{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"from ipywidgets import interact, interact_manual\n",
"set_printoptions(suppress=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Операции с матрицами"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Загрузим координаты изображения из текстового файла, в котором записаны две колонки чисел.\n",
"\n",
"Откуда взялись числа и почему файл называется `los` см. в задаче Task_dataset_los."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"los=loadtxt('d/los.csv', skiprows=1) # параметр skiprows для пропуска заголовков\n",
"\n",
"plot(los,'.'); legend(('1st','2nd')); ylabel('значения'); xlabel('порядковый номер');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Две колонки чисел - это координаты, поэтому отобразим расположение отдельных значений на пересечении этих координат.\n",
"\n",
"Определим `d` как копию уже заданной переменой с загруженными данными. Мы хотим обращаться к этим же данным, но использовать короткое имя для переменной, потому что будем многократно писать его в выражениях. Фактически новых данных при этом не создается - создается еще одна ссылка с новым именем на тот же адрес в памяти."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"d = los\n",
"\n",
"x=d[:,0];\n",
"y=d[:,1];\n",
"plot(x,y,'.-'); xlabel('x'); ylabel('y');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Допустим, что исходные значения в `мм`. Чтобы перевести в `м`, разделим на 1000, или что то же самое - умножим на 0.001 .\n",
"Ясно, что при переводе `мм` в `м` - картинка не меняется. Меняется лишь шкала по осям координат.\n",
"\n",
"Здесь и далее будем задавать одинаковые размеры по осям координат, чтобы имитировать расположение точек на реальной плоскости."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"d = d*[0.001]\n",
"x=d[:,0]; y=d[:,1]; plot(x,y,'.'); axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Если мы умножим матрицу на массив (вектор) из двух чисел, то каждая из колонок умножится на свое число. Например, мы можем \"сжимать\" данные вдоль одной оси, не трогая при этом вторую."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"d_ = d*([.25, 1.0])\n",
"x=d_[:,0]; y=d_[:,1]; plot(x,y,'.'); axis('square');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Попробуйте эффект от шкалирования в стационарных координатах."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ksr8/j8xIIcDXuycwO2NYVH8WzTmfo6dquW3hBtbkFMtVkl7Oq1ed7ik+gQLW\n7S0jM7/C0ATfnZOG8vJX+9h2qP2J0Yz9FTg/1p0Tcp2ZF3BeiVmbW4bGngL96/e222tL2OwBaWCw\nH2VV9uGUScHvrx3Fben2lOnz48N6RdGYrPxK/ru5AIU9db69to6JDeWVO9L4wcINzFmUicKeTObN\nE7WidV7ds8jIK3d10Y0mUPmYTVwzdjCf7SputwZFekKYa0JOtbIBj1EXDot05W+AvUp4vQ3XGheb\n7eym4gp7+rZTb5jAfH39AWb98xve2HCQxRsOcvN8Yz2x9IQwvjd2MFobW+sjvJdXB4tG1bk7kEA1\nInoAdTbNPz7f2+bwwpmFOGrwAPx8TJzThS0AnBsv+5gUJsDPrPAxK8zKXsr/f6an4N9LhxtZ+ZU8\n/sHORvfV1Nv4PMfYJeNbJlhdgbQj9USEd/HqYUiq1cLCO87jjtc2cs2YQYY/eUtO2CfUGl4Vae2x\nqVYLv716BDfOz+AX72xlzuSETn/C3zJhCCnR/V1DCqDR8KLh97y5F9HUss0FtLRubvGGg4QF+XG6\n1tbma7JfJZnAT5ds4WR1HUMGBnZzi0V38OpgAfYam+cNHUj2kY7UoAjH15xrrxFp4JPMbFIo4KPt\nRazOKenSmLppfcumt3tTkHBqGieSIoO5d2oif/tsD/OW70JhrxDe1nk7Pz6M1++awFX/WMdv3tvO\nS7eltlpLVHgnrx6GOE0bHsmuI8cNZ1vaa1BMYECAD/HhQYwf0nIhX6cN+ys6PDfyXTJrfCx+DVaV\n/urK4cxKjWV2qn37AKOL8pKj+vPwZcNYsbOYD7Ye7s4mi27Qa4IFwJoc46saz48P4+Hp9pL+G/Y3\n36CnoYZzIyip/NRUqtXCkrkTmTNpKGYTvLfF/kafnBxxdttHID1+YLvPdfeUBMYPCeXx93dSfFzy\nL3qTXhEskiODiQntZ3hCzenG8+IID/bjxS/2tXlcqtXCfVOTAHs1Kqn81Fyq1cLj14zkgYuT+WDr\nYRaszSMjr5wnrhnJJcMjsWnY1U4tEbAP+Z6+YSxnaut5bNl2j+/6JozrFcFCKcW04ZF8taeM5z8z\nXuEqwNfMnMnxfLWnlO3tLEjz8bH3LDpb5+K74r6LE4mx9OOPH+3imZW7mbd