFBats2pCVL\n8pWWtkijRiXZjgVEvKVLQ5Ly9be/LVL37kkUXzFm0iTbCQB7eAQRAE5Cp05STo6jXbtCOngwRdOn\np9NbCPwIx3E0Y0ZIBQUpmjs3XZdeyjkDIHZQgAHASUpNDSkvb7ikgPLykpSWxjKYwA/hnAEQyyjA\ngJM0d65Zdn7fPttJYEN5T344PEySFA4nMQoG/ADOGVSmrMx2AsA7FGDASdq2TfrjH6X4eCk/33Ya\neO3InnyDHn3gh6SmhrR6NecMpBUrpF/9yqwifO+9ttMA3mEVRJ9hNZrIVVws1a0rsQBe7HAcR4mJ\nycrOTlFFY1KSHAWDycrKSmFFROAInDM40sqVUlaWWQmxb19zD0Vkod3pDkbAgFpSrx7FV6w5fvSr\nHD36QGU4Z3Ck/v2liROlfv0ovhBbKMAAoAaOncdyLOa1AEfjnAEAgwIMAGqg6p78cvToA0finAEA\ngwFfoIZ27JCmTDHPrg8eLHXubDsRvJSZmaeEhEIFAllVvsdxHGVkNGVjZkCcM/hhjiN9+63Upo3t\nJID7WITDZ5gMGTnS0qRRo8zxxRdLH3xgNw8ii+MwJxCoTFqa1KiRFAxKLVvaTgPb9u6VbrxRWrZM\nKi2Vdu7k2hlJaHe6g0cQgRpatqzieNAgezkQOd5/X7rhBqlXL+mvf7WdBohM990njRghtWolffKJ\n7TSwrXlzaelS81TJrl3Shg22EwHuowADaujqq6XJk6XLL5eGDLGdBpFg/XqzMff69WZpZQBH271b\n+uILc1yvntn/CbGtTh0pMdEcn3KKtGmT3TyAF3gE0WcYCgYi16efmmWVJalrV2njRrt5gEjzzTfS\nn/4kLV9uCrCMDNuJEAk+/VSqX988PVCHoYGIQrvTHRRgPsOJAESukhLz6OEFF5hCrFEj24mAyFVW\nRmMbiHS0O91BAeYznAgAAADwAu1Od9D3BAAAAAAeYR8w4AQ5jjR0qNSjh1n9cOxY8+w6AACoubIy\n6fPPpYMHK+bTAtGIETCgBv7yF6lPH7PseF26MVCFb74x+9oAkEIhadIk6bXXzF5PwJE++EBq3Vr6\nyU+kRYtspwHcxRwwn+FZXCDy3Xmn9PrrZoPRTz6RzjzTdiLAvrVrpdRUswLi8OHSHXfYToRIUlgo\nFRRI7drZToIj0e50BwWYz3AiAJFv6VLTiOjenVXeAAD+RbvTHRRgPsOJAAAAAC/Q7nQHfbPACSgr\nM4twAAAAADVBAQacgMWLpfh4afRo6aWXbKcBACC6HDwoZWRIs2bZTgK4h/XbgBOwbJmUn28mkp9+\nujRunO1EiGRlZdK6dVLz5lLHjrbTAPYkJ0v790vBoHTVVdJpp9lOhEhUWmrmz+7bZ76+6ioW5UB0\nYgQMOAErV1YcDxpkLwci3xNPSC1amO0KnnnGdhrAHseR5s8358Gvf222ZwAqExcnnXNOxddZWfay\nAG5iBAw4AWlpZinlZcvMZsxAVVq2ND3+kpSdbTcLYNOWLRVFV7NmUq9edvMgsg0ebPaJGzRIat/e\ndhrAHayC6DOsRgP4w8aNUrduUtu2Zs+juXNtJwLsKCoynRDLl0sHDkgPPWQ7ESJZWRnbd0QS2p3u\noADzGU4EwB8cR9q8WercWQoEbKcBAODE0e50BwWYz3AiAAAAwAu0O93BIC9QTRs2OJo0aRoXIgAA\nPOA43HcRnSjAgGo4cEBKTAxp6tR8DR68iM2YAaAauFaiJg4elJYskcaNC+mxx/KVlrbIdiSgVlGA\nAdXQuLGjM88MSUrRnj3pkmhVoHqKi6UVK8ymogcO2E4DeGvWLKl7d+kXv5AW0YZGNW3aJN1/v6MP\nPgipqChF06enMwqGqEIBBlRDampIeXnDJQW0ZUsSvXGotsGDpfHjzR5yhYW20wDeuvVW6bXXpEsv\nleqy8Q2q6eyzpeTkkPbtM/fdvDzuu4guLMLhM0yG9J7jOEpMTFZ2doqkgCRHwWCysrJSFGB5O/yI\n4mKpXj3bKQDAP7jvRg7ane5gBAz4EUeOfhn0xqH6KL4A4MRw30W0owDzSHp6unr27KmzzjpLU6dO\nrfQ9S5cuVb9+/dSnTx8NHTrU44SojOM4+tOfQgqHhx319+FwEs+kAwBQyxzH0YwZ3HcR3SjAPFBW\nVqbbbrtNoVBIa9eu1fz587V+/fqj3rNv3z5NnDhRb731ltasWaMFCxZYSosjpaaGtGbNkb1w5eiN\nA4Afsnu3VFZmOwX85vjRr3LcdxE9KMA8kJOTo+7du6tz586qV6+exowZo9dff/2o97z00ksaNWqU\n4uPjJUmnnXaajag4Qnkv3KFDwyr9Pr1xqK69e80KcH/4g/Thh7bTAN64+mrptNOk4cOlzz6znQZ+\nUNXoVznuu4gWFGAe2LZtmzp27Hj46w4dOmjbtm1HveeLL77Q7t27NXToUJ1//vl6/vnnvY6JY1Td\nC1eO3jhUz/TpUlKSNHmyWREOiHalpVJOjrRnjxQKSc2a2U4EP+C+i1jBorARoqSkRCtXrtSSJUt0\n4MABJSYmKjExUd26dbMdLWZlZuYpIaFQgUCWJLOaXVycVOeIbgvHcZSR0VSjRiVZSgk/uOCCiuPl\ny+3lALyydavUsKHZeqFdO6lDB9uJ4AfH3nd37ZIKCqTmzc2rXj3uu4gOFGAeiI+P15YtWw5/vXXr\n1sOPGpbr0KGDTjvtNDVs2FANGzbUxRdfrNzc3EoLsAcffPDw8ZAhQzRkyBC3ose0Rx/9re0IiBLB\noNS/v5SYKF10ke00gPs6d5Z27pS++soUY6wcjurgvmvf0qVLtXTpUtsxoh77gHmgtLRUPXr00OLF\ni9WuXTsNHDhQ8+fPV69evQ6/Z/369br99tuVnp6uoqIiBYNBvfLKKzr77LOP+l3sxwAAAAAv0O50\nByNgHoiLi9PMmTM1bNgwlZWV6aabblKvXr00e/ZsBQIB/frXv1bPnj2VlJSkc845R3Fxcfr1r399\nXPEFAAAAwN8YAfMZeiK84zjS449L554rJSRITZvaTgQAQOxyHB5n9RrtTnewCiJQhUOHpE2bpPvu\nk7p3Nxd+AMAP+/prKTdXKimxnQTR4KuvpAkTzDzaq66ynQaoHRRgQBUaNJAee0zKymISOWpHerr0\nu99Jl11mFigAotGnn0pjxkgtWkgpKbbTwO8aNJB69JCefFJ6+WXbaYDawSOIPsNQMOBfd91lllK+\n4AJpyBCpUSPbiQD37NkjHTwotW9vOwmAmqLd6Q4KMJ/hRAAAAIAXaHe6g0cQAQAAAMAjFGBAJb74\nQrrnHmnhQjP/CwAA2Ld7t+0EwMmjAAMq8f770vTp0tVXm3k7AIAfFwpJS5ZIBQW2kyCalJSY+3Gn\nTlK7dlJRke1EwMmhAAMqkZNTcRwM2suB6LNkiXTLLWZ/uTlzbKcBatf995tVPk85RfroI9tpEC3q\n1jWra379tdkiJjfXdiLg5FCAAZX4+c+lSZOkoUOlwYNtp0E0+eQT6amnpNWrpcxM22mA2nPwoLRq\nlTl2HKlPH7t5EF3KO0MbNZI2b7abBThZrILoM6xGA/jbhx9Kl1xijvv0kfLy7OYBasu330q//720\nfLl5ZGzNGtuJEE3WrDGfqz59zIgYvEG70x0UYD7DiQD424ED0uOPm73AEhKkZs1sJwJqX0kJjWQg\nGtDudAcFmM9wIgAAAMALtDvdwRwwAAAAAPAIDwgAR3Ac6YorpK5dzYTfa66R6te3nQoAAEjmPr1p\nk1n0pXdv22mAmmEEDDjGpEnSGWdI6elSXJztNIh2u3ebBgXgZxkZ0gMPSG+/LX33ne00iFZLlkht\n20oXXij985+20wA1xxwwn+FZXCA6/O//miJ/+3bp88+l9u1tJwJqbu1aaf58swLikCFmPzCgtu3f\nb14dOthOEjtod7qDAsxnOBGA6PDOO6YR0bs3I60AgMhEu9MdPIIIABaMGCGdc45Up46jSZOmcYOD\nrzkOn2MAqC4KMACwKDU1pFmz8pWWtsh2FKDG+BwDQPVRgAH/sXq1dOaZ0tix0ty5ttMgFjiOoxkz\nQiooSNH06emMHsCX+BzDa4cOSTk50quv2k4C1AwFGPAf2dnSV19JL78svfmm7TSIBampIeXlDZcU\nUF5eEqMH8KVrrw1pxQo+x/DGvn1S8+Zmq5jrrzfFGOA3FGDAf3z8ccVxMGgvB2KD4zi6++6QwuFh\nkqRwOInRA/iO4zh6442QSkr4HMMbp5xSsWpsUZF5egXwGwow4D9mzjRF2MyZZjNmwE2pqSF9840Z\nNTAYPYD/PPdcSEVFfI7hrQsukLp2NVMG6tWznQY4cSxD7zMsBwr4n+M4SkxMVnZ2iioarpLkKBhM\nVlZWigKBQFU/DkQEx3F0wQXJysnhcwxvFRdTeHmFdqc7GAEDAI8dOffraIwewD9SU0Nas4bPMbxH\n8QW/owADAA+VrxhXPvfrWMyhgR/wOQaAmqMAAyTt2SPRToAXqh79KsfoASIfn2MAqLm6tgMAkeDS\nS6UdO6SBA6VnnpFatbKdCNEqMzNPCQmFCgSyqnyP4zjKyGiqUaOSPEwGVB+fY9gWDkuffGK2kOna\nVRo1ynYioPpYhMNnmAzpDseRNm82F/LRo6W4ONuJEEtKS6V160xj4vrrpTo8mwAfWLhQmjzZbNsx\napT0k5/YToRYMn++9Nhj5vN31VXS0KG2E0Un2p3uoADzGU4EIPp062aKrmBQevJJs8koEOmKi6U1\na0zHVZs20s9+ZjsRgNpGu9MdFGA+w4kARJ9wWGrc2HYKAACORrvTHRRgPsOJAAAAAC/Q7nQHMw0Q\n00pLpU8/NY/SAAAAAG6jAENM++wzqX9/6ZRTzOIbAIAfd/AgW3fAvnBYSkuTJk2Sbr/ddhqg+ijA\nENOys82fBw+a0TDAloIC6f33palTpc8/t50G+GETJ0qnny5deaW0fLntNIhVhYVmBc6pU6Wnn+Zp\nFvgHBRhiWmmp1KmTOQ4G7WZBbJswwexHN2mStIi9axHhsrOlnTulN9+k0Qt72rSRzjjDHBcVSatX\nW40DVBsFGGLaLbeY/b/y86Wbb7adBrFs4MCK4/KRWSASff+9tH27OY6LM49xA7bccIP029+afem6\ndbOdBqieurYDAJHg9NNtJ0CsS0yUzjnHFGLDh9tOA1StYUPpu+/Mo7Kffy41aWI7EWLZAw/YTgCc\nOJah9xmWAwUAAIAXaHe6g0cQAQAAAMAjFGCIWW+9JS1bZuYzAAAAAF6gAEPMyskx+4a0bMmy3wBQ\nHfv3S+vXS2VltpMAFT7+WPrf/zVzaWfMsJ0G+HHMAfMZnsWtfQcPSvXrm9W8AJtKS80S9NnZZpPw\nV16RAgHbqYAKOTnStddKe/ZIv/qVNH267USA2UPx44/NdjIDBkhNm9pOFD1od7qDAsxnOBGA6FVW\nJo0cKfXpY1ZDvPJKOgYQmXbulHbvlnr2tJ0EgJtod7qDAqwaxowZo6ZNm2rQoEEaPHiwevToYS0L\nJwIAAAC8QLvTHRRg1bRhwwYtX75cWVlZWrx4sUaOHKkpU6aofv36nubgRAAAAIAXaHe6gwKsGrKz\ns+U4ji644AJJ0oIFC3TuuefqrbfeUnJysqdZOBFOXmmp9Ic/mOfEg0GpbVvbiQAAQG05dMjM7cbJ\no93pjrq2A/jBe++9p3r16unRRx9VkyZN1KlTJ7Vu3Vrdu3e3HQ01sH69KcAkU3zl57PQAQD8mDVr\npL17pf79pcaNbacBjrZpk3T//WYRo3btpI8+sp0IqBoFWDVcddVVKigo0L333nv47/7xj3+oa9eu\nFlOhpnJyKo6DQYovRJ7XX5f+9S/TkHjqKem882wnAqQnnjCfx7g46e9/l26+2XYioEKjRtJLL5nj\n7dul4mKpXj27mYCqUIBVQ+/evY/7u5u58/hWnz6OEhKmq1693+qSS6i+EHlefFFasMAcL19OAYbI\nkJ1t/iwtleh/RKQ5/XSpUydpyxappMTRxInTNXv2bxWglxURiI2YEXM2bw7p88/zdffdi+TxFD6g\nWoLBiuMjR2wBWxxHOv98qVcvMwKWkGA7EXC8v/3NdFo991xIL7+cr7S0RbYjAZViEQ6fYTLkyXEc\nR4mJycrOTlEwmKysrBR6xxBx1qyR0tLMXmADB0otW9pOBFQoLGSjW0Qu7vO1i3anOyjAfIYT4eQs\nXJiu8eMDCoeT1LhxuubNC2jUqCTbsQAAQC3gPl+7aHe6g0cQETMcx9GMGSGFw8MkSeFwkqZPT+fC\nAgBAFOA+D7+gAEPMSE0NaeXK4ZLKH0UIKC8viWfEAQCIAqmpIeXlcZ9H5KMAQ0wo7xUrLh521N/T\nOwY/OHTIdgLEsl27pEceMVsj7N1rOw1QuWNHv8pxn0ckogBDTDi+V6wcvWOITPv3m32WzjlHqmQn\nDMAzxcWm8PrDH6Rrr7WdBqgc93n4CYtw+AyTIU/ckSsiHX9hliSHlZIQcUpLzaa3AwdKfftK9evb\nTgSY5ei5TCLScJ93D+1OdzAChqhXda9YOXrHEHni4qQJE6QBAyi+EDlouyIScZ+H39S1HQBwW2Zm\nnhISChUIZFX5HsdxlJHRlKVqAQDwGe7z8BseQfQZhoJrprRUCgalPn3Mn7/+tRlhAAAA0aekRFq7\nVjp4ULrgAttp/It2pzsowHyGE6Fm1qwx82gkqV07ads2HqWBfziOtHWr1L49HQfwVnq6FAqZuYgX\nXSR16GA7EfDjMjOlYcOkcFgaNMh8jZqh3ekO5oAhJmRnVxwHgxRf8I9bbjGFV6dO0mef2U6DWPPm\nm9Jjj0njxknPPms7DVA93bub4kuSVq5kKw9EHuaAISaMGyf17Cnl5Ehnnmk7DVB9334rffONOc7O\nrhjJBbyQk1NxHAzaywGciDZtpDPOMI8hBoNmG4U2bWynAipQgCEmNGokDR5sXoCfBIPSP/8pNW3K\nJrjw3pQp0rJlpvg//3zbaYDqW7VKOuUU2ymAyjEHzGd4FheILdu3S3v2mBFc5n8BALxEu9MdFGA+\nw4kAAAAAL9DudAeLcCDqMfkWAAAAkYICDFHvhhvMZNxrrzXL0QMAgOhXVGTmLz7+uJSbazsNUIEC\nDFHv+efNPjY/+QkTcuFfZWXSF19IH35oOwliwe7dUv/+0q23Si+8YDsNUDOTJpmtPD77zFxDgUjB\nHDCf4VlcIPZs3GhWoGvWTBo50vTmAm4qLpZWrDCjB99+Kz38sO1EwIlzHPb9PFm0O91BAeYznAhA\n7CkpkXbtkk4/3XYSAEAsod3pDgown+FEAAAAgBdod7qDOWCIaps2SaWltlMAAAAABiNgPkNPRPUV\nF5tFN+rWNfNn3npLatTIdioAiGzMm0E02bdPysgw8xnbtZMmTLCdyF9od7qDETBErTVrpIMHpYIC\nacMGii/438GD0rJlZhEOVvSCW15+WerUSbr6aik11XYa4OQsWyZdcYU0ZYo0Z47tNIBR13YAwC07\ndphFC775RgoGbacBTl737tK2beZ42DCpZ0+7eRCdcnKkr782r169pFGjbCcCam7gwIrjVauk77+X\nGja0lweQKMAQxYYPl7Zvl7ZsMZsxAn7Xr19FAZaTQwEGd6xaVXF8ZOMV8KNWraTRo6X4eDpjETko\nwBDVAgGpc2fbKYDaEQxKX35pGsV8ruGW994zj3Dn5EiDBtlOA5y8BQtsJwCOxiIcPsNkSCB2sTgC\nAMBLtDvdwSIcAOATFF8AAPgfBRii0iefmNehQ7aTAO5wHEeTJk2jZxK1is8VALiPAgxRKStL+uUv\npRYtpLfftp0GqH2pqSHNmpWvtLRFtqMgisyezecK0emDD6R77pEuvlgKhWynQaxjDpjP8CzuiSko\nkOrUkZo0sZ0EqB3hsJSV5eiGG5L19dcpCgaTlZWVogDPJ+Ikff+9o+bNk1VcnKIWLZK1a1eK6tTh\nc4Xo8MwzUn6+WczoggukZs1sJ/IH2p3uoADzGU4EILatXCmNG5eur74KqLg4SY0bp2vevIBGjUqy\nHQ0+t3BhusaPDygcTlKDBul68UU+V0Cso93pDh5BBAAf6dfP0amnhlRcPEySFA4nafr0dG6QOCmO\n42jGjJDCYfO5KiricwUAbqEAAwAfSU0NKS9vuKTyR8MCystLYs4OTgqfKwDwDgUYos4//mEm2O7Z\nYxHqGlsAACAASURBVDsJULuOHaUoxygYTgafK8QiPtawiQIMUaWoSJo4URo+XGrZUtq923YioPYc\nP0pRjtEK1ByfK8SKlSulG2+UeveWbrvNdhrEMgowRJXc3Iq9v7p2NUUYEA2qGqUox2gFaoLPFWLJ\n7t3SnDnSZ5+Z7WoAWyjAEFWaNzcjYAkJ0kUX2U4D1J6qRynKMVqBE8fnCrHk/POl8h071q0zT80A\nNtS1HSBWpKen684771RZWZluuukm3XvvvZW+7+OPP9agQYP0yiuv6Gc/+5nHKf2vZ09p5kxzTIct\noklmZp4SEgoVCJhu27VrpV27zPe6d5fatzejGRkZTVk6HNVW/rn697+ztHOn9P33Ut++Rz89wOcK\n0eKUU6SnnpJ69JAGDJAaNLCdCLGKfcA8UFZWprPOOkuLFy9W+/btdf755+vll19Wz549j3vf5Zdf\nrkaNGunGG2+stABjPwYAkrRwoZnPkJgoDR7M47aoHTt3micJGja0nQRAJKDd6Q5GwDyQk5Oj7t27\nq3PnzpKkMWPG6PXXXz+uAHviiSc0evRoffzxxzZiAvCR0aPNC6hNbdrYTgAA0Y85YB7Ytm2bOnbs\nePjrDh06aNu2bUe9Z/v27Xrttdc0YcIEehoAAACAKMUIWIS48847NXXq1MNfU4SduHnzpPXrpeD/\nb+/O46Oq7v+Pv4eACCKIgCxhEUUkWJRNUhAFXAiKRREUHvSLttpia/1Ji1+3tta9WMAgiLhh/Qpf\n1hLEDTJQIWhiIKAsqSkosgRSBAtUlkAgmfP7436TEJJACDP33Dvzej4eeTCTmYxvJ3Nvzuecc89J\ndBbgYEoWAACozPffS+edJ9WtazsJYg0FmAvi4+OVm5tbcn/nzp2Kj48v85w1a9Zo+PDhMsbo3//+\ntxYvXqxatWpp0KBB5V7v6aefLrndt29f9e3bN1LRfSUhQdqyRXr9dSkUkgYPtp0IcE8oJNVgTgPO\nkDHSyy87CxJ0705DFLHh+eed5ej37pU++kjq3dt2Iu9IS0tTWlqa7RhRj0U4XFBUVKTLL79cn3zy\niZo3b64ePXpo9uzZSkhIqPD5P//5z/WTn/yERTgAnNL27dL48c5+Ns2aSR9/bDsR/ObIEemJJ5zP\nUF6etGNH6TLdQLRas8YZ+br8cjquTod2Z2QwAuaCuLg4TZkyRf379y9Zhj4hIUFvvPGGAoGARo0a\nVeb5Af76AaiC2rWltm2lESOkrl1tp4Ef1anjjIBJUmEhxRdiQ/futhMg1jEC5jP0RAAAAMANtDsj\ng4FXAAAAAHAJUxARFX76U+fi8cREadgw6fzzbScCAABeFgpJmzZJcXFS+/a20yCWMAXRZxgKLu/I\nEal+fef6BUnat09q2NBuJsCGPXvYSBdVt3atNGuW1LOn1KuXs5ALECvmzJF+9Svphx+k++6Tpk2z\nncibaHdGBlMQ4Xtr15YWX5dfTvGF2GKMdPfdUps2UtOmTgcEUBWpqdKECdKQIdKTT9pOA7ireXOn\n+JKkVavsZkHsYQoifK9zZ2nZMucEyh42iDWBgLMBefFWgytXSrfcYjcT/GHlytLbPXvaywHY0K2b\nswR9o0bSpZeylyLcRQEG36tbV+rXz/kCYlHPntLq1c6S4nl5ttPALx54wNnAPjPTmYIIxJJ69Zy9\nFOPj2X4B7uMaMJ9hLi6Ak339tXTwoHTllVKtWrbTAACiBe3OyKAA8xkOBAAAALiBdmdkMNsVvhYK\n2U4AAAAAVB0FGHztmWecvTtGjpTS022nAQAAflJY6Kym/Prr0u7dttMgVlCAwdf+9CcpJUW67jqp\ndm3baQC7jJG2bi27uh1wssOHnYVbRo+W5s61nQawa9Ag6b/+S8rKco4NwA1cA+YzzMUFUJGNG0tX\nAh02THr5Zbt54F3HjztF+sqV0o4d0uTJthMB9hQWSjVZE7xStDsjgwLMZzgQShlj9MQT4zV27CMK\nsIYsYtyxY9K//uVsyMzhAABnhjZFxWh3RgZTEOFbKSlBTZ26SwsWLLEdBbDunHOkiy+m+AKA6qBN\nATdRgMGXjDF68cWgDh5M1vjxqfTOAACAajHGaMIE2hRwDwUYfCklJagvvxwgKaDVq5P0+uv0WAHA\n6dCuBMqbMSOodeucNsW6dUmMgiHiKMDgO8YYjRsXlDH9JUmhUJL++ld6rADJWWBhzRrp1VeloiLb\naeA1s2ZJl1wi/fSn0ocf2k4D2GeM0ZNPBlVQ4LQpCgqSGAVDxFGAwXdSUoL6xz+cnipHQDk59FgB\nktShg3T11dKDD0o5ObbTwGsyM52tCmbNkr780nYawL6UlKD27CnbpsjOpk2ByKIAg68Uz9M+cqR/\nme/n59NjBUjSVVeV3mY/MJzsiy9Kb/fsaS8H4AXFbYqjR2lTwF0UYPCVlJSgsrNP7KkqRo8VIDmN\n6osvloYPl9q2tZ0GXrNihbPh7KRJUmKi7TSAXbQpYAv7gPlMLO/HYIxRz55jtGpVssqfLCXJKDFx\njDIzk9nDAzGrqEiKi7OdAgC8jTZF1cRyuzOSGAGDb1TeU1WMHiuA4gsATo82BWyqaTsAUFUZGdnq\n3v2Q8vMzZYx03nnlN501xig9vZ6GDEmyExIAAHhecZsiEMis9Dm0KRApTEH0GYaCpbfekl56Sfru\nO+mdd6TBg20nAgBvM0bauVNq2bJ8xxUAR0aGlJoqpadLL7wg9eplO5F9tDsjgwLMZzgQSn3/vVSz\nptSwoe0kgLccOyatXu0sOZ6fL/3pT7YTwbY9e6ROnZxz5oAB0ttv204EeE9ysrRvn9S7t/NVr57t\nRPbR7owMCjCf4UAAcDrbtklDhzorIvbrJ91xh+1E8AJjnD3Atm6VbrjBdhoAfkC7MzIowHyGAwEA\nAABuoN0ZGayCCAAAAAAuoQCDr7z+urR8uXT4sO0kAAAgmoVCthMgWjEF0WdieSj4hx+cBTeMkWrX\nlvbvl+rUsZ0KALwtL6/sIhwAKrdxozR5srMi4lVXSdOn205kVyy3OyOJETD4xsqVTvElSR07UnwB\np7NokfTEE85CHPv3204DW/73f6WuXaUGDaS//MV2GsDbDh6UXntN2rBB+vRT22kQregLg280bSrd\nf7/TK3XttbbTAN731FPSmjXO7VWrnOXHEXtWrnT+zc+XGjWymwXwus6dpbp1neNlxw5p926n/QGE\nEwUYfKNzZ+caMIl52UBV9OxZWoBlZlKAxaoWLaRWrZzGZM+ettMA3larlvTqq86m5YmJ0vnn206E\naMQ1YD7DXFwAVfX3v0uLFzuN7t69pWbNbCeCTXl5UvPmUg0uPgBQRbQ7I4MCzGc4EAAAAOAG2p2R\nQT8YAAAAALiEa8DgC888IxUWOtOorr3WuUAWAAAgkvbuda47b9LEdhJEE0bA4AvXXeecAP/8Z2nr\nVttpAH9i8ZrYkp8vTZzorIJYUGA7DeAvs2c7W960bSt9/LHtNIg2XAPmM8zFBXAm9u6VXnjBWQXx\n+PHSVRER/b7/3tmKIDPTWXjjiy9sJwL84+uvpcOH2cCcdmdkUID5DAcCgDORny9NmuSshNi9u1Sv\nnu1EsKGwMLYbkQCqh3ZnZFCA+QwHAgAAANxAuzMyuAYMAAAAAFxCAQZP27tX6txZ+s1vpL/9zXYa\nAAAQS4yRNm+Wli+3nQTRhAIMnvb559L69dLUqdJLL9lOA/ibMUajR49TURHTSaLdJ58Y9eo1Th9+\naLR3r+00gD/l5krNm0uXXSb99KdOMQaEAwUYPC09vfR27972cgB+N2aM1Lx5UJMn79LkyUtsx0GE\nvfRSUJmZuzRo0BJNnmw7DeBP8fHSkSPO7V272AYH4UMBBk/74x+lpUudpZQHD7adBvCvb7812r07\nKClZr7ySykXVUcwYo08/dX7XUqp+/GN+10B1xMU5K8g2aCDdcouzqiwQDixKC087/3zpxhudLwDV\nd/75QUkDJAW0c2eSFixYoiFDkmzHQgSkpARVWOj8rmvUSNKePUsk8bsGqmPmTKlhQ2cvPSBc+DgB\nQJQzxignJyipvyTp+PEkjR/PKFg0MsZowoSgCgqc33UolKTXXuN3DVRXo0YUXwg/PlIAEOVSUoLa\ntMkZEXEElJ3tjIIhuqSkBJWdze8aALyMAgyexVxr4OwVj4jk5/cv8/38fEbBog2/awDwBwoweJIx\n0o9+JF1xhTRqlHT4sO1EgD+VHxEpxshItOF3DURGKCTl5EhvvcWepAgPCjB4UiAgff21NGOG1KWL\nVLeu7USA/1Q2IlKMkZHowe8aiJwPPpBuvVX69FOpdm3baRANAoazsa8EAgH+gAKokvnzU3XPPQHl\n51e+Al7duqmaPj3Aiog+x+8aiBxjnI7hWES7MzJYhh4AolRGRra6dz+kQCCz5HtHjkjnnlvamDDG\nKD29Ho1yn6vod30yftdA9cRq8YXIYQTMZ+iJAAAAgBtod0YG14DBcw4elL791hnyBwAAAKIJBRg8\nJxiU2rWTmjeXnnrKdhoA8IejR20nAKJXKCSlp0svvigNH04nMc4OBRg8JyPD+Xf3bqmw0G4WIBoZ\nI331lfTqq1Jm5ZcMwWd+8hPpssukX/5S2rrVdhogugQC0u23S088Ic2dK23aZDsR/IwCDJ7UoIHz\nb+/ednMA0ej555199h58UJo503YahMOxY07n1ebN0rRpUk2W2ALCKhCQrrmm9H56ur0s8D9O0fCc\niROll15yeugvucR2GiD69OxZenvFCns5ED5ff106JerSS6VWrezmAaLR7bdLjRs7hVj/irfcA6qE\nVRB9htVoAJytw4edqWq9ekn9+kkPPMAyy9GgoEDKypL+8x9nOiIAnC3anZFBAeYzHAgAwiGWNxYF\nAFQN7c7I4BowAIhBFF8AANhBAQbPKCqS/vpXaeNGlncFAABAdKIAg2ccOCAtXy7dfLPUpYvtNADg\nD199Je3caTsFEBv27nVWkh0wgIU4UH0UYPCMhg2lGTOc/WtYmQ2IvG++kV55RRoyRFq82HYaVNd7\n7zmdVu3aSZ9/bjsNEN0CAemHH6Rf/5ptPFB9LMLhM1wMCSBcJk2S/vEPqU8fKSlJatLEdiJUVygk\n5eRI8fFOZxYAhAPtzsigAPMZDgQAAAC4gXZnZDAFEQAAAABcUtN2AEByrvlatUrq3Vvq1k2qXdt2\nIgAAgFM7fFiqU0eqwZAGzgAfF3jC3LnSY49J11wjvfii7TRAbGKWib8cPy69+qpzHV8oZDsNEFue\nf166+mqpQQMpO9t2GvgNBRg84bPPjKRxkox697adBogd+/ZJzz4rXX+90wEC//jiC+nBB6VOnZyG\nIAD3rF8vrVkjFRUZPfLIOK6TwhmhAIMnXHddUDVr7lKLFkuUmGg7DRA7atVyCrDly6WVK52CDP5w\n4nYdP/qRvRxALCrtLA5qxYpdWrBgic048BkKMFhnjNEXXwRVWJisVq1Sdd559CIBbjn/fKl7d+e2\nMVJWlt08qLorrpCGDpUaN5b69rWdBogtgwdLH31k1K1bUMeOJWv8+FRGwVBlLEPvM9G4HOj8+am6\n556A8vOTVLduqqZPD2jIkCTbsYCYsWCBdPSosx9YfLztNDhTxkiFhc5oJgD3xEL7JRrbnV5AAeYz\n0XYgGGPUs+cYrVqVLCkgySgxcYwyM5MVCARsxwMAACgnVtov0dbu9AqmIMKqlJSgsrMHyDl5SVJA\n2dlJzKUGAACeRfsFZ4MCDNYYY/Tkk0Hl5/cv8/38/CTmUgMAAE8yxmjCBNovqD4KMFiTkhJUbu6J\nvUfF6EUCbDl6VNq61XYKnEphoTRihDR5srRhA/u3AW4rP/pVjPYLqoYCDFZU1ntUjF4kwF3ffuvs\nBda4sfTUU7bT4FRCIWngQGcD5ocesp0GiC20XxAOLMLhM9FyMeSJKwdVJlpXFAK86NAh6bPPnM2Y\n69e3nQYAvCnW2i/R0u70mpq2AyA2ZWRkq3v3QwoEMit9jjFG6en1ouIEBnhdvXrSzTfbTgEA3kb7\nBeHACJjPRFNPRH6+VLeu7RQAAACoSDS1O72Ea8BgRSgkXXKJ1K2b9MQT0uHDthMBAABUz7/+Jb37\nrjR/vu0k8ANGwHwmWnoi1q6VunZ1bjdpIn33nVSD7gDAE/btc64H69eP68G8ZsoUacECqW9faehQ\nqWNH24kApKaWTuHu0UNatcpunnCKlnan19DkhRXZ2VJcnHP7xhspvgCv+K//clZCvP126dNPbafB\nyYJBaflyZ6XKjAzbaQBIUmJiaTtm9WqnEws4FRbhgBV33y3ddpuUliZddJHtNACKNWtWuq/UihXS\nrbfazYNSRUXOyGSxvn2tRQFwgoYNpd69pZo1pZtusp0GfkABBmsaNHCKMADe0aeP9PLLzvWZF19s\nOw1OFBcn5eQ4hfHq1VK7drYTASi2fDmzeVB1XAPmM8zFBRBJBQXOF9d+AQBod0YGBZjPcCAAAADA\nDbQ7I4PBUrguGJT277edAgAAAHAfBRhcdeyYNGmS1KaNc61JKGQ7EQB436FD0tGjtlMAOJUDB6RZ\ns6Sf/UwaNcp2GngZBZhLUlNT1aFDB7Vv315/+ctfyj0+a9YsXXXVVbrqqqvUu3dvZWdnW0gZeeec\nIy1aJO3ZIyUnc8Eq4FX79kkLF0q//a3TqIBdCxc62wP07SulpNhOA6Aie/ZI8+Y5e4E9+qjtNPAy\nrgFzQSgUUvv27fXJJ5+oRYsWuvrqqzVnzhx16NCh5DkrV65UQkKCGjRooNTUVD399NNauXJluddi\nLi4AN/TpI9Wp4zT477/fWWYZdh044Oz91bCh9OMf204DIBbQ7owMlqF3QVZWli677DK1adNGkjR8\n+HC9//77ZQqwH5/w1/THP/6x8vLyXM8JAMXS0qRAwHYKnKh+fenmm22nAACcLSaAuSAvL0+tWrUq\nud+yZctTFljTpk3TzfyVBWARxRcAAJHBCJjHLF++XO+8847S09NtRwm7jz925kffdJPUsqXtNAAA\nAJFTWCgZI9WqZTsJvIYCzAXx8fHKzc0tub9z507Fx8eXe96GDRs0atQopaamquEpLrh4+umnS273\n7dtXffv2DWfciJk0SVq61Lk9d65011128wCoGmOMnnhivMaOfUQBhsZcl5lpNHfueE2cyPsP+MHC\nhdL06dKyZdLbb0tDhthOVHVpaWlKS0uzHSPqsQiHC4qKinT55Zfrk08+UfPmzdWjRw/Nnj1bCQkJ\nJc/Jzc3VDTfcoBkzZpS5Huxkfr0Y8sgR58LxggLnfm6udMKsTAAetHu3s2rpu++mauXKoGbOHKAh\nQ5Jsx4opoZB0/vmpys8Pqk2bAVq9OklNmthOBeBUnnxSev555/aoUdIbb9jNczb82u70Oq4Bc0Fc\nXJymTJmi/v3764orrtDw4cOVkJCgN954Q2+++aYk6bnnntO+ffv0wAMPqEuXLurRo4fl1OF1/Lj0\n7LPSjTdKXbpQfAF+kJkp3Xuv0YoVQRUUJGv8+FT+ELtswwaj/PygpGTl5aWqUSPef8Dr+vcvvf2P\nf9jLAe9iBMxnoqEnIhRi/y/AD/btkxo1SpUUkJSkunVTNX16gFEwFz3/fKqeeiqgUChJcXGpmjuX\n9x/wuuPHpddec65579DB34saRUO704toBsN1FF+APzRsaHTRRUFJTndufn4So2AuMsboo4+CCoWc\n97+oiPcf8INataSHHpISEvxdfCFyaAoDACqUkhLUoUMD5IyASVJA2dlJWrBgic1YMSMlJajsbN5/\nAIg2FGAAgHKMMZowIaj8/P5lvs8omDt4/wEgelGAIeIefli6+25pxgxp/37baQBURfnRl2KMwriB\n9x+IDqGQtGaNtH277STwEgowRNyDD0q9ejn7YmzbZjsNgNOpbPSlGKMwkcX7D0SHN9+ULrrI6YTO\nybGdBl7CKog+w2o0ACJt/vxU3XNPQPn5la+2x4qIkcP7D0SHrVudBTlatrSdpPpod0ZGTdsBAADe\nkpGRre7dDykQyJTkLKn83XdS48ZSnTrOc4wxSk+vRwEQASe//xVt3cH7D3hf27a2E8CrGAHzGXoi\nAAAA4AbanZHBNWCImMJC5wsAAACAgwIMEbN8udSokTR4sDRvnu00AAAA7isokJYtk8aOtZ0EXsE1\nYIiYpUulAwec1Q9btZLuust2IgBnq7BQysiQLrxQ6tTJdproNHy4VFQk3Xab83X++bYTAaiuUEhq\n3Vras8e5f9dd0qWX2s0E+xgBQ8RkZ5fevukmezkAhMe8eVLTplLfvtKkSbbTRKdDh6T33pPmz5dG\njpT27rWdCMDZqFFDuvrq0vtLl9rLAu9gBAwRs2iR9PXX0pIlToMNgL+1aiXt2+fc/vBDZ5QmLs5u\npmiTliYdO+bcvvJK6eKLbaYBEA79+0ubNjn/duliOw28gFUQfYbVaADYEgpJzZs7+9oMGiS9+KJU\nv77tVNHFGGfD1g8+kJo0kX7xC9uJAJwtP3dW0e6MDAown+FAAGDTjh3OpqKBgO0kAIBIo90ZGRRg\nPsOBAAAAADfQ7owMFuFA2O3aJWVlOUPuAAAAAEpRgCHsNm2S7r1XuugiKTnZdhoA8IcvvnCuswMQ\nndLTpSeflHr1kn74wXYa2MQURJ/x01BwXp50+LDUvr3tJADCyRhp/XpnoYhdu6TXXrOdyP/275d6\n93aWnR8+XHr5ZduJAITb3XdL8fHOaoi9ezsLGnmdn9qdfkIB5jMcCABs27PHaTzcequzUXCfPrYT\nRY/Nm51VEAcNsp0EAGh3RgpTEBFWxhg9/vg4DlYgil10kbPHX3IyxVe4tWtH8QXEAtpLsY0CDGGV\nkhLU1Km7tGDBEttRAAAAPIn2UmyjAEPYGGP08MNBHTyYrHHjUunVAQAAOIkxRhMmOO2l8eNpL8Ui\nCjCEzV//GlRu7gBJAWVlJWnOHHp1gFhx/LjtBP71179KaWlSYaHtJAAibcsW6dZbg8rKctpL2dlJ\njILFIAowhIUxRi++GJTU//++k6RJk+jVAaLZli3S738v/ehH0ujRttP405Ej0v/7f1K/fs61dXv2\n2E4EIJKOHDFatCgoY5z2Un5+EqNgMYgCDGGRkhJUXp7Tm+OgVweIdjt2SGPHSl995SxJT/vhzC1b\nJuXnO7cvusj5AhC9cnKCkmgvxToKMJy14rnMR470L/N9enWA6HbNNVLDhs7tvXudETGcmdatpQce\nkFq2ZPVDINoZY/TSSyfOFnLQXoo97APmM17cj2H+/FTdc09A+flJ5R6rWzdV06cHNGRI+ccA+N+0\naVKTJtKNN0rnnWc7jX8Z40xHrFvXdhIAkeLH9pIX253RgALMZ7x2IBhj1LPnGK1alazS4fQyz1Bi\n4hhlZiYrEKjocQAAgOjm1/aS19qd0YIpiDgrKSlBZWefOJf5ZMxtBgAAsY32Ek5U03YA+FtGRrbi\n4w9px45MXXSR1KyZVKdO2ecYY5SeXs9zw+oAAABuyMjIVvfuhxQIZJb5fkGBtHu31Ly5VLMm7aVY\nwRREn/HiULAx0pdfSjNnOhflDxliOxEAG/bskb74Qrr5ZttJvG/LFunOO52FNwYPlq680nYiAG4b\nPVqaMUO64w7pqaekVq1sJyrPi+3OaEAB5jMcCAC85uhRZxGOf/xDGjhQ+t//lTx0CYMnFRZKGRnO\n8v1HjkhTp9pOBMBtW7dKLVpItWvbTlI52p2RQQHmMxwIALwoI0Pq3t3bDQkAwJmh3RkZFGA+w4EA\nAAAAN9DujAxWQUS1ffONtHq1cw0YAAAAgNOjAEO1JSdLPXpIl18uffyx7TQA4A/ff287AQAv+de/\nnDZVt27S2rW208ANFGColmPHpHnznNvffCPVr283DwBv2LHDWVDizTdtJ/GmggLp0kulK66Qfv97\n5z6A2Pboo9LDDzsrSs+aZTsN3EABhmo5cMBZPvn886XWrZ3l5wHEtowM53zwm99IL77I9OSKrFgh\nHTwo5eRIc+ZI55xjOxEA20aMKL29YAHnzlhAAYZqadxYeucdZ/PAjz6SavBJAmLe1VeXjoZv3eos\nS4+ytmyRzj3XuX3bbSzXD0C66Sbp9tuladOcvRQ5L0Q/VkH0GVajAeBld98tffedU1wMG+Z01qCs\n/Hzp738vnYoIAF5FuzMyKMB8hgMBgJcZU9p7a4zRE0+M19ixjyhAly7vBwDfod0ZGUwcAwCEzYl1\nRUpKUFOn7tKCBUvsBfIQ3g8AgEQBhjP03XdSz57S5MnO9V8AUBFjjCZMCOrgwWSNH58a8z2ovB8A\nqurAAWnZMtspEEkUYDgjjRtLTz3lbMD8y1/aTgPAq1JSgsrOHiApoOzspJgf9Zk2Lai1a3k/AFSu\noEC66y6pVSvpjTdYDTGacQ2Yz3hpLu6J13oAQLFQyOjyy8do8+ZkSQFJRomJY5SZmRyT1z4ZY9Sl\nyxitX8/7AeDU5s2TbrxRuvBC20kcXmp3RhNGwFBttBsAVGTBgqC2bnVGexyxPeqTkhLUN9/wfgA4\nvbvu8k7xhcihAAMAhE3xtU5FRf3LfD8/Pykmr30qfj/y83k/AAAOCjBUiTHS9u22UwDwuhOv/Sor\nNkd9eD8AACejAEOVrFolXXyxdM010rvv2k4DwIsqG+0pFmujPsYYjRvH+wHgzB08KM2YIf3mN7aT\nIBIowFAlM2c6/37+ufTpp3azAPCmykd7isXWqE9KSunKhxWLrfcDQNUcOya1bSvdfbc0dar01Ve2\nEyHcatoOAH84dEiKi5OKiqSf/tR2GgBelJGRre7dDykQyCz53q5d0ubNUigkNWsmtW9vlJ5eT0OG\nJFlM6o5ly7IVCh2S5LwfnTqVv7jemNh5PwBUzTnnSNdfL/3tb879mTOlP//ZbiaEF8vQ+4zN5UC/\n/1567z3pvvucYgwATufTT6U+fZzbdepIO3fGzgpfaWnSrbdKhw9LCQlOLzarxwKoig8+kP7wtd7b\nkwAAFElJREFUB6fTe8QIqXVrOzlYhj4yKMB8hgMBgJ8YI3Xt6kypeeghZ0pNnTq2U7nnP/+R3nlH\nio93lpcGgKrwyl6rtDsjgwLMZzgQAPjN7t3SRRd5ozEBAKg62p2RQQHmMxwIAAAAcAPtzshgFUSc\n0rPPSrNnS/n5tpMAAADEpuPHpT17bKdAuFCA4ZTat5emT5datpT27bOdBkA02L9fysuznSJynn9e\neu01Z/ENADgbW7Y4e4G1aCG98ortNAgXCjCc0vDh0uLFzjLSsbJyGYDI2LZNeuAB6ZJLpI8+sp0m\ncvr0kZYuldq0kXJzbacB4GfHjjnFV1aW9NxzttMgXCjAUCFjjB5/fFzJvF+KLwBna98+qXFjKSdH\nuv9+22ki59prpQULpLVrpVatbKcB4GcdOjjL0bdtW75tBv+iAEOFUlKCmjp1lxYsWGI7CoAo0bWr\nc11p8+a2k7ijVStWfgQQPrTNogcFGMoxxmjChKAOHkzW+PGp9LQAAABYRNssulCAoZz584PKyhog\nKaB165I0bx49LQBwOps3204AIFqlpASVnV3aNmMUzN/YB8xnIr0fgzFGCQljtGlTsqSAJKOrrx6j\nVauSFWAuDYAwOX5cmj9f+vvfpWnT/D9Vb/VqqUcP6frrpYcflm65xXYiILpcfPHF2r59u+0YUatN\nmzbatm1bue+zD1hk1LQdAN6SkhLUli1OD4sjoK++cnpahgxJshkNQJQoLJQ6diwdMfr5z6Xeve1m\nOluTJzv/LlsmxcdTgAHhtn37dgqBCKKT3V1MQUSJ4vnFx4/3L/P9/Pwk5hsDCJuaNaW+fUvv+31v\nG2OkUEiq8X9/UUePtpsHAOBtFGAoceL84rICys5mvjGA8HnoIalZM+mZZ0pHj/wqEJBmzpS2bnWK\nyW7dbCcCAHgZ14D5TKTm4hpj1LOnc61X+QJMkowSE8coM5NrwQCER2GhMxoGAKfDtUiRVdn7y/se\nGYyAQZL0P/9T2ehXMUbBAIQXxRcAIBbx5w+SpNdfz5Z0SJ06ZerCCyt+jjFG6en1WIwDAAAgTDZv\n3qzs7GxlZ2fr1ltvVdeuXcs8vnXrVrVt29ZSOkQCUxB9JnJTEKUPPpAefVT68EOpffuw/ycAoFIF\nBdJHH0l33OGfJekzMqTf/95ZdOO226S4ONuJgOgVzVPhJk6cqGuuuUY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"text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('simple_plot.