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Векторы. Матрицы и операции с ними. Библиотека NumPy" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Векторы" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Определение** : *Вектором* в n-мерном евклидовом пространстве $\\R^{n}$ называется упорядоченый набор чисел $x = (x_1, x_2, ..., x_n)$ - собственно, элемент пространства $\\R^{n}$.\n", + "\n", + "Часто вектор удобнее записывать в столбец: \n", + "$$x = \\begin{pmatrix}x_1\\\\x_2\\\\...\\\\x_n\\\\\\end{pmatrix}$$" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Помимо того, что вектор это набор чисел, вектор еще и геометрический объект, мы его можем отобразить на координатной поскости и в пространстве:\n", + "\n", + "![](imgs/sem1/sem1_1.png) | ![](imgs/sem1/sem1_2.png)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Операции над векторами" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Векторы можно складывать и умножать на скаляр(число). Результатом будет вектор, элементами которого являются результаты поэлементного выполнения операции." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Сложение векторов\n", + "\n", + "Геометрически сложение векторов выглядит так:\n", + "\n", + "| для неколлинеарных векторов | для коллинеарных векторов | сложение нескольких векторов |\n", + "| --- | --- | --- |\n", + "| ![](imgs/sem1/sem1_3.png) | ![](imgs/sem1/sem1_4.png) | ![](imgs/sem1/sem1_5.png) |\n", + "\n", + "**Пример**\n", + "\n", + "![](imgs/sem1/sem1_6.png)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Линейные подпространства\n", + "\n", + "- Векторное пространство $\\R^{n}$ **замкнуто** относительно операций сложения и умножения на скаляр.\n", + "\n", + "**Определение**: *Линейным (или векторным) подпространством* векторного пространства $L$ называется множество векторов $M$ $\\subset$ $L$, замкнутое относительно операций сложения и умножения на скаляр.\n", + "\n", + "**Определение**: *Линейной оболочкой векторов $v_1, v_2, ..., v_n$* называется множество всех линейных комбинаций этих векторов с произвольными коэффициентами: $$M = = \\{\\alpha_{1}v_{1} + \\alpha_{2}v_{2} + ... + \\alpha_{n}v_{n} \\ \\ | \\ \\ \\alpha_{i}\\in \\R\\}$$\n", + "\n", + "#### ЛНЗ\n", + "**Определение**: Векторы $v_1, v_2, ..., v_n$ называются *линейно независимыми*, если никакая линейная комбинация этих векторов не равна нуль-вектору. Иными словами, для любых $\\alpha_{i} \\in \\R$, не все из которых нулевые, выполняется $$\\alpha_{1}v_{1} + \\alpha_{2}v_{2} + ... + \\alpha_{n}v_{n} \\ne \\overline{0}$$\n", + "\n", + "![](imgs/sem1/sem1_7.png)\n", + "\n", + "#### Базис\n", + "**Определение**: Пусть $M$ - линейное подпространство. Базисом в $M$ называется минимальная система векторов $v_1, v_2, ..., v_n$, для которой $M = $\n", + "\n", + "![](imgs/sem1/sem1_8.png)\n", + "\n", + "Свойства базиса:\n", + "\n", + "- Базис является ЛНЗ\n", + "- Векторы из $M$ выражаются через базис единственным способом\n", + "- Любую ЛНЗ систему можно дополнить до базиса\n", + "- В любой системе образующих можно выбрать базис\n", + "- Любые два базиса равномощны. (Это свидетельствует о корректности определения *размерности линейного пространства* как размера базиса в этом линейном пространстве)\n", + "\n", + "\n", + "**Теорема**: $n+1$ векторов в $n-мерном$ пространстве всегда линейно зависимы.\n", + "\n", + "**Доказательство**: От противного. Пусть Они ЛНЗ => Можно дополнить до базиса => в базисе n+1 векторов и более => противоречие т.к. любые два базиса равномощны. \n", + "\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Далее поговорим как работать с векторами в `Python` с использованием библиотеки `NumPy`" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Отвлечемся на введение в NumPy" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# !conda install numpy\n", + "# !pip3 install numpy" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Одномерные массивы" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " \n" + ] + } + ], + "source": [ + "a = [1, 2, 3]\n", + "b = np.array(a, dtype='float64')\n", + "print(type(b), type(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Если типы разные, то идет неявный каст к одному.***" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Для list: \n", + "Для np.array: \n" + ] + } + ], + "source": [ + "a = [1, 2, 'a']\n", + "b = np.array(a)\n", + "print(\"Для list:\", type(a[0]),\n", + " \"\\nДля np.array:\", type(b[0]))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 2, 3])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d = np.array([1, 2, 3])\n", + "d" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.ndarray" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Можем посмотреть на все методы класса ``ndarray``.***" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'T',\n", + " '__abs__',\n", + " '__add__',\n", + " '__and__',\n", + " '__array__',\n", + " '__array_finalize__',\n", + " '__array_function__',\n", + " '__array_interface__',\n", + " '__array_prepare__',\n", + " '__array_priority__',\n", + " '__array_struct__',\n", + " '__array_ufunc__',\n", + " '__array_wrap__',\n", + " '__bool__',\n", + " '__class_getitem__',\n", + " '__complex__',\n", + " '__contains__',\n", + " '__copy__',\n", + " '__deepcopy__',\n", + " '__delitem__',\n", + " '__divmod__',\n", + " '__dlpack__',\n", + " '__dlpack_device__',\n", + " '__float__',\n", + " '__floordiv__',\n", + " '__getitem__',\n", + " '__iadd__',\n", + " '__iand__',\n", + " '__ifloordiv__',\n", + " '__ilshift__',\n", + " '__imatmul__',\n", + " '__imod__',\n", + " '__imul__',\n", + " '__index__',\n", + " '__int__',\n", + " '__invert__',\n", + " '__ior__',\n", + " '__ipow__',\n", + " '__irshift__',\n", + " '__isub__',\n", + " '__iter__',\n", + " '__itruediv__',\n", + " '__ixor__',\n", + " '__len__',\n", + " '__lshift__',\n", + " '__matmul__',\n", + " '__mod__',\n", + " '__mul__',\n", + " '__neg__',\n", + " '__or__',\n", + " '__pos__',\n", + " '__pow__',\n", + " '__radd__',\n", + " '__rand__',\n", + " '__rdivmod__',\n", + " '__rfloordiv__',\n", + " '__rlshift__',\n", + " '__rmatmul__',\n", + " '__rmod__',\n", + " '__rmul__',\n", + " '__ror__',\n", + " '__rpow__',\n", + " '__rrshift__',\n", + " '__rshift__',\n", + " '__rsub__',\n", + " '__rtruediv__',\n", + " '__rxor__',\n", + " '__setitem__',\n", + " '__setstate__',\n", + " '__sub__',\n", + " '__truediv__',\n", + " '__xor__',\n", + " 'all',\n", + " 'any',\n", + " 'argmax',\n", + " 'argmin',\n", + " 'argpartition',\n", + " 'argsort',\n", + " 'astype',\n", + " 'base',\n", + " 'byteswap',\n", + " 'choose',\n", + " 'clip',\n", + " 'compress',\n", + " 'conj',\n", + " 'conjugate',\n", + " 'copy',\n", + " 'ctypes',\n", + " 'cumprod',\n", + " 'cumsum',\n", + " 'data',\n", + " 'diagonal',\n", + " 'dot',\n", + " 'dtype',\n", + " 'dump',\n", + " 'dumps',\n", + " 'fill',\n", + " 'flags',\n", + " 'flat',\n", + " 'flatten',\n", + " 'getfield',\n", + " 'imag',\n", + " 'item',\n", + " 'itemset',\n", + " 'itemsize',\n", + " 'max',\n", + " 'mean',\n", + " 'min',\n", + " 'nbytes',\n", + " 'ndim',\n", + " 'newbyteorder',\n", + " 'nonzero',\n", + " 'partition',\n", + " 'prod',\n", + " 'ptp',\n", + " 'put',\n", + " 'ravel',\n", + " 'real',\n", + " 'repeat',\n", + " 'reshape',\n", + " 'resize',\n", + " 'round',\n", + " 'searchsorted',\n", + " 'setfield',\n", + " 'setflags',\n", + " 'shape',\n", + " 'size',\n", + " 'sort',\n", + " 'squeeze',\n", + " 'std',\n", + " 'strides',\n", + " 'sum',\n", + " 'swapaxes',\n", + " 'take',\n", + " 'tobytes',\n", + " 'tofile',\n", + " 'tolist',\n", + " 'tostring',\n", + " 'trace',\n", + " 'transpose',\n", + " 'var',\n", + " 'view'}" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(dir(b)) - set(dir(object))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Например узнаем размер массива.***" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "arr = np.array([5, 6, 2, 1, 10], dtype='int32')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "20" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "arr.nbytes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Если вы не знаете нужной функции, но понимаете, чего хотите, тогда можно воспользоваться поиском в документации.***" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Search results for 'mean value of array'\n", + "----------------------------------------\n", + "numpy.ma.mean\n", + " Returns the average of the array elements along given axis.\n", + "numpy.mean\n", + " Compute the arithmetic mean along the specified axis.\n", + "numpy.nanmean\n", + " Compute the arithmetic mean along the specified axis, ignoring NaNs.\n", + "numpy.put\n", + " Replaces specified elements of an array with given values.\n", + "numpy.full\n", + " Return a new array of given shape and type, filled with `fill_value`.\n", + "numpy.digitize\n", + " Return the indices of the bins to which each value in input array belongs.\n", + "numpy.isrealobj\n", + " Return True if x is a not complex type or an array of complex numbers.\n", + "numpy.unpackbits\n", + " Unpacks elements of a uint8 array into a binary-valued output array.\n", + "numpy.nanquantile\n", + " Compute the qth quantile of the data along the specified axis,\n", + "numpy.ma.dot\n", + " Return the dot product of two arrays.\n", + "numpy.count_nonzero\n", + " Counts the number of non-zero values in the array ``a``.\n", + "numpy.ma.fix_invalid\n", + " Return input with invalid data masked and replaced by a fill value.\n", + "numpy.matrix.partition\n", + " Rearranges the elements in the array in such a way that the value of the\n", + "numpy.ma.MaskedArray.filled\n", + " Return a copy of self, with masked values filled with a given value.\n", + "numpy.ma.MaskedArray.partition\n", + " Rearranges the elements in the array in such a way that the value of the\n", + "numpy.exp\n", + " Calculate the exponential of all elements in the input array.\n", + "numpy.ptp\n", + " Range of values (maximum - minimum) along an axis.\n", + "numpy.sum\n", + " Sum of array elements over a given axis.\n", + "numpy.var\n", + " Compute the variance along the specified axis.\n", + "numpy.copy\n", + " Return an array copy of the given object.\n", + "numpy.prod\n", + " Return the product of array elements over a given axis.\n", + "numpy.block\n", + " Assemble an nd-array from nested lists of blocks.\n", + "numpy.copyto\n", + " Copies values from one array to another, broadcasting as necessary.\n", + "numpy.median\n", + " Compute the median along the specified axis.\n", + "numpy.nanmax\n", + " Return the maximum of an array or maximum along an axis, ignoring any\n", + "numpy.nanmin\n", + " Return minimum of an array or minimum along an axis, ignoring any NaNs.\n", + "numpy.nansum\n", + " Return the sum of array elements over a given axis treating Not a\n", + "numpy.nanvar\n", + " Compute the variance along the specified axis, while ignoring NaNs.\n", + "numpy.allclose\n", + " Returns True if two arrays are element-wise equal within a tolerance.\n", + "numpy.gradient\n", + " Return the gradient of an N-dimensional array.\n", + "numpy.nanmedian\n", + " Compute the median along the specified axis, while ignoring NaNs.\n", + "numpy.ones_like\n", + " Return an array of ones with the same shape and type as a given array.\n", + "numpy.lib.recfunctions.assign_fields_by_name\n", + " Assigns values from one structured array to another by field name.\n", + "numpy.percentile\n", + " Compute the q-th percentile of the data along the specified axis.\n", + "numpy.zeros_like\n", + " Return an array of zeros with the same shape and type as a given array.\n", + "numpy.ma.exp\n", + " Calculate the exponential of all elements in the input array.\n", + "numpy.chararray.copy\n", + " Return a copy of the array.\n", + "numpy.ma.var\n", + " Compute the variance along the specified axis.\n", + "numpy.chararray.view\n", + " New view of array with the same data.\n", + "numpy.nanpercentile\n", + " Compute the qth percentile of the data along the specified axis,\n", + "numpy.chararray.astype\n", + " Copy of the array, cast to a specified type.\n", + "numpy.ma.median\n", + " Compute the median along the specified axis.\n", + "numpy.linalg.svd\n", + " Singular Value Decomposition.\n", + "numpy.ma.ones_like\n", + " Return an array of ones with the same shape and type as a given array.\n", + "numpy.ma.zeros_like\n", + " Return an array of zeros with the same shape and type as a given array.\n", + "numpy.ma.MaskedArray.mean\n", + " Returns the average of the array elements along given axis.\n", + "numpy.ma.MaskedArray.dot\n", + " Masked dot product of two arrays. Note that `out` and `strict` are\n", + "numpy.ma.MaskedArray.var\n", + " Compute the variance along the specified axis.\n", + "numpy.ma.MaskedArray.copy\n", + " Return a copy of the array.\n", + "numpy.polynomial.polyutils.trimcoef\n", + " Remove \"small\" \"trailing\" coefficients from a polynomial.\n", + "numpy.pad\n", + " Pad an array.\n", + "numpy.std\n", + " Compute the standard deviation along the specified axis.\n", + "numpy.take\n", + " Take elements from an array along an axis.\n", + "numpy.isnan\n", + " Test element-wise for NaN and return result as a boolean array.\n", + "numpy.nditer\n", + " Efficient multi-dimensional iterator object to iterate over arrays.\n", + "numpy.reshape\n", + " Gives a new shape to an array without changing its data.\n", + "numpy.quantile\n", + " Compute the q-th quantile of the data along the specified axis.\n", + "numpy.full_like\n", + " Return a full array with the same shape and type as a given array.\n", + "numpy.empty_like\n", + " Return a new array with the same shape and type as a given array.\n", + "numpy.asarray_chkfinite\n", + " Convert the input to an array, checking for NaNs or Infs.\n", + "numpy.ma.ptp\n", + " Return (maximum - minimum) along the given dimension\n", + "numpy.ma.anom\n", + " Compute the anomalies (deviations from the arithmetic mean)\n", + "numpy.fft.ifft2\n", + " Compute the 2-dimensional inverse discrete Fourier Transform.\n", + "numpy.fft.ifftn\n", + " Compute the N-dimensional inverse discrete Fourier Transform.\n", + "numpy.ma.ravel\n", + " Returns a 1D version of self, as a view.\n", + "numpy.fft.irfftn\n", + " Computes the inverse of `rfftn`.\n", + "numpy.linalg.cond\n", + " Compute the condition number of a matrix.\n", + "numpy.linalg.norm\n", + " Matrix or vector norm.\n", + "numpy.histogram_bin_edges\n", + " Function to calculate only the edges of the bins used by the `histogram`\n", + "numpy.ma.MaskedArray.ptp\n", + " Return (maximum - minimum) along the given dimension\n", + "numpy.ma.MaskedArray.anom\n", + " Compute the anomalies (deviations from the arithmetic mean)\n", + "numpy.ma.MaskedArray.ravel\n", + " Returns a 1D version of self, as a view.\n", + "numpy.random.Generator.wald\n", + " Draw samples from a Wald, or inverse Gaussian, distribution.\n", + "numpy.polynomial.Hermite._fit\n", + " Least squares fit of Hermite series to data.\n", + "numpy.random.Generator.choice\n", + " Generates a random sample from a given array\n", + "numpy.random.RandomState.wald\n", + " Draw samples from a Wald, or inverse Gaussian, distribution.\n", + "numpy.polynomial.HermiteE._fit\n", + " Least squares fit of Hermite series to data.\n", + "numpy.polynomial.Laguerre._fit\n", + " Least squares fit of Laguerre series to data.\n", + "numpy.polynomial.Legendre._fit\n", + " Least squares fit of Legendre series to data.\n", + "numpy.polynomial.Chebyshev._fit\n", + " Least squares fit of Chebyshev series to data.\n", + "numpy.random.RandomState.choice\n", + " Generates a random sample from a given 1-D array\n", + "numpy.polynomial.Polynomial._fit\n", + " Least-squares fit of a polynomial to data.\n", + "numpy.random.Generator.lognormal\n", + " Draw samples from a log-normal distribution.\n", + "numpy.random.RandomState.lognormal\n", + " Draw samples from a log-normal distribution.\n", + "numpy.random.Generator.standard_normal\n", + " Draw samples from a standard Normal distribution (mean=0, stdev=1).\n", + "numpy.einsum\n", + " einsum(subscripts, *operands, out=None, dtype=None, order='K',\n", + "numpy.interp\n", + " One-dimensional linear interpolation for monotonically increasing sample points.\n", + "numpy.kaiser\n", + " Return the Kaiser window.\n", + "numpy.nanstd\n", + " Compute the standard deviation along the specified axis, while\n", + "numpy.average\n", + " Compute the weighted average along the specified axis.\n", + "numpy.hamming\n", + " Return the Hamming window.\n", + "numpy.hanning\n", + " Return the Hanning window.\n", + "numpy.loadtxt\n", + " Load data from a text file.\n", + "numpy.polyfit\n", + " Least squares polynomial fit.\n", + "numpy.bartlett\n", + " Return the Bartlett window.\n", + "numpy.blackman\n", + " Return the Blackman window.\n", + "numpy.can_cast\n", + " Returns True if cast between data types can occur according to the\n", + "numpy.random.RandomState.standard_normal\n", + " Draw samples from a standard Normal distribution (mean=0, stdev=1).\n", + "numpy.isfinite\n", + " Test element-wise for finiteness (not infinity and not Not a Number).\n", + "numpy.random.Generator.multivariate_normal\n", + " multivariate_normal(mean, cov, size=None, check_valid='warn',\n", + "numpy.nan_to_num\n", + " Replace NaN with zero and infinity with large finite numbers (default\n", + "numpy.random.RandomState.multivariate_normal\n", + " Draw random samples from a multivariate normal distribution.\n", + "numpy.fft.fft2\n", + " Compute the 2-dimensional discrete Fourier Transform.\n", + "numpy.fft.fftn\n", + " Compute the N-dimensional discrete Fourier Transform.\n", + "numpy.ma.copy\n", + " a.copy(order='C')\n", + "numpy.fft.rfft\n", + " Compute the one-dimensional discrete Fourier Transform for real input.\n", + "numpy.fft.rfftn\n", + " Compute the N-dimensional discrete Fourier Transform for real input.\n", + "numpy.ma.polyfit\n", + " Least squares polynomial fit.\n", + "numpy.random.SFC64\n", + " BitGenerator for Chris Doty-Humphrey's Small Fast Chaotic PRNG.\n", + "numpy.ma.empty_like\n", + " empty_like(prototype, dtype=None, order='K', subok=True, shape=None)\n", + "numpy.random.Generator.f\n", + " Draw samples from an F distribution.\n", + "numpy.random.RandomState.f\n", + " Draw samples from an F distribution.\n", + "numpy.random.Generator.gamma\n", + " Draw samples from a Gamma distribution.\n", + "numpy.random.Generator.gumbel\n", + " Draw samples from a Gumbel distribution.\n", + "numpy.random.Generator.normal\n", + " Draw random samples from a normal (Gaussian) distribution.\n", + "numpy.random.Generator.laplace\n", + " Draw samples from the Laplace or double exponential distribution with\n", + "numpy.random.RandomState.gamma\n", + " Draw samples from a Gamma distribution.\n", + "numpy.random.Generator.logistic\n", + " Draw samples from a logistic distribution.\n", + "numpy.random.Generator.rayleigh\n", + " Draw samples from a Rayleigh distribution.\n", + "numpy.random.Generator.vonmises\n", + " Draw samples from a von Mises distribution.\n", + "numpy.random.RandomState.gumbel\n", + " Draw samples from a Gumbel distribution.\n", + "numpy.random.RandomState.normal\n", + " Draw random samples from a normal (Gaussian) distribution.\n", + "numpy.random.Generator.chisquare\n", + " Draw samples from a chi-square distribution.\n", + "numpy.random.RandomState.laplace\n", + " Draw samples from the Laplace or double exponential distribution with\n", + "numpy.random.Generator.standard_t\n", + " Draw samples from a standard Student's t distribution with `df` degrees\n", + "numpy.random.RandomState.logistic\n", + " Draw samples from a logistic distribution.\n", + "numpy.random.RandomState.rayleigh\n", + " Draw samples from a Rayleigh distribution.\n", + "numpy.random.RandomState.vonmises\n", + " Draw samples from a von Mises distribution.\n", + "numpy.random.RandomState.chisquare\n", + " Draw samples from a chi-square distribution.\n", + "numpy.random.Generator.noncentral_f\n", + " Draw samples from the noncentral F distribution.\n", + "numpy.random.RandomState.standard_t\n", + " Draw samples from a standard Student's t distribution with `df` degrees\n", + "numpy.random.Generator.standard_gamma\n", + " Draw samples from a standard Gamma distribution.\n", + "numpy.random.RandomState.noncentral_f\n", + " Draw samples from the noncentral F distribution.\n", + "numpy.random.RandomState.standard_gamma\n", + " Draw samples from a standard Gamma distribution.\n", + "numpy.random.Generator.negative_binomial\n", + " Draw samples from a negative binomial distribution." + ] + } + ], + "source": [ + "np.lookfor('mean value of array') " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Далее можно почитать документацию про контретную функцию.***" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[0;31mSignature:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mType:\u001b[0m _frommethod\n", + "\u001b[0;31mString form:\u001b[0m \n", + "\u001b[0;31mFile:\u001b[0m ~/miniconda3/envs/py38/lib/python3.8/site-packages/numpy/ma/core.py\n", + "\u001b[0;31mDocstring:\u001b[0m \n", + "mean(self, axis=None, dtype=None, out=None, keepdims=)\n", + "\n", + "Returns the average of the array elements along given axis.\n", + "\n", + "Masked entries are ignored, and result elements which are not\n", + "finite will be masked.\n", + "\n", + "Refer to `numpy.mean` for full documentation.\n", + "\n", + "See Also\n", + "--------\n", + "numpy.ndarray.mean : corresponding function for ndarrays\n", + "numpy.mean : Equivalent function\n", + "numpy.ma.average : Weighted average.\n", + "\n", + "Examples\n", + "--------\n", + ">>> a = np.ma.array([1,2,3], mask=[False, False, True])\n", + ">>> a\n", + "masked_array(data=[1, 2, --],\n", + " mask=[False, False, True],\n", + " fill_value=999999)\n", + ">>> a.mean()\n", + "1.5\n", + "\u001b[0;31mClass docstring:\u001b[0m\n", + "Define functions from existing MaskedArray methods.\n", + "\n", + "Parameters\n", + "----------\n", + "methodname : str\n", + " Name of the method to transform." + ] + } + ], + "source": [ + "?np.ma.mean" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "np.concatenate\n", + "np.conj\n", + "np.conjugate\n", + "np.convolve" + ] + } + ], + "source": [ + "np.con*?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Посмотрим на количественные характеристики ``ndarray``.***" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[[1 2 3 4]\n", + " [2 3 4 3]\n", + " [1 1 1 1]]\n", + "\n", + " [[1 2 3 4]\n", + " [2 3 4 3]\n", + " [1 1 1 1]]]\n" + ] + } + ], + "source": [ + "arr = np.array([[[1, 2, 3, 4],\n", + " [2, 3, 4, 3],\n", + " [1, 1, 1, 1]], \n", + " [[1, 2, 3, 4],\n", + " [2, 3, 4, 3],\n", + " [1, 1, 1, 1]]])\n", + "print(arr)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "len: 2 -- количество элементов по первой оси. \n", + "size: 24 -- всего элементов в матрице. \n", + "ndim: 3 -- размерность матрицы. \n", + "shape: (2, 3, 4) -- количество элементов по каждой оси.\n" + ] + } + ], + "source": [ + "print(\"len:\", len(arr), \"-- количество элементов по первой оси.\",\n", + " \"\\nsize:\", arr.size, \"-- всего элементов в матрице.\",\n", + " \"\\nndim:\", arr.ndim, \"-- размерность матрицы.\",\n", + " \"\\nshape:\", arr.shape, \"-- количество элементов по каждой оси.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Индексы.***" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1, 2)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.array([1, 2, 3, 4])\n", + "a[0], a[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Последний элемент.***" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Можем изменять объекты массива.***" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1, 2, -1, 4])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[2] = -1\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***``ndarray`` можно использовать в циклах. Но при этом теряется главное преимущество `Numpy` -- быстродействие. Всегда, когда это возможно, лучше использовать операции над массивами как едиными целыми.***" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "2\n", + "-1\n", + "4\n" + ] + } + ], + "source": [ + "for i in a:\n", + " print(i)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Задача 1:** Создать numpy-массив, состоящий из первых четырех простых чисел, выведите его тип и размер:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2 3 5 7]\n", + "int64\n", + "\n", + "(4,)\n", + "32\n" + ] + } + ], + "source": [ + "# решение\n", + "\n", + "arr = np.array([2, 3, 5, 7])\n", + "print(arr)\n", + "print(arr.dtype)\n", + "print(type(arr))\n", + "print(arr.shape)\n", + "print(arr.nbytes)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Создание массивов" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 0 0 0 0 0 0]\n", + "[1. 1. 1. 1. 1. 1. 1.]\n" + ] + } + ], + "source": [ + "a = np.zeros(7, dtype=np.int16) # массив из нулей\n", + "b = np.ones(7, dtype=np.float64) # массив из единиц\n", + "print(a)\n", + "print(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Часто нужно создать нулевой массив такой же как другой.***" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0., 0., 0., 0., 0., 0., 0.])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.zeros(7, dtype=np.float64)\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.zeros_like(b, dtype=np.int64)\n", + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Функция `np.arange` подобна `range`. Аргументы могут быть с плавающей точкой. Следует избегать ситуаций, когда (конец-начало)/шаг -- целое число, потому что в этом случае включение последнего элемента зависит от ошибок округления. Лучше, чтобы конец диапазона был где-то посредине шага.***" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1 5 9 13]\n", + "[ 5. 5.2 5.4 5.6 5.8 6. 6.2 6.4 6.6 6.8 7. 7.2 7.4 7.6\n", + " 7.8 8. 8.2 8.4 8.6 8.8 9. 9.2 9.4 9.6 9.8 10. 10.2 10.4\n", + " 10.6 10.8 11. 11.2 11.4 11.6 11.8 12. 12.2 12.4 12.6 12.8 13. 13.2\n", + " 13.4 13.6 13.8 14. 14.2 14.4 14.6 14.8 15. 15.2 15.4 15.6 15.8 16.\n", + " 16.2 16.4 16.6 16.8 17. 17.2 17.4 17.6 17.8 18. 18.2 18.4 18.6 18.8\n", + " 19. 19.2 19.4 19.6 19.8 20. 20.2 20.4 20.6 20.8]\n", + "[1 2 3 4 5 6 7 8 9]\n", + "[0 1 2 3 4]\n" + ] + } + ], + "source": [ + "a = np.arange(1, 16, 4)\n", + "b = np.arange(5., 21, 0.2)\n", + "c = np.arange(1, 10)\n", + "d = np.arange(5)\n", + "print(a)\n", + "print(b)\n", + "print(c)\n", + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Последовательности чисел с постоянным шагом можно также создавать функцией `linspace`. Начало и конец диапазона включаются; последний аргумент -- число точек.***" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 1.73684211 2.47368421 3.21052632 3.94736842 4.68421053\n", + " 5.42105263 6.15789474 6.89473684 7.63157895 8.36842105 9.10526316\n", + " 9.84210526 10.57894737 11.31578947 12.05263158 12.78947368 13.52631579\n", + " 14.26315789 15. ]\n", + "[ 5. 5.77777778 6.55555556 7.33333333 8.11111111 8.88888889\n", + " 9.66666667 10.44444444 11.22222222 12. ]\n" + ] + } + ], + "source": [ + "a = np.linspace(1, 15, 20)\n", + "b = np.linspace(5, 12, 10)\n", + "print(a)\n", + "print(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Задача 2:** создать и вывести последовательность чисел от 10 до 32 с постоянным шагом, длина последовательности -- 12. Чему равен шаг?" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32.]\n", + "2.0\n" + ] + } + ], + "source": [ + "# решение\n", + "\n", + "a = np.linspace(10, 32, 12)\n", + "print(a)\n", + "print(a[1] - a[0])\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Последовательность чисел с постоянным шагом по логарифмической шкале от $10^0$ до $10^3$.***" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 1.87381742 3.51119173 6.57933225 12.32846739\n", + " 23.101297 43.28761281 81.11308308 151.9911083 284.80358684\n", + " 533.66992312 1000. ]\n" + ] + } + ], + "source": [ + "b = np.logspace(0, 3, 12)\n", + "print(b)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Операции над одномерными массивами." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Все арифметические операции производятся поэлементно.***" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32.]\n", + "[ 1. 1.87381742 3.51119173 6.57933225 12.32846739\n", + " 23.101297 43.28761281 81.11308308 151.9911083 284.80358684\n", + " 533.66992312 1000. ]\n" + ] + } + ], + "source": [ + "print(a)\n", + "print(b)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.]\n", + "[ 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55.]\n", + "[ -6. -24. -54. -96. -150. -216. -294. -384. -486. -600. -726.]\n", + "[-1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5]\n" + ] + } + ], + "source": [ + "a = np.linspace(3, 33, 11)\n", + "b = np.linspace(-2, -22, 11)\n", + "print(a + b)\n", + "print(a - b)\n", + "print(a * b)\n", + "print(a / b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Один из операндов может быть скаляром, а не массивом.***" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 15. 30. 45. 60. 75. 90. 105. 120. 135. 150. 165.]\n", + "[ 8. 6. 4. 2. 0. -2. -4. -6. -8. -10. -12.]\n" + ] + } + ], + "source": [ + "print(5*a)\n", + "print(10 + b)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 4. 9. 16. 25. 36. 49. 64. 81. 100. 121.]\n", + "[2.000e+00 4.000e+00 8.000e+00 1.600e+01 3.200e+01 6.400e+01 1.280e+02\n", + " 2.560e+02 5.120e+02 1.024e+03 2.048e+03]\n" + ] + } + ], + "source": [ + "print((a + b) ** 2)\n", + "print(2 ** (a + b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Если типы элементов разные, то идет каст к большему.***" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 3. 7. 11. 15. 19. 23. 27. 31. 35. 39. 43.]\n", + "\n" + ] + } + ], + "source": [ + "print(a + np.arange(11, dtype='int16'))\n", + "print(type(a[0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***В ``Numpy`` есть элементарные функции, которые тоже применяются к массивам поэлементно. Они называются универсальными функциями (``ufunc``).***" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.ufunc" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(np.cos)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.9899925 , 0.96017029, -0.91113026, 0.84385396, -0.75968791,\n", + " 0.66031671, -0.54772926, 0.42417901, -0.29213881, 0.15425145,\n", + " -0.01327675])" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.cos(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_2722/4200754868.py:1: RuntimeWarning: invalid value encountered in log\n", + " np.log(b)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.log(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Логические операции также производятся поэлементно.***" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ True True True True True True True True True True True]\n", + "[False False False False False False False False False False False]\n", + "[False False False True True True True True True True True]\n" + ] + } + ], + "source": [ + "print(a > b)\n", + "print(a == b)\n", + "print(a >= 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Кванторы ``всеобщности`` и ``существования``.***\n", + "$$\\forall$$\n", + "$$\\exists$$" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "c = np.arange(0., 20)\n", + "print(type(c[0]))" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(True, False)" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.any(c == 0.), np.all(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Inplace операции.***" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.7568025 0.2431975 1.2431975 2.2431975 3.2431975 4.2431975\n", + " 5.2431975 6.2431975 7.2431975 8.2431975 9.2431975 10.2431975\n", + " 11.2431975 12.2431975 13.2431975 14.2431975 15.2431975 16.2431975\n", + " 17.2431975 18.2431975]\n" + ] + } + ], + "source": [ + "c += np.sin(4)\n", + "print(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Inplace операции возможны только для операндов одинакового типа.***" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-1.51360499 0.48639501 2.48639501 4.48639501 6.48639501 8.48639501\n", + " 10.48639501 12.48639501 14.48639501 16.48639501 18.48639501 20.48639501\n", + " 22.48639501 24.48639501 26.48639501 28.48639501 30.48639501 32.48639501\n", + " 34.48639501 36.48639501]\n" + ] + } + ], + "source": [ + "c *= 2\n", + "print(c)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.51360499 1.2431975 1.82879834 2.12159875 2.297279 2.41439917\n", + " 2.49805643 2.56079938 2.60959945 2.6486395 2.68058136 2.70719958\n", + " 2.72972269 2.74902821 2.76575967 2.78039969 2.79331735 2.80479972\n", + " 2.81507342 2.82431975]\n" + ] + } + ], + "source": [ + "b = np.arange(1., 21, 1)\n", + "\n", + "d = (b + c)\n", + "d /= b\n", + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***При делении ``ndarray`` на нули, исключения не бросается.***" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. nan inf -inf]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_2722/3088186758.py:1: RuntimeWarning: divide by zero encountered in divide\n", + " print(np.array([0.0, 0.0, 1.0, -1.0]) / np.array([1.0, 0.0, 0.0, 0.0]))\n", + "/tmp/ipykernel_2722/3088186758.py:1: RuntimeWarning: invalid value encountered in divide\n", + " print(np.array([0.0, 0.0, 1.0, -1.0]) / np.array([1.0, 0.0, 0.0, 0.0]))\n" + ] + } + ], + "source": [ + "print(np.array([0.0, 0.0, 1.0, -1.0]) / np.array([1.0, 0.0, 0.0, 0.0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Могут понадобится константы.***" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.718281828459045 3.141592653589793\n" + ] + } + ], + "source": [ + "print(np.e, np.pi)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.\n", + " 19. 20.]\n", + "[ 1. 3. 6. 10. 15. 21. 28. 36. 45. 55. 66. 78. 91. 105.\n", + " 120. 136. 153. 171. 190. 210.]\n" + ] + } + ], + "source": [ + "print(b)\n", + "print(b.cumsum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Посмотрим на сортировку numpy-массивов.***" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.array([1, 5, 6, 10, -2, 0, 18])" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 0 1 5 6 10 18]\n", + "[ 1 5 6 10 -2 0 18]\n" + ] + } + ], + "source": [ + "print(np.sort(a))\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Теперь попробуем как метод.***" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 0 1 5 6 10 18]\n" + ] + } + ], + "source": [ + "a.sort()\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = np.ones(5)\n", + "b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Объединим массивы.***" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-2., 0., 1., 5., 6., 10., 18., 1., 1., 1., 1., 1., 5.,\n", + " 5., 5., 5., 5.])" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.hstack((a, b, 5*b))\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[0;31mSignature:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhsplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindices_or_sections\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mDocstring:\u001b[0m\n", + "Split an array into multiple sub-arrays horizontally (column-wise).\n", + "\n", + "Please refer to the `split` documentation. `hsplit` is equivalent\n", + "to `split` with ``axis=1``, the array is always split along the second\n", + "axis except for 1-D arrays, where it is split at ``axis=0``.\n", + "\n", + "See Also\n", + "--------\n", + "split : Split an array into multiple sub-arrays of equal size.\n", + "\n", + "Examples\n", + "--------\n", + ">>> x = np.arange(16.0).reshape(4, 4)\n", + ">>> x\n", + "array([[ 0., 1., 2., 3.],\n", + " [ 4., 5., 6., 7.],\n", + " [ 8., 9., 10., 11.],\n", + " [12., 13., 14., 15.]])\n", + ">>> np.hsplit(x, 2)\n", + "[array([[ 0., 1.],\n", + " [ 4., 5.],\n", + " [ 8., 9.],\n", + " [12., 13.]]),\n", + " array([[ 2., 3.],\n", + " [ 6., 7.],\n", + " [10., 11.],\n", + " [14., 15.]])]\n", + ">>> np.hsplit(x, np.array([3, 6]))\n", + "[array([[ 0., 1., 2.],\n", + " [ 4., 5., 6.],\n", + " [ 8., 9., 10.],\n", + " [12., 13., 14.]]),\n", + " array([[ 3.],\n", + " [ 7.],\n", + " [11.],\n", + " [15.]]),\n", + " array([], shape=(4, 0), dtype=float64)]\n", + "\n", + "With a higher dimensional array the split is still along the second axis.\n", + "\n", + ">>> x = np.arange(8.0).reshape(2, 2, 2)\n", + ">>> x\n", + "array([[[0., 1.],\n", + " [2., 3.]],\n", + " [[4., 5.],\n", + " [6., 7.]]])\n", + ">>> np.hsplit(x, 2)\n", + "[array([[[0., 1.]],\n", + " [[4., 5.]]]),\n", + " array([[[2., 3.]],\n", + " [[6., 7.]]])]\n", + "\n", + "With a 1-D array, the split is along axis 0.\n", + "\n", + ">>> x = np.array([0, 1, 2, 3, 4, 5])\n", + ">>> np.hsplit(x, 2)\n", + "[array([0, 1, 2]), array([3, 4, 5])]\n", + "\u001b[0;31mFile:\u001b[0m ~/miniconda3/envs/py38/lib/python3.8/site-packages/numpy/lib/shape_base.py\n", + "\u001b[0;31mType:\u001b[0m function" + ] + } + ], + "source": [ + "?np.hsplit\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Расщепление массива.***" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 0 1 5 6 10 18]\n", + "[-2 0 1]\n", + "[5 6]\n", + "[10]\n", + "[18]\n" + ] + } + ], + "source": [ + "x1, x2, x3, x4 = np.hsplit(a, [3, 5, 6])\n", + "print(a)\n", + "print(x1)\n", + "print(x2)\n", + "print(x3)\n", + "print(x4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Функции ``append`` ``delete`` ``insert`` не Inplace функции.***" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 5 10 18]\n", + "[-2 0 1 5 6 10 18]\n" + ] + } + ], + "source": [ + "print(np.delete(a, [2, 4, 1]))\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-2, 0, -1, -1, 1, 5, 6, 10, 18])" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.insert(a, 2, [-1, -1])" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-2. , 0. , 1. , 5. , 6. , 10. , 18. , 2.2, 2.1])" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.append(a, [2.2, 2.1])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cрезы" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Массив в обратном порядоке.***" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([18, 10, 6, 5, 1, 0, -2])" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[::-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Диапазон индексов. Создаётся новый заголовок массива, указывающий на те же данные. Изменения, сделанные через такой массив, видны и в исходном массиве.***" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 0 1 5 6 10 18]\n" + ] + } + ], + "source": [ + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 5, 6])" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[2:5]" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ -2 -1000 1 5 6 10 18]\n" + ] + } + ], + "source": [ + "b = a[0:6] # копия не создается\n", + "b[1] = -1000\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Диапозоны с шагами.***" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 1]\n", + "[-2 0 1 5 0 10 18]\n" + ] + } + ], + "source": [ + "b = a[0:4:2]\n", + "print(b)\n", + "\n", + "# подмассиву можно присваивать скаляр\n", + "a[1:6:3] = 0\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Чтобы скопировать и данные массива, нужно использовать метод ``copy``.***" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2 0 -4 5 0 10 18]\n", + "[-2 0 1 5 0 10 18]\n" + ] + } + ], + "source": [ + "b = a.copy()\n", + "b[2] = -4\n", + "print(b)\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[10 5 0]\n" + ] + } + ], + "source": [ + "print(a[[5,3,1]]) # массив индексов" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Задание 3:** \n", + "- Создать массив чисел от $-4\\pi$ до $4\\pi $, количество точек 100\n", + "- Посчитать сумму поэлементных квадратов синуса и косинуса для данного массива \n", + "- С помощью ``np.all`` проверить, что все элементы равны единице." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1.]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# решение\n", + "\n", + "x = np.linspace(-4*np.pi, 4*np.pi, 100)\n", + "print(np.sin(x)**2 + np.cos(x)**2)\n", + "np.all((np.sin(x)**2 + np.cos(x)**2).round() == 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Матрицы" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Определение**: *Матрицей размера $m \\times n$* нахывается прямоугольная таблица с числами из $m$ строк и $n$ столбцов: \n", + "\n", + "$$\\begin{pmatrix}x_{11}, x_{12}, ... , x_{1n}\\\\x_{21}, x_{22}, ... , x_{2n}\\\\...\\ \\ \\ ...\\ \\ \\ ...\\\\x_{m1}, x_{m2}, ... , x_{mn}\\\\\\end{pmatrix}$$" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Определение**: Квадратная матрица называется *(не)вырожденой*, если ее строки линейно (не)зависимы\n", + "$$\\begin{pmatrix}1\\ \\ \\ \\ \\ \\ 3\\ \\ \\ \\ \\ \\ -1\\\\0\\ \\ \\ \\ \\ \\ -2\\ \\ \\ \\ \\ \\ 0\\\\2\\ \\ \\ \\ \\ \\ 4\\ \\ \\ \\ \\ \\ -2 \\end{pmatrix}$$" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Утверждение**: Строки квадратной матрицы ЛНЗ тогда и только тогда, когда её столбцы ЛНЗ" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Определение**: *Строчным рангом* матрицы $A$ называется размер наибольшего подмножества линейно независимых строк $A$. Аналогчно определяется *столбцовый* ранг.\n", + "\n", + "**Пример**: \n", + "$$\\begin{pmatrix}1\\ \\ \\ \\ \\ \\ 0\\ \\ \\ \\ \\ \\ 0\\ \\ \\ \\ \\ \\ 5\\ \\ \\ \\ \\ \\ -2\\\\0\\ \\ \\ \\ \\ \\ 1\\ \\ \\ \\ \\ \\ 0\\ \\ \\ \\ \\ \\ 0\\ \\ \\ \\ \\ \\ -1\\\\0\\ \\ \\ \\ \\ \\ \\ 0\\ \\ \\ \\ \\ \\ \\ 1\\ \\ \\ \\ \\ \\ \\ 2\\ \\ \\ \\ \\ \\ \\ 3\\\\ \\end{pmatrix} \\\\ Строчный\\ и\\ столбцовый\\ ранг\\ равны\\ 3$$\n", + "\n", + "**Удтверждение**: Строчный и столбцовый ранг равны." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Умножение матрицы на вектор\n", + "\n", + "![](imgs/sem1/sem1_9.png)\n", + "\n", + "Пример с системой линейных уравнений, ее можно очень удобно записать в матричном виде:\n", + "\n", + "![](imgs/sem1/sem1_10.png)\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Линейная регрессия в матричном виде\n", + "- Ищем закономерность в *линейном* виде $$y_k = w_1x_{k1} + w_2x_{k2} + ... + w_nx_{kn}$$\n", + "- В матричном виде уравнение записывается так: \n", + "$$Xw = y$$\n", + "$$X = \\begin{pmatrix}x_{11}, x_{12}, ... , x_{1n}\\\\x_{21}, x_{22}, ... , x_{2n}\\\\...\\ \\ \\ ...\\ \\ \\ ...\\\\x_{m1}, x_{m2}, ... , x_{mn}\\\\\\end{pmatrix}, w = \\begin{pmatrix}w_1\\\\w_2\\\\ ... \\\\ w_{n} \\end{pmatrix}, y = \\begin{pmatrix}w_1\\\\y_2\\\\ ... \\\\ y_{n} \\end{pmatrix}$$\n", + "\n", + "Любой алгоритм машинного обучения очень чувствителен к количеству объектов ($m$) и количеству признаков ($n$) в обучающей выборке:\n", + "\n", + "- Если $m = n$, то решение (скорее всего) единственное.\n", + "- Если $m > n$, то решение (скорее всего) нет.\n", + "- Если $m < n$, то решение (скорее всего) бесконечно много." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Матрицы в NumPy" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 2]\n", + " [3 4]]\n" + ] + } + ], + "source": [ + "a = np.array([[1, 2], [3, 4]])\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2, (2, 2), 2, 4)" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.ndim, a.shape, len(a), a.size" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Обращение по индексу.***" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(4, 4)" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[1][1], a[1,1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Атрибуту ``shape`` можно присвоить новое значение -- кортеж размеров по всем координатам. Получится новый заголовок массива; его данные не изменятся.***" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3 4 5 6 7 8 9]\n", + " [10 11 12 13 14 15 16 17 18 19]]\n" + ] + } + ], + "source": [ + "b = np.arange(0, 20)\n", + "b.shape = (2, 10)\n", + "print(b)" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]]\n" + ] + } + ], + "source": [ + "print(b.reshape((1,20))) # то же самое, что и shape" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]\n" + ] + } + ], + "source": [ + "print(b.ravel()) # стягивание в одномерный массив" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 1. 1.]\n", + " [1. 1. 1.]\n", + " [1. 1. 1.]]\n" + ] + } + ], + "source": [ + "a = np.ones((3, 3)) # подать tuple\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. 0. 0.]\n", + " [0. 0. 0. 0.]\n", + " [0. 0. 0. 0.]]\n" + ] + } + ], + "source": [ + "b = np.zeros((3, 4))\n", + "print(b)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Операции над матрицами\n", + "\n", + "- Сложение матриц\n", + "- Умножение матриц\n", + "- Транспонирование и обратная матрица\n", + "- Определитель матрицы" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Сложение матриц\n", + "- выполняется поэлементно\n", + "- Можно применять только к матрицам одинакового размера\n", + "\n", + "![](imgs/sem1/sem1_11.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[2., 2., 2.],\n", + " [2., 2., 2.],\n", + " [2., 2., 2.]])" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.ones((3, 3)) # подать tuple\n", + "b = np.ones((3, 3)) # подать tuple\n", + "\n", + "\n", + "a + b" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Умножение матриц\n", + "\n", + "- Можно применять только к матрицам, в которых количество столбцов одной матрицы совпадает с количеством строк второй.\n", + "\n", + "![](imgs/sem1/sem1_12.png)\n", + "\n", + "Произведение матриц встречается, когда совокупность векторов умножается на матрицу (например при подаче в нейронную сеть батча данных)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Свойства произведения матриц\n", + "- Ассоциативность: $A(BC) = (AB)C$\n", + "- Дистрибутивность: $A(B + C) = AB + АC$\n", + "- Отсутствие коммутативности: не всегда $AB = BA$\n", + "- Существование нейтрального элемента $E$ (Единичная матрица): $$\\begin{pmatrix}1\\ 0\\ ...\\ 0\\\\0\\ 1\\ ...\\ 0\\\\.........\\\\0\\ 0\\ ...\\ 1\\\\\\end{pmatrix}$$ $$AE = EA = A$$\n", + "- Для квадратных матриц: если $A$ вырождена, то $AB$ также вырождена" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0., 0., 0., 0.],\n", + " [0., 1., 0., 0., 0.],\n", + " [0., 0., 1., 0., 0.],\n", + " [0., 0., 0., 1., 0.],\n", + " [0., 0., 0., 0., 1.]])" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.eye(5)" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[5. 5. 5. 5. 5.]\n", + " [5. 5. 5. 5. 5.]\n", + " [5. 5. 5. 5. 5.]\n", + " [5. 5. 5. 5. 5.]\n", + " [5. 5. 5. 5. 5.]] \n", + "\n", + "[[2. 1. 1. 1. 1.]\n", + " [1. 2. 1. 1. 1.]\n", + " [1. 1. 2. 1. 1.]\n", + " [1. 1. 1. 2. 1.]\n", + " [1. 1. 1. 1. 2.]]\n" + ] + } + ], + "source": [ + "a = 5*np.ones((5, 5))\n", + "b = np.eye(5) + 1\n", + "print(a, '\\n')\n", + "print(b)" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[10. 5. 5. 5. 5.]\n", + " [ 5. 10. 5. 5. 5.]\n", + " [ 5. 5. 10. 5. 5.]\n", + " [ 5. 5. 5. 10. 5.]\n", + " [ 5. 5. 5. 5. 10.]] \n", + "\n", + "[[30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]] \n", + "\n", + "[[30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]\n", + " [30. 30. 30. 30. 30.]]\n" + ] + } + ], + "source": [ + "print(a * b, '\\n') # поэлементное умножение\n", + "print(a @ b, '\\n') # матричное умножение\n", + "print(a.dot(b)) " + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n" + ] + } + ], + "source": [ + "c = np.eye(3)\n", + "print(c)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[['1' '' '' '']\n", + " ['' '2' '' '']\n", + " ['' '' '3' '']\n", + " ['' '' '' 'a']]\n" + ] + } + ], + "source": [ + "d = np.diag([1, 2, 3, 'a'])\n", + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Задание 4:***\n", + "Создать квадратную матрицу размера 8, на главной диаг. арифметическая прогрессия с шагом 3 (начиная с 3), а на побочной -1, остальные элементы 0." + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 3. 0. 0. 0. 0. 0. 0. -1.]\n", + " [ 0. 6. 0. 0. 0. 0. -1. 0.]\n", + " [ 0. 0. 9. 0. 0. -1. 0. 0.]\n", + " [ 0. 0. 0. 12. -1. 0. 0. 0.]\n", + " [ 0. 0. 0. -1. 15. 0. 0. 0.]\n", + " [ 0. 0. -1. 0. 0. 18. 0. 0.]\n", + " [ 0. -1. 0. 0. 0. 0. 21. 0.]\n", + " [-1. 0. 0. 0. 0. 0. 0. 24.]]\n" + ] + } + ], + "source": [ + "# решение\n", + "# print(-1*np.eye(8)[::-1][::-1])\n", + "a = -1*np.eye(8)[::-1] + np.diag(np.arange(3, 27, 3))\n", + "print(a)\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Обратная матрица\n", + "**Определение**: Пусть $A$ - квадратная матрица. Если существует такая матрица $A^{-1}$, что $AA^{-1} = A^{-1}A = E$, то матрица $A^{-1}$ называется *обратной матрицей* к $A$. Матрица $A$ в таком случае называется *обратимой*.\n", + "\n", + "**Утверждение**: Пусть $A$ - квадратная матрица. Если строки (или столбцы) $А$ линейно независимы (т.е. $A$ невырождена), то обратная матрица существует и единствена.\n", + "\n", + "##### Обратная матрица при решении СЛУ\n", + "\n", + "Есть СЛУ: $$Ax = b$$\n", + "\n", + "Если существует $A^{-1}$, то у системы есть единственное решение: $$x = A^{-1}b$$" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Транспонированная матрица\n", + "\n", + "Транспонирование - операция отражения матрицы относительно главной диагонали. Обозначается как $A^{\\top}$\n", + "\n", + "Вектор-столбец при транспонировании переходит в вектор-строку. Поэтому скалярное произведение можно записать так: $$ = x^{\\top}y$$" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1 2]\n", + " [4 5 6]]\n", + "\n", + "[[0 4]\n", + " [1 5]\n", + " [2 6]]\n" + ] + } + ], + "source": [ + "a = np.array([[0, 1, 2], [4, 5, 6]])\n", + "b = a.transpose()\n", + "print(a)\n", + "print()\n", + "print(b)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Определитель матрицы\n", + "\n", + "Определитель квадратной матрицы - это ее числовая характеристика.\n", + "\n", + "- $\\mid a\\mid = a$\n", + "- $\\mid\\begin{pmatrix}a\\ b\\\\c\\ d \\end{pmatrix}\\mid = ad - bc$\n", + "\n", + "![](imgs/sem1/sem1_13.png)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Свойства определителя\n", + "- $\\mid AB \\mid = \\mid A \\mid \\mid B \\mid$ \n", + "- $\\mid A \\mid = 0$ тогда и только тогда, когда $A$ вырожденная" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Вычисление обратной матрицы с помощью определителей\n", + "\n", + "![](imgs/sem1/sem1_14.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2 1]\n", + " [2 3]]\n" + ] + } + ], + "source": [ + "a = np.array([[2, 1], [2, 3]])\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.0" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.det(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Нахождениия обратной.***" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.75 -0.25]\n", + " [-0.5 0.5 ]]\n" + ] + } + ], + "source": [ + "b = np.linalg.inv(a)\n", + "print(b)" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 0.]\n", + " [0. 1.]]\n", + "[[1. 0.]\n", + " [0. 1.]]\n" + ] + } + ], + "source": [ + "print(a.dot(b))\n", + "print(b.dot(a))" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2 1]\n", + " [6 3]]\n", + "0.0\n" + ] + } + ], + "source": [ + "c = np.array([[2, 1], [6, 3]])\n", + "print(c)\n", + "print(np.linalg.det(c))" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "ename": "LinAlgError", + "evalue": "Singular matrix", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mLinAlgError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[83], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m np\u001b[39m.\u001b[39;49mlinalg\u001b[39m.\u001b[39;49minv(c)\n", + "File \u001b[0;32m<__array_function__ internals>:200\u001b[0m, in \u001b[0;36minv\u001b[0;34m(*args, **kwargs)\u001b[0m\n", + "File \u001b[0;32m~/miniconda3/envs/py38/lib/python3.8/site-packages/numpy/linalg/linalg.py:538\u001b[0m, in \u001b[0;36minv\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m 536\u001b[0m signature \u001b[39m=\u001b[39m \u001b[39m'\u001b[39m\u001b[39mD->D\u001b[39m\u001b[39m'\u001b[39m \u001b[39mif\u001b[39;00m isComplexType(t) \u001b[39melse\u001b[39;00m \u001b[39m'\u001b[39m\u001b[39md->d\u001b[39m\u001b[39m'\u001b[39m\n\u001b[1;32m 537\u001b[0m extobj \u001b[39m=\u001b[39m get_linalg_error_extobj(_raise_linalgerror_singular)\n\u001b[0;32m--> 538\u001b[0m ainv \u001b[39m=\u001b[39m _umath_linalg\u001b[39m.\u001b[39;49minv(a, signature\u001b[39m=\u001b[39;49msignature, extobj\u001b[39m=\u001b[39;49mextobj)\n\u001b[1;32m 539\u001b[0m \u001b[39mreturn\u001b[39;00m wrap(ainv\u001b[39m.\u001b[39mastype(result_t, copy\u001b[39m=\u001b[39m\u001b[39mFalse\u001b[39;00m))\n", + "File \u001b[0;32m~/miniconda3/envs/py38/lib/python3.8/site-packages/numpy/linalg/linalg.py:89\u001b[0m, in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m 88\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m_raise_linalgerror_singular\u001b[39m(err, flag):\n\u001b[0;32m---> 89\u001b[0m \u001b[39mraise\u001b[39;00m LinAlgError(\u001b[39m\"\u001b[39m\u001b[39mSingular matrix\u001b[39m\u001b[39m\"\u001b[39m)\n", + "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix" + ] + } + ], + "source": [ + "np.linalg.inv(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Решение НЛУ.***\n", + "$$ A \\cdot x = v $$" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 6.25 -7.5 ]\n", + "[ 6.25 -7.5 ]\n" + ] + } + ], + "source": [ + "v = np.array([5, -10])\n", + "print(np.linalg.solve(a, v))\n", + "print(b.dot(v))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Найдем собственные вектора матрицы A.***\n", + "$$ A \\cdot x = \\lambda \\cdot x $$" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 4.]\n", + "[[-0.70710678 -0.4472136 ]\n", + " [ 0.70710678 -0.89442719]]\n" + ] + } + ], + "source": [ + "l, u = np.linalg.eig(a)\n", + "print(l)\n", + "print(u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Собственные значения матриц A и A.T совпадают.***" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 4.]\n", + "[[-0.89442719 -0.70710678]\n", + " [ 0.4472136 -0.70710678]]\n" + ] + } + ], + "source": [ + "l, u = np.linalg.eig(a.T)\n", + "print(l)\n", + "print(u)" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 1. 1.]\n", + "[[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n" + ] + } + ], + "source": [ + "l, u = np.linalg.eig(np.eye(3))\n", + "print(l)\n", + "print(u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Еще чутка numpy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Маски.***" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]\n", + "[ True False False True False False True False False True False False\n", + " True False False True False False True False]\n", + "[ 0 3 6 9 12 15 18]\n" + ] + } + ], + "source": [ + "a = np.arange(20)\n", + "print(a)\n", + "print(a % 3 == 0)\n", + "print(a[a % 3 == 0])" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[10 0 0 0 0 0 0 0 0 0]\n", + " [ 0 11 0 0 0 0 0 0 0 0]\n", + " [ 0 0 12 0 0 0 0 0 0 0]\n", + " [ 0 0 0 13 0 0 0 0 0 0]\n", + " [ 0 0 0 0 14 0 0 0 0 0]\n", + " [ 0 0 0 0 0 15 0 0 0 0]\n", + " [ 0 0 0 0 0 0 16 0 0 0]\n", + " [ 0 0 0 0 0 0 0 17 0 0]\n", + " [ 0 0 0 0 0 0 0 0 18 0]\n", + " [ 0 0 0 0 0 0 0 0 0 19]]\n", + "145\n" + ] + } + ], + "source": [ + "b = np.diag(a[a >= 10])\n", + "print(b)\n", + "print(np.trace(b))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Шлифонем тестами на производительность" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***Производительность.***" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Без Numpy:" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "49999995000000\n", + "CPU times: user 469 ms, sys: 0 ns, total: 469 ms\n", + "Wall time: 503 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "def summ(a):\n", + " ans = 0\n", + " for i in a:\n", + " ans += i\n", + " return ans\n", + "\n", + "arr = range(10**7)\n", + "\n", + "print(summ(arr))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "C Numpy:" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "49999995000000\n", + "CPU times: user 15.6 ms, sys: 109 ms, total: 125 ms\n", + "Wall time: 108 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "sum_value = np.sum(np.arange(10**7))\n", + "print(sum_value)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Без Numpy:" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.12 s, sys: 578 ms, total: 1.7 s\n", + "Wall time: 1.69 s\n" + ] + } + ], + "source": [ + "%%time\n", + "arr = []\n", + "n = 10**7\n", + "for i in range(n):\n", + " arr.append(i*5)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "С Numpy:" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 93.8 ms, sys: 109 ms, total: 203 ms\n", + "Wall time: 216 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "arr = 5*np.arange(10**7)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Лабораторная 1\n", + "\n", + "Решить 100 numpy задач, дедлайн `01.04.2023`\n", + "\n", + "https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises.ipynb" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "py38", + "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": "3.8.16" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "c0330b53543e07ef1d56d28db427de4965ae0a62dafba4360eb741e652c9c2e1" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/ml_system_design/seminars/sem3.ipynb b/ml_system_design/seminars/sem3.ipynb new file mode 100644 index 0000000..4015fec --- /dev/null +++ b/ml_system_design/seminars/sem3.ipynb @@ -0,0 +1,5343 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "Faqf8pG8itot" + }, + "source": [ + "## Линейные модели, градиентный спуск и метрики" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Линейная регрессия" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KS-4su3tladF" + }, + "source": [ + "**Линейная регрессия** — модель зависимости переменной от одной или нескольких других переменных (факторов, регрессоров, независимых переменных) с линейной функцией зависимости.\n", + "\n", + "Ниже на графике представлена линейная регрессия переменной $y$ от переменной $x$.\n", + "\n", + "Есть коэффициент наклона $a$ и есть коэффициент сдвига $b$.\n", + "\n", + "Эти значения могут изменяться как угодно." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 283 + }, + "id": "monS6MN5k2I0", + "outputId": "059b12b9-1955-47cd-9422-26735ff519e1" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "x = np.arange(-6, 6)\n", + "a = 2\n", + "b = 1\n", + "\n", + "y = a * x + b\n", + "plt.plot(x, y, label=f'y = {a}x + {b}')\n", + "plt.plot([0], [b], 'r*', markersize=10)\n", + "plt.ylabel('y');plt.xlabel('x')\n", + "plt.ylim(-10, 10);plt.xlim(-5, 5)\n", + "plt.grid()\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "CrJiBTo4bN6h" + }, + "outputs": [], + "source": [ + "def draw_ax(a, b, x, ax, ylim=5):\n", + " y = a * x + b\n", + " ax.plot(x, y, label=f'y = {a}x + {b}')\n", + " ax.plot([0], [b], 'r*', markersize=10)\n", + " \n", + " ax.plot([0, 1], [b, b], 'y', linewidth=2)\n", + " ax.plot([1, 1], [b, b+a], 'y', linewidth=2)\n", + "\n", + " ax.set_ylabel('y'); ax.set_xlabel('x')\n", + " ax.set_ylim(-ylim, ylim); ax.set_xlim(-5, 5)\n", + " ax.grid()\n", + " ax.legend(prop={'size': 10})" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XQw67GHzmD3h" + }, + "source": [ + "**Сдвиг**:\n", + "- Если у нас не будет сдвига (коэффициента $b$), то линяя будет проходить через точку (0, 0).\n", + "- Если коэффициент сдвига не равен 0, а к примеру, равен 2, то линяя будет проходить через точку (0, 2).\n", + "\n", + "**Коэффициент наклона**:\n", + "- Если у нас не будет коэффициента наклона, то линяя будет параллельна оси Ох.\n", + "- Если коэффициент наклона больше 0, то линяя идет на увеличение, при этом чем больше коэффициент, тем более наклон крутой.\n", + "- Если коэффициент наклона меньше 0, то линяя идет на уменьшение, при этом чем меньше коэффициент, тем более наклон крутой.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 606 + }, + "id": "lYWYDdbymzQ_", + "outputId": "00c3c0e7-d7a7-41d7-be62-0cb1aba977cd" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "\n", + "fig, ax = plt.subplots(2, 3, figsize=(10, 6))\n", + "x = np.arange(-6, 6)\n", + "\n", + "# 1row, 1column\n", + "a, b = 0, 0\n", + "draw_ax(a, b, x, ax[0][0])\n", + "\n", + "# 1row, 2column\n", + "a, b = 1, 0\n", + "draw_ax(a, b, x, ax[0][1])\n", + "\n", + "# 1row, 3column\n", + "a, b = 0.5, 0\n", + "draw_ax(a, b, x, ax[0][2])\n", + "\n", + "\n", + "# 2row, 1column\n", + "a, b = 0, 2\n", + "draw_ax(a, b, x, ax[1][0])\n", + "\n", + "# 2row, 2column\n", + "a, b = -1, 2\n", + "draw_ax(a, b, x, ax[1][1])\n", + "\n", + "# 2row, 3column\n", + "a, b = -0.5, -2\n", + "draw_ax(a, b, x, ax[1][2])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "usj8aWL8-84W" + }, + "source": [ + "С самим уравнением прямой разобрались, теперь давайте обучим линейную регрессию, ведь по факту она и есть прямая." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "RmcjY5KeviKG" + }, + "source": [ + "#### Получение данных" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VbgNr2MC7c9H" + }, + "source": [ + "Возьмем и сами нагенирируем себе данные и обучим на них линейную модель." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "px8DWvILiEae", + "outputId": "8f12c244-f8f3-48f6-c732-d605cde16d88" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.63007982],\n", + " [-1.06163445],\n", + " [ 0.29634711],\n", + " [ 1.40277112],\n", + " [ 0.68968231],\n", + " [-0.53662936],\n", + " [-1.11947526],\n", + " [ 1.06755846],\n", + " [ 0.1178195 ],\n", + " [ 1.54907163],\n", + " [ 1.29561858],\n", + " [-0.03107509],\n", + " [ 0.56119218],\n", + " [ 0.42105072],\n", + " [-0.4864951 ],\n", + " [ 0.08897764],\n", + " [-0.18577532],\n", + " [-0.17809318],\n", + " [-0.23725045],\n", + " [-0.88623967],\n", + " [-0.47573349],\n", + " [ 0.21734821],\n", + " [-2.65331856],\n", + " [ 0.72575222],\n", + " [-0.38053642],\n", + " [-0.48456513],\n", + " [ 1.57463407],\n", + " [-1.30554851],\n", + " [-0.17241977],\n", + " [ 0.73683739],\n", + " [-1.23234621],\n", + " [ 0.31540267],\n", + " [ 1.74945474],\n", + " [ 0.09183837],\n", + " [-0.30957664],\n", + " [-1.18575527],\n", + " [-0.68344663],\n", + " [-0.31963136],\n", + " [-0.00828463],\n", + " [-0.64257539],\n", + " [ 1.0956297 ],\n", + " [ 0.06367166],\n", + " [-0.57395456],\n", + " [ 0.07349324],\n", + " [ 0.73227135],\n", + " [-1.06560298],\n", + " [-1.68411089],\n", + " [-1.54686257],\n", + " [-0.20437532],\n", + " [-0.286073 ]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "array([ 43.6543408 , -72.68235021, 21.19644643, 107.58765071,\n", + " 69.62063217, -32.57566222, -101.61213107, 87.44514699,\n", + " 17.69898683, 131.00190463, 97.97802247, 2.70819092,\n", + " 52.42715419, 27.74476129, -31.82947365, 1.58209228,\n", + " -9.72570848, 4.57391214, -33.24586607, -74.34292886,\n", + " -22.6419015 , 15.84607909, -202.79645668, 49.05026172,\n", + " -34.9916168 , -33.95608308, 121.78273292, -123.72382672,\n", + " -1.90918067, 64.06753923, -91.73785524, 9.55252237,\n", + " 148.12427806, 22.21183346, -16.35144507, -113.95075954,\n", + " -47.70966758, -22.69082132, -1.79022499, -58.17761844,\n", + " 91.76970817, -12.7798199 , -38.1435921 , 17.48650737,\n", + " 40.52468632, -107.65815151, -134.20798669, -127.22516755,\n", + " -34.31360406, -10.90920383])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_regression\n", + "\n", + "X, y = make_regression(n_samples=50, n_features=1, n_informative=1,\n", + " noise=10, random_state=11)\n", + "\n", + "display(X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "CsCmE9Clj68Z", + "outputId": "8f142659-863a-477a-fb80-05d8a7f9b393" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "fig = plt.figure(figsize=(10, 6))\n", + "plt.scatter(X, y)\n", + "\n", + "plt.xlabel('feature')\n", + "plt.ylabel('target')\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "wuQyanTXsg4P" + }, + "source": [ + "#### Одномерная линейная регрессия" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "2MnA-YZHBxzL" + }, + "source": [ + "##### Из sklearn" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uJFYdPE1_TGm" + }, + "source": [ + "Возьмем модель `LinearRegression` из `sklearn` из модуля `linear_model`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "LsrXG6K5_aLV", + "outputId": "ffd3f68d-0274-4fdf-f013-b3838092ff39" + }, + "outputs": [ + { + "data": { + "text/html": [ + "
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "\n", + "model = LinearRegression()\n", + "model" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "s5qE3TNG_h0_" + }, + "source": [ + "И передадим в неё в метод `fit` данные, которые получили выше." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "h8weuRBk_mHJ", + "outputId": "8017dcfd-345a-48ee-a1e4-a9a1a295d86d" + }, + "outputs": [ + { + "data": { + "text/html": [ + "
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "rS1iXWQG_nz0" + }, + "source": [ + "Всё, модель обучилась, это происходит очень быстро. Обучение линейной модели заключается в поиске коэффициентов, конкретно в нашей задаче - это коэффициент сдвига и наклона." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Yp23Hf8h_5ji" + }, + "source": [ + "Можем эти коэффициента отобразить, если возьмем у модели атрибут `coef_` и `intercept_`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "8RoiC6eN_-8Z", + "outputId": "3885a9b0-3b4e-4172-da10-bad49e8772c5" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([80.41862354]), 0.18171887542100862)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.coef_, model.intercept_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pFDck5gNBHG6" + }, + "source": [ + "Вот и получили два коэффициента, осталось их подставить в уравнение прямой и будет готовая линейная модель." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "id": "UFJn6GsFBaD7" + }, + "outputs": [], + "source": [ + "model_a = model.coef_[0]\n", + "model_b = model.intercept_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "NzfeXeeJHkMe" + }, + "source": [ + "Данная прямая наилучшим образом прошла вдоль точек из обучающей выборки." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "RuEUmXzTBPDE", + "outputId": "9b8ca55c-cfae-474e-f08a-c07166020dc5" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(10, 6))\n", + "\n", + "x = np.arange(-3, 3)\n", + "model_y_sk = model_a * x + model_b\n", + "\n", + "plt.plot(x, model_y_sk, linewidth=2, c='r', label=f'linear_model = {model_a:.2f}x + {model_b:.2f}')\n", + "plt.scatter(X, y) \n", + "plt.plot([0, 1], [model_b, model_b], 'y', linewidth=3)\n", + "plt.plot([1, 1], [model_b, model_b+model_a], 'y', linewidth=3)\n", + "plt.grid()\n", + "plt.xlabel('feature')\n", + "plt.ylabel('target')\n", + "plt.legend(prop={'size': 16})\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "0bPamEKfa5rK" + }, + "source": [ + "Чтобы теперь сделать предсказания этой моделью достаточно вызвать метод `predict` и передать в него данные." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "86a7D1DLbIzm", + "outputId": "225a5377-a197-42eb-8290-b8268c33d056" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([[0.63007982]]), array([50.85187092]))" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pred = model.predict(X[:1])\n", + "\n", + "X[:1], pred" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WPgV0jDvbTci" + }, + "source": [ + "Или же можем можем сделать точно такое же предсказание, если возьмем коэффициент наклона и умножим на значение признака и прибавим к этому коэффициент сдвига. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "ssT9MavubmJZ", + "outputId": "c2a0116a-752d-4dc9-8318-c0ba4b87213d" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[50.85187092]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model_a * X[:1] + model_b" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LyRlTyGBICT6" + }, + "source": [ + "А что значит это \"наилучшим образом вдоль точек из обучающей выборки\"? Как подсчитался этот наилучший образ?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3Fon3qOWIS7P" + }, + "source": [ + "Чем построенная линия ниже, хуже первой?" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "8mGFavM-IXUB", + "outputId": "e92cd78b-486c-468f-a127-421c2b2208fe" + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(10, 6))\n", + "\n", + "x = np.arange(-3, 3)\n", + "a, b = 50, 0\n", + "model_y = a * x + b\n", + "\n", + "plt.plot(x, model_y, linewidth=2, c='r', label=f'linear_model = {a:.2f}x + {b:.2f}')\n", + "plt.scatter(X, y) \n", + "plt.plot([0, 1], [b, b], 'y', linewidth=3)\n", + "plt.plot([1, 1], [b, b+a], 'y', linewidth=3)\n", + "plt.grid()\n", + "plt.xlabel('feature')\n", + "plt.ylabel('target')\n", + "plt.legend(prop={'size': 16})\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "OKsxKEysIb8w" + }, + "source": [ + "А визуально она допускает больше отклонений от синих точек, чем первая. Давайте сравним не визуально, а с помощью цифр." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PK43OAJOJ9nh" + }, + "source": [ + "Для начала составим все данные в одну таблицу:\n", + "- `X` - это точки, на которых строим модель\n", + "- `y` - это настоящая целевая переменная, которую хотим предсказать\n", + "- `pred_model_good` - это значения на линии по координатам `X` первой модели, имеем предсказания модель `LinearRegression`\n", + "- и `pred_bad_model` - это значения на линии по координатам `X` второй модели, которая создана вручную, а не силами `sklearn`" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 206 + }, + "id": "596LHapcI8Ra", + "outputId": "11c37a82-ca4f-4246-add1-fdc308197537" + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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Xypred_good_modelpred_bad_model
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" + ], + "text/plain": [ + " X y pred_good_model pred_bad_model\n", + "0 0.630080 43.654341 50.851871 31.503991\n", + "1 -1.061634 -72.682350 -85.193462 -53.081722\n", + "2 0.296347 21.196446 24.013545 14.817355\n", + "3 1.402771 107.587651 112.990641 70.138556\n", + "4 0.689682 69.620632 55.645021 34.484116" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "df = pd.DataFrame({\n", + " 'X': X[:,0],\n", + " 'y': y,\n", + " 'pred_good_model': model_a * X[:,0] + model_b,\n", + " 'pred_bad_model': a * X[:,0] + b\n", + "})\n", + "\n", + "\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Mw9kAfmtK4Pw" + }, + "source": [ + "Посчитаем отклонения предсказаний от истины для каждой модели.\n", + "\n", + "И здесь на первых 5 объектах тоже видим, что на `sklearn` модели более маленькие отклонения, нежели на второй модели." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 206 + }, + "id": "YeSOjxBjK8I7", + "outputId": "1bfceed7-8cb4-4c42-abe3-ed9fc728c3ef" + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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Xypred_good_modelpred_bad_modelresidual_goodresidual_bad
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" + ], + "text/plain": [ + " X y pred_good_model pred_bad_model residual_good \\\n", + "0 0.630080 43.654341 50.851871 31.503991 7.197530 \n", + "1 -1.061634 -72.682350 -85.193462 -53.081722 -12.511112 \n", + "2 0.296347 21.196446 24.013545 14.817355 2.817099 \n", + "3 1.402771 107.587651 112.990641 70.138556 5.402991 \n", + "4 0.689682 69.620632 55.645021 34.484116 -13.975611 \n", + "\n", + " residual_bad \n", + "0 -12.150350 \n", + "1 19.600628 \n", + "2 -6.379091 \n", + "3 -37.449095 \n", + "4 -35.136517 " + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df['residual_good'] = df['pred_good_model'] - df['y']\n", + "df['residual_bad'] = df['pred_bad_model'] - df['y']\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-l8fSDyULRLR" + }, + "source": [ + "Давайте теперь на всех объектах посчитаем метрику, которая будет позволять оценивать качество построенных линий.\n", + "\n", + "Возьмем MSE - mean squared error." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KB2SivGPL0pq" + }, + "source": [ + "MSE на sklearn модели равняется." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "HAZLA4slLz-b", + "outputId": "58806d83-9bf8-4cc7-bcae-f810e8120a39" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "111.93097544862607" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.mean(df['residual_good'] ** 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "o6TH3Ym2MGtv" + }, + "source": [ + "А MSE на второй модели равняется:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "EabHNLaMMGt8", + "outputId": "65204e86-74a5-4df4-9e17-08db98f565bd" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "873.1554374932329" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.mean(df['residual_bad'] ** 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VL93OuOCMKlR" + }, + "source": [ + "В разы больше, чем на первой модели." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "hikZUrXxsqE4" + }, + "source": [ + "##### Как обучается линейная регрессия" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4CivR_6rCVN1" + }, + "source": [ + "*Как же модель из `sklearn` умудрилась построить такие качественные предсказания?* Ведь у неё была куча вариантов построения, можно менять коэффициенты наклона и сдвига как угодно.\n", + "\n", + "Ответ на вопрос - **методы оптимизации**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xvDvoalkMmkW" + }, + "source": [ + "Ведь ошибка MSE тоже своего рода функция, которая меняется от коэффициента сдвига и наклона.\n", + "\n", + "Можем взять по 100 разных значений коэффициентов сдвига и наклона и посчитать в них MSE и отобразить на трехмерном графике.\n", + "\n", + "Так же отобразим и коэффициента, подобранные моделью из sklearn и наши коэффициенты." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 575 + }, + "id": "MYSGND_5NNii", + "outputId": "3d169bda-23db-4cc9-d98c-f4a990193aa9" + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d.axes3d import Axes3D\n", + "\n", + "\n", + "def mse(w1, w0):\n", + " y_pred = w1 * X[:, 0] + w0\n", + " return np.mean((y - y_pred) ** 2)\n", + "\n", + "\n", + "coefs_a = np.linspace(50, 100, num=100)\n", + "coefs_b = np.linspace(-10, 10, num=100)\n", + "w1, w0 = np.meshgrid(coefs_a, coefs_b)\n", + "\n", + "\n", + "fig = plt.figure(figsize=(15, 12))\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "\n", + "zs = np.array([mse(i, j) for i, j in zip(np.ravel(w1), np.ravel(w0))])\n", + "Z = zs.reshape(w1.shape)\n", + "\n", + "ax.plot_surface(w1, w0, Z, alpha=.5)\n", + "ax.scatter(model_a, model_b, mse(model_a, model_b), c='r', s=5)\n", + "ax.scatter(a, b, mse(a, b), c='r', s=5)\n", + "\n", + "ax.set_xlabel(r'$w_1$')\n", + "ax.set_ylabel(r'$w_0$')\n", + "ax.set_zlabel('MSE')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Z6h9XzopP8Ou" + }, + "source": [ + "И видим, что дейстивительно, модель с коэффициентом `a` равным где-то 80, и с небольшим коэффициентом `b` лучше, чем модель с коэффициентом `a=50`, ведь ошибка у второй модели выше, чем у первой.\n", + "\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "V4LqAG5jsyQj" + }, + "source": [ + "##### Градиентный спуск" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PmbkaRRNQ5SX" + }, + "source": [ + "*Как модель дошла до самой лучшей точки?*\n", + "\n", + "А она обучалась с помощью градиентного спуска - это метод оптимизации." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dA1lWisVRnq7" + }, + "source": [ + "**Обсудим, что такое градиент и зачем надо спускаться.**\n", + "\n", + "_Градиентом_ функции $f$ называется $n$-мерный вектор из частных производных. \n", + "\n", + "$$ \\nabla f(x_{1},...,x_{d}) = \\left(\\frac{\\partial f}{\\partial x_{i}}\\right)^{d}_{i=1}.$$\n", + "\n", + "К примеру, если функция зависит от трех переменных: $F(x, y, z)$, то её градиент будет равен \n", + "\n", + "$$\\nabla f(x, y, z) = (\\frac{\\partial f}{\\partial x}, \\frac{\\partial f}{\\partial y}, \\frac{\\partial f}{\\partial z}) $$\n", + "\n", + "При этом, __градиент задает направление наискорейшего роста функции__. Значит, антиградиент будет показывать направление ее скорейшего убывания, что будет полезно нам в нашей задаче минимизации функционала ошибки. \n", + "\n", + "**Градиентный спуск** — метод нахождения локального минимума с помощью движения вдоль антиградиента." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "K88irooYxpS9" + }, + "source": [ + "Давайте попробуем реализовать программно градиентный спуск, чтобы лучше понять как он работает." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zxKpYu5bWRH6" + }, + "source": [ + "Зададим две функции:\n", + "1. func - функция параболы $f(x) = x^2$\n", + "2. gr_func - производная функции параболы $\\nabla f(x) = 2x$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "id": "WYxZMCWzWQlS" + }, + "outputs": [], + "source": [ + "def func(x):\n", + " return x ** 2\n", + "\n", + "# функция градиента\n", + "def gr_func(x):\n", + " return 2 * x" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pJdDL_TvWufg" + }, + "source": [ + "Можем отрисовать эту функцию на графике.\n", + "\n", + "Действительно видим параболу." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "id": "TFnN5zo6Wmqw", + "outputId": "c5d9f425-9a76-4a58-c1a4-1b4265ac2765" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# для картинки\n", + "D = 5\n", + "\n", + "X = np.linspace(-D, +D, 20)\n", + "Y = func(X)\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gpghPbl5W3nY" + }, + "source": [ + "Чтобы найти минимум этой функции мы можем воспользоваться методом оптимизации - градиентный спуск, для этого нужно задать начальную точку, откуда будем считать градиенты и скатываться в минимум.\n", + "\n", + "Зеленая звездочка - это и есть точка старта." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "id": "a4CEhDEWXJMW", + "outputId": "a1e964b2-a644-45b6-9e0b-0bf862b56b57" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# первоначальное точка\n", + "start_point = 5\n", + "\n", + "# для картинки\n", + "D = 10\n", + "\n", + "X = np.linspace(-D, +D, 20)\n", + "Y = func(X)\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "plt.plot(start_point, func(start_point), '-*g', label = 'GD');\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "OZY4SxJ8XuaB" + }, + "source": [ + "Теперь в этой точке можем посчитать градиент.\n", + "\n", + "Он равняется 10, т.к. начальная точка равна 5, а производная будет равняться $\\nabla f(x) = 2\\cdot x = 2 \\cdot 5 = 10$ " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "bgQK7dm4ZOVw", + "outputId": "dc512a3c-90fb-4584-db79-7b0cc6fd7916" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grad = gr_func(start_point)\n", + "grad" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wxB4rqsKZO3K" + }, + "source": [ + "Можем отрисовать направление градиента, он показывает наискорейший рост функции и действительно видим, зеленый вектор идет вверх. 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "plt.plot(start_point, func(start_point), '*g', label='start_point')\n", + "\n", + "next_point_1 = start_point + grad\n", + "plt.plot([start_point, next_point_1], func(np.array([start_point, next_point_1])), '--g', label='grad')\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xMI7xm24Zo0h" + }, + "source": [ + "Но если будем двигаться по этому вектору, то к минимуму функции не придем, поэтому нужно идти в противоположгном направлении, а значит брать **антиградиент**.\n", + "\n", + "Но если мы пойдем от текущей точке $5$ в сторону антиградиента $-10$, то окажемся в точке $-5$, а это так же удалено от минимума, как и наша стартовая точка." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "id": "AHzUE456ZyQS", + "outputId": "c22df950-a4b3-415e-f410-f2d98b415614" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "plt.plot(start_point, func(start_point), '*g', label='start_point')\n", + "\n", + "next_point_1 = start_point - grad\n", + "plt.plot([start_point, next_point_1], func(np.array([start_point, next_point_1])), '--g', label='antigrad')\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cJ9vM4-Jayqf" + }, + "source": [ + "Поэтому чтобы не перескакивать минимальное состояние функции мы можем делать шаг в сторону антиградиента не полностью, а только на какую-то долю, для этого нужно ввести значения **шага обучения** (скорость обучения, learning rate) - это значения, замедляющее шаги градиентного спуска, чтобы не пропустить локальный минимум. " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "id": "cLP5hwpIbSE7", + "outputId": "a51ce935-f8b2-44e6-aab8-58aca85e0cf1" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "plt.plot(start_point, func(start_point), '*g', label='start_point')\n", + "\n", + "next_point_1 = start_point - grad * learning_rate\n", + "plt.plot([start_point, next_point_1], func(np.array([start_point, next_point_1])), '--*g', label='antigrad')\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "M5G3YV2Ydjnz" + }, + "source": [ + "Вот мы и получили новую точку с координатой $x=4$. \n", + "\n", + "Теперь в этой точке можем снова рассчитать значение градиента." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "HqqfwmXcd4x3", + "outputId": "03ffbec2-eb25-4291-cdaa-a157ccedf213" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4.0" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "curr_point = next_point_1\n", + "curr_point" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "hqaso7MFdxU3", + "outputId": "34dc4db0-d0c0-416f-f34c-53322b3ef533" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "8.0" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grad = gr_func(curr_point)\n", + "grad" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-AImpol6dxU5" + }, + "source": [ + "Отрисуем направление градиента, который показывает наискорейший рост функции.\n", + "\n", + "А синим пометим уже пройденный шаг." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "id": "3pn7Qfh0dxU5", + "outputId": "b6afae12-cb1a-4025-dabf-864a3a6d8f33" + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "plt.plot(start_point, func(start_point), '*g', label='start_point')\n", + "plt.plot([start_point, next_point_1], func(np.array([start_point, next_point_1])), '--*b', label='prev step')\n", + "\n", + "next_point_2 = curr_point + grad\n", + "\n", + "plt.plot([curr_point, next_point_2], func(np.array([curr_point, next_point_2])), '--g', label='grad')\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Nq_9K48ldxU6" + }, + "source": [ + "Но если будем двигаться по этому вектору, то к минимуму функции не придем, поэтому нужно идти в противоположном направлении, а значит брать **антиградиент**.\n", + "\n", + "Но при этом помним, что если сходить на полный антиградиент, то можем перелететь минимум, поэтому домножим на скорость обучения." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "id": "HiHId2wFdxU6", + "outputId": "4d367980-22ef-4f26-9810-eae64c919b01" + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "plt.plot(start_point, func(start_point), '*g', label='start_point')\n", + "plt.plot([start_point, next_point_1], func(np.array([start_point, next_point_1])), '--*b', label='prev step')\n", + "\n", + "next_point_2 = curr_point - learning_rate * grad\n", + "plt.plot([curr_point, next_point_2], func(np.array([curr_point, next_point_2])), '--*g', label='antigrad')\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gS0Z1swagJ7M" + }, + "source": [ + "И получаем еще одну точку, которая уже ближе к минимуму функции.\n", + "\n", + "Оформим небольшой цикл для градиентного спуска." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 926 + }, + "id": "qZc1XOjuqyvz", + "outputId": "2c50fd60-910a-4cb6-c1ff-3d697a5cb265" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Итерация: 0\n", + "Текущая точка 5| Следующая точка 4.0\n", + "--------------------------------------------------------\n", + "Итерация: 1\n", + "Текущая точка 4.0| Следующая точка 3.2\n", + "--------------------------------------------------------\n", + "Итерация: 2\n", + "Текущая точка 3.2| Следующая точка 2.56\n", + "--------------------------------------------------------\n", + "Итерация: 3\n", + "Текущая точка 2.56| Следующая точка 2.048\n", + "--------------------------------------------------------\n", + "Итерация: 4\n", + "Текущая точка 2.048| Следующая точка 1.6384\n", + "--------------------------------------------------------\n", + "Итерация: 5\n", + "Текущая точка 1.6384| Следующая точка 1.31072\n", + "--------------------------------------------------------\n", + "Итерация: 6\n", + "Текущая точка 1.31072| Следующая точка 1.0485760000000002\n", + "--------------------------------------------------------\n", + "Итерация: 7\n", + "Текущая точка 1.0485760000000002| Следующая точка 0.8388608000000002\n", + "--------------------------------------------------------\n", + "Итерация: 8\n", + "Текущая точка 0.8388608000000002| Следующая точка 0.6710886400000001\n", + "--------------------------------------------------------\n", + "Итерация: 9\n", + "Текущая точка 0.6710886400000001| Следующая точка 0.5368709120000001\n", + "--------------------------------------------------------\n", + "минимум 0.5368709120000001, количество затраченных итераций: 9\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# первоначальное точка\n", + "start_point = 5\n", + "\n", + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "# начальная точка\n", + "next_point = start_point\n", + "\n", + "x = []\n", + "x.append(next_point)\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "\n", + "# количество итерация \n", + "n = 10\n", + "for i in range(n):\n", + " current_point = next_point\n", + "\n", + " # движение в негативную сторону вычисляемого градиента\n", + " next_point = current_point - learning_rate * gr_func(current_point)\n", + " x.append(next_point)\n", + " # print(next_point) \n", + "\n", + " # остановка когда достигнута необходимая степень точности\n", + " print(f\"Итерация: {i}\")\n", + " print(f\"Текущая точка {current_point}| Следующая точка {next_point}\")\n", + " print(\"--------------------------------------------------------\")\n", + " \n", + " \n", + "\n", + "print(f\"минимум {next_point}, количество затраченных итераций: {i}\") \n", + "X_grad = np.array(x)\n", + "plt.plot(X_grad, func(X_grad), '-*g', label = 'GD')\n", + "plt.legend()\n", + "plt.xlabel('X')\n", + "plt.ylabel('Y')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "f7Nfx3xqqtLp" + }, + "source": [ + "Прошли 10 шагов и практически находимся в минимуме функции." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "R_FZFLAjrN6v" + }, + "source": [ + "А если мы сделаем больше итераций, то наверняка алгоритм сойдется к 0.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "9mIcLlcSrKiG", + "outputId": "61132eea-bdc0-45e1-a9cb-a1f941c7a128" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Итерация: 0\n", + "Текущая точка 5| Следующая точка 4.0\n", + "--------------------------------------------------------\n", + "Итерация: 1\n", + "Текущая точка 4.0| Следующая точка 3.2\n", + "--------------------------------------------------------\n", + "Итерация: 2\n", + "Текущая точка 3.2| Следующая точка 2.56\n", + "--------------------------------------------------------\n", + "Итерация: 3\n", + "Текущая точка 2.56| Следующая точка 2.048\n", + "--------------------------------------------------------\n", + "Итерация: 4\n", + "Текущая точка 2.048| Следующая точка 1.6384\n", + "--------------------------------------------------------\n", + "Итерация: 5\n", + "Текущая точка 1.6384| Следующая точка 1.31072\n", + "--------------------------------------------------------\n", + "Итерация: 6\n", + "Текущая точка 1.31072| Следующая точка 1.0485760000000002\n", + "--------------------------------------------------------\n", + "Итерация: 7\n", + "Текущая точка 1.0485760000000002| Следующая точка 0.8388608000000002\n", + "--------------------------------------------------------\n", + "Итерация: 8\n", + "Текущая точка 0.8388608000000002| Следующая точка 0.6710886400000001\n", + "--------------------------------------------------------\n", + "Итерация: 9\n", + "Текущая точка 0.6710886400000001| Следующая точка 0.5368709120000001\n", + "--------------------------------------------------------\n", + "Итерация: 10\n", + "Текущая точка 0.5368709120000001| Следующая точка 0.4294967296000001\n", + "--------------------------------------------------------\n", + "Итерация: 11\n", + "Текущая точка 0.4294967296000001| Следующая точка 0.3435973836800001\n", + "--------------------------------------------------------\n", + "Итерация: 12\n", + "Текущая точка 0.3435973836800001| Следующая точка 0.27487790694400005\n", + "--------------------------------------------------------\n", + "Итерация: 13\n", + "Текущая точка 0.27487790694400005| Следующая точка 0.21990232555520003\n", + "--------------------------------------------------------\n", + "Итерация: 14\n", + "Текущая точка 0.21990232555520003| Следующая точка 0.17592186044416003\n", + "--------------------------------------------------------\n", + "Итерация: 15\n", + "Текущая точка 0.17592186044416003| Следующая точка 0.140737488355328\n", + "--------------------------------------------------------\n", + "Итерация: 16\n", + "Текущая точка 0.140737488355328| Следующая точка 0.11258999068426241\n", + "--------------------------------------------------------\n", + "Итерация: 17\n", + "Текущая точка 0.11258999068426241| Следующая точка 0.09007199254740993\n", + "--------------------------------------------------------\n", + "Итерация: 18\n", + "Текущая точка 0.09007199254740993| Следующая точка 0.07205759403792794\n", + "--------------------------------------------------------\n", + "Итерация: 19\n", + "Текущая точка 0.07205759403792794| Следующая точка 0.057646075230342354\n", + "--------------------------------------------------------\n", + "Итерация: 20\n", + "Текущая точка 0.057646075230342354| Следующая точка 0.04611686018427388\n", + "--------------------------------------------------------\n", + "Итерация: 21\n", + "Текущая точка 0.04611686018427388| Следующая точка 0.03689348814741911\n", + "--------------------------------------------------------\n", + "Итерация: 22\n", + "Текущая точка 0.03689348814741911| Следующая точка 0.029514790517935284\n", + "--------------------------------------------------------\n", + "Итерация: 23\n", + "Текущая точка 0.029514790517935284| Следующая точка 0.02361183241434823\n", + "--------------------------------------------------------\n", + "Итерация: 24\n", + "Текущая точка 0.02361183241434823| Следующая точка 0.018889465931478583\n", + "--------------------------------------------------------\n", + "Итерация: 25\n", + "Текущая точка 0.018889465931478583| Следующая точка 0.015111572745182867\n", + "--------------------------------------------------------\n", + "Итерация: 26\n", + "Текущая точка 0.015111572745182867| Следующая точка 0.012089258196146294\n", + "--------------------------------------------------------\n", + "Итерация: 27\n", + "Текущая точка 0.012089258196146294| Следующая точка 0.009671406556917036\n", + "--------------------------------------------------------\n", + "Итерация: 28\n", + "Текущая точка 0.009671406556917036| Следующая точка 0.007737125245533628\n", + "--------------------------------------------------------\n", + "Итерация: 29\n", + "Текущая точка 0.007737125245533628| Следующая точка 0.006189700196426903\n", + "--------------------------------------------------------\n", + "Итерация: 30\n", + "Текущая точка 0.006189700196426903| Следующая точка 0.004951760157141522\n", + "--------------------------------------------------------\n", + "Итерация: 31\n", + "Текущая точка 0.004951760157141522| Следующая точка 0.003961408125713218\n", + "--------------------------------------------------------\n", + "Итерация: 32\n", + "Текущая точка 0.003961408125713218| Следующая точка 0.0031691265005705745\n", + "--------------------------------------------------------\n", + "Итерация: 33\n", + "Текущая точка 0.0031691265005705745| Следующая точка 0.00253530120045646\n", + "--------------------------------------------------------\n", + "Итерация: 34\n", + "Текущая точка 0.00253530120045646| Следующая точка 0.0020282409603651678\n", + "--------------------------------------------------------\n", + "Итерация: 35\n", + "Текущая точка 0.0020282409603651678| Следующая точка 0.0016225927682921343\n", + "--------------------------------------------------------\n", + "Итерация: 36\n", + "Текущая точка 0.0016225927682921343| Следующая точка 0.0012980742146337075\n", + "--------------------------------------------------------\n", + "Итерация: 37\n", + "Текущая точка 0.0012980742146337075| Следующая точка 0.001038459371706966\n", + "--------------------------------------------------------\n", + "Итерация: 38\n", + "Текущая точка 0.001038459371706966| Следующая точка 0.0008307674973655728\n", + "--------------------------------------------------------\n", + "Итерация: 39\n", + "Текущая точка 0.0008307674973655728| Следующая точка 0.0006646139978924582\n", + "--------------------------------------------------------\n", + "Итерация: 40\n", + "Текущая точка 0.0006646139978924582| Следующая точка 0.0005316911983139665\n", + "--------------------------------------------------------\n", + "Итерация: 41\n", + "Текущая точка 0.0005316911983139665| Следующая точка 0.00042535295865117324\n", + "--------------------------------------------------------\n", + "Итерация: 42\n", + "Текущая точка 0.00042535295865117324| Следующая точка 0.0003402823669209386\n", + "--------------------------------------------------------\n", + "Итерация: 43\n", + "Текущая точка 0.0003402823669209386| Следующая точка 0.00027222589353675085\n", + "--------------------------------------------------------\n", + "Итерация: 44\n", + "Текущая точка 0.00027222589353675085| Следующая точка 0.0002177807148294007\n", + "--------------------------------------------------------\n", + "Итерация: 45\n", + "Текущая точка 0.0002177807148294007| Следующая точка 0.00017422457186352054\n", + "--------------------------------------------------------\n", + "Итерация: 46\n", + "Текущая точка 0.00017422457186352054| Следующая точка 0.00013937965749081642\n", + "--------------------------------------------------------\n", + "Итерация: 47\n", + "Текущая точка 0.00013937965749081642| Следующая точка 0.00011150372599265314\n", + "--------------------------------------------------------\n", + "Итерация: 48\n", + "Текущая точка 0.00011150372599265314| Следующая точка 8.920298079412252e-05\n", + "--------------------------------------------------------\n", + "Итерация: 49\n", + "Текущая точка 8.920298079412252e-05| Следующая точка 7.136238463529802e-05\n", + "--------------------------------------------------------\n", + "Итерация: 50\n", + "Текущая точка 7.136238463529802e-05| Следующая точка 5.7089907708238416e-05\n", + "--------------------------------------------------------\n", + "Итерация: 51\n", + "Текущая точка 5.7089907708238416e-05| Следующая точка 4.567192616659073e-05\n", + "--------------------------------------------------------\n", + "Итерация: 52\n", + "Текущая точка 4.567192616659073e-05| Следующая точка 3.653754093327259e-05\n", + "--------------------------------------------------------\n", + "Итерация: 53\n", + "Текущая точка 3.653754093327259e-05| Следующая точка 2.923003274661807e-05\n", + "--------------------------------------------------------\n", + "Итерация: 54\n", + "Текущая точка 2.923003274661807e-05| Следующая точка 2.3384026197294454e-05\n", + "--------------------------------------------------------\n", + "Итерация: 55\n", + "Текущая точка 2.3384026197294454e-05| Следующая точка 1.8707220957835564e-05\n", + "--------------------------------------------------------\n", + "Итерация: 56\n", + "Текущая точка 1.8707220957835564e-05| Следующая точка 1.4965776766268452e-05\n", + "--------------------------------------------------------\n", + "Итерация: 57\n", + "Текущая точка 1.4965776766268452e-05| Следующая точка 1.1972621413014761e-05\n", + "--------------------------------------------------------\n", + "Итерация: 58\n", + "Текущая точка 1.1972621413014761e-05| Следующая точка 9.578097130411809e-06\n", + "--------------------------------------------------------\n", + "Итерация: 59\n", + "Текущая точка 9.578097130411809e-06| Следующая точка 7.662477704329448e-06\n", + "--------------------------------------------------------\n", + "Итерация: 60\n", + "Текущая точка 7.662477704329448e-06| Следующая точка 6.129982163463559e-06\n", + "--------------------------------------------------------\n", + "Итерация: 61\n", + "Текущая точка 6.129982163463559e-06| Следующая точка 4.903985730770847e-06\n", + "--------------------------------------------------------\n", + "Итерация: 62\n", + "Текущая точка 4.903985730770847e-06| Следующая точка 3.923188584616677e-06\n", + "--------------------------------------------------------\n", + "Итерация: 63\n", + "Текущая точка 3.923188584616677e-06| Следующая точка 3.138550867693342e-06\n", + "--------------------------------------------------------\n", + "Итерация: 64\n", + "Текущая точка 3.138550867693342e-06| Следующая точка 2.5108406941546735e-06\n", + "--------------------------------------------------------\n", + "Итерация: 65\n", + "Текущая точка 2.5108406941546735e-06| Следующая точка 2.008672555323739e-06\n", + "--------------------------------------------------------\n", + "Итерация: 66\n", + "Текущая точка 2.008672555323739e-06| Следующая точка 1.606938044258991e-06\n", + "--------------------------------------------------------\n", + "Итерация: 67\n", + "Текущая точка 1.606938044258991e-06| Следующая точка 1.2855504354071928e-06\n", + "--------------------------------------------------------\n", + "Итерация: 68\n", + "Текущая точка 1.2855504354071928e-06| Следующая точка 1.0284403483257543e-06\n", + "--------------------------------------------------------\n", + "Итерация: 69\n", + "Текущая точка 1.0284403483257543e-06| Следующая точка 8.227522786606034e-07\n", + "--------------------------------------------------------\n", + "Итерация: 70\n", + "Текущая точка 8.227522786606034e-07| Следующая точка 6.582018229284827e-07\n", + "--------------------------------------------------------\n", + "Итерация: 71\n", + "Текущая точка 6.582018229284827e-07| Следующая точка 5.265614583427862e-07\n", + "--------------------------------------------------------\n", + "Итерация: 72\n", + "Текущая точка 5.265614583427862e-07| Следующая точка 4.2124916667422894e-07\n", + "--------------------------------------------------------\n", + "Итерация: 73\n", + "Текущая точка 4.2124916667422894e-07| Следующая точка 3.3699933333938316e-07\n", + "--------------------------------------------------------\n", + "Итерация: 74\n", + "Текущая точка 3.3699933333938316e-07| Следующая точка 2.6959946667150655e-07\n", + "--------------------------------------------------------\n", + "Итерация: 75\n", + "Текущая точка 2.6959946667150655e-07| Следующая точка 2.1567957333720524e-07\n", + "--------------------------------------------------------\n", + "Итерация: 76\n", + "Текущая точка 2.1567957333720524e-07| Следующая точка 1.725436586697642e-07\n", + "--------------------------------------------------------\n", + "Итерация: 77\n", + "Текущая точка 1.725436586697642e-07| Следующая точка 1.3803492693581135e-07\n", + "--------------------------------------------------------\n", + "Итерация: 78\n", + "Текущая точка 1.3803492693581135e-07| Следующая точка 1.1042794154864907e-07\n", + "--------------------------------------------------------\n", + "Итерация: 79\n", + "Текущая точка 1.1042794154864907e-07| Следующая точка 8.834235323891926e-08\n", + "--------------------------------------------------------\n", + "Итерация: 80\n", + "Текущая точка 8.834235323891926e-08| Следующая точка 7.067388259113541e-08\n", + "--------------------------------------------------------\n", + "Итерация: 81\n", + "Текущая точка 7.067388259113541e-08| Следующая точка 5.653910607290833e-08\n", + "--------------------------------------------------------\n", + "Итерация: 82\n", + "Текущая точка 5.653910607290833e-08| Следующая точка 4.5231284858326664e-08\n", + "--------------------------------------------------------\n", + "Итерация: 83\n", + "Текущая точка 4.5231284858326664e-08| Следующая точка 3.618502788666133e-08\n", + "--------------------------------------------------------\n", + "Итерация: 84\n", + "Текущая точка 3.618502788666133e-08| Следующая точка 2.8948022309329066e-08\n", + "--------------------------------------------------------\n", + "Итерация: 85\n", + "Текущая точка 2.8948022309329066e-08| Следующая точка 2.3158417847463252e-08\n", + "--------------------------------------------------------\n", + "Итерация: 86\n", + "Текущая точка 2.3158417847463252e-08| Следующая точка 1.8526734277970603e-08\n", + "--------------------------------------------------------\n", + "Итерация: 87\n", + "Текущая точка 1.8526734277970603e-08| Следующая точка 1.4821387422376482e-08\n", + "--------------------------------------------------------\n", + "Итерация: 88\n", + "Текущая точка 1.4821387422376482e-08| Следующая точка 1.1857109937901186e-08\n", + "--------------------------------------------------------\n", + "Итерация: 89\n", + "Текущая точка 1.1857109937901186e-08| Следующая точка 9.485687950320948e-09\n", + "--------------------------------------------------------\n", + "Итерация: 90\n", + "Текущая точка 9.485687950320948e-09| Следующая точка 7.588550360256759e-09\n", + "--------------------------------------------------------\n", + "Итерация: 91\n", + "Текущая точка 7.588550360256759e-09| Следующая точка 6.070840288205408e-09\n", + "--------------------------------------------------------\n", + "Итерация: 92\n", + "Текущая точка 6.070840288205408e-09| Следующая точка 4.856672230564326e-09\n", + "--------------------------------------------------------\n", + "Итерация: 93\n", + "Текущая точка 4.856672230564326e-09| Следующая точка 3.885337784451461e-09\n", + "--------------------------------------------------------\n", + "Итерация: 94\n", + "Текущая точка 3.885337784451461e-09| Следующая точка 3.108270227561169e-09\n", + "--------------------------------------------------------\n", + "Итерация: 95\n", + "Текущая точка 3.108270227561169e-09| Следующая точка 2.4866161820489353e-09\n", + "--------------------------------------------------------\n", + "Итерация: 96\n", + "Текущая точка 2.4866161820489353e-09| Следующая точка 1.989292945639148e-09\n", + "--------------------------------------------------------\n", + "Итерация: 97\n", + "Текущая точка 1.989292945639148e-09| Следующая точка 1.5914343565113183e-09\n", + "--------------------------------------------------------\n", + "Итерация: 98\n", + "Текущая точка 1.5914343565113183e-09| Следующая точка 1.2731474852090548e-09\n", + "--------------------------------------------------------\n", + "Итерация: 99\n", + "Текущая точка 1.2731474852090548e-09| Следующая точка 1.0185179881672439e-09\n", + "--------------------------------------------------------\n", + "минимум 1.0185179881672439e-09, количество затраченных итераций: 99\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# первоначальное точка\n", + "start_point = 5\n", + "\n", + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "# начальная точка\n", + "next_point = start_point\n", + "\n", + "x = []\n", + "x.append(next_point)\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "\n", + "# количество итерация \n", + "n = 100\n", + "for i in range(n):\n", + " current_point = next_point\n", + "\n", + " # движение в негативную сторону вычисляемого градиента\n", + " next_point = current_point - learning_rate * gr_func(current_point)\n", + " x.append(next_point) \n", + "\n", + " # остановка когда достигнута необходимая степень точности\n", + " print(f\"Итерация: {i}\")\n", + " print(f\"Текущая точка {current_point}| Следующая точка {next_point}\")\n", + " print(\"--------------------------------------------------------\")\n", + " \n", + " \n", + "\n", + "print(f\"минимум {next_point}, количество затраченных итераций: {i}\") \n", + "X_grad = np.array(x)\n", + "plt.plot(X_grad, func(X_grad), '-*g', label = 'GD')\n", + "plt.legend()\n", + "plt.xlabel('X')\n", + "plt.ylabel('Y')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BWV6HvSRrTO0" + }, + "source": [ + "Но здесь значения самой лучшей минимальной точки на последних шагах очень похожи и на самом деле мы могли не ждать столько итераций и выйти из цикла раньше.\n", + "\n", + "Для этого введем значение eps, с помощью которого будем проверять разницу между текущей точкой и следующей точкой и если она меньше eps (а значит точки очень близки), то можем выйти из алгоритма." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "nrM5GLhBxpS9", + "outputId": "f3c037e1-83fe-480c-aa05-272bf7e647dd" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Итерация: 0\n", + "Текущая точка 5| Следующая точка 4.0\n", + "--------------------------------------------------------\n", + "Итерация: 1\n", + "Текущая точка 4.0| Следующая точка 3.2\n", + "--------------------------------------------------------\n", + "Итерация: 2\n", + "Текущая точка 3.2| Следующая точка 2.56\n", + "--------------------------------------------------------\n", + "Итерация: 3\n", + "Текущая точка 2.56| Следующая точка 2.048\n", + "--------------------------------------------------------\n", + "Итерация: 4\n", + "Текущая точка 2.048| Следующая точка 1.6384\n", + "--------------------------------------------------------\n", + "Итерация: 5\n", + "Текущая точка 1.6384| Следующая точка 1.31072\n", + "--------------------------------------------------------\n", + "Итерация: 6\n", + "Текущая точка 1.31072| Следующая точка 1.0485760000000002\n", + "--------------------------------------------------------\n", + "Итерация: 7\n", + "Текущая точка 1.0485760000000002| Следующая точка 0.8388608000000002\n", + "--------------------------------------------------------\n", + "Итерация: 8\n", + "Текущая точка 0.8388608000000002| Следующая точка 0.6710886400000001\n", + "--------------------------------------------------------\n", + "Итерация: 9\n", + "Текущая точка 0.6710886400000001| Следующая точка 0.5368709120000001\n", + "--------------------------------------------------------\n", + "Итерация: 10\n", + "Текущая точка 0.5368709120000001| Следующая точка 0.4294967296000001\n", + "--------------------------------------------------------\n", + "Итерация: 11\n", + "Текущая точка 0.4294967296000001| Следующая точка 0.3435973836800001\n", + "--------------------------------------------------------\n", + "Итерация: 12\n", + "Текущая точка 0.3435973836800001| Следующая точка 0.27487790694400005\n", + "--------------------------------------------------------\n", + "Итерация: 13\n", + "Текущая точка 0.27487790694400005| Следующая точка 0.21990232555520003\n", + "--------------------------------------------------------\n", + "Итерация: 14\n", + "Текущая точка 0.21990232555520003| Следующая точка 0.17592186044416003\n", + "--------------------------------------------------------\n", + "Итерация: 15\n", + "Текущая точка 0.17592186044416003| Следующая точка 0.140737488355328\n", + "--------------------------------------------------------\n", + "Итерация: 16\n", + "Текущая точка 0.140737488355328| Следующая точка 0.11258999068426241\n", + "--------------------------------------------------------\n", + "Итерация: 17\n", + "Текущая точка 0.11258999068426241| Следующая точка 0.09007199254740993\n", + "--------------------------------------------------------\n", + "Итерация: 18\n", + "Текущая точка 0.09007199254740993| Следующая точка 0.07205759403792794\n", + "--------------------------------------------------------\n", + "Итерация: 19\n", + "Текущая точка 0.07205759403792794| Следующая точка 0.057646075230342354\n", + "--------------------------------------------------------\n", + "Итерация: 20\n", + "Текущая точка 0.057646075230342354| Следующая точка 0.04611686018427388\n", + "--------------------------------------------------------\n", + "Итерация: 21\n", + "Текущая точка 0.04611686018427388| Следующая точка 0.03689348814741911\n", + "--------------------------------------------------------\n", + "Итерация: 22\n", + "Текущая точка 0.03689348814741911| Следующая точка 0.029514790517935284\n", + "--------------------------------------------------------\n", + "Итерация: 23\n", + "Текущая точка 0.029514790517935284| Следующая точка 0.02361183241434823\n", + "--------------------------------------------------------\n", + "Итерация: 24\n", + "Текущая точка 0.02361183241434823| Следующая точка 0.018889465931478583\n", + "--------------------------------------------------------\n", + "Итерация: 25\n", + "Текущая точка 0.018889465931478583| Следующая точка 0.015111572745182867\n", + "--------------------------------------------------------\n", + "Итерация: 26\n", + "Текущая точка 0.015111572745182867| Следующая точка 0.012089258196146294\n", + "--------------------------------------------------------\n", + "Итерация: 27\n", + "Текущая точка 0.012089258196146294| Следующая точка 0.009671406556917036\n", + "--------------------------------------------------------\n", + "Итерация: 28\n", + "Текущая точка 0.009671406556917036| Следующая точка 0.007737125245533628\n", + "--------------------------------------------------------\n", + "Итерация: 29\n", + "Текущая точка 0.007737125245533628| Следующая точка 0.006189700196426903\n", + "--------------------------------------------------------\n", + "Итерация: 30\n", + "Текущая точка 0.006189700196426903| Следующая точка 0.004951760157141522\n", + "--------------------------------------------------------\n", + "Итерация: 31\n", + "Текущая точка 0.004951760157141522| Следующая точка 0.003961408125713218\n", + "--------------------------------------------------------\n", + "Итерация: 32\n", + "Текущая точка 0.003961408125713218| Следующая точка 0.0031691265005705745\n", + "--------------------------------------------------------\n", + "Итерация: 33\n", + "Текущая точка 0.0031691265005705745| Следующая точка 0.00253530120045646\n", + "--------------------------------------------------------\n", + "Итерация: 34\n", + "Текущая точка 0.00253530120045646| Следующая точка 0.0020282409603651678\n", + "--------------------------------------------------------\n", + "Итерация: 35\n", + "Текущая точка 0.0020282409603651678| Следующая точка 0.0016225927682921343\n", + "--------------------------------------------------------\n", + "Итерация: 36\n", + "Текущая точка 0.0016225927682921343| Следующая точка 0.0012980742146337075\n", + "--------------------------------------------------------\n", + "Итерация: 37\n", + "Текущая точка 0.0012980742146337075| Следующая точка 0.001038459371706966\n", + "--------------------------------------------------------\n", + "Итерация: 38\n", + "Текущая точка 0.001038459371706966| Следующая точка 0.0008307674973655728\n", + "--------------------------------------------------------\n", + "Итерация: 39\n", + "Текущая точка 0.0008307674973655728| Следующая точка 0.0006646139978924582\n", + "--------------------------------------------------------\n", + "Итерация: 40\n", + "Текущая точка 0.0006646139978924582| Следующая точка 0.0005316911983139665\n", + "--------------------------------------------------------\n", + "Итерация: 41\n", + "Текущая точка 0.0005316911983139665| Следующая точка 0.00042535295865117324\n", + "--------------------------------------------------------\n", + "Итерация: 42\n", + "Текущая точка 0.00042535295865117324| Следующая точка 0.0003402823669209386\n", + "--------------------------------------------------------\n", + "минимум 0.0003402823669209386, количество затраченных итераций: 42\n" + ] + }, + { + "data": { + "image/png": 