8J/delMiFwyL4/UfZ\n7Cs90e5zJEQE88sZw/k8p4SlWQU90GrhDp0OFkqpOKXUGqVUtlJqp1LqQcf9A5VSq5RSuY7/3TKj\nN2RgIDUBK8ZjAAASvUlEQVT1Np5b3bEKV7elW+nv78MfP85uM4MwdYi9mYred2mzJ/n7mJmaHNGo\nRuqG/RU8df0YAnzN/Pytbw1tE3nnBUM5f+hA5n2YzeGjnVv5K3pWV3oWdcDDWusRQDpwv1JqBPAo\nsFprnQysdnzdZc7FXrqDiT0DAnyZPjKK9XkVbdZZSIqy7ziWEBnM41eP7JVXLXrKrNRYzM4CQo7d\n6aMGBPDn60azreAY/1id2+5zmEyKp24YQ51N88h/e76mqei4TgcLrfURrfVmx+0qYBcQA8wEFjkO\nWwRc29VGgn0yzey41ObbwQpX0SEBQNsZhMsds/N5JSdkzqIdqVYLr885n9BAXyyBvq5kthmjBnF9\naiz/+Hwvv353e7vn0BoWxK+uHM7a3DJ+9HqWnHMv55Y5C6XUUOBcYAMQpbV2lqEuAqJaecxcpVSm\nUiqztLT9qxz25Cn7IrF7O5gaPW14lGsXLZuGvNITrj/MzAMV/PDVjTy53F7xSuYsjLkgKZyXb0ul\nuKqav36623X/zHGDAXvC1q0L2h8unjNoACYFK7OLucXA8cJzuhwslFLBwH+Bn2mtjzf8nrb3LVvs\nX2qt52ut07TWaRERxnYpv33iUAaHBHT4D8q+I1k6l54TiQb+u7mQ2S+t56b565n98nq+2FOKUvYK\n1b0xHdtTJiSE8cMLhvKvbw64guu2gmM4c62qDQTdhpe1jRwvPKdLwUIp5Ys9UCzWWi9z3F2slBrk\n+P4goKRrTTzLZFLMSo1lXW5ph2skpFotnDvE4qp3Ua81mw5UunYcV8DstDivL1/nbX45IwVrWCC/\nXLqNUzV1rs2Zwf4pkRAe1Objncc7U74sgZ7b8U20rStXQxSwENiltf5bg299ANzhuH0H8H7nm9fc\ndeNjsWl4d0thhx/r/MN0Lu56cuaoRrUkrhsf6/WrP71NoJ8Pf501hoMVp/ifd7aSkVfO41eP5MdT\nE/D3MbGsnd/T2R3fkrEE+vLmpkONdl4T3qMra0MmAT8AtiulvnXc9yvgz8DbSqm7gHxgdtea2Fh8\neBBpVgtLsw7x46kJHVpf0HCX8d6+uMubTEgI48rR0Xy8vYhPdxS5alaEBvrx509y+DynmGnDW5y6\nAs6umRkSFshDb29l2ZZCrnekkgvv0ZWrIeu01kprPUZrPc7x72OtdbnW+hKtdbLW+lKtddu51p1w\nfWos+0pPdqjyt1PT2hG9oZZEbzAsyn5FpOEVpzmT4kmKDOaJD3Ya2l/l2nExjI0L5a+f5nCyunN1\nUUX36RUZnE1dOWYQAb4mlmb13BaCom1TkiNcu9krx272fj4m5n1vJIcqTvPSl22n3IN9Turxq0dQ\nUlXNi1/s7e4miw7qlcFiQIAvl4+MZtnmwg6lf4vuY19sls7w6P6gIMxRnfyCpHCuGTuYF7/Yx8Hy\nU4aeZ+a4wSxYu59DFe0fL3pOrwwWAGNjQzhVU89zn3V8g2PRPVKtFhbNOZ9+PmZ++/4OV1bmr688\nB1+T4qG3vzVUtPeRGcMxKfjzJzk90WxhUK8NFqe6uMGx6B5RAwL4n8tTWJtbxvJt9ty86JAArk+N\nJTO/kqdXtL+14eDQfvx4aiIfbT/CBvm9eo1eGyy6usGx6D63pVsZHRPCvOXZHD9jL0wc3t8fMB7c\nf3RhIoNCApi3PLvDmzeJ7tFrg4Vzg2Nfs2JiQuc2OBbdw2xS/OH7oyg7Uc0zK+yp4Bckhp8tvmxq\nP7j38zPz6BXD2Xn4uExke4leGyzAPgN/6wQr3+wrp6RKqi55kzGxodyebmXR+nx++94OAP515/n4\nmU1MTDQW3L83djDjh4Tyx49zeHZV29s6iO7Xq4MFwB0XDKXOpvlPxkFPN0U0cekIeyLW6xn53PpK\nBgG+Zm5IiyUjr4Jjp2rbebT9EuyN58Vx7HQtf1/d9rYOovv1+mARHx7EJcMjWZyRbyjxR/ScbQXH\nXGs+nDu+3Xz+EKrrbLz3rbF0/bIT9l3cZCLb83p9sACYMyme8pM1UjHay6QnhOHv27ig76iYEEbH\nhLBk40FDBW8a7RqnZIMiT+oTwWJiYhjDo/vz6rr9UnHJizjX4lxyTiRaQ029/Xdz8/lDyCmq4ttD\nRw09xxv3pJMQEUQ/367tGie6pk8EC6UUcybFk1NUxaPLtsm41oukWi28cMt4Ivr7u+qgDgkLJNDP\nzJKNxuaZUq0Wnrp+DFXV9SzZKFdGPKVPBAuAuIH9AHhrU4FMhHmZAF8zV42OZnvhcZ5ZuZu7F23i\ngsQwPtx6hKoz7U90AqRaBzIhfiALvsqjpq79gsDC/fpMsNh88GizyTTheXuKq/j98mze3mQv+e9c\nlToopB+na+t5/1vj80z3XZxE0fEzvLtFtg/wBK/f69Qo5yrH6jqbTIR52PEztXy49TBvZxaw9dBR\nfEyKVKuFzQcrsdk0vj4mrh03mMz8Shauy+PY6VpD9UQuTA5nVMwAnvssl9KqaiYmhksyXg/qM8HC\nORH2xPs72FN8gsSItsu5Cfey2TQZeeW8k1XAx9uPUF1nIyWqP7+56hy+f24MYcH+ZOVXNio0NDkp\njAVr9/PMyt2ugjltvfmVUlwxMpqnVu7hmZV78PfdKyUQe1CfCRZgDxhPzx7LjOfW8sbGg9x3UZKn\nm9TnFR49zdLMAt7JOkRB5Wn6B/hwQ1oss9PiGB0T0qiSWdNd5Pv5moHGBXPae+PrBv8bfYxwjz4V\nLACGRw9gclI4i745wN2TE1zFY4X7nKmtZ2V2Me9kHmLd3jK0hklJYfzi8hQuHxlNgCMItGdqSiT/\nt2YvNm28ovrExHAUe9BIFfae1ueCBcBdU+K587VNfLT9MN8/V2o5dpV9+FBGZP8Athce470thRw/\nU0dMaD8evCSZWeNjiRsY2OHnTbVaeGTGcP70SQ4/v3SYoR5CqtXC8Oj+5Fec4jdXjZBeRQ/qk8Fi\nanIESZHBLFy3n2vHxXSoqG9vtOlABRv3l5Oe4N4Jv8qTNby3pZA/fLyLOscycV+z4srRg5idFsfE\nhDBMpq6d2zmT43n5qzy2FRqrp5qVX8mekhPUO3a7T4nuLwGjh/TJYGEyKe6aHM9jy7azYX9Fn+6q\nrskpZs6/MtFAQBcm/EqOn2HH4WPsKDzOjsJj7Dx8nMImGxYr4N6piTw0PcU9jce+FeU1Ywbx5qZD\nHD9Ty4CAtvcNeXvTQVd9C5mz6Fl9MlgAfP/cGJ5asZtX1u7vs8Gitt7Gb9/f6Zr0qzHw5tFaU3j0\nNDsKj7Pz8DF2FB5jx+HjlFZVu45JCA9ivNXC7ROt+PuY+NMnOdTV2/D1MTE1JdLtr+Pac2NYtD6f\nT7cXMfu8uFaPW5tbytuZZ3MspOhRz+qzwSLA18xtE4bwjzV7ySs9QUJEsKeb5FZZ+ZX84aNsCipP\n42NSrmFCwzePzaY5UH6SHYftgWFn4XF2HD7GUcfycJOC5Mj+TEkOZ9TgEEbFhHDOoP70b/LpPjo2\ntFv3VhkXF8qgkAD+8XkuiZHBzX5GVn4lK3YW8dbGg67AqLBvCSG9ip7TZ4MFwG0Trbz0ZR6vfX2A\nJ68d5enmdFm9TbO/7AQfbj3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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"@interact(k1=(.2,5,.1), k2=(.2,5,.1))\n",
