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Python_Introduction.ipynb.txt
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Python_Introduction.ipynb.txt
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Introduction to Python\n",
"You will need to have a version of Python installed (hopefully a new version like 3.9 and above). You will also need to have some of the standard Python libraries installed, either via 'pip install ...' or via a conda environment. Libraries that you will need for this class include: numpy, scipy, matplotlib. \n",
"\n",
"For folks who are used to matlab, note that Python starts with the zero index while Matlab starts with index 1. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4\n",
"4\n",
"1.0\n",
"-12\n",
"0\n"
]
}
],
"source": [
"# Basic Operations \n",
"# -- similar to many basic programming languages (C, etc.)\n",
"\n",
"# use the python function 'print' to print the output\n",
"print(2 + 2)\n",
"print(2 * 2)\n",
"print(2 / 2)\n",
"print(2 - 2 * 7) # Order of operations matters\n",
"print((2 - 2) * 7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Notice a big difference with C or Matlab -- no semicolons needed at the end of statements! However, we will need colon symbols for indicating an indented block (see the loops below)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4\n"
]
}
],
"source": [
"# Assign variables using '=' symbol\n",
"a = 2 + 2\n",
"print(a)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"45\n"
]
}
],
"source": [
"# Loops\n",
"count = 0 # Initialize the variable \"count\"\n",
"\n",
"# Add all the numbers 1-10\n",
"for ii in range(10): # note that range(10) = [0, 2, ..., 9]\n",
" count = ii + count # indicate a code block to loop over by indenting the code lines\n",
" \n",
"print(count)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10\n"
]
}
],
"source": [
"counter = count # Assign count to counter\n",
"\n",
"# Subtract numbers until count is not greater than 10\n",
"while (counter > 10):\n",
" counter = counter - 1\n",
"print(counter)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3\n",
"3\n"
]
}
],
"source": [
"# Create a vector (this is also called an 'array')\n",
"A_Vector = [1, 2, 3, 4]\n",
"\n",
"# Access a particular element of the vector\n",
"print(A_Vector[2]) # prints 3 because A_vector[0] is the start of the vector!\n",
"print(A_Vector[-2]) # prints 3 because A_vector[-1] is the end of the vector, i.e. we are counting backwards from the end\n",
"\n",
"# best way to work with vectors and multi-dimensional 'arrays'\n",
"# is to use the NumPy library, which is imported as follows:\n",
"import numpy as np # call the numpy library np for shorthand\n",
"\n",
"B_Vector = np.ones(4) # same as B_Vector = [1, 1, 1, 1]\n",
"A_Vector = np.array([1, 2, 3, 4])\n",
"\n",
"# np.zeros(N) -- make a vector of N elements, all initialized to 0\n",
"# np.random.randn(N) -- make a vector of N elements, all randomly initialized between (0, 1)\n",
"# np.eye(N) -- make the identity matrix of size N x N\n",
"\n",
"# Create a numpy-style Matrix\n",
"\n",
"A_Matrix = np.array([[1, 2, 3, 4],\n",
" [5, 6, 7, 8]])\n",
"\n",
"# Matrices are like stacks of vectors so [], zeros, ones, eye.. all work to\n",
"# create matrices as well.\n",
"\n",
"# np.zeros((N, N, N)) -- Make a N x N x N tensor with elements all initialized to 0 "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[30 70] (2, 4) (4, 2)\n",
"A = [[1 2 3 4]\n",
" [5 6 7 8]]\n",
"A^2 = [[ 1 4 9 16]\n",
" [25 36 49 64]]\n"
]
}
],
"source": [
"# Operations on Vectors/Matrices\n",
"\n",
"# matrices and vectors have to have one matching \n",
"# dimension to be multiplied together\n",
"mat_vec_product = A_Matrix @ A_Vector \n",
"\n",
"# The dimension of numpy objects can be accessed by .shape and\n",
"# the .T operator takes the transpose (NxM to MxN)\n",
"print(mat_vec_product, A_Matrix.shape, A_Matrix.T.shape)\n",
"\n",
"# square every element in the matrix A. Note that this is different than doing A @ A\n",
"elementwise_square = A_Matrix ** 2 \n",
"\n",
"# can print multiple things by separating with a comma in the print function\n",
"print('A = ', A_Matrix)\n",
"print('A^2 = ', elementwise_square)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Create a function in Python \n",
"# Time, and fuctions of time f(t) are represented by vectors \n",
"\n",
"# numpy.linspace(-100, 100, 200) generates a 200-dimensional vector by splitting up the\n",
"# interval (-100, 100) into a uniform grid. Default is to omit the last point (t=100)\n",
"the_time = np.linspace(-100, 100, 200) \n",
"\n",
"F1 = (the_time ** 2) * np.sin(the_time) # defining t^2 * sin(t)\n",
"F2 = (the_time ** 2) # defining t^2"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# For plotting, we need to import another standard python library\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(the_time, F1, 'r-', linewidth=2) # Plots F1(t) in a red solid line\n",
"plt.plot(the_time, F2, 'k--', linewidth=2) # Plots F2(t) in a black dashed line\n",
"plt.xlabel('Time') # Adds the label \"time\" to the x-axis\n",
"plt.ylabel('Functions') # Adds the label \"functions\" to the y-axis\n",
"plt.legend(['F1','F2']) # Creates a legend with entries \"F1\", \"F2\"\n",
"plt.grid(True) # Turns on the grid lines \n",
"plt.title('Plots of F1 and F2') # Gives the plot a title\n",
"plt.show() # actually show the plot (more important when not using a Jupyter notebook)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ax - b = [-1.11022302e-16 1.33226763e-15]\n",
"sum(AAxx - bb) = 8.780823290699402e-14\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"<ipython-input-5-f32bcafc0812>:14: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