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The type of the file is taken from the extension. Here we have used a `png` file, but `svg` and `pdf` output will also work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Object-based approach" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get a more detailed control over the plot it's better to look at the objects that `matplotlib` is producing. Remember, when we talked about classes we said that it is an object with attributes and methods (functions) that are accessed using dot notation. Here are steps to completely control the plot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we define a figure object. We do not have to define the figure class - it is defined within `matplotlib` itself, along with a lot of useful methods. We call the constructor of the figure object in the same way as in the previous section, by calling `pyplot.figure()`. We can and will control its size (the units default to inches) by passing additional arguments to the constructor:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = pyplot.figure(figsize=(12, 9))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will then define two axes on this figure. The numbers refers to the positions of the edges of the axes with respect to the figure window (between 0 and 1):" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "axis1 = fig.add_axes([0.1, 0.1, 0.8, 0.8]) # left, bottom, width, height\n", "axis2 = fig.add_axes([0.4, 0.7, 0.2, 0.15])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will then add data to the both axes:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "axis1.plot(x, y)\n", "axis2.plot(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will then set the range of the second axis:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "axis2.set_xbound(0.7, 0.8)\n", "axis2.set_ybound(0.3, 0.7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we'll see what it looks like:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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e+PnPzQr4GWfYTuhfBQUFFBQU2I5RLYWFkJZmzuiW6BgyxEyW/dGPbCcRP1LR\nLTHx5pvmSDQN/Yiebt3MsJXVq6Fdu5o/TkpKCiUlJZVfl5aWkpKSctRtzjiimrvyyiv52c9+xrZt\n28K6b4Uji26pnbp14aab4HvfM4XX44/DiBGmMBg+HM47z3ZC/zn2B8GRI0faCxMmHRUYfVdfDcOG\nwVdfwdln204jfqP2EokJtZZEX0KCWe2ubYtJTk4Oq1evZsOGDZSXlzN+/HgGDRp01G02b95c+fui\noiJc1yU5OTms+0r0OA707Wv2T8ydC4cOmSMIv/td04sqwaajAqOvYcNvWrlEqktFt0RdWZkZn3vp\npbaTBF8kiu7ExERGjx5Nbm4umZmZ5OXlkZGRwZgxYxg7diwAb7zxBp06dSIrK4u7776b11577aT3\nldg7/3x47DEzNKlPH7MK3qcPvPaaKcYlWEpKzObaHj1sJwk+DcqRmtKRgRJ1//wnzJoF//637STB\nt307tGxpPnwbNLCd5sT8cvxakBw+bKZdPv64Ofv7zjvhxz+GRo1sJ/MHr79mx4yBmTP1PhsLO3ZA\nSooZlFO/vu00Ems6MlA87f33zY5vib5GjUw7gc/2f0kMJCaaIzs//BD++19YvBjatDE9359+ajud\n1JaOCoyds86CLl3go49sJxG/UdEtURUKwQcfmB44iY1IT6eU4OneHV5+GZYuNQXEhRfCoEHm76qH\nF3PlBA4cMD9o5+baThI/LrnELCiJVIeKbomqJUvMDu8jjm6WKLvqKrPqpeJJTqVFC/jLX0y7ybe/\nDXfcYa6UvPCCKeTEH2bOhI4doXFj20nix6WXmsmfItWholui6v33tcoda507m4KpNi0D+fn5pKen\nk5aWxqhRo054u7lz55KUlMSbb75Z+b3WrVvTtWtXsrKy6NmzZ81DSMw0aGCOQVu6FB5+2IwQb90a\nHngAtmyxnU5ORUcFxl6fPrBsmenvFgmXim6JqunTdWpJrDmOOcXk7bdrdv9QKMTw4cOZNm0ay5Yt\nY9y4caxcubLK2913330MOGb8XUJCAgUFBSxYsICioqKahRArEhLgiitg2jR47z0oLTUTL2+91Vy1\nEm/SUYGxV68e9Opl9kiIhEtFt0TNwYPmsqcGDcZebYruoqIi2rdvT6tWrUhKSiIvL49JVcw9fvrp\npxkyZAjnHjP+znVdQppF7nuZmTB2rLli0qaNGS1+2WXw1lsaNe8l69bBtm2QnW07SfxRX7dUl4pu\niZp588x/Gj8KAAAgAElEQVRZwU2a2E4Sfy67DD7+GPbsqf59y8rKaHlEE35qaiplZWVH3Wbjxo1M\nnDiRn/70p8cdo+Y4Dpdffjk5OTk888wzNcov3tG4Mdx/v+n7/sEP4Pe/N/3D//hHzV5fEllTp5qr\nEwn6NI859XVLdemvqUSN+rntOfNMMyQjWqswd99991G93kcW3oWFhRQXF/P222/z97//nVmzZkUn\nhMRU3bpw880wf75ZAX/nHdP3fd99pg1F7NBRgfZ07w4bNmjfg4Svju0AElzvvw/33GM7RfyqODpw\n4MDq3S8lJYWSkpLKr0tLS0lJSTnqNvPmzSMvLw/Xddm6dStTp04lKSmJQYMG0bx5cwCaNGnCtdde\nS1FREX379j3ueUaMGFH5+/79+9NffUi+4DjQr5/5tWYNPP20ObN4wADz9z0oe2cLCgoo8PiB9/v3\nm57il16ynSQ+1alj/h4UFMANN9hOI36giZQSFfv2mbaSjRvNqqvE3rJlcPXVpufTqcbsrMOHD9Oh\nQwemT59O8+bN6dmzJ+PGjTvhOPehQ4cycOBArrvuOvbu3UsoFOKMM85gz5495Obm8sc//pHcYw4Q\n9vp0P6meHTvg2WfhqafMpL577oFrrjFFSVB48TU7bRr86U9m4q/Y8cQTsGKFmQgq8UETKcVzPv7Y\nHF2ngtuejh3NhrcqDh45qcTEREaPHk1ubi6ZmZnk5eWRkZHBmDFjGDt27HG3d46o6Ddv3kzfvn3J\nysqid+/eDBw48LiCW4LnrLPg3nth9WrzzyeegHbt4G9/05Fq0aSjAu3TZkqpDq10S1Tcf79ZXf3z\nn20niW8/+Qm0bw+/+IXtJEfz4qqhRNbcufD445Cfb3rB77oL2ra1narmvPiaTUuD114zA43EjlAI\nmjUzBwecd57tNBILWukWz9EmSm+ozdGBIrWRkwOvvgqLF5vhO717m5aTGTM0LTUSVq+G3buhWzfb\nSeJbQgJcfLFWuyU8Krol4nbuNJPtLrjAdhK59FIoKoJdu2wnkXiVmgoPPWSOHLziCrj9dnPqw8sv\nQ3m57XT+VXFUYHX2a0h0XHqpim4JT1hFt+M4VziOs9JxnFWO4/y6ij8/03GcyY7jLHQcZ4njOD+M\neFLxjQ8/NCcY1KtnO4mccYZZYdRZsmLb6aebdqfly03b2UsvfTNq/vPPbafzHx0V6B2XXGLeY3UF\nR07llEW34zgJwGhgAJAJ3Og4TvoxN7sDWOa6bjfgYuBvjuMEaN+6VIdaS7zlyivNqlh15Ofnk56e\nTlpa2lHncR9r7ty5JCUl8eabb1b7vhKfEhJMsfjuu+as740bISMDbrrJbMBW4XJqe/eaE0suu8x2\nEgGzVyExEVatsp1EvC6cle6ewKeu625wXfcgMB4YfMxtXKDh179vCHzpuu6hyMUUP5k+3VxuE2+4\n6iqzKhZuMRMKhRg+fDjTpk1j2bJljBs3jpVVHIESCoW47777GDBgQLXvKwLQqRP885/mWMucHLjl\nFjPU6fnnzbGjUrWCAjP2vVEj20kETIuPplNKOMIpulOAz474uvTr7x1pNNDRcZyNwCLg55GJJ37z\nxRdmQlePHraTSIUOHcx5yUuXhnf7oqIi2rdvT6tWrUhKSiIvL49JkyYdd7unn36aIUOGcO6551b7\nviJHatQI7r4bPvnEtJ688YY5CeLXvza94HI0tZZ4j44OlHBEqgVkALDAdd1LHMdpC7zrOE4X13V3\nH3tDTaELtg8+gIsuCtZQDL9znG+mU3bufOrbl5WV0bJly8qvU1NTKSoqOuo2GzduZOLEiXzwwQdH\n/Vk49xU5kYQE0w515ZXmdI5//MP8AH/hhTB8uGmniPeNg65r/i7/97+2k8iRLrnEDIUKhczrWIIj\nktNpwymNyoAjT59M/fp7RxoKPATguu4ax3HWAenAvGMf7MiiW4JH/dzedNVV8Mgj8KtfRebx7r77\nbvVrS1RVDNd54AFz9OAvfmFOOxk+3LShxOvgrVWr4MCB8H6AlthJSYHGjWHRIp2bHjTHLhCPHDmy\nxo8VTtE9F2jnOE4rYBOQB9x4zG02AJcBhY7jNAXSgLU1TiW+NX06/PSntlPIsS6+GPLyzHTAs846\n+W1TUlIoKSmp/Lq0tJSUlKM7yubNm0deXh6u67J161amTp1KnTp1wrpvBV31knCcfjr8+Mdw220w\ncyaMHg1/+AN873twxx1mE2Y0RHJ1K5KmTjVXAuJ9xd+LKlpMVHTLiYQ1kdJxnCuAJzE94M+6rvuw\n4zi3A67rumMdx2kOvAA0//ouD7muO66Kx9FEygArKTHn727erMtrXnTFFaZ4uf76k9/u8OHDdOjQ\ngenTp9O8eXN69uzJuHHjyDhBdTN06FAGDhzIddddF/Z9vTjdT/yjrAzGjIGxY81mzOHDYeBAc4JE\ntHjlNZubaxY2rr3WdhI51oQJ8OyzGkgWdFGfSOm6br7ruh1c123vuu7DX39vjOu6Y7/+/SbXdQe4\nrtvl61/HFdwSfB98YFZUVXB7U7jTKRMTExk9ejS5ublkZmaSl5dHRkYGY8aMYezYscfd3jliye1E\n9xWJpJQU03ayYQP86EcwahS0aWP+uXWr7XTRs3u3OVZRp0N5U//+5ijHgwdtJxGvCmulO2JPppXu\nQLvlFrPh6fbbbSeRqnz6KXzrW2aV0Palaa+sGkpwzJsHf/87TJxoxs0PH26uvEWKF16zU6bA44/r\nlAwvy842LVCayBxcUV/pFjkV19UmSq9r3970xy5aZDuJSORVnO/96aeQng7XXQd9+sArrwRn3LyO\nCvS+iumUIlVR0S0RsWqVaStp1852EjmZAQPMFECRoGrc2JzvvXYt3HefKcTPO89sviw79twtn3n3\nXfN3WLzr0kt1JUJOTEW3RETFKrfttgU5uW99y5wAIRJ0iYkweDC8957Zb7Jtmzlm74Yb4MMP/Tdu\nfuNG+OoryMy0nUROpm9fmDsX9u61nUS8SEW3RMT06Wot8YOLLoLCQjPAQSReZGSYPtv166FfPxg2\nDLp2Naef7NljO114Zs40BZ02qntbw4bmtfXRR7aTiBfpr6/UWihkVpJUdHtfs2bm8vupRsLn5+eT\nnp5OWlpalUNwJk+eTNeuXcnKyqJnz54UFhZW/lnr1q2P+jMRrzjzTLPBcsUKeOwx0yPdqpUZvLN6\nte10J/fhh+YHBvE+tZjIiajollpbvNgUcqmptpNIOC666OQtJqFQiOHDhzNt2jSWLVvGuHHjWLly\n5VG3ueyyy1i0aBELFizg2Wef5bbbbqv8s4SEBAoKCliwYIFGwIsnOY4ZKT9xojn1JCnJbLq8+moz\nfMaLV4JmzjR/d8X7tJlSTkRFt9Ta9Ok6N9ZPLrrIrJqdSFFREe3bt6dVq1YkJSWRl5fHpEmTjrpN\ngwYNKn+/e/duEo645u26LiEvVi0iVWjdGh5+2Az3GjIE7r8f0tLM0Xzbt9tOZ2zbZlpjNOnQH/r0\ngeXLzQRgkSOp6JZa01GB/tKvn1k1O9FGsrKyMlq2bFn5dWpqKmVVHPswceJEMjIyGDhwIM8991zl\n9x3H4fLLLycnJ4dnnnkm4vlFoqF+fRg6FObPh5dfNivg559v5g4sWWI3W2Eh9OplVuTF+047DXr3\nhhkzbCcRr6ljO4D428GDZgLXSy/ZTiLhOv98c3l9zZraHfF4zTXXcM011zBr1ix+97vf8e677wJQ\nWFhI8+bN+eKLL7j88svJyMigb9++x91/xIgRlb/v378//fv3r3kYkQhxHLNSeeBAAc2bFzB/vv1B\nJx9+qNYSv6no6x40yHYS8RIV3VIrc+ea8cvnnGM7iYTLcb5Z7a6q6E5JSaGkpKTy69LSUlJSUk74\neH379mXt2rVs27aN5ORkmjdvDkCTJk249tprKSoqOmXRLeI1R/4gePAg1K070lqWmTNNC4z4xyWX\nwBFbXUQAtZdILam1xJ9OtpkyJyeH1atXs2HDBsrLyxk/fjyDjlmuWbNmTeXvi4uLKS8vJzk5mb17\n97J7924A9uzZwzvvvEOnTp2i9u8hEgs22zr27DHtLb162csg1ZedDZ99Blu22E4iXqKVbqmV6dPh\n//0/2ymkuvr1M0emVSUxMZHRo0eTm5tLKBTi1ltvJSMjgzFjxuA4DsOGDWPChAm89NJL1K1bl/r1\n6/Of//wHgM2bN3PttdfiOA6HDh3ipptuIjc3N4b/ZiLBMns2dOtmes7FP+rUMe+zH3wA3/2u7TTi\nFY4bw7FcjuO4sXw+ia59+6BJE9i0yQwEEP8Ihcz/uyVLoEWL2D+/4zjovUD8xNZrdsQI2L9f7SV+\n9OSTsGyZGcIkwfH1e0GN5m+rvURqrLDQTN5Swe0/CQlmup1Gwot4m4bi+JeG5MixVHRLjamf299O\nNSRHROwqLzeb1W2fniI1k5kJu3bBhg22k4hXqOiWGtNQHH871ZAcEbFr/nxzwlCjRraTSE04jlmY\n0mq3VFDRLTWyY4fpVevd23YSqansbFi3zky7O1Z+fj7p6emkpaUxatSo4/588uTJdO3alaysLHr2\n7ElhYWHY9/WagoIC2xEqeSWLV3KAt7LEmka/+5+KbjmSim6pkQ8/NAV3vXq2k0hNJSWZY8iOqJcB\nCIVCDB8+nGnTprFs2TLGjRvHypUrj7rNZZddxqJFi1iwYAHPPvsst319IG049/UaLxV1XsnilRzg\nrSyxNnOm+rn97pJLzFVh7RsXUNEtNaTWkmCoGJJzpKKiItq3b0+rVq1ISkoiLy+PSZMmHXWbBg0a\nVP5+9+7dJCQkhH1fETm1UMhM+9VKt7+1aQN168Inn9hOIl6goltqRJsog6GqzZRlZWW0bNmy8uvU\n1FTKysqOu+/EiRPJyMhg4MCBPPfcc9W6r4ic3NKlcO650LSp7SRSG+rrliOp6JZq27IFSkqge3fb\nSaS2evWCxYvN1Lvquuaaa1ixYgUTJ07kd7/7XbXv7ziOJ36NHDnSegavZfFKDi9libUPP9Qqd1Bc\neqm5OiyiiZRSbR98YNoS6ujV43sNGpiz1ufM+ebKRUpKCiUlJZW3KS0tJSUl5YSP0bdvX9auXcu2\nbdvCvq8G44ic3MyZcNVVtlNIJFx8Mdx1l2kZStBSZ1zT/36pNvVzB0u/fkcfHZiTk8Pq1avZsGED\n5eXljB8/nkGDBh11nzVr1lT+vri4mPLycpKTk8O6r4icnOtqKE6QtGhh2oQWLrSdRGzTWqVU2/vv\nw5132k4hkXLRRfDYY998nZiYyOjRo8nNzSUUCnHrrbeSkZHBmDFjcByHYcOGMWHCBF566SXq1q1L\n/fr1+c9//nPS+4pI+NasgcREaN3adhKJlIq+7uxs20nEJieWl3kdx3F1WdnfNmyAnBz4/HNdJguK\n7duhZUv48kuzy15E7HruOXjvPXj1VdtJJFLefBP+9S94+23bSaS2HMfBdd0abfRQ2STVUnFqiQru\n4GjUCNq2heLiyDzeqYbjPProo2RlZZGdnU3nzp2pU6cO27dvD+u+schRWlrKJZdcQmZmJp07d+ap\np56qVY7aZKkQCoXIzs6OSKtObbLs2LGD73znO2RkZJCZmcmcOXOs5Hj88cfp1KkTXbp04aabbqK8\nvLzGOcLJsnPnTgYNGkS3bt3o3LkzL7zwQtj3rQkNxQme/v3NEZC1fKmK37muG7Nf5unEz77/fdcd\nM8Z2Com04cNd969/rf3jHD582G3btq27fv16t7y83O3atau7YsWKE95+ypQp7qWXXlqj+0Yrx6ZN\nm9wFCxa4ruu6u3btctPS0mqco7ZZKjz22GPuTTfd5A4cOLDGOSKR5Qc/+IH73HPPua7rugcPHnR3\n7NgR8xxlZWXu+eef7x44cMB1Xde94YYb3BdffLFGOcLN8uCDD7r33Xef67qu+8UXX7jJycnuwYMH\nI/qaPVLbtq67dGmtH0Y8JjvbdWfNsp1CauvrWrZGdbDWKyVsrqtNlEF17GbKmqrucJxx48Zx4403\n1ui+0crRrFkzunXrBsAZZ5xBRkZGrc4ar00WMCfAvP3225VTP2ujNll27tzJzJkzGTp0KAB16tTh\nzDPPjHkOgMOHD7Nnzx4OHTrE3r17adGiRY1yhJvFcRx27doFwK5duzjnnHOoU6dOVIZBbdwIX30F\n2goRPDo6UFR0S9g++cSMDm/TxnYSibSLLjLj4EOh2j1OdYbj7Nu3j/z8fK6//vpq3zeaOY60fv16\nFi5cSK9evWqUIxJZ7rnnHh555JGInBVdmyzr1q2jcePGDB06lOzsbIYNG8a+fftinqNFixb84he/\n4LzzziMlJYVGjRpx2WWX1ShHuFmGDx/O8uXLadGiBV27duXJJ5+s9r9HuCpaS9TCFzwakiP6ay1h\nq+jntjAnQqKsWTNo3NhMwYuVKVOm0LdvXxo1ahS7J61Gjt27dzNkyBCefPJJzjjjDCtZ3nrrLZo2\nbUq3bt2ObNOzkuXQoUMUFxdzxx13UFxcTIMGDXj44YdjnmP79u1MmjSJDRs2sHHjRnbv3s2rUd5x\nOG3aNLKysti4cSMLFizgjjvuYPfu3VF5Lg3FCa6+fWHePKjhz6oSACq6JWyFhfowCLKqRsJXV3UG\n64wfP/6oloHqDuWJVg4wBeaQIUO4+eabGTx4cI0yRCJLYWEhkydPpk2bNtx444188MEH3HLLLVay\npKam0rJlS3r06AHAkCFDKK7h7tva5Hjvvfdo06YNycnJJCYmct111/HRRx/VKEe4WZ5//nmuu+46\nANq2bcv555/PypUrI/qarTBzps7nDqozzoDMTFN4S5yqaTN4TX6hjZS+1rq1665caTuFRMvzz7vu\nDTfU7jEOHTpUubHswIEDbteuXd3ly5cfd7vt27e7ycnJ7t69e6t932jncF3Xvfnmm9177rmnRs8d\n6SwVCgoKar2RsrZZ+vXr537yySeu67ruiBEj3F/96lcxzzFnzhy3U6dO7r59+9xQKOT+4Ac/cEeP\nHl2jHOFm+dnPfuaOGDHCdV3X/fzzz93U1FT3yy+/jOhr1nVd98svXbdhQ9c9eLDGDyEed889rvvw\nw7ZTSG1Qi42UGo4jYdm4EXbtgrQ020kkWvr1g9/+1myYrWkLUTiDdQAmTpzIgAEDqF+//invG+sc\nhYWFvPLKK3Tu3JmsrCwcx+HBBx/kiiuuiHmWSKttlqeeeoqbbrqJgwcP0qZNG55//vmY5+jZsydD\nhgwhKyuLpKQksrKyKm8frSy/+93v+OEPf0iXLl0A+Otf/0pycjJARIdBFRZCr15QR5/MgXXBBfDy\ny7ZTiC0ajiNhmTABXngBpkyxnUSixXUhNRVmzIB27WynEYk//+//wZlnwu9/bzuJRMvGjdC1K2zZ\nov1RfqXhOBJ1H31kfkKX4HIcs9pd275uEakZDcUJvhYt4PTTYfVq20nEBhXdEhYV3fEhEpspRaT6\n9uwxpwfV4nRK8YkLLjCfqRJ/VHTLKe3fD4sXQ06O7SQSbZEakiMi1TN7tmk7iGJLv3iEiu74paJb\nTmn+fOjYERo0sJ1Eoq1jRzMNb+NG20lE4ouOCowfKrrjl4puOaXCQrWWxIuEBDPAQS0mIrGloTjx\no0sX2LABtm+3nURiTUW3nJL6ueOL+rpFYqu8HObOhQsvtJ1EYqFOHejRw7QUSXxR0S0n5boquuPN\nRRepr1sklubPN8d0nnWW7SQSK2oxiU8quuWk1qyB006Dli1tJ5FYyc6Gdetg2zbbSUTig/q544+K\n7vikoltOSqvc8ScpyRxbVlhoO4lIfND53PGnd28oKoJDh2wnkVhS0S0npaI7PmlIjkhshEIwa5aK\n7niTnGwmAC9dajuJxJKKbjkpFd3xSZspRWJj6VI491xo2tR2Eok1tZjEHxXdckI7dsDatdCtm+0k\nEmu9epmBSHv22E4iEmw6KjB+qeiOPyq65YTmzIHu3U2Pr8SXBg3MdLw5c2wnEQk2baKMXyq644+K\nbjkhtZbENx0dKBJdrquV7niWlmauKG/aZDuJxIqKbjkhFd3xTZspRaJrzRozKKV1a9tJxIaEBOjT\nBz7+2HYSiRUV3VKlw4dNa0GfPraTiC0XXmiOtCovt51EJJgqVrkdx3YSsUUtJvFFRbdUadkyaN4c\nGje2nURsadQI2raF4mLbSUSCSf3coqI7vqjoliqptURARweKRJOG4khODixaBPv3204isaCiW6qk\nolvArMJpM6VI5G3cCNu3Q0aG7SRi0+mnm9eArijGBxXdUiUV3QJmFa6w0EzNE5HImTkT+vY1m+kk\nvqnFJH7or7scZ/Nm+PJLSE+3nURsa9bM9PVrVLFIZOmoQKmgojt+qOiW43z8sTm1RCswAurrFokG\nbaKUChVFt+vaTiLRprJKjqPWEjmShuSIRNa2bbB+PWRl2U4iXtCypTmvfd0620kk2lR0y3FUdMuR\nKobkaBVGJDIKC6F3b1NoiTiOWkzihYpuOcqBA7BgAfTsaTuJeMX555sPhTVrbCcRCQb1c8uxLrjA\n/DAmwaaiW45SXAwdOsAZZ9hOIl7hOBoJLxJJ6ueWY114oVa644GKbjmKWkukKn376gNBJBL27YMl\nS3Q1UY7WrZu5mrhzp+0kEk0quuUoKrqlKr17w+zZtlOI+N+CBdCxI9SvbzuJeElSEnTvDnPm2E4i\n0aSiWyq5ropuqVqXLrB2rVZhRGpr9mzo1ct2CvEibaYMPhXdUmn9etO/26qV7STiNUlJ5nizuXNt\nJxHxt9mzzZUjkWOp6A4+Fd1SqWKV23FsJxEvUouJSO2p6JYT6dPHtJccPmw7iUSLim6ppNYSORkV\n3SK1U1YGe/dC27a2k4gXNW4MTZvC8uW2k0i0qOiWSiq65WR69zarMBqSI1Izc+aYv0e6mignohaT\nYFPRLQDs2gWrVmkssZxYairUratRxSI1VVF0i5yIiu5gU9EtABQVmYL7tNNsJxEvU4uJSM2pn1tO\nRUV3sKnoFkCtJRIeFd0iNXPoEMyfDzk5tpOIl2VkwNatsGWL7SQSDSq6BTBF94UX2k4hXterl4pu\nkZpYssQcx3rWWbaTiJclJJjFjY8/tp1EokFFtxAKmUKqTx/bScTruneHpUvNKGsRCZ9aSyRcajEJ\nLhXdwooV5qiic8+1nUS8rkEDc/lzwQLbSUT8RUW3hEtFd3Cp6Bb1c0u1qK9bpPpUdEu4evY0Cxvl\n5baTSKSp6BYV3VItFed1i0h4tm2DTZugY0fbScQPGjaE9u11RTGIVHSLim6pFq10i1RPUZE5tSQx\n0XYS8Qu1mASTiu44t3UrbN6sFRgJX7t2sHs3bNxoO4mIP8yebU7+EQmXiu5gUtEd5z7+2HwYaAVG\nwuU4ajERqQ71c0t1VRTdrms7iUSSiu44V1io1hKpPp3XLRKeUMj8gKqVbqmO1q3Na2fDBttJJJJU\ndMc59XNLTaivWyQ8q1bB2WdD06a2k4ifOI5aTIJIRXccKy+H4mKtwEj19expRlofOmQ7iYi3qbVE\nakpFd/Co6I5jCxdC27Zw5pm2k4jfNGoE551nplOKyImp6JaaUtEdPCq645haS6Q21GIicmoquqWm\nsrPhk0/MaVESDCq645iKbqkNFd0iJ7d7N3z6KXTtajuJ+NFpp0G3buacdwkGFd1xynV1conUjopu\nkZObPx+6dDHFk0hNqMUkWFR0x6nPPjOb4Nq0sZ1E/Coz0wzI2bbNdhIRb1JridSWiu5gUdEdpypa\nSxzHdhLxq8RE6N5dlz5FTkRFt9TWBReYIXahkO0kEgkquuOU+rklEtRiIlI111XRLbXXtCmccw6s\nXGk7iUSCiu44paJbIkHj4EWqVlJi/nneeXZziP+pxSQ4VHTHoT17YMUK0xogUhu9epmiW5c+RY5W\nscqtFj6pLRXdwaGiOw7NnWuOsKpXz3YS8btmzeCss8yxaCLyjdmzNe1XIkNFd3Co6I5Dai2RSFJf\nt8jx1M8tkZKZCZs2wdattpNIbanojkP6MJBIUtEtcrQDB2DxYujRw3YSCYLERMjJ0UlRQaCiO864\nrunB1WVPiRQV3SJHW7QI2reHM86wnUSComL/jPhbWEW34zhXOI6z0nGcVY7j/PoEt+nvOM4Cx3GW\nOo7zQWRjSqRs2AAJCZCaajuJBEW3brBqldmgKyK6miiR17Oniu4gOGXR7ThOAjAaGABkAjc6jpN+\nzG3OAv4OfNt13U7Ad6KQVSKgqMj8xKwd9RIpp50GnTvDvHm2k4h4g4puibRevcznt+vaTiK1Ec5K\nd0/gU9d1N7iuexAYDww+5jbfAya4rlsG4Lqu2v09Sq0lEg06r1vkGyq6JdKaNYOGDWH1attJpDbC\nKbpTgM+O+Lr06+8dKQ1IdhznA8dx5jqOc3OkAkpkzZljLlOJRJL6ukWMzZvhq68gLc12EgkatZj4\nX50IPk42cAlwOvCx4zgfu6573M9kI0aMqPx9//796d+/f4QiyKkcPAgLF5pd0CKR1Ls33HOPufSp\n1iWJZxULGwk6pkAirGIz5fe/bztJfCkoKKCgoCAijxVO0V0GHDnINvXr7x2pFNjquu5+YL/jOB8C\nXYGTFt0SW0uXQqtWcOaZtpNI0LRqZQruzz7T2GuJb2otkWjp1Qtef912ivhz7ALxyJEja/xY4fws\nPhdo5zhOK8dx6gJ5wORjbjMJ6Os4TqLjOA2AXsCKGqeSqFA/t0SL46jFRARUdEv0ZGebxbMDB2wn\nkZo6ZdHtuu5hYDjwDrAMGO+67grHcW53HGfY17dZCUwDFgOzgbGu6y6PXmypCfVzSzSp6JZ4d/iw\nOcVH77MSDaefbs5/X7jQdhKpqbB6ul3XzQc6HPO9Mcd8/SjwaOSiSaQVFcFdd9lOIUHVqxfcf7/t\nFCL2LF8OzZvDOefYTiJBVdHXravW/qStHnFi504zGKdzZ9tJJKh69DCT+MrLbScRsUOtJRJtFed1\niwUy1xEAACAASURBVD+p6I4Tc+dCVhbUidR5NSLHaNgQ2rUzhbdIPFLRLdGmcfD+pqI7TqifW2JB\nfd0Sz2bP1mV/ia70dHMW/Jdf2k4iNaGiO05UjH8XiSYV3RKvtm9XC59EX2KiaeVTi4k/qeiOA66r\njRcSGyq6JV7NnWuOdEtKsp1Egk593f6lojsOfPYZhEIaWiLR16GDuey5ZYvtJCKxpX5uiRWNg/cv\nFd1xoGKVW+O5JdoSErTRR+LTnDkquiU2Kla6Xdd2EqkuFd1xQP3cEku9eqnFROKL62qlW2KnRQuo\nXx/WrLGdRKpLRXccUD+3xFLv3lrplviyZg00aGCKIZFYUF+3P6noDrhDh6C42Ox2FomFXr3MprLD\nh20nEYkNHRUosaa+bn9S0R1wy5ZBy5bQqJHtJBIvzjkHmjaFFStsJxGJDbWWSKxp74w/qegOOLWW\niA06OlDiiYpuibXu3WHJEjhwwHYSqQ4V3QGnoltsUNEt8WLvXli+3JzRLRIrZ5wB7drB4sW2k0h1\nqOgOOI1/FxtUdEu8KC6GzExzmoRILKmv239UdAfYrl2wbh106WI7icSbzp1h/XrYudN2EpHo0vnc\nYov6uv1HRXeAzZsH3bppLLHEXlKSudw+d67tJCLRpX5usUXHBvqPiu4AU2uJ2KQhORIPdFyg2NKx\nI2zcCF99ZTuJhEtFd4BpEqXYpL5uCbrSUti3D9q2tZ1E4lFiojnFRKvd/qGiO8B0conYVFF0u67t\nJCLRUdHP7Ti2k0i8Ul+3v6joDqjSUjh4EFq3tp1E4lVKCtSrB2vX2k4iEh3q5xbb1NftLyq6A6qi\nn1srMGKTWkwkyFR0i20VxwbqiqI/qOgOKPVzixeo6JagOngQFiyAnBzbSSSepaZC3brmeGDxPhXd\nAaV+bvEC9RtKUC1ZAq1awVln2U4i8U7vs/6hojuADh+G+fO1AiP2ZWfDsmVw4IDtJCKRVVSkI1nF\nG9TX7R8qugNo2TJo0QLOPtt2Eol3DRpAWhosWmQ7iUhkqYVPvELj4P1DRXcA6cNAvEQfCBJEGj4m\nXtGjh1nYKC+3nURORUV3AKmfW7xElz4laHbuhPXroXNn20lEoGFDaNMGFi+2nURORUV3AGkFRrxE\nK90SNPPmQbdukJRkO4mI0bOnFjf8QEV3wOzeDWvWQNeutpOIGBkZ8PnnsG2b7SQikaEWPvEanWDi\nDyq6A2b+fOjSxZzbKeIFiYnQvTvMnWs7iUhk6GqieI2Kbn9Q0R0w6ucWL9KlTwkSrXSL12RmQmkp\nfPWV7SRyMiq6A0YrMOJFWoWRoCgtNadEtG5tO4nIN+rUMXMR5s2znURORkV3wGgFRryoYqXbdW0n\nEamdivdYx7GdRORoWtzwPhXdAbJxI+zfb44OEvGS1FRz0sP69baTiNSOriaKV6no9j4V3QFS8WGg\nFRjxIvV1SxDoaqJ4VcVMBF1R9C4V3QFSVKQVGPEurcKI3x0+bE6IysmxnUTkeKmpkJAAGzbYTiIn\noqI7QHRyiXiZVrrF71asgGbNIDnZdhKR4zmOFje8TkV3QBw+bHYta6VbvKpHD1i4EA4etJ1EpGbU\nzy1ep6Lb21R0B8SKFdC0qVZgxLvOPBNatYKlS20nEakZ9XOL1+mKorep6A4IfRiIH2gVRvxMK93i\ndTk5uqLoZSq6A0L93OIHWoURv9qzB1atgm7dbCcRObGKK4pLlthOIlVR0R0QKrrFD7TSLX5VXAyd\nOsFpp9lOInJyep/1LhXdAbBnD3z6KXTtajuJyMl16mSOs9q503YSkepRC5/4ha4oepeK7gDQCoz4\nRVKSuTw/b57tJCLVo35u8QutdHuXiu4AUGuJ+IlWYcSPtNItftG5M5SUwI4dtpPIsVR0B4CKbvET\nrcKI32zebAqYdu1sJxE5tTp1ICsL5s61nUSOpaI7ADT+XfxEK93iNxXvsQn6xBSf0PusN+ktxOc+\n/xx279YKjPhH69bmDNnSUttJRMKjfm7xG11R9CYV3T5X8WHgOLaTiITHcbQKI/6ifm7xm4qi23Vt\nJ5Ejqej2Oa3AiB9pFUb8IhQyvbF6nxU/Oe88U3CXlNhOIkdS0e1zWoERP9JKt/jFp59Co0Zw7rm2\nk4iEz3FMbaD3WW9R0e1jWoERv8rJgfnz4fBh20lETk5XE8WvdEXRe1R0+9jKldCkCTRubDuJSPUk\nJ0OzZrBihe0kIienq4niVyq6vUdFt4/pqEDxM30giB9opVv8qkcPWLAADh2ynUQqqOj2MQ3FET9T\nX7d43f79sGwZZGfbTiJSfY0aQcuWsHSp7SRSQUW3j6noFj/TSrd43cKF0KEDNGhgO4lIzeh91ltU\ndPvU3r3wySfQrZvtJCI107WrORlizx7bSUSqpn5u8TsV3d6iotun5s+HzEyoV892EpGaOe006NQJ\niottJxGpmq4mit/16gWzZ9tOIRVUdPvUnDnQu7ftFCK1o75u8TJtVhe/69zZDMjZscN2EgEV3b6l\nFRgJAl36FK/68kvYvBnS020nEam5pCTIyjIzPcQ+Fd0+paJbgkAr3eJVc+eaI9cSE20nEakdLW54\nh4puH9q40WykbNvWdhKR2mnfHnbuNCuKIl6ihQ0JChXd3qGi24cqhjU4ju0kIrXjOGYkvFa7xWvU\nzy1BUVF0u67tJKKi24e0AiNBolUY8RrX1fusBEfLlqZNav1620lERbcP6eQSCRL1dYvXrFtnjmNt\n0cJ2EpHacxwtbniFim6fOXzYnNGty54SFD17mk1roZDtJCKGVrklaFR0e4OKbp9ZvhyaN4ezz7ad\nRCQyzj0XGjUy0ylFvED93BI0Krq9QUW3z8yerRUYCR59IIiXaKVbgqZHD1i0CMrLbSeJbyq6fUYf\nBhJE6usWrzh40BQn3bvbTiISOQ0bmmOGFy+2nSS+qej2GRXdEkRa6RavWLwY2rQxRYpIkPTqZa6W\niz0qun1k1y6zq75LF9tJRCIrK8vsV9i/33YSiXfq55ag0uKGfSq6fWTePOjaFerWtZ1EJLIaNIAO\nHWDhQttJJN7paqIElYpu+1R0+4g+DCTI1NctXqCVbgmqjh3h889h2zbbSeKXim4f0cklEmRahRHb\nduyAkhLo1Ml2EpHIS0w0G4S1uGGPim6f0FhiCTqtdItt8+aZ/QV16thOIhIdvXtrM6VNKrp94rPP\nTOHdqpXtJCLRkZ4OmzfDl1/aTiLxSgsbEnS6omiXim6fqPgwcBzbSUSiIzHRDHCYO9d2EolX6ueW\noOvVy7zOXdd2kvikotsntAIj8UCrMGKLWvgkHjRvDqefDqtX204Sn1R0+4Q2UUo8UF+32FJaCqEQ\nnHee7SQi0aXFDXtUdPvAwYPm/OKcHNtJRKKr4sNAlz4l1tTCJ/Gid28V3bao6PaBJUvMBsozz7Sd\nRCS6WrSAevXM5FWRWFI/t8QLjYO3R0W3D8yZY34yFYkHuvQpNqifW+JFdjYsWwb799tOEn9UdPuA\nPgwknqivW2Lt0CEoLlYLn8SHBg3MEa0LFthOEn9UdPuAim6JJ1rpllhbvhxSUqBRI9tJRGJD77N2\nqOj2uK++MrvqMzNtJxGJje7dYdEis4FYJBbUzy3xRpsp7VDR7XFz55r+K40llnjRsCG0aQOLF9tO\nIvFCVxMl3mil2w4V3R6nDwOJR+rrlljSSrfEm7Q0cyV9yxbbSeKLim6P08klEo+0CiOxsmePmc7X\ntavtJCKxk5Dw/9u79yCpqmuP478NDA9RUEAQEUREAQEB5TEDKAMi4gsSk/hMcst7E81TEnMTLcvk\nmpRV0dyoAY3GxCTGREWNV0UBA6IDCgMyDi95iaKIoAPIU0AYmH3/2NNxRIbpmT6n93l8P1VUGGy7\nf2V1Ti9Or72WOzjMdTa/KLojjLXESCvmyCJfFi6UzjxTatrUdxIgv7i5kX8U3RG2dq3UrJk7VQ+k\nSZ8+0saN0tatvpMg6UpLpaIi3ymA/OMwZf5RdEcYd7mRVo0bu68+uduNsFF0I60GD3bf9FRV+U6S\nHhTdEUbRjTQrKnIFERAWaym6kV7HHy+1bSutXu07SXpQdEcYhyiRZkVF3OlGuNaulZo3l046yXcS\nwA/Oz+QXRXdE7dsnLVvmFoUAaTRkiBvldvCg7yRIqtJSbmwg3ThMmV9ZFd3GmLHGmFXGmLeMMTcd\n4XGDjDGVxpjLgouYTosXS6edJrVs6TsJ4Ee7dlKHDm5FNxAGWkuQdhTd+VVn0W2MaSTpPkkXSOot\n6SpjTM9aHneHpH8FHTKN6OcG6OtGuCi6kXYDBkhvvSXt2eM7STpkc6d7sKQ11tp11tpKSZMljT/M\n434o6Z+S2G8UAIpugKIb4dm92x0gO+ss30kAf5o1cyNa33jDd5J0yKbo7iRpfY2fP6j+s38zxpwo\n6UvW2gckmeDipRdFN0DRjfBkluI0a+Y7CeAXLSb50ySg5/mdpJq93rUW3rfddtu/f19cXKzi4uKA\nIiTHli3S5s1Sr16+kwB+1VyS06aN7zRIkvnzOUQJSK7ofuYZ3ymiq6SkRCUlJYE8l7HWHvkBxhRK\nus1aO7b655slWWvtnTUeszbzW0ntJO2WdJ21dsohz2Xrej1I06ZJd98tvfSS7ySAf6NGST/9qXTh\nhb6TIEnGj5euuUa6/HLfSQC/3n5bGjlSWr++7sdCMsbIWtugro5s2ksWSupujDnZGNNU0pWSPldM\nW2u7Vf86Ra6v+3uHFtzI3vz5tJYAGbSYIGgsxQE+c+qp0t697ltFhKvOottae1DSDyTNkLRc0mRr\n7UpjzPXGmOsO968EnDF16OcGPkPRjaCtXSs1bSp17uw7CeCfMfR150ud7SWBvhjtJXWqqnJrWVet\ncjOKgbTbssXdidm6VWrc2HcaJME//iE995z01FO+kwDR8KtfubGBd9zhO0n0hd1egjxas0Zq3ZqC\nG8hgSQ6CxiZK4PO4050fFN0Rs2ABHwbAoYqK3FkHIAjz59PPDdQ0eLBUViYdPOg7SbJRdEcMhyiB\nLyospK8bwdi927XvsRQH+Mxxx0mdOknLl/tOkmwU3RHDIUrgizhMiaCUlUl9+0rNm/tOAkQLLSbh\no+iOkL17pZUrpQEDfCcBoqVPH2nDBneYEsgFowKBw6PoDh9Fd4SUl0tnnCG1aOE7CRAtTZpIAwfy\ngYDcUXQDh0fRHT6K7gjhECVQOw5TIlfWsv4dqM2ZZ0rvvivt2uU7SXJRdEcI/dxA7ejrRq7efdd9\na8JSHOCLCgqk/v2lhQt9J0kuiu4IYXIJULshQ6TXX3cLpICGyLSWmAattQCSjxaTcFF0R8RHH7mv\ndE47zXcSIJqOP979YkkOGop+buDIKLrDRdEdEQsWuOH03IEBakeLCXJB0Q0cWabottZ3kmSi6I4I\n+rmBulF0o6FYigPUrUsXV3CvX+87STJRdEcEk0uAujHBBA31xhtu3jtLcYDaGeNqEa6z4aDojoCD\nB91p4cGDfScBoq1PH3cHZts230kQN7SWANmhrzs8FN0RsHKl1KGD1Lat7yRAtLEkBw1F0Q1kh6I7\nPBTdEUA/N5A9+rpRX9ZSdAPZGjhQWrxYqqz0nSR5KLojgKIbyB5FN+qLpThA9lq1krp2lZYt850k\neSi6I4C1xED2CgtZkoP6KS117xtGsgLZKSzk5kYYKLo9277d3YXp3993EiAeMktyVq70nQRxMX8+\nrSVAfQwbJs2d6ztF8lB0e1ZaKg0aJBUU+E4CxAd3YVAf9HMD9TN8OEV3GCi6PXvtNffmBpA9+rqR\nrT173LciZ5/tOwkQH927S59+Kr3/vu8kyULR7dlrr7mvcQBkj6Ib2SorYykOUF/G0GISBopuj/bv\nd1vS+NoTqJ++fVmSg+xkDlECqB9aTIJH0e1Rebn7CqdVK99JgHhhSQ6yRT830DDDhrlv4xEcim6P\n5s6lnxtoqKIiN5UCqI21TC4BGmrAAOmdd6QdO3wnSQ6Kbo/o5wYajgkmqMt770mNGklduvhOAsRP\n06buADI3N4JD0e2JtdzpBnJRWOjaS1iSg9pkWktYigM0zPDhtJgEiaLbkzVrpBYtWEsMNFT79lK7\ndizJQe04RAnkhsOUwaLo9oTWEiB3jA7EkXCIEshNUZG0cKFUWek7STJQdHtCawmQO4pu1GbPHmnF\nCpbiALlo3Vrq1k1avNh3kmSg6PaEO91A7phggtq88YZbitOihe8kQLwxOjA4FN0ebN4sVVS4DwQA\nDde3r1tTvH277ySIGlpLgGDQ1x0cim4P5s51h3saN/adBIi3Jk1c+wBLcnAoim4gGJk73db6ThJ/\nFN0e0M8NBIe+bhzKWiaXAEHp0kUqKHCLcpAbim4PXnuNohsICkU3DvXee24298kn+04CxJ8xtJgE\nhaI7z/bulZYulQYP9p0ESIbCQun111mSg89kVr+zFAcIBocpg0HRnWcLF7oDlEcd5TsJkAzt20tt\n20qrVvlOgqignxsIFne6g0HRnWeMCgSCV1hIiwk+Q9ENBKtvX2nDBmnLFt9J4o2iO884RAkEj75u\nZOzdKy1fzlIcIEiNG7ubG/Pm+U4SbxTdeVRV5d6w3OkGgkXRjYyyMql3b5biAEEbNowWk1xRdOfR\nihVSu3ZShw6+kwDJcuaZLMmBQ2sJEI7hwzlMmSuK7jxiVCAQjsySnNdf950EvmUmlwAI1pAh0pIl\n0qef+k4SXxTdeTR3Lq0lQFhoMUFmKQ5FNxC8li2lXr1cCxcahqI7j7jTDYSHCSZYt84V3izFAcLB\n6MDcUHTnyYYN0q5dUo8evpMAyVRUJC1YwJKcNMvc5WYpDhAOluTkhqI7TzKtJXwYAOFo315q04Yl\nOWlGawkQrswEE25uNAxFd56wFAcIH33d6UbRDYSrY0fpuOO4udFQFN15wlIcIHxFRW56BdJn7143\nlnXgQN9JgGRjdGDDUXTnwa5d0urVbEgDwlZUxCGftCork844g6U4QNg4TNlwFN15sGCBNGCA1KyZ\n7yRAsvXrJ23cKG3a5DsJ8m32bGnECN8pgOTjMGXDUXTnAaMCgfxo3Nj9f23OHN9JkG8lJRTdQD70\n7Om2/374oe8k8UPRnQccogTyp7jYFWBIj/373TeK55zjOwmQfI0aSUOH0mLSEBTdITtwwK2mHjrU\ndxIgHYqLXasB0mPhQun006Vjj/WdBEgHDlM2DEV3yJYskTp3dvODAYSvf39p/Xpp82bfSZAvtJYA\n+ZWZ1436oegOGaMCgfxq0sR9INDXnR4lJe4bDgD5MXCgG9H5ySe+k8QLRXfIOEQJ5B993emxf7+b\nzU4/N5A/zZu7qWyvv+47SbxQdIfI2s/WvwPInxEj6OtOi7Iy6bTT3JY8APnD6MD6o+gO0XvvucL7\nlFN8JwHS5ayzpHXrpC1bfCdB2OjnBvzgMGX9UXSHKHOX2xjfSYB0oa87PejnBvwYOtSN6jxwwHeS\n+KDoDhH93IA/tJgkX2Ul/dyAL23bSp06ScuW+U4SHxTdIWIpDuAPhymTr6xM6taNkayAL4wOrB+K\n7pBs2+Z6Svv3950ESKezzpLefVf6+GPfSRAWWksAv+jrrh+K7pDMmycNGeJ6SwHkX0GBuwvz6qu+\nkyAss2dTdAM+ZYpua30niQeK7pAwKhDwb8QIWkySqrLS3dw491zfSYD06tbNHaR8/33fSeKBojsk\nHKIE/KOvO7neeMONY6WfG/DHGFpM6oOiOwT79knl5VJhoe8kQLqdfba0dq20davvJAga/dxANHCY\nMnsU3SEoL5dOP1065hjfSYB0KyiQioro604i+rmBaOBOd/YoukPAqEAgOmgxSZ7KSndnjfncgH/9\n+7tJUdu3+04SfRTdIZg7l35uICooupOnvFzq2lVq1853EgAFBdKgQVJpqe8k0UfRHTBrmVwCRMnA\ngdI777jZ+UgGWkuAaKHFJDsU3QF76y2pZUvppJN8JwEgubswhYX0dSdJSYkbBwkgGjhMmR2K7oAx\nKhCIHlpMkuPAAffhznxuIDqKiqSyMmn/ft9Joo2iO2C0lgDRw5Kc5Cgvl7p0kY4/3ncSABmtWknd\nu0uLFvlOEm0U3QHjTjcQPYMGSWvWcLo+CejnBqKJvu66UXQHqKJC2rRJ6t3bdxIANTVtSl93UtDP\nDUQTfd11o+gO0Lx50tChUiP+qwKRQ193/B044O6k0c8NRE/mTre1vpNEF+VhgGgtAaJrxAjXmoD4\nWrxY6txZat/edxIAh+rcWWrRwrXy4fAougPEIUogugYNklavpq87zmgtAaJt2DD6uo+EojsgO3ZI\ny5dLgwf7TgLgcJo1k4YM4QMhzkpKOEQJRFlxsfTKK75TRBdFd0BeecX1c7do4TsJgNrQYhJfBw+6\nvzBxpxuIrvPPl2bOlKqqfCeJJorugMyY4d5sAKKLw5TxtXix1KkT/dxAlJ1yinTMMdKyZb6TRBNF\nd0BmzpTGjPGdAsCRDB4srVrl2sEQL/RzA/EwZoyrifBFFN0BWLtW2rVL6tvXdxIAR9KsmTtQSV93\n/NDPDcTDmDHu2398EUV3AGbOdK0lxvhOAqAuxcX0dccN/dxAfBQXS6Wl0t69vpNED0V3AGbMoLUE\niAv6uuNnyRLphBOkDh18JwFQl9atpX79+EbxcCi6c3TggJtcMnq07yQAsjF4sLRihbRzp+8kyBat\nJUC80GJyeBTdOSork046SerY0XcSANlo3tz1dc+d6zsJsjV7NkU3ECfnn0/RfTgU3TmitQSIH1pM\n4uPgQWnOHPq5gTgZNEh6/33po498J4kWiu4cMSoQiB+K7vhYutT1cp9wgu8kALLVpIk0apT00ku+\nk0QLRXcOdu50CxvOOcd3EgD1MWSItHy5G/WJaKOfG4gnWky+iKI7B6+8IhUWsvodiJvmzaWBA+nr\njgP6uYF4yizJsdZ3kuig6M4BrSVAfNFiEn1VVfRzA3HVrZvUsqX05pu+k0QHRXcOZsxwX58AiJ8R\nIyi6o27pUun445kOBcQVLSafR9HdQO+9J+3YIZ15pu8kABqisNDdgfnkE99JUBtaS4B4y7SYwKHo\nbqDM6vdG/BcEYqlFC+nss+nrjjIOUQLxNnKku8Z++qnvJNGQVclojBlrjFlljHnLGHPTYf751caY\nJdW/XjPG9A0+arTQWgLEHy0m0UU/NxB/xx4r9e3LSviMOotuY0wjSfdJukBSb0lXGWN6HvKwtZLO\ntdb2k3S7pD8FHTRKDh6UZs2i6AbirrjYtTAget58U2rbVjrxRN9JAOSCFpPPZHOne7CkNdbaddba\nSkmTJY2v+QBr7Xxr7Y7qH+dL6hRszGgpK5M6deLDAIi7wkJ3WI++7uihtQRIhjFjOEyZkU3R3UnS\n+ho/f6AjF9XfkjQ9l1BRl+nnBhBvRx0lDRggzZvnOwkOVVJCawmQBIMHS+++K1VU+E7iX5Mgn8wY\nM1LStZKG1/aY22677d+/Ly4uVnEMb2XMmCHdcovvFACCkJnXzcz96Mj0c0+a5DsJgFw1aeIOVM6a\nJV19te809VdSUqKSgA7/GFvHqiBjTKGk26y1Y6t/vlmStdbeecjjzpT0tKSx1tp3ankuW9frRd2u\nXa6tpKLC3SUDEG+zZkm/+AVTTKJk2TLpssukNWt8JwEQhAcekBYskB5+2HeS3BljZK01Dfl3s2kv\nWSipuzHmZGNMU0lXSppySIAucgX3N2oruJOipMR9VULBDSRDUZG0ZIm0e7fvJMigtQRIlsySnJjf\nd81ZnUW3tfagpB9ImiFpuaTJ1tqVxpjrjTHXVT/s55LaSLrfGLPIGPN6aIk9mzGDr6GBJDnqKKl/\nf/q6o4RDlECynHqq1Ly5tGKF7yR+1dleEuiLJaC9pEcPafJkd/gKQDLceqv739tv95sDrp+7Qwep\nvFzq3Nl3GgBB+c53XA314x/7TpKbsNtLUG3dOmnbNqlfP99JAAQpc5gS/q1YIbVuTcENJE2mxSTN\nKLrrYeZMafRoVr8DSTN0qJvXvX277ySYMUMaNcp3CgBBGzXKHVjft893En8oH+uBfm4gmY46Sjr3\nXOnFF30nwZQp0rhxvlMACNpxx0m9e6d7UhRFd5ZY/Q4k27hx0nPP+U6Rbh9/7Hq5zzvPdxIAYUh7\niwlFd5bKy6UTTnDr3wEkzyWXuDvd+/f7TpJe06a5r6BbtPCdBEAY0r4SnqI7S7SWAMl24onS6adL\nr77qO0l6TZkijR/vOwWAsAwZIq1dK23e7DuJHxTdWZo5k9YSIOnGjXOFH/Jv3z53nb34Yt9JAISl\noMAtvnrpJd9J/KDozsKuXVJZGRvSgKTL9HXHfJ1ALL3yijtk1b697yQAwpTmFhOK7izMnu1Wv7ds\n6TsJgDD16eNGgi5b5jtJ+tBaAqTDmDHuW6003tyg6M4C/dxAOhhDi4kP1jIqEEiL7t1dm8nKlb6T\n5B9Fdxbo5wbSg9GB+Vde7mal9+jhOwmAsBmT3tGBFN11eP99acsWacAA30kA5MM550jvvCNt2OA7\nSXpkWkuM8Z0EQD5kWkzShqK7Dqx+B9KloEC68ELphRd8J0kPWkuAdBk1yo1nTdtKeErJOtBaAqQP\nLSb5s26d9MEHUlGR7yQA8qVNG6lXL2nePN9J8oui+wgOHnSzJCm6gXQZO9bdhfnkE99Jku/5591s\n7iZNfCcBkE9pbDGh6D6CRYvczNjOnX0nAZBPrVu7O69pPOiTb7SWAOmUxnndFN1HQGsJkF60mIRv\nxw6ptJSRrEAaFRZKa9a4YRVpQdF9BMznBtLr0kulqVOlAwd8J0muF19002KOPtp3EgD5llkJP2uW\n7yT5Q9Fdi08+kRYuZPU7kFYnn+xay0pLfSdJLrZQAumWthYTiu5azJkjDRzIHRggzdhOGZ7KSmn6\ndOmSS3wnAeBLZklOWlbCU3TXgtYSAJm+7rR8IOTTq69Kp54qderkOwkAX04/3e1BWb3ad5L8opGx\nFQAAEkpJREFUoOiuBUU3gLPOkvbsSc8HQj7RWgLAmHS1mFB0H8YHH0gVFax+B9LOGFpMwmAtowIB\nOJkWkzSg6D6MzOr3xo19JwHgG6MDg/fmm1JVldS3r+8kAHw77zzXbrZ/v+8k4aPoPgxaSwBkjBwp\nLV8ubdrkO0lyZFpLjPGdBIBvbdtKPXqkY1IURfchWP0OoKZmzdz1YOpU30mSg9YSADWdf76b2590\nFN2HePllN5+3SxffSQBEBS0mwdm4UXrrLencc30nARAVl10mPflk8idFUXQf4tFHpWuu8Z0CQJRc\ndJH7C/nevb6TxN8LL0hjx7ptdAAguUlRBQXSggW+k4SLoruGvXvd3awrr/SdBECUtG3rPhTStK44\nLIwKBHAoY9wNz0cf9Z0kXBTdNTz/vNtC2bGj7yQAoobRgbnbvdtt+x071ncSAFFz9dWuxaSy0neS\n8FB010BrCYDajBvn/mJeVeU7SXzNmCENHiwde6zvJACi5tRTpW7d3DCLpKLorrZ1q1RS4pr5AeBQ\n3btLbdpICxf6ThJftJYAOJKkt5hQdFd76inpggukVq18JwEQVbSYNNzBg+4Q5aWX+k4CIKouv9xd\nJ3bv9p0kHBTd1WgtAVAXRgc2XGmpdOKJUteuvpMAiKr27aWhQ5N7naXolrRunbRihXThhb6TAIiy\nIUOkLVukd97xnSR+aC0BkI0kt5hQdEt6/HHpK1+Rmjb1nQRAlDVqJF1yiTtQifphCyWAbIwfL82d\nK23a5DtJ8Ci6RWsJgOzRYlJ/q1dLu3a5WecAcCRHHy1dfLEbH5g0qS+6ly6VduyQhg/3nQRAHIwe\nLb3xhpt4hOxMmeIOUDZK/ScOgGwktcUk9ZfAzF1uPgwAZOOoo6SRI6Xp030niQ/6uQHUx/nnu7Mz\nSTs/k+pSs6pKeuwxWksA1A+jA7O3ebP7RnHkSN9JAMRFQYEbH/jYY76TBCvVRfecOW7ZRZ8+vpMA\niJNLLpH+9S9p3z7fSaJv6lTXktO8ue8kAOIk02Jire8kwUl10c0BSgAN0aGDdMYZ0uzZvpNEH60l\nABqisFCqrJTKy30nCU5qi+59+6T/+z/pqqt8JwEQR7SY1O3TT6VZs6SLLvKdBEDcGCNdfXWyDlSm\ntuieNk3q21fq3Nl3EgBxlCm6k/TVZ9BmzZL69ZPatfOdBEAcXXONNHm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"text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each axis contains additional objects that can be modified." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wrF27Fg8//DAKCgp8uo+628A33HKbmnfiBPC1rwXmsfwN3c31dAPyjFd1tf91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\nEB0lJVJ5uXTwoO8k0UbRHTBaS4DoYUlOclRUSF26SCef7Ds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"text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "axis2.set_xscale('log')\n", "axis1.set_xlabel(r'$x$', fontsize=16)\n", "fig" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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17MQJ4GtfC85j+Ru+W+r5BuQZsJoa/+syWnZ2NrKzs1WX4ZOcHCA+Xs74JmPM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\nEg8U3wGj5QSIHg7bSY7SUqlLF+m443wnAZDVsqXUvbu0ZIn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"text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "axis1.set_xticks([0, 1, 2])\n", "axis1.set_xticklabels(['Start', 'Middle', 'End'])\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adding multiple axes by hand is often annoying (although sometimes necessary). There are a number of tools that can be used to simplify this in standard cases: `add_subplot` is the standard one. When you want a figure containing multiple subplots all the same size, with `r` rows and `c` columns, the command is `add_subplot(r, c, )`. For example:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dGmbO9J1Eiss0vYgjH/uyVGTFnLXw6KPwve/5TpJuV10F774LK1f6TiJx9cYb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\ngIO4UOd6rPx06gR06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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = pyplot.figure(figsize=(12, 9))\n", "x = numpy.linspace(0.0, 1.0)\n", "for subplot in range(1, 7):\n", " axis = fig.add_subplot(2, 3, subplot)\n", " axis.plot(x, numpy.sin(numpy.pi*x*subplot))\n", " axis.set_xlabel(r'$x$')\n", " axis.set_ylabel(r'$y$')\n", " axis.set_title(r'$\\sin({} \\pi x)$'.format(subplot))\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `tight_layout` function call at the end ensures that the axis labels and titles do not overlap with other subplots." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Higher dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot three-dimensional objects, we need to modify the *axis* so that it knows a third dimension is required. To do this, we import another module and modify the command that sets up the axis object." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ptg1bwtd83D2gw2KTRJQwVhfTqCgThTEh8dQVDS+z+922JNmDjo+P8R3f8R2F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\nI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RYW5ra93PXr1zFr1iwkJSWhuLjYIbPuK948KAp9/PHHuPfee32+LkICHQXBhBCfSkhI\nQE1NDf/1hQsXWmXWEhMTERcXB51OB51OhzvvvBOHDx8O2iC4o1QqFbp3747x48dj/PjxYFkWDQ0N\nKC8vx65du7Bs2TKo1WqMGDECeXl5yM7ORmRkpENQzG2kcw6KbTabQ1AsLJ+Qe1DMsiwsFgvMZjPC\nw8PdBrb//ve/UVhYiOeeew7jx4+X5c+1Z88erF27FuXl5VIvhRDFoyCYEOJTWVlZOH36NKqrq9G7\nd29s3rwZmzZtcvjMuHHjMHPmTNjtdpjNZlRWVmLu3LkSrThwqFQqdO3aFWPGjMGYMWPAsiwaGxvx\n/fffw2g0YsWKFWAYBsOHD0dubi5ycnLQpUsXl0ExAD4o5uqKzWYzAHkHxQzD8P2V3ZU/sCyLLVu2\nYM2aNdiwYQNSU1P9ukZvHhQB4MiRI8jPz0dxcTFiY2P9uURCAhIFwYQQn9JoNCgqKsLo0aP5ne8Z\nGRlYtWoVVCoV8vPzkZ6ejnvuuQeDBg2CRqNBfn4++vfvL/XSA45KpUJ0dDTuuece3HPPPWBZFs3N\nzaioqIDRaMT7778Ps9mMoUOHwmAwQK/XIzY21mVQHBYWBgAOmWKLxcIP8xDWFEsVFHPlD6GhoW7H\nS7e0tGD+/PlgGAbffvstwsPD/b5Obx4Ua2pq8MADD2DDhg24/fbb/b5GQgIRtUgjhBDCa2lpQWVl\nJUwmE8rLy9HY2IghQ4bwHSji4uLaHPUsHODBMIxDTbE/ptp5W/5w7tw5FBQUYPLkyZg8ebKkGezi\n4mLMnj2bf1BcsGCBw4Pi1KlT8eWXXyI5ORksyyI0NNRj3TAhhEd9ggkhhLSfxWLBgQMHYDKZUFZW\nhvr6egwcOBB6vR55eXno1atXm0GxsFcxFxQLJ9uJGXyyLIsbN27Abrd7nP62fft2vPnmm1i1ahWG\nDBki2t9PCJEdCoIJIYR0HtfJgwuKr1y5goyMDOTm5iIvLw+JiYleB8VcezZh+URngmK73Y7m5mZo\nNBqEh4e7/P+x2Wx4+eWXce7cOXz88cfo2rVrh/4uQohiUBBMCCFEfHa7HUePHoXRaERpaSkuXLiA\ntLQ0fqrdbbfd5rHXMMuyDuUTwqCY+6c3QbHFYkFLSwt0Oh1fr+zs559/Rn5+PpffYgMAAAbdSURB\nVO677z7MmTMn4HogE0JcoiCYEEKI7zEMg+PHj8NoNMJkMqG6uhp9+vTha4pTU1PbDIqdRz1ztcRc\ntlgYFLMsi5aWFthsNrflDwBQVlaGRYsWYcWKFcjLyxP95yaEyBYFwYQQQvyPYRicOnWKzxSfPn0a\nSUlJfPlEenp6u4NibtSzWq2G2WxGSEiI2/IHhmHwzjvvoLy8HOvXr8ctt9ziyx+XECI/FAQTQgiR\nHsuyOHfuHJ8pPnHiBHr16sWXT9xxxx1us7ncn7fb7bBYLLBarQDAB8X19fVQqVTo3bs3AKC+vh4z\nZszAoEGDsHjxYn5cNCEkqFAQTAghRH5YlsX58+dhMplgMpnw448/onv37nz5xODBgx1anFksFnz6\n6ad46KGHEBkZCY1Gw2+w+9e//oVnn30WcXFxGDp0KA4cOIAlS5bg8ccfl9UAD0KIX1EQTAghRP5Y\nlsWlS5dgMplQWlqKw4cPo0uXLtDr9ejfvz/eeOMNREdH4/PPP0d0dHSrP2+1WlFUVASj0YiQkBAc\nOHAAUVFR+N3vfoff/e53uPPOO5GSkkJBMSHBg4JgQgiRWnFxMebMmcMPRJg/f77D969du4aJEyei\npqYGdrsd8+bNw6RJk6RZrEywLIu6ujq8++67eOuttzBy5EgAQE5ODgwGA7KysqDT6QAATU1NmDt3\nLrp27Yo333wTWq0WLMvi+PHjfFC9d+9eHDt2zGUATQgJSBQEE0KIlBiGQVpaGnbv3o34+HhkZWVh\n8+bNSE9P5z+zfPlyXLt2DcuXL0ddXR369euHy5cvB3UtK8MweOWVV/Dhhx/is88+w6hRo1BfX4+y\nsjKYTCZUVVUhNDQUqampqKqqwvPPP49HHnmEMr2EEI7bi0HwXlkJIcSP9u/fj9TUVCQnJwMAJkyY\ngK1btzoEwSqVCtevXwcAXL9+Hd27dw/qABgAnnrqKZw+fRoHDhxAfHw8AKBbt24YN24cxo0bB5Zl\nce3aNfzjH//Af/3Xf+Hee++VeMWEEKUI7qsrIYT4SW1tLZKSkvivExMTsX//fofPFBYWYuzYsYiP\nj0djYyO2bNni72XKzl/+8hckJye7fRhQqVSIiYnB1KlT/bwyQojS0bgcQgiRiZKSEmRmZuLixYs4\ndOgQZsyYgcbGRqmXJanbb7896LPhhBDfoCCYEEL8ICEhATU1NfzXFy5cQEJCgsNn1q5di/HjxwO4\nGfz16dMHJ06c8Os6CSEkWFAQTAghfpCVlYXTp0+juroaFosFmzdvxtixYx0+k5ycjF27dgEALl++\njJMnTyIlJUWK5RJCSMCjd0yEEOIHGo0GRUVFGD16NN8iLSMjA6tWrYJKpUJ+fj4WLVqESZMmYdCg\nQQCAv/3tb+jWrZvEKyeEkMBELdIIIYQQQkigctsijcohCCGEEEJI0KEgmBBCCCGEBB0KggkhhBBC\nSNChIJgQQgghhAQdCoIJIYQEneLiYqSnpyMtLQ2vv/66y8/MmjULqampGDJkCP7nf/7HzyskhPga\nBcGEEEKCCsMwKCwsRElJCY4dO4ZNmza1GkqyY8cOnDlzBqdOncKqVatQUFAg0WoJIb5CQTAhhJCg\nsn//fqSmpiI5ORmhoaGYMGECtm7d6vCZrVu34oknngAAZGdno6GhAZcvX5ZiuYQQH6EgmBBCiF9N\nmTIFPXv25IeCuOLLUoTa2lokJSXxXycmJqK2ttbjZxISElp9hhCibBQEE0II8avJkyejpKTE7fep\nFIEQ4g8UBBNCCPErg8GA2NhYt9/3dSlCQkICampq+K8vXLiAhISEVp85f/68x88QQpSNgmBCCCGy\n4utShKysLJw+fRrV1dWwWCzYvHkzxo4d6/CZsWPH4tNPPwUAVFRUoGvXrujZs6doayCESC9E6gUQ\nQggh/qTRaFBUVITRo0eDYRhMmTIFGRkZWLVqFVQqFfLz83Hfffdh+/bt6Nu3LyIjI7F27Vqpl00I\nERkFwYQQQmTFH6UIf/zjH/HTTz85/G/Tpk1z+LqoqEjUv5MQIi9UDkEIIcTvWJYFy7Iuv0elCIQQ\nf6BMMCGEEL969NFHYTQa8euvv+LWW2/F0qVLYbFYqBSBEOJXKndP4v/H4zcJIYQQQgiRMZW7b1A5\nBCGEEEIICToUBBNCCCGEkKBDQTAhhBBCCAk6FAQTQgghhJCgQ0EwIYQQQggJOhQEE0IIIYSQoENB\nMCGEEEIICToUBBNCCCGEkKBDQTAhhBBCCAk6bY1NdjtlgxBCCCGEEKWiTDAhhBBCCAk6FAQTQggh\nhJCgQ0EwIYQQQggJOhQEE0IIIYSQoENBMCGEEEIICToUBBNCCCGEkKDz/wAD3yGm5ijamgAAAABJ\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d.axes3d