"def _scale(k1=1.0, k2=1.0):\n",
" d_ = d*([k1, k2])\n",
" x=d_[:,0]; y=d_[:,1]; \n",
" plot(x,y,'.-'); axis('square');xlim(0,100);ylim(0,100);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Должно быть ясно, что для получения определенной пропорции достаточно изменить один из коэффициентов.\n",
"\n",
"Согласованное изменение коэффициентов равнозначно изменению единиц шкалы без изменения пропорций.\n",
"Например, если размеры в см разделить примерно на 4, то получим размеры в дюймах."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Перемножение матриц\n",
"\n",
"Перемножение - главная операция линейной алгебры. В формулах обозначается точкой. Функция называется `dot()`.\n",
"\n",
"$$ A \\cdot B = С $$\n",
"\n",
"Результаты умножения каждой колонки из $A$ на коэффициент из каждой колонки $B$ суммируются с получением колонки в итоговой матрице $C$. Получается, что первая строчка $B$ определяет вклад иксов в итоговые колонки, а вторая строчка - вклад игреков.\n",
"\n",
"Мы можем смешивать вклад обеих колонок в разных пропорциях. Если вклад одной из колонок нам не нужен - мы его обнуляем (перемножаем на 0).\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 1.8 0.9]\n",
" [-0.8 2. ]]\n"
]
},
{
"data": {
"image/png": 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2aXsvgMnU+/uO9hWtNatzD/HHD3fT0NzGA5eO5UcXjCLUJEuzihP5TVi4mjVq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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"@interact(k1=(.2,5,.1), k2=(.2,5,.1), k3=(-1,1,.1), k4=(-1,1,.1))\n",
"def _scale(k1=2.0, k2=3.0, k3=0, k4=0):\n",
" R=array([[k1, k4], [k3, k2]])\n",
" print(R)\n",
" d_ = d.dot(R)\n",
" x=d_[:,0]; y=d_[:,1]; \n",
" plot(x,y,'.-'); axis('square');xlim(0,100);ylim(0,100);\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Коэффициенты по диагонали (k1, k2) ведут себя точно также, как отдельные множители для каждой из колонок в предыдущих примерах. \n",
"\n",
"Если менять коэффициенты k3 или k4 , то рисунок наклоняется. \n",
"А если их изменять в противоположных направлениях - рисунок вращается!!!\n",
"\n",
"Чтобы понять, что происходит, вспомним тригонометрию...\n",
"При вращении (движении точки по окружности) изменяется один параметр - угол $\\alpha$. А координаты точки при этом равны $sin(\\alpha)$ и $cos(\\alpha)$.\n",
"\n",
"Например, чтобы повернуть все точки матрицы на 90 градусов (в радианах $\\frac{\\pi}{2}$), надо \n",
"от $x$ отнять $cos(0)$ и прибавить $cos(\\frac{\\pi}{2})$ (из 1 сделать 0), \n",
"а из $y$ отнять $sin(0)$ и прибавить $sin(\\frac{\\pi}{2})$ (из 0 сделать 1)."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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1tHtcWybFhBIfGcKO494h/pTccueqRBXi69/4dQ6/Dd/mceemgyRGh/L8inkE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\nT/n/GG5zOIRHYYsAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"alpha = pi/2\n",
"d_ = d.dot([[cos(alpha), sin(alpha)], \n",
" [-sin(alpha), cos(alpha)]])\n",
"x=d_[:,0]; y=d_[:,1]; plot(x,y,'.-'); axis('square');"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[-0.8660254 0.5 ]\n",
" [-0.5 -0.8660254]]\n"
]
},
{
"data": {