"To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
" x, _, _, _ = np.linalg.lstsq(A, b)\n",
"<ipython-input-5-f32bcafc0812>:22: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
"To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
" xx, _, _, _ = np.linalg.lstsq(AA, bb)\n"
]
}
],
"source": [
"# Linear System Solving (2 equations + 2 unknowns) \n",
"\n",
"# Imagine we have the following 2 algebraic equations\n",
"# z + 2y = 1\n",
"# 4z + 5y = 1\n",
"\n",
"A = np.array([[1, 2], [4, 5]])\n",
"b = np.array([1, 1])\n",
"\n",
"# The following will solve Ax = b in a least-squares sense (if an exact solution doesn't exist)\n",
"# Note that this is usually what A\\b does in matlab\n",
"\n",
"# if function returns a bunch of stuff, and you don't care about that stuff, use a _\n",
"x, _, _, _ = np.linalg.lstsq(A, b) \n",
"print('Ax - b = ', A @ x - b)\n",
"\n",
"# Even for very large system\n",
"\n",
"AA = np.random.randn(100, 100)\n",
"bb = np.random.randn(100)\n",
"\n",
"xx, _, _, _ = np.linalg.lstsq(AA, bb) \n",
"print('sum(AAxx - bb) = ', np.sum(AA @ xx - bb)) # get like 1e-14, pretty close to zero\n",
"\n",
"# You might get a FutureWarning here -- this is letting you know something\n",
"# might be off in the lstsq function -- in this case it is fine"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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fT3p6OlOnTr1w93pt6LeaF91/VSrHswv5cstxu0NRStmsbDXWrFmzSEtLY+vWrQwaNIj09HSmT5/OgQMHLimzatUqhgwZQkJCAoGBgdxzzz0sWbKEFStWMHjwYNLS0gBreJOqjB8/nqlTp+J0OnnnnXcuDPteG3oF4kXXtGtCSmwYs1YeYlS3ZLvDUUoBjHyOgjoezh3glltu4bHHHmPt2rUUFBTQo0cPrr/+embOnFlpmcqGXTfGVHsSuzFjxvD8889z7bXX0qtXL+Li4qpVviJ6BeJFjgDhrj7NWbo7g/0ZeXaHo5SyUWRkJEOGDOH+++9n7Nix9O/fn2XLlrF7t3XPWH5+Pjt37rykTL9+/Vi8eDEZGRk4nU5mzpzJNddcw4ABA1i8eDH79lk9PctXYcHlw76HhoZyww038PDDD3Pfffd55Jw0gXjZ7b2b4wgQZq06ZHcoSimbjR07lg0bNnDXXXeRkJDAtGnTGDt27IV50cvP/ZGUlMSf/vQnhg4dSvfu3enZsydjxowhISGBKVOm8L3vfY/u3btz5513Xnasu+66i7/85S/06NGDPXusWVPvueceRIThw4d75HxsrcISkRHAi4ADeMMY81y59Y8D97jeBgIdgQRjzGkR2Q/kAE6gxBjTu84Cr4amMaFc26EJ7685xGPXtyM4UHO2Ug3Vrbfeekm11LXXXnvZ0OxgTTB13t13311he8XIkSMvmytkwoQJFxrHBw0adEk33pycHJYuXcr999/vsfngbUsgIuIAXgGuBw4Dq0RkjjHmwhkbY/4C/MW1/c3Az4wxZa/VhhpjMuow7Bq5u28Lvt56gnnbTnBj1yS7w1FKNUB33303Bw4cqHC+kJqy8+dwX2C3MWavMaYImAWMucL2Y4HKW5t82OB2CSTHhGo1llLKNm+//TYbN24kPj7eY/u0sworBSj7jXoY6FfRhiISDowAJpVZbICvRMQArxtjplRSdiIwESAxMfGSS8PqyM3NrXFZgF5xTj7deYqPvlhAo1D/qMaq7Tn7Iz3n+ikmJobs7OwLPZecTmel84rXV+6cszGGwsJCt/8/2JlAKuqDVnGfNbgZWFau+mqQMeaoiDQBvhaR7caYJZft0EosUwB69+5thgwZUqNgFy1aRE3LAjTvnMsnf1vMqfCW3Dq4dY33U5dqe87+SM+5ftq3bx9FRUXExcUhIuTY0I3XblWdszGGzMxMYmNj6dGjh1v7tDOBHAaal3nfDDhaybZ3Ua76yhhz1PV8UkQ+wqoSuyyB+IrWCZGkN4/lw7VHmOgnCUSp+qJZs2YcPnyYU6dOAVBYWEhoaKjNUdUtd845NDSUZs2aub1POxPIKqCtiKQBR7CSxGVdDUQkBrgG+EGZZRFAgDEmx/V6OPBMnURdC9/vmcJvP97C1qPZdEqOtjscpRqMoKCgC3dtg3XV5e6v7PrCG+dsW2W8MaYEq03jS2Ab8K4xZouIPCQiD5XZ9FbgK2NM2TvxEoGlIrIBWAl8Zoz5oq5ir6lR3ZIJcggfrj1sdyhKKVVrtt4HYoyZC8wtt+y1cu+nAdPKLdsLdPdyeB7XKCKYazs0Yfb6o0we2YFAHWBRKeXH9Busjn2vZzMycs/xzS6fv31FKaWuSBNIHRvavgkxYUF8sqGy/gJKKeUfNIHUseDAAEZ0bspXW09QWOy0OxyllKoxTSA2GNU9idxzJSzacdLuUJRSqsY0gdhgQKs44iKC+WTjMbtDUUqpGtMEYoNARwA3dk1i/rYT5J0rsTscpZSqEU0gNhnVLYnC4lLmbTthdyhKKVUjmkBs0ie1MYnRIXyq1VhKKT+lCcQmAQHCqG7JLN5xirMFxXaHo5RS1aYJxEajuiVR5Czlqy3H7Q5FKaWqTROIjdKbx9KsUZhWYyml/JImEBuJCDd3T2bp7gxO5xXZHY5SSlWLJhCb3dQ1CWepYd5W7Y2llPIvmkBs1jk5muaNw5i7WauxlFL+RROIzUSEG7sksWx3BmfztTeWUsp/aALxASO7JlHsNHpToVLKr2gC8QHdm8WQHBPK51qNpZTyI7YmEBEZISI7RGS3iEyuYP0QETkrIutdjyfdLetPRISRXZNYsjODnEKtxlJK+QfbEoiIOIBXgJFAJ2CsiHSqYNNvjDHprscz1SzrN27s2pQiZykLtusQ70op/2DnFUhfYLcxZq8xpgiYBYypg7I+qUfzRiRGhzB3k1ZjKaX8Q6CNx04BDpV5fxjoV8F2A0RkA3AU+IUxZks1yiIiE4GJAImJiSxatKhGwebm5ta4rLu6xjpZsO0EX8xbSGigePVY7qiLc/Y1es4Ng56zZ9iZQCr6hjTl3q8FWhpjckXkRmA20NbNstZCY6YAUwB69+5thgwZUqNgFy1aRE3LuiusRSbzpqygpEl7hnRL9uqx3FEX5+xr9JwbBj1nz7CzCusw0LzM+2ZYVxkXGGOyjTG5rtdzgSARiXenrD/qndqY+MgQPt+kgysqpXyfnQlkFdBWRNJEJBi4C5hTdgMRaSoi4nrdFyveTHfK+iNHgDCiSyILtp+koMhpdzhKKXVFtiUQY0wJMAn4EtgGvGuM2SIiD4nIQ67NbgM2u9pAXgLuMpYKy9b9WXjejV2SKCh2snin9sZSSvk2O9tAzldLzS237LUyr18GXna3bH3QN60xjSOCmbvpOCO6JNkdjlJKVUrvRPcxgY4AhndKZP62ExQWazWWUsp3aQLxQSO7JpFX5OSbXRl2h6KUUpXSBOKDBraOIyYsiM/1pkKllA/TBOKDghwBXN8pka+3neBciVZjKaV8kyYQH3Vj16bkFJawfHem3aEopVSFNIH4qEFt4okKCdSxsZRSPksTiI8KCXRwXadEvtp6gmJnqd3hKKXUZTSB+LCRXZpytqCYb/doNZZSyvdoAvFhg9slEBHs0GospZRP0gTiw0KDHAzrmMiXW45rNZZSyudoAvFxN3VL4ky+VmMppXyPJhAfd027BCJDAvlso1ZjKaV8iyYQHxca5OD6Tol8seU4RSVajaWU8h2aQPzATV2TOFtQzLI9OjaWUsp3aALxA1e3iycqVKuxlFK+RROIHwgJdDC8U1O+3HJcx8ZSSvkMTSB+YlS3JHIKS1iqQ7wrpXyErTMSisgI4EXAAbxhjHmu3Pp7gCdcb3OBh40xG1zr9gM5gBMoMcb0rqu47TCoTTwxYUF8tvEYwzom2h1O3Sp1wsmtcGQNnNkPeafAGAgMgegUaNwKUnpBo5Z2R6pUg2JbAhERB/AKcD1wGFglInOMMVvLbLYPuMYYc0ZERgJTgH5l1g81xjSIn+TBgQHc0DmRuZuOU1jsJDTIYXdI3nd8E6yeCtvmWEkDICAIIuJBHFCcDwWnL24f2xLajYBud0JKTxCxJ26lGgg7r0D6AruNMXsBRGQWMAa4kECMMcvLbL8CaFanEfqYm7ol8+7qwyzZeYrhnZvaHY73HN8E856G3fMgMAzaj4D2N7quMtIgoEzN67lcyNwNh76DvYtgzTRY+To06QQDH4Uu34fAYJtORKn6TYwx9hxY5DZghDHmAdf7cUA/Y8ykSrb/BdChzPb7gDOAAV43xkyppNxEYCJAYmJir1mzZtUo3tzcXCIjI2tU1lNKSg0/XZhPl3gHD3UP9frx6vqcA5znSNv3Fs0Of0ZJYASHmo/haPJISoLcjyGwOJeEU8tJOfIpkXkHKAyJY3/qPRxvOhSk6iY/X/h3rmt6zg1Dbc556NChaypsJjDGVPkAIoAA1+t2wGggyJ2yV9jn7VjtHuffjwP+Wcm2Q4FtQFyZZcmu5ybABmBwVcfs1auXqamFCxfWuKwnTf5gg+n0289NQVGJ149Vp+d8crsxr/Q35qloYz75qTF5mbXbX2mpMTu/MmbKUGufrw4yZu+SKov5yr9zXdJzbhhqc87AalPBd6q7vbCWAKEikgLMB+4DplU7jV3qMNC8zPtmwNHyG4lIN+ANYIwx5sKAUMaYo67nk8BHWFVi9d5NXZPJK3KyaMdJu0PxnN3z4d/XQu5J+MEHMOofEN64dvsUgbbXwwPz4fv/gYKzMH0UfPxjKMjyTNxKNXDuJhAxxuQD38O6SrgV6FTLY68C2opImogEA3cBcy45qEgL4ENgnDFmZ5nlESISdf41MBzYXMt4/EL/Vo2JiwhmzobLcq1/2vguvH0HNEqFHy2BNtd5dv8i0PU2mLQSrvoZrJ8Jr/SD7XM9exylGiC3E4iIDADuAT5zLatVA7wxpgSYBHyJVT31rjFmi4g8JCIPuTZ7EogD/iUi60VktWt5IrBURDYAK4HPjDFf1CYefxHoCODm7snM23aS7MJiu8Opnc0fwEc/ghYD4L65EJPivWMFhcF1T8OD861eXLPGwqePQXGB946pVD3nbhL4CfAr4CPXl3wrYGFtD26MmQvMLbfstTKvHwAeqKDcXqB7bY/vr27pkcK05fv5YtNx7ujTvOoCvmjH5/DhRGjeH+5+F4LD6+a4yT3gwYWw4BlY/k84uAJunwoJ7evm+ErVI25dgRhjlhhjRhtj/ux6v9cY86h3Q1OV6d4shtS4cD5ad8TuUGrm6Dp4bwI07QZ3v1N3yeO8wGAY/ge4533IPQ5ThsD6t+s2BqXqAbcSiIi0E5EpIvKViCw4//B2cKpiIsItPVJYsS+TY2f9rAom5wTMvBsiEqwrj9Bo+2Jpez08tMy6v2T2wzD3l0hpiX3xKOVn3G0DeQ9YB/wGeLzMQ9nklvQUjIE56/2oMb2kCN75ARRmwV1vQ2SC3RFBdBKMmw39fwwrX6f7hich95TdUSnlF9xNICXGmFeNMSuNMWvOP7wambqi1PgI0pvH+lc11qI/wuGVMOYVSOpmdzQXOQJhxB/h1ilE5eyyqrSOrrM7KqV8nrsJ5BMReUREkkSk8fmHVyNTVbq1Rwrbj+ew/Xi23aFUbe9iWPoC9LwXunzP7mgq1v1O1vV4zur6+58bYMM7dkeklE9zN4Hci1VltRxY43qsvmIJ5XWjuiXhCBBmr/PxaqyCM1Z33bg2MOJPdkdzRblRrWHiImjWBz6aCF/9xhoNWCl1GXd7YaVV8Gjl7eDUlcVFhnBNuwQ+Xn+E0lJ7xjRzy1e/te4y//4bEBxhdzRVi4iH8bOhzwNWV9+379C715WqgLu9sIJE5FERed/1mCQiQd4OTlXtlh4pHDtbyIq9mVVvbId938C6t2DgJEhOtzsa9zmC4Ka/wagXrFF+3xgGp3ZWWUyphsTdKqxXgV7Av1yPXq5lymbDOyUSFRrIu6sP2R3K5YoL4JOfWMOUXDPZ7mhqpvd9cO8n1hXIG8Ng51d2R6SUz3A3gfQxxtxrjFngetwH9PFmYMo9oUEOxqQn8/nm45wt8LGhTb75O5zeY/2Kr+ubBT2p5UCrXaRRqlWdtfQf1oyISjVw7g5l4hSR1saYPQCuoUy0ZdFH3Nm7Bf9bcZA5648wbkCq3eFYsg7B8pegy23Qeqjd0dRebHO4/0trNN95T8OJLTD6n9YYW8DJ7EI2Hz3Lvox8jpwp4EhWPmfyisk9V0JeUQnOUkNggBDoCCAkMIDGEcHERQQTFxlCUkwoafERpMZH0LxROMGB7v6uU8pe7iaQx4GFIrIXEKAl1pDuygd0SYmmY1I0764+7DsJZN7T1vN1T9sYhIcFh8Ntb0LTLpj5vyfzwBaej32ShceCOJVz7sJm4cEOUmLDiIsMJjk2lIiQQBwBQonTUFJaSkGRk9P5xezPzCMzt4j8oou/xRwBQmpcOF1TYujaLJauKTF0To4mIsTOyUOVqphb/yuNMfNFpC3QHiuBbDfGnKuimKojIsIdvZvxu0+2svVoNp2SbRweBODQStj8Pgz+pfXLvZ7Yn5HH7PVHmLO+F2lFj/HC2X/xRPZDNEt9lqi2g+iSEkObhEhiw4OQaszHfiaviH2Zeew7lce+jDy2H8/m272ZzHaNMuAIELokR9OvVRx9UxvTJ60xMWHah0XZ74oJRESuNcYsEJHyd361FhGMMR96MTZVDbekp/Cnudt5d/Uhnh7d2b5AjIEvfgWRTWHQT+yLw0NKnKV8vvk4U5ftY+3BLERgQKs4rhk0nuy4m0n+4n4ePfhT6PZ3SGEjptAAACAASURBVB1fo2M0igimUUQwPVs0umT5yZxCNh85y9oDWazcd5ppy/YzZcleRKBTUjRXtY3nmrYJ9EptREigwxOnq1S1VHUFcg2wALi5gnUGa7In5QMaRQQzvHMiH607wuSRHQgNsukLZftncGQ1jH4ZQvx3zumCIif/W3GAqcv2cfRsIalx4Uwe2YEx6ckkxYS5tkqF5gvg/fthzv+D45vhhmetLsAe0CQqlGs7hHJth0QACoudrD9kJZPlezJ4c+k+Xl+8l7AgBwNax3F123gGt0ugVXxEta6AlKqpKyYQY8xTrpfPGGP2lV0nImlei0rVyJ19mvPpxmN8ueU4Y9K9ODlTZUpLYeGz1h3n3cfW/fE9oKTU8Na3+3lpwW5O5ZyjX1pjnhnThWs7NCEgoIIv5bBGcPd7MO8p+PZlOL4Jvv9viGnm8dhCgxz0bxVH/1ZxPDqsLXnnSvh2TyZLdp1iyc5TLNhuTXOcEhvG4HYJXNMungGt47W6S3mNuy1zHwA9yy17H+t+EOUjBrWOJzUunP9+e8CeBLL1Izi51ZqD3OF/jb4Ltp/g/5YWcDJ/C31SG/HK3T3pm+bGkG+OQOvKIykdPv0pvDrI6qHVabRX440ICeS6Tolc18m6QjmYmc9iVzKZs/4IM1ceJEAgvXksV7dNYHC7BLo3iyHQob28lGdU1QbSAegMxJRrB4kGQmt7cBEZAbwIOIA3jDHPlVsvrvU3AvnABGPMWnfKNkQBAcIP+rfkD59tY8vRs3ROjqm7gztLYOGfIKEjdPbRwRIrcSSrgGc+2cKXW06QHCFMndCHIe0Tql8N1O12SOkJH/wQ3h0Hve+HG/54oauvt7WIC2dcXEvG9W9JsbOUdQez+GbXKZbsyuClBbt4cf4uokIDGdQ6nqvbxTO4bQLNG/vp/TnGWGOs5WVA3klrqJy8DMjPgHO5UJQLRXkXn4sLwDjBlEJpKb1zs2GL69/FEQSOYNcjCBwh1uugUAiJcj2irefgyIvLQmOsK9CwRhAaCwENLzFX9TOxPTAKiOXSdpAc4MHaHFhEHMArwPXAYWCViMwxxmwts9lIoK3r0Q/r7vd+bpZtkG7v1Zy/frWDt749wHPfr8Mh0ze9B5m74I63/OYPqbTU8N9v9/PnL3ZgMDwxogNtSw8ytEOTmu80rjXc/xUs+L11H8z+Zdbw9c3r9r7bIEcAfdMa0zetMT8f3p4zeUUs35NpJZSdp/hiy3EAUuPCaRVexNnYI/RNa1ymfccHOEvgzD44tR3O7IczByDrgOv5IJRUMplacKTrEeF6RFoTl4kDAhwgARQ4TxMZ7/p3Li0BZxGUnLPmrDmXC85iKM6zXp/LqfxY50mAlUTCG0NY43LPjS5/f/4RFA5WhyScpYaSUkOxs5QSp6GyW1XL/6wRsXrqBQYEEOgQAgOkztrAqmoD+Rj4WEQGGGO+9fCx+wK7XfObIyKzgDFA2SQwBvivMcYAK0QkVkSSgFQ3ynpOzgmisncBQ7yye0+KCQ9iTPcUZq8/wq9GdiQmvA7qv0udsOR5a4rajhX1t/A9x84W8Ph7G1m6O4Mh7RP4wy1daNYonEWLPDAkTGAwDP89tBpiNa7/53oY8GMY+mvb7shvFBHMTd2SuKlbEsYY9mbk8c3OU3yzK4Nlu06yYNZ6wGo/6ZvWmN6pjeiT2pjWCZE4Kmr78bTck9YcLCc2w8ntcHIbZOywvtjPC4mBRi0gvq01m2R0MkQ0sSYmi2hizXIZ3thKElXYsmgRQ4YMcT8+ZwkU5cC5HExhNgW5WeSePUPB2VMU5ZyiJDcTk38aR+EZgrOzCMncQ1jxWsKd2YSYwkp3W2QCySKSLBNBFpGcNRdfZ5lIzhJBlol0rYsglzDyTCj5hJBHKKaSwUQChAsJxUouwoOdHR7/BnO3onqiiFx2xWGMub8Wx04Byv61Hsa6yqhqmxQ3y3rOwmfpuukjGF2ri646M25AS95ZfYj31hzigavrYNDkbXPg9F64fbr1c8jHfbrxKP/34SaKnYY/3tqVsX2be+cXW5th8MiKiw3s2z+DUX+H1td6/ljVICK0ToikdUIkEwalMX/BQhLb92TV/tOs2n+ab3ZlXJioLCzIQcekKLqkxNAlOYZOydG0aRJZu15+hdlWsji6Fo64HtmHL66PaQ4JHawRDJp0hIT20LiV9YvdC6wbO4s4k1fE6bwizuS7nvOKXMuLL12eX0Sx02CNBJXoelwUFuQgPNhBWLCDiIhAooOcNAnMI8GRR1xAHjHkEmVyiSzNIaI0h/DSbMJLckhyZtOqJJvQkiOElJwlyFn1dNXFAaGUBIZT7AinKCCcIkcYRQFhFAeEUCzB1oNgiiSIzNKrPP7ZuZtAPi3zOhS4FajtJBQV/cWWv2qrbBt3ylo7EJkITARITExk0aJF1QjR0uxsAG2Ks1n69SeUBEVVu7wd2sQG8O+F22lVcoCAGn455ubmVv15GUOvNb/HEZbMypNRcKqK7W1UUmqYub2I+QdLaBUTwI+6hZBYsJfFi/de2Matc66uyDHEdm9Fu52vEP7WrWTE9WVP6/spCE/y7HFqqCA/j4xd60gD0lLg9mQHJ/PD2J3l5EB2KQeys3l3ZRb/dd0wL0B8mNA0IoCmEUJSRABNwoVGoQE0DhXCAi/9/xZUlEVs1hZizm4hNmsLEXkHENefa0FoU7Kj25KTMJycqLbkRrbEGVhmyP8sICsH2FDleRhjOOeEvGJDbrEhrxhyiww5xcZ6LrKW5xQZzhY6yV80l9wiQ1FpxfsTIDIIIoOFqGAhMkhoEiNExQe6lkFkkLUuKliICBLCAin391Z6fk+ux6WKXI+KJguQ0mKCinMJLMm58OxwFroeBeWeCwksKSDMWUCkM5OA4mICSosIKL34vKpRa4//33b3TvQPLjkxkZnAvFoe+zBQ9jblZlyelCrbJtiNsgAYY6YAUwB69+5tqnXZet6OQtgzlas6JELzvtUvb4PsRkd5dOY6Spp0ZHjnpjXaxyJ3LvP3LoLFe+DmFxnSa1iNjlMXjmYV8MiMtaw/lM8DV6XxxMgOBFXQG8mtc66RIVAyEVa8SvySvxC/+v9Bvx/BVT+z5h+xkTvnXFpqOHA6n81HzrL7ZC57M/LYeyqXZcfyyC8qumTbtJBsrgvfRT/ZRufiLSQVHwCsX8sZjdLZn3IT2XHdyYvrioTHERwYgAg4Sw2lxuAsvfi6qKSUvKISCoqc5Bc5L7zOO+ckp7CYrPxisgqKOJNfzNn8YoqclWQDIDo0kMYRITSKCCYuIIf+LZJoHBFMo/BgGkcEuZ6tmzobhwcTHRZUN9V3deScF/5v17SvZVugRS2PvQpo67qf5AhwF3B3uW3mAJNcbRz9gLPGmGMicsqNsp4T39Z6ztjlNwnkxi5Neb5RGK8v2VvjBOKWpf+w7jr34fs+lu/J4Mcz1lLsNLx6T09GdrXpl39gCFz1U+uzmv8MrPgXrH7Tmrhq4KNWXb6PCggQ0uIjSIu/dEIwYwynDu8id8diHIeWE3tyJTEFh6EA8iSczY5OvB9wNUuK2rOupCUl+YHWXywA+1wP9wUHBhAR7CA8OJCo0EBiw4NoFW8NHxMbHkxseBCNwoOICbNen08QseFBl/xgsJJm99p9KMq9BCIiOVysOjLAceCJ2hzYGFMiIpOAL7G64r5pjNkiIg+51r8GzMXqwrsbqxvvfVcqW5t4rii2BaXiICBzl9cO4WmBjgAeuCqNpz/Zyur9p+md6oUp7I+us65Arvud9eXog2atPMhvZm8mLT6C18f1olWCD9wdH5UIt7xiJZMlf7HaR1b+G7rfCX0ehKZd7I6wcsZYPaH2L4P9S5EDS2mSdZAmYPVCajkIWj4MqYOIaNqNfgEO+gH