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fKSlJkiRJkpRbkyfD3XcHx08/DfvsE24e/S3LSIWrZk0YNCg4vvde+PzzcPNIkiRJkqTCY906uPhiyMmBdu2Ci2KaZaTC17bt9h8cF18MGRlhJ5IkSZIkSYVB9+7w00/BYqcBA8JOo1ywjFRs6N8f9t0XFi7cPvlKkiRJkiRpV8aMgaFDIS4ORoyAcuXCTqRcsIxUbEhNDX5wxMUFG82OHh12IkmSJEmSFKuWLoUuXYLjW24JJmirULCMVOw49li49dbg+KqrYPHicPNIkiRJkqTYk5MDHTvCb79Bw4Zw551hJ1IeWEYqttx+OzRqBGvXQocOkJ0ddiJJkiRJkhRLHn0UPvwQSpWCkSMhMTHsRMoDy0jFlsTE4AdJ6dIwaRI8/HDYiSRJkiRJUqz4+uvtZ1U+/jjUrh1qHOWdZaRizwEHwBNPBMd9+sBXX4WbR5IkSZIkhW/jRmjfHrZsgXPPhU6dwk6kf8EyUrHp8suhdevgB0z79sEPHEmSJEmSVHz16gVz50JaGjz3HEQiYSfSv2AZqdgUicDgwVCtGsybBz17hp1IkiRJkiSF5c03YcCA4HjYMKhYMdw8+tcsIxW7KlSAoUOD40GDYMKEUONIkiRJkqQQrFwZnEEJcN11cPrp4ebRbrGMVGw77TS44Ybg+PLLYfnycPNIkiRJkqSCE40GfcDKlXDooXD//WEn0m6yjFTsu+8+OOwwWL0aLrss+EEkSZIkSZKKvqefDk7RTk6GUaOgRImwE2k3WUYq9v3+Ayc5Gd55Z/seEZIkSZIkqeiaO3f7DIn774d69cLNoz3CMlKFwyGHwEMPBcc33gjffhtuHkmSJEmSlH8yM6FdO9i8Odgjsnv3sBNpD7GMVOHRrRs0b779B1JmZtiJJEmSJElSfujTB2bO3D7cNs4Kq6jwv6QKj0gEhgyBihVh1iy47bawE0mSJEmSpD3to4/g4YeD4+eeg6pVw82jPcoyUoVLWho8/3xw/Mgj8MEH4eaRJEmSJEl7zpo1cMklwfDaTp2gZcuwE2kPs4xU4XPOOdClS3DcsSP8+mu4eSRJkiRJ0u6LRuGqq+Dnn+HAA+Gxx8JOpHxgGanC6ZFHoHZtWLYsKCaj0bATSZIkSZKk3TF8OIwZAwkJMHIklCkTdiLlA8tIFU6lS8OoUcEPqNdeCzazlSRJkiRJhdOPPwaDawHuvBOOOirUOMo/lpEqvBo0gHvuCY6vvRbmzw83jyRJkiRJyrutW4N9Itevh+OOg1tuCTuR8pFlpAq3m26CE06ADRvg4othy5awE0mSJEmSpLy4916YPBlSUmDECIiPDzuR8lFMl5HZ2dn06dOHWrVqUbJkSfbff3/uueceon/YHzAajXL77bdTtWpVSpYsSdOmTfnhhx9CTK0CFR8PL74IqakwdSr07Rt2IkmSJEmSlFuTJ28/63HgQNhnn3DzKN/FdBn5wAMP8PTTT9O/f3/mzp3LAw88wIMPPshTTz217T4PPvggTz75JIMGDWLq1KmULl2aZs2asXnz5hCTq0DVrAmDBgXHffvC55+Hm0eSJEmSJP2zdeuCsxyzs6FdO2jfPuxEKgCRaDR2xxCfffbZVKlSheeff37bdW3atKFkyZKMGDGCaDRKtWrV6NmzJzfeeCMA6enpVKlShaFDh9K2bdtcfZyMjAxSU1NJT08nJSUlXz4XFYBLLgmWc++7L3zzTbC8W5IkSZIkxabLLgsG0tasGfwdX65c2Im0G3Lbr8X0yshjjjmGiRMn8v333wPwzTff8Nlnn3HGGWcAsGDBApYvX07Tpk23PSY1NZXGjRszefLkXb7fzMxMMjIydrioCOjfP1jOvXAhdOwIOTlhJ5IkSZIkSTvz/PNBERmJBNuvWUQWGzFdRt5yyy20bduWgw46iMTERI488kh69OhB+/8t212+fDkAVapU2eFxVapU2XbbzvTr14/U1NRtlxo1auTfJ6GCk5oKo0dDUhKMHw/9+oWdSJIkSZIk/dmXX8I11wTHd90VDKZVsRHTZeQrr7zCyJEjGTVqFDNmzGDYsGE8/PDDDBs2bLfeb+/evUlPT992WbJkyR5KrNA1bhxseAvQpw+89Va4eSRJkiRJ0nYrVkDr1pCVBS1bwm23hZ1IBSwh7AB/56abbtq2OhKgXr16LFq0iH79+tGxY0fS0tIAWLFiBVWrVt32uBUrVnDEEUfs8v0mJyeTnJycr9kVoiuugOnTg6E27doFxwccEHYqSZIkSZKKty1b4Pzz4eef4aCDYNgwiIvpdXLKBzH9X3zjxo3E/elJGR8fT87/9gKsVasWaWlpTJw4cdvtGRkZTJ06lSZNmhRoVsWYJ56AY46B9PTglZb168NOJEmSJElS8dazJ3z6KZQtG2yv5uDZYimmy8gWLVpw77338uabb7Jw4ULGjRvHo48+SqtWrQCIRCL06NGDvn378vrrrzN79mw6dOhAtWrVaNmyZbjhFa6kJHj1VahaFb79NpjQFbuD4yVJkiRJKtqGDYOnngqOR4yAOnXCzaPQRKLR2G1o1q1bR58+fRg3bhwrV66kWrVqXHTRRdx+++0kJSUBEI1GueOOOxg8eDBr167luOOOY+DAgdSuXTvXHye3o8dVCH3xBZx0UrAU/P774eabw04kSZIkSVLx8tVXcOyxkJkJd9wBd94ZdiLlg9z2azFdRhYUy8gi7pln4KqrIBKBt9+GZs3CTiRJkiRJUvGwahU0aABLlsDZZ8N//uM+kUVUbvs1/+ur6OvcGTp1Ck7Tvugi+OmnsBNJkiRJklT0bd0KF1wQFJG1awenZ1tEFns+A1T0RSLQvz80bgy//QatWsGGDWGnkiRJkiSpaOvVCz7+GMqUgXHjIDU17ESKAZaRKh6Sk+G116BKFZg1a/tKSUmSJEmStOeNHAmPPRYcDxsGdeuGm0cxwzJSxcfee8OYMZCQAC+/DI8+GnYiSZIkSZKKnq+/hiuvDI5vuw1atw43j2KKZaSKl+OP3/7KTK9e8MEH4eaRJEmSJKkoWb062B5t0yZo3hzuuivsRIoxlpEqfrp2hY4dIScH2raFhQvDTiRJkiRJUuG3dWvwd/aiRbDffjBqFMTHh51KMcYyUsVPJAJPPw0NGsCvvwav2GzcGHYqSZIkSZIKt1tvhYkToVQpGD8e9tor7ESKQZaRKp5KloSxY6FiRZg5Ezp3dqCNJEmSJEn/1ujR8NBDwfGQIVCvXrh5FLMsI1V81awJr7wSLBkfORKefDLsRJIkSZIkFT6zZsHllwfHvXrBBReEm0cxzTJSxdvJJ8PDDwfHPXvCxx+HGkeSJEmSpEJlzZrt25+ddhrcd1/YiRTjLCOl666D9u0hOzt49Wbx4rATSZIkSZIU+7KzoV07+Okn2HdfeOklB9boH1lGSpEIDB4MRxwBq1ZB69awaVPYqSRJkiRJim19+sC77wZzGcaNgwoVwk6kQsAyUoJg0te4cVC+PHz1FVx9tQNtJEmSJEnalVdfhX79guPnngsW+Ei5YBkp/W7ffYPpX3FxMGwYDBwYdiJJkiRJkmLPt9/CpZcGxzfcEJyqLeWSZaT0R02bwgMPBMc9esCnn4YaR5IkSZKkmLJ2LbRsCRs2wCmnbP8bWsoly0jpz3r2hAsvhK1b4bzzYOnSsBNJkiRJkhS+nJxgAOz8+VCzJrz8MiQkhJ1KhYxlpPRnkQg8/zzUqwcrV0KbNpCZGXYqSZIkSZLCdeed8NZbUKJEMHehUqWwE6kQsoyUdqZ06eAH6157wZdfQteuDrSRJEmSJBVf48fDPfcEx4MHQ/36ocZR4WUZKe3K/vvDSy9tXyk5eHDYiSRJkiRJKnhz50KHDsFx9+5wySXh5lGhZhkp/Z1mzeC++4Lja6+FL74IN48kSZIkSQUpPR1atYJ16+CEE+Dhh8NOpELOMlL6JzffHAyy2bIl2D9y2bKwE0mSJEmSlP9ycoIVkfPmQfXq8MorkJgYdioVcpaR0j+JRGDIEDjkEFi+PCgms7LCTiVJkiRJUv7q2xdefx2Sk2HsWKhSJexEKgIsI6XcKFMmGGiTmgqTJ8N114WdSJIkSZKk/PPGG3DHHcHx00/DUUeFm0dFhmWklFsHHggjRwYrJQcNgueeCzuRJEmSJEl73vffQ/v2wfE118Bll4WbR0WKZaSUF2edBXffHRx37QpTp4abR5IkSZKkPWndOmjZEjIy4Nhj4bHHwk6kIsYyUsqrW28NfjBnZQUDbZYvDzuRJEmSJEm7LycHOnaEuXOhWjV49VVISgo7lYoYy0gpr+LiYNgwOOgg+PlnOP98B9pIkiRJkgq/++8P5iUkJsJrr0FaWtiJVARZRkr/RkoKjB8PZcvCZ59Bz55hJ5IkSZIk6d97+234v/8LjgcMgKOPDjePiizLSOnfqlMHRowIjvv3h6FDQ40jSZIkSdK/Mn8+tGsH0Sh07gxXXhl2IhVhlpHS7jjnHLjjjuD4qqtg+vRw80iSJEmSlBfr10OrVrB2bbAa8sknw06kIs4yUtpdt98OZ58NmZnQujWsXBl2IkmSJEmS/lk0CpdfDnPmBPtDvvYaJCeHnUpFnGWktLvi4oLTtWvXhiVL4MILYevWsFNJkiRJkvT3HnoIxoyBhIRgcna1amEnUjFgGSntCampwcSxMmXg44+hV6+wE0mSJEmStGvvvw+9ewfHTz4Jxx4bbh4VG5aR0p5Sty4MGxYcP/YYjBwZbh5JkiRJknZmwQJo2xZycoLTtK+6KuxEKkYsI6U9qXVruO224PjKK+Hrr8PNI0mSJEnSH23cGAysWbMGjjoKBgyASCTsVCpGLCOlPe2uu+CMM2DTpuAH/OrVYSeSJEmSJCkYWHPllfDNN1C5cjCwpkSJsFOpmLGMlPa0+PjgFO3994dFi4Kl7w60kSRJkiSF7fHHYdSoYGDNmDFQo0bYiVQMWUZK+WGvvWD8eChdGiZOhFtvDTuRJEmSJKk4+/BDuOmm4PjRR+GEE8LNo2LLMlLKL4ceCkOGBMcPPQSjR4ebR5IkSZJUPC1aBBdeCNnZ0KEDdOsWdiIVY5aRUn46/3y4+ebg+PLLYdascPNIkiRJkoqXTZuCYaurV0P9+jBokANrFCrLSCm/3XsvnH76jhPLJEmSJEnKb9EoXHUVzJgBFSvC2LFQsmTYqVTMWUZK+S0+Hl56CWrVgp9+gnbtgqXxkiRJkiTlp/79Yfjw4O/SV16BffYJO5FkGSkViPLlYdy44BWod9+FPn3CTiRJkiRJKsomTYLrrw+OH3oITj453DzS/1hGSgXl8MPh+eeD43794NVXw80jSZIkSSqaliwJZhhkZwdn5/XoEXYiaRvLSKkgXXQR9OwZHF96KXz7bahxJEmSJElFzObN0KYNrFoVLIp59lkH1iimWEZKBe3+++GUU2DDBmjZEtauDTuRJEmSJKkoiEbhmmtg2rTt24WVKhV2KmkHlpFSQUtIgNGjg42D58+H9u0hJyfsVJIkSZKkwm7QIBgyBOLi4OWXg0GqUoyxjJTCULEijB0LJUrAW2/BnXeGnUiSJEmSVJh99hl07x4c338/nHZauHmkXbCMlMJSvz4MHhwc33MPjB8fahxJkiRJUiH1889w3nmwdStccAHceGPYiaRdsoyUwnTJJXDddcFxhw4wd264eSRJkiRJhUtmZlBErlgB9erBCy84sEYxzTJSCttDD8GJJ8K6ddCqFaSnh51IkiRJklRYdO8OU6ZAuXLBwJrSpcNOJP0ty0gpbImJ8MorUL06zJsXrJB0oI0kSZIk6Z8MHhxcIhF46SXYf/+wE0n/yDJSigWVKwcDbZKT4fXXoW/fsBNJkiRJkmLZ5MnQrVtwfO+90Lx5uHmkXLKMlGLFUUfBoEHB8R13wBtvhJtHkiRJkhSbfvkF2rSBLVuCf2+5JexEUq5ZRkqx5NJLoWvX4Lh9e/j++1DjSJIkSZJiTFYWnH9+UEjWrQtDhjiwRoWKZaQUax59FI47DjIyoGXLYLCNJEmSJEkA118Pn38OqakwfjyULRt2IilPLCOlWJOUBGPGQLVqMHcudOzoQBtJkiRJErzwAgwcGKyEHDkSDjww7ERSnllGSrEoLQ1eey0oJseNg/vvDzuRJEmSJClMX34JV18dHN91F5x1Vrh5pH/JMlKKVUcfDQMGBMf/93/w9tvh5pEkSZIkhWPFCmjdOtgv8txz4bbbwk4k/WuWkVIs69QJunSBaBTatYP588NOJEmSJEkqSFu2wAUXwM8/Q506MHw4xFnnqPDy2SvFuieegCZNYO1aaNUK1q8PO5EkSZIkqaDceCN88kkwqGb8eEhJCTuRtFssI6VYl5wMr74a7CM5Zw5cfnmwUlKSJEmSVLQNHw5PPhkcv/giHHRQuHmkPcAyUioMqlULCsnExGDS9kMPhZ1IkiRJkpSfvvoq2LYL4Pbbg70ipSLAMlIqLI49dvsrYr17w3vvhZtHkiRJkpQ/Vq0KBtZs3gxnnw133BF2ImmPsYyUCpMuXeCKKyAnB9q2hZ9+CjuRJEmSJGlP2roVLrwQFi+GAw8MTs92YI2KEJ/NUmESiUD//tCoEfz2WzDQZsOGsFNJkiRJkvaUm2+Gjz6CMmWCgTXlyoWdSNqjLCOlwqZECXjtNahcGWbNgo4dITs77FSSJEmSpN01ZAg8+mhwPGwY1K0bbh4pH1hGSoVR9erBQJukpKCYvPZaJ2xLkiRJUmE2YQJceWVwfNttwZ6RUhFkGSkVVscfDyNGBKduP/003H132IkkSZIkSf/GZ5/BBRcEZ71deincc0/YiaR8YxkpFWbnnx/sIQlw550waFCocSRJkiRJeTR7NrRosX1y9rPPBotOpCLKMlIq7K65Bm6/ffvxq6+Gm0eSJEmSlDuLFkHz5rB2LRx7LIweDQkJYaeS8pVlpFQU3HkndOkS7BvZvj18+GHYiSRJkiRJf2fVKjj9dFi2DA45JNgzslSpsFNJ+c4yUioKIhEYMADatIGsLDj3XJgxI+xUkiRJkqSdWbcOzjwTvv8eataEd9+FvfYKO5VUIGK+jPz555+5+OKLqVChAiVLlqRevXpMnz592+3RaJTbb7+dqlWrUrJkSZo2bcoPP/wQYmIpJPHxMHIknHwyrF8PZ5wB8+eHnUqSJEmS9EdZWcGk7OnToWJFeO892HvvsFNJBSamy8jffvuNY489lsTERN5++23++9//8sgjj7DXH14tePDBB3nyyScZNGgQU6dOpXTp0jRr1ozNmzeHmFwKSXIyjB8PRx4JK1cGS/5/+SXsVJIkSZIkgJwc6NgRPvgASpeGt96COnXCTiUVqEg0Go2GHWJXbrnlFj7//HM+/fTTnd4ejUapVq0aPXv25MYbbwQgPT2dKlWqMHToUNq2bZurj5ORkUFqairp6emkpKTssfxSaFasCDY//vFHOPxwmDQJUlPDTiVJkiRJxVc0CtddB089BYmJ8MYbwQISqYjIbb8W0ysjX3/9dRo2bMj5559P5cqVOfLII3n22We33b5gwQKWL19O06ZNt12XmppK48aNmTx58i7fb2ZmJhkZGTtcpCKlSpVgqX+VKvDNN8Eekq4WliRJkqTw3HdfUEQCDBtmEaliK6bLyJ9++omnn36aAw88kHfffZerr76a7t27M2zYMACWL18OQJUqVXZ4XJUqVbbdtjP9+vUjNTV126VGjRr590lIYdlvP3jnHUhJCVZGtmsH2dlhp5IkSZKk4ufZZ+H//i84fuIJuOiicPNIIYrpMjInJ4f69etz3333ceSRR9K5c2euvPJKBg0atFvvt3fv3qSnp2+7LFmyZA8llmLMEUfAf/4T7CU5bhxcfXVwaoAkSZIkqWCMGwdXXRUc33ordO8ebh4pZDFdRlatWpW6devucN3BBx/M4sWLAUhLSwNgxYoVO9xnxYoV227bmeTkZFJSUna4SEXWSSfBqFEQFxe8Gnf77WEnkiRJkqTiYdKkYBVkTg506gR9+4adSApdTJeRxx57LPPmzdvhuu+//5599tkHgFq1apGWlsbEiRO33Z6RkcHUqVNp0qRJgWaVYlrr1vD7iuK+fbfvUyJJkiRJyh8zZ8I550BmJrRsCU8/DZFI2Kmk0MV0GXn99dczZcoU7rvvPubPn8+oUaMYPHgwXbt2BSASidCjRw/69u3L66+/zuzZs+nQoQPVqlWjZcuW4YaXYs2VV8I99wTH110HL78cbh5JkiRJKqp++gmaN4eMDDjhhOBstYSEsFNJMSESjcb2BnJvvPEGvXv35ocffqBWrVrccMMNXHnlldtuj0aj3HHHHQwePJi1a9dy3HHHMXDgQGrXrp3rj5Hb0eNSoReNBvuT9O8PiYnw5ptw2mlhp5IkSZKkomPFCjj2WPjxRzjssOBU7XLlwk4l5bvc9msxX0YWBMtIFSs5OcFk7dGjoXRp+OgjOOqosFNJkiRJUuGXkRHs2//111CrFnz+OVStGnYqqUDktl+L6dO0JeWDuDgYNgyaNoUNG+DMM+FPe7NKkiRJkvIoMxNatQqKyEqV4N13LSKlnbCMlIqj5GQYOxYaNoTVq6FZM1i2LOxUkiRJklQ4ZWfDxRfDhx9CmTLw9ttw4IFhp5JikmWkVFyVLQtvvRX8D3LRoqCQ/O23sFNJkiRJUuESjcK118Krr0JSEowfDw0ahJ1KilmWkVJxVqkSvPdecOrAnDnQogVs3Bh2KkmSJEkqPO6+G55+GiIRGDECTj017ERSTLOMlIq7ffcN9jIpVy7YXPnCC2Hr1rBTSZIkSVLse/ppuPPO4Lh/fzj//FDjSIWBZaQkqFcPJkyAEiXgjTegc+fgVANJkiRJ0s6NGQNduwbHd9wB11wTbh6pkLCMlBQ47jgYPRri42HIEOjdO+xEkiRJkhSbPvwwGFgTjcJVVwVlpKRcsYyUtN0558DgwcHxAw/AY4+Fm0eSJEmSYs2MGXDuuZCVBeedF5yeHYmEnUoqNCwjJe3o8suhX7/g+IYbgg2YJUmSJEkwfz6ccQasXw8nnxz8vRQfH3YqqVCxjJT0VzffDD16BMeXXQZvvx1qHEmSJEkK3S+/wOmnw8qVcOSRMH48JCeHnUoqdCwjJf1VJAKPPALt2weTtc87D6ZODTuVJEmSJIUjPT1YEblgAey/f7BgIyUl7FRSoWQZKWnn4uKCQTbNm8PGjXDmmTB3btipJEmSJKlgbd4c7K//zTdQpQq8917wr6R/xTJS0q4lJsKrr0LjxrBmTXBKwpIlYaeSJEmSpIKxdStcdBF88kmwEvKdd2C//cJOJRVqlpGS/l7p0vDmm3DQQbB0KTRrBr/+GnYqSZIkScpf0ShcffX2vSH/8x844oiwU0mFnmWkpH9WoQK8+y5Urx6cqn322bBhQ9ipJEmSJCn/9OkDzz0XbGE1ahScdFLYiaQiwTJSUu7UrBkUknvtBVOmwPnnw5YtYaeSJEmSpD3vqafg3nuD40GDoHXrcPNIRYhlpKTcq1s3OGW7ZMlgetwVV0BOTtipJEmSJGnPeflluO664Piee+DKK8PNIxUxlpGS8qZJExgzBuLj4cUXoVevsBNJkiRJ0p7x/vvQoUOwX2S3bnDbbWEnkoocy0hJeXfWWfDCC8HxI4/AQw+Fm0eSJEmSdte0adCqVbAd1YUXwhNPQCQSdiqpyLGMlPTvdOgADz8cHPfqBUOHhhpHkiRJkv61efPgzDODQZ1Nm8KwYcHgGkl7nN9Zkv69nj3hppuC406dYMKEcPNIkiRJUl79/DOcfjqsXg0NG8LYsZCcHHYqqciyjJS0ex54ADp2hOxsuOAC+PzzsBNJkiRJUu789hs0bw6LF8OBB8Jbb0HZsmGnkoo0y0hJuycSgWefDfaR3LwZzj4b5swJO5UkSZIk/b2NG6FFi+Dvl6pV4b33oFKlsFNJRZ5lpKTdl5gIr7wCxxwDa9dCs2awaFHYqSRJkiRp57ZuDYbUfP45lCsH774L++4bdiqpWLCMlLRnlCoV7Bl5yCGwbFlQSK5eHXYqSZIkSdpRNAqdO8Mbb0CJEsHfMfXqhZ1KKjYsIyXtOeXLwzvvQM2a26fRrV8fdipJkiRJ2q53bxgyBOLjYfRoOO64sBNJxYplpKQ9q3r14BSHChVg2jRo0wayssJOJUmSJEnw2GPBEE6AwYPhnHPCzSMVQ5aRkva8gw4KptCVLh1sAn3ppZCTE3YqSZIkScXZiBFwww3Bcb9+cPnl4eaRiinLSEn5o1EjGDsWEhLgpZfg+uuDvVkkSZIkqaC9/TZcdllw3KMH3HxzqHGk4swyUlL+Of10GDYsOH7yyeDVR0mSJEkqSFOmwHnnBRO027eHRx6BSCTsVFKxlesyctmyZfmZQ1JR1a4dPP54cHzbbfDcc6HGkSRJklSMzJ0LZ50FGzdC8+bwwgsQ57osKUy5/g485JBDGDVqVH5mkVRUXXddMLEOoEsXGD8+1DiSJEmSioElS4KztdasgcaN4dVXISkp7FRSsZfrMvLee++lS5cunH/++axZsyY/M0kqiu69F664Ihhk07YtfPJJ2IkkSZIkFVW//grNmsHSpcGAzTffDAZsSgpdrsvIa665hlmzZvHrr79St25dJkyYkJ+5JBU1kQgMGgQtW0JmJpxzDsyaFXYqSZIkSUXNhg1w9tnBKdrVq8O770KFCmGnkvQ/kWg07+Nt+/fvz/XXX8/BBx9MQkLCDrfNmDFjj4UrKBkZGaSmppKenk5KSkrYcaSibdOm4BXKTz+FtDT44guoVSvsVJIkSZKKgi1b4Nxzg+nZe+0Fn30GdeuGnUoqFnLbryXs8pZdWLRoEWPHjmWvvfbi3HPP/UsZKUl/q2RJeP11OPHEYGXk6afD559D5cphJ5MkSZJUmOXkwOWXB0VkyZLBqdkWkVLMyVOT+Oyzz9KzZ0+aNm3Kt99+S6VKlfIrl6SirFw5eOcdOOYYmD8fzjgDPvoIXJksSZIk6d+IRuGmm2DECIiPhzFjoEmTsFNJ2olc7xnZvHlzbr75Zvr378/YsWMtIiXtnqpV4b33oFIlmDEDWrUK9pKUJEmSpLx66CF49NHg+IUX4Kyzws0jaZdyXUZmZ2cza9YsOnTokJ95JBUnBx4YnEJRpgx8+CFccglkZ4edSpIkSVJhMnQo3HxzcPzQQ2BvIcW0XJeR77//PtWrV8/PLJKKowYNYNw4SEwMTqXo3j04xUKSJEmS/smECdCpU3B8001w443h5pH0j3JdRkpSvmnaNNjbJRKBgQPhnnvCTiRJkiQp1n3+OVxwQXB2VceO8MADYSeSlAuWkZJiwwUXQP/+wfEdd8CgQeHmkSRJkhS75syBs8+GzZuD/SGffTZY3CAp5llGSood11wDt9++/fi118LNI0mSJCn2LFoEzZrB2rVwzDHwyivBtk+SCgXLSEmx5c47oUuXYN/Idu3go4/CTiRJkiQpVqxaBaefDsuWwSGHBHtGlioVdipJeWAZKSm2RCIwYAC0aQNZWXDuufD112GnkiRJkhS29euDU7K//x5q1IB33oHy5cNOJSmPLCMlxZ74+GCgzUknwbp10Lw5zJ8fdipJkiRJYcnKgtatYdo0qFAB3nsPqlcPO5Wkf8EyUlJsKlEC/vMfOOIIWLky2BNm+fKwU0mSJEkqaDk5cOml8P77wSnZb74JBx0UdipJ/5JlpKTYlZISnHqx//7w009BIblyZdipJEmSJBWUnBzo2hVeegkSEmDsWGjcOOxUknaDZaSk2FalSnAKRloazJoFJ5wAS5eGnUqSJElSftu6FTp2hEGDgr3lhw0LFihIKtQsIyXFvv32g0mTgk2q582D445zD0lJkiSpKMvMhPPPD/aS/31P+Xbtwk4laQ+wjJRUONSuDZ99BgceCIsWwfHHw5w5YaeSJEmStKdt2ABnnw3jx0NyMowbZxEpFSGWkZIKj5o14dNP4bDDgmE2J54IX34ZdipJkiRJe8ratXDaafDBB1C6NLz1FrRoEXYqSXuQZaSkwqVKFfj4Yzj6aFizBk49NXhbkiRJUuG2ciWcdBJMngx77QUTJ8Ipp4SdStIeZhkpqfDZay94//2giFy/Hpo3hzfeCDuVJEmSpH9ryZJgK6Zvvtm+AMGp2VKRZBkpqXAqUyYoIM89N9jculUrePnlsFNJkiRJyqsffgiGVH7//Y5bM0kqkiwjJRVeJUrAmDFw8cWwdWuwqfXgwWGnkiRJkpRbs2YFKyIXL95xaKWkIssyUlLhlpgIw4bB1VdDNApdusDDD4edSpIkSdI/mTIlGEq5YgUccUSwIrJGjbBTScpnlpGSCr+4OBgwAG65JXj7ppugT5+gnJQkSZIUez78EJo2DaZnH3MMfPQRVK4cdipJBcAyUlLREIlAv37BBaBvX7juOsjJCTeXJEmSpB29/jqceSZs2ACnnQbvvQflyoWdSlIBsYyUVLTccgsMHBiUk089BVdcEewnKUmSJCl8o0ZB69bbh1BOmAClS4edSlIBsoyUVPRcfTUMHw7x8TB0KLRtG/yyI0mSJCk8gwYFwyezs+GSS+CVVyA5OexUkgqYZaSkounii+G11yApKfj3nHOC00AkSZIkFbwHHtg+dLJr12DRQEJC2KkkhcAyUlLRde658OabUKpUsA9Ns2aQnh52KkmSJKn4iEbh1lu3D5u89dZgO6U46wipuPK7X1LR1rQpfPBBsCH255/DySfDqlVhp5IkSZKKvpwcuPba7UMmH3gA7r032N9dUrFlGSmp6GvSBD7+GCpXhq+/hhNOgKVLw04lSZIkFV1bt8Kll8KAAUH5+PTT0KtX2KkkxQDLSEnFw+GHw6efQo0a8N13cNxxMH9+2KkkSZKkoiczE84/H158MRgqOWIEXHVV2KkkxQjLSEnFR+3a8NlncOCBsGgRHH88zJkTdipJkiSp6NiwAc4+G8aPDyZljxsH7dqFnUpSDLGMlFS81KwZrJA87DBYvhxOPBG+/DLsVJIkSVLht3YtnHZasGd76dLw1lvQokXYqSTFGMtIScVPlSrBHpJHHw1r1sCppwZvS5IkSfp3Vq6Ek06CyZOD4ZEffACnnBJ2KkkxyDJSUvG0117w/vvBL0jr10Pz5vDGG2GnkiRJkgqfJUuCLZC++SZ44X/SpOCFf0naCctIScVXmTLw5ptwzjnBJtutWsHLL4edSpIkSSo8fvghGA75/fc7bokkSbtgGSmpeCtRAl59Fdq3h61bg821Bw8OO5UkSZIU+2bNClZELl4cDIv89NNgWKQk/Q3LSElKTIThw+GqqyAahS5d4OGHw04lSZIkxa4pU4JhkCtWwOGHwyefBCsjJekfFKoy8v777ycSidCjR49t123evJmuXbtSoUIFypQpQ5s2bVixYkV4ISUVTnFxMHAg3Hxz8PZNN0GfPkE5KUmSJGm7Dz+Epk2D6dlNmsBHHwV7RUpSLhSaMnLatGk888wzHPanvSeuv/56JkyYwJgxY5g0aRLLli2jdevWIaWUVKhFInD//dCvX/B2375w3XWQkxNuLkmSJClWvP46nHkmbNgQFJLvvRcMh5SkXCoUZeT69etp3749zz77LHv94Ydceno6zz//PI8++iinnHIKDRo0YMiQIXzxxRdMmTIlxMSSCrVbboEBA4Ljp56CK64I9pOUJEmSirNRo6B162D4Y8uWMGFCMBRSkvKgUJSRXbt25ayzzqJp06Y7XP/VV1+xZcuWHa4/6KCDqFmzJpMnT97l+8vMzCQjI2OHiyTt4Jpr4MUXIT4ehg6Ftm2DX7okSZKk4mjQILj4YsjOhksugTFjgmGQkpRHMV9Gvvzyy8yYMYN+v582+QfLly8nKSmJcuXK7XB9lSpVWL58+S7fZ79+/UhNTd12qVGjxp6OLakouPjiYNJ2UhK89hqcc05wOookSZJUnDzwAFx9dbCf+jXXBC/WJySEnUpSIRXTZeSSJUu47rrrGDlyJCX24CsuvXv3Jj09fdtlyZIle+x9SypiWraEN9+EUqWC/XCaNYP09LBTSZIkSfkvGoVbbw22MQLo3Rv69w+GP0rSvxTTP0G++uorVq5cSf369UlISCAhIYFJkybx5JNPkpCQQJUqVcjKymLt2rU7PG7FihWkpaXt8v0mJyeTkpKyw0WSdqlpU/jgAyhXDj7/HE4+GVatCjuVJEmSlH9ycuDaa7cPd7z/frjvvmDooyTthpguI0899VRmz57NzJkzt10aNmxI+/bttx0nJiYyceLEbY+ZN28eixcvpkmTJiEml1TkNGkCH30ElSrB11/DCSfA0qVhp5IkSZL2vK1b4dJLg6GOkQgMHAg33xx2KklFRExv8lC2bFkOPfTQHa4rXbo0FSpU2Hb9FVdcwQ033ED58uVJSUnh2muvpUmTJhx99NFhRJZUlB1xBHz6abBS8rvv4LjjghWTBxwQdjJJkiRpz8jMDIY3jh8fDHMcNgzatw87laQiJKZXRubGY489xtlnn02bNm044YQTSEtLY+zYsWHHklRU1akDn30WFJCLFsHxx8OcOWGnkiRJknbfhg1w9tlBEZmcDGPHWkRK2uMi0Wg0GnaIsGVkZJCamkp6err7R0rKneXL4fTTYfZsKF8e3n4bGjUKO5UkSZL076xdC2eeCZMnQ+nS8J//wKmnhp1KUiGS236t0K+MlKRQpKXBxx9D48awZk3wi9rHH4edSpIkScq7lSvhpJOCIrJcuWArIotISfnEMlKS/q3y5eH99+GUU2D9ejjjDHjzzbBTSZIkSbm3ZEmw9dA330CVKjBpEjiDQVI+soyUpN1RtmxQQLZoAZs3Q8uWMHp02KkkSZKkf/bDD8FQxu+/h5o1g2GNhx0WdipJRZxlpCTtrhIl4LXXoF072LoVLroInn027FSSJEnSrs2eHayIXLwYatcOisgDDww7laRiwDJSkvaExER48UW46iqIRqFzZ3jkkbBTSZIkSX81dSqceCKsWAGHHw6ffBKsjJSkAmAZKUl7SlwcDBwIvXoFb994I9x+e1BOSpIkSbHgo4+C4TS//QZNmgRvV6kSdipJxYhlpCTtSZEIPPAA3Hdf8PY990CPHpCTE2osSZIkiQkTgqGLGzZA06bw3nuw115hp5JUzFhGSlJ+6N0b+vcPjp98Eq64IthPUpIkSQrDqFHQqhVkZgZDFydMgDJlwk4lqRiyjJSk/NK1KwwfDvHxMHQotG0b/PInSZIkFaRnnoGLL4bsbLjkEhgzJhjCKEkhsIyUpPz0+y97SUnBxO1zz4WNG8NOJUmSpOLiwQe3D1m85prgRfKEhLBTSSrGLCMlKb+1agVvvAGlSsG770KzZpCeHnYqSZIkFWXRKNx2G9x8c/D279sIxVkDSAqXP4UkqSCcdhq8/z6kpsJnn8Epp8CqVWGnkiRJUlGUkwPdu28fqnj//cFxJBJuLknCMlKSCs4xx8DHH0OlSjBjBpxwAvz8c9ipJEmSVJRs3QqXXRasgoxEYODA7asjJSkGWEZKUkE64gj49FOoXh2++w6OOw5+/DHsVJIkSSoKMjPhggu2D1EcPhyuvjrsVJK0A8tISSpodeoEp2ofcAAsXAjHHw9z5oSdSpIkSYXZhg3QogWMG7d9eOLFF4edSpL+wjJSksKwzz7BCslDD4VffoETT4Rp08JOJUmSpMJo7Vo4/fRgj/LSpeGtt+Dcc8NOJUk7ZRkpSWFJS4NJk6BRI1izJhhq8/HHYaeSJElSYbJyJZx8MnzxBZQrFxSSp54adipJ2iXLSEkKU/ny8MEHwS+Q69fDGWfAm2+GnUqSJEmFwZIlwVDEmTOhcuXghe0mTcJOJUl/yzJSksJWtmxwKk2LFrB5M7RsCaNHh51KkiRJseyHH4JhiPPmQY0awRZAhx8edipJ+keWkZIUC0qUCDYZv+gi2Lo1+Pf++yEaDTuZJEmSYs2kSUERuXgxHHhgMByxdu2wU0lSrlhGSlKsSEyEF1+Ea64JSsjevaFNG8jICDuZJEmSYkE0Co8+GuwJuXIlHHFEsCKyZs2wk0lSrllGSlIsiY+H/v3hmWcgKQnGjQsG3Pz3v2EnkyRJUpjWr4e2baFnT8jOhosvhs8/hypVwk4mSXliGSlJsSYSgc6dg1e5q1cP9gFq1AjGjAk7mSRJksIwbx40bgyvvAIJCfDUUzB8OJQqFXYyScozy0hJilWNGsGMGXDKKbBhA1xwAdx0U7CnpCRJkoqH8ePhqKOCM2WqVg0mZnfrFryALUmFkGWkJMWySpXg3XehV6/g7YcfhtNOC/YIkiRJUtGVnQ233gqtWsG6dXD88cEL1cceG3YySdotlpGSFOsSEuCBB+DVV6FMmeDV8Pr1YcqUsJNJkiQpP6xeDWecAf36BW/36AETJ0JaWqixJGlPsIyUpMKiTRv48ks46CD4+Wc44QQYNCiYqihJkqSiYfp0aNAA3n8/2BNy1Ch47DFITAw7mSTtEZaRklSYHHxwUEi2aQNbtsDVV8Nll8GmTWEnkyRJ0u56/nk47jhYvBgOOCA4E+aii8JOJUl7lGWkJBU2ZcsGk7UffBDi4mDYsGDvoAULwk4mSZKkfyMzEzp3hk6dguNzzglWSNarF3YySdrjLCMlqTCKRILJ2u+/DxUrwtdfQ8OGwbAbSZIkFR6LFwfDaZ59Nvgdr29fGDcOUlPDTiZJ+cIyUpIKs1NOCaYqNmoEa9YEG5337Qs5OWEnkyRJ0j+ZODHYH3LaNChfHt5+G267LTj7RZKKKH/CSVJhV6MGfPIJdOkSDLPp0wdatoS1a8NOJkmSpJ2JRuGBB+D004PJ2UceCV99Bc2ahZ1MkvKdZaQkFQXJycFk7RdeCI4nTICjjoLZs8NOJkmSpD/KyAiGEd5yS3A2y6WXwuefw777hp1MkgqEZaQkFSWXXRb8MrvPPjB/Phx9NLz0UtipJEmSBDB3brC9zrhxkJi4/cXkkiXDTiZJBcYyUpKKmgYNgtN8TjsNNm6Edu2gRw/YsiXsZJIkScXXmDFBETlvHuy9N3z6abDNTiQSdjJJKlCWkZJUFFWoEGyAfuutwdtPPBEMu/nll3BzSZIkFTdbt8JNN8EFF8D69XDyycEAwsaNw04mSaGwjJSkoio+Hu69F8aPh5QU+OyzYNXk55+HnUySJKl4WLkyGFLz8MPB2zfdBO+9B5Urh5tLkkJkGSlJRd2558K0aXDIIcHKyJNOgqeeCqY4SpIkKX9MnRq8EPzRR1CmTHCa9oMPQkJC2MkkKVSWkZJUHNSuDVOmwIUXBqcKde8Ol1wS7CkpSZKkPScaDQbTHH88LF0KderAl1/CeeeFnUySYoJlpCQVF2XKBJO1H3ssOIV75Eho0iSYui1JkqTdt2kTXH45XH11MDywdeugiDz44LCTSVLMsIyUpOIkEgkma3/4IVSpArNmQcOG8MYbYSeTJEkq3BYsgGOPhaFDIS4O7r8fXn012LtbkrSNZaQkFUcnnABffRWsjExPhxYt4I47ICcn7GSSJEmFz7vvBi/wfv01VKwYDKm5+ebghWBJ0g4sIyWpuNp7b/j4Y+jaNXj77rvh7LNhzZpQY0mSJBUaOTnQty+ccUbwO9RRRwUv+J56atjJJClmWUZKUnGWlAT9+8Pw4VCiBLz9dvCq/syZYSeTJEmKbWvXQsuW0KdPMLSmc2f45BOoWTPsZJIU0ywjJUnBZO3Jk6FWrWC/oyZNgoJSkiRJfzV7drAKcsIESE6G55+HZ54JXtyVJP0ty0hJUuCII4LTis48EzZvho4dg1O4s7LCTiZJkhQ7XnoJjj4a5s8PVkF+9lkwQVuSlCuWkZKk7fbaK3iF/447grcHDoSTToKffw41liRJUui2bIEePaBdO9i4EU47LXght2HDsJNJUqFiGSlJ2lFcHNx5J7zxBpQrF5y+Xb8+TJoUdjJJkqRwLF8eDKV54ong7VtvDfbarlgx3FySVAhZRkqSdu6ss2D6dDjsMFi5MvgF/NFHgw3aJUmSiovPPw9emP30UyhbFsaNg3vvhfj4sJNJUqFkGSlJ2rX99w9WRl58MWRnQ8+ecNFFsH592MkkSZLyVzQKTz0VbFnzyy9Qt27wQm3LlmEnk6RCzTJSkvT3SpUKJms/9RQkJMDo0cGm7d9/H3YySZKk/LFxI3ToAN27w9atcMEFMHUq1K4ddjJJKvQsIyVJ/ywSgW7d4OOPoWpV+PbbYLP28ePDTiZJkrRn/fgjNGkCI0YEp2I/8gi8/DKUKRN2MkkqEiwjJUm5d+yxMGMGHH88rFsHrVoFG7hnZ4edTJIk6V+bvmw6pww7hemjH4MGDWDWLKhcGSZOhBtuCF6YlSTtEZaRkqS8SUsLfjHv0SN4u18/OOMMWL061FiSJEn/1vCZw/ho4Ue8OPQGSE8PtqSZMQNOPDHsaJJU5ESiUceiZmRkkJqaSnp6OikpKWHHkaTC46WXoFOnYF+lmjVh7NhgNYEkSVKMW7R2Eas3riaSkUHzEc1ZlZhFpQ3wTtYFRK+/noqpVdmn3D5hx5SkQiO3/ZplJJaRkrRbZs+G1q1h/nxIToYBA+CKK8JOJUmS9Lcid/3h1OsosJMzsaN3FPs/lyUp13Lbr3matiRp99SrB9OmQYsWkJkZrJTs3Dk4liRJilEvVLiCuJz/vfGnIjIhLoERrUYUeCZJKg4sIyVJu69cuWCydt++wQbvzz4bDLlZvDjsZJIkSTvKymLqdefx4HfPk7OLv4indppK+8PaF2wuSSomLCMlSXtGXBzcdhu8/TaULx+slmzQIBh2I0mSFAM2L/qRW66sxTHlXuO7SlAhWhKAuP/9aRznn8iSlO/8SStJ2rOaNYPp0+HII4MJ26efDg88AG5RLEmSQjRtwjM0eLQOD+y3jJw4uLj8SXx0zVTSyqTRoFoDBp01iAbVGpBWJo3KpSuHHVeSiiwH2OAAG0nKF5s2wTXXwNChwdutW8OQIeDPWUmSVIAyt2zm7odb8MDmD8iOg8qbE3jm9CdpefLVwe1bM0mKTyISiRCNRsnKziI5ITnk1JJU+DjARpIUrpIl4YUX4OmnITERxo6FRo1g7tywk0mSpGJixo+f0fD2NO7LCorItuv24dueP24rIgGSE5KJRIIJNpFIxCJSkvKZZaQkKf9EInDVVfDpp7D33jBvXlBIvvpq2MkkSVIRlpWdxR2vdaPR8OOZUyKdShvg1TKX89JDC6hYsWbY8SSpWLOMlCTlv8aNYcYMOOkkWL8ezj8fevWCrVvDTiZJkoqYmctn0ujhOtw9ZwDZcXD+jyX49owJtOn5fPBCqSQpVJaRkqSCUbkyvP8+3Hhj8PZDDwXDbVauDDeXJEkqErZkb+Guj+7gqEEN+GbzQipshNGz6vDKAz9R6eSzw44nSfofy0hJUsFJSAhKyDFjoEwZ+OgjqF8/OI1bkiTpX5q1YhaNn67PnZ/czdZIDq3/C99mdeKCl2dD1aphx5Mk/YFlpCSp4J13Hnz5JdSpAz//DCecAF26wG+/hZ1MkiQVIltztnLvpL40HFSfr3+dQ/mN8NLrSbx67kiqPPZsMERPkhRTLCMlSeE4+OCgkLziiuDtwYOD615+GaLRcLNJkqSYN2flHI5+6nD+7+M+bCGbc7+Db784grbDviLSrl3Y8SRJu2AZKUkKT0oKPPccTJoEBx0EK1bARRfBmWfCggVhp5MkSTFoa85W+n14Fw0GHsFXa//LXpvgxTeTGdfkCdI+ng6HHhp2REnS37CMlCSF74QTYOZMuOsuSEqCd96BQw6BBx+ELVvCTidJkmLE3FVzOebRQ7j10zvJimRz9jyY81NzLh47n0j37hAfH3ZESdI/sIyUJMWG5GS4/XaYNQtOOgk2bYKbb4aGDWHq1LDTSZKkEGXnZPPQu7dzZP9Dmbbhe1I3w7CP9+L1C8ZR7ZW3oXr1sCNKknLJMlKSFFvq1IEPP4QhQ6B8+aCcbNIEunWD9PSw00mSpAI2b+Vcjru/Nr2m3ENmXA5n/ADfbrqcDq8vItKyZdjxJEl5ZBkpSYo9kQhceil89x106BAMtBkwAOrWhddec8CNJEnFQHZONo+M78UR/Q9lypafSNkMz8+owZvdp7L3489D2bJhR5Qk/QsxXUb269ePo446irJly1K5cmVatmzJvHnzdrjP5s2b6dq1KxUqVKBMmTK0adOGFStWhJRYkrRHVaoEw4bBBx/AAQfAsmVw3nlw7rmweHHY6SRJUj75YdkcTrh7X2785iE2x+dw+oI45pT/Py5/7ScijRqFHU+StBtiuoycNGkSXbt2ZcqUKbz//vts2bKF008/nQ0bNmy7z/XXX8+ECRMYM2YMkyZNYtmyZbRu3TrE1JKkPe7UU2H2bPi//4PERJgwIVgl+dhjsHVr2OkkSdIekhPN4YkXu3L404fxRWQpZTPh2QX1eOfOH6lx0z2QkBB2REnSbopEo4XnXLdVq1ZRuXJlJk2axAknnEB6ejqVKlVi1KhRnHfeeQB89913HHzwwUyePJmjjz46V+83IyOD1NRU0tPTSUlJyc9PQZK0u779Frp0gc8/D96uXx8GD4YGDcLNJUmSdsv8+V9y+fMt+LTESgBOXZrE8yc9xj7trg62cJEkxbTc9msxvTLyz9L/N7igfPnyAHz11Vds2bKFpk2bbrvPQQcdRM2aNZk8efIu309mZiYZGRk7XCRJhcQhh8AnnwQFZLlyMGMGNGoE118P69eHnU6SJOVRTk42/ftfwuFDG/NpiZWUzoKnM07g/YdWsE/7aywiJamIKTRlZE5ODj169ODYY4/l0EMPBWD58uUkJSVRrly5He5bpUoVli9fvsv31a9fP1JTU7ddatSokZ/RJUl7WlwcXHklzJ0LbdtCTg48/nhw6vaECWGnkyRJubTg6w85tWdFrv11BBsT4eSVpZl9yqtc9cgkIn/6O0+SVDQUmjKya9euzJkzh5dffnm331fv3r1JT0/fdlmyZMkeSChJKnBpafDSS/D221CrFixZAuecA23awM8/h51OkiTtQk7mZp6++xzqvXoqH5dbS6ksGJBwDh889iu1Tm0TdjxJUj4qFGVkt27deOONN/joo4+oXr36tuvT0tLIyspi7dq1O9x/xYoVpKWl7fL9JScnk5KSssNFklSINW8Oc+ZAr14QHw9jx8LBB8OAAZCdHXY6SZL0BwvfH8Np11fgmugENiTBCel7MfuCj7jmtv8Ql5QcdjxJUj6L6TIyGo3SrVs3xo0bx4cffkitWrV2uL1BgwYkJiYyceLEbdfNmzePxYsX06RJk4KOK0kKU6lS8MADwR6SjRvDunXQrRsceyx8803Y6SRJKvaia9YwuMfx1PvoAj6sspGSW+CJSpfw0cOr2O/wk8KOJ0kqIDE9Tfuaa65h1KhR/Oc//6FOnTrbrk9NTaVkyZIAXH311bz11lsMHTqUlJQUrr32WgC++OKLXH8cp2lLUhGTnQ3PPAO9e0NGRrBa8oYb4I47oHTpsNNJklS8RKMsfrE/nT7pyfs1tgBwXGYVhnR6gwP2axhyOEnSnpLbfi2my8jILqamDRkyhEsvvRSAzZs307NnT1566SUyMzNp1qwZAwcO/NvTtP/MMlKSiqhly6B7d3jtteDtffeFp58OTuuWJEn5Lvrjj7xw17lcX/1b1iVDia0R+h3clWvbPk58XHzY8SRJe1CRKCMLimWkJBVxEyZA167BgBuACy8Mpm/n4YUrSZKUB1u2sPSRO7hy7gO8s18OAE2owdDOb1G76qEhh5Mk5Yfc9msxvWekJEl7RIsW8N//wvXXQ1wcjB4dDLgZPBhycsJOJ0lSkRKdPJmhrffj0PR+vLNfDsk5cTx0RC8+7bPAIlKSZBkpSSomypSBRx+FadOgQQNYuxa6dIETToBvvw07nSRJhV96Osu6daRF/2O4rOFS0ktA46T9mNltDjee+4CnZUuSAMtISVJxU78+TJkCjz0WDLP5/HM44gi47TbYtCnsdJIkFT7RKNExY3jxnH04pMxw3qwNSdE4HmhyO5/dPI+DKh0cdkJJUgyxjJQkFT8JCdCjB8ydC+ecA1u3wn33wWGHwQcfhJ1OkqTCY9Eifml9GueOu4AOp6SztiQ0LFOHr7vOptfpd5EQlxB2QklSjLGMlCQVXzVqwPjxMHYsVKsG8+fDaafBJZfAqlVhp5MkKXZt3Ur0kUcY1aY2h9SZyIQ6kBiN494T7mLy9XOoW6lu2AklSTHKMlKSVLxFItCqVbBKslu34O0RI+Cgg2DIEIhGw04oSVJsmT6dFccfSZtpN9K+RRa/lYT65ery1dUzufXk210NKUn6W5aRkiQBpKTAU08F+0kefjisWQOXXw4nnwzz5oWdTpKkUE1fNp1TXjiRaT3bMvqyRhxywhzGHQyJxHPPSXczpdtM6lWpF3ZMSVIhYBkpSdIfNWoUTNx+8EEoWRImTQr2krzzTsjMDDudJEmhGD7uTj5a8gnttoym7XlRfi0FR1Q4lGldvuL/TuxDYnxi2BElSYWEZaQkSX+WmAg33QT//S+ccQZkZcFddwUrJidNCjudJEkFYtHaRXw18y2mtzuJYUvfBGB+BYgnjivrX8krF43l8LTDQ04pSSpsItGom2FlZGSQmppKeno6KSkpYceRJMWSaBTGjIHu3WHFiuC6yy6Dhx6CChXCzSZJUn7JzibS95/3fozeUez/nJQk/U9u+zVXRkqS9HciEbjgAvjuO+jSJbhuyJBgwM2IEQ64kSQVPTNnMqPZYRy6Ytd3SYhLYESrEQWXSZJUZFhGSpKUG+XKwaBB8PnncMghsHo1XHIJnH46zJ8fdjpJknbfhg3M79WJtvfVp8Hx/2VOFUjYxZ+MUztNpf1h7Qs4oCSpKLCMlCQpL445BmbMgHvvhRIl4IMP4NBDg7ezssJOJ0nSv7L8PyPoekUaB5d4ntGHRIlEof0BrXmt7TgA4v73p2Ocf0JKknaT/yeRJCmvkpLg1lth9mxo2jSYsv1//wf16wcrJyVJKiQyFn1Pn251OeDLSxh48Hq2xsMZKQ34+qqZjGj/GvWr1ietTBoNqjVg0FmDaFCtAWll0qhcunLY0SVJhZQDbHCAjSRpN0SjMGoUXH89rFoVXNe5M9x/P+y1V7jZJEnahcysTTz9VAfuXfkaq0sFfxI2yk7jgYte4KSDz9jxvlszSYpPIhKJEI1GycrOIjkhOYzYkqQY5gAbSZIKQiQC7dvD3Llw+eXBdYMHw8EHw+jRDriRJMWU7JxsXnyzH3Vu34vr17/K6lJRaq9P5rWGDzHlrmV/KSIBkhOSiUQiAEQiEYtISdJusYyUJGlPqFABnn8ePv4Y6tSBFSugbVs46yxYsCDsdJKkYi4ajfLWnHEceVdVOky/lUUlM6m6PsLgUhfy7X3ptD7rxm2FoyRJ+ckyUpKkPenEE+Gbb+DOO4O9Jd9+O5i+/dBDsGVL2OkkScXQlKVTOOnxwznrtdbMjltF6mbot+xg5l/zHVfe9DIJia50lCQVHMtISZL2tORkuOMOmDULTjoJNm2CXr3gqKNg8uSw00mSiom5q+bSetiZNHm+CZ9kzCZ5K9z0TRl+ajCcW575L6Vq1Q47oiSpGLKMlCQpv9SpAx9+CEOGQPnywYrJY44JJnBPnOh+kpKkfLE0YymdRlzAoQMOYdzCt4nLgcu/hh/WX8aDQ3+m/HmXhB1RklSMWUZKkpSfIhG49FL47rtgwE18fFBENm0KjRvD2LGQkxN2SklSEfDbpt+4edRlHPjIvjz/4xhyIlHO/Q5mf3E4z9/2JTUeewH+ZrqpJEkFwTJSkqSCUKlSMODmxx+hWzcoUQKmTYM2baBu3WD1ZFZW2CklSYXQpi2beHDE1ex3X2Ue/GEom+OyOX4RfD6nMeOvnkTd974OtgqRJCkGRKJRzxHLyMggNTWV9PR0UnylUJJUEFauhCefhAEDYO3a4Lrq1aFnT+jUCcqUCTWeJCn2bc3ewtAXb+DOeYP5uUTwgtahK+D+rOM5s+sTRI48MuSEkqTiJLf9mmUklpGSpBBlZMDgwfDoo/DLL8F15ctD9+7BCsoKFcLNJ0mKOdEtWxj/wk3c+v0gvkvJBKBmOtyTcxLtrxlEfO06ISeUJBVHlpF5YBkpSQrd5s3w4ovw4IMwf35wXenS0Lkz3HBDsGpSklS8bdrEpGdu5ZYfnmZK5aCErLARbos/mauvfp4SNWqFHFCSVJxZRuaBZaQkKWZkZ8Nrr0G/fjBzZnBdYiJccgn06hVM6JYkFS9r1zJrwO30/vEZ3tonOB271Ba4PulEbuo8jNS0fUIOKElS7vs1B9hIkhRL4uPhggtgxgx45x048UTYsgVeeAEOPhjOOw+mTw87pSSpICxfzsLeV9OhS2WO2PIUb+2TRXwOXJ18HPO7z6fv7R9bREqSCh3LSEmSYlEkAs2awccfwxdfwDnnQDQarJo86ig47TSYODG4TpJUtPz0E6uuuZQenapTJ2EQL9bdQjQCF5RuzNxrvmXgLZ9StfL+YaeUJOlfsYyUJCnWNWkC//kPzJkTnK4dHw8ffABNm0LjxjB2LOTkhJ1SkrS7Zs1iffvzuefyA9i/3DCeOCqbrAQ4tezhTLtiKqNvnMKBVeqGnVKSpN1iGSlJUmFxyCEwfDj8+GMwabtECZg2Ddq0gbp1YcgQyMoKO6UkKa8++4yss89gQKfDOaDaq9x+cpR1yVC/TG3ea/8uH9wwk4bVG4WdUpKkPcIBNjjARpJUSK1cCU8+CQMGwNq1wXXVq0PPnnDllcE0bklSzJm+bDq93u/FgyVaUP+pV3kl/Qv+7xT4sXxw+/6la9C3+YNccMgFxEVcPyJJKhycpp0HlpGSpEItIwMGD4ZHH4VffgmuK18euncPVlBWqBBuPknSdlu30r3/WTyV/h4t58LiVJhRLbipSomK3H7KXXSq34mk+KRwc0qSlEeWkXlgGSlJKhI2b4YXX4QHH4T584PrSpeGzp3hhhuCVZOSpFAsWj6P1aOHEBk+nKan/cJvJbffViqhJFc1vJq7Tr6LMkllwgspSdJusIzMA8tISVKRkp0dTN3u1w9mzgyuS0wMht/06gV16oQaT5KKlfR0GDiQSNat/3jX6B3F/k8zSVIhltt+zQ1IJEkqauLj4YILYMYMeOcdOPFE2LIFXngBDj4YzjsPpk8PO6UkFW3Ll8Mtt7CyTnX6vnMr5Tbu+q4JcQmMaDWi4LJJkhQiy0hJkoqqSASaNYOPP4YvvoBzzoFoNFg1edRRcNppMHFicJ0kac/46Se4+mq+OromHec9QI0r19PnFFhbCsqXKL/Th0ztNJX2h7Uv4KCSJIXDMlKSpOKgSRP4z39gzpzgdO34ePjgA2jaFBo3hrFjIScn7JSSVHjNmsWWdm0Zfe4BHJs1iIaXbWH4EZCVAI33bsyIViN4q/1bAMT978+wOP8ckyQVQ/7fT5Kk4uSQQ2D4cPjxx2DSdokSMG0atGkDdevCkCGQlRV2SkkqPD77jFXnNuXeboezb9XRtD0vyhc1ITGSQPt67ZlyxRSmdJpC+8Pas3fK3qSVSaNBtQYMOmsQDao1IK1MGpVLVw77s5AkqcA4wAYH2EiSirGVK+HJJ2HAAFi7NriuenXo2ROuvDKYxi1J2lE0Cm++yYwB/8dTyd/wUj3ITAhuqpJcgauO7kaXBl2oWrbqXx6auTWTpPgkIpEI0WiUrOwskhOSC/gTkCRpz3Oadh5YRkqSir2MDHjmGXj00WDoAkD58tC9e7CCskKFcPNJUizYupUtL49k3Mg+PFltCZ/X3H7TURUO47oTenFe3fMsFyVJxZJlZB5YRkqS9D+bNwencT/4YHAqNwSrIzt3hhtuCFZNSlJxs2kTq55/kmffu5+BB67l5//9yZAQjeOCA86l+0k307h643AzSpIUMsvIPLCMlCTpT7Kz4dVX4f77YebM4LrExGD4Ta9eUKdOqPEkqUCkp/N1///jqdnPMerAzdtOxa5Maa5qdA1djutBtbLVws0oSVKMsIzMA8tISZJ2IRqFd98NSslJk4LrIhFo3Rp694YGDcLNJ0n5YOuypYzr342nVr3Bp9Wzt13fIL4G1zW7nQuOvMRTsSVJ+hPLyDywjJQkKRcmTw5Kyddf335d06ZBKXnyyUFJKUmF2Or/TufZF7oxMDqVpb+fip0D55c9mmvbPMjR+x5HxJ91kiTtlGVkHuTmi5WTk0NWVlYBJyu8kpKSiIuLCzuGJCk/zJkT7Ck5alRwOjdAo0Zwyy1w7rngz39JhczMT17hqfG9GVn6p22nYlfKTOCqfVpzVdtHqJbqfrmSJP0Ty8g8+KcvVlZWFgsWLCAnJyeEdIVTXFwctWrVIikpKewokqT8snAhPPIIPPdcMPgG4KCD4OaboV078P8BkmLE9GXT6fV+Lx487UEaVmsIwNacrfxn/P08+fljfJKyZtt9G6xPoXvDrlzQug8lEkuGFVmSpELHMjIP/u6LFY1GWbx4MVu2bKFatWqu9suFnJwcli1bRmJiIjVr1vRUFkkq6lauhCefhP79IT09uK5GDbj+emjbFqpWDTefpGKv+9vdeerLp+jeqDu3N7qR5169lQELXmFJyeDMp4RsOG99Ta496y6anNLR318lSfoXLCPz4O++WFu2bGH+/PlUq1aN1NTUkBIWPunp6SxbtowDDjiAxMTEsONIkgpCRgY88ww8+igsX779+qOPhlatoGVLqF07tHiSipdFaxexeuNqIpEIZ7zYjJWbVlMiJ46c7Byy/vfraaUN0CXnSK7q8CR7H3ZcuIElSSrkLCPz4O++WJs3b2bBggXsu+++lCzpaRq5tWnTJhYuXEitWrUoUaJE2HEkSQVp82YYPhxeeAGmTt3xtoMP3l5MNmzo0BtJ+SZy1x9+vkSBnfy42XTZj5SouV+BZZIkqSjLbRnpOce55KkaeePXS5KKsRIloHNnmDIFfv4Znn4aTj8dEhJg7ly4775g4E2NGtCtG3zwAWzZEnZqSYVdNApz5vDbPbfxQqt9OXQFQQkJfykiE+ISGNFqhEWkJEkhcGUkuVsZ6Qq/vPHrJkn6i7Vr4e23Ydy44N/167ffVq4cnH12sGKyWTMoUyakkJIKlexsmDKF9eNf4fWZo3m50greOQC2xP/9w77q/BX1q9YvmIySJBUTroxUrlxyySXcd999eXrMO++8wxFHHOF0cUlS3pQrBxddBK+8AqtWwZtvQqdOULlyUFSOGAHnnQeVKsE55wSnea9aFXZqSbEmMxPeeotNnS/nteMrcMETx1E5+UnaH7eCCXWCIrJeYnXubdSb8ReOByDuf3/2xPnnjyRJofP/xkVQNBqladOmNGvW7C+3DRw4kHLlyrF06VK++eYb3nrrLbp37w7Ahg0b2H///bnhhht2eMzChQtJSUnh2WefBaB58+YkJiYycuTI/P9kJElFU4kScOaZ8OyzsGwZfPYZ9OwJ++0X7Dk5YQJccQWkpcGJJ8Jjj8GCBWGnlhSW9HR46SWyLjyPNxuV45LnzqJyxSGc1yydMYfApkQ4MKkqfY6+mTlXz2HWrUu49Yz7aFCtAWll0mhQrQGDzhq07e3KpSuH/RlJklRseZo2RfM07SVLllCvXj0eeOABunTpAsCCBQuoV68eTz/9NJdccgmdOnUiISGBQYMGbXvcJ598wqmnnsqHH37I8ccfTzQa5ZRTTqFEiRK8/fbb2+43YMAAhg4dyrRp03b68Qvr102SFLJoFL79NjiVe/x4mDFjx9sPPzw4lbtly+DYPYqlomvZMnj9dbLHj+Pjnyby8kHZvFYXfvvDTMmaSZW58MiLaXt4e45MO3Kn+5Znbs0kKT6JSCRCNBolKzuL5ITkAvxEJEkqHpymnQd5KiOjUdi4MZygpUrl6Y+uYcOG0a1bN2bNmsW+++7LqaeeSrly5Rg7dizZ2dlUqFCBkSNHctZZZ+3wuBtuuIHXX3+db775hmeffZa77rqLOXPmsPfee2+7z+LFi9lnn32YP38++++//18+tmWkJGmPWLw4KCXHj4dPPgn2h/vdvvtuLyaPPTYYkCOpcJs3D8aPJ2f8OCb/PJWXD4Uxh8CKP2wjm5ZcgQsOb8eFh7bl6OpHExfxZC9JkmKBZWQe5KmM3LAhvE3116+H0qXz9JCWLVuSnp5O69atueeee/j222+pVKkSX3/9NfXr12f58uVUqVJlh8ds2rSJI488koMPPph3332XwYMHc/HFF//lfaelpXH//fdz6aWX/uU2y0hJ0h7366/wxhtBMfnuu7Bp0/bbKlaEFi2CYvK006BkyV29F0khm75sOr3e78WDpz1Iw7T6MH06jB9PdPw4vkr/jpcPhVcOgSWp2x9TPimV8w69kLaHtuWEfU4gPu4fJtRIkqQCl9sy0iUERdzgwYM55JBD+OSTT3jttdeoVKkSAIsWLSI+Pp7Klf+6X07JkiV54oknaN68OWecccZOi0iAatWqsWjRonzNL0nSNhUqQMeOwWXjRnjvvaCYnDABVq+GIUOCS6lS0Lx5UEyedRaULx92ckl/MPzroXy08CNefOJyGo5cw5wtP/PyofDyafDjH75dyyaWoVXd1rQ9pC1N92tKYnxieKElSdIeYxmZV6VKBSsUw/rYeVS5cmW6dOnC+PHjadmy5bbrN23aRHJy8k731QF4/vnnKVWqFLNnzyY9PZ3U1NS/3KdkyZJsDOuUdUlS8Vaq1PZTtLduhU8/3X469+LFMHZscImPh5NOCu537rlQo0aYqaVia9Gy/7J64gQiH09idMV3oBQ8nzCbN9rAT38oIEsmlKRFnRa0PaQtZxx4BiUSPMNGkqSixjIyryKRPJ8qHbaEhAQS/rSPVsWKFdm4cSNZWVkkJSXtcNvo0aN54403mDx5MhdddBHXX389L7zwwl/e75o1a7attJQkKTQJCXDyycHl8cfh66+3F5OzZ8PEicHl2muhYcPtJWbdug7AkfLTypXByuXx49m34RvBdTWB/20StSFpxyJyVOtRtKjTgjJJIW2JJEmSCoS7PRdTRxxxBAD//e9/d7h+xYoVdO3alb59+3L44YczdOhQhg8fvsMkbQj2hPzxxx858sgjCyqyJEn/LBKB+vXh7rth1iyYPx8efhiOOy64bfp0+L//g0MPhTp1oFcv+OILyMkJO7lUNPz0Ezz6KNETjufbw9J49PlONC/3Bolb/3CfP70GkBCXwIhWI7io3kUWkZIkFQOujCymKlWqRP369fnss8+2FZMAnTt35uCDD6ZHjx4ANGrUiJtuuonOnTszZ86cbadrT5kyheTkZJo0aRJCekmScmn//aFnz+CyYsW2VVq8/z788AM89FBwqVIlOI27ZUs45RRITg47uVQ4RKMwcyaMH8/qt17lg83/5d394b2jYNmpO961YqmKrN64+i/vYmqnqdSvWr9g8kqSpNC5MrIY69SpEyNHjtz29vDhw/nggw8YMmQIcXHbnxp33XUX5cqV4/rrr9923UsvvUT79u0p9S/2sZQkKRRVqkCnTsFE7tWr4ZVXoF07SEkJisrBg+HMM6FSJWjbFl5+GTIywk4thWL6sumcMuwUpi+b/tcbt26Fjz8mq8e1TDq6KrfdWJ+jfrmbymf9l4vOg6FHwrIUKBGfTLP9m/HI6Y8w5+o5vNP+HQDi/vcnSJx/ikiSVCxFotFoNOwQYfu70eObN29mwYIF1KpVixIlitYG2ps2baJOnTqMHj06TyscV69eTZ06dZg+fTq1atXa6X2K8tdNklTEZGXBxx9v32fyl1+235aYCKeeun0ATlpaOBmlAtb97e489eVTdG/UnSfOeAI2bSL63nvMf2M47/74Du+lbeSjfWH9nxYR16tQl2a1z+T0/U/nuJrHUTKx5LbblmYs5ahnj6JGSg2uOPIKnv/6eZZkLGHaldOonlK9YD9BSZK0x/1dv/ZHlpEU3zIS4OOPP2bdunW0aNEi14+ZPn06P/74IxdeeOEu71PUv26SpCIqJwemTQtKyXHjYN687bdFInD00UEx2aoVHHhgWCmlfLFo7SJWb1xNJBLhjJFnsHLDSirGleXmpTX5Yt13TEvLZmnqjo+plJDK6Qc25/Q6Z3LafqdRtWzVv/0YmVszSYpPIhKJEI1GycrOIjnBbREkSSoKLCPzoDiXkfnFr5skqUj47rvtKyanTt3xtrp1txeTDRo4mVuFXuSuPzyHowSDZn7/938So3Ect9fhnH7keTQ78AwOTzucuIinW0uSJMvIPLGM3PP8ukmSipyff4bXXw+KyQ8/DPbN+1316tC4MRx00PZLnTpQtmxocaW/tWULW3+Yx+yZ7zFlwSdM/m027yUuZkWJrTu9exwRrj/6Bu48+U4nXkuSpJ3KbRnpNG1JkqTc2HtvuPrq4LJ2Lbz1VlBMvvUWLF0aXP6sevUdC8rfL9WquZJS+WL6sun0er8XD572IA2rNYT09GCF73ffsfy76Uz55Usmb57PlFJrmF4VNib974H/0JtP6zzdideSJGmPsIyUJEnKq3Llgknc7drB5s3w6afw7bfbSh+++y6Y0P17SfnBBzs+vmzZnZeUBxwASUk7/ZDSLuXkBM+z775j+Ix7+SjzE4be2ZLsLzczpcSvTK4BU6rDonLAn2YPpm6Jp3FWZZqUOYijazQh+fAGnDKhDXHEkUPOtn8lSZL2FMtISZKk3VGiBJx2WnD5ozVrggE4fywov/sOfvwR1q0LBuVMm7bjY+LjYb/94OCD/1pU7rVXwX1OCtVfVjf+bvNm+OGHvzyn5q38L9P22sz88vDcsUASDKj2MwNa7fh+I1E4NKEaR1c8nCYHnsrR9c6gTqWDdtjzcWnGUtLKpP1l4nXl0pUL5pOXJElFnntG4p6R+cGvmyRJu5CVBfPn/7Wk/O67oKTclcqVd15S1qwJcQ4QKUq6j72Sp2Y/R/fSp/LE8iO2PT+yF/7ET6lRZleB2ZXZ9u/3Ff/5fU7sMJGjqh1F2eR/3sfUideSJOnfcM9ISZKkWJSUFEzirlt3x+ujUfjlF5g7968l5dKlsHJlcJk0acfHlSwZDMv5c0lZu3Zwm0K305WO2dmwcOG2/8aLfpjG6sXziCxYwOiz06EMDF89kYTZE/mhPCw8DeZXgE2JefvYCXEJDD13KKfUOiXXj/lj8RiJRCwiJUnSHmUZKUmSFAsikWCwTbVqcOqpO962bt3OT/n+/nvYtAlmzgwuf35/++yz89WUlSo5QGcP2OXp1H+0YQPDP3iYjxZ+xIvPdKXh3H22/bdbE5fJ/PIwvzy0bwNUBRoD/ztvaW1JePSYHd9diYQSHFLpEOpVqUe9yv+7VKnHzxk/0/DZv2aY2mmqg2ckSVJMsYyUJEmKdWXLQsOGweWPtm4NVtf9eTXl3Lnw22/BbQsXwttv7/i4vfbaeUlZqxYkFL1fD/9cGu6sRNxVsfh3hePwb4YHJeM3w2kY2XuH/waLFnzN8qXzWL1+JSNaAyXhua1fMi/pS5YcD0vPgoxd7WTzp544LhJHt6O6cc1R13BA+QOIj4v/y0OWrVsW3NfBM5IkKcYVmd82BwwYwEMPPcTy5cs5/PDDeeqpp2jUqFHYsXaQq1fP97Dly5fTr18/3nzzTZYuXUpqaioHHHAAF198MR07dqRUqVLsu+++LFq0CIASJUpQpUoVGjVqxFVXXcUpp+T+lB5JklTAEhKCCdwHHAAtWmy/PhqF1au3F5N/LCoXLgyKyi++CC5/lJgIBx7416KyTp2gEA1Rwl0JZJMNQHwknhopNSiZEJyGXiqpFN0bd2fozKFcesSlO/z74GkP/qE0fJGG1Rr+5W1gp9f95fpKh7No1iesnjeTzQt+YFTmUIiHoZ8+RdzjT7G8LKwtAWtKwpcNgAY7fg4bk+DdA3e8rlrZahxQ/gAO2OsASiaWZMC0AX/53KddOe0fVzdWLl3ZwTOSJKlQKBIDbEaPHk2HDh0YNGgQjRs35vHHH2fMmDHMmzePypX/+Rewghpg0/3t7jz15VN0b9SdJ854YrfeV2789NNPHHvssZQrV4677rqLevXqkZyczOzZsxk8eDBdunThnHPOYd999+WKK67gyiuvJCsri4ULFzJixAiee+457rnnHm677bY8f2wH2EiSFKM2bdo+kfmPReW8ecFtu7L33kExefDBwTCdAj7NO5Ld529vP5w0vmH5tn8PphJzWUVb6vEhP7GSDexFSZ6KnMW10Tf4jc1UoBRPRM5gazSH63mb39jMXpSgO01YzjpyiDIyOouNkS0kZUeosyrK7LTd/1ziI/H0Pbkv1za+ltJJpbddP+OXGTQY3OAvqxu/6vxVrk61dvCMJEkKU24H2BSJMrJx48YcddRR9O/fH4CcnBxq1KjBtddeyy233PKPj89LGRmNRtm4ZWOusy1OX8yvG38lEonQanQrVm1cRaVSlRh34Tii0SgVSlWgZmrNXL2vUomliOThF//mzZvz7bff8t1331G6dOm/3B6NRolEIuy777706NGDHj167HD7HXfcQd++ffnvf/9LnTp1cv1xwTJSkqRCJycHlizZ8VTv349XrAglUtXusLIswcnGCfzl9OUdRP93e3Qn99vZdfkgLhJH+3rtaX1wa6qnVOe3Tb9x+ojT/3K/XZWLSzOWctSzR/1ldeO0K6dRPaV6/n8CkiRJu6HYTNPOysriq6++onfv3tuui4uLo2nTpkyePHmnj8nMzCQzM3Pb2xkZGbn+eBu3bKRMvzL/PjCwauMqjhtyXJ4ft773+h1ePf87v/76K++99x733XffTotI4B+Lzeuuu4577rmH//znP/Tq1SvPeSVJUiESFxcMvNlnH2jWbMfbfvtt+wCd3/ejLADLyz+b+ztH/vTvzm7Li10UmPGReK5tdC2PT338L7f9+XTqGb/MAHK/j2P1lOosvG7httWNnRt0dnWjJEkqcgp9Gbl69Wqys7OpUqXKDtdXqVKF7777bqeP6devH3fddVdBxAvN/PnziUajf1nRWLFiRTZv3gxA165deeCBB3b5PsqXL0/lypVZuHBhfkaVJEmxbq+94Oijg0tBuisPZeQeNqLNCC4ee/Ffrv/yyi8BeHzq4/9YMv6bfRz/WDxGIhGLSEmSVOQU+jLy3+jduzc33HDDtrczMjKoUaNGrh5bKrEU63uvz9PHm7l85k5XQn522WcckXZErt9PqcRSefq4O/Pll1+Sk5ND+/btd1gduiu/n8otSZJU0KJ3REm8O5Gt0a175P1FiBAluu3fP5aIuyoWd3Z9bktGVzpKkiT9VaEvIytWrEh8fDwr/rSX0YoVK0hL2/kO48nJySQn/7tfAiORSK5Plf5dycRg0uOff5ktmVgyz+8rtw444AAikQjz5s3b4fr99tsvyFSy5D++j19//ZVVq1ZRq1atfMkoSZJUUG497lbe/OFNZq+cTb3K9bi64dU8//XzLFy7EIB9y+27Q7FYu3ztXRaOeSkZXekoSZK0o0JfRiYlJdGgQQMmTpxIy5YtgWCAzcSJE+nWrVu44f7n35yis7sqVKjAaaedRv/+/bn22mt3uW/k33niiSeIi4vb9nWVJEkqaNXLVmdhxsJc379EfAkyszNJTkgmKT6JfVL3YdWGVVx91NX0PaUv6zLXUTa57A4lIrDTYvHvCkdLRkmSpH+n0JeRADfccAMdO3akYcOGNGrUiMcff5wNGzZw2WWXhR0NCO8UnYEDB3LsscfSsGFD7rzzTg477DDi4uKYNm0a3333HQ0aNNh233Xr1rF8+XK2bNnCggULGDFiBM899xz9+vXjgAMOyNeckiRJu7Lg+gU8M+UZjqlyDHtX2pvNGzYz5vsxnFHnDFJLpJJSIoWs7CyS4pPYkrOFMkllWJ+1njJJZdiSs4Wk+KQdfu9KKbF9suPOSsQ/XmfhKEmStOdFotFoNOwQe0L//v156KGHWL58OUcccQRPPvkkjRs3ztVj/270+ObNm1mwYAG1atWiRIkS+RE9X/3yyy/cd999vPnmmyxdupTk5GTq1q3L+eefzzXXXEOpUqXYd999WbRoERCsNE1LS+Poo4/mqquu4uSTT/5XH7ewf90kSZIkSZKUe3/Xr/1RkSkjd0dRLiPD4tdNkiRJkiSp+MhtGRlXgJkkSZIkSZIkFWOWkZIkSZIkSZIKhGWkJEmSJEmSpAJhGSlJkiRJkiSpQFhG5pJzfvLGr5ckSZIkSZL+zDLyH8THxwOQlZUVcpLC5fev1+9fP0mSJEmSJCkh7ACxLiEhgVKlSrFq1SoSExOJi7O//Sc5OTmsWrWKUqVKkZDgU0ySJEmSJEkBm6J/EIlEqFq1KgsWLGDRokVhxyk04uLiqFmzJpFIJOwokiRJkiRJihGWkbmQlJTEgQce6KnaeZCUlOQqUkmSJEmSJO3AMjKX4uLiKFGiRNgxJEmSJEmSpELLpWuSJEmSJEmSCoRlpCRJkiRJkqQCYRkpSZIkSZIkqUC4ZyQQjUYByMjICDmJJEmSJEmSVPj83qv93rPtimUksG7dOgBq1KgRchJJkiRJkiSp8Fq3bh2pqam7vD0S/ae6shjIyclh2bJllC1blkgkEnacPS4jI4MaNWqwZMkSUlJSwo6jQsDnjPLK54zyyueM8srnjPLK54zywueL8srnjPKqODxnotEo69ato1q1asTF7XpnSFdGAnFxcVSvXj3sGPkuJSWlyD7hlT98ziivfM4or3zOKK98ziivfM4oL3y+KK98ziivivpz5u9WRP7OATaSJEmSJEmSCoRlpCRJkiRJkqQCYRlZDCQnJ3PHHXeQnJwcdhQVEj5nlFc+Z5RXPmeUVz5nlFc+Z5QXPl+UVz5nlFc+Z7ZzgI0kSZIkSZKkAuHKSEmSJEmSJEkFwjJSkiRJkiRJUoGwjJQkSZIkSZJUICwjJUmSJEmSJBUIy8gi4N577+WY/2/v3mNrvv84jr9aetFRHUp1o4opc59N025jaNQlGyNmJm4zt5UxJthFsQtDSIiMLdQSyzaSYRebVSmhVFXd6jKkSFEy0rqv2r5/fyxOVr1Yu59zTvX5SE7ifL7vz7fvk/PJux/vfs/3REbKz89PAQEBxcacO3dOvXv3lp+fn+rWraupU6cqLy+v1PNevXpVgwcPlr+/vwICAjRy5EjduHHjIbwCuFpiYqI8PDyKfaSkpJQ476WXXioSP3bsWCdmDldq1KhRkfd/3rx5pc65c+eOYmJiVLt2bVWvXl39+/fXpUuXnJQxXOXMmTMaOXKkQkNDVa1aNTVp0kSxsbHKzc0tdR41pvJZtmyZGjVqJF9fX4WHh2vv3r2lxq9bt07NmzeXr6+vWrdurU2bNjkpU7ja3Llz9dxzz6lGjRqqW7eu+vbtqxMnTpQ6Z/Xq1UVqiq+vr5MyhqvNmjWryPvfvHnzUudQYyq34va6Hh4eiomJKTaeGlO57NixQy+//LKCg4Pl4eGhDRs2FDpuZpo5c6bq16+vatWqKSoqSidPnnzgecu6F6qoaEY+AnJzczVgwACNGzeu2OP5+fnq3bu3cnNzlZSUpK+//lqrV6/WzJkzSz3v4MGDlZ6ervj4eP3888/asWOHRo8e/TBeAlwsMjJSFy9eLPR46623FBoaqmeffbbUuaNGjSo0b/78+U7KGu5gzpw5hd7/CRMmlBr/7rvv6qefftK6deu0fft2XbhwQf369XNStnCV48ePq6CgQCtWrFB6eroWL16s5cuX6/3333/gXGpM5fH9999r8uTJio2N1f79+9W2bVtFR0fr8uXLxcYnJSVp0KBBGjlypNLS0tS3b1/17dtXR44ccXLmcIXt27crJiZGe/bsUXx8vO7evavu3bvr5s2bpc7z9/cvVFPOnj3rpIzhDlq2bFno/d+5c2eJsdQYpKSkFFov8fHxkqQBAwaUOIcaU3ncvHlTbdu21bJly4o9Pn/+fC1ZskTLly9XcnKyHnvsMUVHR+vOnTslnrOse6EKzfDIiIuLs5o1axYZ37Rpk3l6elpWVpZj7IsvvjB/f3/766+/ij3X0aNHTZKlpKQ4xn799Vfz8PCw8+fP/99zh3vJzc21wMBAmzNnTqlxnTt3tokTJzonKbidkJAQW7x48b+Oz87ONi8vL1u3bp1j7NixYybJdu/e/RAyhDubP3++hYaGlhpDjalcOnbsaDExMY7n+fn5FhwcbHPnzi02/rXXXrPevXsXGgsPD7cxY8Y81Dzhni5fvmySbPv27SXGlLRXRuUQGxtrbdu2/dfx1Bjcb+LEidakSRMrKCgo9jg1pvKSZOvXr3c8LygosKCgIFuwYIFjLDs723x8fOzbb78t8Txl3QtVZFwZWQns3r1brVu3Vr169Rxj0dHRunbtmtLT00ucExAQUOiquKioKHl6eio5Ofmh5wzX+vHHH3XlyhWNGDHigbHffPON6tSpo1atWmnGjBm6deuWEzKEu5g3b55q166t9u3ba8GCBaXe/iE1NVV3795VVFSUY6x58+Zq2LChdu/e7Yx04UZycnJUq1atB8ZRYyqH3NxcpaamFqoPnp6eioqKKrE+7N69u1C89Pf+hnpSOeXk5EjSA+vKjRs3FBISogYNGqhPnz4l7oXxaDp58qSCg4PVuHFjDR48WOfOnSsxlhqDf8rNzdWaNWv05ptvysPDo8Q4agwkKSMjQ1lZWYVqSM2aNRUeHl5iDSnPXqgiq+rqBPDwZWVlFWpESnI8z8rKKnFO3bp1C41VrVpVtWrVKnEOHh0rV65UdHS0nnzyyVLj3njjDYWEhCg4OFiHDh3StGnTdOLECf3www9OyhSu9M477+iZZ55RrVq1lJSUpBkzZujixYtatGhRsfFZWVny9vYucm/bevXqUVcqmVOnTmnp0qVauHBhqXHUmMrjzz//VH5+frH7lePHjxc7p6T9DfWk8ikoKNCkSZP0/PPPq1WrViXGhYWFadWqVWrTpo1ycnK0cOFCRUZGKj09/YF7HlR84eHhWr16tcLCwnTx4kXNnj1bL774oo4cOaIaNWoUiafG4J82bNig7OxsDR8+vMQYagzuuVcnylJDyrMXqshoRrqp6dOn6/PPPy815tixYw+86TIqt/Kso8zMTG3evFlr16594Pn/eQ/R1q1bq379+urWrZtOnz6tJk2alD9xuExZ1szkyZMdY23atJG3t7fGjBmjuXPnysfH52GnCjdQnhpz/vx59ejRQwMGDNCoUaNKnUuNAfBvxMTE6MiRI6Xe/0+SIiIiFBER4XgeGRmpFi1aaMWKFfr4448fdppwsZ49ezr+3aZNG4WHhyskJERr167VyJEjXZgZKoKVK1eqZ8+eCg4OLjGGGgP8ezQj3dSUKVNK/auLJDVu3PhfnSsoKKjINzDd+/baoKCgEufcf5PUvLw8Xb16tcQ5cD/lWUdxcXGqXbu2XnnllTL/vPDwcEl/X/VEo6Bi+i+1Jzw8XHl5eTpz5ozCwsKKHA8KClJubq6ys7MLXR156dIl6koFVdb1cuHCBXXp0kWRkZH68ssvy/zzqDGPrjp16qhKlSqO/ck9pdWHoKCgMsXj0TR+/HjHFy2W9cojLy8vtW/fXqdOnXpI2cGdBQQEqFmzZiW+/9QY3HP27Flt2bKlzJ/MoMZUXvfqxKVLl1S/fn3H+KVLl9SuXbti55RnL1SR0Yx0U4GBgQoMDPy/nCsiIkKffvqpLl++7PjodXx8vPz9/fX000+XOCc7O1upqanq0KGDJGnr1q0qKChw/GcQ7q+s68jMFBcXp6FDh8rLy6vMP+/AgQOSVKjgomL5L7XnwIED8vT0LHKLh3s6dOggLy8vJSQkqH///pKkEydO6Ny5c4X+ioyKoyzr5fz58+rSpYs6dOiguLg4eXqW/bbV1JhHl7e3tzp06KCEhAT17dtX0t8fvU1ISND48eOLnRMREaGEhARNmjTJMRYfH089qSTMTBMmTND69euVmJio0NDQMp8jPz9fhw8fVq9evR5ChnB3N27c0OnTpzVkyJBij1NjcE9cXJzq1q2r3r17l2keNabyCg0NVVBQkBISEhzNx2vXrik5OVnjxo0rdk559kIVmqu/QQf/3dmzZy0tLc1mz55t1atXt7S0NEtLS7Pr16+bmVleXp61atXKunfvbgcOHLDffvvNAgMDbcaMGY5zJCcnW1hYmGVmZjrGevToYe3bt7fk5GTbuXOnPfXUUzZo0CCnvz44z5YtW0ySHTt2rMixzMxMCwsLs+TkZDMzO3XqlM2ZM8f27dtnGRkZtnHjRmvcuLF16tTJ2WnDBZKSkmzx4sV24MABO336tK1Zs8YCAwNt6NChjpj714yZ2dixY61hw4a2detW27dvn0VERFhERIQrXgKcKDMz05o2bWrdunWzzMxMu3jxouPxzxhqTOX23XffmY+Pj61evdqOHj1qo0ePtoCAAMvKyjIzsyFDhtj06dMd8bt27bKqVavawoUL7dixYxYbG2teXl52+PBhV70EONG4ceOsZs2alpiYWKim3Lp1yxFz/5qZPXu2bd682U6fPm2pqan2+uuvm6+vr6Wnp7viJcDJpkyZYomJiZaRkWG7du2yqKgoq1Onjl2+fNnMqDEoXn5+vjVs2NCmTZtW5Bg1pnK7fv26o/ciyRYtWmRpaWl29uxZMzObN2+eBQQE2MaNG+3QoUPWp08fCw0Ntdu3bzvO0bVrV1u6dKnj+YP2Qo8SmpGPgGHDhpmkIo9t27Y5Ys6cOWM9e/a0atWqWZ06dWzKlCl29+5dx/Ft27aZJMvIyHCMXblyxQYNGmTVq1c3f39/GzFihKPBiUfToEGDLDIysthjGRkZhdbVuXPnrFOnTlarVi3z8fGxpk2b2tSpUy0nJ8eJGcNVUlNTLTw83GrWrGm+vr7WokUL++yzz+zOnTuOmPvXjJnZ7du37e2337bHH3/c/Pz87NVXXy3UkMKjKS4urtjfU//8myg1BmZmS5cutYYNG5q3t7d17NjR9uzZ4zjWuXNnGzZsWKH4tWvXWrNmzczb29tatmxpv/zyi5MzhquUVFPi4uIcMfevmUmTJjnWV7169axXr162f/9+5ycPlxg4cKDVr1/fvL297YknnrCBAwfaqVOnHMepMSjO5s2bTZKdOHGiyDFqTOV2r4dy/+PemigoKLCPPvrI6tWrZz4+PtatW7ci6ygkJMRiY2MLjZW2F3qUeJiZOeUSTAAAAAAAAACVWtlv2AQAAAAAAAAA5UAzEgAAAAAAAIBT0IwEAAAAAAAA4BQ0IwEAAAAAAAA4Bc1IAAAAAAAAAE5BMxIAAAAAAACAU9CMBAAAAAAAAOAUNCMBAAAAAAAAOAXNSAAAALid/Px8RUZGql+/foXGc3Jy1KBBA33wwQcuygwAAAD/hYeZmauTAAAAAO73xx9/qF27dvrqq680ePBgSdLQoUN18OBBpaSkyNvb28UZAgAAoKxoRgIAAMBtLVmyRLNmzVJ6err27t2rAQMGKCUlRW3btnV1agAAACgHmpEAAABwW2amrl27qkqVKjp8+LAmTJigDz/80NVpAQAAoJxoRgIAAMCtHT9+XC1atFDr1q21f/9+Va1a1dUpAQAAoJz4AhsAAAC4tVWrVsnPz08ZGRnKzMx0dToAAAD4D7gyEgAAAG4rKSlJnTt31u+//65PPvlEkrRlyxZ5eHi4ODMAAACUB1dGAgAAwC3dunVLw4cP17hx49SlSxetXLlSe/fu1fLly12dGgAAAMqJKyMBAADgliZOnKhNmzbp4MGD8vPzkyStWLFC7733ng4fPqxGjRq5NkEAAACUGc1IAAAAuJ3t27erW7duSkxM1AsvvFDoWHR0tPLy8vi4NgAAQAVEMxIAAAAAAACAU3DPSAAAAAAAAABOQTMSAAAAAAAAgFPQjAQAAAAAAADgFDQjAQAAAAAAADgFzUgAAAAAAAAATkEzEgAAAAAAAIBT0IwEAAAAAAAA4BQ0IwEAAAAAAAA4Bc1IAAAAAAAAAE5BMxIAAAAAAACAU9CMBAAAAAAAAOAUNCMBAAA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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# установка минимального значения, на которое должны изменяться веса\n", + "eps = 0.0001\n", + "\n", + "# первоначальное точка\n", + "start_point = 5\n", + "\n", + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "# начальная точка\n", + "next_point = start_point\n", + "\n", + "x = []\n", + "x.append(next_point)\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.plot(X, Y, 'r', label='Y(X)')\n", + "\n", + "# количество итерация \n", + "n = 100\n", + "for i in range(n):\n", + " current_point = next_point\n", + "\n", + " # движение в негативную сторону вычисляемого градиента\n", + " next_point = current_point - learning_rate * gr_func(current_point)\n", + " x.append(next_point)\n", + "\n", + " # остановка когда достигнута необходимая степень точности\n", + " print(f\"Итерация: {i}\")\n", + " print(f\"Текущая точка {current_point}| Следующая точка {next_point}\")\n", + " print(\"--------------------------------------------------------\")\n", + " \n", + " if(abs(current_point - next_point) <= eps):\n", + " break\n", + "\n", + "print(f\"минимум {next_point}, количество затраченных итераций: {i}\") \n", + "X_grad = np.array(x)\n", + "plt.plot(X_grad, func(X_grad), '-*g', label = 'GD')\n", + "plt.legend()\n", + "plt.xlabel('X')\n", + "plt.ylabel('Y')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BJWalgdYr2sU" + }, + "source": [ + "И да, алгоритму понадобилось всего лишь 42 итерации, разница между двумя точками оказалась меньше `eps`, а значит можем выйти из цикла схождения алгоритма - это называется критерий останова." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "iSHnElKexpS8" + }, + "source": [ + "##### Алгоритм градиентного спуска\n", + "\n", + "1. Инициализация начальной точки\n", + "2. Цикл по k = 1,2,3,...:\n", + "\n", + "- $ w_{k} = w_{k-1} - \\eta\\nabla f(w_{k-1}) $\n", + "\n", + "- Если $||w_{k} - w_{k-1}|| < \\epsilon$, то завершить.\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "AGx1IbTptNvK" + }, + "source": [ + "#### Своя реализация линейной регрессии\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8w_t8Y7Ns9WV" + }, + "source": [ + "Теперь зная, как работает метод оптимизации градиентный спуск, можем вернуться к задаче обучения линейной регрессии, но уже не с помощью `sklearn`, а вручную." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dhbHnbLHu14I" + }, + "source": [ + "Берем те же самые данные, но вдобавок еще возвращем коэффициент наклона (коэффициент сдвига по умолчанию в такой генерации равен 0)." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "8ZD69Hs6tSAX", + "outputId": "980d2644-0aa8-4a7c-f93c-58a69a000105", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.63007982],\n", + " [-1.06163445],\n", + " [ 0.29634711],\n", + " [ 1.40277112],\n", + " [ 0.68968231],\n", + " [-0.53662936],\n", + " [-1.11947526],\n", + " [ 1.06755846],\n", + " [ 0.1178195 ],\n", + " [ 1.54907163],\n", + " [ 1.29561858],\n", + " [-0.03107509],\n", + " [ 0.56119218],\n", + " [ 0.42105072],\n", + " [-0.4864951 ],\n", + " [ 0.08897764],\n", + " [-0.18577532],\n", + " [-0.17809318],\n", + " [-0.23725045],\n", + " [-0.88623967],\n", + " [-0.47573349],\n", + " [ 0.21734821],\n", + " [-2.65331856],\n", + " [ 0.72575222],\n", + " [-0.38053642],\n", + " [-0.48456513],\n", + " [ 1.57463407],\n", + " [-1.30554851],\n", + " [-0.17241977],\n", + " [ 0.73683739],\n", + " [-1.23234621],\n", + " [ 0.31540267],\n", + " [ 1.74945474],\n", + " [ 0.09183837],\n", + " [-0.30957664],\n", + " [-1.18575527],\n", + " [-0.68344663],\n", + " [-0.31963136],\n", + " [-0.00828463],\n", + " [-0.64257539],\n", + " [ 1.0956297 ],\n", + " [ 0.06367166],\n", + " [-0.57395456],\n", + " [ 0.07349324],\n", + " [ 0.73227135],\n", + " [-1.06560298],\n", + " [-1.68411089],\n", + " [-1.54686257],\n", + " [-0.20437532],\n", + " [-0.286073 ]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "array([ 43.6543408 , -72.68235021, 21.19644643, 107.58765071,\n", + " 69.62063217, -32.57566222, -101.61213107, 87.44514699,\n", + " 17.69898683, 131.00190463, 97.97802247, 2.70819092,\n", + " 52.42715419, 27.74476129, -31.82947365, 1.58209228,\n", + " -9.72570848, 4.57391214, -33.24586607, -74.34292886,\n", + " -22.6419015 , 15.84607909, -202.79645668, 49.05026172,\n", + " -34.9916168 , -33.95608308, 121.78273292, -123.72382672,\n", + " -1.90918067, 64.06753923, -91.73785524, 9.55252237,\n", + " 148.12427806, 22.21183346, -16.35144507, -113.95075954,\n", + " -47.70966758, -22.69082132, -1.79022499, -58.17761844,\n", + " 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "fig = plt.figure(figsize=(10, 6))\n", + "plt.scatter(X, y)\n", + "\n", + "plt.xlabel('feature')\n", + "plt.ylabel('target')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1uqNje3QuFjX" + }, + "source": [ + "Функция, которую здесь оптимизируем - это MSE, её график для конкретно нашей задачи рисовали выше." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qPe_CIdRvPcI" + }, + "source": [ + "Реализуем две функции:\n", + "1. mserror - функция среднеквадратичной ошибки $MSE = \\frac{1}{n}\\sum_{i=0}^n{(\\text{y}_i-\\text{y_pred}_i})^2 = \\frac{1}{n}\\sum_{i=0}^n{(\\text{y}_i-(w_1\\cdot X_i + w_0)})^2 = \\frac{1}{n}\\sum_{i=0}^n{(\\text{y}_i-w_1\\cdot X_i - w_0})^2$\n", + "\n", + "\n", + "2. gr_mserror - градиент функции MSE. Распишем его отдельно для коэффициента сдвига и коэффициента наклона:\n", + "\n", + "Сдвиг:\n", + "$\\frac{∂ MSE}{∂ w_0} = \\frac{1 \\cdot 2}{n}\\sum({y_i -\\text{y_pred}_i})\\cdot -1$\n", + "\n", + "Наклон:\n", + "$\\frac{∂ MSE}{∂ w_1} = \\frac{1 \\cdot 2}{n}\\sum({y_i -\\text{y_pred}_i})\\cdot -X$" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "id": "fXl31ElsvPcI" + }, + "outputs": [], + "source": [ + "# функция, определяющая среднеквадратичную ошибку\n", + "def mserror(X, w1, w0, y):\n", + " y_pred = w1 * X[:, 0] + w0\n", + " return np.sum((y - y_pred) ** 2) / len(y_pred)\n", + "\n", + "# функция градиента\n", + "def gr_mserror(X, w1, w0, y):\n", + " y_pred = w1 * X[:, 0] + w0\n", + " return np.array([2/len(X)*np.sum((y - y_pred)) * (-1),\n", + " 2/len(X)*np.sum((y - y_pred) * (-X[:, 0]))])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "c375lB7cubo1" + }, + "source": [ + "И остается запустить цикл градиентного спуска.\n", + "\n", + "В начале инициализировали коэффициенты, затем на каждом шаге считаем градиент, умножаем его на шаг обучения и вычитаем его из предыдущих значений коэффициентов и так далее пока не поймем, что точки коэффициентов очень похожи друг на друга на соседних итерациях." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "qyOwUsWZyCrz", + "outputId": "7521fd22-ab6a-40f6-a36e-ee928a84a52f" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Итерация: 0\n", + "Текущая точка (0, 0)| Следующая точка (13.245106098282543, -1.3921748530551812)\n", + "MSE 5436.432058517568\n", + "--------------------------------------------------------\n", + "Итерация: 1\n", + "Текущая точка (13.245106098282543, -1.3921748530551812)| Следующая точка (24.283455474773014, -2.270634896573517)\n", + "MSE 3812.4417335187304\n", + "--------------------------------------------------------\n", + "Итерация: 2\n", + "Текущая точка (24.283455474773014, -2.270634896573517)| Следующая точка (33.487719285860635, -2.777322881591963)\n", + "MSE 2689.1325642433894\n", + "--------------------------------------------------------\n", + "Итерация: 3\n", + "Текущая точка (33.487719285860635, -2.777322881591963)| Следующая точка (41.166652649401456, -3.0191730536904307)\n", + "MSE 1910.2491839412482\n", + "--------------------------------------------------------\n", + "Итерация: 4\n", + "Текущая точка (41.166652649401456, -3.0191730536904307)| Следующая точка (47.57624618267611, -3.0762482285482444)\n", + "MSE 1368.9634120527255\n", + "--------------------------------------------------------\n", + "Итерация: 5\n", + "Текущая точка (47.57624618267611, -3.0762482285482444)| Следующая точка (52.92889586922186, -3.008051361710758)\n", + "MSE 992.010595522475\n", + "--------------------------------------------------------\n", + "Итерация: 6\n", + "Текущая точка (52.92889586922186, -3.008051361710758)| Следующая точка (57.40095014665679, -2.8584119151984995)\n", + "MSE 728.9953237861758\n", + "--------------------------------------------------------\n", + "Итерация: 7\n", + "Текущая точка (57.40095014665679, -2.8584119151984995)| Следующая точка (61.138926872179695, -2.659260887873855)\n", + "MSE 545.1558383956526\n", + "--------------------------------------------------------\n", + "Итерация: 8\n", + "Текущая точка (61.138926872179695, -2.659260887873855)| Следующая точка (64.2646390341644, -2.433540404481531)\n", + "MSE 416.45122384278307\n", + "--------------------------------------------------------\n", + "Итерация: 9\n", + "Текущая точка (64.2646390341644, -2.433540404481531)| Следующая точка (66.87942435861689, -2.19744033614948)\n", + "MSE 326.2142980059075\n", + "--------------------------------------------------------\n", + "Итерация: 10\n", + "Текущая точка (66.87942435861689, -2.19744033614948)| Следующая точка (69.06763839104693, -1.9621124640486494)\n", + "MSE 262.86371600250254\n", + "--------------------------------------------------------\n", + "Итерация: 11\n", + "Текущая точка (69.06763839104693, -1.9621124640486494)| Следующая точка (70.8995416710495, -1.7349797608563151)\n", + "MSE 218.33518111153128\n", + "--------------------------------------------------------\n", + "Итерация: 12\n", + "Текущая точка (70.8995416710495, -1.7349797608563151)| Следующая точка (72.4336880101809, -1.520732529514591)\n", + "MSE 187.00253533348857\n", + "--------------------------------------------------------\n", + "Итерация: 13\n", + "Текущая точка (72.4336880101809, -1.520732529514591)| Следующая точка (73.71890162494748, -1.322082889991646)\n", + "MSE 164.93367151659535\n", + "--------------------------------------------------------\n", + "Итерация: 14\n", + "Текущая точка (73.71890162494748, -1.322082889991646)| Следующая точка (74.79591515037744, -1.1403332478296038)\n", + "MSE 149.37600820692927\n", + "--------------------------------------------------------\n", + "Итерация: 15\n", + "Текущая точка (74.79591515037744, -1.1403332478296038)| Следующая точка (75.69872770576566, -0.9758019720797207)\n", + "MSE 138.39982870713823\n", + "--------------------------------------------------------\n", + "Итерация: 16\n", + "Текущая точка (75.69872770576566, -0.9758019720797207)| Следующая точка (76.45573166825358, -0.8281398136089831)\n", + "MSE 130.65048482717629\n", + "--------------------------------------------------------\n", + "Итерация: 17\n", + "Текущая точка (76.45573166825358, -0.8281398136089831)| Следующая точка (77.09064819864122, -0.6965630242691534)\n", + "MSE 125.17587305548757\n", + "--------------------------------------------------------\n", + "Итерация: 18\n", + "Текущая точка (77.09064819864122, -0.6965630242691534)| Следующая точка (77.62330450567968, -0.5800232339912165)\n", + "MSE 121.30608466627997\n", + "--------------------------------------------------------\n", + "Итерация: 19\n", + "Текущая точка (77.62330450567968, -0.5800232339912165)| Следующая точка (78.07028004458385, -0.47732954550339834)\n", + "MSE 118.5693021415083\n", + "--------------------------------------------------------\n", + "Итерация: 20\n", + "Текущая точка (78.07028004458385, -0.47732954550339834)| Следующая точка (78.44544409060278, -0.3872347313389438)\n", + "MSE 116.63292990920401\n", + "--------------------------------------------------------\n", + "Итерация: 21\n", + "Текущая точка (78.44544409060278, -0.3872347313389438)| Следующая точка (78.76040322042036, -0.3084946422381159)\n", + "MSE 115.26232714854191\n", + "--------------------------------------------------------\n", + "Итерация: 22\n", + "Текущая точка (78.76040322042036, -0.3084946422381159)| Следующая точка (79.024874019221, -0.23990778502053262)\n", + "MSE 114.29184073360233\n", + "--------------------------------------------------------\n", + "Итерация: 23\n", + "Текущая точка (79.024874019221, -0.23990778502053262)| Следующая точка (79.24699368416267, -0.18034036428991163)\n", + "MSE 113.60444739461153\n", + "--------------------------------------------------------\n", + "Итерация: 24\n", + "Текущая точка (79.24699368416267, -0.18034036428991163)| Следующая точка (79.43357901354796, -0.12874079838376576)\n", + "MSE 113.11743065929035\n", + "--------------------------------------------------------\n", + "Итерация: 25\n", + "Текущая точка (79.43357901354796, -0.12874079838376576)| Следующая точка (79.590342471717, -0.08414673157126629)\n", + "MSE 112.77229367773498\n", + "--------------------------------------------------------\n", + "Итерация: 26\n", + "Текущая точка (79.590342471717, -0.08414673157126629)| Следующая точка (79.72207253439184, -0.045686805736328245)\n", + "MSE 112.5276488913149\n", + "--------------------------------------------------------\n", + "Итерация: 27\n", + "Текущая точка (79.72207253439184, -0.045686805736328245)| Следующая точка (79.83278429207604, -0.012578874154160535)\n", + "MSE 112.35420203791824\n", + "--------------------------------------------------------\n", + "Итерация: 28\n", + "Текущая точка (79.83278429207604, -0.012578874154160535)| Следующая точка (79.92584527446147, 0.01587410273549933)\n", + "MSE 112.23121107508297\n", + "--------------------------------------------------------\n", + "Итерация: 29\n", + "Текущая точка (79.92584527446147, 0.01587410273549933)| Следующая точка (80.00408061916187, 0.0402895757954151)\n", + "MSE 112.14398472877181\n", + "--------------------------------------------------------\n", + "Итерация: 30\n", + "Текущая точка (80.00408061916187, 0.0402895757954151)| Следующая точка (80.06986101275434, 0.061211690132424876)\n", + "MSE 112.08211443091523\n", + "--------------------------------------------------------\n", + "Итерация: 31\n", + "Текущая точка (80.06986101275434, 0.061211690132424876)| Следующая точка (80.12517625583499, 0.07911787359402343)\n", + "MSE 112.03822398727151\n", + "--------------------------------------------------------\n", + "Итерация: 32\n", + "Текущая точка (80.12517625583499, 0.07911787359402343)| Следующая точка (80.1716968258466, 0.09442541434069902)\n", + "MSE 112.0070849682984\n", + "--------------------------------------------------------\n", + "Итерация: 33\n", + "Текущая точка (80.1716968258466, 0.09442541434069902)| Следующая точка (80.21082541475698, 0.10749781647693545)\n", + "MSE 111.98499059416774\n", + "--------------------------------------------------------\n", + "Итерация: 34\n", + "Текущая точка (80.21082541475698, 0.10749781647693545)| Следующая точка (80.24374008920961, 0.11865080004710715)\n", + "MSE 111.96931241806891\n", + "--------------------------------------------------------\n", + "Итерация: 35\n", + "Текущая точка (80.24374008920961, 0.11865080004710715)| Следующая точка (80.2714304469608, 0.1281578677088226)\n", + "MSE 111.95818633748331\n", + "--------------------------------------------------------\n", + "Итерация: 36\n", + "Текущая точка (80.2714304469608, 0.1281578677088226)| Следующая точка (80.29472791571294, 0.13625540033755565)\n", + "MSE 111.95029014106852\n", + "--------------------------------------------------------\n", + "Итерация: 37\n", + "Текущая точка (80.29472791571294, 0.13625540033755565)| Следующая точка (80.3143311509696, 0.14314727172458203)\n", + "MSE 111.94468586607258\n", + "--------------------------------------------------------\n", + "Итерация: 38\n", + "Текущая точка (80.3143311509696, 0.14314727172458203)| Следующая точка (80.33082733176776, 0.14900899149088742)\n", + "MSE 111.9407080587951\n", + "--------------------------------------------------------\n", + "Итерация: 39\n", + "Текущая точка (80.33082733176776, 0.14900899149088742)| Следующая точка (80.34471002169886, 0.15399139770567302)\n", + "MSE 111.93788455593705\n", + "--------------------------------------------------------\n", + "Итерация: 40\n", + "Текущая точка (80.34471002169886, 0.15399139770567302)| Следующая точка (80.35639415306127, 0.15822392825594017)\n", + "MSE 111.93588031188328\n", + "--------------------------------------------------------\n", + "Итерация: 41\n", + "Текущая точка (80.35639415306127, 0.15822392825594017)| Следующая точка (80.3662286006031, 0.16181750411360082)\n", + "MSE 111.93445756119772\n", + "--------------------------------------------------------\n", + "Итерация: 42\n", + "Текущая точка (80.3662286006031, 0.16181750411360082)| Следующая точка (80.37450673505678, 0.16486705930322332)\n", + "MSE 111.93344756203358\n", + "--------------------------------------------------------\n", + "Итерация: 43\n", + "Текущая точка (80.37450673505678, 0.16486705930322332)| Следующая точка (80.3814752830035, 0.16745375234425586)\n", + "MSE 111.93273055134894\n", + "--------------------------------------------------------\n", + "Итерация: 44\n", + "Текущая точка (80.3814752830035, 0.16745375234425586)| Следующая точка (80.38734176642754, 0.16964689278727177)\n", + "MSE 111.93222152388138\n", + "--------------------------------------------------------\n", + "Итерация: 45\n", + "Текущая точка (80.38734176642754, 0.16964689278727177)| Следующая точка (80.39228075088505, 0.1715056145957146)\n", + "MSE 111.93186014187545\n", + "--------------------------------------------------------\n", + "Итерация: 46\n", + "Текущая точка (80.39228075088505, 0.1715056145957146)| Следующая точка (80.39643909406131, 0.17308032584082383)\n", + "MSE 111.93160357509205\n", + "--------------------------------------------------------\n", + "Итерация: 47\n", + "Текущая точка (80.39643909406131, 0.17308032584082383)| Следующая точка (80.39994035542131, 0.17441396169048307)\n", + "MSE 111.9314214197364\n", + "--------------------------------------------------------\n", + "Итерация: 48\n", + "Текущая точка (80.39994035542131, 0.17441396169048307)| Следующая точка (80.40288850166267, 0.17554306513125753)\n", + "MSE 111.93129209244117\n", + "--------------------------------------------------------\n", + "Итерация: 49\n", + "Текущая точка (80.40288850166267, 0.17554306513125753)| Следующая точка (80.40537102092192, 0.17649871736794565)\n", + "MSE 111.93120027093673\n", + "--------------------------------------------------------\n", + "Итерация: 50\n", + "Текущая точка (80.40537102092192, 0.17649871736794565)| Следующая точка (80.40746154046687, 0.1773073374625193)\n", + "MSE 111.93113507749824\n", + "--------------------------------------------------------\n", + "Итерация: 51\n", + "Текущая точка (80.40746154046687, 0.1773073374625193)| Следующая точка (80.40922202734937, 0.17799136854473532)\n", + "MSE 111.93108878953852\n", + "--------------------------------------------------------\n", + "Итерация: 52\n", + "Текущая точка (80.40922202734937, 0.17799136854473532)| Следующая точка (80.41070463870736, 0.17856986587197987)\n", + "MSE 111.9310559243356\n", + "--------------------------------------------------------\n", + "Итерация: 53\n", + "Текущая точка (80.41070463870736, 0.17856986587197987)| Следующая точка (80.41195327769022, 0.1790590001450439)\n", + "MSE 111.93103258931154\n", + "--------------------------------------------------------\n", + "Итерация: 54\n", + "Текущая точка (80.41195327769022, 0.1790590001450439)| Следующая точка (80.41300490199842, 0.1794724877994691)\n", + "MSE 111.93101602080289\n", + "--------------------------------------------------------\n", + "Итерация: 55\n", + "Текущая точка (80.41300490199842, 0.1794724877994691)| Следующая точка (80.41389062449502, 0.1798219584829086)\n", + "MSE 111.93100425662863\n", + "--------------------------------------------------------\n", + "Итерация: 56\n", + "Текущая точка (80.41389062449502, 0.1798219584829086)| Следующая точка (80.41463663902786, 0.18011726858776034)\n", + "MSE 111.93099590363774\n", + "--------------------------------------------------------\n", + "Итерация: 57\n", + "Текущая точка (80.41463663902786, 0.18011726858776034)| Следующая точка (80.41526499929918, 0.18036676852314196)\n", + "MSE 111.93098997268032\n", + "--------------------------------------------------------\n", + "Итерация: 58\n", + "Текущая точка (80.41526499929918, 0.18036676852314196)| Следующая точка (80.41579427417048, 0.18057753036794924)\n", + "MSE 111.93098576144426\n", + "--------------------------------------------------------\n", + "Итерация: 59\n", + "Текущая точка (80.41579427417048, 0.18057753036794924)| Следующая точка (80.4162400990548, 0.18075554163382535)\n", + "MSE 111.93098277127257\n", + "--------------------------------------------------------\n", + "Итерация: 60\n", + "Текущая точка (80.4162400990548, 0.18075554163382535)| Следующая точка (80.41661563991356, 0.18090587007021305)\n", + "MSE 111.9309806481053\n", + "--------------------------------------------------------\n", + "Итерация: 61\n", + "Текущая точка (80.41661563991356, 0.18090587007021305)| Следующая точка (80.41693198374094, 0.18103280375061692)\n", + "MSE 111.93097914054856\n", + "--------------------------------------------------------\n", + "Итерация: 62\n", + "Текущая точка (80.41693198374094, 0.18103280375061692)| Следующая точка (80.4171984672076, 0.18113997007799426)\n", + "MSE 111.93097807010358\n", + "--------------------------------------------------------\n", + "Итерация: 63\n", + "Текущая точка (80.4171984672076, 0.18113997007799426)| Следующая точка (80.41742295327681, 0.18123043682693823)\n", + "MSE 111.93097731002919\n", + "--------------------------------------------------------\n", + "Итерация: 64\n", + "Текущая точка (80.41742295327681, 0.18123043682693823)| Следующая точка (80.41761206404517, 0.1813067978911081)\n", + "MSE 111.93097677033369\n", + "--------------------------------------------------------\n", + "Итерация: 65\n", + "Текущая точка (80.41761206404517, 0.1813067978911081)| Следующая точка (80.41777137674777, 0.18137124601724236)\n", + "MSE 111.93097638711887\n", + "--------------------------------------------------------\n", + "Итерация: 66\n", + "Текущая точка (80.41777137674777, 0.18137124601724236)| Следующая точка (80.41790558876512, 0.1814256344741146)\n", + "MSE 111.93097611501378\n", + "--------------------------------------------------------\n", + "Итерация: 67\n", + "Текущая точка (80.41790558876512, 0.1814256344741146)| Следующая точка (80.41801865654197, 0.18147152931880287)\n", + "MSE 111.9309759218029\n", + "--------------------------------------------------------\n", + "Итерация: 68\n", + "Текущая точка (80.41801865654197, 0.18147152931880287)| Следующая точка (80.41811391254866, 0.18151025367739462)\n", + "MSE 111.93097578461146\n", + "--------------------------------------------------------\n" + ] + } + ], + "source": [ + "# установка минимального значения, на которое должны изменяться веса\n", + "eps = 0.0001\n", + "\n", + "# первоначальное точка\n", + "w1 = 0\n", + "w0 = 0\n", + "\n", + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "next_w1 = w1\n", + "next_w0 = w0\n", + "# количество итерация \n", + "n = 100\n", + "for i in range(n):\n", + " cur_w1 = next_w1\n", + " cur_w0 = next_w0\n", + "\n", + " # движение в негативную сторону вычисляемого градиента\n", + " next_w0 = cur_w0 - learning_rate * gr_mserror(X, cur_w1, cur_w0, y)[0]\n", + " next_w1 = cur_w1 - learning_rate * gr_mserror(X, cur_w1, cur_w0, y)[1]\n", + "\n", + " # остановка когда достигнута необходимая степень точности\n", + " print(f\"Итерация: {i}\")\n", + " print(f\"Текущая точка {cur_w1, cur_w0}| Следующая точка {next_w1, next_w0}\")\n", + " print(f\"MSE {mserror(X, cur_w1, cur_w0, y)}\")\n", + " print(\"--------------------------------------------------------\")\n", + " \n", + " if (abs(cur_w1 - next_w1) <= eps) and (abs(cur_w0 - next_w0) <= eps):\n", + " break" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "yNm--2XU9mNg" + }, + "source": [ + "А мы получили точно такую же метрику, которая получалась у `LinearRegression` из `sklearn`.\n", + "\n", + "Сравним полученные коэффициенты с теми, которые были сгенерированы вместе с данными." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yh6UMSWP9z5C", + "outputId": "d1b132a5-b54d-492e-ff59-84a165996c2f" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Коэффициенты наклона True 80.65667909277211, trained 80.41811391254866\n", + "Коэффициенты сдвига True 0, trained 0.18151025367739462\n" + ] + } + ], + "source": [ + "print('Коэффициенты наклона', end=' ')\n", + "print(f'True {coeffs}, trained {next_w1}')\n", + "\n", + "print('Коэффициенты сдвига', end=' ')\n", + "print(f'True 0, trained {next_w0}')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ALbIVv6J9-tX" + }, + "source": [ + "А они очень похожи.\n", + "\n", + "А визуализированные кривые наслаиваются друг на друга" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "Vux7A3Da-WW6", + "outputId": "cfa10d85-94f5-40d3-997a-dd7a8619c437" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(10, 6))\n", + "\n", + "x = np.arange(-3, 3)\n", + "our_model_y = next_w1 * x + next_w0\n", + "\n", + "plt.plot(x, model_y_sk, linewidth=4, alpha=0.5, c='r', label=f'sklearn linear_model = {model_a:.2f}x + {model_b:.2f}')\n", + "plt.plot(x, our_model_y, '--g', linewidth=2, label=f'our linear_model = {next_w1:.2f}x + {next_w0:.2f}')\n", + "plt.scatter(X, y) \n", + "plt.grid()\n", + "plt.xlabel('feature')\n", + "plt.ylabel('target')\n", + "plt.legend(prop={'size': 16})\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "rEmVJTfv_EZ-" + }, + "source": [ + "### Многомерная линейная регрессия\n", + "\n", + "Сейчас мы посмотрели на то, как обучается линейная регрессия для задач с одним признаком.\n", + "\n", + "Построим себе данные поинтересней, состоящие из 4 признаков, это уже отрисовать не сможем.\n", + "\n" + ] + }, + { + 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33.69756994,\n", + " -24.66640928, -35.64805852, -76.68888106, -129.08694753,\n", + " 59.65011241, -158.52958483, -61.09970272, -97.83194751,\n", + " 36.42924987, -49.96145024, 104.10943674, -80.90767725,\n", + " 99.76081282, 152.70106779])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_regression\n", + "\n", + "X, y = make_regression(n_samples=50, n_features=4, n_informative=4,\n", + " noise=10, random_state=11)\n", + "\n", + "display(X, y)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "L389l2QmCBeI" + }, + "source": [ + "#### Из sklearn" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SQDLd3sv_ubX" + }, + "source": [ + "Обучим для начала модель из `sklearn`" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "3ArQO5TI_qOq", + "outputId": "4602856f-72a2-41bd-b945-efed584e99a1", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model = LinearRegression()\n", + "model.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "L0SIDCaB_qOs" + }, + "source": [ + "Посмотрим обученные коэффициенты и теперь давайте их называть весами.\n", + "\n", + "Есть веса при признаках - это и есть коэффициенты наклона но по каждой оси.\n", + "\n", + "И есть один свободный вес - коэффициент сдвига." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "l0TPVblH_-2H" + }, + "source": [ + "Получаем 4 веса при признаках - значения для каждого признака, которые сообщают, насколько нужно наклонить прямую относительно каждой оси.\n", + "\n", + "И один сдвиг - свободный вес." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "qsgZhUMk_qOs", + "outputId": "aeeb1dbd-d8e5-45b8-804b-3920395e6a1f", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([59.51225616, 57.72556421, 44.70715115, 24.87193091]),\n", + " -1.6392969526147305)" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.coef_, model.intercept_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Kl5cJtLhcmn5" + }, + "source": [ + "Можем сделать предсказания этой моделью, сначала через метод `predict`." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "zUGT6x6ucsLj", + "outputId": "f20ad239-b090-477a-9534-75752a910003", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([37.14897504])" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.predict(X[:1])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QcgBXyOAcx1-" + }, + "source": [ + "А теперь с помощью перемножения весов на признаки, суммирования их и добавления свободного веса." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "h99wvhpTc4Qk", + "outputId": "58291f95-4cd6-49da-b6dd-6e13b984fab2", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "37.148975042692896" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum(model.coef_ * X[0]) + model.intercept_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Lq2hstvtBDTo" + }, + "source": [ + "Давайте посчитаем ошибку на предсказаниях модели, при этом получим предсказания не одним способом (через `model.predict`), а еще и вторым, сами перемножим веса (`model.coef_`) на значения признаков (`X`) и добавим значение сдвига (`model.intercept_`)\n", + "\n", + "Выходит, что неважно, как мы получаем предсказания они всё равно одинаковые." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 206 + }, + "id": "lEyoJKCWAUvz", + "outputId": "b0e0419a-b0bc-45b6-b62d-48d1c0b6b685", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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0123ypred_fitpred_dot
00.858667-1.2640741.1148700.43477743.59907437.14897537.148975
11.291275-0.9642050.0717600.27160633.32261329.51165429.511654
21.067558-1.0616340.2173480.11782012.92842913.25748613.257486
30.0710200.921575-0.3768300.91998356.76209161.82045461.820454
40.2754070.186325-1.1398060.141805-28.240755-21.923992-21.923992
\n", + "
" + ], + "text/plain": [ + " 0 1 2 3 y pred_fit pred_dot\n", + "0 0.858667 -1.264074 1.114870 0.434777 43.599074 37.148975 37.148975\n", + "1 1.291275 -0.964205 0.071760 0.271606 33.322613 29.511654 29.511654\n", + "2 1.067558 -1.061634 0.217348 0.117820 12.928429 13.257486 13.257486\n", + "3 0.071020 0.921575 -0.376830 0.919983 56.762091 61.820454 61.820454\n", + "4 0.275407 0.186325 -1.139806 0.141805 -28.240755 -21.923992 -21.923992" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.DataFrame(X)\n", + "df['y'] = y\n", + "df['pred_fit'] = model.predict(X)\n", + "df['pred_dot'] = X.dot(model.coef_) + model.intercept_\n", + "\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vmltua2HAR7I" + }, + "source": [ + "Посчитаем отклонения предсказаний от истины." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 206 + }, + "id": "yXq4rvEuAR7I", + "outputId": "d966ee93-19ca-4920-a5ec-0d7d0dcdb240", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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0123ypred_fitpred_dotresidual
00.858667-1.2640741.1148700.43477743.59907437.14897537.148975-6.450099
11.291275-0.9642050.0717600.27160633.32261329.51165429.511654-3.810959
21.067558-1.0616340.2173480.11782012.92842913.25748613.2574860.329057
30.0710200.921575-0.3768300.91998356.76209161.82045461.8204545.058363
40.2754070.186325-1.1398060.141805-28.240755-21.923992-21.9239926.316763
\n", + "
" + ], + "text/plain": [ + " 0 1 2 3 y pred_fit pred_dot \\\n", + "0 0.858667 -1.264074 1.114870 0.434777 43.599074 37.148975 37.148975 \n", + "1 1.291275 -0.964205 0.071760 0.271606 33.322613 29.511654 29.511654 \n", + "2 1.067558 -1.061634 0.217348 0.117820 12.928429 13.257486 13.257486 \n", + "3 0.071020 0.921575 -0.376830 0.919983 56.762091 61.820454 61.820454 \n", + "4 0.275407 0.186325 -1.139806 0.141805 -28.240755 -21.923992 -21.923992 \n", + "\n", + " residual \n", + "0 -6.450099 \n", + "1 -3.810959 \n", + "2 0.329057 \n", + "3 5.058363 \n", + "4 6.316763 " + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df['residual'] = df['pred_fit'] - df['y']\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "jGVAfwy7AR7I" + }, + "source": [ + "И на всех объектах считаем метрику MSE - mean squared error, напомню, что более подробно про неё рассказываю в этом [видео](https://youtu.be/vh2smjQyhp8) и в этом [ноутбуке](https://colab.research.google.com/drive/14Oxi6sI25mP4JbovLiJ57e7H5sbN2I3p)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "USkbwCNVAR7I" + }, + "source": [ + "MSE равняется." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "oVK_d05wAR7J", + "outputId": "a9087eb5-0879-4b4b-9562-ad8681386a65", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "92.64429127220508" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.mean(df['residual'] ** 2)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "id": "Tfem6RubAMjf" + }, + "source": [ + "##### Своя реализация линейной регрессии" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zL6O2KJQCPk_" + }, + "source": [ + "Берем те же самые данные, где брали 4 признака, но еще возвращаем веса при признаках, а свободный вес по умолчанию в такой генерации равен 0." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "FIviYjjJCPlA", + "outputId": "8245f99b-6432-4137-94d3-c57e67121077", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.85866717, -1.26407368, 1.11487028, 0.43477699],\n", + " [ 1.29127473, -0.96420485, 0.07175977, 0.2716063 ],\n", + " [ 1.06755846, -1.06163445, 0.21734821, 0.1178195 ],\n", + " [ 0.07101978, 0.92157523, -0.37682984, 0.91998254],\n", + " [ 0.27540666, 0.18632534, -1.13980565, 0.14180489],\n", + " [ 0.29634711, 1.40277112, -1.54686257, 1.29561858],\n", + " [-1.68728061, -1.69734212, -0.41145394, -0.04527514],\n", + " [ 0.5936862 , 0.37050633, 1.34537807, 1.01594215],\n", + " [-0.86335252, -0.13054147, -0.52308763, -0.25127692],\n", + " [ 0.65402488, 1.79948007, 1.5466061 , 1.60987398],\n", + " [ 1.0956297 , 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0.42105072, -1.06560298, -0.88623967, -0.47573349],\n", + " [-0.49673048, 0.50502192, 0.93878313, -0.67502027],\n", + " [-0.06766856, -0.41320975, 0.1200828 , -0.69897169],\n", + " [ 0.73683739, 1.57463407, -0.03107509, -0.68344663],\n", + " [ 0.59527845, -0.68280162, -0.71355993, -1.90828954],\n", + " [ 0.81776957, 0.03679475, -0.04870254, 1.7915311 ],\n", + " [ 2.20185631, -0.0370669 , 1.93290543, -1.99357153]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "array([ 43.59907368, 33.3226129 , 12.92842886, 56.76209111,\n", + " -28.24075472, 64.36182392, -220.93063391, 134.81614163,\n", + " -111.85450024, 244.9327123 , 106.23869476, 83.15972598,\n", + " 22.1607008 , -87.67552386, -94.67026039, -29.62752165,\n", + " 119.90179833, -16.36526242, -71.2734975 , -33.77825083,\n", + " 24.31113443, 102.14682115, 1.12585934, -48.81175726,\n", + " -58.59186113, -111.47215424, -12.5784088 , -14.21337533,\n", + " 64.61172215, 10.81251385, 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"source": [ + "coeffs" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-jcBg1trGk5C" + }, + "source": [ + "Для удобства реализации градиентного спуска от записи поэлементной через сумму ($MSE = \\frac{1}{n}\\sum_{i=0}^n{(\\text{y}_i-\\text{y_pred}_i})^2$) перейдем к матричной форме записи.\n", + "\n", + "Предсказания линейной модели - это перемножение весов на признаки плюс свободный вес.\n", + "\n", + "$$y_{pred} = X\\cdot w + w_0$$\n", + "\n", + "При этом очень важно, чтобы соблюдались размерности матрицы $X$ и вектора $w$.\n", + "У нас размерности равны" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "EQUqgDEnHRiP", + "outputId": "0d4bdb56-6ed3-4663-b396-1c9b9aa2eeb5", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((50, 4), (4,))" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X.shape, coeffs.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "d8T_yqOeHX8G" + }, + "source": [ + "А значит, чтобы объеты могли матрично перемножиться, нужно чтобы количество столбцов первой матрицы было равно количеству строк второй (но у нас не матрица, а вектор).\n", + "\n", + "У нас совпадают, так что можем их перемножать и получаем ничто иное, как *скалярное произведение* - все значения в признаках перемножаются на соответсвующие веса и складываются.\n", + "\n", + "\n", + "А значит можем переписать формулу:\n", + "$$y_{pred} = \\langle X, w\\rangle + w_0$$\n", + "\n", + "\n", + "Но вот только мешается свободный вес. Можно пойти на одну хитрость и добавить фиктивный признак в данные, который для каждого объекта равен 1.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "id": "qRd4q1PYIG-_", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.85866717, -1.26407368, 1.11487028, 0.43477699, 1. ],\n", + " [ 1.29127473, -0.96420485, 0.07175977, 0.2716063 , 1. ],\n", + " [ 1.06755846, -1.06163445, 0.21734821, 0.1178195 , 1. ],\n", + " [ 0.07101978, 0.92157523, -0.37682984, 0.91998254, 1. ],\n", + " [ 0.27540666, 0.18632534, -1.13980565, 0.14180489, 1. ],\n", + " [ 0.29634711, 1.40277112, -1.54686257, 1.29561858, 1. ],\n", + " [-1.68728061, -1.69734212, -0.41145394, -0.04527514, 1. ],\n", + " [ 0.5936862 , 0.37050633, 1.34537807, 1.01594215, 1. ],\n", + " [-0.86335252, -0.13054147, -0.52308763, -0.25127692, 1. ],\n", + " [ 0.65402488, 1.79948007, 1.5466061 , 1.60987398, 1. ],\n", + " [ 1.0956297 , -0.30957664, 0.72575222, 1.54907163, 1. ],\n", + " [-0.39117313, 1.53422235, -0.16419295, 0.36036665, 1. ],\n", + " [ 0.68731235, -1.82300958, 0.8791138 , 1.84636487, 1. ],\n", + " [-1.0616544 , -0.68448467, -0.47621448, 0.83031043, 1. ],\n", + " [-1.1288944 , 0.01699688, -0.42442882, -0.1329099 , 1. ],\n", + " [ 0.51002802, 0.33871394, -1.17212003, -1.04596765, 1. ],\n", + " [ 1.08771086, 0.53382172, 0.39521201, 0.12286753, 1. ],\n", + " [-1.55107946, 0.94303598, 0.34115344, 0.13827322, 1. ],\n", + " [-1.57749431, 1.31094364, -0.79286501, -0.07174941, 1. ],\n", + " [-1.53214252, 0.21886858, 0.18566325, 1.83277654, 1. ],\n", + " [ 1.20910164, -0.8430661 , -0.14189358, 0.38535414, 1. ],\n", + " [ 1.65920462, 0.37864068, -0.46456606, 0.15384125, 1. ],\n", + " [-1.44071935, 1.47651282, -0.13155348, 0.1944292 , 1. ],\n", + " [-0.00828463, -0.31963136, -0.53662936, 0.31540267, 1. ],\n", + " [-0.37842255, -0.48897544, -0.64439382, 0.69914084, 1. ],\n", + " [-0.23725045, -1.23234621, -0.17241977, 0.09183837, 1. ],\n", + " [-0.18577532, -0.38053642, 0.08897764, 0.06367166, 1. ],\n", + " [ 1.4924715 , -1.11523722, -0.70541403, -0.04723257, 1. ],\n", + " [ 0.51655239, -0.08940364, 0.68212971, 0.15072201, 1. ],\n", + " [ 1.74945474, -0.286073 , -0.48456513, -2.65331856, 1. ],\n", + " [ 2.15667443, -0.82943725, -0.52937203, 1.56170369, 1. ],\n", + " [-1.08019383, -0.43205762, 0.51608404, 0.45539286, 1. ],\n", + " [-0.17809318, -0.57395456, -0.20437532, -0.4864951 , 1. ],\n", + " [-0.53085824, -0.86986194, -1.15526422, 0.79667185, 1. ],\n", + " [ 0.76616062, -0.99402769, -0.26434233, 1.54220922, 1. ],\n", + " [ 0.85615205, -0.04480262, -0.47748923, -0.15406552, 1. ],\n", + " [ 0.68968231, 0.56119218, -1.30554851, -1.11947526, 1. ],\n", + " [ 0.87427277, 0.0716521 , -1.63905163, -0.64730263, 1. ],\n", + " [-1.29742262, -0.71496244, 0.51447963, 0.25771638, 1. ],\n", + " [-1.68411089, -1.18575527, 0.60010201, 0.69556726, 1. ],\n", + " [ 0.63007982, 0.07349324, 0.73227135, -0.64257539, 1. ],\n", + " [-0.10514925, -1.58396258, -1.37177369, -0.02831834, 1. ],\n", + " [-2.04905726, 0.86705521, -0.26196107, 0.57897111, 1. ],\n", + " [ 0.42105072, -1.06560298, -0.88623967, -0.47573349, 1. ],\n", + " [-0.49673048, 0.50502192, 0.93878313, -0.67502027, 1. ],\n", + " [-0.06766856, -0.41320975, 0.1200828 , -0.69897169, 1. ],\n", + " [ 0.73683739, 1.57463407, -0.03107509, -0.68344663, 1. ],\n", + " [ 0.59527845, -0.68280162, -0.71355993, -1.90828954, 1. ],\n", + " [ 0.81776957, 0.03679475, -0.04870254, 1.7915311 , 1. ],\n", + " [ 2.20185631, -0.0370669 , 1.93290543, -1.99357153, 1. ]])" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X = np.column_stack([X, np.ones((50))])\n", + "X" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "HmRcuBRDIS0y" + }, + "source": [ + "И теперь всё предсказание линейной модели будет равняться:\n", + "\n", + "$$y_{pred} = \\langle X, w\\rangle$$\n", + "\n", + "\n", + "А наша ошибка MSE преобразиться и будет выглядить следующим образом:\n", + "\n", + "$$MSE = \\frac{1}{n}\\sum^{n}_{i=1}(y_{i} - \\text{y_pred}_i)^{2} = \\frac{1}{n}\\sum^{n}_{i=1}(y_{i} - \\langle X_i, w\\rangle)^{2} = \\frac{1}{n}||Y - X w||^{2}$$\n", + "\n", + "\n", + "где используется $L_{2}$ норма:\n", + "\n", + "$$||Y - X w|| = \\sqrt{\\sum_{i=1}^n{(y_i-X_iw)^2}} $$\n", + "\n", + "$$MSE = \\frac{1}{n}\\sqrt{\\sum_{i=1}^n{(y_i-X_iw)^2}} ^{2} = \\frac{1}{n}\\sum_{i=1}^n{(y_i-X_iw)^2}$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "yjbmJkF4CPlC" + }, + "source": [ + "Реализуем две функции только уже с матричными операциями:\n", + "1. mserror_mat - функция среднеквадратичной ошибки для матриц\n", + "\n", + "\n", + "2. gr_mserror_mat - градиент функции MSE для матрицы:\n", + "\n", + "$\\frac{∂ MSE}{∂ w} = \\frac{1 \\cdot 2}{n}({Y - Xw}) \\cdot-X$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "id": "_GlN3Fb4CPlC", + "tags": [] + }, + "outputs": [], + "source": [ + "# функция, определяющая среднеквадратичную ошибку\n", + "def mserror_mat(X, w, y):\n", + " y_pred = X @ w\n", + " return np.sum((y - y_pred) ** 2) / len(y_pred)\n", + "\n", + "# функция градиента\n", + "def gr_mserror_mat(X, w, y):\n", + " y_pred = X @ w\n", + " return 2/len(X)*(y - y_pred) @ (-X)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "siwPK0oQCPlC" + }, + "source": [ + "И остается запустить цикл градиентного спуска.\n", + "\n", + "В начале инициализировали коэффициенты. Т.к. у нас 5 признаков (4 настоящих плюс один фиктивный), то будет 5 весов." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "PBs-gz9sK9Eo", + "outputId": "4eefc925-6d0d-48be-80fb-76411c4d673f", + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0., 0., 0., 0., 0.])" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# первоначальное точка\n", + "weights = np.zeros(X.shape[1])\n", + "weights" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vfDPdqojLykB" + }, + "source": [ + "Затем запускаем цикл по обучению и меняем веса, при этом не каждый вес отдельно, а все веса сразу вместе.\n", + "\n", + "И если веса начнут плохо изменяться, то можем выйти по критерию останова:\n", + "\n", + "$$||w_{new} - w_{old}|| ≤ eps$$" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "hsA08x8UCPlC", + "outputId": "65060637-1a17-45cc-f4fd-12ee2543280e", + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Итерация: 0\n", + "Текущая точка [0. 0. 0. 0. 0.]| Следующая точка [11.76469989 8.02019663 7.1529662 3.12227706 -0.71246521]\n", + "MSE 7901.284047919272\n", + "--------------------------------------------------------\n", + "Итерация: 1\n", + "Текущая точка [11.76469989 8.02019663 7.1529662 3.12227706 -0.71246521]| Следующая точка [21.07996752 15.00192791 13.15169841 5.97919733 -1.2826889 ]\n", + "MSE 5491.413352110748\n", + "--------------------------------------------------------\n", + "Итерация: 2\n", + "Текущая точка [21.07996752 15.00192791 13.15169841 5.97919733 -1.2826889 ]| Следующая точка [28.48213061 21.0576616 18.18254548 8.55326802 -1.72604536]\n", + "MSE 3846.369420368778\n", + "--------------------------------------------------------\n", + "Итерация: 3\n", + "Текущая точка [28.48213061 21.0576616 18.18254548 8.55326802 -1.72604536]| Следующая точка [34.38479911 26.29452131 22.40202941 10.84471509 -2.06001325]\n", + "MSE 2714.9929661406427\n", + "--------------------------------------------------------\n", + "Итерация: 4\n", + "Текущая точка [34.38479911 26.29452131 22.40202941 10.84471509 -2.06001325]| Следующая точка [39.10795216 30.8120046 25.94151547 12.86498442 -2.30214304]\n", + "MSE 1931.9222400828064\n", + "--------------------------------------------------------\n", + "Итерация: 5\n", + "Текущая точка [39.10795216 30.8120046 25.94151547 12.86498442 -2.30214304]| Следующая точка [42.8999458 34.70086936 28.91118413 14.6321765 -2.46889448]\n", + "MSE 1387.0040664906423\n", + "--------------------------------------------------------\n", + "Итерация: 6\n", + "Текущая точка [42.8999458 34.70086936 28.91118413 14.6321765 -2.46889448]| Следующая точка [45.95419736 38.04279216 31.40339917 16.16788817 -2.57504099]\n", + "MSE 1006.0899187520283\n", + "--------------------------------------------------------\n", + "Итерация: 7\n", + "Текущая точка [45.95419736 38.04279216 31.40339917 16.16788817 -2.57504099]| Следующая точка [48.42186138 40.91052058 33.49555668 17.49507148 -2.63343403]\n", + "MSE 738.8060039075306\n", + "--------------------------------------------------------\n", + "Итерация: 8\n", + "Текущая точка [48.42186138 40.91052058 33.49555668 17.49507148 -2.63343403]| Следующая точка [50.42148205 43.36832699 35.25248994 18.63662244 -2.65498752]\n", + "MSE 550.6561006176497\n", + "--------------------------------------------------------\n", + "Итерация: 9\n", + "Текущая точка [50.42148205 43.36832699 35.25248994 18.63662244 -2.65498752]| Следующая точка [52.04636149 45.47263149 36.7284959 19.61448849 -2.64878917]\n", + "MSE 417.85498691229355\n", + "--------------------------------------------------------\n", + "Итерация: 10\n", + "Текущая точка [52.04636149 45.47263149 36.7284959 19.61448849 -2.64878917]| Следующая точка [53.37019893 47.27270499 37.96904019 20.44914032 -2.62227769]\n", + "MSE 323.90720485464516\n", + "--------------------------------------------------------\n", + "Итерация: 11\n", + "Текущая точка [53.37019893 47.27270499 37.96904019 20.44914032 -2.62227769]| Следующая точка [54.45141845 48.81139396 39.01219008 21.1592957 -2.58144728]\n", + "MSE 257.3166668961423\n", + "--------------------------------------------------------\n", + "Итерация: 12\n", + "Текущая точка [54.45141845 48.81139396 39.01219008 21.1592957 -2.58144728]| Следующая точка [55.33650004 50.12582934 39.88981729 21.76181406 -2.53105516]\n", + "MSE 210.038369394656\n", + "--------------------------------------------------------\n", + "Итерация: 13\n", + "Текущая точка [55.33650004 50.12582934 39.88981729 21.76181406 -2.53105516]| Следующая точка [56.06255115 51.24809716 40.62860694 22.27170356 -2.47481859]\n", + "MSE 176.4228514139174\n", + "--------------------------------------------------------\n", + "Итерация: 14\n", + "Текущая точка [56.06255115 51.24809716 40.62860694 22.27170356 -2.47481859]| Следующая точка [56.65929839 52.20585828 41.25090327 22.70219922 -2.41559373]\n", + "MSE 152.4912980600221\n", + "--------------------------------------------------------\n", + "Итерация: 15\n", + "Текущая точка [56.65929839 52.20585828 41.25090327 22.70219922 -2.41559373]| Следующая точка [57.15063499 53.02291165 41.77541792 23.06488303 -2.35553336]\n", + "MSE 135.4345952200435\n", + "--------------------------------------------------------\n", + "Итерация: 16\n", + "Текущая точка [57.15063499 53.02291165 41.77541792 23.06488303 -2.35553336]| Следующая точка [57.55582741 53.71969964 42.21782313 23.3698259 -2.29622284]\n", + "MSE 123.26530927825932\n", + "--------------------------------------------------------\n", + "Итерация: 17\n", + "Текущая точка [57.55582741 53.71969964 42.21782313 23.3698259 -2.29622284]| Следующая точка [57.89045924 54.31375717 42.59124804 23.62573786 -2.2387952 ]\n", + "MSE 114.57482521743945\n", + "--------------------------------------------------------\n", + "Итерация: 18\n", + "Текущая точка [57.89045924 54.31375717 42.59124804 23.62573786 -2.2387952 ]| Следующая точка [58.16717236 54.82010769 42.90669406 23.84011751 -2.18402727]\n", + "MSE 108.36322966694733\n", + "--------------------------------------------------------\n", + "Итерация: 19\n", + "Текущая точка [58.16717236 54.82010769 42.90669406 23.84011751 -2.18402727]| Следующая точка [58.39625082 55.25161031 43.17338224 24.01939505 -2.13241891]\n", + "MSE 103.91977162382656\n", + "--------------------------------------------------------\n", + "Итерация: 20\n", + "Текущая точка [58.39625082 55.25161031 43.17338224 24.01939505 -2.13241891]| Следующая точка [58.58608266 55.61926249 43.39904384 24.16906562 -2.08425763]\n", + "MSE 100.73863892376886\n", + "--------------------------------------------------------\n", + "Итерация: 21\n", + "Текущая точка [58.58608266 55.61926249 43.39904384 24.16906562 -2.08425763]| Следующая точка [58.74352627 55.93246299 43.59016329 24.29381107 -2.03967075]\n", + "MSE 98.45948265070291\n", + "--------------------------------------------------------\n", + "Итерация: 22\n", + "Текущая точка [58.74352627 55.93246299 43.59016329 24.29381107 -2.03967075]| Следующая точка [58.87420226 56.1992396 43.75218136 24.39760973 -1.99866711]\n", + "MSE 96.82533656557291\n", + "--------------------------------------------------------\n", + "Итерация: 23\n", + "Текущая точка [58.87420226 56.1992396 43.75218136 24.39760973 -1.99866711]| Следующая точка [58.98272662 56.42644562 43.88966508 24.48383401 -1.96117004]\n", + "MSE 95.65279460128872\n", + "--------------------------------------------------------\n", + "Итерация: 24\n", + "Текущая точка [58.98272662 56.42644562 43.88966508 24.48383401 -1.96117004]| Следующая точка [59.07289774 56.61992931 44.00644977 24.55533657 -1.92704328]\n", + "MSE 94.81084525169739\n", + "--------------------------------------------------------\n", + "Итерация: 25\n", + "Текущая точка [59.07289774 56.61992931 44.00644977 24.55533657 -1.92704328]| Следующая точка [59.14784688 56.78467946 44.10575783 24.61452568 -1.89611097]\n", + "MSE 94.20583098575997\n", + "--------------------------------------------------------\n", + "Итерация: 26\n", + "Текущая точка [59.14784688 56.78467946 44.10575783 24.61452568 -1.89611097]| Следующая точка [59.21015955 56.9249504 44.19029817 24.66343085 -1.86817307]\n", + "MSE 93.77074823912531\n", + "--------------------------------------------------------\n", + "Итерация: 27\n", + "Текущая точка [59.21015955 56.9249504 44.19029817 24.66343085 -1.86817307]| Следующая точка [59.26197383 57.04436924 44.26234925 24.70375952 -1.8430169 ]\n", + "MSE 93.45762768740872\n", + "--------------------------------------------------------\n", + "Итерация: 28\n", + "Текущая точка [59.26197383 57.04436924 44.26234925 24.70375952 -1.8430169 ]| Следующая точка [59.3050602 57.14602762 44.32382866 24.73694599 -1.82042578]\n", + "MSE 93.23210310542908\n", + "--------------------------------------------------------\n", + "Итерация: 29\n", + "Текущая точка [59.3050602 57.14602762 44.32382866 24.73694599 -1.82042578]| Следующая точка [59.34088647 57.23256032 44.37635126 24.76419334 -1.8001853 ]\n", + "MSE 93.06953693827623\n", + "--------------------------------------------------------\n", + "Итерация: 30\n", + "Текущая точка [59.34088647 57.23256032 44.37635126 24.76419334 -1.8001853 ]| Следующая точка [59.3706709 57.30621236 44.42127792 24.78650929 -1.78208767]\n", + "MSE 92.95225422283875\n", + "--------------------------------------------------------\n", + "Итерация: 31\n", + "Текущая точка [59.3706709 57.30621236 44.42127792 24.78650929 -1.78208767]| Следующая точка [59.39542553 57.36889645 44.45975624 24.80473686 -1.76593481]\n", + "MSE 92.86756633726901\n", + "--------------------------------------------------------\n", + "Итерация: 32\n", + "Текущая точка [59.39542553 57.36889645 44.45975624 24.80473686 -1.76593481]| Следующая точка [59.41599184 57.42224197 44.49275474 24.8195803 -1.75154016]\n", + "MSE 92.80635805630789\n", + "--------------------------------------------------------\n", + "Итерация: 33\n", + "Текущая точка [59.41599184 57.42224197 44.49275474 24.8195803 -1.75154016]| Следующая точка [59.43306995 57.46763676 44.5210914 24.83162725 -1.73872982]\n", + "MSE 92.76207666444269\n", + "--------------------------------------------------------\n", + "Итерация: 34\n", + "Текущая точка [59.43306995 57.46763676 44.5210914 24.83162725 -1.73872982]| Следующая точка [59.44724279 57.50626287 44.54545765 24.84136737 -1.727343 ]\n", + "MSE 92.73000824392085\n", + "--------------------------------------------------------\n", + "Итерация: 35\n", + "Текущая точка [59.44724279 57.50626287 44.54545765 24.84136737 -1.727343 ]| Следующая точка [59.45899592 57.53912698 44.56643846 24.84920822 -1.71723203]\n", + "MSE 92.70675922222419\n", + "--------------------------------------------------------\n", + "Итерация: 36\n", + "Текущая точка [59.45899592 57.53912698 44.56643846 24.84920822 -1.71723203]| Следующая точка [59.46873398 57.56708635 44.58452915 24.85548855 -1.70826207]\n", + "MSE 92.68988472679756\n", + "--------------------------------------------------------\n", + "Итерация: 37\n", + "Текущая точка [59.46873398 57.56708635 44.58452915 24.85548855 -1.70826207]| Следующая точка [59.47679431 57.59087096 44.60014958 24.86048955 -1.70031058]\n", + "MSE 92.67762200788442\n", + "--------------------------------------------------------\n", + "Итерация: 38\n", + "Текущая точка [59.47679431 57.59087096 44.60014958 24.86048955 -1.70031058]| Следующая точка [59.48345818 57.61110234 44.61365591 24.86444433 -1.69326667]\n", + "MSE 92.66869910455937\n", + "--------------------------------------------------------\n", + "Итерация: 39\n", + "Текущая точка [59.48345818 57.61110234 44.61365591 24.86444433 -1.69326667]| Следующая точка [59.48896018 57.62830972 44.62535067 24.86754585 -1.68703034]\n", + "MSE 92.66219742859573\n", + "--------------------------------------------------------\n", + "Итерация: 40\n", + "Текущая точка [59.48896018 57.62830972 44.62535067 24.86754585 -1.68703034]| Следующая точка [59.49349594 57.64294363 44.63549103 24.8699536 -1.68151169]\n", + "MSE 92.65745300854614\n", + "--------------------------------------------------------\n", + "Итерация: 41\n", + "Текущая точка [59.49349594 57.64294363 44.63549103 24.8699536 -1.68151169]| Следующая точка [59.49722865 57.65538766 44.64429587 24.87179919 -1.67663011]\n", + "MSE 92.65398547098278\n", + "--------------------------------------------------------\n", + "Итерация: 42\n", + "Текущая точка [59.49722865 57.65538766 44.64429587 24.87179919 -1.67663011]| Следующая точка [59.50029441 57.66596832 44.65195173 24.87319104 -1.67231349]\n", + "MSE 92.65144693426757\n", + "--------------------------------------------------------\n", + "Итерация: 43\n", + "Текущая точка [59.50029441 57.66596832 44.65195173 24.87319104 -1.67231349]| Следующая точка [59.5028067 57.67496359 44.65861769 24.8742183 -1.66849746]\n", + "MSE 92.64958520640201\n", + "--------------------------------------------------------\n", + "Итерация: 44\n", + "Текущая точка [59.5028067 57.67496359 44.65861769 24.8742183 -1.66849746]| Следующая точка [59.50486012 57.68261005 44.66442966 24.87495413 -1.66512467]\n", + "MSE 92.64821726459807\n", + "--------------------------------------------------------\n", + "Итерация: 45\n", + "Текущая точка [59.50486012 57.68261005 44.66442966 24.87495413 -1.66512467]| Следующая точка [59.50653352 57.68910909 44.66950384 24.87545843 -1.66214407]\n", + "MSE 92.64721013003997\n", + "--------------------------------------------------------\n", + "Итерация: 46\n", + "Текущая точка [59.50653352 57.68910909 44.66950384 24.87545843 -1.66214407]| Следующая точка [59.50789259 57.6946321 44.67393975 24.87578011 -1.65951032]\n", + "MSE 92.64646706515495\n", + "--------------------------------------------------------\n", + "Итерация: 47\n", + "Текущая точка [59.50789259 57.6946321 44.67393975 24.87578011 -1.65951032]| Следующая точка [59.50899202 57.69932497 44.6778227 24.87595901 -1.65718319]\n", + "MSE 92.64591760420645\n", + "--------------------------------------------------------\n", + "Итерация: 48\n", + "Текущая точка [59.50899202 57.69932497 44.6778227 24.87595901 -1.65718319]| Следующая точка [59.50987733 57.70331183 44.68122591 24.87602749 -1.65512699]\n", + "MSE 92.64551034659182\n", + "--------------------------------------------------------\n", + "Итерация: 49\n", + "Текущая точка [59.50987733 57.70331183 44.68122591 24.87602749 -1.65512699]| Следующая точка [59.51058637 57.70669831 44.68421236 24.87601171 -1.65331012]\n", + "MSE 92.645207742673\n", + "--------------------------------------------------------\n", + "Итерация: 50\n", + "Текущая точка [59.51058637 57.70669831 44.68421236 24.87601171 -1.65331012]| Следующая точка [59.5111506 57.70957431 44.68683624 24.87593277 -1.65170463]\n", + "MSE 92.64498231774262\n", + "--------------------------------------------------------\n", + "Итерация: 51\n", + "Текущая точка [59.5111506 57.70957431 44.68683624 24.87593277 -1.65170463]| Следующая точка [59.51159614 57.7120163 44.68914426 24.87580759 -1.65028579]\n", + "MSE 92.6448139347927\n", + "--------------------------------------------------------\n", + "Итерация: 52\n", + "Текущая точка [59.51159614 57.7120163 44.68914426 24.87580759 -1.65028579]| Следующая точка [59.51194465 57.71408934 44.69117675 24.87564965 -1.64903173]\n", + "MSE 92.6446878082462\n", + "--------------------------------------------------------\n", + "Итерация: 53\n", + "Текущая точка [59.51194465 57.71408934 44.69117675 24.87564965 -1.64903173]| Следующая точка [59.51221409 57.71584881 44.69296856 24.87546966 -1.64792314]\n", + "MSE 92.64459306103737\n", + "--------------------------------------------------------\n", + "Итерация: 54\n", + "Текущая точка [59.51221409 57.71584881 44.69296856 24.87546966 -1.64792314]| Следующая точка [59.5124193 57.71734177 44.69454986 24.87527603 -1.64694298]\n", + "MSE 92.64452167517669\n", + "--------------------------------------------------------\n", + "Итерация: 55\n", + "Текущая точка [59.5124193 57.71734177 44.69454986 24.87527603 -1.64694298]| Следующая точка [59.51257255 57.71860828 44.6959468 24.87507531 -1.64607619]\n", + "MSE 92.64446772754471\n", + "--------------------------------------------------------\n", + "Итерация: 56\n", + "Текущая точка [59.51257255 57.71860828 44.6959468 24.87507531 -1.64607619]| Следующая точка [59.51268398 57.7196824 44.69718209 24.87487257 -1.64530948]\n", + "MSE 92.64442683265162\n", + "--------------------------------------------------------\n", + "Итерация: 57\n", + "Текущая точка [59.51268398 57.7196824 44.69718209 24.87487257 -1.64530948]| Следующая точка [59.5127619 57.72059311 44.69827546 24.87467163 -1.64463114]\n", + "MSE 92.64439573573438\n", + "--------------------------------------------------------\n", + "Итерация: 58\n", + "Текущая точка [59.5127619 57.72059311 44.69827546 24.87467163 -1.64463114]| Следующая точка [59.51281319 57.72136501 44.69924408 24.87447536 -1.64403083]\n", + "MSE 92.64437201518268\n", + "--------------------------------------------------------\n", + "Итерация: 59\n", + "Текущая точка [59.51281319 57.72136501 44.69924408 24.87447536 -1.64403083]| Следующая точка [59.51284344 57.72201907 44.70010292 24.87428582 -1.64349942]\n", + "MSE 92.64435386456748\n", + "--------------------------------------------------------\n", + "Итерация: 60\n", + "Текущая точка [59.51284344 57.72201907 44.70010292 24.87428582 -1.64349942]| Следующая точка [59.51285724 57.72257307 44.70086505 24.87410447 -1.64302888]\n", + "MSE 92.64433993270397\n", + "--------------------------------------------------------\n", + "Итерация: 61\n", + "Текущая точка [59.51285724 57.72257307 44.70086505 24.87410447 -1.64302888]| Следующая точка [59.51285835 57.72304216 44.70154189 24.87393226 -1.6426121 ]\n", + "MSE 92.64432920608364\n", + "--------------------------------------------------------\n", + "Итерация: 62\n", + "Текущая точка [59.51285835 57.72304216 44.70154189 24.87393226 -1.6426121 ]| Следующая точка [59.51284979 57.72343918 44.70214342 24.87376976 -1.64224283]\n", + "MSE 92.644320922282\n", + "--------------------------------------------------------\n", + "Итерация: 63\n", + "Текущая точка [59.51284979 57.72343918 44.70214342 24.87376976 -1.64224283]| Следующая точка [59.51283403 57.72377508 44.7026784 24.87361724 -1.64191556]\n", + "MSE 92.64431450605201\n", + "--------------------------------------------------------\n", + "Итерация: 64\n", + "Текущая точка [59.51283403 57.72377508 44.7026784 24.87361724 -1.64191556]| Следующая точка [59.51281304 57.72405912 44.70315452 24.87347473 -1.6416254 ]\n", + "MSE 92.64430952205504\n", + "--------------------------------------------------------\n", + "Итерация: 65\n", + "Текущая точка [59.51281304 57.72405912 44.70315452 24.87347473 -1.6416254 ]| Следующая точка [59.51278841 57.7242992 44.70357851 24.87334211 -1.64136808]\n", + "MSE 92.64430563981963\n", + "--------------------------------------------------------\n", + "Итерация: 66\n", + "Текущая точка [59.51278841 57.7242992 44.70357851 24.87334211 -1.64136808]| Следующая точка [59.5127614 57.72450202 44.70395632 24.87321911 -1.64113979]\n", + "MSE 92.64430260770115\n", + "--------------------------------------------------------\n", + "Итерация: 67\n", + "Текущая точка [59.5127614 57.72450202 44.70395632 24.87321911 -1.64113979]| Следующая точка [59.51273299 57.72467326 44.70429315 24.87310537 -1.64093719]\n", + "MSE 92.64430023348214\n", + "--------------------------------------------------------\n", + "Итерация: 68\n", + "Текущая точка [59.51273299 57.72467326 44.70429315 24.87310537 -1.64093719]| Следующая точка [59.51270398 57.72481775 44.70459363 24.87300046 -1.64075733]\n", + "MSE 92.64429836988138\n", + "--------------------------------------------------------\n", + "Итерация: 69\n", + "Текущая точка [59.51270398 57.72481775 44.70459363 24.87300046 -1.64075733]| Следующая точка [59.51267495 57.7249396 44.70486179 24.87290393 -1.64059761]\n", + "MSE 92.64429690370082\n", + "--------------------------------------------------------\n", + "Итерация: 70\n", + "Текущая точка [59.51267495 57.7249396 44.70486179 24.87290393 -1.64059761]| Следующая точка [59.51264637 57.72504227 44.70510124 24.87281529 -1.64045571]\n", + "MSE 92.6442957476727\n", + "--------------------------------------------------------\n", + "Итерация: 71\n", + "Текущая точка [59.51264637 57.72504227 44.70510124 24.87281529 -1.64045571]| Следующая точка [59.51261856 57.72512872 44.70531515 24.87273404 -1.64032962]\n", + "MSE 92.64429483431937\n", + "--------------------------------------------------------\n", + "Итерация: 72\n", + "Текущая точка [59.51261856 57.72512872 44.70531515 24.87273404 -1.64032962]| Следующая точка [59.51259179 57.72520146 44.70550631 24.8726597 -1.64021752]\n", + "MSE 92.64429411131276\n", + "--------------------------------------------------------\n", + "Итерация: 73\n", + "Текущая точка [59.51259179 57.72520146 44.70550631 24.8726597 -1.64021752]| Следующая точка [59.51256621 57.7252626 44.70567721 24.87259177 -1.64011783]\n", + "MSE 92.64429353795867\n", + "--------------------------------------------------------\n", + "Итерация: 74\n", + "Текущая точка [59.51256621 57.7252626 44.70567721 24.87259177 -1.64011783]| Следующая точка [59.51254194 57.72531395 44.70583007 24.87252978 -1.64002916]\n", + "MSE 92.64429308252382\n", + "--------------------------------------------------------\n", + "Итерация: 75\n", + "Текущая точка [59.51254194 57.72531395 44.70583007 24.87252978 -1.64002916]| Следующая точка [59.51251904 57.72535702 44.70596682 24.87247329 -1.63995024]\n", + "MSE 92.64429272019784\n", + "--------------------------------------------------------\n", + "Итерация: 76\n", + "Текущая точка [59.51251904 57.72535702 44.70596682 24.87247329 -1.63995024]| Следующая точка [59.51249755 57.72539312 44.70608921 24.87242186 -1.63988 ]\n", + "MSE 92.64429243153427\n", + "--------------------------------------------------------\n", + "Итерация: 77\n", + "Текущая точка [59.51249755 57.72539312 44.70608921 24.87242186 -1.63988 ]| Следующая точка [59.51247745 57.72542332 44.70619878 24.87237508 -1.63981745]\n", + "MSE 92.64429220125481\n", + "--------------------------------------------------------\n", + "Итерация: 78\n", + "Текущая точка [59.51247745 57.72542332 44.70619878 24.87237508 -1.63981745]| Следующая точка [59.51245872 57.72544857 44.7062969 24.87233258 -1.63976173]\n", + "MSE 92.6442920173288\n", + "--------------------------------------------------------\n", + "Итерация: 79\n", + "Текущая точка [59.51245872 57.72544857 44.7062969 24.87233258 -1.63976173]| Следующая точка [59.51244134 57.72546964 44.70638478 24.87229399 -1.63971209]\n", + "MSE 92.64429187026263\n", + "--------------------------------------------------------\n", + "Итерация: 80\n", + "Текущая точка [59.51244134 57.72546964 44.70638478 24.87229399 -1.63971209]| Следующая точка [59.51242524 57.72548719 44.70646353 24.87225898 -1.63966784]\n", + "MSE 92.64429175254996\n", + "--------------------------------------------------------\n" + ] + } + ], + "source": [ + "# установка минимального значения, на которое должны изменяться веса\n", + "eps = 0.0001\n", + "\n", + "# размер шага (learning rate)\n", + "learning_rate = 0.1\n", + "\n", + "next_weights = weights\n", + "# количество итерация \n", + "n = 100\n", + "for i in range(n):\n", + " cur_weights = next_weights\n", + "\n", + " # движение в негативную сторону вычисляемого градиента\n", + " next_weights = cur_weights - learning_rate * gr_mserror_mat(X, cur_weights, y)\n", + "\n", + " # остановка когда достигнута необходимая степень точности\n", + " print(f\"Итерация: {i}\")\n", + " print(f\"Текущая точка {cur_weights}| Следующая точка {next_weights}\")\n", + " print(f\"MSE {mserror_mat(X, cur_weights, y)}\")\n", + " print(\"--------------------------------------------------------\")\n", + " \n", + " if np.linalg.norm(cur_weights - next_weights, ord=2) <= eps:\n", + " break" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "r2s0LuwhMWAg" + }, + "source": [ + "Вышли раньше из обучения, т.к. веса перестали сильно изменяться и мы стали топтаться на одном месте." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3IfMej7yCPlC" + }, + "source": [ + "И получили точно такую же метрику, которая получалась у `LinearRegression` из `sklearn`.\n", + "\n", + "И давайте сравним полученные коэффициенты с теми, которые были сгенерированы вместе с данными." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iaxxRtstCPlD", + "outputId": "1837b72c-7dbd-4acc-dfd5-32b48d685a9d", + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Веса при признаках\n", + "True [59.32158596 58.74342238 44.07539836 25.03682142],\n", + "Trained [59.51242524 57.72548719 44.70646353 24.87225898]\n", + "\n", + "Вес свободный True 0, trained -1.6396678387172885\n" + ] + } + ], + "source": [ + "print('Веса при признаках')\n", + "print(f'True {coeffs},\\nTrained {next_weights[:-1]}')\n", + "\n", + "print('\\nВес свободный', end=' ')\n", + "print(f'True 0, trained {next_weights[-1]}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Метрики качества линейной регрессии\n", + "\n", + "В задачах машинного обучения мы хотим сравнивать несколько моделей машинного обучения и выбирать наилучшую из них. Решение о том, какая модель хорошая, а какая плохая, принимается на основе одной или нескольких *метрик* моделей машинного обучения.\n", + "\n", + "Без метрик обучение моделей вообще теряет всякий смысл – как же определить, какая из зоопарка обученных моделек хорошая, а какая плохая? Давайте разберёмся, как определить лучшую модель с помощью математики" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Интуиция за метриками стоит очень простая – давайте как-нибудь усредним отклонения по всем точкам и получим одно число – метрику качества линейной регрессии, т.е. насколько модель отклоняется от реальных данных." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Метрики принимают на вход два вектора, предсказания модели и истинные значения, после чего вычисляют по этим векторам качество модели.\n", + "\n", + "Сначала загрузим данные эксперимента" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.datasets import make_regression\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "features, y = make_regression()\n", + "\n", + "\n", + "reg = LinearRegression().fit(features, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Теперь получим два вектора – предказанное значение $\\hat{y}$ и истинное значение $y$:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [], + "source": [ + "y_pred = reg.predict(features) # предсказанное значение\n", + "y_true = y # истинное значение" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Теперь посмотрим, какие функции можно применять к этим двум наборам точек" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mean absolute error\n", + "\n", + "Для оценки качества регрессии можно использовать среднюю абсолютную ошибку" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MAE = 2.604094717639782e-13\n" + ] + } + ], + "source": [ + "from sklearn.metrics import mean_absolute_error\n", + "\n", + "print(\"MAE = %s\" % mean_absolute_error(\n", + " reg.predict(features), y)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Mean Absolute Error* - это просто сумма отклонений истинных значений $y$ от предсказаний нашей модели:\n", + "\n", + "$$\n", + "\\text{absolute error} = |y_1 - \\hat{y}_1| + |y_2 - \\hat{y}_2| + \\ldots\n", + "$$\n", + "\n", + "А потом мы эту сумму делим на количество точек - получаем среднюю ошибку\n", + "\n", + "Метрика принимает только положительные значения! Чем ближе к нулю, тем лучше модель." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### MSE\n", + "\n", + "Mean Squared Error (MSE) - это базовая метрика для определения качества линейной регрессии\n", + "\n", + "Для каждого предсказанного значения $\\hat{y}_i$ мы считаем квадрат отклонения от фактического значения и считаем среднее по полученным величинам" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MSE = 1.0322079481242069e-25\n" + ] + } + ], + "source": [ + "from sklearn.metrics import mean_squared_error\n", + "\n", + "mse = mean_squared_error(y_true, y_pred)\n", + "\n", + "print('MSE = %s' % mse)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "В целом логика та же, что в *MAE*, только усреднять мы будем квадраты ошибок \n", + "$$\n", + "\\text{absolute error} = (y_1 - \\hat{y}_1)^2 + (y_2 - \\hat{y}_2)^2 + \\ldots\n", + "$$\n", + "\n", + "Эта метрика тоже принимает только положительные значения! Чем ближе к нулю, тем лучше модель." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Эта ошибка визуально похожа на *MSE*, но на графике видно, что *MAE*(красная линия) почти всегда меньше по значению, чем MSE (синяя линия). Это значит, что *MSE* более \"пессимистична\" и сильнее штрафует за большие ошибки - т.е. MSE лучше применять, когда вы уверены что в выборке нет \"выборосов\" (англ. outliers) - значений, который очень сильно отличаются от остальных точек. В этом случае MSE может быть очень плохой, а на деле ситуация приемлема. Если выбросы есть, лучше применять MAE.\n", + "\n", + "![rmse_vs_mae](https://248006.selcdn.ru/public/Data-science-4/img/rmse_vs_mae.png)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### $R^2$ (коэффициент детерминации)\n", + "\n", + "Название - *coefficient of determination*. Наилучшее возможное значение 1.0, чем меньше тем хуже. Если этот коэффициент близок к 1, то условная дисперсия модели (то есть разброс предсказаний модели $\\hat{y}$ относительно разброса самой целевой переменной $y$ ) достаточно мала - то есть модель неплохо описывает данные. Коэффициент может быть даже отрицательным - то это значит, что модель совсем уж плохая.\n", + "\n", + "Эта метрика хороша тем, что она *нормализована*, то есть не превышает единицу - удобно сравнивать разные модели. Например, метрика $MSE$ может принимать ничем не ограниченные значения больше нуля - это не всегда удобно." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "В библиотеке *sklearn* есть готовая реализация этой метрики." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "r2_score = 1.0\n" + ] + } + ], + "source": [ + "from sklearn.metrics import r2_score\n", + "\n", + "print(\"r2_score = %s\" % r2_score(y_true, y_pred))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Про другие ошибки можно почитать в [официальной документации](https://scikit-learn.org/stable/modules/model_evaluation.html#regression-metrics) в разделе про метрики регрессии." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Логистическая регрессия\n", + "\n", + "`Логистическая регрессия = sigmoid(linear_regression) = вероятности предсказания по классам`" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([[-0.86305361],\n", + " [-1.4372011 ],\n", + " [ 0.19592225],\n", + " [-0.87164985],\n", + " [ 0.00982831],\n", + " [ 1.30282593],\n", + " [ 0.16134434],\n", + " [-0.9223264 ],\n", + " [-0.10173176],\n", + " [ 0.41006497],\n", + " [ 0.27129997],\n", + " [-0.71111212],\n", + " [-2.98259876],\n", + " [-0.09300387],\n", + " [ 0.82285659],\n", + " [ 0.16493473],\n", + " [-0.40806382],\n", + " [ 0.62136283],\n", + " [ 0.76258897],\n", + " [-0.11001122],\n", + " [-1.26261842],\n", + " [ 0.04513441],\n", + " [ 0.50026937],\n", + " [-0.6784482 ],\n", + " [ 0.2182344 ]]),\n", + " array([0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1,\n", + " 1, 0, 1]))" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import make_classification\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "X, y = make_classification(n_samples=25, n_features=1, n_informative=1,\n", + " n_redundant=0, random_state=11, n_clusters_per_class=1,\n", + " class_sep=0.4)\n", + "\n", + "X, y" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [], + "source": [ + "model_lr = LinearRegression().fit(X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def sigmoid(x):\n", + " return 1 / (1 + np.exp(-x))\n", + "\n", + "x = np.linspace(-3, 3, num=100)\n", + "model_lr_a, model_lr_b = model_lr.coef_, model_lr.intercept_\n", + "model_lr_y = model_lr_a * x + model_lr_b\n", + "\n", + "plt.figure(figsize=(10, 2))\n", + "plt.plot(x, sigmoid(model_lr_y), linewidth=2, label='sklearn')\n", + "plt.scatter(X, y, c=y, s=100, edgecolors='black')\n", + "plt.ylabel('pred');plt.xlabel('x')\n", + "plt.yticks(np.arange(0, 2), ['0 class', '1 class'])\n", + "plt.ylim(-0.1, 1.1);plt.xlim(-3.5, 2)\n", + "plt.title('LogisticRegression')\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([[5.1, 3.5, 1.4, 0.2],\n", + " [4.9, 3. , 1.4, 0.2],\n", + " [4.7, 3.2, 1.3, 0.2],\n", + " [4.6, 3.1, 1.5, 0.2],\n", + " [5. , 3.6, 1.4, 0.2],\n", + " [5.4, 3.9, 1.7, 0.4],\n", + " [4.6, 3.4, 1.4, 0.3],\n", + " [5. , 3.4, 1.5, 0.2],\n", + " [4.4, 2.9, 1.4, 0.2],\n", + " [4.9, 3.1, 1.5, 0.1],\n", + " [5.4, 3.7, 1.5, 0.2],\n", + " [4.8, 3.4, 1.6, 0.2],\n", + " [4.8, 3. , 1.4, 0.1],\n", + " [4.3, 3. , 1.1, 0.1],\n", + " [5.8, 4. , 1.2, 0.2],\n", + " [5.7, 4.4, 1.5, 0.4],\n", + " [5.4, 3.9, 1.3, 0.4],\n", + " [5.1, 3.5, 1.4, 0.3],\n", + " [5.7, 3.8, 1.7, 0.3],\n", + " [5.1, 3.8, 1.5, 0.3],\n", + " [5.4, 3.4, 1.7, 0.2],\n", + " [5.1, 3.7, 1.5, 0.4],\n", + " [4.6, 3.6, 1. , 0.2],\n", + " [5.1, 3.3, 1.7, 0.5],\n", + " [4.8, 3.4, 1.9, 0.2],\n", + " [5. , 3. , 1.6, 0.2],\n", + " [5. , 3.4, 1.6, 0.4],\n", + " [5.2, 3.5, 1.5, 0.2],\n", + " [5.2, 3.4, 1.4, 0.2],\n", + " [4.7, 3.2, 1.6, 0.2],\n", + " [4.8, 3.1, 1.6, 0.2],\n", + " [5.4, 3.4, 1.5, 0.4],\n", + " [5.2, 4.1, 1.5, 0.1],\n", + " [5.5, 4.2, 1.4, 0.2],\n", + " [4.9, 3.1, 1.5, 0.2],\n", + " [5. , 3.2, 1.2, 0.2],\n", + " [5.5, 3.5, 1.3, 0.2],\n", + " [4.9, 3.6, 1.4, 0.1],\n", + " [4.4, 3. , 1.3, 0.2],\n", + " [5.1, 3.4, 1.5, 0.2],\n", + " [5. , 3.5, 1.3, 0.3],\n", + " [4.5, 2.3, 1.3, 0.3],\n", + " [4.4, 3.2, 1.3, 0.2],\n", + " [5. , 3.5, 1.6, 0.6],\n", + " [5.1, 3.8, 1.9, 0.4],\n", + " [4.8, 3. , 1.4, 0.3],\n", + " [5.1, 3.8, 1.6, 0.2],\n", + " [4.6, 3.2, 1.4, 0.2],\n", + " [5.3, 3.7, 1.5, 0.2],\n", + " [5. , 3.3, 1.4, 0.2],\n", + " [7. , 3.2, 4.7, 1.4],\n", + " [6.4, 3.2, 4.5, 1.5],\n", + " [6.9, 3.1, 4.9, 1.5],\n", + " [5.5, 2.3, 4. , 1.3],\n", + " [6.5, 2.8, 4.6, 1.5],\n", + " [5.7, 2.8, 4.5, 1.3],\n", + " [6.3, 3.3, 4.7, 1.6],\n", + " [4.9, 2.4, 3.3, 1. ],\n", + " [6.6, 2.9, 4.6, 1.3],\n", + " [5.2, 2.7, 3.9, 1.4],\n", + " [5. , 2. , 3.5, 1. ],\n", + " [5.9, 3. , 4.2, 1.5],\n", + " [6. , 2.2, 4. , 1. ],\n", + " [6.1, 2.9, 4.7, 1.4],\n", + " [5.6, 2.9, 3.6, 1.3],\n", + " [6.7, 3.1, 4.4, 1.4],\n", + " [5.6, 3. , 4.5, 1.5],\n", + " [5.8, 2.7, 4.1, 1. ],\n", + " [6.2, 2.2, 4.5, 1.5],\n", + " [5.6, 2.5, 3.9, 1.1],\n", + " [5.9, 3.2, 4.8, 1.8],\n", + " [6.1, 2.8, 4. , 1.3],\n", + " [6.3, 2.5, 4.9, 1.5],\n", + " [6.1, 2.8, 4.7, 1.2],\n", + " [6.4, 2.9, 4.3, 1.3],\n", + " [6.6, 3. , 4.4, 1.4],\n", + " [6.8, 2.8, 4.8, 1.4],\n", + " [6.7, 3. , 5. , 1.7],\n", + " [6. , 2.9, 4.5, 1.5],\n", + " [5.7, 2.6, 3.5, 1. ],\n", + " [5.5, 2.4, 3.8, 1.1],\n", + " [5.5, 2.4, 3.7, 1. ],\n", + " [5.8, 2.7, 3.9, 1.2],\n", + " [6. , 2.7, 5.1, 1.6],\n", + " [5.4, 3. , 4.5, 1.5],\n", + " [6. , 3.4, 4.5, 1.6],\n", + " [6.7, 3.1, 4.7, 1.5],\n", + " [6.3, 2.3, 4.4, 1.3],\n", + " [5.6, 3. , 4.1, 1.3],\n", + " [5.5, 2.5, 4. , 1.3],\n", + " [5.5, 2.6, 4.4, 1.2],\n", + " [6.1, 3. , 4.6, 1.4],\n", + " [5.8, 2.6, 4. , 1.2],\n", + " [5. , 2.3, 3.3, 1. ],\n", + " [5.6, 2.7, 4.2, 1.3],\n", + " [5.7, 3. , 4.2, 1.2],\n", + " [5.7, 2.9, 4.2, 1.3],\n", + " [6.2, 2.9, 4.3, 1.3],\n", + " [5.1, 2.5, 3. , 1.1],\n", + " [5.7, 2.8, 4.1, 1.3],\n", + " [6.3, 3.3, 6. , 2.5],\n", + " [5.8, 2.7, 5.1, 1.9],\n", + " [7.1, 3. , 5.9, 2.1],\n", + " [6.3, 2.9, 5.6, 1.8],\n", + " [6.5, 3. , 5.8, 2.2],\n", + " [7.6, 3. , 6.6, 2.1],\n", + " [4.9, 2.5, 4.5, 1.7],\n", + " [7.3, 2.9, 6.3, 1.8],\n", + " [6.7, 2.5, 5.8, 1.8],\n", + " [7.2, 3.6, 6.1, 2.5],\n", + " [6.5, 3.2, 5.1, 2. ],\n", + " [6.4, 2.7, 5.3, 1.9],\n", + " [6.8, 3. , 5.5, 2.1],\n", + " [5.7, 2.5, 5. , 2. ],\n", + " [5.8, 2.8, 5.1, 2.4],\n", + " [6.4, 3.2, 5.3, 2.3],\n", + " [6.5, 3. , 5.5, 1.8],\n", + " [7.7, 3.8, 6.7, 2.2],\n", + " [7.7, 2.6, 6.9, 2.3],\n", + " [6. , 2.2, 5. , 1.5],\n", + " [6.9, 3.2, 5.7, 2.3],\n", + " [5.6, 2.8, 4.9, 2. ],\n", + " [7.7, 2.8, 6.7, 2. ],\n", + " [6.3, 2.7, 4.9, 1.8],\n", + " [6.7, 3.3, 5.7, 2.1],\n", + " [7.2, 3.2, 6. , 1.8],\n", + " [6.2, 2.8, 4.8, 1.8],\n", + " [6.1, 3. , 4.9, 1.8],\n", + " [6.4, 2.8, 5.6, 2.1],\n", + " [7.2, 3. , 5.8, 1.6],\n", + " [7.4, 2.8, 6.1, 1.9],\n", + " [7.9, 3.8, 6.4, 2. ],\n", + " [6.4, 2.8, 5.6, 2.2],\n", + " [6.3, 2.8, 5.1, 1.5],\n", + " [6.1, 2.6, 5.6, 1.4],\n", + " [7.7, 3. , 6.1, 2.3],\n", + " [6.3, 3.4, 5.6, 2.4],\n", + " [6.4, 3.1, 5.5, 1.8],\n", + " [6. , 3. , 4.8, 1.8],\n", + " [6.9, 3.1, 5.4, 2.1],\n", + " [6.7, 3.1, 5.6, 2.4],\n", + " [6.9, 3.1, 5.1, 2.3],\n", + " [5.8, 2.7, 5.1, 1.9],\n", + " [6.8, 3.2, 5.9, 2.3],\n", + " [6.7, 3.3, 5.7, 2.5],\n", + " [6.7, 3. , 5.2, 2.3],\n", + " [6.3, 2.5, 5. , 1.9],\n", + " [6.5, 3. , 5.2, 2. ],\n", + " [6.2, 3.4, 5.4, 2.3],\n", + " [5.9, 3. , 5.1, 1.8]]),\n", + " array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_iris\n", + "from sklearn.linear_model import LogisticRegression\n", + "X, y = load_iris(return_X_y=True)\n", + "X, y" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/pakorolev/miniconda3/envs/py38/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:458: ConvergenceWarning: lbfgs failed to converge (status=1):\n", + "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n", + "\n", + "Increase the number of iterations (max_iter) or scale the data as shown in:\n", + " https://scikit-learn.org/stable/modules/preprocessing.html\n", + "Please also refer to the documentation for alternative solver options:\n", + " https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n", + " n_iter_i = _check_optimize_result(\n" + ] + }, + { + "data": { + "text/plain": [ + "array([0, 0])" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model = LogisticRegression().fit(X, y)\n", + "model.predict(X[:2])\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[9.81813537e-01, 1.81864490e-02, 1.43884301e-08],\n", + " [9.71751811e-01, 2.82481591e-02, 3.00932288e-08]])" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.predict_proba(X[:2, :])\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Метрики задачи классификации" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "После отбра признаков, выбора и, конечно, реализации модели и получения некоего результата в виде класса или вероятности принадлежности к классу, следующим шагом будет выяснение того, насколько эффективна модель." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Матрица ошибок (Confusion Matrix)\n", + "\n", + "Матрица ошибок - одна из интуитивно понятных метрик, используемых для определения точности модели. Она используется для задачи классификации, где выходные данные могут быть двух или более классов. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Возьмем два примера с, абстрактно, двумя классами - \"плохой\" и \"хороший\" - и подумаем, что в каждом конкретном случае для нас будет важнее предсказать.