"image/png": 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alI6tKwqjQsuK3Sdq9TWewVMa8INblsPe4D3q3zuGn0wfxo/OHcqK3eW8mbuX\n/63bz+srCxiYGMOV49O5Iiudfgk9Alhq1dU04KtGsjMSibBaqKlzIYA9JjLQRVLtZLEIkzISmZSR\nyAOXZPLRhiLezN3Lwwu38cgn25gyOJGrstKZlZlGj0hroIurOpmmdMJEW2Z1BHj2izwenL8Z0LRO\nd1RQXsXbq/bx5qoCTfl0A5rSCVO+gX1A7xhy8yv4cEMh763djzEgAlkD7AzpE0tSbBRJsZEkxUV5\nfnc/3lpUyYtf7ao/Z62mdbqd/r1j+PH0ofzw3CGa8gkjWsPvRnJ3l3PdsznU1pn6RUoArCLU+bzP\nybGRGITyo9W0tPiSjpoNH0ernfUpn2V5ZYigKZ8QoQOvwtAP5q7i/XWF9Y/PHpbMD88bSm1dHd96\nYQW1ThcRPlMWu1yGiqoaSo/UUHqkmtIj1by7eh+Lt5ZgcC/bN3VIEj+ZPkyDfZjRlE9o0YAfZo5W\nOznzL59x8FgtFmgQ2KH1OXzvvDgnfzio8ORymfqUz/z1hVTV1OFIjOEqTfkEFQ34Yca7XOEfLx/d\n4bls2trAq8KDpnyClwb8MLKr9CgzHl3CxWP68sg1YwNdHBUGNOUTXIIm4IvIbqASqAOcpyqUBvz2\nue2F5azYXcFnPzuLPnG6GLbqOpryCQ7BFvAnGGNKWzpWA37bfbr5ALe/tJL7LjiNO76REejiqDCm\nKZ/A0YAfBo7X1jHzsc+xWaTNi5Yo1Zk05dO1ging7wIqcHcLf9oY88xJ++8E7gQYMGBAVn5+fqeW\npzt5YtEOHvp4K6/cPpFpQ5MDXRylGtGUT9cIpoDfzxizT0T6AAuBHxpjPm/qWK3ht97+g8c47+El\nfGNYEk/f3OL7rFTAnSrlMzMzlZhIHfjfXkEztYIxZp/n32IReQeYCDQZ8FXrPfjBZlzG8OsLRwa6\nKEq1Ss8oG1dmpXNlVnqDlM/dr68lNmqjpny6QKcGfBHpCViMMZWe32cAv+vMa4aDpTtLmb+ukB+f\nN5T+vXUZQhV6TjWXj6Z8Ok+npnREJAN4x/PQBsw1xjzY3PGa0mmZs87Fhf/4kqM1Tj655yyiI7Tn\ng+oeNOXTfkGR0jHG5AFjOvMa4eaVnHy2HqjkqZuyNNirbqU1KZ/R6b04dKyG7IwkHQXeDjrSNoSU\nHqnmnL8tZmz/BF7+9kTNc6puz7eXz3tr91PtdAEQZbMw9w6d58mrtTV87bgdQh76aCvHaur4fxdn\narBXYcGslI3BAAAgAElEQVS7YtdDV4/he2cNxvu/vrbOvUaDahsN+CHi9RV7eH1lAReMTmVIn9hA\nF0epLjdtWDJRnsGFFhGyMxIDXKLQowE/BKzcXc4v3l4PwIKNB8jNr2jhGcEjN7+CJxbtIDe/gmpn\nHYu3Ftc/Vqotshx25tyRjT0mgixHgqZz2kGbvUPA81/uwtvU4v0qGwr/2XPzK7jumWXU1jVuJ4q0\nWZinOVjVRlkOO5MGJbL1QGWgixKStIYf5I5UO+u7qFnFvbBJKHyVra1z8eD8TfXBXgBH75j6HGyN\n08Uv3lrHO6v2aY1ftcnw1Dh2lx3lWE1doIsScrSGH+SeWLSDg1W1/OmK0ZQf7djCJl2luPI4P5iz\nmlV7DmK1CBhDhM3Cd84azO/e30it04WIsKesirvfWIMAUbpurmqlEalxGAPbiys5PT0h0MUJKRrw\ng9iesiqe/2IXV4zrx/UTBwS6OC3Kza/g7VV7+WB9Icdq6/j7dWNJt8c0WD1reGpc/ePFW4t5/LMd\nGKDWGTqpKhVYw1PjANhSpAG/rTTgB7EHP9iEzSrcO2tEoIvSIt98vQB/u3oMl47tB9AgiGc57A0e\nP7l4J06XwWYNjVSVCjxHYk+ibBa2FWkev6004AeppTtK+XjjAX42YxipvYJ/Favnv8yrz9dbBIoO\nH2/xOVkOO49eO4YfzlvDDZMGtLi4ek5eGfaYyA6v2atCm9UiDE2J1YbbdtCAH4ScdS5+9/4m0u09\nmD0t+FexWr2nggWbDmARd+NsWxqWLx7Tj38tzmPd3kPNHpObX8E1Ty2jzmdUuI60DG/DU+L5fHtJ\noIsRcrSXThCat6KALUWV3HfBaUE/X07hoWPc+Uouab2ief5bZ3DPjOFtbny9cHQqufkV7D94rMn9\nOXllDYI9QLXTxZ8+2Mzjn23XHj5haERqHCWV1ZQfrQl0UUKKBvwgc6iqlkcWbGXSoN7MGpUa6OKc\n0rGaOu58OZeqaifP3XIG5wzvw13nDGlzrfuC0WkAfLihqMn92RmJ2CwnppIQzzeJlfkVPLxgGzc+\nl6NBP8wM8zTcbtU8fptowA8yj326jUPHarn/4pFBPV+OMYZ731rHhv2HeOy6cfU9J9ojIzmW09Li\neX3Fnib75Gc57Pz6wtMAuGWyg5/NGM4NEwc06NPvz3lVfEcHq+A0oj7gHw5wSUKL5vCDyPYDlby8\nLJ/rJg4gs2+vQBfnlJ5YtIP/rd3Pz2cO5/yRKR0+37j+vZi7vICHF2wl0ta4T/51Ewfwpw+3YLNY\nuOucIeTmV/DW6r0cr3VhDEwa1Ltd1125u5z/rS2kT1wkYhFyd1ewaGsxLgNWEWZPG8QV49MZ2icW\niyV4P4DDTZ+4KBJiIrThto004AcJYwy/n7+ZmEgrPz1/WKCLc0ofbyzibwu2cenYvnz/7MF+OWfP\nKPd/RZdpuk9+dISVCQPtLN1ZCnjmVZmdzfNf5vHB+iIOHK5u8zVz8yu49umcBu0DMZFWXJ6Hdcbw\n9Od5PP15HnFRNsY57GQNcHcrHdO/F3HRER14xaojRIThKXGa0mkjDfhBYtHWYj7fVsKvLzyNxNio\nQBenWZsLD3P362sYk96Lv1x5ut/STrNGpfH8l7twmeZ7+UwdksRfP9pKSWU1yXFRZDnsjO0/nu0H\nPufhhVuZmZmCzdr6LOXTS3bWB3uLwA/PHco3hiVz43M51DpdRNgsPHz1GKqdLnLzK8jNr+CxT7dh\njPv44anx9ZN4ZQ3oTf/ePYI6DdfdjEiN461V+zDG6H1vJQ34QaDG6eL3728mI7knt0weGOjiNKvs\nSDWzX1pJXLSNZ26Z4NceRFkOOz86byiPfbKd/5s5osmG36mDk4CtLN1ZWj+oy2oRfjpjON99NZe3\nV+/jmgn9W3W93PwKPtl0oP6xzWrhG8OS6785+I4OBrhifDoAh4/XsrbgYP0HwLur9/Nqzh4AkmKj\nGD/A/QEQG2Wj9Eg1Zw5N1q6jnWRYahxHqp3srTimazu3kgb8IPDS0t3sKj3KC986g0hbcLaj1zhd\nfO/VVZQeqeaN70wmJd7/g8G+e9ZgXly6m5V7KriNQY32j+rXi/hoG1/tOBHwAWZmpjAmvRd//WgL\nRYeOMXVIy0E2J68MbyJHgKuy0uufc/JoYF/x0RFMG5rMtKHJANS5DNuLK+s/AFblu8ckeP390+3c\nPi2Db00ZqAty+9kIn546GvBbJzijSxgpPVLNPz7dztnDkzlnRJ9AF6dJxhj+33sbWL67nL9edTpj\n+nfO/CXREVYuH9ePBRuLKDvSOCdvtQiTByfy1Y4yfJfmFBEuG9uP0iM1PLpwe6u6aWZnJBLh+XC1\nWYUrPTX4trJahBGp8dw4ycEj14xl8c/P4a5zTqzM5DLw7Od5TP3zZ8x4dAl/+nAzOXll1Na52nU9\ndcKwFE/A14bbVtOAH0C5+RV8+8UVVNU4+fWFIwNdnGa9tHQ385YX8P2zBzeoWXeG6ycOoLbO8Paq\nfU3uP3NIEvsOHiO/rKrB9qpaJ0CDidhOxZ26mUSUzcK0of5dEPvcESlERViwCkRHWPjHdWP59YWn\nkRQbxfNf7OK6Z3IY//uF3DVnFW/m7qWkslq7grZDXHQE/RJ6aMNtG2hKJ0By8yu4/tkcapwurBbh\n0LHaQBepSV9uL+X38zcz/bQUfjZjeKdfb1hKHOMHJPDC0l3U1NWRndEwGE8ZkgTAVztLGZjUs357\ndkYSEdbt1NYZLJbWLX93xsDenDUsmU2F/u3L3Vw7wOxpGVQer+WrHaUs2lLCoq3FzF9fCLgHk2F0\nmui2Gp6qPXXaQmv4AZKTV0aN0/O13pigXJB5V+lRvj8nlyHJsTx23dgu64c+eXAi+w8eb3IUbUZS\nTxJ7RvLS0t0Ntmc57My9I5tePWwM6RPb6oA5dUgSeyuOUVBe1fLBbZDlsDc56jguOoJZo9L4y1Wn\nk/PL83j/h2dy5pAkjHF/Ozle6+KxT7ZxqCo4KwDBZnhqHDtLjpz4W1KnpAE/QAYlumunbZ1srKsc\nPl7L7JdWYLUIz906gdiorvsyGOnpWunbJ99r1Z6DHKyqZduBI40+DM4Y2Jvvnz2EzYWVbGnlCMwp\ng9333du/vytZLMKofr24+/xhREdYsIi7u+cX20uZ/OdPeeC9jRSUV2m65xRGpMbhdBl2lR4NdFFC\nggb8AHl//X5E4LJx/YLuK3ydy/DDuavJL6viyZuyurwHxJlDk90rZUGjefJz8spweRpsm5pS4ZoJ\n/YmyWXhlWX6rrjWkTyxJsVEs3Rm4b1jeFNBPZwznP9+dwoc/nsasUam8mpPPN/66iKufWsrDC7bq\nnEFNOLEYik6x0Boa8AMgN7+CD9YXYQx8uKEw0MVp5M8fbmbJthJ+e2lmQL55eOfJB7jSp7skuHvX\nREVYGjz2Ze8ZycVj+vLO6n0cPt5yWkREmDI4kaU7G/b86Wq+KaDT0uJ55JqxfPF/53DGIDsu4/62\nU13rIiev67+JBLOMpFhsFtE8fit1esAXkVkislVEdojILzr7eqHAt1bamh4lXenN3L08+8Uubpns\n4MZJjoCV45Ix/Zg6JJHFW4qpc50IxN7a8BkD7QgwMLHxt4+bsx1U1dTxdu7eVl1ryuBESiqr2VF8\nxF/F94u0Xj34v1mnEeXpPmqAd1bt488fbtaavkekzUJGck8N+K3UqQFfRKzAE8A3gZHA9SISvP0P\nu0h2RiIR1qZTFoGUm1/Or95ez5TBifzmosC/TTdnO9h/6DifbSlusD3LYef3l42izsD/1u5v9Lwx\n/RMYk96LV3LyW1Vrn+rp+RPItE5zvI3RP585jEvG9mVHyVGeWpLHDc9qesdreGq89sVvpc6u4U8E\ndhhj8owxNcBrwKWdfM2gl+Ww8+SNWQBcOb5fUOTv9x88xndeWUVaQjT/unE8EW2Yk6azTD8thZT4\nKF7JaZyPH5Eaz8i0eN5qpr/+zZMHsrPkaKuCeP/eMaTbewSk4bY13OmeoQxPicPbUara6eLhBVs1\n6ONuuN1bcYwj1c5AFyXodfZfdT+gwOfxXs+2sDd9ZArjBiSwYX/gG5uqapzc8fJKjtfW8dwtE0iI\niQx0kQD3t58bJjr4fFsJu5vohXFlVjrr9x1iWxO1u4tOT8MeE9HqxtspgxPJyStvkD4KNtkZiUTa\nLPWjeJfuLNOGXGB4ii6G0loBr8aJyJ0islJEVpaUhNcaleePTGHd3kMUHmp6ab+uYIzh5/9Zx6bC\nwzx+/TiGprR/IZPOcN3E/lgtwtzlexrtu3RsX2wW4a1VjXP10RFWrjmjPws3H2jV/Z0yOIlDx2r5\n7XsbgzaAetsvzhyaVL/N34u/hKLhuvpVq3V2wN8H+E5fmO7ZVs8Y84wxZoIxZkJycnInFye4zBjp\nXsLQd9bGrvaPT3cwf30hv5g1Iijn8kmJj2ZmZgpvrCzgeG1dg31JsVGcPTyZd1fva7JmftMkB3Uu\nwz2vr2kxiHvHGbySkx/UteYsh52fTHf32wd3Q26wtAEFSr+EHkTbLLyZWxC071uw6OyAvwIYKiKD\nRCQSuA54r5OvGTKG9IklI7lng9kVu0pufgU/nreaRz/ZxhXj+nHnNzK6vAytdVO2g4NVtby/rnEX\n1ivHp3PgcDVf7micfy+urMYisCyvvMUg7m30a+1cPIHkremfMzwZY6jvABCuVhccpLrOxao9B4P6\nwzoYdGrAN8Y4gR8AHwObgTeMMRs785qh5vyRKSzbWdalc+nk5ldw/TM5/Hete/DX1RPSg3oBickZ\niQxO7tlk4+25p/WhV48I3mqiC2ZOXhneTjotpT6yMxLrG0SDceTzybIcdv5x/Thio2w8/+WugJQh\nWEYA+77Pwf5hHWidnsM3xnxgjBlmjBlsjHmws68XamaMTMXpMizeWtzywX5w4PBx7ntnPTWe6Xkt\nuKcrCGYiws3ZDtYWHOT+dzc0CDBRNisXj0nj441FVJ400MrbyOk9x6mCeJbDznVnuLOPz94yISh6\nTrUkLjqCayb0Z/66QooOHe/Sa7uXh1zGQx9v5dqnl/Hs53nsKauizmW6/IMgOyMRWzMjs1VDAW+0\nDXfj+ieQFBvFgo2dm9Zx1rn495e7OO/hJewoOYLNIlglNGqzAIP7xALwchM59ivHp1PtdPHB+oYp\nH28f9oFJPUmOjWT8gFPP43/uCPdi7DGR/lvJq7PdNnUgLmN4adnuLr3unJx8nJ52E6fL8OAHm/nG\nQ4sY/psPuerJpTz08dYuGyuQ5bDzywtGAPCrC04LiQ/rQNGAH2AWi3D+yBQWby2m2lnX8hPaITe/\ngov/+RW/e38TWQ47n95zFq9/ZzL3zBgedPP4NGfd3kP1v5/8tX1s/wQyknvy4le7G9Ussxx27pg2\niKLD1S0OzhmR5u7tsbkwdHp79O8dw4yRqcz9eg9VNV3TD33hxgO8v24/AlgFomwWHrxsFH+98nTG\n90+oX0ms2uniX4t24OyCxV4uHN0X8EwzrZqlAT8IzBiZwtGaOr+P9Kw4WsMv3lrHlU8u5WBVDU/d\nNJ4XbzsDR2LPZqfvDVa+o5OtlobfSrzpms1FlU1OMnb+yBRE4OMNp/4W1S+hB3FRtpDr3jd72iAO\nHattdhCaP+XmV/CdV1dSU2ewWYXrJg5g7h3Z3Jjt4Joz+vN/3zytwcyfn24p5uJ/fsWcnPxOTfOk\nxEcRF21rckyGOkEXQAkCkwcn0jPSyoKNBzhneMe7Rq7cXc5zX+Tx1Y5SjtW6+M43MvjReUPp2YVT\nHPtblsPO87eewa3/Xs6l4/o2+qDyLqjuO6Wy95g+cdGMH2Dn441F/Hj60GavISIMT40LuZkXsxx2\nxqT34oUvd3HjxAGdum7Bl9tL8PaAdbkMfRN6NHgvGiz+Mqg3xZXV/PrdDdz37gbAvQJYZ3yrFBGG\npcSx/UBwzYcUbLSGHwSiI6ycPbwPn2w+gKuDIz3fW7OPq59exkcbD3C0po6HrhrDLy84LaSDvdc3\nhiVzenqvJkfdzsp059+bW19gZmYKmwoPt7jQyYi0OLYUVQZ05sy2EhG+feYg8kqPsnhb5zb+9+3l\nXojdcor2n/pvjwN7883Radw8+cQkfJ05UGxon1i2B9kEeMFGA36QOH9kCiWV1azZ274eMzVOF49/\nup27X19b30VNgP0BHMXbGaYMSWL1noMcPWnelImDEnH0jmFQUs8ma5AzM92D3D7eWHTK8w9Pjafy\nuJP9XdzrpaMuGJ1GWq/oTu+imV9RVX+91tbUpw1NPjFQzLg7KnSGoSlxlB+tofRIdaecvzvQgB8k\nzhneB5tF2tVbZ/WeCi5+/EseXriN7MGJRNksIdUDpy2mDk7C6TIs313eaN/p/ROodrqaDEKOxJ6M\nSI1r8f6e5l1Qw8/r3Ha2CKuFWyYP5KsdZWzqpPmZcvMreGrxTgA+2dz6/6feNM91Z/THAMs6qYY/\nLMXdk0vz+M3TgB8kesVEkJ2RyIJNp66B+jpa7eS3/9vIFU8u5fDxWp6/dQJzZk9i7h3ZIdUDpy0m\nDLQTabWwtImRtcP6xLLv4LFGtX+vGZmprMgvP2UNcFj9CkqhFzRumDiAHhFW/v1V59Tyc/LK6qew\naOsApyyHnT9feTqXj+vHk4t38of5m/zegDvMMw+U5vGbpwE/iMzITCGv5GirFuJYtLWYGY9+zotL\nd3NLtoOF95zFeae589ih1gOnLaIjrIx3JPDJ5gONen14J35r7v7NzEzBmFPPXRQfHUFSbCT/W7s/\n4CNI26pXTARXZaXz3pr9FFf6PyWVnZHY7NKTrXXh6Wk4XYbnvtjl92kQ+sRFEa89dU5JA34Qme4J\n2AtPEZDKjlTzk9dWc9sLK+gRaeXN707mt5eO6tJFxgNtUGJPdpVWNeqCObSFr/Qj0+JJt/c4ZR4/\nN7+C8qM1bCmqDMl5WW6bOpCaOhev5jSeXbSjshx27vb0cvrj5aPbVaHYWlRZP72zv6dBEBHSEnqw\nZFtJyL1vXUUDfhDpm9CDjKSevLxsd6P/sMYY3lm9l+mPLGH++kJ+fN5Q5v/oTLIcvQNT2ACyeRZn\n8e2CCeDoHUOk1dJsDV9EmJmZylc7yhpNw+DlXiTd/XsozsuSkRzLeSP6MCcnv9Hsov4w0VOrT46L\natfzszMSifBMd2GxnHq6i7bKza9gR/ER9lYcC8kP666gAT+I5OZXsKe8isJDx7n26WXkehomC8qr\nuPWFFdz9+loGJvVk/o+mcff5w4iyhc4UAP502di+9SMqfRumbVYLab2iWbjpQLN/7DMzU6mpc7F4\na9NrL4TaJGpNuX3aIMqO1vDfNf4fiJUU6w70r63Y066AmuWw89JtZyACl4xpPJ6iI3Lyyuq7NYfi\nh3VX0IAfRNy1yxPzk9zzxlq+9e/lnPfwEnJ3l/PbSzJ587tT6hunwlXWwN7cM30YAD86d2h90MjN\nr6Cgooq80qPN1vCyHHbio23NjvrMctgZmRZPv4TokG30npyRyGlp8Tz/5S6/jyfY6+mW+eH6onbX\noicPTuK01HiKK/3bfTI7IxFbEK4VHUw04AcR7+yOVnHPUZJfXsXibSU4XS4euXYst04ZWN9oFu6+\nd/Zg+sRFMufr/Pqg05p0zJqCgxytqWNLUWWzk3tZrRYG94kLyWAP7tTV7WcOYtuBI9z71jq/pjbW\necaJdHTdgDH9E1hbcNCvH0hZDjv3znJPovb/Ls4M2fevM2nADyLe/sr3zBjOdRMH1KcWhOZ7noSr\ntXsPUX60ln0Hj3P1k0u598212GMi6xsErc3U8Nxzp7uDTLXTxZImpqWuOFJD4cFjIZ0DTrdHA/Cf\nlXv9ms/OzkjyS8prTHovDh93srvs1COf22qypzyJscGxLnOw0YAfZLxdKq8Yn15f2w/VXHJn8k1/\nuYA3Vu7lV++sr5+pkWZqjt5vUd6g9dHGIv752fb6gOhNC20vPhLSDX+5+QfrP/z8OZ1BlsPOzMxU\nIq0W5tw+qd216DGe0bbr2jmyvDneNgYdbdu08OnLF2IaTEKVkahfT0/iDdzVtS6aCu11LtNgAjUv\n3/u67UAl/12zn4cXbCPKtoP7L87kxaW76s938iRsoSQ7wz3i+rjTVf/YX6YOSeLDDUWkJvRo9zmG\n9oklOsLCmoKDXDq2n9/K5q3Zl1bW+O2c3YnW8INYdx5A1VHewH39pAH134QirdKqb0Xe++pt/DbA\ncaeL+95ZzzbPKM1TTQ4WCrIcdubckc1Zw5JxGfyaKx/uGY28rQOjkW1WC6P79WqwzoE/RFgtJMRE\naA2/GVrDVyEry2Eny2HnyvHp9d+EgFZ/K8rOSCQ6wkKN0/0twRsTLbhrsT+ZPiykP2yzHHaeuimL\naX9dxMMLtjHvzmy/nNf7QbmlqJJzRrR/Ou+U+Gg+2lDE8l1lTBzkvw/WpNgoDfjN0ICvQp438Ps+\nbu3zvOkde0wkv3t/I7VOFxE2S8gHe68ekVbuOmcwv/3fJpbuKGXKkKQOn7NXjwjSekV3aAqD3PwK\nPt5YhNNluPn55cy9w39dYJNiIzXgN0MDvgprvh8Ww1PjumWbyfUTB/DM53n8bcFW3hqciPhhHcBh\nKXEdWhmswURsdf5tK0mKjWJjJ80YGuo0h6+UR3dtM4mOsPLDc4eyas/BZkcYt1VCTARbD1SyfFf7\nev+4l6x0hx+rn6dYSIqNotTPg7q6Cw34SoWBqyekM6B3DA8v3NrhBtzc/Ao+WF9InScd094pFp65\nOQuAm7Idfv2QralzUVntZNnOxlNohzsN+EqFgQirhR+fN5QN+w7zcTsW2fHVVDqmPaYNTcYi+HWm\n19z8Cv6zsgCAb72wImTHUXQWDfhKhYnLxvUjI7knjyzcWh+w28Nf6RiLRUiIiaT8qP/6zOfkleGs\n6/iHUXelAV+pMGG1CHdPH8a2A0d4f93+dp8ny2HnldsnIrhnLu1IOqZHhIWVuyv8OPXDiQnUInQC\ntUY04CsVRi4cncaI1Dge+2Q7zjpXu88zcVAiKfHRGNrf4yc3v4L9h46z9YD/FpvJcti5c1oGAH+/\nbmy3a4DvqE4L+CLygIjsE5E1np8LOutaSqnWsViEe84fxq7So7y9umPz5aclRFN46Fi7n++eyM79\nuz/nr+9njwFg3AAN9ifr7H74jxpj/tbJ11BKtcH5I1M4Pb0XD328haJDx5k6JKldNeG+vXqwubD9\n/d296RbBv9NYOF3uby42nUq8EU3pKBVmRIRLxvSlpLKGRxdua3c6Ja1XNPsPHWt3N8+RafGAexoL\nfy42U+tptLVZNLydrLPvyA9EZJ2I/FtEmnw3ReROEVkpIitLSvwzKEQpdWrVTvd6tx1ZyKTOGI7X\nuliyrX1/t97Vs67KSvdrrt3bNuFtvFUndCjgi8gnIrKhiZ9LgSeBwcBYoBB4uKlzGGOeMcZMMMZM\nSE5O7khxlFKtlJ2RRJTN++ff9q6VufkVvJqTD8Cdr+S26xtCgSfg9+8d0+bnnorT0+VUA35jHcrh\nG2Omt+Y4EXkWeL8j11JK+U+Ww87cO7L528dbWJZXztFqZ5ue7zv4ytnOuXAKyt0Nvv17t39e/aZ4\n++FHaEqnkc7spZPm8/ByYENnXUsp1XZZDjsv3DaRjKSe3Pfueo7V1LX6udkZifU5cpulfQ2uBeVV\nREdYSPasUuUvBRVHEWB1gX9X0+oOOvMj8K8isl5E1gHnAHd34rWUUu0QHWHlwctHU1B+jL9/ur3V\nz8ty2Hnw8lEA3H3+0Hbl4Asqqki3x/hl9k6v3PwK3lm9HwMhvURlZ+m0gG+MudkYM9oYc7ox5hJj\nTGFnXUsp1X6TBydyzYR0nv0ij01tmFZ4vCfI923nUocF5cfob/dvOqfBPD9+7NvfXWiSSynFry44\njYQeEfzynfWtnmenR4QVgOO1rU8F+dpddpSDx2r9WgvPzkisH/sbyktUdhYN+EopEmIiuf/ikawt\nOMidL69sVRD2BvwFGw+0OWh/vrWEqpo61uw56NfUy5j0XlgsMHFQb7/27e8uNOArpQBIT+iBReDT\nLcXc8GzLQdg7yvazLcVtDtqLtxUDHRsH0JS9Fceoc/m/b393oQFfKQVAzq7y+t+rna4WFxDJ3eMO\n8O0J2qd5RtlaxL+pl7zSIwAMTu7pl/N1N7qmrVIKcOe/I20WqmtdGKCihXnqJ3hq0O2ZCyfDE5Cv\nHJ/OdRMH+K02nldy1H3+pFi/nK+70Rq+Ugpwd7WcMzubn80cxrgBCcxZvoedJUeaPX50egIAZw1L\nbnO+vNrpnv7gSj+nXnaWHMUeE4G9Z6TfztmdaMBXStVzL+Q+lKduyiLKZuWeN9Y2O2++d/tZw5Pb\nHLS9Af/E9A7+kVdyhIxkrd03RwO+UqqRlPho/nDZKNYWHOT+/27giUU7GjXK1s9Z045piKtr3QE/\n0t8Bv/QoGUmav2+O5vCVUk26eExfXlu+h7nLC7CIOzj7pm68/fWt7ZizpqbOW8O3+q28lcdrKams\n1hr+KWgNXynVLO9oWpeBmpN64nSshu8erOXPlE59g6320GmWBnylVLPOHt6nPii7DBQdOk7u7nKe\nWLSDtXvck5Mt3lrc5oFTJ2r4/gtBn24+AJz4MFGNaUpHKdUs7zTKX24v4etd5bySk8+cr/PxXeTq\nww1FfLa1uE09dXYUu3v/bCmspE98dIfLmZtfwb8W7wTg3rfW0c8eowOvmqA1fKXUKWU57Px4+jDm\nzJ7ElMGJuIx7sJU35rd14FVufgWvLPMuntK6aRxaopOmtY4GfKVUq4gIP50xnCibBatApFWI9Pze\nloFXDYJznX+Cc3ZGIlERbS9LuNGUjlKq1bwpnpy8svqg6v29tSmU7IxErBbB6TLYrP4Jzt5BY20t\nS7iR9q443xkmTJhgVq5cGehiKKU62UMfb+GJRTt56qbxzBqV1vIT1CmJSK4xZkJLx2lKRynV5Yal\nxP91p50AAAc6SURBVAEw1POv6hoa8JVSXc474Mo74lZ1DQ34Sqku5+1/X+3UPvNdSQO+UqrLeQP+\n6ysK/LbaVW5+RZNz/qgTtJeOUqrL7a2oAtwB/901+zq8HGFufgXXPr0MlzGN5vxRJ2gNXynV5Yor\nqwH/LXGYk1eG02VwGR14dSoa8JVSXW7y4KT6Sdf80Rff+/z2rL4VTjTgK6W6XJbDzqPXjgHgmgn9\nO5x+yXLYibQKZwyyazrnFDTgK6UC4uIx/ZjgsPPZlgM8sWh7hxtbbVYLY9ITNNifggZ8pVTATBrU\nm30Hj/Pwgm3c+FxOh4K+RQRX8EwcEJQ6FPBF5GoR2SgiLhGZcNK+X4rIDhHZKiIzO1ZMpVR3FGE9\nMdd+RxtbRcAVRFPFBKOO1vA3AFcAn/tuFJGRwHVAJjAL+JeI+G8tM6VUtzBtWDIRVnfjrYh0qLHV\nIoLG+1PrUMA3xmw2xmxtYtelwGvGmGpjzC5gBzCxI9dSSnU/WQ47r92RzcDEGCKsFvol9Gj3uSxa\nw29RZ+Xw+wEFPo/3erY1IiJ3ishKEVlZUlLSScVRSgWrrIG9eenbE3EZwz2vr2n3aNk6l2Hd3oM6\n0vYUWgz4IvKJiGxo4udSfxTAGPOMMWaCMWZCcnKyP06plAoxjsSeXDm+H0vzyvjbx1vb3ICbm1/B\n4eNO1hQc6nDjb3fW4tQKxpjp7TjvPqC/z+N0zzallGpSai/32rYG9yyaX24vaXUXy2U7S+t/9zb+\navfMxjorpfMecJ2IRInIIGAosLyTrqWU6gamDkmun1TNAK/k5LNgYxG5u8tbTPN4l0zUkban1qHJ\n00TkcuBxIBmYLyJrjDEzjTEbReQNYBPgBO4yxug8qEqpZvkunxgfbePVnD3c+UounhkYmp0ULTe/\ngn8u2gGAxSLcf1Gm1u6b0aGAb4x5B3inmX0PAg925PxKqfCS5bDXB+vrJg7gzpdXsmiruzNHda2L\npTtLGwXznLxSaus8vXOMoaKqpkvLHEp0emSlVFCKsFr4wblDWbqzjGqnCwO8s2ofqfHRFFdW1y9W\nXnTIPfOmpnNapgFfKRW0TqR5SnG54Lkvd/HzN9cB7gAfG2WlstqdLbZqOqdFGvCVUkHNN81TW+fi\n8c92YHA37PaMstUHfKPpnBbp5GlKqZBx1vA+REVYsApER1j40XnDiPY81nROy7SGr5QKGVkO93z3\nOXll9Tn84alxDR6r5mnAV0qFFN8UT1OPVfM0paOUUmFCA75SSoUJDfhKKRUmNOArpVSY0ICvlFJh\nQgO+UkqFCTFBtCSYiJQA+YEuB5AElLZ4VHjSe9M0vS/N03vTNH/eF4cxpsUVpIIq4AcLEVlpjJkQ\n6HIEI703TdP70jy9N00LxH3RlI5SSoUJDfhKKRUmNOA37ZlAFyCI6b1pmt6X5um9aVqX3xfN4Sul\nVJjQGr5SSoUJDfhKKRUmNOA3QUR+KiJGRJI8j0VE/iEiO0RknYiMD3QZu5qI/N7z2teIyAIR6evZ\nHtb3RkQeEpEtntf+jogk+Oz7pee+bBWRmYEsZ1cTkatFZKOIuERkwkn7wva+AIjILM9r3yEiv+jK\na2vAP4mI9AdmAHt8Nn8TGOr5uRN4MgBFC7SHjDGnG2PGAu8D93u2h/u9WQiMMsacDmwDfgkgIiOB\n64BMYBbwLxGxBqyUXW8DcAXwue/GcL8vntf6BO6/m5HA9Z570iU04Df2KHAv7iUzvS4FXjZuOUCC\niKQFpHQBYow57POwJyfuT1jfG2PMAmOM0/MwB0j3/H4p8JoxptoYswvYAUwMRBkDwRiz2RiztYld\nYX1fcL/WHcaYPGNMDfAa7nvSJTTg+xCRS4F9xpi1J+3qBxT4PN7r2RZWRORBESkAbuREDV/