/D+tO+uyCYs6VlFLkLKWoxPVwXTUEiNXg6xAhIMDqWRTsCCAiJJCwYAfhQQ69h8XHuFuF5ZWKf2PMXKwkUXbZa2VeG+DH7pb1GkcQhaFNCc/wnwQCcEef5rwwfxevL9nrnQTy7StW//jevjcws7PU8Nzn2/j3N/u4pl0CL9/dg6hQH7sjO74tfG8KDH4clr0AG2bBmmnQYiCkj7V6tHmp4dhtpaXWnC4HV8D+pXBgGZx19V8Jj7PmShkwyUocTTpdsQt3aJDDviF2lFdUdSNh+bvPL3H+pr6GID88hfDM3XaHUS3hwYGM79+SlxbsZvfJXNo08eCv7+xjsOUj6DvRuqHKh+SdK+Ens9Yxb9tJJgxM5Tc3dfTtX67xba17Ra7/Paz7H6yZanX//fQxaHMdtLvB6rnVqKX3Y8k/DUfWwOFVcHi19brQ1cQbHg+pg6xBMlsOsnpK+ck9P8o7qroC+dsV1hnA3v6IdSg/PAWOrrfueXCjn7mvGD8wldeX7GXKkj08f5sH63zXTLU+i76+1bU5I/ccE6auZNuxHJ4Z05nxvjI/ijvCG8OgR2Hg/7OqBzd/AFtmw87PrfWNW1ttcEnp1vzy8e2sK5Tq9rIrLYXc49akX5m7ab37Szj0onXvRc4xaxsJsEYV6DQGmvWGZn2t7rR+0E1b1Z2qbiSsB1PJeUZ+eIp1U1PWAatPup+Ijwzhrj7NmfHdQSYNbUuLOA/cyFZyzmr8bTfCpz6LQ6fzGf/mSo6dLeCN8b1rd0e5nUSsIVFSesLwP1idN/YssNqb9iyADTMvbhscZV2ZRCRYV4KhMdbQKeen3DVO676LwiwoPAu5J+DsESi9OP1xckAwJHa0bnxs0hGSe0JyD78eTVnVDXcb0YOAh4HBrkWLgNeNMT42Cbf3FIS5BifM2O1TX5rueGRoG2atOsRLC3bx19s9cBWy5SPIO2V1Q/URO47nMP7N7ygocjLjgX70aumFNh87iEBCO+vR/yFrWfYxOLbBunnzzH7rR03+acg+aiWJ4gLXnVLiGmIj2mrgDo2BlF7Q6RZroq+YFtC4Fd9sOsCQob7bBVv5Lne78b4KBAH/cr0f51r2gDeC8kX54a4EkrkLGG5rLNWVGB3KD/q3ZOqyfTwypHXteiIZAytehfj21i9WH7DmwBnun7aKkMAA3ntoIO2b+sfNnjUWnWQ9PEUOV72NUhVwtwWsjzHmXmPMAtfjPqBuR4ezWXGQ61ecn/XEOu+ha1oTEujgxfm1jP/wKji23rr68IH68EU7TvKDN76jUXgQHzzcAJKHUj7E3QTiFJHW59+ISCvA6Z2QfJSI1VvGz3pinZcQFcL4gS2Zs+Eo245l13xHK6dYg9p1v8tzwdXQx+uP8MD01bRKiOC9hwb679DkSvkpdxPI48BCEVkkIouwprn9udei8lVxbf32CgTg4WtaEx0axB8+24oxlQ0WfQX5p2Hrx1byCI6oensvmr58Pz99Zz29WjZi5sT+JET55o2MStVnV0wgItJHRJoaY+ZjDV/yIZANfIU7o5vVN/FtrO6PhbX4BW+j2PBgfnZdW5btzuTrrSeqv4MNM62eaL3u9XxwbjLG8I+vd/LUnC1c1zGR6ff3JdrXbhBUqoGo6grkdazBIsEai2oyMB04gWuAwgYlzjUmlp9WYwHc078lbZpE8uzcbZwrqUYtpDHWXdLN+kJiZ6/FdyXOUsOTH2/hxfm7uL1XM169p6fe2ayUjapKIA5jzGnX6zuBKcaYD4wxvwXaeDc0H1R2UEU/FeQI4LejOnEgM583l+53v+CB5ZCx07ZhS86VOHl01jreWnGAHw1uxfO3dfPtu8uVagCqTCAicr6r7zCsto/zajqSr/9q3BoCAq0pNv3YNe0SuL5TIi/O38n+jDz3Cq2ZZjWed7rFq7FVJPdcCT+ctprPNh7jVyM78KsbO9bZlJ1KqcpVlUBmAotF5GOgAPgGQETaAGe9HJvvCQy2koifJxCA34/pQlBAAJM/3EhpaRUN6hcaz++s8ylZT+cVcc+/V/Dt3kz+cls3fnRN66oLKaXqxBUTiDHmWazeVtOAq8zFrjsBWCM0NzxNOtSLBNI0JpRf39SRFXtPM3PVwStvvGEWOM9Brwl1Ett5R7IKuO215Ww/nsNrP+jF7b2bV11IKVVnqqxENsasMMZ8ZIzJK7NsZ0MaifcSCR3g9D5ruAg/d2ef5gxqE8cfPt3G7pO5FW9kjDVwYrM+ddp4vvVoNt//13JO5ZzjrR/24/pOiVUXUkrVKW2FrK6EDoCxGpT9nIjw9zvSCQt2MOnttRQWV9Ar69B31rnW4dXHgu0nuP215QC8M3EAfdPqybhWStUzmkCqq0lH6/nUDnvj8JDE6FD+dkd3th/P4XefVDCp4/q3ISiizhrPpy3bxwPTV5MaH8HsHw+iU3J0nRxXKVV9tiQQEWksIl+LyC7X82XTrolIcxFZKCLbRGSLiPykzLqnReSIiKx3PW6ss+DP98Q6ua3ODultQ9s34eEhrZm58hBvLr04R3WA85w18m6n0V4f2ruopJTfzt7M059s5doOibz7owE0jQn16jGVUrVj1xXIZGC+MaYtMN/1vrwS4OfGmI5Af+DHItKpzPp/GGPSXY+6mdoWrJ5YcW3qRUN6WY8Pb88NnRP5/Wdb+WrLcQDiM76Dc9nQfaxXj33sbAF3TfmWt1Yc4MGr03h9XC8iQhpeL3Gl/I1dCWQM1h3tuJ4vqx8xxhw731BvjMkBtgEpdRbhlSS0r1dXIAABAcILd/agW7NYHp21jqW7Mkg8sRBimkPq1V477rLdGYx6aSk7jufwyt09+fVNnXAE6D0eSvkDuxJIojHmGFiJArji1HEikgr0AL4rs3iSiGwUkTcrqgLzqoSO1kQ+9aAnVllhwQ7evLc3qXER/Gr6lzQ6vR663emVea8Li50888lW7nnjOxpFBPPxpEHc1M2Dc1wopbxOajQqqzs7FpkHNK1g1a+B6caY2DLbnjHGVJgERCQSWAw8a4z50LUsEcjAmpf990CSMeb+SspPBCYCJCYm9po1a1aNzic3N5fISKsdIOHkMjpvfZ7Vvf5BbpR/zU7ojpwiw6EV7/FI6QxebPYi3dukenT/u884+c/mcxzLMwxrEcgd7YMJcfjGVUfZf+eGQs+5YajNOQ8dOnSNMab3ZSuMMXX+AHZgfekDJAE7KtkuCPgSeOwK+0oFNrtz3F69epmaWrhw4cU3J7YZ81S0Metn1Xh/Pq201JS83M9s+10v0/KJT83P311vzhYU1Xq3J7ILzM/eWWdaPvGp6f/HeWbJzpMeCNazLvl3biD0nBuG2pwzsNpU8J1qV0vlHOBe4DnX88flNxBrsKP/ANuMMX8vty7JuKrAgFuBzd4Nt5y482Ni1a92kAuObcBxahu0fYhJ8W3416LdLNudwW9HdWJE56YEVLON4mR2IVOW7GXGdwdxlhoeHtKaSUPbaEO5Un7Orr/g54B3ReSHwEHgdgARSQbeMMbcCAzCmnt9k4isd5X7P2P1uHpeRNKxqrD2Az+q0+gdQa6eWPXjXpDLbJgJjmAymlzNL65vz3WdEnni/Y08MmMtnZKiGT+gJTd2S7riPBwFRU6W7c7gg7WHmbftBM5Sw5j0FB4d1pa0eHsno1JKeYYtCcQYk4k1um/55UeBG12vlwIV/tQ1xozzaoDuaNIRjqyxOwrPKymCTe9B+5GUBFn1penNY5n7k6uZs+EIryzcw+QPN/HbjzfTOTmGrikxNIkKISzYQWGxkyNZhew6kcPGw2cpcpYSFxHMuP6pjB/QklRNHErVK1qHUFNNu1o32RWehdAYu6PxnN3zID8Tut8Nxy4udgQIt/Zoxi3pKWw8fJbPNx9n7YEzzF5/hJzCkgvbxYYH0TohkgmDUhnUJp4BreIIDtQBD5SqjzSB1FRiV+v5xBZoOdDeWDxpw9sQkQBthsGxZZetFhG6N4+le/MLnegoLHZS5CwlNNChyUKpBkT/2muqaRfr+Xjdtt97Vf5p2PEFdL3DaudxU2iQg+jQIE0eSjUw+hdfU1FJENYYTmyyOxLP2fwBlBZDuneHLlFK1Q+aQGpKxGoHOV6PEsiGmZDYxTovpZSqgiaQ2mja1RoTy1lS9ba+7tROq1eZlwdOVErVH5pAaiOxC5QUwuk9dkdSexveBnFAtzvsjkQp5Sc0gdTGhYZ0P6/GKnXChnegzXUQecVxLZVS6gJNILUR3x4Cgvw/gexbDDlHoftddkeilPIjmkBqIzDYmiP9hJ935d0wy7oZsn3dTeyolPJ/mkBqq2kX/74COZcD2z6Bzt+DIJ1CVinlPk0gtZWUDrknIPuo3ZHUzNaPoTgf0u+2OxKllJ/RBFJbKT2t5yNr7Y2jptbPhMatoVkfuyNRSvkZTSC1ldjF6v561A8TyJn9cGCpde+H+MaMgEop/6EJpLaCw6FJJzi6zu5Iqm/ju9Zz9zvtjUMp5Zc0gXhCSg8rgXhpfnmvMMYauiT1aohtYXc0Sik/pAnEE5J7QsEZOLPP7kjcd+g7OL1Xhy5RStWYJhBPSO5hPftTQ/r6GRAUAZ3G2B2JUspP2ZJARKSxiHwtIrtcz40q2W6/iGwSkfUisrq65etMYmdwhPhPO0hRPmz+yEoeIZF2R6OU8lN2XYFMBuYbY9oC813vKzPUGJNujOldw/Le5wiyRub1lwSy/TMoytF7P5RStWJXAhkDTHe9ng7cUsflPS+5Bxxdbw1M6OvWz4CYFtBykN2RKKX8mBgbeg6JSJYxJrbM+zPGmMuqoURkH3AGMMDrxpgp1SnvWjcRmAiQmJjYa9asWTWKOTc3l8jIyqt7Eo8vpOP2F1jV+wXyItNqdIy6EFKYQf8VD3Cg5R3sT7vyFUhV51wf6Tk3DHrO1TN06NA15WqBLMYYrzyAecDmCh5jgKxy256pZB/JrucmwAZgsOu9W+XLP3r16mVqauHChVfeIHOvMU9FG/PdlBofo04s+asVZ+aeKjet8pzrIT3nhkHPuXqA1aaC79TAGqUjNxhjrqtsnYicEJEkY8wxEUkCTlayj6Ou55Mi8hHQF1gCuFW+TjVKhchEq3ts3wftjqZixlhDl7QYCI1b2R2NUsrP2dUGMge41/X6XuDj8huISISIRJ1/DQzHuoJxq3ydE4Hm/eDgd3ZHUrnDqyFzlzaeK6U8wq4E8hxwvYjsAq53vUdEkkVkrmubRGCpiGwAVgKfGWO+uFJ527XoD2cP+u7IvOtnQFA4dLa/z4FSyv95rQrrSowxmcCwCpYfBW50vd4LdK9Oeds17289H1wBXb5nbyzlFRfC5g+h480QEmV3NEqpekDvRPekpG4QGGa1g/iaHZ/BubNafaWU8hhNIJ7kCIKUXtYViK9Z+xbENIfUwXZHopSqJzSBeFrLgXB8IxRk2R3JRWf2w96F0GMcBOg/uVLKM/TbxNNaXQOmFA4stzuSi9b+FyQAevzA7kiUUvWIJhBPa9bHagfZt9juSCzOYlg3A9oOh5gUu6NRStUjmkA8LTDE6s67b4ndkVh2fgm5x6HXBLsjUUrVM5pAvCFtMJzcCrn23yDP2ukQlQRtrrc7EqVUPaMJxBtaXWM9230VknUIdn1tNZ47bLnlRylVj2kC8YakdAiJsb8dZN3/rOee4+yNQylVL2kC8YYAB7QaDLvmWQMY2sFZbPW+an0txLawJwalVL2mCcRb2o2AnKNwfJM9x9/2iXX8vhPtOb5Sqt7TBOItbYdbzzu/tOf4370OjdIuxqGUUh6mCcRbIptYw5rs/KLqbT3t6Do4tMK6+tA7z5VSXqLfLt7UbgQcWVP33Xm/ex2CI6HHPXV7XKVUg6IJxJva3QAY2PVV3R0z9yRs/sAadTc0pu6Oq5RqcDSBeFPTbhDdzGrQriurp4KzSBvPlVJepwnEm0Ss2f92z4eCM94/XlE+rHzdajiPb+v94ymlGjRbEoiINBaRr0Vkl+u5UQXbtBeR9WUe2SLyU9e6p0XkSJl1N9b9Wbipy/egtBi2fer9Y617C/Iz4arHvH8spVSDZ9cVyGRgvjGmLTDf9f4Sxpgdxph0Y0w60AvIBz4qs8k/zq83xswtX95nJPeERqmw5UPvHsdZDMv/CS0GQMsB3j2WUkphXwIZA0x3vZ4O3FLF9sOAPcaYA16NyhtEoMv3Ye9iyDnhveNseg/OHtKrD6VUnRFjw1AbIpJljIkt8/6MMeayaqwy698E1hpjXna9fxqYAGQDq4GfG2MqbGQQkYnARIDExMRes2bNqlHMubm5REZG1qhsWP5h+q38MXtajedQi+/XaB9XIqVO+qyaRGlACKt7/8NKWh5Qm3P2V3rODYOec/UMHTp0jTGm92UrjDFeeQDzgM0VPMYAWeW2PXOF/QQDGUBimWWJgAPrCupZ4E13YurVq5epqYULF9a4rDHGmDdHGvNiujGlpbXbT0VWTzPmqWhjtn3m0d3W+pz9kJ5zw6DnXD3AalPBd6rXxvg2xlxX2ToROSEiScaYYyKSBFzpTruRWFcfF+p/yr4WkX8DddBCXUs974WPJsL+b6z5QjyluAAWPQfN+kL7kZ7br1JKVcGuNpA5wL2u1/cCH19h27HAzLILXEnnvFuxrmx8W6fR1o19K//t2f2u/Lc1aOKwJz1WdaWUUu6wK4E8B1wvIruA613vEZFkEbnQo0pEwl3ry3dhel5ENonIRmAo8LO6CbsWgsKg9w+tmwozdntmn3kZ8M3frCHb0672zD6VUspNtkxTZ4zJxOpZVX75UeDGMu/zgbgKtvPPGZL6PwzfvgLLX4LRL9V+f18/BUW5cMOfar8vpZSqJr0TvS5FNrEGONww05putjYOroD1/4MBP4YmHTwTn1JKVYMmkLp21WMgATD/mZrvo7gAPvkJRKfA4F96LjallKoGTSB1Lba5ddWw6V04vKZm+5j3Ozi1HUb/E0IaVl92pZTv0ARih6t+BpGJ8OlPoKSoemW3z4XvXoV+D0Gby5qRlFKqzmgCsUNIFIz6hzVf+sJnSR7hxAAABaxJREFU3S93fDN88IA1vtZ1T3srOqWUcosmELt0uMm6uXDZC7Dx3aq3z9gFM26D0Gi4622rW7BSStnIlm68yuXGv8LpvTD7YTCl0P2uirfbvwzec913ee8nEJ1U8XZKKVWH9ArEToHBcNcMaDkQPvoRfPQQZO65uP70XvjsFzD9Zusu9glzoUlH++JVSqky9ArEbqExcM8HsOhP1nweG2ZCVDIYJ+SeAHFA7/usoUp0jnOllA/RBOILAoPhuqegzwOwdbbVWB7ggIQO/7+9uwuVogzAOP5/UKMy+tSiVLJCLCvClLCCkOqiKDoRBgWFRJd9WARh3eRNUCFRRAVRlqAYYUISZUVJ3UWZhppJYpbHNI3ow4hUfLqYkQ4SHBl39j3uPj847OzAmX1eds8+O7Nz3oFpA9WpvxERI0wKZCQ5ZUL1PyIREceAfAcSERGNpEAiIqKRFEhERDSSAomIiEZSIBER0UgKJCIiGkmBREREIymQiIhoRLZLZ+gaSXuAHxr++jjglw7GORZkzP0hY+4PRzPmc22PP3xlXxXI0ZD0pe2ZpXN0U8bcHzLm/tDGmHMIKyIiGkmBREREIymQI/dK6QAFZMz9IWPuDx0fc74DiYiIRrIHEhERjaRAIiKikRTIEZB0g6TNkrZIml86T9skTZK0WtImSRslzSudqRskjZK0VtK7pbN0g6RTJS2X9G39XF9ZOlPbJD1cv6Y3SFom6fjSmTpN0iJJuyVtGLLudEkfSfquvj2tE4+VAhmGpFHAi8CNwDTgTknTyqZq3QHgEdsXAbOA+/pgzADzgE2lQ3TR88Aq2xcCl9HjY5c0AXgQmGn7EmAUcEfZVK14A7jhsHXzgY9tTwE+ru8ftRTI8K4Attjeansf8CYwUDhTq2zvtP1Vvfwn1RvLhLKp2iVpInAT8GrpLN0g6WTgGuA1ANv7bP9WNlVXjAZOkDQaOBH4qXCejrP9GfDrYasHgMX18mLg1k48VgpkeBOA7UPuD9Ljb6ZDSZoMTAc+L5ukdc8BjwIHSwfpkvOBPcDr9WG7VyWNLR2qTbZ3AAuBH4GdwO+2PyybqmvOsr0Tqg+IwJmd2GgKZHj6n3V9ce6zpJOAt4GHbP9ROk9bJN0M7La9pnSWLhoNXA68bHs68BcdOqwxUtXH/QeA84BzgLGS7iqb6tiWAhneIDBpyP2J9OBu7+EkjaEqj6W2V5TO07KrgVskbaM6RHmtpCVlI7VuEBi0fWjPcjlVofSy64Hvbe+xvR9YAVxVOFO3/CzpbID6dncnNpoCGd4XwBRJ50k6jupLt5WFM7VKkqiOjW+y/WzpPG2z/ZjtibYnUz2/n9ju6U+mtncB2yVNrVddB3xTMFI3/AjMknRi/Rq/jh4/cWCIlcDcenku8E4nNjq6ExvpZbYPSLof+IDqrI1FtjcWjtW2q4G7gfWS1tXrHrf9XsFM0XkPAEvrD0ZbgXsK52mV7c8lLQe+ojrTcC09OKWJpGXAbGCcpEHgCeAp4C1J91IV6e0deaxMZRIREU3kEFZERDSSAomIiEZSIBER0UgKJCIiGkmBREREIymQiBZIOkPSuvpnl6Qd9fJeSS+VzhfRCTmNN6JlkhYAe20vLJ0lopOyBxLRRZJmH7reiKQFkhZL+lDSNkm3SXpG0npJq+rpZJA0Q9KnktZI+uDQlBQRpaVAIsq6gGoa+QFgCbDa9qXA38BNdYm8AMyxPQNYBDxZKmzEUJnKJKKs923vl7SeaqqcVfX69cBkYCpwCfBRNX0To6imIo8oLgUSUdY/ALYPStrv/76UPEj19ylgo+2ev9xsHHtyCCtiZNsMjD90vXJJYyRdXDhTBJACiRjR6ssozwGelvQ1sI7+uYZFjHA5jTciIhrJHkhERDSSAomIiEZSIBER0UgKJCIiGkmBREREIymQiIhoJAUSERGN/Av2KpNkxhwuIQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Ordinary Differential Equations (ODE)\n",
"from scipy.integrate import solve_ivp # import the standard ODE solver in Python\n",
"\n",
"TSpan = [0, 10] # Initial Time and Final Time\n",
"t = np.linspace(0, 10, 1000)\n",
"X_initial = [1, 0] # Initial Conditions\n",
"\n",
"# solve_ivp wants a true function with arguments -- good time to show how to do that:\n",
"# define a function that takes t and X0 as arguments, and returns \n",
"def ode_test(t, X0): \n",
" X = np.zeros(2)\n",
" lam = 2\n",
" zeta = 1\n",
" X[0] = X0[1]\n",
" X[1] = - lam * X0[0] - zeta * X0[1]\n",
" return X\n",
"\n",
"# Now that we have defined a function that we want to call, solve the ODE\n",
"# Calls the function ode_test at each time step and solves for new state\n",
"# given initial state then repeats at every time step.\n",
"ode_test_solution = solve_ivp(ode_test, TSpan, X_initial, t_eval=t)\n",
"T_out = t\n",
"Y_out = ode_test_solution.y.T # transpose the solution for indexing later\n",
"\n",
"plt.figure()\n",
"plt.plot(T_out, Y_out)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Solutions')\n",
"plt.legend(['Position', 'Velocity'])\n",
"plt.title('Position and Velocity')\n",
"plt.grid(True)\n",
"\n",
"plt.figure()\n",
"plt.plot(T_out, Y_out[:, 0]) # The \":\" here takes all elements in the rows \n",
" # associated with the first column. This is called\n",
" # index slicing and it is incredibly useful.\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Solutions')\n",
"plt.legend('Position')\n",
"plt.title('Just Position')\n",
"plt.grid(True)\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Animate your plots (if time)\n",
"import matplotlib.animation as animation # import the standard animation library\n",
"\n",
"# Enable an interactive plot in a Jupyter notebook\n",
"%matplotlib notebook\n",
"\n",
"# Define a function to update your animation\n",
"def update_line(num, t, data, line):\n",
" line.set_data(t[:num], data[:num])\n",
" return line,"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"application/javascript": [
"/* Put everything inside the global mpl namespace */\n",
"window.mpl = {};\n",
"\n",
"\n",
"mpl.get_websocket_type = function() {\n",
" if (typeof(WebSocket) !== 'undefined') {\n",
" return WebSocket;\n",
" } else if (typeof(MozWebSocket) !== 'undefined') {\n",
" return MozWebSocket;\n",
" } else {\n",