import Axes3D\n", "\n", "fig = pyplot.figure(figsize=(12, 9))\n", "axis = fig.add_axes([0.1, 0.1, 0.8, 0.8], projection='3d')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then construct, for example, a parametric spiral:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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u+43H42iahi/DkNqyYO9e2LVLZ9cujV27NHbu1Ni508OuXfDppxq7djl/371b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cw4edJI2PvkE6PDXP/+GqNG+ZkzJ5vkZJGEhIQi96PdDj17qgwYoAIqGRmwebPItm0CH34o8tBD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Pr1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"text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = numpy.linspace(0.0, 10.0, 500)\n", "x = numpy.cos(2.0*numpy.pi*t)\n", "y = numpy.sin(2.0*numpy.pi*t)\n", "z = 0.1*t\n", "\n", "axis.plot(x, y, z)\n", "axis.set_xlabel(r'$x$')\n", "axis.set_ylabel(r'$y$')\n", "axis.set_zlabel(r'$z$')\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to plot a surface, then we need to construct *2d arrays* containing the locations of the $x$ and $y$ coordinates, and a 2d array containing the \"height\" of the surface. For structured data (ie, where the $x$ and $y$ coordinates lie on a regular grid) the `meshgrid` function helps. For example, the function\n", "\n", "$$ \\phi(x, y) = \\sin^2 ( \\pi x y ) \\cos( 2 \\pi y^2 ), \\qquad x \\in [0, 1], \\quad y \\in [0, 1], $$\n", "\n", "would be plotted using" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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z8smNMc6q2Z5XCin2+lJpT/CMGTNG/Jpp06aVfbt+JyFY1EQpEx9gxcgsIDPj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\nOGpqatTH165da3OyFhERgZCQEPj5+cHPzw+TJk1CZWWlx4bghyVJEoKDg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = pyplot.figure(figsize=(12, 9))\n", "axis = fig.add_axes([0.1, 0.1, 0.8, 0.8], projection='3d')\n", "\n", "x = numpy.linspace(0.0, 1.0)\n", "y = numpy.linspace(0.0, 1.0)\n", "\n", "X, Y = numpy.meshgrid(x, y) \n", "# x, y are vectors\n", "# X, Y are 2d arrays\n", "\n", "phi = numpy.sin(numpy.pi*X*Y)**2 * numpy.cos(2.0*numpy.pi*Y**2)\n", "\n", "axis.plot_surface(X, Y, phi)\n", "axis.set_xlabel(r'$x$')\n", "axis.set_ylabel(r'$y$')\n", "axis.set_zlabel(r'$\\phi$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a lot of options to modify the appearance of this plot. Important ones include the colormap (note the US spelling), which requires importing the `cm` module from `matplotlib`, and the `stride` parameters changing the appearance of the grid. For example" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/8Pwzf6WP28EVIwbyt7XbeGXDdt45ewYT83IB+GxHMT1sNnJsyRucnl2/DSUW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mpKgAr9eHx+MmIiKC2NhYmjVtSuOYGBo1akSjhg0xGAxcvnyZMQ8/THxcXJ2k0el00q59ew4d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\nitnupMRqw2R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1akqRyUJqdh4ikQib01+7FqJV0yg0kGYRwdwREURMaCAxoYEcuZzGq9/u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ZKGuPrCKaqsrFbsylS4NepcJWUllAQCpALIysmjiZU5+jraaKipytremupoaqijraGOloaG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\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j89HOsSJCqSCHUqm0gBgqOpQ/Jgrb61UkH+vHjx9z9OhRjhw5QkREBFZWVvj4eNPMx4cG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\nRERERE6MYZCIiIjIif0PWVR9DDtS3owAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib import cm\n", "\n", "fig = pyplot.figure(figsize=(12, 9))\n", "axis = fig.add_axes([0.1, 0.1, 0.8, 0.8], projection='3d')\n", "\n", "p = axis.plot_surface(X, Y, phi, rstride=1, cstride=2, cmap = cm.coolwarm)\n", "axis.set_xlabel(r'$x$')\n", "axis.set_ylabel(r'$y$')\n", "axis.set_zlabel(r'$\\phi$')\n", "fig.colorbar(p, shrink=0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further reading" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As noted earlier, the [matplotlib documentation](http://matplotlib.org/api/pyplot_summary.html) contains a lot of details, and the [gallery](http://matplotlib.org/gallery.html) contains a lot of examples that can be adapted to fit. There is also an [extremely useful document](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-4-Matplotlib.ipynb) as part of [Johansson's lectures on scientific Python](https://github.com/jrjohansson/scientific-python-lectures), and an [introduction by Nicolas Rougier](http://www.labri.fr/perso/nrougier/teaching/matplotlib/matplotlib.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# scipy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`scipy` is a package for scientific Python, and contains many functions that are essential for mathematics. It works particularly well with `numpy`. We briefly introduced it above for tackling Linear Algebra problems, but it also includes\n", "\n", "* Scientific constants\n", "* Integration and ODE solvers\n", "* Interpolation\n", "* Optimization and root finding\n", "* Statistical functions\n", "\n", "and much more." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *numerical quadrature* problem involves solving the *definite* integral\n", "\n", "$$ \\int_a^b f(x) \\, \\text{d} x, $$\n", "\n", "or a suitable generalization. `scipy` has a module, `scipy.integrate`, that includes a number of functions to solve these types of problems. For example, to solve\n", "\n", "$$ I = \\int_0^{\\pi} \\sin^2(x) \\, \\text{d} x, $$\n", "\n", "the `quad` function can be used as:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The result is (1.5707963267948966, 1.743934249004316e-14).\n" ] } ], "source": [ "from numpy import sin\n", "from scipy.integrate import quad\n", "\n", "def integrand(x):\n", " \"\"\"\n", " The integrand \\sin^2(x).\n", " \n", " Parameters\n", " ----------\n", " \n", " x : real (list)\n", " The point(s) at which the integrand is evaluated\n", " \n", " Returns\n", " -------\n", " \n", " integrand : real (list)\n", " The integrand evaluated at x\n", " \"\"\"\n", " \n", " return sin(x)**2\n", "\n", "result = quad(integrand, 0.0, numpy.pi)\n", "print(\"The result is {}.\".format(result))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The steps we have taken are:\n", "\n", "1. Define the integrand by defining a function. This function takes the points at which the integrand is evaluated. By using `numpy` we can do this with a single command.\n", "2. Import the `quad` function.\n", "3. Call the `quad` function, passing the function defining the integrand, and the lower and upper limits.\n", "\n", "The result we get back, as seen from the screen output, is *not just* $I$. It is a tuple containing both $I$, and also the *accuracy* with which `quad` believes it has computed the result. The quadrature is a *numerical approximation*, so can never be perfect. You should check this error estimate to ensure the result is \"good enough\" for your purposes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also pass additional parameters if needed. Consider the problem\n", "\n", "$$ I_a = \\int_0^{\\pi} \\sin^2 (a x) \\, \\text{d} x. $$\n", "\n", "If we wanted to solve this for many values of $a$, say $a = 1, 2, \\dots, 5$, we could create a function taking a parameter, and then pass that parameter through:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For a=1, the result is 1.5707963267948966.\n", "For a=2, the result is 1.5707963267948966.\n", "For a=3, the result is 1.5707963267948966.\n", "For a=4, the result is 1.5707963267948966.\n", "For a=5, the result is 1.5707963267948968.\n" ] } ], "source": [ "from numpy import sin\n", "from scipy.integrate import quad\n", "\n", "def integrand_param(x, a):\n", " \"\"\"\n", " The integrand \\sin^2(a x).\n", " \n", " Parameters\n", " ----------\n", " \n", " x : real (list)\n", " The point(s) at which the integrand is evaluated\n", " a : real\n", " The parameter for the integrand\n", " \n", " Returns\n", " -------\n", " \n", " integrand : real (list)\n", " The integrand evaluated at x\n", " \"\"\"\n", " \n", " return sin(a*x)**2\n", "\n", "for a in range(1, 6):\n", " result, accuracy = quad(integrand_param, 0.0, numpy.pi, args=(a,))\n", " print(\"For a={}, the result is {}.\".format(a, result))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that when passing the parameters using the `args` keyword argument, we put the parameters in a tuple. This shows how to pass more than one parameter: keep adding parameters to the argument list, and add them to the tuple. For example, to solve\n", "\n", "$$ I_{a,b} = \\int_0^{\\pi} \\sin^2(ax + b) \\, \\text{d} x $$\n", "\n", "we write" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For a=1, b=0, the result is 1.5707963267948966.\n", "For a=1, b=1, the result is 1.570796326794897.\n", "For a=1, b=2, the result is 1.570796326794897.\n", "For a=2, b=0, the result is 1.5707963267948966.\n", "For a=2, b=1, the result is 1.5707963267948961.\n", "For a=2, b=2, the result is 1.5707963267948961.\n" ] } ], "source": [ "from numpy import sin\n", "from scipy.integrate import quad\n", "\n", "def integrand_param2(x, a, b):\n", " \"\"\"\n", " The integrand \\sin^2(a x + b).\n", " \n", " Parameters\n", " ----------\n", " \n", " x : real (list)\n", " The point(s) at which the integrand is evaluated\n", " a : real\n", " The parameter for the integrand\n", " b : real\n", " The second parameter for the integrand\n", " \n", " Returns\n", " -------\n", " \n", " integrand : real (list)\n", " The integrand evaluated at x\n", " \"\"\"\n", " \n", " return sin(a*x+b)**2\n", "\n", "for a in range(1, 3):\n", " for b in range(3):\n", " result, accuracy = quad(integrand_param2, 0.0, numpy.pi, args=(a, b))\n", " print(\"For a={}, b={}, the result is {}.\".format(a, b, result))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving ODEs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a link between the solution of integrals and the solution of differential equations. Unfortunately, the numerical solution of an ODE is more complex than the solution of an integral. Fortunately, `scipy` contains a number of methods for these as well.\n", "\n", "The methods in `scipy` solve ODEs of the form\n", "\n", "$$ \\frac{\\text{d} \\vec{y}}{\\text{d} t} = \\vec{f} \\left( \\vec{y}, t \\right), \\qquad \\vec{y}(0) = \\vec{y}_0. $$\n", "\n", "For example, the ODE\n", "\n", "$$ \\frac{\\text{d} y}{\\text{d} t} = e^{-t} - y, \\qquad y(0) = 1 $$\n", "\n", "has $f(y, t) = e^{-t} - y$.\n", "\n", "The method for using `scipy` is similar to the integration case.\n", "\n", "1. Define a function that specifies the system, by defining the RHS.