vzQnf\nBj70/K73pWnhfl8C+vrDbolDEfkESG1i133Ar3Cnc8LSqe6NMea/xpj7gPtE5JfAD4D/16UFDJCW\n7ovnmPsAJzCnK8sWSK25Lyq4hF3AN8ZMb2q7iIwGBgFrRQTcX81XichEYB/Q3+fwdM+2bqW5e9OE\nOcAHuAN+t783Ld0XEfkWcBFwnjkxsCXs70szuv19aUFAX7+mdDyMMeuNMX2MMQONMQNxf9Uab4z5\n/+3cPUoDURTF8f9BMCtwASmCW3AHioVil0qwC+hC7LV2AZYDCuIGxDQ2EXegrU0q9Vi8KVJbzAj3\n/Kr5KN7lFoeZucP7ADrgtP8jZQ/4tP0+Zr1DkzTbOD0G3vrj0r2RdECb+RzZXm/c6oC5pImkKW2o\n/TxGjf9M9b4sgZmkqaRt2gC7G2rxck/4f3QPHNIGTGvgbNxyRnEpaRf4oW1hveivV+/NNTABHvs3\nwyfbC9srSbfAK+1Tz7nt7xHrHJSkE+AK2AHuJL3Y3q/eF9tfki6AB2ALuLG9Gmr9bK0QEVFEPulE\nRBSRwI+IKCKBHxFRRAI/IqKIBH5ERBEJ/IiIIhL4ERFF/AK1ODWtoG2vKgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"@interact(alpha=(-180.,360.,5.))\n",
"def _scale(alpha=0):\n",
" ro=deg2rad(alpha)\n",
" R=array([[cos(ro), sin(ro)], \n",
" [-sin(ro), cos(ro)]])\n",
" print(R)\n",
" d_ = d.dot(R)\n",
" x=d_[:,0]; y=d_[:,1]; \n",
" plot(x,y,'.-'); axis('equal');#xlim(0,100);ylim(0,100);\n",
" title('Вращение на {} градусов'.format(alpha))\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Обратите внимание на коэффициенты при 60, 45, 90, -90, 180, 360 градусах. Бегунок можно двигать стрелочками, если мышкой неудобно.\n",
"\n",
"Вращение на 90 градусов фактически равно замене местами $x$ и $y$ и замене знака у $x$.\n",
"\n",
"Если заменить координаты местами и не заменить знак, то будет \"зеркальное\" отображение исходной картинки относительно биссектрисы угла."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Remau2pWIOI0xyU09Ts/Q/VxSXAQ/nZJIjzBryYDLQJWfll9EhBkXxFJR7eKV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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x=d[:,1]; y=d[:,0]; \n",
"plot(x,y,'.-'); axis('equal');\n",
"plot([0,40], [0,40], 'r:');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Замена знака у $x$ и $y$ соответствует вращению вокруг начала координат на 180 градусов."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Wy87jeew8lkdOib4EgYeL1hTsBXBrn/bcPySUgNZu+Ld25dDpIqYsiKOySoez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\nfAAogsIHgCIofAAogsIHgCIofAAo4g01LGHdqlg17gAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x=d[:,0]; y=d[:,1];\n",
"plot(-x,-y,'.-'); axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Поправьте элементы матрицы вращения $R$ так, чтобы изображение лося было правдоподобным, таким, каким его видели жители Урала с вершины горы, когда создавали.\n",
"Критерий успеха: рога торчат вертикально, спина идет горизонтально."
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[-1. 0.5 ]\n",
" [ 0.25 -1. ]]\n"
]
},
{
"data": {
"image/png": 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WA/iXh20ifF9TAmXECJE774ze+YqKRMqVEzl6NPRjHTki0r69yD33MDXR0fOd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\n2vu2djuFPD+f4ZulSwO74Rc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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"R=array([[-1, .5], \n",
" [.25, -1]])\n",
"d_ = d.dot(R)\n",
"x=d_[:,0]; y=d_[:,1]; plot(x,y,'.-'); axis('equal');\n",
"print(R)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Вывод: сочетание взаимных влияний двух показателей может оказывать эффекты вращения и наклона на паттерн расположения точек в пространстве.\n",
"\n",
"При этом используются простые операции - умножения и сложения. Результат (повернутая матрица) - массив чисел той же размерности с сохраненным взаимным расположением точек.\n",
"Например, координаты точки из передней ноги в результате любых поворотов и искажений будут находится в промежутке между координатами морды и задней ноги."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}