" alert('Your browser does not have WebSocket support. ' +\n",
" 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
" 'Firefox 4 and 5 are also supported but you ' +\n",
" 'have to enable WebSockets in about:config.');\n",
" };\n",
"}\n",
"\n",
"mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
" this.id = figure_id;\n",
"\n",
" this.ws = websocket;\n",
"\n",
" this.supports_binary = (this.ws.binaryType != undefined);\n",
"\n",
" if (!this.supports_binary) {\n",
" var warnings = document.getElementById(\"mpl-warnings\");\n",
" if (warnings) {\n",
" warnings.style.display = 'block';\n",
" warnings.textContent = (\n",
" \"This browser does not support binary websocket messages. \" +\n",
" \"Performance may be slow.\");\n",
" }\n",
" }\n",
"\n",
" this.imageObj = new Image();\n",
"\n",
" this.context = undefined;\n",
" this.message = undefined;\n",
" this.canvas = undefined;\n",
" this.rubberband_canvas = undefined;\n",
" this.rubberband_context = undefined;\n",
" this.format_dropdown = undefined;\n",
"\n",
" this.image_mode = 'full';\n",
"\n",
" this.root = $('<div/>');\n",
" this._root_extra_style(this.root)\n",
" this.root.attr('style', 'display: inline-block');\n",
"\n",
" $(parent_element).append(this.root);\n",
"\n",
" this._init_header(this);\n",
" this._init_canvas(this);\n",
" this._init_toolbar(this);\n",
"\n",
" var fig = this;\n",
"\n",
" this.waiting = false;\n",
"\n",
" this.ws.onopen = function () {\n",
" fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
" fig.send_message(\"send_image_mode\", {});\n",
" if (mpl.ratio != 1) {\n",
" fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
" }\n",
" fig.send_message(\"refresh\", {});\n",
" }\n",
"\n",
" this.imageObj.onload = function() {\n",
" if (fig.image_mode == 'full') {\n",
" // Full images could contain transparency (where diff images\n",
" // almost always do), so we need to clear the canvas so that\n",
" // there is no ghosting.\n",
" fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
" }\n",
" fig.context.drawImage(fig.imageObj, 0, 0);\n",
" };\n",
"\n",
" this.imageObj.onunload = function() {\n",
" fig.ws.close();\n",
" }\n",
"\n",
" this.ws.onmessage = this._make_on_message_function(this);\n",
"\n",
" this.ondownload = ondownload;\n",
"}\n",
"\n",
"mpl.figure.prototype._init_header = function() {\n",
" var titlebar = $(\n",
" '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
" 'ui-helper-clearfix\"/>');\n",
" var titletext = $(\n",
" '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
" 'text-align: center; padding: 3px;\"/>');\n",
" titlebar.append(titletext)\n",
" this.root.append(titlebar);\n",
" this.header = titletext[0];\n",
"}\n",
"\n",
"\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
"\n",
"}\n",
"\n",
"\n",
"mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
"\n",
"}\n",
"\n",
"mpl.figure.prototype._init_canvas = function() {\n",
" var fig = this;\n",
"\n",
" var canvas_div = $('<div/>');\n",
"\n",
" canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
"\n",
" function canvas_keyboard_event(event) {\n",
" return fig.key_event(event, event['data']);\n",
" }\n",
"\n",
" canvas_div.keydown('key_press', canvas_keyboard_event);\n",
" canvas_div.keyup('key_release', canvas_keyboard_event);\n",
" this.canvas_div = canvas_div\n",
" this._canvas_extra_style(canvas_div)\n",
" this.root.append(canvas_div);\n",
"\n",
" var canvas = $('<canvas/>');\n",
" canvas.addClass('mpl-canvas');\n",
" canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
"\n",
" this.canvas = canvas[0];\n",
" this.context = canvas[0].getContext(\"2d\");\n",
"\n",
" var backingStore = this.context.backingStorePixelRatio ||\n",
"\tthis.context.webkitBackingStorePixelRatio ||\n",
"\tthis.context.mozBackingStorePixelRatio ||\n",
"\tthis.context.msBackingStorePixelRatio ||\n",
"\tthis.context.oBackingStorePixelRatio ||\n",
"\tthis.context.backingStorePixelRatio || 1;\n",
"\n",
" mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
"\n",
" var rubberband = $('<canvas/>');\n",
" rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
"\n",
" var pass_mouse_events = true;\n",
"\n",
" canvas_div.resizable({\n",
" start: function(event, ui) {\n",
" pass_mouse_events = false;\n",
" },\n",
" resize: function(event, ui) {\n",
" fig.request_resize(ui.size.width, ui.size.height);\n",
" },\n",
" stop: function(event, ui) {\n",
" pass_mouse_events = true;\n",
" fig.request_resize(ui.size.width, ui.size.height);\n",
" },\n",
" });\n",
"\n",
" function mouse_event_fn(event) {\n",
" if (pass_mouse_events)\n",
" return fig.mouse_event(event, event['data']);\n",
" }\n",
"\n",
" rubberband.mousedown('button_press', mouse_event_fn);\n",
" rubberband.mouseup('button_release', mouse_event_fn);\n",
" // Throttle sequential mouse events to 1 every 20ms.\n",
" rubberband.mousemove('motion_notify', mouse_event_fn);\n",
"\n",
" rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
" rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
"\n",
" canvas_div.on(\"wheel\", function (event) {\n",
" event = event.originalEvent;\n",
" event['data'] = 'scroll'\n",
" if (event.deltaY < 0) {\n",
" event.step = 1;\n",
" } else {\n",
" event.step = -1;\n",
" }\n",
" mouse_event_fn(event);\n",
" });\n",
"\n",
" canvas_div.append(canvas);\n",
" canvas_div.append(rubberband);\n",
"\n",
" this.rubberband = rubberband;\n",
" this.rubberband_canvas = rubberband[0];\n",
" this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
" this.rubberband_context.strokeStyle = \"#000000\";\n",
"\n",
" this._resize_canvas = function(width, height) {\n",
" // Keep the size of the canvas, canvas container, and rubber band\n",
" // canvas in synch.\n",
" canvas_div.css('width', width)\n",