\n", "2. Import the function that solves ODEs (`odeint`)\n", "3. Call the function, passing the RHS function, the initial data $\\vec{y}_0$, the times at which the solution is needed, and any parameters.\n", "\n", "To solve our example, we use:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The shape of the result is (50, 1).\n", "The value of y at t=1 is 0.7357588629292717.\n" ] } ], "source": [ "from numpy import exp\n", "from scipy.integrate import odeint\n", "\n", "def dydt(y, t):\n", " \"\"\"\n", " Defining the ODE dy/dt = e^{-t} - y.\n", " \n", " Parameters\n", " ----------\n", " \n", " y : real\n", " The value of y at time t (the current numerical approximation)\n", " t : real\n", " The current time t\n", " \n", " Returns\n", " -------\n", " \n", " dydt : real\n", " The RHS function defining the ODE.\n", " \"\"\"\n", " \n", " return exp(-t) - y\n", "\n", "t = numpy.linspace(0.0, 1.0)\n", "y0 = [1.0]\n", "\n", "y = odeint(dydt, y0, t)\n", "print(\"The shape of the result is {}.\".format(y.shape))\n", "print(\"The value of y at t=1 is {}.\".format(y[-1,0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the result for $y$ is not a vector, but a two dimensional array. This is because `scipy` will solve a general *system* of ODEs. This scalar case is a system of size $1$, but it still returns an array. To solve a system, the RHS function must take a vector for `y`, return a vector for `dydt`, and the initial data `y0` must be a vector. All these vectors must be the same size.\n", "\n", "The output is the numerical approximation to $y$ at the input times $t$, and can be immediately plotted:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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o3Dg45ZS08bJ//9zVSFoRW00kSSpT3/gG3HwzHH44XHxx7mokFZIn3pIklYA5\nc2Dw4HTqfe650KJF7ookNcSpJhi8JUnlb9EiGDEiLd4ZPx7WWSd3RZKWZquJJEkVoH17uOMO2HRT\n6N3bNfNSpTF4S5JUQlq2hEsuSWvmd90Vnngid0WSmoqtJpIklahbboFjjoGxY2G//XJXIwlWr9XE\nWzckSSpR++8Pm22WQvecOfDd77pmXipnnnhLklTiXn89TTzZbTf4/e9TO4qkPLy5UpKkCrb55jB1\n6mcB/P33c1ckaVUYvCVJKgNt28KkSfDlL0PPnvDqq7krkrSyDN6SJJWJFi1Sq8moUant5LHHclck\naWXY4y1JUhm67TY46qi0Zn7YsNzVSNXDzZUYvCVJ1eepp2DffeHb34ZTT3XiiVQMBm8M3pKk6jRv\nHgwZAjvumBbvOPFEKiynmkiSVKU22QQeegjeeQf23hsWLcpdkaRlKUrwDiEMDCHMDCHMCiGc2sDP\n24YQJoUQng4hPBtCOKLez14NIUwPITwVQni8GPVKklRO2rRJWy67dHHiiVTKCt5qEkJoBswC+gJv\nAtOAkTHGmfWuOQ1oG2M8LYTQEXgR2DDG+HEI4WWgW4zxvRX8HltNJElV7/zz4Zxz4NZbYeedc1cj\nVZ5SbzXpDrwUY3wtxrgYGA8MXeqaCKxT9/06wMIY48d1j0OR6pQkqeydeGKadDJoEEycmLsaSfW1\nKMLv2ASYW+/xG6QwXt8FwKQQwptAG+Cgej+LwD0hhCXAZTHGsYUsVpKkcjd0aOr9HjoUXnkFTjrJ\niSdSKVhh8A4hjAf+ATwCPBxjfLEAdQwAnoox7hlC2JIUtLePMf4D6BljnB9CWL/u+RkxxqkFqEGS\npIqx007wyCOwzz4wZw789rdpAY+kfFb4f8EY48gQQmegB3BCCKEvcCvwkxjjfxrxO+YBm9d7vGnd\nc/UdCfyi7vfNCSG8AmwD/DXGOL/u+XdCCLeQTssbDN5jxoz57/c1NTXU1NQ0ojxJkipTp07w8MNp\nwc5++8H48elGTEmNV1tbS21tbZO81wpvrgwh7FJ33aN1j4cD04HBMcbfrPAXhNCcdLNkX2A+8Dhw\ncIxxRr1rLgTejjGeEULYEPgrsAPwEdAsxviPEMLawBTgjBjjlAZ+jzdXSpLUgMWL4VvfgieegNtv\nT20oklbN6txc2Zi/dNoLWBxCOBn4J/A68A7wUmN+QYxxSQjheFJobgZcEWOcEUIYnX4cLwPOBP4Y\nQnim7mXJzY2OAAAaoUlEQVQ/iDG+G0L4EnBLCCHW1XptQ6FbkiQtW8uWMHYsnH027LprWje/ww65\nq5KqT2NOvL8KrPPpiXfdc98EXo4x3l/g+hrNE29Jklbshhvg+OPh6qth4MDc1Ujlx5XxGLwlSWqs\nhx+GAw+EM86A0aNzVyOVF4M3Bm9JklbG7Nlp1vfQoWnhTjM3ZkiNYvDG4C1J0spauDBNO9loIxg3\nDlq3zl2RVPpKfXOlJEkqQR06wD33pNPuvn1hwYLcFUmVzeAtSVIVa90arrsOeveG3XZLLSiSCsPg\nLUlSlWvWLI0a/N73UgD/y19yVyRVJoO3JEkC0oSTK66AffeFCRNyVyNVHm+ulCRJn/Pkkyl8n3wy\nfPe7EFbpNjKpMjnVBIO3JElN6fXX07jBmho4/3xo3jx3RVJpMHhj8JYkqam9/35atLPWWnD99bD2\n2rkrkvJznKAkSWpy7drB5Mmw3nrp5Ptvf8tdkVTeDN6SJGmZWrWCK6+EwYNh111hxozcFUnly1YT\nSZLUKFddBd//Ptx4YzoBl6qRrSaSJKngDj889XqPGAHXXpu7Gqn8eOItSZJWynPPwT77wLHHwg9/\n6LhBVRenmmDwliSpmObNS+G7Rw+44AJo0SJ3RVJxGLwxeEuSVGwffADDh0PLljB+PLRpk7siqfDs\n8ZYkSUXXti3cfjtssIHjBqXGMHhLkqRV1rIlXHEFDBmSxg3OnJm7Iql02ZElSZJWSwjw059Cp06w\nxx4wYQL07p27Kqn0eOItSZKaxBFHwNVXpzXzN96Yuxqp9HhzpSRJalLTp6dNlyedBN/9ruMGVVmc\naoLBW5KkUjJ3LgwaBH36wHnnQfPmuSuSmobBG4O3JEmlZtGi1HbStm3adLnWWrkrklaf4wQlSVLJ\nad8e7rwzzffec094553cFUl5GbwlSVLBtGoF48ZBv36w224we3buiqR8HCcoSZIKKgQ480zYfPM0\nZnDiRNhll9xVScXnibckSSqKY46BsWPTsp1Jk3JXIxWfwVuSJBXN4MFwxx0wejRccknuaqTicqqJ\nJEkqujlzYO+9Yfjw1IbirG+VC8cJYvCWJKncvPNOajvZaiu4/PJ0I6ZU6hwnKEmSys7668P998P7\n78M++8AHH+SuSCosg7ckScpmrbXgT3+CL385TTyZNy93RVLhGLwlSVJWzZvDhRfCIYekWd/PP5+7\nIqkwnOMtSZKyCwFOPRU22SRtubzxRthjj9xVSU3LE29JklQyDj0UrrsuTTu54Ybc1UhNyxNvSZJU\nUvr2hXvvTTdcvvEGfPe7jhtUZXCcoCRJKklz56ZZ3337wm9+k3rBpdyc443BW5KkSrRoEey3Xxo9\nePXV0Lp17opU7ZzjLUmSKlL79nD33dCsGQwYAO+9l7siadUZvCVJUklbYw24/nro1g169UotKFI5\nMnhLkqSS16xZ6vM++ug06/vZZ3NXJK08e7wlSVJZGT8eTjghjRvs0yd3Nao29nhLkqSqMXJkCt0H\nHZRCuFQunOMtSZLKTp8+n836fvPNNOtbKnW2mkiSpLL1+utp1veAAfDrX6decKmQnOONwVuSpGr1\n3nswdChstBGMG5emoEiFYo+3JEmqWuuuC1OmwCefpJPvRYtyVyQ1zOAtSZLKXuvW6UbL7beH3r3h\njTdyVyT9L4O3JEmqCM2bw/nnwze+kWZ9P/dc7oqkz3OqiSRJqhghwPe/DxtvDH37wk03we67565K\nSjzxliRJFefrX4drroEDD4Sbb85djZR44i1JkirSXnulmy4HD4b58+H443NXpGrnOEFJklTRXnkF\nBg6EYcPgzDNTO4q0qpzjjcFbkiQt24IF6eT7K1+Byy6Dli1zV6Ry5RxvSZKk5ejYEe67D955Jy3b\n+cc/clekamTwliRJVWHttWHixLThsk8fePvt3BWp2hi8JUlS1WjRAi6/HPbeG3r2hDlzclekauJU\nE0mSVFVCgJ/9DDbZJG25vO026NYtd1WqBp54S5KkqjR6NFx0UTr9vvvu3NWoGhi8JUlS1dpvP7jl\nFjj8cLj66tzVqNLZaiJJkqpaz57wwAPp5PvNN+EHP3DWtwrDOd6SJEnAvHkpfPfpA+edB83sC1AD\nXKCDwVuSJK2+RYvSnO8vfAHGjYM11shdkUqNC3QkSZKaQPv26UbLJUvS6ff77+euSJXE4C1JklRP\n69Zwww1pvfwee8D8+bkrUqUweEuSJC2leXO44AIYPjzdfDlrVu6KVAmcaiJJktSAEOD001O/9x57\nwK23QvfuuatSOfPEW5IkaTmOPhrGjoV99oE778xdjcqZwVuSJGkFBg+GSZPgyCPhqqtyV6NyZauJ\nJElSI+y662eLdv72NxftaOU5x1uSJGklzJsHAwfCnnu6aKcauUAHg7ckSSoeF+1ULxfoSJIkFdGn\ni3Y+/thFO2o8g7ckSdIqaN0abrzRRTtqvKIE7xDCwBDCzBDCrBDCqQ38vG0IYVII4ekQwrMhhCMa\n+1pJkqRcPl20c+CBadHOSy/lrkilrOA93iGEZsAsoC/wJjANGBljnFnvmtOAtjHG00IIHYEXgQ2B\nT1b02nrvYY+3JEnKZuxY+L//g9tug512yl2NCqXUe7y7Ay/FGF+LMS4GxgNDl7omAuvUfb8OsDDG\n+HEjXytJkpTdqFFwySWp53vKlNzVqBQVI3hvAsyt9/iNuufquwDoEkJ4E5gOnLgSr5UkSSoJQ4fC\nLbfAYYfBddflrkalplQW6AwAnoox7hlC2BK4J4Sw/cq+yZgxY/77fU1NDTU1NU1WoCRJUmP06gX3\n3ZdOvt96C04+OXdFWh21tbXU1tY2yXsVo8e7BzAmxjiw7vEPgRhjPKfeNbcDv4gxPlz3+D7gVNJ/\nGCz3tfXewx5vSZJUMl5/HQYMgH33hbPPdstlpSj1Hu9pQOcQQqcQQitgJDBpqWteA/oBhBA2BLYC\nXm7kayVJkkrO5pvD1Knw0ENwxBGweHHuipRbwYN3jHEJcDwwBXgeGB9jnBFCGB1COKbusjOB3UII\nzwD3AD+IMb67rNcWumZJkqSm0KFDajtZuDD1f//zn7krUk6ujJckSSqwxYvhmGNgxgy4/Xbo2DF3\nRVpVpd5qIkmSVNVatoQ//AH23DPdfPnaa7krUg6lMtVEkiSpooUAZ50FG26YwvfkybDddrmrUjEZ\nvCVJkoroxBNT+O7XD266CXbfPXdFKhZbTSRJkops5Mi0YGfYMJg4MXc1KhZPvCVJkjLo2xfuvBOG\nDIF33kkr51XZDN6SJEmZdOsGDz4IAwemLZenn+6inUrmOEFJkqTM5s9PK+Z79YLzz4fmzXNXpGVZ\nnXGCBm9JkqQS8P77acnOhhvCuHGwxhq5K1JDnOMtSZJU5tq1g7vugo8/hkGD4IMPclekpmbwliRJ\nKhGtW8ONN8KXvwx9+qS+b1UOg7ckSVIJad4cLr44TTvp2RNefjl3RWoqTjWRJEkqMSHAmDGp37t3\nb7jjDujaNXdVWl0Gb0mSpBL1rW/B+utD//5www2p/UTly1YTSZKkEjZsWArdBx0EEybkrkarwxNv\nSZKkEtenD9x9N+yzT9py+a1v5a5Iq8LgLUmSVAZ23BH+/GcYMCBNO/npT91yWW5coCNJklRG3nor\nrZjv0QMuuMAtl8XmAh1JkqQqseGGUFsLM2fCyJHw73/nrkiNZfCWJEkqM+3awZ13Qoyw995uuSwX\nBm9JkqQy1Lp1mnay9dZQU+OWy3Jg8JYkSSpTzZvDRRfBvvtCr15uuSx1TjWRJEkqY59uudxgg7Tl\ncvJk2GGH3FWpIQZvSZKkCnDccdCxI+y1F9x0E+yxR+6KtDRbTSRJkirEiBFw/fUwfDhMnJi7Gi3N\nE29JkqQK0rdvmngyZAgsWADf/GbuivQpg7ckSVKF6dYNHnwwbbl8+2047TS3XJYCN1dKkiRVqPnz\n05bLmho47zxoZpPxaludzZUGb0mSpAq2aBEMHQqbbAJ//CO0apW7ovLmynhJkiQ1qH17uOsu+Ne/\nUt/3P/6Ru6LqZfCWJEmqcGuuCRMmwKabppsvFyzIXVF1MnhLkiRVgRYt4PLLU/Du3Rtefz13RdXH\nqSaSJElVIgQ46yxYf/20Yv6uu6BLl9xVVQ+DtyRJUpU5+eQUvvfcE265BXbdNXdF1cFWE0mSpCp0\n6KFw5ZVp4smdd+aupjoYvCVJkqrU3nvDrbfCkUfCtdfmrqby2WoiSZJUxXbdFe67L4Xwd96Bk07K\nXVHlcoGOJEmSeP116N8fDjgAfv5zV8wvi5srMXhLkiStrgULYNAg2H57uOSSNIJQn+fmSkmSJK22\njh3h/vvT6fewYfDhh7krqiwGb0mSJP1XmzZw++3QujUMHAjvv5+7osph8JYkSdLntGoF112XWk72\n2AP+9rfcFVUGg7ckSZL+R7Nm8LvfwYEHQs+eMGdO7orKny3zkiRJalAI8JOfpC2Xu+8Od9wBXbvm\nrqp8GbwlSZK0XMceCx06pHGDEyakEK6VZ6uJJEmSVmj48NT3PWxY2napleeJtyRJkhqlXz+YPBmG\nDIGFC+Goo3JXVF4M3pIkSWq0nXaC2loYMCAt3PnBD3JXVD7cXClJkqSVNm9e6vkeNAjOOSdNQakG\nrozH4C1JklRs774LgwfDVlvB2LHQsmXuigrPlfGSJEkquvXWg3vugbffhgMOgH/9K3dFpc3gLUmS\npFW29tppykm7dqnv+733cldUugzekiRJWi0tW8K4cdCtW1ox/+abuSsqTQZvSZIkrbZmzeC882Dk\nSOjVC2bPzl1R6XGcoCRJkppECPCjH31+xfyOO+auqnQYvCVJktSkRo1KN14OGAA33ZTaT2SriSRJ\nkgrgwANh/Pi0an7ixNzVlAZPvCVJklQQe+4Jd96ZZn0vXAhHH527orwM3pIkSSqYbt3gwQc/v2I+\nrNL6mfLn5kpJkiQV3Lx5KXwPHAi//GX5rph3ZTwGb0mSpFJXCSvmXRkvSZKkkrf0ivkPP8xdUXEZ\nvCVJklQ0n66Yb9sW+veHRYtyV1Q8Bm9JkiQVVcuWcPXV8LWvpRnf8+fnrqg4DN6SJEkqumbN4Le/\nTXO+e/WCOXNyV1R4jhOUJElSFiHAj38MHTt+tmK+a9fcVRWOwVuSJElZHXssdOiQer4nTEghvBLZ\naiJJkqTshg+H665Lq+YnTcpdTWF44i1JkqSS0K8fTJ4M++6bZn4fcUTuipqWwVuSJEklY+ed4YEH\nPlsxf8opuStqOm6ulCRJUsmZOzeF7yFD4Oyz042YpcCV8Ri8JUmSKs3ChTBoEGy7LVx6KbQogV4N\nV8ZLkiSp4nToAPfdB2+8kW6+/Oij3BWtHoO3JEmSSlabNnDbbbDGGjBwILz/fu6KVp3BW5IkSSWt\nVSu49lro0gX69IG33spd0aoxeEuSJKnkNW8OF16YRg326gWvvJK7opVXlOAdQhgYQpgZQpgVQji1\ngZ+fEkJ4KoTwZAjh2RDCxyGE9nU/ezWEML3u548Xo15JkiSVnhBgzBg48UTo3RuefTZ3RSun4FNN\nQgjNgFlAX+BNYBowMsY4cxnXDwZOijH2q3v8MtAtxvjeCn6PU00kSZKqxPXXw0knwS23wG67Fe/3\nlvpUk+7ASzHG12KMi4HxwNDlXH8wcH29xwFbYiRJklTPwQfDVVfB0KFp22U5KEag3QSYW+/xG3XP\n/Y8QwprAQODmek9H4J4QwrQQwqiCVSlJkqSyMnBgmnhy5JHp5stSVwJjyD9nCDA1xrio3nM9Y4zz\nQwjrkwL4jBjj1IZePGbMmP9+X1NTQ01NTSFrlSRJUmY9esD996cQvnAhnHBC075/bW0ttbW1TfJe\nxejx7gGMiTEOrHv8QyDGGM9p4No/ATfGGMcv471+Cvw9xvibBn5mj7ckSVKVevVV6N8fRo6EM84o\n3Ir5Uu/xngZ0DiF0CiG0AkYCk5a+KITQDtgDuLXec2uFENrUfb820B94rgg1S5IkqYx88YswdSrc\ncQccdxwsWZK7ov9V8OAdY1wCHA9MAZ4HxscYZ4QQRocQjql36X7A3THGD+s9tyEwNYTwFPAocFuM\ncUqha5YkSVL52WADeOABePHFdPPlv/+du6LPK3irSbHYaiJJkiSAjz6CQw6Bv/89jRts06bp3rvU\nW00kSZKkomndGm68ETp1gr59YcGC3BUlBm9JkiRVnBYtYOxY2HPPtOVy7twVv6bgNeUuQJIkSSqE\nEOAXv4COHaFXL7j7bthmm3z1GLwlSZJU0b73PejQAfr0gUmTYOed89Rhq4kkSZIq3hFHwKWXwqBB\ncO+9eWoweEuSJKkq7Lsv3HxzmngyYULxf7+tJpIkSaoau+8OU6akk++FC2H06OL9boO3JEmSqkrX\nrvDQQ2nF/MKFcNpphVsxX58LdCRJklSV5s+HAQPSrO9zz4VmjWjCXp0FOgZvSZIkVa333oMhQ+BL\nX4I//AFatlz+9W6ulCRJklbBuuumnu9334X994d//atwv8vgLUmSpKq21lowcWIK4QMGwKJFhfk9\nBm9JkiRVvZYt4aqroFs32GOP1P/d1AzekiRJEunmyvPOgxEj0or5OXOa9v0dJyhJkiTVCQFOPz2t\nmN99d5g8GXbYoWne2+AtSZIkLeXYY1P43muvtO2yd+/Vf09bTSRJkqQGDB8O114LBxwAt922+u9n\n8JYkSZKWYa+94I47YNQoGDdu9d7LBTqSJEnSCsyYkUYNzp3r5kqDtyRJkgrq9dehUyeDt8FbkiRJ\nBefKeEmSJKnEGbwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFYHBW5IkSSoCg7ckSZJUBAZvSZIk\nqQgM3pIkSVIRGLwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFYHBW5IkSSoCg7ckSZJUBAZvSZIk\nqQgM3pIkSVIRGLwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFYHBW5IkSSoCg7ckSZJUBAZvSZIk\nqQgM3pIkSVIRGLwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFYHBW5IkSSoCg7ckSZJUBAZvSZIk\nqQgM3pIkSVIRGLwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFYHBW5IkSSoCg7ckSZJUBAZvSZIk\nqQgM3pIkSVIRGLwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFYHBW5IkSSoCg7ckSZJUBAZvSZIk\nqQgM3pIkSVIRGLwlSZKkIjB4S5IkSUVg8JYkSZKKwOAtSZIkFUFRgncIYWAIYWYIYVYI4dQGfn5K\nCOGpEMKTIYRnQwgfhxDaN+a1kiRJUjkoePAOITQDLgAGAF8FDg4hbFP/mhjjr2OMO8YYvwacBtTG\nGBc15rXSstTW1uYuQSXIz4Ua4udCDfFzoaZWjBPv7sBLMcbXYoyLgfHA0OVcfzBw/Sq+Vvov/4Wp\nhvi5UEP8XKghfi7U1IoRvDcB5tZ7/Ebdc/8jhLAmMBC4eWVfK0mSJJWyUru5cggwNca4KHchkiRJ\nUlMKMcbC/oIQegBjYowD6x7/EIgxxnMauPZPwI0xxvGr8NrC/oNIkiRJQIwxrMrrihG8mwMvAn2B\n+cDjwMExxhlLXdcOeBnYNMb44cq8VpIkSSp1LQr9C2KMS0IIxwNTSK0tV8QYZ4QQRqcfx8vqLt0P\nuPvT0L281xa6ZkmSJKmpFfzEW5IkSVLp3Vy5XI1ZphNC+F0I4aUQwtMhhK7FrlHF14gFTYeEEKbX\nfU0NIWyXo04VV2OXb4UQdg4hLA4hHFDM+pRHI/8cqalb6vZcCOGBYteo4mvEnyNtQwiT6rLFsyGE\nIzKUqSIKIVwRQngrhPDMcq5Z6cxZNsG7Mct0Qgh7A1vGGL8MjAYuKXqhKqpGLll6Gdg9xrgDcCYw\ntrhVqtgau3yr7rqzgbuLW6FyaOSfI+2AC4HBMcZtgeFFL1RF1ch/X3wbeD7G2BXoA5wbQih4u66y\nupL0mWjQqmbOsgneNG6ZzlBgHECM8TGgXQhhw+KWqSJb4ecixvhojPH9uoeP4iz4atDY5VvfASYA\nbxezOGXTmM/FIcDNMcZ5ADHGBUWuUcXXmM9FBNap+34dYGGM8eMi1qgiizFOBd5bziWrlDnLKXg3\nZpnO0tfMa+AaVZaVXbL0TeDOglakUrDCz0UIYWNgvxjjxcAqjYVS2WnMvy+2AtYLITwQQpgWQjis\naNUpl8Z8Li4AuoQQ3gSmAycWqTaVrlXKnP41iapGCKEPcCTQK3ctKgm/Ber3chq+BenPxa8BewJr\nA38JIfwlxjg7b1nKbADwVIxxzxDClsA9IYTtY4z/yF2Yyks5Be95wOb1Hm9a99zS12y2gmtUWRrz\nuSCEsD1wGTAwxri8vzpSZWjM52InYHwIIQAdgb1DCItjjJOKVKOKrzGfizeABTHGj4CPQggPATsA\nBu/K1ZjPxZHALwBijHNCCK8A2wB/LUqFKkWrlDnLqdVkGtA5hNAphNAKGAks/QfkJOAb8N+tl4ti\njG8Vt0wV2Qo/FyGEzYGbgcNijHMy1KjiW+HnIsa4Rd3Xl0h93scZuiteY/4cuRXoFUJoHkJYC9gF\ncH9EZWvM5+I1oB9AXR/vVqQb91XZAsv+29BVypxlc+LdmEU8McbJIYRBIYTZwD9J/4WqCtbIBU0/\nAdYDLqo73VwcY+yer2oV2kos7vrvS4pepIqukX+OzAwh3A08AywBLosxvpCxbBVYI/99cSbwx3qj\n5X4QY3w3U8kqghDCdUAN0CGE8DrwU6AVq5k5XaAj6f+3a4c2FYAxFEZ7JQKNIHgGIHgciilYgrXe\nGBi2IGyALIYZ+uel50xw5ZemAMCAa3o1AQCAqyW8AQBggPAGAIABwhsAAAYIbwAAGCC8AQBggPAG\nAIABwhsAAAYIb4Clkjwm+Ti9A2AL4Q2w10tVfZ0eAbCF8AZYKMlrVb1X1UOSu9N7ADZId5/eAMAB\nSS7d/XZ6B8AWLt4AC/1fuX9O7wDYRHgD7PRcVZ9JnpLcnB4DsIHwBtjpu6ruq+q2u39PjwHYwI83\nAAAMcPEGAIABwhsAAAYIbwAAGCC8AQBggPAGAIABwhsAAAYIbwAAGCC8AQBgwB+HrummWkijkQAA\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pyplot.plot(t, y[:,0])\n", "pyplot.xlabel(r'$t$')\n", "pyplot.ylabel(r'$y$')\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Passing parameters is also similar to the integration case. For example, consider the problem\n", "\n", "$$ \\frac{\\text{d}}{\\text{d} t} \\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} -y + \\alpha \\\\ x \\end{pmatrix}, \\qquad \\begin{pmatrix} x \\\\ y \\end{pmatrix}(0) = \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}. $$\n", "\n", "If $\\alpha$ is zero, the solution is a circle in the $x, y$ plane. We solve this using `odeint`, denoting the state vector $\\vec{z} = (x, y)^T$:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy\n", "from scipy.integrate import odeint\n", "\n", "def dzdt(z, t, alpha):\n", " \"\"\"\n", " Defining the ODE dz/dt.\n", " \n", " Parameters\n", " ----------\n", " \n", " z : real, list\n", " The value of z at time t (the current numerical approximation)\n", " t : real\n", " The current time t\n", " alpha : real\n", " Parameter\n", " \n", " Returns\n", " -------\n", " \n", " dzdt : real\n", " The RHS function defining the ODE.\n", " \"\"\"\n", " \n", " dzdt = numpy.zeros_like(z)\n", " x, y = z\n", " dzdt[0] = -y + alpha\n", " dzdt[1] = x\n", " \n", " return dzdt\n", "\n", "t = numpy.linspace(0.0, 50.0, 1000)\n", "z0 = [1.0, 0.0]\n", "alpha = 1e-5\n", "\n", "z = odeint(dzdt, z0, t, args=(alpha,))" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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qu4h0mRPMAABMXVWzlF1EAACgRwTsLnriiXJ83evy1gEAQO9YItJFVf1KAwCg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\nJWBDn1i/fvQ2fmvWtE9eAzAVl18ecdh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = pyplot.figure(figsize=(12,12))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.plot(z[:,0], z[:,1])\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$y$')\n", "ax.set_xlim(-1.1, 1.1)\n", "ax.set_ylim(-1.1, 1.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further reading" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Earlier we introduced `scipy` for Linear Algebra, and gave links there. Most of those links cover the full `scipy` package. The [scipy documentation](http://docs.scipy.org/doc/scipy/reference/) is comprehensive. Johansson [also has a tutorial on scipy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-3-Scipy.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: Lorenz attractor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Lorenz system is a set of ordinary differential equations which can be written\n", "\n", "$$ \\frac{\\text{d} \\vec{v}}{\\text{d} \\vec{t}} = \\vec{f}(\\vec{v}) $$\n", "\n", "where the variables in the state vector $\\vec{v}$ are\n", "\n", "$$ \\vec{v} = \\begin{pmatrix} x(t) \\\\ y(t) \\\\ z(t) \\end{pmatrix} $$\n", "\n", "and the function defining the ODE is\n", "\n", "$$ \\vec{f} = \\begin{pmatrix} \\sigma \\left( y(t) - x(t) \\right) \\\\ x(t) \\left( \\rho - z(t) \\right) - y(t) \\\\ x(t) y(t) - \\beta z(t) \\end{pmatrix}. $$\n", "\n", "The parameters $\\sigma, \\rho, \\beta$ are all real numbers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Write a function `dvdt(v, t, params)` that returns $\\vec{f}$ given $\\vec{v}, t$ and the parameters $\\sigma, \\rho, \\beta$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "Fix $\\sigma=10, \\beta=8/3$. Set initial data to be $\\vec{v}(0) = \\vec{1}$. Using `scipy`, specifically the `odeint` function of `scipy.integrate`, solve the Lorenz system up to $t=100$ for $\\rho=13, 14, 15$ and $28$.\n", "\n", "Plot your results in 3d, plotting $x, y, z$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3\n", "\n", "Fix $\\rho = 28$. Solve the Lorenz system twice, up to $t=40$, using the two different initial conditions $\\vec{v}(0) = \\vec{1}$ and $\\vec{v}(0) = \\vec{1} + \\vec{10^{-5}}$.\n", "\n", "Show four plots. Each plot should show the two solutions on the same axes, plotting $x, y$ and $z$. Each plot should show $10$ units of time, ie the first shows $t \\in [0, 10]$, the second shows $t \\in [10, 20]$, and so on.\n", "\n", "This shows the *sensitive dependence on initial conditions* that is characteristic of chaotic behaviour." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: Mandelbrot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Mandelbrot set is also generated from a sequence, $\\{ z_n \\}$, using the relation\n", "\n", "$$ z_{n+1} = z_n^2 + c, \\qquad z_0 = 0. $$\n", "\n", "The members of the sequence, and the constant $c$, are all complex. The point in the complex plane at $c$ is in the Mandelbrot set only if the $|z_n| < 2$ for all members of the sequence. In reality, checking the first 100 iterations is sufficient.\n", "\n", "**Note**: the Python notation for a complex number $x + \\text{i} y$ is `x + yj`: that is, `j` is used to indicate $\\sqrt{-1}$. If you know the values of `x` and `y` then `x + yj` constructs a complex number; if they are stored in variables you can use `complex(x, y)`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Write a function that checks if the point $c$ is in the Mandelbrot set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "Check the points $c=0$ and $c=\\pm 2 \\pm 2 \\text{i}$ and ensure they do what you expect. (What *should* you expect?)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3\n", "\n", "Write a function that, given $N$\n", "\n", "1. generates an $N \\times N$ grid spanning $c = x + \\text{i} y$, for $-2 \\le x \\le 2$ and $-2 \\le y \\le 2$;\n", "2. returns an $N\\times N$ array containing one if the associated grid point is in the Mandelbrot set, and zero otherwise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4\n", "\n", "Using the function `imshow` from `matplotlib`, plot the resulting array for a $100 \\times 100$ array to make sure you see the expected shape." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 5\n", "\n", "Modify your functions so that, instead of returning whether a point is inside the set or not, it returns the logarithm of the number of iterations it takes. Plot the result using `imshow` again." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 6\n", "\n", "Try some higher resolution plots, and try plotting only a section to see the structure. **Note** this is not a good way to get high accuracy close up images!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: The shortest published Mathematical paper" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A [candidate for the shortest mathematical paper ever](http://www.ams.org/journals/bull/1966-72-06/S0002-9904-1966-11654-3/S0002-9904-1966-11654-3.pdf) shows the following result:\n", "\n", "$$ 27^5 + 84^5 + 110^5 + 133^5 = 144^5. $$\n", "\n", "This is interesting as\n", "\n", "> This is a counterexample to a conjecture by Euler ... that at least $n$ $n$th powers are required to sum to an $n$th power, $n > 2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Using Python, check the equation above is true." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "The more interesting statement in the paper is that\n", "\n", "$$ 27^5 + 84^5 + 110^5 + 133^5 = 144^5. $$\n", "\n", "is\n", "\n", "> the smallest instance in which four fifth powers sum to a fifth power.\n", "\n", "Interpreting \"the smallest instance\" to mean the solution where the right hand side term (the largest integer) is the smallest, we want to use Python to check this statement.\n", "\n", "We are going to need to generate all possible combinations of four integers $a, b, c, d$ and test if $a^5 + b^5 + c^5 + d^5$ matches $e^5$ where $e$ is another integer. \n", "\n", "The problem is the number of combinations grows very fast - the standard formula says that for a list of length $\\ell$ there are\n", "\n", "$$ \\begin{pmatrix} \\ell \\\\ k \\end{pmatrix} = \\frac{\\ell!}{k! (\\ell-k)!} $$\n", "\n", "combinations of length $k$. For $k=4$ as needed here we will have $\\ell (\\ell-1) (\\ell-2) (\\ell-3) / 24$ combinations.\n", "\n", "Show, by getting Python to compute the number of combinations $N = \\begin{pmatrix} \\ell \\\\ 4 \\end{pmatrix}$ that $N$ grows roughly as $\\ell^4$. To do this, plot the number of combinations and $\\ell^4$ on a log-log scale. Restrict to $\\ell \\le 50$.\n", "\n", "You may find the `combinations` function from the `itertools` package useful." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3\n", "\n", "With 17 million combinations to work with, we'll need to be a little careful how we compute. To check the interesting statement in the paper,\n", "\n", "1. Construct a `numpy` array containing all integers in $1, \\dots, 144$ to the fifth power. \n", "2. Construct a list of all combinations of four elements from this array.\n", "3. Construct a list of sums of all these combinations.\n", "4. Loop over one list and check if the entry appears in the other list (ie, use the `in` keyword).\n", "\n", "By printing out any entries that pass this check, you should see only the solution given in the paper." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" }, "nbconvert": { "title": "Scientific Python" } }, "nbformat": 4, "nbformat_minor": 0 }