" canvas_div.css('height', height)\n",
"\n",
" canvas.attr('width', width * mpl.ratio);\n",
" canvas.attr('height', height * mpl.ratio);\n",
" canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
"\n",
" rubberband.attr('width', width);\n",
" rubberband.attr('height', height);\n",
" }\n",
"\n",
" // Set the figure to an initial 600x600px, this will subsequently be updated\n",
" // upon first draw.\n",
" this._resize_canvas(600, 600);\n",
"\n",
" // Disable right mouse context menu.\n",
" $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
" return false;\n",
" });\n",
"\n",
" function set_focus () {\n",
" canvas.focus();\n",
" canvas_div.focus();\n",
" }\n",
"\n",
" window.setTimeout(set_focus, 100);\n",
"}\n",
"\n",
"mpl.figure.prototype._init_toolbar = function() {\n",
" var fig = this;\n",
"\n",
" var nav_element = $('<div/>');\n",
" nav_element.attr('style', 'width: 100%');\n",
" this.root.append(nav_element);\n",
"\n",
" // Define a callback function for later on.\n",
" function toolbar_event(event) {\n",
" return fig.toolbar_button_onclick(event['data']);\n",
" }\n",
" function toolbar_mouse_event(event) {\n",
" return fig.toolbar_button_onmouseover(event['data']);\n",
" }\n",
"\n",
" for(var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" // put a spacer in here.\n",
" continue;\n",
" }\n",
" var button = $('<button/>');\n",
" button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
" 'ui-button-icon-only');\n",
" button.attr('role', 'button');\n",
" button.attr('aria-disabled', 'false');\n",
" button.click(method_name, toolbar_event);\n",
" button.mouseover(tooltip, toolbar_mouse_event);\n",
"\n",
" var icon_img = $('<span/>');\n",
" icon_img.addClass('ui-button-icon-primary ui-icon');\n",
" icon_img.addClass(image);\n",
" icon_img.addClass('ui-corner-all');\n",
"\n",
" var tooltip_span = $('<span/>');\n",
" tooltip_span.addClass('ui-button-text');\n",
" tooltip_span.html(tooltip);\n",
"\n",
" button.append(icon_img);\n",
" button.append(tooltip_span);\n",
"\n",
" nav_element.append(button);\n",
" }\n",
"\n",
" var fmt_picker_span = $('<span/>');\n",
"\n",
" var fmt_picker = $('<select/>');\n",
" fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
" fmt_picker_span.append(fmt_picker);\n",
" nav_element.append(fmt_picker_span);\n",
" this.format_dropdown = fmt_picker[0];\n",
"\n",
" for (var ind in mpl.extensions) {\n",
" var fmt = mpl.extensions[ind];\n",
" var option = $(\n",
" '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
" fmt_picker.append(option);\n",
" }\n",
"\n",
" // Add hover states to the ui-buttons\n",
" $( \".ui-button\" ).hover(\n",
" function() { $(this).addClass(\"ui-state-hover\");},\n",
" function() { $(this).removeClass(\"ui-state-hover\");}\n",
" );\n",
"\n",
" var status_bar = $('<span class=\"mpl-message\"/>');\n",
" nav_element.append(status_bar);\n",
" this.message = status_bar[0];\n",
"}\n",
"\n",
"mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
" // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
" // which will in turn request a refresh of the image.\n",
" this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
"}\n",
"\n",
"mpl.figure.prototype.send_message = function(type, properties) {\n",
" properties['type'] = type;\n",
" properties['figure_id'] = this.id;\n",
" this.ws.send(JSON.stringify(properties));\n",
"}\n",
"\n",
"mpl.figure.prototype.send_draw_message = function() {\n",
" if (!this.waiting) {\n",
" this.waiting = true;\n",
" this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
" }\n",
"}\n",
"\n",
"\n",
"mpl.figure.prototype.handle_save = function(fig, msg) {\n",
" var format_dropdown = fig.format_dropdown;\n",
" var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
" fig.ondownload(fig, format);\n",
"}\n",
"\n",
"\n",
"mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
" var size = msg['size'];\n",
" if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
" fig._resize_canvas(size[0], size[1]);\n",
" fig.send_message(\"refresh\", {});\n",
" };\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
" var x0 = msg['x0'] / mpl.ratio;\n",
" var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
" var x1 = msg['x1'] / mpl.ratio;\n",
" var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
" x0 = Math.floor(x0) + 0.5;\n",
" y0 = Math.floor(y0) + 0.5;\n",
" x1 = Math.floor(x1) + 0.5;\n",
" y1 = Math.floor(y1) + 0.5;\n",
" var min_x = Math.min(x0, x1);\n",
" var min_y = Math.min(y0, y1);\n",
" var width = Math.abs(x1 - x0);\n",
" var height = Math.abs(y1 - y0);\n",
"\n",
" fig.rubberband_context.clearRect(\n",
" 0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
"\n",
" fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
" // Updates the figure title.\n",
" fig.header.textContent = msg['label'];\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
" var cursor = msg['cursor'];\n",
" switch(cursor)\n",
" {\n",
" case 0:\n",
" cursor = 'pointer';\n",
" break;\n",
" case 1:\n",
" cursor = 'default';\n",
" break;\n",
" case 2:\n",
" cursor = 'crosshair';\n",
" break;\n",
" case 3:\n",
" cursor = 'move';\n",
" break;\n",
" }\n",
" fig.rubberband_canvas.style.cursor = cursor;\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_message = function(fig, msg) {\n",
" fig.message.textContent = msg['message'];\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
" // Request the server to send over a new figure.\n",
" fig.send_draw_message();\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
" fig.image_mode = msg['mode'];\n",
"}\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function() {\n",
" // Called whenever the canvas gets updated.\n",
" this.send_message(\"ack\", {});\n",
"}\n",
"\n",
"// A function to construct a web socket function for onmessage handling.\n",
"// Called in the figure constructor.\n",
"mpl.figure.prototype._make_on_message_function = function(fig) {\n",
" return function socket_on_message(evt) {\n",
" if (evt.data instanceof Blob) {\n",
" /* FIXME: We get \"Resource interpreted as Image but\n",
" * transferred with MIME type text/plain:\" errors on\n",
" * Chrome. But how to set the MIME type? It doesn't seem\n",
" * to be part of the websocket stream */\n",
" evt.data.type = \"image/png\";\n",
"\n",
" /* Free the memory for the previous frames */\n",
" if (fig.imageObj.src) {\n",
" (window.URL || window.webkitURL).revokeObjectURL(\n",
" fig.imageObj.src);\n",
" }\n",
"\n",
" fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
" evt.data);\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
" else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
" fig.imageObj.src = evt.data;\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
"\n",
" var msg = JSON.parse(evt.data);\n",
" var msg_type = msg['type'];\n",
"\n",
" // Call the \"handle_{type}\" callback, which takes\n",
" // the figure and JSON message as its only arguments.\n",
" try {\n",
" var callback = fig[\"handle_\" + msg_type];\n",
" } catch (e) {\n",
" console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
" return;\n",
" }\n",
"\n",
" if (callback) {\n",
" try {\n",
" // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
" callback(fig, msg);\n",
" } catch (e) {\n",
" console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
" }\n",
" }\n",
" };\n",
"}\n",
"\n",
"// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
"mpl.findpos = function(e) {\n",
" //this section is from http://www.quirksmode.org/js/events_properties.html\n",
" var targ;\n",
" if (!e)\n",
" e = window.event;\n",
" if (e.target)\n",
" targ = e.target;\n",
" else if (e.srcElement)\n",
" targ = e.srcElement;\n",
" if (targ.nodeType == 3) // defeat Safari bug\n",
" targ = targ.parentNode;\n",
"\n",
" // jQuery normalizes the pageX and pageY\n",
" // pageX,Y are the mouse positions relative to the document\n",
" // offset() returns the position of the element relative to the document\n",
" var x = e.pageX - $(targ).offset().left;\n",
" var y = e.pageY - $(targ).offset().top;\n",
"\n",
" return {\"x\": x, \"y\": y};\n",
"};\n",
"\n",
"/*\n",
" * return a copy of an object with only non-object keys\n",
" * we need this to avoid circular references\n",
" * http://stackoverflow.com/a/24161582/3208463\n",
" */\n",
"function simpleKeys (original) {\n",
" return Object.keys(original).reduce(function (obj, key) {\n",
" if (typeof original[key] !== 'object')\n",
" obj[key] = original[key]\n",
" return obj;\n",
" }, {});\n",
"}\n",
"\n",
"mpl.figure.prototype.mouse_event = function(event, name) {\n",
" var canvas_pos = mpl.findpos(event)\n",
"\n",
" if (name === 'button_press')\n",
" {\n",
" this.canvas.focus();\n",
" this.canvas_div.focus();\n",
" }\n",
"\n",
" var x = canvas_pos.x * mpl.ratio;\n",
" var y = canvas_pos.y * mpl.ratio;\n",
"\n",
" this.send_message(name, {x: x, y: y, button: event.button,\n",
" step: event.step,\n",
" guiEvent: simpleKeys(event)});\n",
"\n",
" /* This prevents the web browser from automatically changing to\n",
" * the text insertion cursor when the button is pressed. We want\n",
" * to control all of the cursor setting manually through the\n",
" * 'cursor' event from matplotlib */\n",
" event.preventDefault();\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" // Handle any extra behaviour associated with a key event\n",
"}\n",
"\n",
"mpl.figure.prototype.key_event = function(event, name) {\n",
"\n",
" // Prevent repeat events\n",
" if (name == 'key_press')\n",
" {\n",
" if (event.which === this._key)\n",
" return;\n",
" else\n",
" this._key = event.which;\n",
" }\n",
" if (name == 'key_release')\n",
" this._key = null;\n",
"\n",
" var value = '';\n",
" if (event.ctrlKey && event.which != 17)\n",
" value += \"ctrl+\";\n",
" if (event.altKey && event.which != 18)\n",
" value += \"alt+\";\n",
" if (event.shiftKey && event.which != 16)\n",
" value += \"shift+\";\n",
"\n",
" value += 'k';\n",
" value += event.which.toString();\n",
"\n",
" this._key_event_extra(event, name);\n",
"\n",
" this.send_message(name, {key: value,\n",
" guiEvent: simpleKeys(event)});\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
" if (name == 'download') {\n",
" this.handle_save(this, null);\n",
" } else {\n",
" this.send_message(\"toolbar_button\", {name: name});\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
" this.message.textContent = tooltip;\n",
"};\n",
"mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
"\n",
"mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
"\n",
"mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
" // Create a \"websocket\"-like object which calls the given IPython comm\n",
" // object with the appropriate methods. Currently this is a non binary\n",
" // socket, so there is still some room for performance tuning.\n",
" var ws = {};\n",
"\n",
" ws.close = function() {\n",
" comm.close()\n",
" };\n",
" ws.send = function(m) {\n",
" //console.log('sending', m);\n",
" comm.send(m);\n",
" };\n",
" // Register the callback with on_msg.\n",
" comm.on_msg(function(msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
" ws.onmessage(msg['content']['data'])\n",
" });\n",
" return ws;\n",
"}\n",
"\n",
"mpl.mpl_figure_comm = function(comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = $(\"#\" + id);\n",
" var ws_proxy = comm_websocket_adapter(comm)\n",
"\n",
" function ondownload(figure, format) {\n",
" window.open(figure.imageObj.src);\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy,\n",