\n", + "\n", + "1. Предположим, что мы решаем задачу классификации, где предсказываем, болен человек или нет: *1*, если болен, и *0*, если здоров. Скажем, из 100 человек только 5 больны. Так как больных всего 5% от общего числа людей, то даже очень плохая модель (прогнозирование всех как здоровых) даст нам точность в 95% - это частая проблема для данных с несбалансированными классами. Поэтому в этом случае мы хотим правильно классифицировать всех больных людей - если здоровые будут отнесены к больным, то в данном случае это повлечет за собой явно меньше неприятностей.\n", + "\n", + "2. Теперь давайте представим, что нам надо классифицировать, является ли электронное письмо спамом или нет. Присвоим метку *1*, если это спам, и *0*, если не является спамом. Предположим, что модель классифицировала важное письмо, которого вы отчаянно ждете, как *спам*. В этой ситуации это может быть довольно трагично, ведь в письме может находиться важная информация. Соответственно, в задаче классификации электронных писем более важно минимизировать количество объектов, отнесенных к классу \"плохой\".\n", + "\n", + "Оба этих случая могут быть исследованы с помощью матрицы ошибок, элементы которой как раз таки указывают на ошибочную классификацию в первом и во втором примере. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Матрица ошибок представляет собой таблицу с двумя измерениями - {\"Actual\", \"Predicted\"}, каждое из которых представлено множеством прогнозируемых классов. Фактические результаты - это столбцы, а прогнозируемые - строки.\n", + "\n", + "![](https://248006.selcdn.ru/public/DS_Block2_M6_final/conf_mtrx.png)\n", + "\n", + "Сама по себе матрица ошибок не является показателем производительности как таковым, однако почти все метрики (Recall, Precision, Accuracy, AUC-ROC Curve) основаны на значениях внутри нее." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Теперь давайте разберемся в терминах матрицы ошибок: что означают все ее атрибуты TP, TN, FP и FN?\n", + "\n", + "![](https://248006.selcdn.ru/public/DS_Block2_M6_final/terms.png)\n", + "\n", + "Итак,\n", + "- *True Positives (TP)*: Фактический класс объекта был *1 (True)* и прогнозируемый также *1 (True)*\n", + "- *True Negatives (TN)*: Фактический класс объекта был *0 (False)* и прогнозируемый также *0 (False)*\n", + "- *False Positives (FP)*: Фактический класс объекта был *0 (False)*, а прогнозируемый - *1 (True)*. False - потому что модель предсказала неверно, positives - потому что предсказанный класс был положительным\n", + "- *False Negatives (FN)*: Фактический класс объекта был *1 (True)*, а прогнозируемый - *0 (False)*. False - потому что модель предсказала неверно, negatives - потому что предсказанный класс был отрицательным\n", + "\n", + "Логично, что идеальным сценарием является получение такой матрицы, в которой модель дает FP == 0 и FN == 0, однако в реальной жизни любая модель в большинстве случаев не будет давать 100% точности." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.datasets import make_classification, load_iris\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.linear_model import LogisticRegression\n", + "from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay\n", + "\n", + "\n", + "X, y = make_classification(n_samples=1800, n_features=2, n_informative=1,\n", + " n_redundant=0, random_state=11, n_clusters_per_class=1,\n", + " class_sep=0.4)\n", + "\n", + "\n", + "X_train, X_test, y_train, y_test = train_test_split(\n", + " X, y, test_size=0.2, random_state=42)\n", + "\n", + "model = LogisticRegression().fit(X_train, y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vexV5Rp1XvhPwa7ol/qgn3trv+HzHrEJJ0j9XttVTk+MlSQOHl0oWQx+sbuuNEAGPshiG4dXl0itXrlR6erpeeOEFXXzxxZo7d65ef/11ffXVVw3m8n+pvLxcNptNP+zpLGsE7WL4p9TYPt4OAWg2dUatNunvKisrk9V66mcfuONErrh+/Ri1ahPc5OvUVtZo1VWLmzXW5uL1h+r88Y9/1HfffacZM2aoqKhIffr00bp1634z0QMA4Ara+F6WkZFB2x4AgGZyWiR7AACaG8/GBwDAz5m5jc+qNgAA/ByVPQDAFMxc2ZPsAQCmYOZkTxsfAIBmsGXLFg0bNkyxsbGyWCxavXq1Y19tba2mTp2q3r17q02bNoqNjdWf/vQnFRYWOl2jpKREaWlpslqtioyM1NixY1VRUeFyLCR7AIApuPUSnCZ0BSorK5WYmKgFCxY02Hfs2DHt3LlTmZmZ2rlzp95++23l5eXpuuuuczouLS1NX3zxhdavX6+1a9dqy5Ytuv32213+7rTxAQCmYMi9n8+5+rjZoUOHaujQoSfdZ7PZtH79eqex5557ThdffLEOHjyo+Ph47d69W+vWrdMnn3yifv36SZLmz5+va665Rk8++aRiY2MbHQuVPQDAFDxV2ZeXlztt1dXVHomvrKxMFotFkZGRkqTs7GxFRkY6Er0kpaSkKCAgQDt27HDp2iR7AABcEBcXJ5vN5tiysrLcvmZVVZWmTp2qG2+80fHc/aKiIrVv397puKCgIEVFRamoqMil69PGBwCYgqdW4xcUFDi9CMfdV6/X1tbqhhtukGEYWrhwoVvXOhWSPQDAFDyV7K1Wq8feenci0R84cEAbN250um5MTIyOHDnidHxdXZ1KSkoUExPj0n1o4wMA4AUnEv3evXv1r3/9S+3atXPan5ycrNLSUuXm5jrGNm7cKLvdrqSkJJfuRWUPADCFln6oTkVFhfbt2+f4nJ+fr127dikqKkodOnTQ73//e+3cuVNr165VfX29Yx4+KipKwcHB6tmzp4YMGaJx48Zp0aJFqq2tVUZGhkaPHu3SSnyJZA8AMAnDsMhwI9m7em5OTo4GDx7s+DxlyhRJUnp6uh588EG98847kqQ+ffo4nffBBx9o0KBBkqRly5YpIyNDV155pQICAjRq1CjNmzfP5dhJ9gAANINBgwbJME796/xf23dCVFSUli9f7nYsJHsAgCnwPnsAAPwcL8IBAAB+i8oeAGAKLb1A73RCsgcAmIKZ2/gkewCAKZi5smfOHgAAP0dlDwAwBcPNNr4vV/YkewCAKRiSGvEcm18931fRxgcAwM9R2QMATMEuiyw8QQ8AAP/FanwAAOC3qOwBAKZgNyyy8FAdAAD8l2G4uRrfh5fj08YHAMDPUdkDAEzBzAv0SPYAAFMg2QMA4OfMvECPOXsAAPwclT0AwBTMvBqfZA8AMIXjyd6dOXsPBtPCaOMDAODnqOwBAKbAanwAAPycIffeSe/DXXza+AAA+DsqewCAKdDGBwDA35m4j0+yBwCYg5uVvXy4smfOHgAAP0dlDwAwBZ6gBwCAnzPzAj3a+AAA+DkqewCAORgW9xbZ+XBlT7IHAJiCmefsaeMDAODnqOwBAObAQ3UAAPBvZl6N36hk/8477zT6gtddd12TgwEAAJ7XqGQ/YsSIRl3MYrGovr7enXgAAGg+PtyKd0ejFujZ7fZGbSR6AMDp6kQb353NFVu2bNGwYcMUGxsri8Wi1atX/yIeQzNmzFCHDh0UFhamlJQU7d271+mYkpISpaWlyWq1KjIyUmPHjlVFRYXL392t1fhVVVXunA4AQMsxPLC5oLKyUomJiVqwYMFJ9z/++OOaN2+eFi1apB07dqhNmzZKTU11yq1paWn64osvtH79eq1du1ZbtmzR7bff7logakKyr6+v15w5c3TWWWcpPDxcX3/9tSQpMzNTr7zyissBAADgj4YOHaqHHnpI119/fYN9hmFo7ty5euCBBzR8+HCdf/75Wrp0qQoLCx0dgN27d2vdunV6+eWXlZSUpP79+2v+/PlasWKFCgsLXYrF5WT/8MMPa8mSJXr88ccVHBzsGD/vvPP08ssvu3o5AABaiMUDm1ReXu60VVdXuxxJfn6+ioqKlJKS4hiz2WxKSkpSdna2JCk7O1uRkZHq16+f45iUlBQFBARox44dLt3P5WS/dOlSvfjii0pLS1NgYKBjPDExUV999ZWrlwMAoGV4qI0fFxcnm83m2LKyslwOpaioSJIUHR3tNB4dHe3YV1RUpPbt2zvtDwoKUlRUlOOYxnL5d/aHDx9Wly5dGozb7XbV1ta6ejkAAHxKQUGBrFar43NISIgXo2kclyv7Xr166cMPP2ww/uabb+qCCy7wSFAAAHichyp7q9XqtDUl2cfExEiSiouLncaLi4sd+2JiYnTkyBGn/XV1dSopKXEc01guV/YzZsxQenq6Dh8+LLvdrrffflt5eXlaunSp1q5d6+rlAABoGafRW+8SEhIUExOjDRs2qE+fPpKOrwXYsWOH7rzzTklScnKySktLlZubq759+0qSNm7cKLvdrqSkJJfu53KyHz58uNasWaPZs2erTZs2mjFjhi688EKtWbNGV111lauXAwDAL1VUVGjfvn2Oz/n5+dq1a5eioqIUHx+vSZMm6aGHHlLXrl2VkJCgzMxMxcbGOh5k17NnTw0ZMkTjxo3TokWLVFtbq4yMDI0ePVqxsbEuxdKkZ+NffvnlWr9+fVNOBQDAK1r6Fbc5OTkaPHiw4/OUKVMkSenp6VqyZInuv/9+VVZW6vbbb1dpaan69++vdevWKTQ01HHOsmXLlJGRoSuvvFIBAQEaNWqU5s2b53LsTX4RTk5Ojnbv3i3p+Dz+iRYDAACnpRZ+692gQYNk/MrfECwWi2bPnq3Zs2ef8pioqCgtX77ctRufhMvJ/tChQ7rxxhv10UcfKTIyUpJUWlqqSy+9VCtWrNDZZ5/tdlAAAMBzXF6Nf9ttt6m2tla7d+9WSUmJSkpKtHv3btntdt12223NESMAAO47sUDPnc1HuVzZb968Wdu2bVP37t0dY927d9f8+fN1+eWXezQ4AAA8xWIc39w531e5nOzj4uJO+vCc+vp6l1cHAgDQYlp4zv504nIb/4knntCECROUk5PjGMvJydHdd9+tJ5980qPBAQAA9zWqsm/btq0slp/nKiorK5WUlKSgoOOn19XVKSgoSLfeeqvj94EAAJxWTqOH6rS0RiX7uXPnNnMYAAA0MxO38RuV7NPT05s7DgAA0Eya/FAdSaqqqlJNTY3T2P99ExAAAKcNE1f2Li/Qq6ysVEZGhtq3b682bdqobdu2ThsAAKclD731zhe5nOzvv/9+bdy4UQsXLlRISIhefvllzZo1S7GxsVq6dGlzxAgAANzgcht/zZo1Wrp0qQYNGqQxY8bo8ssvV5cuXdSxY0ctW7ZMaWlpzREnAADuMfFqfJcr+5KSEnXu3FnS8fn5kpISSVL//v21ZcsWz0YHAICHnHiCnjubr3I52Xfu3Fn5+fmSpB49euj111+XdLziP/FiHAAAcPpwOdmPGTNGn332mSRp2rRpWrBggUJDQzV58mTdd999Hg8QAACPMPECPZfn7CdPnuz455SUFH311VfKzc1Vly5ddP7553s0OAAA4D63fmcvSR07dlTHjh09EQsAAM3GIjffeuexSFpeo5L9vHnzGn3BiRMnNjkYAADgeY1K9s8880yjLmaxWLyS7Ef9/g8KCgxp8fsCLSHtq396OwSg2fxYUadNfVvoZib+6V2jkv2J1fcAAPgsHpcLAAD8ldsL9AAA8AkmruxJ9gAAU3D3KXimeoIeAADwLVT2AABzMHEbv0mV/YcffqibbrpJycnJOnz4sCTpr3/9q7Zu3erR4AAA8BgTPy7X5WT/1ltvKTU1VWFhYfr0009VXV0tSSorK9Mjjzzi8QABAIB7XE72Dz30kBYtWqSXXnpJrVq1coxfdtll2rlzp0eDAwDAU8z8iluX5+zz8vI0YMCABuM2m02lpaWeiAkAAM8z8RP0XK7sY2JitG/fvgbjW7duVefOnT0SFAAAHsecfeONGzdOd999t3bs2CGLxaLCwkItW7ZM9957r+68887miBEAALjB5Tb+tGnTZLfbdeWVV+rYsWMaMGCAQkJCdO+992rChAnNESMAAG4z80N1XE72FotFf/nLX3Tfffdp3759qqioUK9evRQeHt4c8QEA4Bkm/p19kx+qExwcrF69enkyFgAA0AxcTvaDBw+WxXLqFYkbN250KyAAAJqFuz+fM1Nl36dPH6fPtbW12rVrlz7//HOlp6d7Ki4AADyLNn7jPfPMMycdf/DBB1VRUeF2QAAAwLM89ta7m266Sa+++qqnLgcAgGeZ+Hf2HnvrXXZ2tkJDQz11OQAAPIqf3rlg5MiRTp8Nw9C3336rnJwcZWZmeiwwAADgGS638W02m9MWFRWlQYMG6b333tPMmTObI0YAAHxOfX29MjMzlZCQoLCwMJ1zzjmaM2eODOPnFoFhGJoxY4Y6dOigsLAwpaSkaO/evR6PxaXKvr6+XmPGjFHv3r3Vtm1bjwcDAECzaeHV+I899pgWLlyo1157Teeee65ycnI0ZswY2Ww2TZw4UZL0+OOPa968eXrttdeUkJCgzMxMpaam6ssvv/To1LhLyT4wMFBXX321du/eTbIHAPgUT83Zl5eXO42HhIQoJCSkwfHbtm3T8OHDde2110qSOnXqpL/97W/6+OOPJR2v6ufOnasHHnhAw4cPlyQtXbpU0dHRWr16tUaPHt30YH/B5Tb+eeedp6+//tpjAQAA4Evi4uKcprOzsrJOetyll16qDRs2aM+ePZKkzz77TFu3btXQoUMlSfn5+SoqKlJKSorjHJvNpqSkJGVnZ3s0ZpcX6D300EO69957NWfOHPXt21dt2rRx2m+1Wj0WHAAAHuWBFfUFBQVOue5kVb10/MVx5eXl6tGjhwIDA1VfX6+HH35YaWlpkqSioiJJUnR0tNN50dHRjn2e0uhkP3v2bN1zzz265pprJEnXXXed02NzDcOQxWJRfX29RwMEAMAjPDRnb7VaG1XYvv7661q2bJmWL1+uc889V7t27dKkSZMUGxvb4k+cbXSynzVrlu644w598MEHzRkPAAB+4b777tO0adMcc++9e/fWgQMHlJWVpfT0dMXExEiSiouL1aFDB8d5xcXFDR5N765GJ/sTPxUYOHCgRwMAAKAltPRDdY4dO6aAAOelcYGBgbLb7ZKkhIQExcTEaMOGDY7kXl5erh07dujOO+9seqAn4dKc/a+97Q4AgNNaC//0btiwYXr44YcVHx+vc889V59++qmefvpp3XrrrZKO59RJkybpoYceUteuXR0/vYuNjdWIESPcCLQhl5J9t27dfjPhl5SUuBUQAAD+YP78+crMzNRdd92lI0eOKDY2Vn/+8581Y8YMxzH333+/Kisrdfvtt6u0tFT9+/fXunXrPP74eZeS/axZs2Sz2TwaAAAALaGl2/gRERGaO3eu5s6de+prWiyaPXu2Zs+e3fTAGsGlZD969Gi1b9++uWIBAKD5mPh99o1+qA7z9QAA+CaXV+MDAOCTTFzZNzrZn/ipAAAAvoj32QMA4O9MXNm7/CIcAADgW6jsAQDmYOLKnmQPADAFM8/Z08YHAMDPUdkDAMyBNj4AAP6NNj4AAPBbVPYAAHOgjQ8AgJ8zcbKnjQ8AgJ+jsgcAmILlp82d830VyR4AYA4mbuOT7AEApsBP7wAAgN+isgcAmANtfAAATMCHE7Y7aOMDAODnqOwBAKZg5gV6JHsAgDmYeM6eNj4AAH6Oyh4AYAq08QEA8He08QEAgL+isgcAmAJtfAAA/J2J2/gkewCAOZg42TNnDwCAn6OyBwCYAnP2AAD4O9r4AADAX1HZAwBMwWIYshhNL8/dOdfbSPYAAHOgjQ8AAPwVlT0AwBTMvBqfyh4AYA6GBzYXHT58WDfddJPatWunsLAw9e7dWzk5OT+HZBiaMWOGOnTooLCwMKWkpGjv3r1ufMmTI9kDANAMfvjhB1122WVq1aqV/vGPf+jLL7/UU089pbZt2zqOefzxxzVv3jwtWrRIO3bsUJs2bZSamqqqqiqPxkIbHwBgCi3dxn/ssccUFxenxYsXO8YSEhIc/2wYhubOnasHHnhAw4cPlyQtXbpU0dHRWr16tUaPHt30YH+Byh4AYA4eauOXl5c7bdXV1Se93TvvvKN+/frpD3/4g9q3b68LLrhAL730kmN/fn6+ioqKlJKS4hiz2WxKSkpSdna2R786yR4AYAonKnt3NkmKi4uTzWZzbFlZWSe939dff62FCxeqa9euev/993XnnXdq4sSJeu211yRJRUVFkqTo6Gin86Kjox37PIU2PgAALigoKJDVanV8DgkJOelxdrtd/fr10yOPPCJJuuCCC/T5559r0aJFSk9Pb5FYT6CyBwCYg4fa+Far1Wk7VbLv0KGDevXq5TTWs2dPHTx4UJIUExMjSSouLnY6pri42LHPU0j2AADTcLeF74rLLrtMeXl5TmN79uxRx44dJR1frBcTE6MNGzY49peXl2vHjh1KTk5263v+Em18AACaweTJk3XppZfqkUce0Q033KCPP/5YL774ol588UVJksVi0aRJk/TQQw+pa9euSkhIUGZmpmJjYzVixAiPxkKyBwCYg2Ec39w53wUXXXSRVq1apenTp2v27NlKSEjQ3LlzlZaW5jjm/vvvV2VlpW6//XaVlpaqf//+WrdunUJDQ5se50mQ7AEApuCNx+X+7ne/0+9+97tTX9Ni0ezZszV79uymB9YIzNkDAODnqOwBAOZg4lfckuwBAKZgsR/f3DnfV9HGBwDAz1HZo4Frr9mra6/dq+joSknSgQM2Lf/becrJiZUktW37o8aO3aUL+hSpdetaHTpk1YqV5+qjj+K8GTZwSsWfBGv3KxEq+SJYP34XqAHPfa+4lJO/VWzHzEjtWxmuvtNL1SO9QpJUcShQny+0qmh7iKq+D1RY+3olDDumc+8oV2BwS34TuIU2PvCz779vrcWL++hwYYQsFkMpV+ZrRuaHypgwRAcP2nTvPdvVpk2NZs0eoPLyEA0a9I2mT/tId999tfZ/HeXt8IEG6n4MUGSPWp0zqlJbJpxxyuMK1ofqv58FK6x9vdN4eX6QDLuUNOsHhXesU9neVtqR2VZ1P1p04dSy5g4fHuKN1finC6+28bds2aJhw4YpNjZWFotFq1ev9mY4+MmOj8/SJzmxKiyM0OHDVr22NFFVVUHq0eN7SVLPnt/rnTXdtGdPOxUVhWvFivNUWdlKXbr+4OXIgZM7a0CV+kwqV9xVp35H+LHiAH3yUKQufaJEAUHO/1WPvbxayVk/qEP/akXE1evsK6rU89ajKlgf1tyhw5NO/M7enc1HeTXZV1ZWKjExUQsWLPBmGPgVAQF2DRxwQKGhdfpq9/GKaPfuMzRgwEGFh1fLYjE0cMABBQfX69//bu/laIGmMezStvuj1GtshSK71jXqnJqjAQq2+fCKLZiKV9v4Q4cO1dChQxt9fHV1tdN7g8vLy5sjLEjq1KlUTz+1XsHB9frxxyDNmXO5DhbYJEmPZF2m6dM+0huvv626Oouqq4/v//bbCC9HDTTNFy9FyBIodb+5olHHHz0QqD3/G64L76eF70to4/uIrKwsp3cIx8WxIKy5HDoUofEZQzRp8tV6970uuuee7YqPO/4ftj/d/G+1Ca/V9OmDNfHuVL29qrumT/9InTqVejdooAn++3kr5f01XMlZJbJYfvv4Y8UB2jjuTMUP+VFdbqhs/gDhOR56650v8qkFetOnT9eUKVMcn8vLy0n4zaSuLtBRqe/bF6VuXUs0fHie3nyzp667bq/+fMc1OnjweKWfn99W5537nX73u7167rmLvBk24LLvckNU9d8Arb6ig2PMqLdo52M2ffVauEZsLHKMHysO0L/+dKbOvKBaSbNZowLf4VPJPiQk5JTvDUbzsgQYatXKrpDQ46uUf7lOxW63KMCXe1wwrYTrjikm2Xnh3sbbzlTC8Eqdc/0xx9iJRB91bq0ueeQHWXyqLwrJ3G18n0r2aBm33LJLOTmxOnKktVq3rtOgQd/o/N5H9EDmIBUUWHX4cLgmTPhEL798gY6WBys5+ZAuuKBIDz440NuhAydVW2nR0YM//+eu4lCQSna3UojNrjax9Qpp67zQLiDIUNgZdlk7H1+sdyLRt4mt14VTS1Vd8nOmDzuTRXo+o4Xfenc6IdmjgUhbte69Z7uion5UZWUr5edH6oHMQfr00+NtzhkzB2nMmF16cOZmhYXVqbAwQk89fYk++emhO8DppuTzYP0r/UzH552PRkqSOo+oVPKjv92O//ajUB090EpHD7TSqoHOf87Tvjrk0ViB5uDVZF9RUaF9+/Y5Pufn52vXrl2KiopSfHy8FyMzt7nPJv3q/sLCCD388OUtFA3gvuikapeS8v+dp5ekc0Ye0zkjj53iaPgK2vhekpOTo8GDBzs+n1h8l56eriVLlngpKgCAX+Jxud4xaNAgGT48BwIAgC9gzh4AYAq08QEA8Hd24/jmzvk+imQPADAHE8/Z81gIAAD8HJU9AMAULHJzzt5jkbQ8kj0AwBxM/AQ92vgAAPg5KnsAgCnw0zsAAPwdq/EBAIC/orIHAJiCxTBkcWORnTvnehvJHgBgDvafNnfO91G08QEA8HNU9gAAU6CNDwCAvzPxanySPQDAHHiCHgAA8FdU9gAAU+AJegAA+Dva+AAAwF9R2QMATMFiP765c76vItkDAMyBNj4AAPBXJHsAgDkYHtia6NFHH5XFYtGkSZMcY1VVVRo/frzatWun8PBwjRo1SsXFxU2/ya8g2QMATOHE43Ld2Zrik08+0QsvvKDzzz/faXzy5Mlas2aN3njjDW3evFmFhYUaOXKkJ75qAyR7AABcUF5e7rRVV1ef8tiKigqlpaXppZdeUtu2bR3jZWVleuWVV/T000/riiuuUN++fbV48WJt27ZN27dv93jMJHsAgDmcWKDnziYpLi5ONpvNsWVlZZ3yluPHj9e1116rlJQUp/Hc3FzV1tY6jffo0UPx8fHKzs72+FdnNT4AwBwMufdO+p+6+AUFBbJarY7hkJCQkx6+YsUK7dy5U5988kmDfUVFRQoODlZkZKTTeHR0tIqKitwI8uRI9gAAU/DUK26tVqtTsj+ZgoIC3X333Vq/fr1CQ0ObfE9PoY0PAICH5ebm6siRI7rwwgsVFBSkoKAgbd68WfPmzVNQUJCio6NVU1Oj0tJSp/OKi4sVExPj8Xio7AEA5mDIzYfqNP7QK6+8Uv/5z3+cxsaMGaMePXpo6tSpiouLU6tWrbRhwwaNGjVKkpSXl6eDBw8qOTm56TGeAskeAGAOLfgEvYiICJ133nlOY23atFG7du0c42PHjtWUKVMUFRUlq9WqCRMmKDk5WZdccknTYzwFkj0AAF7wzDPPKCAgQKNGjVJ1dbVSU1P1/PPPN8u9SPYAAHOwS7K4eb4bNm3a5PQ5NDRUCxYs0IIFC9y7cCOQ7AEApuCp1fi+iNX4AAD4OSp7AIA5mPgVtyR7AIA5mDjZ08YHAMDPUdkDAMzBxJU9yR4AYA5e/umdN5HsAQCmwE/vAACA36KyBwCYA3P2AAD4ObshWdxI2HbfTfa08QEA8HNU9gAAc6CNDwCAv3Mz2ct3kz1tfAAA/ByVPQDAHGjjAwDg5+yG3GrFsxofAACcrqjsAQDmYNiPb+6c76NI9gAAc2DOHgAAP8ecPQAA8FdU9gAAc6CNDwCAnzPkZrL3WCQtjjY+AAB+jsoeAGAOtPEBAPBzdrskN34rb/fd39nTxgcAwM9R2QMAzIE2PgAAfs7EyZ42PgAAfo7KHgBgDiZ+XC7JHgBgCoZhl+HGm+vcOdfbSPYAAHMwDPeqc+bsAQDA6YrKHgBgDoabc/Y+XNmT7AEA5mC3SxY35t19eM6eNj4AAH6Oyh4AYA608QEA8G+G3S7DjTa+L//0jjY+AADNICsrSxdddJEiIiLUvn17jRgxQnl5eU7HVFVVafz48WrXrp3Cw8M1atQoFRcXezwWkj0AwBxOPBvfnc0Fmzdv1vjx47V9+3atX79etbW1uvrqq1VZWek4ZvLkyVqzZo3eeOMNbd68WYWFhRo5cqSnvzltfACASdgNyeL+nH15ebnTcEhIiEJCQhocvm7dOqfPS5YsUfv27ZWbm6sBAwaorKxMr7zyipYvX64rrrhCkrR48WL17NlT27dv1yWXXNL0WH+Byh4AABfExcXJZrM5tqysrEadV1ZWJkmKioqSJOXm5qq2tlYpKSmOY3r06KH4+HhlZ2d7NGYqewCAORiGJHd+Z3+8si8oKJDVanUMn6yq/yW73a5Jkybpsssu03nnnSdJKioqUnBwsCIjI52OjY6OVlFRUdPjPAmSPQDAFAy7IcONNr7xU7K3Wq1Oyb4xxo8fr88//1xbt25t8v3dQbIHAJiDYZd7lX3Tzs3IyNDatWu1ZcsWnX322Y7xmJgY1dTUqLS01Km6Ly4uVkxMTNPjPAnm7AEAaAaGYSgjI0OrVq3Sxo0blZCQ4LS/b9++atWqlTZs2OAYy8vL08GDB5WcnOzRWKjsAQCm4Kk2fmONHz9ey5cv19///ndFREQ45uFtNpvCwsJks9k0duxYTZkyRVFRUbJarZowYYKSk5M9uhJfItkDAMyihdv4CxculCQNGjTIaXzx4sW65ZZbJEnPPPOMAgICNGrUKFVXVys1NVXPP/9802M8BZ9O9if+llVXX+3lSIDm82NFnbdDAJrNjxX1klyvmpuiTrVuPRq/TrUuHd+Y7xQaGqoFCxZowYIFTQ2rUSxGS/wbbiaHDh1SXFyct8MAALipoKDAafGaJ1VVVSkhIcEjP2eLiYlRfn6+QkNDPRBZy/HpZG+321VYWKiIiAhZLBZvh2MK5eXliouLa/A7U8Af8Oe75RmGoaNHjyo2NlYBAc23Zryqqko1NTVuXyc4ONjnEr3k4238gICAZvubIH5dU35nCvgK/ny3LJvN1uz3CA0N9ckk7Sn89A4AAD9HsgcAwM+R7OGSkJAQzZw5s1HPggZ8DX++4a98eoEeAAD4bVT2AAD4OZI9AAB+jmQPAICfI9kDAODnSPZotAULFqhTp04KDQ1VUlKSPv74Y2+HBHjEli1bNGzYMMXGxspisWj16tXeDgnwKJI9GmXlypWaMmWKZs6cqZ07dyoxMVGpqak6cuSIt0MD3FZZWanExMRmfxkJ4C389A6NkpSUpIsuukjPPfecpOPvJYiLi9OECRM0bdo0L0cHeI7FYtGqVas0YsQIb4cCeAyVPX5TTU2NcnNzlZKS4hgLCAhQSkqKsrOzvRgZAKAxSPb4Td9//73q6+sVHR3tNB4dHe2RV0YCAJoXyR4AAD9HssdvOuOMMxQYGKji4mKn8eLiYsXExHgpKgBAY5Hs8ZuCg4PVt29fbdiwwTFmt9u1YcMGJScnezEyAEBjBHk7APiGKVOmKD09Xf369dPFF1+suXPnqrKyUmPGjPF2aIDbKioqtG/fPsfn/Px87dq1S1FRUYqPj/diZIBn8NM7NNpzzz2nJ554QkVFRerTp4/mzZunpKQkb4cFuG3Tpk0aPHhwg/H09HQtWbKk5QMCPIxkDwCAn2POHgAAP0eyBwDAz5HsAQDwcyR7AAD8HMkeAAA/R7IHAMDPkewBAPBzJHsAAPwcyR5w0y233KIRI0Y4Pg8aNEiTJk1q8Tg2bdoki8Wi0tLSUx5jsVi0evXqRl/zwQcfVJ8+fdyK65tvvpHFYtGuXbvcug6ApiPZwy/dcsstslgsslgsCg4OVpcuXTR79mzV1dU1+73ffvttzZkzp1HHNiZBA4C7eBEO/NaQIUO0ePFiVVdX67333tP48ePVqlUrTZ8+vcGxNTU1Cg4O9sh9o6KiPHIdAPAUKnv4rZCQEMXExKhjx4668847lZKSonfeeUfSz633hx9+WLGxserevbskqaCgQDfccIMiIyMVFRWl4cOH65tvvnFcs76+XlOmTFFkZKTatWun+++/X798vcQv2/jV1dWaOnWq4uLiFBISoi5duuiVV17RN99843j5Stu2bWWxWHTLLbdIOv4K4aysLCUkJCgsLEyJiYl68803ne7z3nvvqVu3bgoLC9PgwYOd4mysqVOnqlu3bmrdurU6d+6szMxM1dbWNjjuhRdeUFxcnFq3bq0bbrhBZWVlTvtffvll9ezZU6GhoerRo4eef/55l2MB0HxI9jCNsLAw1dTUOD5v2LBBeXl5Wr9+vdauXava2lqlpqYqIiJCH374oT766COFh4dryJAhjvOeeuopLVmyRK+++qq2bt2qkpISrVq16lfv+6c//Ul/+9vfNG/ePO3evVsvvPCCwsPDFRcXp7feekuSlJeXp2+//VbPPvusJCkrK0tLly7VokWL9MUXX2jy5Mm66aabtHnzZknH/1IycuRIDRs2TLt27dJtt92madOmufzvJCIiQkuWLNGXX36pZ599Vi+99JKeeeYZp2P27dun119/XWvWrNG6dev06aef6q677nLsX7ZsmWbMmKGHH35Yu3fv1iOPPKLMzEy99tprLscDoJkYgB9KT083hg8fbhiGYdjtdmP9+vVGSEiIce+99zr2R0dHG9XV1Y5z/vrXvxrdu3c37Ha7Y6y6utoICwsz3n//fcMwDKNDhw7G448/7thfW1trnH322Y57GYZhDBw40Lj77rsNwzCMvLw8Q5Kxfv36k8b5wQcfGJKMH374wTFWVVVltG7d2ti2bZvTsWPHjjVuvPFGwzAMY/r06UavXr2c9k+dOrXBtX5JkrFq1apT7n/iiSeMvn37Oj7PnDnTCAwMNA4dOuQY+8c//mEEBAQY3377rWEYhnHOOecYy5cvd7rOnDlzjOTkZMMwDCM/P9+QZHz66aenvC+A5sWcPfzW2rVrFR4ertraWtntdv3P//yPHnzwQcf+3r17O83Tf/bZZ9q3b58iIiKcrlNVVaX9+/errKxM3377rZKSkhz7goKC1K9fvwat/BN27dqlwMBADRw4sNFx79u3T8eOHdNVV13lNF5TU6MLLrhAkrR7926nOCQpOTm50fc4YeXKlZo3b57279+viooK1dXVyWq1Oh0THx+vs846y+k+drtdeXl5ioiI0P79+zV27FiNGzfOcUxdXZ1sNpvL8QBoHiR7+K3Bgwdr4cKFCg4OVmxsrIKCnP+4t2nTxulzRUWF+vbtq2XLljW41plnntmkGMLCwlw+p6KiQpL07rvvOiVZ6fg6BE/Jzs5WWlqaZs2apdTUVNlsNq1YsUJPPfWUy7G+9NJLDf7yERgY6LFYAbiHZA+/1aZNG3Xp0qXRx1944YVauXKl2rdv36C6PaFDhw7asWOHBgwYIOl4BZubm6sLL7zwpMf37t1bdrtdmzdvVkpKSoP9JzoL9fX1jrFevXopJCREBw8ePGVHoGfPno7Fhids3779t7/k/7Ft2zZ17NhRf/nLXxxjBw4caHDcwYMHVVhYqNjYWMd9AgIC1L17d0VHRys2NlZff/210tLSXLo/gJbDAj3gJ2lpaTrjjDM0fPhwffjhh8rPz9emTZs0ceJEHTp0SJJ0991369FHH9Xq1av11Vdf6a677vrV38h36tRJ6enpuvXWW7V69WrHNV9//XVJUseOHWWxWLR27Vp99913qqioUEREhO69915NnjxZr732mvbv36+dO3dq/vz5jkVvd9xxh/bu3av77rtPeXl5Wr58uZYsWeLS9+3atasOHjyoFStWaP/+/Zo3b95JFxuGhoYqPT1dn332mT788ENNnDhRN9xwg2JiYiRJs2bNUlZWlubNm6c9e/boP//5jxYvXqynn37apXgANB+SPfCT1q1ba8uWLYqPj9fIkSPVs2dPjR07VlVVVY5K/5577tHNN9+s9PR0JScnKyIiQtdff/2vXnfhwoX6/e9/r7vuuks9evTQuHHjVFlZKUk666yzNGvWLE2bNk3R0dHKyMiQJM2ZM0eZmZnKyspSz549NWTIEL377rtKSEiQdHwe/a233tLq1auVmJioRYsW6ZFHHnHp+1533XWaPHmyMjIy1KdPH23btk2ZmZkNjuvSpYtGjhypa665RldffbXOP/98p5/W3XbbbXr55Ze1ePFi9e7dWwMHDtSSJUscsQLwPotxqpVFAADAL1DZAwDg50j2AAD4OZI9AAB+jmQPAICfI9kDAODnSPYAAPg5kj0AAH6OZA8AgJ8j2QMA4OdI9gAA+DmSPQAAfu7/A9+n6y1MG+yhAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cm = confusion_matrix(y_test, model.predict(X_test))\n", + "\n", + "disp = ConfusionMatrixDisplay(confusion_matrix=cm,\n", + " display_labels=model.classes_)\n", + "disp.plot()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Мы знаем, что будет какая-то ошибка в предсказаниях модели и что это будет либо FP, либо FN, но что именно следует минимизировать, зависит исключительно от потребностей бизнеса и контекста проблемы, которую требуется решить. Например, в нашем примере с классификацией больных людей более важно минимизировать FN - нам важнее правильно распознать больных людей, чем ошибочно отнести здоровых к больным. Напротив, в примере со спамом менее важно пропустить надоедливую рекламу, чем важное письмо - здесь нам актуальнее минимизировать FP." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Теперь рассмотрим метрики классификации, основанные на терминах матрицы ошибок." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Accuracy (доля правильных ответов)\n", + "\n", + "Теперь давайте разберемся с метриками классификации, основанными на матрице ошибок.\n", + "\n", + "Наиболее очевидной мерой качества модели классификации является доля правильных ответов (иногда *accuracy* переводят как *точность*, но этот термин отведен для другой метрики - *precision*) - эту меру мы встречали в предыдущих уроках по классификации, и означает она не что иное, как отношение числа верных прогнозов к общему количеству прогнозов:\n", + "\n", + "\n", + "\n", + "![](https://248006.selcdn.ru/public/DS_Block2_M6_final/accuracy.png)\n", + "\n", + "В терминах матрицы ошибок accuracy приобретает вид:\n", + "\n", + "$$\n", + "Accuracy = \\frac{TP + TN}{TP + FP + FN + TN}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Доля правильных ответов является хорошей мерой, когда классы сбалансированы или почти сбалансированы - их соотношение в конечной выборке должно быть примерно одинаковым. Например, как в датасете Iris - там данные идеально сбалансированы, поэтому метрика дает точный ответ.\n", + "\n", + "Эта метрика совершенно не подходит в качестве меры, если один из классов явно преобладает над другим. Допустим, мы хотим оценить работу спам-фильтра почты. У нас есть 100 не-спам писем, 90 из которых наш классификатор определил верно (True Negative = 90, False Positive = 10), и 10 спам-писем, 5 из которых классификатор также определил верно (True Positive = 5, False Negative = 5).\n", + "\n", + "Тогда accuracy:\n", + "\n", + "$$\n", + "Accuracy = \\frac{5 + 90}{5 + 90 + 10 + 5} = 86,4\n", + "$$\n", + "\n", + "Однако если мы просто будем предсказывать все письма как не-спам, то получим более высокую accuracy:\n", + "\n", + "$$\n", + "Accuracy = \\frac{0 + 100}{0 + 100 + 0 + 10} = 90,9\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8472222222222222" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "\n", + "accuracy_score(y_test, model.predict(X_test))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Precision, recall\n", + "\n", + "Для оценки качества работы алгоритма на каждом из классов по отдельности введем метрики precision (точность) и recall (полнота).\n", + "\n", + "\n", + "\n", + "$$\n", + "Precision = \\frac{TP}{TP + FP}\n", + "$$\n", + "\n", + "\n", + "$$\n", + "Recall = \\frac{TP}{TP + FN}\n", + "$$\n", + "\n", + "`Precision` можно интерпретировать как долю объектов, названных классификатором положительными и при этом действительно являющимися положительными, \n", + "\n", + "а `Recall` показывает, какую долю объектов положительного класса из всех объектов положительного класса нашел алгоритм." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Precision и recall не зависят, в отличие от accuracy, от соотношения классов и потому применимы в условиях несбалансированных выборок." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7888888888888889" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import recall_score\n", + "\n", + "recall_score(y_test, model.predict(X_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8930817610062893" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import precision_score\n", + "\n", + "precision_score(y_test, model.predict(X_test))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Когда стоит использовать *точность*, а когда *полноту*?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Если мы хотим сосредоточиться на минимизации ложных позитивов (вспомним пример со спамом, где нам накладнее пропустить одно важное письмо, чем получить несколько писем со спамом), мы применяем *точность*, а если нам более важно минимизировать риск пропустить хоть один позитивный результат (а здесь подойдет пример с больными, где нам опаснее получить ложноотрицательный ответ и отнести больного к здоровым), то следует использовать *полноту*.\n", + "\n", + "Также следует отметить, что точность и полнота не зависят от соотношения размеров классов. Даже если объектов одного из классов на порядки больше, данные показатели будут корректно отражать качество работы алгоритма." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Лаба 3\n", + "\n", + "\n", + "Найти датасет ( можно посмотреть на [kaggle](https://www.kaggle.com/datasets), [PapersWithCode](https://paperswithcode.com/datasets) или [sklearn](https://scikit-learn.org/stable/datasets.html)), обучить на нем линейную или логистическую регрессию. Так же необходимо посчитать метрики у обученной модели.\n" + ] + } + ], + "metadata": { + "colab": { + "provenance": [], + "toc_visible": true + }, + "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": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/ml_system_design/seminars/sem_4.ipynb b/ml_system_design/seminars/sem_4.ipynb new file mode 100644 index 0000000..750dc58 --- /dev/null +++ b/ml_system_design/seminars/sem_4.ipynb @@ -0,0 +1,2384 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "45e744e4-abbb-4572-a696-53d83e53ac36", + "metadata": { + "tags": [] + }, + "source": [ + "# Семинар 4\n", + "## Дерево решений, композиции алгоритмов\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "94996e48-9d13-4d79-b912-1d03a98cb8c3", + "metadata": {}, + "source": [ + "## Дерево решений" + ] + }, + { + "cell_type": "markdown", + "id": "64918135-d4bf-47b2-98be-f2c3418a4a76", + "metadata": {}, + "source": [ + "### Классификация" + ] + }, + { + "cell_type": "markdown", + "id": "767f1de4-1278-4b0e-890c-eecc16eb2477", + "metadata": {}, + "source": [ + "Чтобы понять деревья принятия решений, давайте просто построим одно такое дерево и посмотрим, как оно вырабатывает прогнозы. \n", + "\n", + "Следующий код обучает классификатор `DecisionTreeClassifier` на наборе данных `iris`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "895555e9-deb5-4746-b09d-4bd12d845136", + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.datasets import load_iris\n", + "from sklearn.tree import DecisionTreeClassifier, plot_tree" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b9e0d816-b995-44b6-9093-02913f17dfcf", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
DecisionTreeClassifier(max_depth=2)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "DecisionTreeClassifier(max_depth=2)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "iris = load_iris()\n", + "X = iris.data[:, 2:] #длина и ширина лепестка \n", + "y = iris.target\n", + "tree_clf = DecisionTreeClassifier(max_depth=2)\n", + "tree_clf.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "id": "af429158-8a9f-4cdd-a2d0-38a8bde3f1f2", + "metadata": {}, + "source": [ + "Вы можете визуализировать обученное дерево принятия решений" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "5451ccb8-91d9-4d1e-9531-39899d8ebb94", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tree(tree_clf);" + ] + }, + { + "cell_type": "markdown", + "id": "d88c4816-ef84-4d4f-ab9c-12ab40215e87", + "metadata": {}, + "source": [ + "Атрибут `samples` узла подсчитывает, к скольким обучающим образцам он применяется. Например, `100` обучающих образцов имеют длину лепестка больше 2.45 см (глубина 1, справа), среди которых `54` образца имеют ширину лепестка меньше 1.75 см (глубина 2, слева). \n", + "\n", + "Атрибут `value` узла сообщает, к скольким обучающим образцам каждого класса применяется этот узел: например, правый нижний узел применяется к `О` образцов ириса щетинистого, `1` образцу ириса разноцветного и `45` образцам ириса виргинского. \n", + "\n", + "Атрибут `gini` (`показатель Джини (Gini)`) узла измеряет его загрязненность (`inpurity`): узел \"чист\" (`gini=O`), если все обучающие образцы, к которым он применяется, принадлежат одному и тому же классу. Скажем, поскольку узел на глубине 1 слева применяется только к обучающим образцам ириса щетинистого, он чистый и его показатель Джини равен `О`." + ] + }, + { + "cell_type": "markdown", + "id": "5b57fd4f-4de2-4e88-9050-bdfe00ca50da", + "metadata": {}, + "source": [ + "*Одним из многих качеств деревьев принятия решений является то, что они требуют совсем небольшой подготовки данных. В частности, для них вообще не нужно масштабирование признаков.*" + ] + }, + { + "cell_type": "markdown", + "id": "c76867e8-21ab-499d-812a-c64969c198cb", + "metadata": {}, + "source": [ + "Дерево принятия решений также в состоянии оценивать вероятность принадлежности образца определенному классу `k`: сначала происходит обход дерева, чтобы найти листовой узел для данного образца, и затем возвращается пропорция обучающих образцов класса `k` в найденном узле." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b9ad8671-d9c4-4c00-8a86-58a123e3e06e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0. , 0.02173913, 0.97826087]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tree_clf.predict_proba([X[132]])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "eede6519-b26b-4e8e-b1f6-f1c8b45a1048", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tree_clf.predict([X[132]])" + ] + }, + { + "cell_type": "markdown", + "id": "c7165ddd-a8a4-4c66-8fef-aba3241030be", + "metadata": {}, + "source": [ + "### Гиперпараметры реrуляризации" + ] + }, + { + "cell_type": "markdown", + "id": "f6982729-b85d-4693-aec3-e19a565088a1", + "metadata": {}, + "source": [ + "Деревья принятия решений выдвигают очень мало предположений об обучающих данных (в противоположность линейным моделям, которые очевидным образом предполагают, что данные линейны, к примеру).\n", + "\n", + "Так как нет никакх ограничений, дерево будет адаптировать себя к обучающим данным, очень близко подгоняясь к ним и, скорее всего, допуская переобучение.\n", + "\n", + "Во избежание переобучения обучающими данными вы должны ограничивать свободу дерева принятия решений во время обучения. Такой прием называется регуляризацией\n", + "\n", + "Гиперпараметры регуляризации зависят от используемого алгоритма, но обычно вы можете, по крайней мере, ограничить максимальную глубину дерева принятия решений. В `Scikit-Learn` максимальная глубина управляется гиперпараметром `max_depth`\n", + "\n", + "Класс `DecisionTreeClassifier` имеет несколько других параметров, которые похожим образом ограничивают форму дерева принятия решений: \n", + "- `min_samplеs_sрlit` (минимальное число образцов, которые должны присутствовать в узле, прежде чем его можно будет расщепить).\n", + "- `min_samples_leaf` (минимальное количество образцов, которое должен иметь листовой узел).\n", + "- `min_weight_fraction_leaf` (то же, что и `min_samplеs_lеаf`, но выраженное в виде доли от общего числа взвешенных образцов).\n", + "- `max_leaf_nodes` (максимальное количество листовых узлов).\n", + "- и `max_features` (максимальное число признаков, которые оцениваются при расщеплении каждого узла). \n", + "\n", + "Увеличение гиперпараметров `min_*` или уменьшение гиперпараметров `max_*` будет регуляризировать модель." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4b2e3de6-4ebd-4644-8b56-df2b7a1ff7e6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
DecisionTreeClassifier()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "DecisionTreeClassifier()" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "iris = load_iris()\n", + "X = iris.data[:, 2:] #длина и ширина лепестка \n", + "y = iris.target\n", + "tree_clf = DecisionTreeClassifier()\n", + "tree_clf.fit(X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "91eb9c03-a51e-4d6a-9eb9-cbc8eb4db3f0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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BGMPEiRPx8ccfAwC6desGOzs79OzZEwsWLAAAeHp64tSpU9DU1OT2F7fcsFAoxMSJE5GUlMTtW1hYCFdXV3Ts2BGamprYvXs3AGDFihXw8fFBVVUVwsLCmvR6CCGSo3LEhLQgWS+Ty+PxoKenJ/JEQWOqqqrg7++P7du3S3TMCxcuICsrC1999ZVE+x88eBBr1qzB+vXr4ejoCED2+5kQeUODAUJaEP2RahvUz4S0LMoZIIQQQpQcDQYIIYQQJUcJhIS0gpycHGmHoNCofwlpWTQYIKQF6evrQ0tLC56entIOReFpaWnRo4eEtBBKICSkheXn57d6Gd1ff/0V//nPf7By5Uqu/K+0/fHHH/jmm28QEhKCUaNGtfrx9PX10bNnz1Y/DiHKgAYDhMiZnJwcWFhYYNKkSdi5c6e0wxExbdo0REdHIyMjA3369JF2OIQQMdFggBA58vr1a1haWqKyshKXLl2ClpaWtEMSUVpaCgsLC2hoaOD8+fNo3769tEMihIiBniYgRI4sWLAAf/75Jw4dOiRzAwEA6NixIw4dOoQ///wTQUFB0g6HECImGgwQIieOHj2KH3/8ERs2bMC///1vaYdTL2NjY6xfvx5btmzBr7/+Ku1wCCFioNsEhMiB/Px8mJqags/n45dffhGZ2VAWMcbg5uYGgUCA2NhYzJkzB+np6XjvvfekHRohpA40GCBExgmFQjg4OODevXu4cuWK3Ezr+/z5c5iamqJr1664fPkykpOTuVkQCSGyhW4TECLjli1bhtTUVBw8eFBuBgIA4OLigh49eiAzMxMqKircrI2EENlDgwFCZJhAIMCyZcsQFhYGW1tbaYfTJEuXLsWzZ8/AGANjDKdPn5Z2SISQetBtAkJkVEFBAUxMTPDpp58iPj4eampq0g6pyYRCIaKiojB79mwYGRkhIyND2iERQupAgwFCZMzixYsxfPhwrF69GmlpacjKykL37t2lHVaz1FwdUFWli5GEyCIaDBAiQ8rLy9GxY0eMGzcOsbGxOH78OIYPHy7tsAghCo4GA4TIkKtXr8LExATt2rWDvb09OnTogJiYGHTq1KlNjt8W8yooI5pHgcg6mrWQEBly6dIl7vuzZ8/Cy8sLHTp0aJNj5+fnw8jICK9evWqT4ykTLS0t5OTk0ICAyCwaDBAiQ/744w8AgKOjI9atW4f+/fu32bELCgrw6tUr7N+/H0ZGRm12XEWXk5MDT09PFBQU0GCAyCwaDBAiQ7Zv346vv/4aVlZWUovByMgIZmZmUjs+IaTtUWovITJEV1dXqgMBQohyosEAIYQQouToNgGRO5Tx3jxtndkuEAjg5eWFpUuXws/PD4sWLUJUVBQmTZqEtWvXAgDWr1+PNWvWID4+vsXzJBwdHXH58mXs378fI0aMEFmXlpaGxYsXAwAePnyI4cOHY8OGDeDz+aiqqoKamhqmTp0KLy+vFo2JEFlDgwEiVyjjvfmkkdk+YcIE+Pn5AQDmzZuHYcOG4cSJE9z6wMBAXL16Vay2SktL0bFjR7GPvX//fkRERNS5bvDgwRAIBAAAHx8fjBkzhlv3+++/t9kjnYRIGw0GiFyhjPfmae3M9tOnTyMmJga7d++Gt7c3vL29a1UdNDAwwM2bN5vUbllZGX7++WccOHAAzs7OmD9/vtj7fvDBB41uU1FRgQsXLmD37t0AAFVVVbi6ukJHRwebN2/GRx991KR4CZE3NBggcoky3mXT0KFDcfToUfj7+0NbWxuOjo7cJ29JXL9+HVu3bsXt27cxduxYREdHQ1dXFwAQHh4ucnUBeDNT4qJFi5p8nPj4eDg5OXEDl9jYWOjp6SExMREBAQH47bffJH4NhMgDSiAkpA7Tp0+vd93jx48REhIiUbulpaUYN24cbG1tsWbNmjrbHjp0KGxsbLB//36JjiFtAQEB2LZtG4KCgprd1tmzZ5GSkoJJkyZhypQp3EAAAIKCgiAQCES+JBkIAG/++H/xxRfcz3p6egAAHo+Hhw8fNu9FECIHaDBASB127NhR7zoDAwOEhYVJ1G5kZCRcXV2RnJyMhIQEPHjwQGT96tWrsXDhQiQmJuLHH3/E69evJTqOtDDGEBQUhO3btyM4OLjZ7QUEBCAlJQXV1dUYO3YsfHx8uJkPw8PDwefzRb5WrVrV5GNUVlbi4sWLIlNEv3z5EgCQnZ0tMgAhRFHRbQKi1IRCITw8PPDixQt89tlnKC0txd69e2FhYYFLly4hNDQUd+7cwbNnz1BaWopTp07hyZMnWLBgAX7++ecmHy81NRXh4eEAAGdnZ6SlpcHd3Z1bf+HCBaxbtw6qqqqwsLDA9evXYWFh0WKvt7Vt374ddnZ28PPzQ25uLmJiYmBgYCCyzaZNmxAVFYWCggI8ePAA0dHRDbbZqVMnTJ06FVOnTkVOTg7++usvAG+uDIhz9cHX1xcCgQBHjx7F9evXsWjRIsybNw8rV65Ehw4dEB8fD0dHR5HcBkdHR64M9I8//tjUbiBE7tBggCi1o0eP4tNPP8X333+PiIgIpKam1trG0NAQ+/btQ3BwMOLi4mBsbFxnW05OTqiqqhJZtnHjRpiamnI/FxYWonPnzgAAbW1tPH/+XGT7yspK7o9SXetl3cyZM7nva26DpKenIy4uDhEREfDz88PcuXMxd+5ckf3Wr1+PS5cuQUNDo8H2jYyMmpw4WpMU+LaNGzdy33/++ef4/PPPRda/PUcEIcqABgNEqeXm5sLc3BwAYG5uXudgYMCAAQCADz/8EIWFhfW2debMmUaPp6Ojg5cvX0JHRwdFRUW1stTV1dVRXV0NVVVVFBUVoUuXLk15OTLJysoKWVlZDW4TGBiIwMDANoqIEPIuyhkgSq13797IzMwEAO7fd6moqHDfNzTjt5OTU6172FeuXBHZxtraGvHx8QDeZLC/W3p44MCBEAgEEAqFyMjIQL9+/SR5WYQQ0iQ0GCBKbcyYMbh58yacnJxw/vx5qKurS9zWmTNnamW3v32LAACmTZuG3377Dba2tuDxeOjRo4fI0wnBwcFYuXIl7O3tMWPGjDabvliapPXkRmhoKP7973+Dz+c3qW4BIYpIhTX0UYcQGXP58mWYm5sjIyOjxeoMVFZWQl1dHRERESgsLGyRLHhZ1VD/tUbfStOmTZvQsWNHTJs2DS4uLti1axe6d+/OrQ8NDYWFhUWtEsUtTdH6lSgmujJAlN7o0aNhb2+P2NhYfPXVV9IOR2EJhUK4u7tjyJAh8Pf3h4+PDwBwT0uEhobCy8sLrq6u4PF4KCsrQ15ensjTFk2RmpqKoUOHAvjfkxvvWrp0KXg8HhISEiR7UYQoCBoMEKV38uRJnDt3DnFxcQqRsCerap7ciI+Ph4mJSZ3bGBoa4uTJk7CyskJcXFy9bYmTn9HYkxtz5sxBZmYmDh8+jLlz56KioqJ5L5AQOUZPExBC2oSsPblRM/Dr1q0bjIyMcP/+ffTq1Uvs10OIIqErA4RISCAQYMGCBa16DENDQ+6Tb80n5Zs3b8Le3h7W1tZi/VGUFbL25EZNlcFXr17h5s2beP/995v8mghRFHRlgBAZpq2tXWuin2+++Qa7du1Ct27d8Pnnn8PJyUk6wTXRmDFjEBMTAycnJ/Tq1avZT240Ztq0afD09MTu3bsxYsQI7smNbdu2ISwsDEFBQbh27RqqqqrwzTffKMWTG4TUhwYDRKGlp6dj7ty50NLSAo/HQ2hoKAIDA5GRkYGysjJERETA1NQUfD4fZmZmSE1NhYuLC549e4a0tDR4enpi3rx58PHxgZqaGu7duwc9PT0cPHhQ5DinTp3CihUrUFVVhYCAAEycOBFLly7FmTNnoKmpiZUrV9b6ZCqOkpIS8Hg8dO/eHVu2bEGXLl3w8OFDGBoaAnhzqbugoAD6+vot0l+tqV27doiOjhZ5cgP4X7W/0NBQbtvZs2dz30tS9hl4U8b46NGjIsvenleiofknCFE2NBggCu3EiRMICQmBq6srqqurAQDLly+HlpYWMjMzER4ejgMHDgAA3NzcsHbtWvTs2RPHjx/Hhg0bYGlpiXnz5gEALC0tsWvXLixatAi//vord8+ZMYZly5bh7NmzUFNTg729PcaPH4/Tp08jJSUF7dq1445dY9++fdi1a5fIMlNTU5EyuQCQkpICPT09REVFISQkBJs3bxZpqyYxTh4GA8CbJzdKSkqgqamJQ4cOSTscQsj/R4MBotD8/f2xfPlyHDhwAJMnT4arqyvCw8O5e8nt2v3vFDA2NoaqqioMDAxgYmICFRUVkUvZNclvAwcOxO3bt2FpaQkAePr0KW7dusU9xvbixQs8ffoUYWFh8PX1RYcOHRAWFiYyYY+Xlxe8vLwajb9mKl13d3dERkYCgMiEOvJWsvjkyZPSDoEQUgdKICQKTVtbG1u2bMGePXsQHByMZ8+eIS4uDklJSdi4caNIktrbyWtvf1+jJunt0qVL6N27N7dcX18fffr0wenTpyEQCHDlyhUYGBiAx+MhKioKPB4PERERIm3t27evVgJczRWIGhUVFSgvLwcAJCUlccd8//33cefOHRQXF8vVVYGmaosEzSlTpqBr167YsmULt6yuBM3GqhkSIu/oygBRaDt27MCRI0cgFArh4+MDXV1ddOnSBXw+v8n38DMyMhAdHQ09PT0sW7YMycnJAN58Ul+yZAmcnZ2hqqqKrl274vDhwxgzZgzKy8shFAqxbds2kbbEuTJQWFgIV1dXdOzYEZqamtzseytWrICPjw+qqqq4+99EMqtWrYKjoyNKSkq4ZXUlaEZGRsLV1ZWrZjh58mSRaoaEyDsaDBCFNm/evFqfuH/77bda272dsf/29LXp6enc9/7+/ujfvz/3c80negAYNmwYhg0bJtLmH3/80YzI3zz/npGRUWt53759kZSU1Ky2W4q8J2h+8MEHtZbVlaCZmpqK8PBwAP+rZihpZURCZBENBgghEpP3BM261JWg2Vg1Q0LkHQ0GCBHD3r17pR2CTJL3BM261JWg2Vg1Q0LkHSUQEqXQnAlvmsLQ0BDjxo0D8GYAUVNBcPLkydw2wcHBsLOzg5eXFyorK+ttqymVButqc+jQodwkQK1FnhM061NXgmZj1QwJkXd0ZYCQFqStrY0jR45wP8+dO1ekgE5WVhYePHiApKQkrFixAj///DMmTpxYZ1viVhqsr83Tp0+3+mBAnhM0AWDx4sX47bffUFVVhTt37mDDhg11JmjWVc2QEIXCCJEjGRkZDADLyMhgjDHm7+/P0tPTGWOMxcfHs+DgYPb48WPG5/OZra0tc3NzY0KhkN29e5e5ubkxxhjj8XisuLiYMcaYm5sbu3v3LisrK2OTJ09mDg4ObOTIkayoqEii+MzNzbnv9+zZw4yMjJitrS2Ljo5mjDG2detW9tNPPzHGGLt06RLz9/evty1LS0vu+xEjRrCnT5/WuV1Dbb4dD2O1+0/cda3N29ubXbt2rc2P2xak2a+EiItuExC55uHhgZiYGADAoUOH4OHhAV1dXe5Sdffu3cWaqz4yMhKOjo5ISEjA5MmTa112jouLq3XZ2cPDo8E2x4wZg+vXr+PkyZNYv349Hj161KREtLoS2epCyW2EkOai2wRErtnY2CAoKAgVFRXIzs6GqakpHj16hJkzZ6KwsBAPHz6EmZkZ96gYUPfMeNnZ2bh48SKioqJQWVkJOzs7keM4OzvD2dm5SbHp6OgAAN577z3w+Xzk5ORwiWhA49UDxa002JQ2ZRUlaBIiXXRlgMg1FRUV2NjYICwsDEOGDAEAHDx4ECNGjEBiYiJcXFxqTYWrq6uL+/fvQygU4saNGwCAPn36YM6cORAIBEhJScGyZctE9pHkykDNH+iqqiqcP38evXr1EklE++OPP2BjYwMAePDgQa0460pkKysrw7Nnz0S2q69NQggRFw0GiNzz8PDA6tWruT/OTk5O2LRpE0aPHo2nT5/W2n7WrFn44osv4O3tjW7dugEA/Pz8EBcXB0dHRzg6OuL06dMi+zg7O0MgEIh81dyeqM+GDRtgZWUFa2trjB07Fh9//DFMTU3RrVs32NnZ4caNG3BzcwMAeHp6oqKiQmT/mkS2YcOGcTP6paSk1HpWvr4225I0ntZoSongmqc6+Hw+4uLiAIj/tEZeXh66du3K7V/znoqNjYW1tTWcnJxw//59AMDChQuho6MjUtGQELkg5ZwFQppE1pOx7O3t2dixY5u0j1AoZNOnTxdr2/DwcHbz5k2xtnV2dmYjR44UWdZaCYRvJ2i2prcTIjdu3Mh27tzJGGNs2LBh7P79+2LtV2Ps2LHs1q1brKioiFlbW9e7b12vrbKykllZWbHy8nKWnJzM/Pz8uHVvJ6gyJvvvWUIYowRCQlpUYmKiyKOF4lBTU8P27dvF2nbBggX47LPPxNr29OnTdZZeborZs2fj/PnzAIAzZ85g0aJFePLkCRwcHGBnZwd3d3dUVVWJ7MPn87lPxu7u7sjLy8Pr16/h6ekJR0dHjBo1iruF0hypqalcIaKaEsH1KSkpAY/Hw6RJk7gEy5qyw507d+bKDtcnJSUFdnZ2+Oabb8AYw+3bt2FkZAQNDQ3Y2Njg6tWrzX49hEgTDQYIIfWS5ac1mvIURUpKCpdDEhISAkD8pzXef/995Obm4ty5c/jnn39w5MgRkWMDqDUgIkTe0NMEhJB6yfrTGuKWCNbT0wPw5kpFZGQkAPGf1tDU1ISmpiYAYNy4cUhPT4eRkZHI1Q01NbUmxU6IrKHBAJFLOTk50g5BLjW13xp6WmPatGkICAio92mN3r17izytMXjwYK4q4LtlmOPi4rBixQqRZQYGBg0madY8ReHr64v4+Hjs3LkTAHD//n2RCoEVFRVgjEFTUxNJSUlcqeOapzX+9a9/iTyt8erVK27wAADFxcV47733AABJSUkwMjKCoaEhcnJyUFFRgUuXLsHY2Fj8TiVEBtFggMgVfX19aGlpwdPTU9qhyC0tLS3o6+uLvb2HhwesrKxw/fp1AG+e1vDy8sKxY8fQoUOHWtvXPK1hbGws8rSGn58f9uzZAwCYP38+hg8fzu0jyZWBukoEC4VCTJw4UWSK58LCQri6uqJjx47Q1NTE7t27AaDOssM1txPefrQ0OTkZS5YsgZaWFj755BMsW7YM7dq1w7x588Dn89G+fXv89NNPTYqdEFmjwt4d1hMi4/Lz8xtM9iIN09fXR8+ePWstv3z5MszNzZGRkQEzMzMpRNY4Ho8HPT29epM0L1y4gKysLHz11VcStb927VqMHDlS7CTNdy1cuBC//fYbLl++DC0tLQDy0a+E0GCAEAKA/mi1FupXIg/oaQJCCCFEyVHOACEEAHDr1i0AlJzZ0qg/iTyg2wSEKLn8/HwsXboUUVFRUFNTo2fmW4Gqqiqsra2xefNmmJqaSjscQmqhKwOEKKkXL15g5cqV2LRpE7S1tbF161YMHToURUVF0g5NoTDGcPnyZaxbtw5mZmbw9PTEsmXLGqyLQEhboysDhCiZ8vJybN26FcuXL8fr168RFBSE+fPnc8/Sk9YhFAqxa9cuhISE4MWLF5gzZw4WL14MXV1daYdGCA0GCFEW1dXViImJwbfffou///4b06ZNQ0hICN5//31ph6ZUSkpKsG7dOoSHh0NDQwNLliyBv78/V+WQEGmgpwkIUQIJCQkYOHAgJk+eDBMTE1y7dg3bt2+ngYAUdOrUCSEhIcjNzcWECROwcOFC9OnTBwcOHBCZL4GQtkSDAUIU2LVr1+Dq6gonJyeoq6vj3LlzOHr0KIyMjKQdmtIzMDDAtm3bcP36dZiamsLT0xMWFhY4c+aMtEMjSogGA4QooPv378PX1xcmJia4ffs2YmNjkZaWVmuCICJ9ffr0wX//+18kJSVBU1MTQ4YMweeff07TIpM2RYMBQhRIUVERFi9eDENDQxw/fhybN29GdnY23N3dRWYTJLLH1tYWqamp+Pnnn3Hnzh2Ympriyy+/xN9//y3t0IgSoARCQhRARUUFtm3bhmXLluHVq1eYP38+goKC0LlzZ2mHRiRQWVmJnTt3IjQ0FMXFxZg3bx6Cg4Oho6Mj7dCIgqLBACFyjDGGw4cP45tvvkFeXh58fX0RFhaGDz74QNqhkRZQXFyM8PBwrFu3Du3bt8fSpUsxc+ZMevKAtDi6TUCIHNm3bx+ysrIAAAKBAJaWlvDw8EDfvn1x9epV7Ny5kwYCCuS9997Df/7zH9y+fRtubm6YP38+jIyMEBMTg+rqajx69AgbNmygpxBIs9FggBA5cfr0aUyZMgWnTp3CyJEj4eDgAODNoODYsWPo16+flCMkreWDDz5AREQErl27hn//+9+YOHEiLC0tceLECQQGBmLjxo3SDpHIObpNQIgceP78Ofr27Qs1NTU8evQIn3zyCVauXIkvvviCEgOV0Llz5xAUFIQLFy7gk08+wf3793H58mX0799f2qEROUVzExAiB4YOHYonT55AXV0dAwYMgJmZGcaOHUsDASVlb28PV1dXtGvXDlevXkVlZSX4fD6ePHkCNTU1aYdH5BANBkiryM/PR0FBgbTDkFv6+vro2bMn93NxcTH+9a9/4aOPPkKnTp1QUVFB94mVXHl5OTp06ID+/fvj77//RllZGV69eiUyxwSdh83z7nmoyOg2AWlx+fn5MDIywqtXr6QditzS0tJCTk6O0vwiIi2PzsPmU6bzkK4MkBZXUFCAV69eYf/+/VT2VgI5OTnw9PREQUGBUvwSIq2DzsPmUbbzkAYDpNUYGRnBzMxM2mEQotToPCTioEcLCSGEECVHgwFCCCFEydFggMg0gUCADz/8EBEREQCA5ORkWFtbw9bWFteuXQMArF+/HgYGBrh+/XqrxJCWlgYVFRWUlJSILK+qqoKnpyccHBzg6+sLoVAIADA0NASfzwefz0dcXFyrxERIW5Ll87C6uho+Pj6ws7ODra0tbt68CQDg8/mws7MDn8/Hvn37WiUmRUI5A0TmTZgwAX5+fgCAb7/9FidOnEBxcTFmzJiBkydPIjAwUOzpXktLS9GxY8cmHf+HH36Aubl5reX//e9/8cknn2D//v1Ys2YNjhw5gvHjx0NbWxsCgaBJxyBE1snqeXjlyhWUl5cjKSkJSUlJWL9+PTdo+f3339GpU6cmHUdZ0ZUBIjNOnz4NX19fAIC3tzcSEhJE1peVlUFNTQ26urro2bMnnj9/Lla7ZWVl2LdvH1xcXLB9+/YmxZScnAxjY+M6f6HUTDMLAGZmZjh37hwAoKSkBDweD5MmTRI7RkJkhbydhz169ABjDIwxFBYWQl9fHwCgqqoKV1dXjBo1Cvfu3WvS8ZQRDQaIzBg6dCjat28Pf39/aGtrw9HRUWR9YWGhyJS87dq1Q0VFRb3tXb9+HbNmzcKoUaNQXFyM6OhozJ8/HwAQHh7OXcqv+Vq1alWtNjZt2oTZs2fX2X7fvn25X5Tx8fEoLCwEAKSkpCAxMREuLi4ICQlpWicQImXydh7q6+tDXV0dffr0QUBAAGbNmgUAiI2Nxblz5zB//nwEBAQ0uR+UDd0mIDIlICAA/fr1q3Mkr6Ojg5cvX3I/C4VCaGho1NvW2bNnkZKSgnnz5uGLL74Q+VQRFBSEoKCgBmNJTEyEiYmJSEW3t40YMQICgQCOjo7o168fDAwMAAB6enoAAHd3d0RGRjZ4DEJkkTydh6dPn0a7du3w559/4tKlS5g/fz4OHTrEnYc8Ho8bfJD60ZUBIjMYYwgKCsL27dsRHBxca72WlhaEQiFevHiBv//+G126dGmwvYCAAKSkpKC6uhpjx46Fj48PMjIyAIj3iSQrKwtnzpyBi4sLrl69Cm9vb5H1KioqWLduHRISEqCnp4fRo0ejoqIC5eXlAICkpCT07t27OV1CSJuTt/OQMcb94dfX10dRUREAcAOW7Oxs6OrqStYZyoQR0sIyMjIYAJaRkdGk/bZu3cpWrVrFGGMsKCiIRUdHs7Nnz7L58+dz2yQmJrLBgwcza2trduXKFW65t7c3u3btWoPtZ2dns+PHjzcppho8Ho8VFxczxhibO3cue/XqFXv06BHj8/nM0dGRrVixgjHG2OPHj5mZmRmzs7NjQ4YMYfn5+U0+lqT9R8jblOU8rKysZOPHj2f29vbM0tKSpaSkMMYYMzc3Z7a2tszW1pZlZWU1+VjKdh7SYIC0uJY8idLS0pixsTHbsWNHvdusW7eO9evXj/3555/NPp4sULZfQqR10HnYPMp2HlLOAJFpVlZWyMrKanCbwMBABAYGtlFEhCgfOg8VH+UMELkxffr0etc9fvxY4sz90tJSjBs3Dra2tlizZk2t9bGxsfjss89gYWEhsjwmJgaOjo7g8/lIS0sDAPz4448YNGgQBg0ahF9++UWieAiRVdI6Bx8/foyhQ4fCxsYG+/fvF1m3atUqkXPTxsYGPB4PNjY2yM7OligepSTtSxNE8cjb5bWNGzeynTt3MsYYGzZsGLt//77I+oKCAlZeXs7Mzc25ZQ8ePGAeHh6surpaZNu+ffuyyspKVlpayszMzCSKR976j8gmeXofNXYOzps3j8XFxbHKykpmZWXFysrKGGOMvXz5kk2aNEnk3CwvL2eMMXb27Fk2depUiWOSp/5rCXRlgMgcoVAId3d3DBkyBP7+/vDx8QEAbvQfGhoKLy8vuLq6gsfjoaysDHl5eXB3d5foeKmpqRg6dCgAwNnZmfuUX0NPT6/Wo1OnTp2CpqYmnJ2d4eXlxZVI7dWrF8rKylBcXAwdHR2J4iFE2mTtHLxw4QIcHR3Rrl07WFhYcCWP66o/UHOuFhcXo3///hLFo4xoMEBkztGjR/Hpp58iPj4eJiYmdW5jaGiIkydPwsrKqsH6/05OTrUeXbpy5YrINm8XUdHW1harotqTJ09QUFCAuLg4DB48GFu2bAEADB8+HEZGRjA1NaVnm4nckrVzsLKyEqqqqiLri4qKcO3aNQwePFhk28ePH8PGxgazZs0Cj8dr6ktXWpRASGRObm4uV4Pc3NwcqamptbYZMGAAAODDDz/kKv/V5cyZM40er6aIio6ODoqKivDRRx+JtY+DgwNUVFTg5OSE5cuX4+XLl9i2bRtu376NiooKODo64vPPP4eKikqj7REiS2TtHFRXV0d1dTVUVVVRVFSELl26YOPGjXVWFjQwMEBKSgouXLiAxYsX49SpU40en9CVASKDevfujczMTADg/n3X239gGWP1tiXOpxJra2vEx8cDeFNW2MrKqtEYbWxsuHauXLmCXr16QVVVFR06dED79u3RsWNHVFRUNBgbIbJK1s7BgQMHQiAQQCgUIiMjA/369UNubi6WL18OFxcX3L59GytWrEBlZSWqq6sBvLmCoKWl1eTXrqzoygCROWPGjEFMTAycnJzQq1cvqKurS9yWOJ9Kpk2bBk9PT+zevRsjRoxAjx498PjxY2zbtg1hYWEQCARYvnw5bt26hSFDhiAqKgrGxsb48MMPwefzoampiQMHDqBTp04YN24cBg8ejOrqavj7+3OXNgmRJ7J2DgYHB2PKlClYsmQJZsyYgQ4dOohMS2xhYYFvv/0W+fn58PT0hJqaGlRUVLjbd6RxKow+upAWdvnyZZibmyMjIwNmZmYStVFZWQl1dXVERESgsLCwzrKoiqol+o+Q5r6PlPkcBJTvPKQrA0QmjR49GiUlJdDU1MShQ4ekHQ4hSofOQeVCgwEik06ePCntEAhRanQOKhe6oUkIIYQoORoMEIUmEAiwYMGCVj2GoaEhlyX99vPW1dXV6Nu3LyUxEaXXFuchANy7dw+amppcUaLy8nJMnz4djo6OGD16dKsfX57RbQJCmklbWxsCgaDW8ujoaPTs2bPtAyJESa1ZswY2Njbcz5s3b4arqysNBMRAVwaI1KWnp8PS0hIODg4IDQ0F8GYGNB6Ph0GDBnHPJPP5fAQGBsLKygqhoaEICAiAhYUFNm7cCADw8fHB1KlTMWTIEEyYMAFVVVUixzl16hTs7OxgbW2N6OhoAMDSpUthbW0NBwcHpKenSxR/SUkJeDweJk2axFVOq6qqQmxsLMaPHy9Rm4S0NXk/D+/evQsVFRWRAfipU6eQnJwMPp+PHTt2SNSu0pDqzAhEITV1go8lS5awEydOMMYYq6qqYowxVlpayhhj7PLly2zSpEmMMcZ4PB5LTk5mVVVVrHv37iwzM5NVVlZyEwJ5e3tz860HBwezX375hZ09e5bNnz+fVVdXM2tra1ZeXs6EQiGztrZmQqGQDRo0iFVWVoocu0ZUVBTj8XgiX3Pnzq0Vf0FBAWOMsZ9++onNnj2b+37//v1sz549bPPmzWL3HWPKN0EKaR3Kdh5Onz6d3b17l3l7e7Nr164xxhj79NNP2eHDh1llZSWzt7dnf//9d6v1n7yj2wRE6vz9/bF8+XIcOHAAkydPhqurK8LDw7mKZO3a/e9tamxsDFVVVRgYGMDExAQqKioiBVFqSqgOHDgQt2/fhqWlJQDg6dOnuHXrFjcZyosXL/D06VOEhYXB19cXHTp0QFhYGAwMDLi2vLy84OXl1Wj8enp6AAB3d3dERkaiqqoKhw8fxq+//ipSGIUQWSbP5+GdO3cAAB9//LHIch0dHW6CI2tra/z555/o0aOHhD2k2GgwQKROW1sbW7ZsQUVFBczNzWFpaYm4uDgkJycjIyNDZMKft0ug1lXzPzMzE+bm5rh06ZLIHOf6+vro06cPTp8+DQ0NDa6gCo/Hg4uLCw4ePIiIiAh899133D779u3Drl27RNo3NTXlLocC4EoOa2pqIikpCb1798bjx4/x+PFjDB8+HA8ePEBVVRUGDRqEQYMGtUR3EdIq5Pk8zMrKwo0bN+Di4oJr164hNzcX8fHxXNlwJycnZGVl4auvvmqJrlJINBggUrdjxw4cOXIEQqEQPj4+0NXVRZcuXcDn88WaJ+BtGRkZiI6Ohp6eHpYtW4bk5GQAgKqqKpYsWQJnZ2eoqqqia9euOHz4MMaMGYPy8nIIhUJs27ZNpC1xPpEUFhbC1dUVHTt2hKamJnbv3o3u3bvj0qVLAIC9e/eipKSEBgJE5snzeThu3DiMGzcOwJuchQULFqB9+/YIDg6Gj48PvvvuOzg7O6NXr15Neh3KhMoRkxYnrTKeNb8E5H0Oc2Urg0paB52HzaNs5yE9TUAIIYQoObpNQBTG3r17pR0CIUqPzkP5RFcGiEzJy8uDu7t7qx/H0NCQu8dYWlqKcePGwdbWFmvWrGl033ernJ09exaDBw+GnZ0dzp07V+9+eXl56Nq1K1et8OnTpwCAoUOHiiRZESJNsn4OTpkyBV27dhW7sueMGTO410PnYP1oMECUkra2No4cOQIAiIyMhKurK5KTk5GQkIAHDx40uO+7Vc6++eYb/P777zh16pRIFnRdeDweBAIBBAIBunbtCgA4ffp0M18NIfJH0nNw1apVCA8PF+sYeXl5ePjwocgyOgfrRoMB0iZmz56N8+fPAwDOnDmDRYsW4cmTJ3BwcICdnR3c3d1rVSrj8/koKSkB8OYZ/ry8PLx+/Rqenp5wdHTEqFGj8PLly2bHlpqayj337OzsjLS0tHq3ravKmVAohI6ODjp27AihUIiCgoJ6909JSYGdnR2++eYbUO4uaUuKcg5+8MEHYre7Zs0akUciAToH60ODAdImPDw8EBMTAwA4dOgQPDw8oKuri7i4OCQlJaF79+5ISEhotJ3IyEg4OjoiISEBkydPRkREhMj6uLg47hJgzZeHh0eDbRYWFqJz584A3nxaqSkpXJfVq1fXmnBFU1MT+fn5ePLkCa5fv47CwsI6933//feRm5uLc+fO4Z9//uE+FRHSFhTlHBTXX3/9BQD46KOPuGV0DtaPEghJm7CxsUFQUBAqKiqQnZ0NU1NTPHr0CDNnzkRhYSEePnwIMzMzGBoacvu8XcykZgSfnZ2NixcvIioqCpWVlbCzsxM5jrOzM5ydnZsUm46ODl6+fAkdHR0UFRWJ/PJ4W31VzjZt2oQvv/wSurq6+Pe//y1SPe1tmpqa0NTUBPDmuej09HS4ubk1KVZCJKUI52BTrFq1CosXLxZZRudg/WgwQNqEiooKbGxsEBYWhiFDhgAADh48iBEjRmDatGkICAiodclOV1cX9+/fR+/evXHjxg0AQJ8+fTB48GCuCEllZaXIPnFxcVixYoXIMgMDA+4TUV2sra0RHx8PX19fxMfHY+fOnQCA+/fvi5Qura/Kmbm5Oc6cOYOCggLMmjUL7733HsrKyvDq1SuuVDEAFBcX47333gMAJCUlwcjIqEl9SEhzKMI5WJ/nz5+jffv20NLS4pbl5eVh5syZKCsrw59//onIyEhMmDCBzsH6SG1WBKKw6pvg4+LFi0xNTY3l5OQwxhjLzMxk/fv3Z6NGjWITJkxge/bsYXfv3mVubm6MMcbi4uJY//792aRJk5i9vT27e/cuKysrY15eXszBwYE5ODiw48ePSxSjubk5931xcTEbPXo0s7GxYStXrmSMMVZZWclsbW3r3f/tyVBWrlzJ+Hw+c3V1ZXfu3OFiX7Jkicg+J0+eZGZmZszW1pZ5eXlxE7O8G4+yTZBCWkdd7yNFOAcXLVrE+vbtyz777DM2b948xhhj3377LYuPj6/zOG+/HnHPQcaU7zykwQBpcfJwEtnb27OxY8fWu/78+fMsIiJC4vbDw8PZzZs3xdrW2dmZjRw5kvtZHvqPyD5Zfx+15Dk4Y8YMkT/sTfXuOciY7PdfS6PbBEQpJSYmNri+uRMLvZtk2BB6rIkoo5Y8B9+dz6Cp6BykpwkIIYQQpUeDAUIIIUTJ0W0C0mpycnKkHYJcon4jLYneT5JRtn6jwQBpcfr6+tDS0oKnp6e0Q5FbWlpa0NfXl3YYRI7Redh8ynQeqjBG9RhJy8vPz8fff/+NTZs2ITY2FgMHDkRISAjef/99aYcmcy5duoSQkBAUFRUhMDAQY8eORdeuXUVKHhMiifz8/AbLYzfV4cOHsXr1aqxbtw58Pr/F2pUUYwwLFy7EhQsXEBMT0+K/X/T19ZXmPKTBAGkVqamp8Pb2xoMHDxAeHo6ZM2dCVZVSVOrz8uVLBAYGYteuXXB1dcXOnTubVIOdkNaWlZUFS0tL+Pn54YcffpB2OJzCwkIMGDAA3bt3R2JiItq1owvekqDfzqRFlZeXY9GiRbCzs0PXrl2RlZUFf39/Ggg0onPnzoiMjMTx48dx+fJl9O/fv8GKbYS0pdLSUkyYMAF9+vQRa5rvtqSrq4vo6GicP38eoaGh0g5HbtFvaNJirly5AgsLC6xfvx4rVqxAUlKSSJ1z0rjhw4fj+vXrcHZ2xsSJEzFhwoQWvcxLiCQCAgLw999/49ChQ2jfvr20w6ll8ODB+M9//oPvv/9erMmWSG10m4A0m1AoxKpVqxAWFoZ+/fohKioKxsbG0g5L7h06dAizZs2Curo6IiMjMWLECGmHRJRQdHQ0Jk2ahD179sDHx0fa4dSrqqoKw4YNQ3Z2NrKystC1a1dphyRXaDBAmuXmzZvw9vbGpUuXsHjxYnz33XfQ0NCQdlgK49GjR5g2bRpOnjwJX19fbNiwgZvqlZDWdufOHQwYMAAjR47E/v37RWYxlEWPHj2CiYkJLCwscPz4cbo92QTUU6RJrl+/jurqalRXV2PTpk0YMGAAXrx4gdTUVCxfvpwGAi3s/fffx/Hjx7Fz504cPnwYxsbGOHv2LIA3SYd5eXnSDZAorIqKCnh4eOBf//oXtm3bJvMDAeDN+fLTTz/h999/x8aNG6UdjnyR2qwIRO6cPn2aAWAnT55kfD6fAWBz5sxhpaWl0g5NKfz111+Mx+MxAGzu3Lns+++/Z126dGHPnz+XdmhEAS1YsICpq6uzixcvSjuUJps/fz5TV1dnly5dknYocoNuExCxVFVVwczMDK9evcLjx4/RpUsX7NmzB46OjtIOTanUXJFZvHgxevTogYcPH2LWrFlYu3attEMjCuTUqVP4/PPPsXbtWsyfP1/a4TRZRUUFbGxsUFhYiMuXL9OtNTHQbQIilk2bNuHq1avIzc2FkZERvL29YW9vL+2wlI6qqirc3Nzw5ZdfQigUoqysDBs3bsTNmzelHRpREI8ePcKUKVPw+eef4+uvv5Z2OBLR0NBAdHQ0/vnnH8yaNQv0mbdxNBggYgkJCeG+v3HjBhISElBeXi7FiJTXP//8gzNnzuDBgwcA3ly1mTFjhpSjIvKMMYbNmzfj+fPn8PLygpqaGvbu3SvXCXi9e/fG9u3bceDAAURFRSE5ORlnzpyRdlgyi24TELGcPn0aVVVVGDBgALp16yYXyUSKTigUIj8/HykpKbC0tMSnn34q7ZCInLp58yaMjIzw1VdfITIyEnFxcXBycpJ2WC3iyy+/xOHDhzF8+HDk5eXhwoUL0g5JJlHdRiKWoUOHSjsE8o527dqhV69e6NWrl7RDIXLuxo0bAIBdu3bB3d0d2dnZCjEYePz4MQwMDNCtWzekpKSgqKgI1dXVcn3Fo7Uo3WCgpSfuUDbKNHGHvKH3tvjofSzq0qVLAN7M0hcbG4uqqioEBARIOarmKykpwZ49e/Ds2TNUVVWBMYZ79+7hk08+kXZoskeKTzK0uXv37jEtLS0GgL4k/NLS0mL37t2T9n8leQe9t+l93Bx9+/ZlAJipqSmLi4tj1dXV0g6pxZSWlrLw8HDWsWNHBoBt375d2iHJJKW6MlBQUIBXr15h//79MDIyknY4cicnJweenp4oKCigT1Uyht7b4qP3cW1hYWEoKCjA9OnTFS4fSEtLCwsWLICfnx++++47jBkzRtohySSlGgzUMDIygpmZmbTDIKTF0XubSMLd3V3aIbS6zp07U1XCBlAWBSGEEKLklPLKQEsQCATw8vLC0qVL4efnh0WLFiEqKgqTJk3iqsGtX78ea9asQXx8PPr379+ix3d0dMTly5exf//+OmezEwgEWLZsGaqrqzFnzhyMHTsWfD4fVVVVUFNTw9SpU+Hl5dWiMRH5Jcvv57y8PAwcOBD9+vUDAMTGxqJr164wNDRE9+7dAQDffvstnJ2dWzSm+lCipvgkSdSk/m0eSZNjaTDQDBMmTICfnx8AYN68eRg2bBhOnDjBrQ8MDMTVq1fFaqu0tBQdO3YU+9j79+9HREREnevKysqwbt06/P7777UmDvr999/RqVMnsY9DlIesvp8BgMfj4eeffxZZpq2tDYFAIPYxWkJ+fj6MjIzw6tWrNj2uvNLS0kJOTo7Yf5yof5uvqX1egwYDYjh9+jRiYmKwe/dueHt7w9vbu9ZzqgYGBk0uCVtWVoaff/4ZBw4cgLOzc5NqgH/wwQf1rktLS0OHDh0wcuRIaGlpYdu2bTAwMICqqipcXV2ho6ODzZs346OPPmpSvEQxyNv7GQBSUlJgZ2cHOzs7rFixAioqKigpKQGPx0P37t2xZcsWdOnSpUnxSoISNcUnSaIm9W/zNCc5lgYDYhg6dCiOHj0Kf39/aGtrw9HRsVmfSK5fv46tW7fi9u3bGDt2LKKjo6GrqwsACA8PF/k0BgAuLi5YtGiR2O0/efIEubm5SE9PR3x8PEJDQ7F9+3bExsZCT08PiYmJCAgIwG+//SbxayDyS97ez++//z5yc3OhpaWFr776CkeOHIGbmxtSUlKgp6eHqKgohISEYPPmzRK/hqaiRM3WRf3b9mgwIKaAgAD069cP9+7da3ZbZ8+eRUpKCubNm4cvvvhC5LJ9UFAQgoKCmtW+jo4ObGxsoKGhAScnJ6xcuRIAoKenB+DNJVd5nImMtBx5ej9rampCU1MTADBu3Dikp6fDzc2Nez+7u7sjMjKyWccgRNnR0wRiYIwhKCgI27dvR3BwcLPbCwgIQEpKCqqrqzF27Fj4+PggIyMDwJtPUnw+X+Rr1apVTWp/4MCByMnJAWMMV65c4crVvnz5EgCQnZ3NfXIjykfe3s/FxcXc90lJSejduzcqKiq4ibJqlsmb6dOn17vu8ePHIpODNUVpaSnGjRsHW1tbrFmzpt7tXFxcsGDBApFlq1atgoWFhciytLQ07raMopBW3z9+/BhDhw6FjY0N9u/fL9ExWo2Uix61qYyMDAaAZWRkNGm/rVu3slWrVjHGGAsKCmLR0dHs7NmzbP78+dw2GzduZGZmZqxnz57Mw8ODW+7t7c2uXbvWYPvZ2dns+PHjTYrpyy+/ZJ988gkzMTFhK1euZIwxNnfuXPbq1SvGGGNbtmxhdnZ2zN7enuXm5jLGGDM3N2e2trbM1taWZWVlNel4jEnef6T1NeX/Rt7ezydPnmRmZmbM1taWeXl5scrKSvb48WNmZmbG7Ozs2JAhQ1h+fr7Yx2rO+1gezoGNGzeynTt3MsYYGzZsGLt//36tbZKTk9mwYcNE/s9fvnzJJk2axMzNzUW29fDwYObm5qy4uLhJcUjSV/LQvw1prO/nzZvH4uLiWGVlJbOysmJlZWUtevzm9B8NBiSUlpbGjI2N2Y4dO+rdZt26daxfv37szz//bPbxZIG8n6iKrLn/N8r0fm7rwUBlZSVzc3NjTk5ObNasWczb25sxxrg/uiEhIczT05N9/vnnzN7enr169YrdvXuXubm5NTk+xhgbP348V2p57dq1LDY2ts5tjh07JjIYWLZsGUtNTRUZDCQlJbHvv/+e8Xg8uRwMyFrfW1tbs6qqKsYYY7Nnz2YXL16U8JXVrTn9R7cJJGRlZYWsrCzuUay6BAYG4vr16zS1LJF59H5uPUePHsWnn36K+Ph4mJiY1LmNoaEhTp48CSsrK8TFxdXblpOTU63bLleuXBHZprCwEJ07dwbw5vHL58+fi6w/d+4cTExMRHI7ioqKcO3aNQwePFhk202bNmH27NlNebkyRdb6vrKykntyp6710kQJhIQQ0opyc3Nhbm4OADA3N0dqamqtbQYMGAAA+PDDD1FYWFhvW2fOnGn0eDo6Onj58iV0dHRQVFRU6xHiTZs2Yc+ePbh8+TK3bOPGjbVmKUxMTISJiQnee++9Ro8pq2St79XV1bkplIuKitrkcVhx0ZWBZpLFRJR3k4AcHR2ho6OD48ePSxQLUS6U2NayevfujczMTADg/n3X25MDMcbqbUucT6fW1taIj48HAMTHx8PKykpkfW5uLsaPH4+FCxfil19+wbFjx5Cbm4vly5fDxcUFt2/fxooVK5CVlYUzZ87AxcUFV69ehbe3tyQvX6pkre8HDhwIgUAAoVCIjIwMrqqmLKArA820Y8eOetcZGBggLCxMonYjIyPh6uqKadOmwcXFBZMnT+ZKrwLA6tWrsXDhQvD5fNjZ2cHd3R3t27dHcXExrl27JtJWY9XdCHmbtN7TwJviQu+q6z0NAD/88AP3qU+WjRkzBjExMXByckKvXr2grq4ucVvifDqdNm0aPD09sXv3bowYMQI9evTA48ePsW3bNoSFhSErKwvAmxLUx48fx8iRIzFy5EhufwsLC3z77bcAgDlz5gAA+Hw+fvrpJ4njlhZZ6/vg4GBMmTIFS5YswYwZM9ChQweJ42lxLZq9IOOak1whL4kodSUB1cR37NgxiWKpQQmEsosS28QnjacJKioqGGOM7dixg3uSQ9HJQgIhY8rV95RA2AbkIRGlviQgQuoia+9pRU5sGz16NOzt7REbG4uvvvpK2uEoFep78dBtAjHJQyJKXUlAhNRH1t7TipzYdvLkSWmHoLSo78VDVwbEJA+JKHUlARFSH1l7TytTYltLEAgEtRItW5qbmxt4PB4sLS1x7ty5Vj2WrGmL/gWAe/fuQVNTE9evXwcALF++HPb29hg4cGCbzrdBVwbEJA+JKPv27eP2fzsJyNfXFwKBAEePHsX169ebNEkMUVyy9p5WpsQ2eREdHQ0NDQ3k5eVh2rRp3GCOtJw1a9bAxsaG+3nhwoVYsmQJhEIhjI2NMWvWLKipqbV6HDQYEFO7du0QHR0NdXV1REREcJdML126BAAIDQ3ltn37Xua7c7CLq1OnTjh69KjIsrczud9///0G7+HWxAUAu3fvligGothk7T1do+bKwrvefk/XaM5si20hPT0dc+fOhZaWFng8HkJDQxEYGIiMjAyUlZUhIiICpqam4PP5MDMzQ2pqKlxcXPDs2TOkpaXB09MT8+bNg4+PD9TU1HDv3j3o6enh4MGDIsc5deoUVqxYgaqqKgQEBGDixIlYunQpzpw5A01NTaxcubLWlRhxaGhoAHjzREf//v1bpE9akrz37927d6GioiIy3XBNn5eXl+P//u//2mQgANBgoElGjx6NkpISaGpq4tChQ9IOh5Bmo/d06zpx4gRCQkLg6uqK6upqAG8uA2tpaSEzMxPh4eE4cOAAgDeX5NeuXYuePXvi+PHj2LBhAywtLTFv3jwAgKWlJXbt2oVFixbh119/5QrWMMawbNkynD17FmpqarC3t8f48eNx+vRppKSkoF27dtyxa+zbtw+7du0SWWZqaoqNGzfWeg329va4desWoqKiWrh3mk/e+3f16tVYtGiRyMAbAObNm4fDhw/D39+/hXqqcTQYaAJKRCGKht7Trcvf3x/Lly/HgQMHMHnyZLi6uiI8PJy73N6u3f9+BRsbG0NVVRUGBgYwMTGBioqKyK2bmmTPgQMH4vbt27C0tAQAPH36FLdu3cLQoUMBAC9evMDTp08RFhYGX19fdOjQAWFhYTAwMODa8vLygpeXl1iv4dy5c8jPz8fo0aO5Y8gKee7fO3fuAAA+/vjjWus2btyIVatWwdbWFr6+vnj//fcl6J2moQRCKZFWckpycjIsLS1hbW2NxYsXt/rxifJpi/f2/fv3MWrUKDg4OEhcEbEtaGtrY8uWLdizZw+Cg4Px7NkzxMXFISkpCRs3bhRJynw7WfPt72vUJHleunRJZMpmfX199OnTB6dPn4ZAIMCVK1dgYGAAHo+HqKgo8Hi8WkXH9u3bVyvhs+YTcg3GGCorKwG8ucXz9iOfskKe+zcrKws3btyAi4sL4uLiMGPGDLx+/ZqbmltTUxNaWlpo3759s/tJHHRlQMG9m5yyZs0aREVF4bPPPoOTkxMePnyIDz74QIoREtJ0QUFB2LZtW60KhrJmx44dOHLkCIRCIXx8fKCrq4suXbqAz+c3+R5zRkYGoqOjoaenh2XLliE5ORkAoKqqiiVLlsDZ2Rmqqqro2rUrDh8+jDFjxqC8vBxCoRDbtm0TaUucT67l5eVwcXEBAFRVVeH7779vUrxtQZ77d9y4cRg3bhwAwMfHBwsWLED79u0xY8YM3Lx5ExUVFfD09ISurm6TXofEWrL6kaxranWmtLQ0NmjQIMbn81lISAhjjLGvv/6a2dvbs4EDB7LMzEzGGGM8Ho99/fXXzNLSkoWEhLDZs2czc3NztmHDBsbYmzngfX19mZOTExs/fjwTCoUi88f//vvvzNbWlg0ePJgdPHiQMcbYkiVL2ODBgxmfz2dpaWkSvd6//vqL+fv7i8xBHxwczNLT01llZSXj8XissLBQ7PaoAqHsUqb3dkVFBbOysmITJkxgDg4OLCUlpUn7S6MCYXO9fQ7LC1mpQCgOeezfujSn/+jKQAMUMTmlZjSqqamJCRMmQEdHp+U6jMgNeX5vFxQU4MqVKzh06BA0NDQwcuRIXLx4sZV6ihDlQIOBBihicsrXX3+NxMREfPLJJxg3bhyys7PRt29fCXuIyCt5fm/r6Oigd+/e3ONY6urqEAqFIjErmr1790o7BIVG/UsJhA1SxOQUFRUV6OrqQlVVlSsPS5SPPL+3O3ToAD09Pbx48QKlpaUoLy+Xi4FAXl4e3N3dW/04hoaG3L1ocaeNBoApU6aga9eu2LJlS4Pb7dy5E5aWlhg8eDDCw8MBANnZ2TA1NW2TpOi6yHrfxsbGwtraGk5OTrh//36jx5kxYwb3ep48eQJra2vweDw4Ojri0aNHAN78f/Xo0aOZr+h/ZP8MkiJFTE757rvv8Pnnn0NdXR19+vThPsUR5SLP720A+P777zFy5EhUVFRIPKWyotLW1saRI0cAiDdtdI1Vq1bB0dERJSUlDbY/ZMgQTJs2DQBgZ2cHb29v9O3bFxs3bsTx48db9sXIGEn6VigUYv369UhMTMTFixexbNmyBqcJz8vLw8OHD7niQ/r6+khOToaqqir27t2LXbt2YcmSJYiKioKFhUXLvbgWzl+QaZSc0jyUQCi76L0tvpZOIPT392fp6emMMcbi4+NZcHAwe/z4MePz+czW1pa5ubkxoVAoMv3z21Mvu7m5sbt377KysjI2efJk5uDgwEaOHMmKiooken1vT/UszrTRb9uzZw/bvHmz2Mfi8/ns6dOnjDEmkjjKWMskECpC32ZnZ7Mvv/yS+9nKyqrBY8ycOZMJBII6pwr/4Ycf2JEjR+qMhzGawpgQQqTGw8MDMTExAIBDhw7Bw8MDurq63G2X7t27IyEhodF2IiMj4ejoiISEBEyePLnWLZS4uLhat1A8PDwabLOxaaOb47///S/+7//+D/r6+i3W5rsUoW/f3g5485hmff766y8AqDWj55UrV2BpaYktW7bAzMyswbgkRbcJ2gAlpxBFRe9twMbGBkFBQaioqODunT969AgzZ85EYWEhHj58CDMzMxgaGnL71DUbZHZ2Ni5evIioqChUVlbCzs5O5DjOzs5wdnZuUmyNTRstqaysLGzevLnVbwsoQt++m5vV0FwDq1atqrMYnKmpKc6fP4/Dhw9j5cqV2L59e5NiFQcNBgghpBlUVFRgY2ODsLAwDBkyBABw8OBBjBgxAtOmTUNAQECt6Z91dXVx//599O7dGzdu3AAA9OnTB4MHD+ZyJmqq/9WIi4urNS25gYEB98m5LjXTRvv6+iI+Ph47d+4E8KaCozjJZ8+fP0f79u2hpaXFLXvw4AGmT5+OI0eOiCxvDYrQt4aGhsjJyUFFRQUuXboEY2NjAHX3bV5eHmbOnImysjL8+eefiIyMxJQpU7j8AW1t7dbr8ybfWJBjkt5Peft+VGvq3bs3Gzt2LGOMsZKSEjZ27FhmY2PDVq9e3ei+eXl5TENDg7t/6+fnx3g8HuPxeKx9+/bs+fPn9e7r4ODAtLW12bFjx7hlXl5erHv37iLbUc6A7FLE9/bLly+Zg4MDs7OzYw4ODiwvL6/R40yfPp17PTdu3GAmJiYi97EZa52iQxcvXmRqamosJyeHMcZYZmYm69+/Pxs1ahSbMGEC27Nnj0hfx8XFsf79+7NJkyYxe3t77r62l5cXc3BwYA4ODuz48eNNjo8x0fvIxcXFbPTo0czGxoatXLmSMcZYZWUls7W1rbXfokWLWN++fdlnn33G5s2bxxhj7Ntvv2Xx8fEi2/n6+rJevXpxv19u3rzJGGudnAHGFKNvY2Ji2ODBg5mDgwPLz89njNXdtzXefj3nz59ndnZ2jM/nMxcXF/bw4cM642Gsee9tGgyIoa1+Yb79H7tx40a2c+dOxhhjw4YNY/fv329w31mzZjEHB4dayVx3795lDg4ODe774MEDFhISIjIYeDcexmgwIMsU8b1dVlbGHjx4wBhj7NSpU8zf37/BY9y9e5eNHDlS5PW8+weKMfmsQNgU9vb23MCrLufPn2cRERFitTVjxgxWWVnZ6HY3btxglpaWbMWKFdwyeapAKC5p9G19vLy82MCBA0WWUQKhhGbPno3z588DAM6cOYNFixbhyZMncHBwgJ2dHdzd3Wsle/D5fO7RG3d3d+Tl5eH169fw9PSEo6MjRo0a1SLP7qempnLFWpydnZGWllbvtnXNiV0jNjYWX3zxRYPHorkJFI8ivLfbt2/PvTc1NDSgqtrwr6s1a9Zg/vz5zY5P3iUmJnKPv9Vl0KBB+Oqrr8Rqa9u2bWLVcOjbty/S09PxzTffiB2nPJJG39YnKioKFy5ckHj/dyn1YEARMlWBN2WH6yv2ceTIEbi5uTX6GohiUZT3NgBUVFQgNDQUAQEB9W5TXxY2IUQ8Sp1AqAiZqg3NiZ2XlwctLS3861//atKxifxThPd2DT8/P8yaNUsk1nfVl4VNCBGPUg8GFCFT9e2yw9euXUNubi7i4+PRvn17/PzzzyK3CIRCIQoKCkRqwRPFpAjvbQAICwtDr169MGHCBG6ZuFnYNVXyWkNOTk6rta0omtNH1L+SaVa/SZy9IIcUNVO1xrvV4AYPHsz++ecf7ufbt28zT0/PWvt9+eWX7JNPPmEmJibcsd6NhzHZT+5RZor43s7Pz2dqampc1vqiRYsYY+JnYTPW8gmE9+7dY1paWgwAfYnxpaWlxVXpo/6VzT6vocLYOx8PFNjly5dhbm6OjIyMVqvi1Bw8Hg96enr1JqhcuHABWVlZYieovOvw4cPQ1dUV67LulClTcPPmTZEEFVnvP2Um6/83LfnenjlzJjZv3txo8lV2djZ8fX0xatQokcS25vZVfn4+CgoKmryfMtLX168zsbkh1L/NI0mfAwANBojYqP9kF/3fiI/6ipDalPppAkIIIYQoaQIhJadIhvpN9tH/UeOojwipTakGA/r6+tDS0oKnp6e0Q5FbWlparTpLGZEMvbebht7HhIhSqpwBoHWSU0JDQxEXF4cDBw7U+bx/W6qqqsKsWbOQl5eHmJgY6Orqtmj7kiankNbXUu/tCxcuYObMmfD394evr28LRNY8R48exbJly7By5UqucmFz0fuYEFFKNxhoaQcPHsTkyZOxZ88e+Pj4SDscAMDDhw9hYmKCQYMG4fjx4yLFZAhpyD///AMTExP0798ff/zxR6MlgNsCYwyTJk3CyZMnceXKFXzyySfSDokQhUODgWa4c+cOBgwYgJEjR2L//v0y9Uf35MmTGD58ONavX4+vv/5a2uEQOVBdXY3hw4cjIyMDWVlZeP/996UdEqeoqAgDBgxA165dkZycDHV1dWmHRIhCkf6wX05VVFTAw8MD//rXv7Bt2zaZGggAgKurKwIDAxEcHIyMjAxph0PkwIYNG3Dq1ClERUXJ1EAAeDOHQUxMDC5fvowlS5ZIOxxCFA5dGZBQUFAQNm3ahNTUVFhYWEg7nDpVVFTA2toaRUVFuHz5Mt577z1ph0Rk1MWLF2FjY4O5c+ciPDxc2uHUKzw8HAsXLsQff/zRYvkDhBAaDEjk999/h6urK9auXSvzU6bm5uZiwIABGDNmDPbt2yftcIgMevnyJQYMGAA9PT0kJydDQ0ND2iHVq7q6Gq6ursjMzERWVhY6d+4MFRUVdOjQQdqhESLXaDDQRI8ePYKJiQksLCxw/PhxmUiwasyBAwfg6emJn376CVOmTJF2OESGMMbg6emJY8eOITMzE//3f/8n7ZAa9eTJE5iYmMDY2Bja2trQ19fHtm3bpB0WIXKNBgNNUF1djaFDh+LGjRvIysqSq6mBfXx88PPPP+Py5cv49NNPpR0OkRF79+7Fl19+iYMHD2LixInSDkcslZWV+OWXXzBx4kQMGjQIFRUVyMzMlHZYhMg1Ggw0wcqVK/Htt98iLi4OTk5O0g6nSUpKSmBubo6OHTsiLS0Nmpqa0g6JSNnNmzdhbm6OCRMmYPfu3dIOR2zHjh3DqFGj8Nlnn+HWrVtQV1fHq1evoKamJu3QCJFbsn+NW0akpaVh6dKlWLx4sdwNBACgU6dOiImJwY0bNxAcHCztcIiUvX79Gh4eHvjwww+xefNmaYfTJK6urti9ezdev34NxhgqKipw7do1aYdFiFyjwYAYXrx4wV2SDA0NlXY4EhswYADCw8OxadMmHDt2TNrhEClauHAhbt68iUOHDqFjx47SDqdJ1NTU8OWXX+LWrVv4z3/+Ax0dHboqQEgz0W2CBnz99dfQ1dXFtWvXEB8fj8zMTKmXG24uxhhGjx6N1NRUHDp0CHPnzkV6ejo6deok7dBIK0tNTcXMmTMRGhqKcePGYcuWLfD395d2WIQQGUCDgQb07t0bvXr1QlxcHH7++We4ublJO6QW8ezZM5iYmMDAwAAZGRlIS0uDlZWVtMMirSwsLAybN28GYwz29vY4cuSIzBXLIoRIh1LNWtgUpaWl+Ouvv3Dv3j2YmZnB398fPXv2xMCBA6UdWrMNGzYMPXv2RHp6OlRUVHD9+nUaDCiBa9euQSgUol27dsjNzcXChQulXmCoNSYOU1Q0uRJpTTQYqEdmZiYYYxAKhcjJyYG/vz9MTEykHVaLWLp0KRYsWICai0J//PEHpk2bJuWoSGtLTExEUVERAMDMzEzqMxLm5+fDyMgIr169kmoc8kJLSws5OTk0ICCtggYD9cjLywMATJo0CWvXrpW5Wu3NMXr0aAwfPhx79uzBnDlzcPfuXWmHRNpASUkJPv74Y+zduxc8Hk/a4aCgoACvXr3C/v37YWRkJO1wZFpOTg48PT1RUFBAgwHSKihnoAFVVVUKn6XMGANjTC4qKZLmkbX38+XLl2Fubo6MjAyYmZlJOxyZRn1FWhtdGWiALP3ibC0qKiqURKYklOH9TAiRTLMGA5T80zySJARRn4uvOQlX1M/io8Q2QhQAk9C9e/eYlpYWA0BfEn5paWmxe/fuUZ/LSP9SP7dtP2dkZDAALCMjo8n7MsbY2bNnWY8ePdiOHTsYY4wlJSWxwYMHMxsbG3b16lXGGGPr1q1j3bp1Y9euXZPoGA3p1KkT4/F4jMfjccd718GDB5m+vj73c+/evbl9Tp8+LfaxmttXhDRG4isDlPzTPJIkBFGfi685CVfUz+KTdmLbhAkT4OfnBwD49ttvceLECRQXF2PGjBk4efIkAgMDcfXqVbHaKi0tbVI1xs8++wwCgaDe9VVVVYiNjcWHH37ILdPW1m5wH0Kkpdk5A0ZGRpTQ0saoz9sG9bPsOH36NGJiYrB79254e3vD29tbJOm1rKwMampq0NXVha6uLp4/fy5Wu2VlZfj5559x4MABODs7Y/78+WLHdOfOHdjb26Nfv37YsGED2rdvL7I+OjoaX3zxBdatW8ctKykpAY/HQ/fu3bFlyxZ06dJF7OMR0poohZwQIvOGDh2K9u3bw9/fH9ra2nB0dBRZX1hYiM6dO3M/t2vXDhUVFfW2d/36dcyaNQujRo1CcXExoqOjuYFAeHg4+Hy+yNeqVatqtZGbm4tz587h/fffx48//iiyrqqqCocPH8aECRNElqekpCAxMREuLi4ICQlpcj8Q0lrkYjAwffr0etc9fvxY4pOqtLQU48aNg62tLdasWVNn20OHDoWNjQ32798v0THkCfVz26B+lkxAQAC2bduGoKCgWut0dHTw8uVL7mehUAgNDY162zp79ixSUlIwadIkTJkyBbq6uty6oKAgCAQCka9FixbVakNPTw8A4O7ujqysLJF1+/fvx/jx42s9stvQPoRIk1wMBnbs2FHvOgMDA4SFhUnUbmRkJFxdXZGcnIyEhAQ8ePBAZP3q1auxcOFCJCYm4scff8Tr168lOo68oH5uG9TPTccYQ1BQELZv317nFNxaWloQCoV48eIF/v7770YvvwcEBCAlJQXV1dUYO3YsfHx8kJGRAUC8KwOlpaWoqqoCACQlJaF3794i67OzsxEVFQUXFxfcvn0bc+bMQUVFBcrLy+vdhxBpkqk6A0KhEB4eHnjx4gU+++wzlJaWYu/evbCwsMClS5cQGhqKO3fu4NmzZygtLcWpU6fw5MkTLFiwAD///HOTj5eamsrVZnd2dkZaWhrc3d259RcuXMC6deugqqoKCwsLXL9+HRYWFi32eqWF+rltUD+3nO3bt8POzg5+fn7Izc1FTEwMDAwMRLZZvnw5XF1doaKigq1btzbaZqdOnTB16lRMnToVOTk5+OuvvwC8uTJQ19WHt92+fRu+vr7o1KkTdHV1ERUVBQCYN28eVq5cidWrV3PbWlhY4IcffsCTJ0/g6uqKjh07QlNTE7t3725qNxDSamRqMHD06FF8+umn+P777xEREYHU1NRa2xgaGmLfvn0IDg5GXFwcjI2N62zLycmJG7nX2LhxI0xNTbmf377PqK2tXSvpqLKykrvMV9d6eUX93Daon1vOzJkzue9rboGkp6cjLi4OERER8PPzg729fa0+Xr9+PS5dutTgLQPgTbJoU54cMTU1xeXLl2st37hxY61lly5dAgB069aNu/pAiKyRqcFAbm4uzM3NAQDm5uZ1/vIcMGAAAODDDz9EYWFhvW2dOXOm0ePV3GfU0dFBUVERPvroI5H16urqqK6uhqqqKoqKihQm85f6uW1QP7cuKyurRu+7BwYGIjAwsI0iIkR+yVTOQO/evZGZmQkA3L/vert0LmtgWgUnJ6da9/2uXLkiso21tTXi4+MBAPHx8bWm8R04cCAEAgGEQiEyMjLQr18/SV6WzKF+bhvUz21HWkmZNVxcXLBgwQKRZatWrap1GyYtLQ0qKiooKSmRKB5CWotMXRkYM2YMYmJi4OTkhF69ekFdXV3itsT5JDVt2jR4enpi9+7dGDFiBHr06IHHjx9j27ZtCAsLQ3BwMKZMmYIlS5ZgxowZ6NChg8TxyBLq57ZB/dx2Wjspc9q0aXBxccHkyZPRvXt3kW1SUlJq7VdcXIxr167VWv7DDz9wV4sIkSmSli5srfKYFRUVjDHGduzYwVatWtWibcsSSfqvJftc0fu5OX1F/Sy+tu7nyspK5ubmxpycnNisWbOYt7c3Y4wxc3NzxhhjISEhzNPTk33++efM3t6evXr1it29e5e5ubk1OT7GGBs/fjxXannt2rUsNja2zm2OHTvG5s+fzy1btmwZS01N5eJi7E255O+//57xeDxWXFzcpDioHDFpbTJ1ZQAARo8ejZKSEmhqauLQoUPSDkdhUT+3DernliVrSZnnzp2DiYkJOnXqxC0rKirCtWvXsGTJEpFtN23ahN27d+OPP/5o0msmpC3I3GDg5MmT0g5BKVA/tw3q55Yla0mZmzZtwp49e0SeLNi4cSMCAgJEtktMTISJiQnee++9Ro9JiDTI3GCAEELqU5OU6ebm1iJJmY1dGahJyvT19UV8fDx27twpsn1ubi7Gjx+P58+f4+nTp+DxeMjNzUVaWhqAN/UIVqxYgffeew9nzpxBcnIyrl69Cm9vb/zyyy9NffmEtBqFGAwIBAIcP34ca9eubdXj3Lt3D59++ikyMjLQv39/TJ8+HX/++ScA4Pz583j48KFIWVNF1hZ9PmXKFPz+++8ICQnB7NmzW+04sqwt+tnNzQ0FBQV4/fo1wsPDYW9v32rHai5ZS8qsebSx5v9p5MiRGDlyJLe/hYUFvv32WwDAnDlzAAB8Ph8//fSTxHET0hoUYjDQVtasWQMbGxvu55oM5ry8PPj6+irNQKCtrFq1Co6OjvQYViuLjo6GhoYG8vLyMG3aNO7xRFnUrl07REdHQ11dHREREdxtgJrCPqGhody2bw8gJanoCLypUnj06FGRZXU9nVDzuOe7auJ6G01hTGRRm9UZSE9Ph6WlJRwcHLgTNjAwEDweD4MGDeKemebz+QgMDISVlRVCQ0MREBAACwsLrrKXj48Ppk6diiFDhmDChAm1LvOdOnUKdnZ2sLa2RnR0NABg6dKlsLa2hoODA9LT0yWK/+7du1BRUalzzvbY2Fh88cUXErXbmuS9zz/44AOJ9mtr8t7PNdX5iouL0b9/f4naaEujR4+Gvb09YmNj8dVXX0k7HEIUg6SPITT1UZclS5awEydOMMYYq6qqYowxVlpayhhj7PLly2zSpEmMMcZ4PB5LTk5mVVVVrHv37iwzM5NVVlYyMzMzxhhj3t7ebMeOHYwxxoKDg9kvv/zCzp49y+bPn8+qq6uZtbU1Ky8vZ0KhkFlbWzOhUMgGDRrEKisrRY5dIyoqivF4PJGvuXPn1op/+vTp7O7du8zb25tdu3ZNZJ2VlRV78uSJWP1Qoy0eLZT3PmeMsT179rDNmzeL3Uc12vKRN0XoZzs7O9atWzf2xx9/NKGnZOcRTkVHfUVaW5vdJvD398fy5ctx4MABTJ48Ga6urggPD+cuSbZr979QjI2NoaqqCgMDA5iYmEBFRUXk3mBNNvHAgQNx+/ZtWFpaAgCePn2KW7duYejQoQCAFy9e4OnTpwgLC4Ovry86dOiAsLAwkQlOvLy84OXl1WDsd+7cAQB8/PHHtdbl5eVBS0sL//rXvyToldYlz30uTxShn8+dO4f8/HyMHj2aOwYhRHm02WBAW1sbW7ZsQUVFBczNzWFpaYm4uDgkJycjIyMD8+fP57Z9Oxv47e9rZGZmwtzcHJcuXRIp96mvr48+ffrg9OnT0NDQQGVlJdTV1cHj8eDi4oKDBw8iIiIC3333HbfPvn37sGvXLpH2TU1NRSYcycrKwo0bN+Di4oJr164hNzcX8fHxaN++PX7++WeZvEUAyHefyxN57mfGGIRCIdTV1dGpUyeR5+WVCSVqEmXXZoOBHTt24MiRIxAKhfDx8YGuri66dOkCPp9fq4Z6YzIyMhAdHQ09PT0sW7YMycnJAABVVVUsWbIEzs7OUFVVRdeuXXH48GGMGTMG5eXlEAqF2LZtm0hb4nx6GjduHMaNGwfgzX3dBQsWoH379gCAI0eO4Ndff21S/G1FnvscABYvXozffvsNVVVVuHPnDjZs2NCkmNuKPPdzeXk5XFxcAABVVVX4/vvvmxQvEZ88JWoSJSTp/QVp3cOq6569PJJ2OeKmkMc+l8d72dTPDUtLS2ODBg1ifD6fhYSEMMYY+/rrr5m9vT0bOHAgy8zMZIy9yc34+uuvmaWlJQsJCWGzZ89m5ubmbMOGDYyxN/3s6+vLnJyc2Pjx45lQKORyMxhj7Pfff2e2trZs8ODB7ODBg4yxN3khgwcPZnw+n6WlpTX5tb7t6tWr9eZu1IdyBkhro0cLCSFy4cSJEwgJCYGrqyuqq6sBAMuXL4eWlhYyMzMRHh6OAwcOAHhzSX7t2rXo2bMnjh8/jg0bNsDS0hLz5s0DAFhaWmLXrl1YtGgRfv31V246Z8YYli1bhrNnz0JNTQ329vYYP348Tp8+jZSUFLRr1447do2m3Payt7fHrVu3EBUV1cK9Q0jzyN1gYO/evdIOQelQn7cN6ueGUaImIa2nzeoM1MjLy4O7u3urH8fQ0JC7zy/unOQ17t27B01NTVy/fh3Am7nSa4qKdOjQocF655s2bYKNjQ1GjRqFly9fAnhTSa9Hjx4t8KokI+t9HhsbC2trazg5OeH+/fv1bpeUlIR+/fqJ/CLOzs6GqalprbnkpUFR+vn333+HjY0NbG1t4ePjg+rqajx//hxWVlZt8vrqU5OouWfPHgQHB+PZs2eIi4tDUlISNm7cKFJ6WJxETeBNUaDevXtzy99O1BQIBLhy5QoMDAzA4/EQFRUFHo+HiIgIkbb27dvH/X6o+aq5AlGDMYbKykoAUOpETSK72nww0Fa0tbVx5MgRAP+bkzw5ORkJCQl48OBBg/vWVWlQIBBg7969GDx4cL2VBgsKCvDbb78hOTkZEyZMwI8//ggAiIqKEvkDpqgk6XOhUIj169dDIBDgP//5D5YtW1Zv+8bGxrh48aLIwKpv375y+xSCpFq7n52cnJCSksIlL6ampqJLly6IiYlp+RfTBDt27IC9vT34fH6tRM3Y2NgmtZWRkQEnJyfcuXMHo0eP5pa/najp4OCAyZMnA3hTBpnP52Pr1q0YO3asSFteXl4QCAQiX+++J8vLy+Hs7Aw+n4/Ro0dToiaROS02GJg9ezbOnz8P4E3N70WLFuHJkydwcHCAnZ0d3N3da1VU4/P5XKlZd3d35OXl4fXr1/D09ISjo6PIp+vmSE1N5S7JOTs7c5OI1KU5lQYvXrwIHo8HFRUVuLi4ICUlpdmxN0QR+vz27dswMjKChoYGbGxscPXq1Xrb1NbWhpaWVrNjaypl6+eaioQ1n7Trqq8hDfPmzcO5c+eQmpqK+fPnQ1VVFb/99hsEAgFWrVrFlfkVCATcJ++3ywG/XaHR398fZ86cweHDh9GuXTvw+XzuscJhw4YhMTERZ8+exeHDhwEAf/zxBwQCAZKTk/Hvf/+7ybG3b9+eGygkJSXBzs5O0m4gpFW02GDAw8OD++Rw6NAheHh4QFdXl7uM1717dyQkJDTaTmRkJBwdHZGQkIDJkyfXuiQXFxdX65Kch4dHg202Nif521avXl3vJecjR47Azc2tRY7TEhShz9/eDkCtP6qyQBn7ee/evejbty+ePXuGrl27NvraCCHyrcUSCG1sbBAUFISKigruPu6jR48wc+ZMFBYW4uHDhzAzM4OhoSG3T11TjWZnZ+PixYuIiopCZWVlrRG0s7MznJ2dmxRbY3OS12hupUEdHR3k5uYCAIqKirgM5daiCH1es10NNTW1Jh2nLShjP/v4+MDHxwf+/v7473//2+igRJ5QoiYhtbXYlQEVFRXY2NggLCwMQ4YMAQAcPHgQI0aMQGJiIlxcXGrNLa6rq4v79+9DKBTixo0bAIA+ffpgzpw5EAgESElJqXVvU5JPTzVzkgNAfHw8Vwjm3SSqtysNxsXFYcaMGXj9+jUA1Ko0KBQK8fjxY5H9Bw4ciHPnzgF4c1nx7byD1qAIfW5oaIicnBxUVFQgNTUVxsbGAIDnz5/j1atXEvZMy1K2fi4vL+e+79y5s1RuzTRGlpM1i4uL4ejoCHt7ezg6OuLevXv1bivrSbFEiUhaoKCuIhgXL15kampqLCcnhzHGWGZmJuvfvz8bNWoUmzBhAtuzZw+7e/cuc3NzY4wxFhcXx/r3788mTZrE7O3t2d27d1lZWRnz8vJiDg4OzMHBgR0/flyi+MzNzbnvi4uL2ejRo5mNjQ1buXIlY4yxyspKZmtrW+/+7xaAGTx4MPvnn3+4n2/fvs08PT1r7bd+/XpmbW3Nhg8fzl68eFFnPIy1XNEhRejzmJgYNnjwYObg4MDy8/MZY4x9++23LD4+XmS77Oxs5uTkxN577z3m5OTELl++zBhjIgVjGuorcSl7P2/bto3xeDxmb2/Ppk2bxk2A9Pbra6ivxNWcfeuKpTW83dcbN25kO3fuZIwxNmzYMHb//v069ykrK2MPHjxgjDF26tQp5u/vX2/7L168YKWlpbV+P7z7nqaiQ6S1yV0FQnHZ29uzsWPH1rv+/PnzLCIiQuL2Dx06xE6fPi3Wtl5eXmzgwIEiy+SpAqG4WrLPZ8yYwc3G15AbN24wS0tLtmLFCpHl8liBUFzS6Odnz54xGxsbNnPmTJHlLd3P/v7+LD09nTHGWHx8PAsODmaPHz9mfD6f2draMjc3NyYUCkUGAzwejxUXFzPGGHNzc+MGXpMnT2YODg5s5MiRrKioqMnxMSY6GBg/fjy7d+8eY4yxtWvXstjY2Eb3T0hIYAEBAU06DmM0GCBtT+6KDokrMTGxwfWDBg3CoEGDJG5//PjxYm+rLNXGWrLP362zX5++ffuKZIkrA2n0c5cuXbhHDVtTTbKmpaUlDh06hFmzZnHJmu3atcPcuXORkJAgkp9Rl5pkTV9fXxw6dAgREREil93j4uKwYsUKkX0MDAwafHyyqQnCFRUVCA0NRWRkZGMvmxCpU9jBACFE/ihCsmYNPz8/zJo1q9GBCyGygAYDhBCZ0VCy5rRp0xAQEFBvsmbv3r1FkjUHDx7MlQmuqf5XQ5IrAzXJmr6+voiPj8fOnTsBvEnWfLfCaFhYGHr16oUJEyZwy54/f4727dvLZEImIc0eDOTk5LREHEqnOf1Gfd64lugj6ufGtUYfeXh4wMrKiisH7uTkBC8vLxw7dgwdOnSotf2sWbPwxRdfwNjYGN26dQPw5lO5n58f9uzZAwCYP38+hg8fzu0jyZWBadOmwdPTE7t378aIESPQo0cPCIVCTJw4EUlJSdx2f//9N5YtWwZbW1skJCRg8ODBWLlyJdavXw8HBwc4OTlx2+bk5CAgIAC3bt3CkCFDEB4ejgEDBjQpLkJahKTJBvfu3WNaWloMAH1J+KWlpcUlJFGfS79/qZ/btp/lISlOVpJi5aGviHxTYeyda25NkJ+fj4KCAkl3V3r6+vp1lj1uCPW5+CTp3xrUz+KTtJ8vX74Mc3NzZGRkwMzMrBUiUxzUV6S1Nes2Qc+ePSX+ZUskQ33eNqifCSHKRGFnLSSEEEKIeOhpAkKIVFGiZuOoj0hro8EAIUQq9PX1oaWlBU9PT2mHIhe0tLSgr68v7TCIgmpWAiEhhDRHSyVqRkVFYdOmTdiyZQsGDx7cApE1T0FBATw8PNCnTx/88MMPUFVt/h3Z5iTEEtIYGgwQQuTahQsXYGNjg8DAQKxevVra4XD++OMPuLi4IDw8nGYgJDKPBgOEELn18uVLDBgwAPr6+khOToa6urq0QxKxcOFCbNiwAampqRg4cKC0wyGkXjQYIITIJcYYJk2ahJMnTyIzMxO9evWSdki1VFRUwNbWFs+ePUNmZiY30REhsoYeLSSEyKU9e/YgJiYGERERMjkQAAANDQ3ExMSgoKAA06dPrzWvAiGygq4MEELkTk5ODiwsLDBx4kS5mCI4JiYGEydOxK5du+Dr6yvtcAiphQYDhBC58vr1a1haWqKyshIXL15Ex44dpR2SWKZNm4bo6GhcunQJRkZG0g6HEBE0GCCEyJXZs2cjMjISFy9exL///W9phyO20tJSWFhYQENDA+fPn0f79u2lHRIhHMoZIITIjaNHj+LHH3/Ehg0b5GogAAAdO3bEoUOH8Oeff9KjhkTm0JUBQohcyM/Ph6mpKfh8Pn755ReoqKhIOySJbN26Ff7+/vjvf/+LMWPGSDscQgDQYIAQIsOqq6tx7tw52NrawsHBAffu3cOVK1fQpUsXaYcmMcYY3NzcIBAIcOXKFbx48QIffPABlRomUkWDAUKIzDpx4gRGjBiBhQsXYt26dUhMTISNjY20w2q258+fw9TUFB999BFev34Na2trbNq0SdphESVGOQOEEJmVlZWFjh07Ys2aNZg+fbrcPDnQmPLycnz99ddISUlBaWkprl69Ku2QiJKjWQsJITLr8uXLeP36Nbp27YqtW7eiuLgYUVFR0g6r2c6cOYPAwEAYGBggJycHjx49knZIRMnRlQFCiMxKSEhAVVUVOnTogL1792L37t3SDqlFeHp64ty5czA0NAQAvHjxggYERKooZ4AQIrMmTZqEHj16YPny5dDQ0JB2OC2OMYbDhw9j/fr1EAgE6NChg7RDIkqKBgOEEEKIkqPbBIQQQoiSowRCQhREfn4+CgoKpB2GXNDX10fPnj0l2pf6WXzN6WfStmgwQIgCyM/Ph5GREV69eiXtUOSClpYWcnJymvyHivq5aSTtZ9L2aDBAiAIoKCjAq1evsH//fpoRrxE5OTnw9PREQUFBk/9IUT+Lrzn9TNoeDQYIUSBGRkYwMzOTdhgKj/qZKBpKICSEEEKUHA0GCCGNmj59er3rHj9+jJCQEInaLS0txbhx42Bra4s1a9bU2fbQoUNhY2OD/fv3S3QMeUL9TKSFBgOEkEbt2LGj3nUGBgYICwuTqN3IyEi4uroiOTkZCQkJePDggcj61atXY+HChUhMTMSPP/6I169fS3QceUH9TKSFBgOEEI5QKIS7uzuGDBkCf39/+Pj4AAAsLCwAAKGhofDy8oKrqyt4PB7KysqQl5cHd3d3iY6XmpqKoUOHAgCcnZ2RlpYmsv7ChQtwdHREu3btYGFhgevXr0v+4mQI9TORNTQYIIRwjh49ik8//RTx8fEwMTGpcxtDQ0OcPHkSVlZWiIuLq7ctJycn8Pl8ka8rV66IbFNYWIjOnTsDALS1tfH8+XOR9ZWVlVBVVa13vbyifiayhp4mIIRwcnNzYW5uDgAwNzdHampqrW0GDBgAAPjwww9RWFhYb1tnzpxp9Hg6Ojp4+fIldHR0UFRUhI8++khkvbq6Oqqrq6GqqoqioiJ06dKlKS9HZlE/E1lDVwYIIZzevXsjMzMTALh/36WiosJ939DUJuJ8YrW2tkZ8fDwAID4+HlZWViLrBw4cCIFAAKFQiIyMDPTr10+SlyVzqJ+JrKErA4QQzpgxYxATEwMnJyf06tUL6urqErclzifWadOmwdPTE7t378aIESPQo0cPPH78GNu2bUNYWBiCg4MxZcoULFmyBDNmzFCYWf2on4msoVkLCVEAly9fhrm5OTIyMppdDKeyshLq6uqIiIhAYWEhgoODWyhK2dCcvqJ+Fl9L9hVpfXRlgBAiYvTo0SgpKYGmpiYOHTok7XAUFvUzkSU0GCCEiDh58qS0Q1AK1M9EllACISGkRQkEAixYsKDV2i8uLoajoyPs7e3h6OiIe/futdqxZFlr9zMATJkyBV27dsWWLVta9ThE+ujKACFErqirq2P//v344IMP8McffyA8PJz+WLWSVatWwdHRESUlJdIOhbQyujJAiBJKT0+HpaUlHBwcEBoaCgAIDAwEj8fDoEGDuEfT+Hw+AgMDYWVlhdDQUAQEBMDCwgIbN24EAPj4+GDq1KkYMmQIJkyYgKqqKpHjnDp1CnZ2drC2tkZ0dDQAYOnSpbC2toaDgwPS09ObHHv79u3xwQcfAAA0NDS4YjmySJ77GQDXz0QJMEKI3MvIyGAAWEZGhljbL1myhJ04cYIxxlhVVRVjjLHS0lLGGGOXL19mkyZNYowxxuPxWHJyMquqqmLdu3dnmZmZrLKykpmZmTHGGPP29mY7duxgjDEWHBzMfvnlF3b27Fk2f/58Vl1dzaytrVl5eTkTCoXM2tqaCYVCNmjQIFZZWSly7BpRUVGMx+OJfM2dO7fO11BeXs7s7e3ZrVu3mtBTTe+r5uyrCP28Z88etnnz5ib00hvN6WfS9ug2ASFKyN/fH8uXL8eBAwcwefJkuLq6Ijw8nCtM067d/341GBsbQ1VVFQYGBjAxMYGKiorIc/E1lfQGDhyI27dvw9LSEgDw9OlT3Lp1i6uJ/+LFCzx9+hRhYWHw9fVFhw4dEBYWBgMDA64tLy8veHl5ifUa/Pz8MGvWLBgaGjavM1qRIvQzUQ40GCBECWlra2PLli2oqKiAubk5LC0tERcXh+TkZGRkZGD+/Pnctm9Xwnv7+xqZmZkwNzfHpUuXuIl2AEBfXx99+vTB6dOnoaGhwT1Xz+Px4OLigoMHDyIiIgLfffcdt8++ffuwa9cukfZNTU25y+U1wsLC0KtXL0yYMKG5XdGq5L2fifKgwQAhSmjHjh04cuQIhEIhfHx8oKuriy5duoDP59cqVduYjIwMREdHQ09PD8uWLUNycjIAQFVVFUuWLIGzszNUVVXRtWtXHD58GGPGjEF5eTmEQiG2bdsm0pY4n1j//vtvLFu2DLa2tkhISMDgwYOxcuXKpnVAG5HnfgaAxYsX47fffkNVVRXu3LmDDRs2NClmIj+oAiEhCkBa1d58fHywYMEC9O/fv82O2VyyUoGwKZStn0nbk900XEIIIYS0CbpNQAiR2N69e6UdglKgfiatja4MEEIIIUqOBgOEKLG8vDy4u7u3+nEMDQ0xbtw4AEBpaSnGjRsHW1tbrFmzpt59mlJ2uK42s7OzYWpq2uole8Uly30NALGxsbC2toaTkxPu379f73ZJSUno16+fyKOKstbXpOloMEAIaXXa2to4cuQIACAyMhKurq5ITk5GQkICHjx4UOc+NWWHz507h+DgYISHh9fbfl1t9u3bVykflZOkr4VCIdavXw+BQID//Oc/WLZsWb3tGxsb4+LFi+jRowe3TFn7WpHQYIAQBTR79mycP38eAHDmzBksWrQIT548gYODA+zs7ODu7l6rpC2fz+dq0Lu7uyMvLw+vX7+Gp6cnHB0dMWrUKLx8+bLZsaWmpnIFcpydnZGWllbndk0pOyxum61BEfr69u3bMDIygoaGBmxsbHD16tV629TW1oaWllazYyOyhQYDhCggDw8PxMTEAAAOHToEDw8P6OrqIi4uDklJSejevTsSEhIabScyMhKOjo5ISEjA5MmTERERIbI+Li4OfD5f5MvDw6PBNgsLC9G5c2cAb/6wPH/+vMHtKyoquHr9LdVmS1KEvn57OwC1Bi9E8dHTBIQoIBsbGwQFBaGiooK7n/vo0SPMnDkThYWFePjwIczMzERK+b5d9a6m/Eh2djYuXryIqKgoVFZWws7OTuQ4zs7OcHZ2blJsOjo6ePnyJXR0dFBUVISPPvqowe3FKTvc1DZbkiL0dc12NdTU1Jp0HCL/6MoAIQpIRUUFNjY2CAsLw5AhQwAABw8exIgRI5CYmAgXFxe8W29MV1cX9+/fh1AoxI0bNwAAffr0wZw5cyAQCJCSklLrXrIkn1atra252vzx8fFcJb66ktbqKjv8/PlzvHr1Sqw224Ii9LWhoSFycnJQUVGB1NRUGBsbA6i7r4lioisDhCgoDw8PWFlZ4fr16wAAJycneHl54dixY+jQoUOt7WfNmoUvvvgCxsbG6NatG4A3n8r9/PywZ88eAMD8+fMxfPhwbh9JPq1OmzYNnp6e2L17N0aMGIEePXpAKBRi4sSJSEpK4rarr+zw+vXr4eDgACcnpwbbbEvy3tfq6uqYN28e+Hw+2rdvj59++gkA6uzrnJwcBAQE4NatWxgyZAjCw8MxYMCAJsVFZJA0p0wkhLQMWZ8u1t7eno0dO7be9efPn2cRERFitTVjxgxuat6G3Lhxg1laWrIVK1aILG/LKYylQVb6Wh76ivwPXRkghLS6xMTEBtcPGjQIgwYNEqutdyfdqU/fvn2Rnp4u1raKhPqaSIJyBgghhBAlR1cGCFEgOTk50g5B5rVEH1E/N476SL7QYIAQBaCvrw8tLS14enpKOxS5oKWlBX19/SbvR/3cNJL2M2l7Koy988wLIUQu5efno6CgQNphyAV9fX307NlTon2pn8XXnH4mbYsGA4QQQoiSowRCQgghRMnRYIAQQghRcjQYIIQQQpQcDQYIIYQQJUeDAUIIIUTJ0WCAEEIIUXI0GCCEEEKUHA0GCCGEECVHgwFCCCFEydFggBBCCFFyNBgghBBClBwNBgghhBAlR4MBQgghRMnRYIAQQghRcjQYIIQQQpQcDQYIIYQQJUeDAUIIIUTJ0WCAEEIIUXI0GCCEEEKUHA0GCCGEECX3/wBLPOW0SeU1qwAAAABJRU5ErkJggg==", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tree(tree_clf);" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "76196f06-3718-42e5-bdcd-651ef7995a8d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
DecisionTreeClassifier(max_depth=2)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "DecisionTreeClassifier(max_depth=2)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tree_clf = DecisionTreeClassifier(max_depth=2)\n", + "tree_clf.fit(X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5d55685a-4bcb-4b08-b8d8-dfcf08327c23", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tree(tree_clf);" + ] + }, + { + "cell_type": "markdown", + "id": "9d4fb6e8-ac23-4f03-b3d5-4601b90b8696", + "metadata": {}, + "source": [ + "### Регрессия\n", + "\n", + "Деревья принятия решений также способны иметь дело с задачами регрессии. Давайте построим дерево регрессии с применением класса `DecisionTreeRegressor` из `Scikit-Learn`, обучив его на зашумленномнаборе данных с `max_depth=2`:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "018ec935-f891-4d85-a0a0-dcce08c57726", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
DecisionTreeRegressor(max_depth=2)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "DecisionTreeRegressor(max_depth=2)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.tree import DecisionTreeRegressor, plot_tree\n", + "from sklearn.datasets import make_regression\n", + "\n", + "X, y = make_regression(n_samples=150, n_features=2, noise=10)\n", + "\n", + "tree_reg = DecisionTreeRegressor(max_depth=2 )\n", + "tree_reg.fit(X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "ad8891eb-037e-4ec0-bcdb-aec87c2a4f22", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tree(tree_reg);" + ] + }, + { + "cell_type": "markdown", + "id": "b6d9ea82-92d2-463d-8a00-def5658832ea", + "metadata": {}, + "source": [ + "Это дерево выглядит очень похожим на дерево классификации, которое мы строили ранее.\n", + "Главное отличие в том, что вместо прогнозирования класса в каждом узле оно прогнозирует значение.\n", + "\n", + "Обратите внимание, что спрогнозированное значение для каждой области всегда будет средним целевым значением образцов в этой области. Алгоритм расщепляет каждую область так, чтобы расположить большинство обучающих образцов как можно ближе к спрогнозированному значению." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "4a9cd783-9748-4b55-877a-e8d45b6ac079", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "12.938154389121735\n" + ] + } + ], + "source": [ + "from sklearn.tree import DecisionTreeRegressor, plot_tree\n", + "from sklearn.datasets import make_regression\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.metrics import mean_absolute_error\n", + "\n", + "X, y = make_regression(n_samples=150, n_features=1, noise=10)\n", + "\n", + "X_train, X_test, y_train, y_test = train_test_split(\n", + " X,\n", + " y,\n", + " test_size=0.2,\n", + " random_state=42\n", + ")\n", + "\n", + "\n", + "tree_reg = DecisionTreeRegressor()\n", + "tree_reg.fit(X_train, y_train)\n", + "\n", + "y_pred = tree_reg.predict(X_test)\n", + "print(mean_absolute_error(y_test, y_pred))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "81e06757-4fe7-4f48-83a5-0c5b7bbe6ff5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "plt.scatter(X_test.ravel(), y_test)\n", + "plt.scatter(X_test.ravel(), y_pred)" + ] + }, + { + "cell_type": "markdown", + "id": "ec794d2a-6c68-4333-bc1b-06a5a139a9ab", + "metadata": {}, + "source": [ + "### Композиции алгоритмов" + ] + }, + { + "cell_type": "markdown", + "id": "00b241e5-1e39-467c-b3b3-3f634cad6df6", + "metadata": {}, + "source": [ + "Предположим, вы задаете сложный вопрос тысячам случайных людей и затем агрегируете их ответы. Во многих случаях вы обнаружите, что такой агрегированный ответ оказывается лучше, чем ответ эксперта. Это называется `коллективным разумом`.\n", + "\n", + "Аналогично если вы агрегируете прогнозы группы прогнозаторов (таких как классификаторы или регрессоры), то часто будете получать лучшие прогнозы, чем прогноз от наилучшего индивидуального прогнозатора. Группа прогнозаторов называется `ансамблем`. \n", + "\n", + "Cоответственно, прием носит название `ансамблевое обучение`, а алгоритм ансамблевого обучения именуется `ансамблевым методом`.\n", + "\n", + "Например, вы можете обучать группу классификаторов на основе деревьев принятия решений, задействовав для каждого отличающийся случайный поднабор обучающего набора. Для вырабатывания прогнозов вы лишь получаете прогнозы всех индивидуальных деревьев и прогнозируете класс, который стал обладателем большинства голосов. \n" + ] + }, + { + "cell_type": "markdown", + "id": "864fadb1-cae9-4c54-b840-e8a05bf8f775", + "metadata": {}, + "source": [ + "#### Bootstrap" + ] + }, + { + "cell_type": "markdown", + "id": "6dd32d51-0e93-486e-95c9-151c65e22842", + "metadata": {}, + "source": [ + "Можно представить себе мешок, из которого достают шарики: выбранный на каком-то шаге шарик возвращается обратно в мешок, и следующий выбор опять делается равновероятно из того же числа шариков. Отметим, что из-за возвращения среди них окажутся повторы." + ] + }, + { + "cell_type": "markdown", + "id": "ece89bd2-7d39-4799-991a-28dabb988616", + "metadata": {}, + "source": [ + "![](./imgs/sem4/bootstrap.jpg)" + ] + }, + { + "cell_type": "markdown", + "id": "061a316a-0359-47d4-bbe6-7b1093eb6469", + "metadata": {}, + "source": [ + "#### Bagging (от Bootstrap aggregation)\n", + "\n", + "Bagging - это обучение каждого алгоритма МО на одной из выборок (у каждого алгоритма своя выборка), полученной методом bootstrap, с последующим усреднением ответа от каждого предиктора - в случае регрессии, в случае классификации - ответ выбирается посредством голосования (какой класс предсказался больше всего раз, тот и выберем)." + ] + }, + { + "cell_type": "markdown", + "id": "8cf961d8-26cf-4ca1-9c83-c44fb5ae00f4", + "metadata": { + "tags": [] + }, + "source": [ + "![](./imgs/sem4/bagging.png)\n" + ] + }, + { + "cell_type": "markdown", + "id": "054a8a82-7d71-4b3e-a32d-25dc0281c959", + "metadata": {}, + "source": [ + "Эффективность бэггинга достигается благодаря тому, что базовые алгоритмы, обученные по различным подвыборкам, получаются достаточно различными, и их ошибки взаимно компенсируются при голосовании, а также за счёт того, что объекты-выбросы могут не попадать в некоторые обучающие подвыборки." + ] + }, + { + "cell_type": "markdown", + "id": "b34215e6-e821-4bae-84d3-d090386c9393", + "metadata": {}, + "source": [ + "В библиотеке `scikit-learn` есть реализации `BaggingRegressor` и `BaggingClassifier`, которые позволяют использовать большинство других алгоритмов \"внутри\"." + ] + }, + { + "cell_type": "markdown", + "id": "567199e8-ce12-4958-b2c9-f78a76996523", + "metadata": {}, + "source": [ + "Показанный ниже код обучает ансамбль из `500` классификаторов на основе деревьев принятия решений, каждый из которых обучается на `100` обучающих экземплярах, случайно выбранных из обучающего набора. \n", + "Параметр `n_jobs` сообщает `ScikitLearn` количество процессорных ядер для использования при обучении и прогнозировании (`-1`указывает на необходимость участия всех доступных ядер):" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "a5b7a1a3-23df-4a5a-a842-87e4d130a033", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9333333333333333" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.ensemble import BaggingClassifier\n", + "from sklearn.tree import DecisionTreeClassifier\n", + "from sklearn.datasets import load_digits\n", + "from sklearn.metrics import accuracy_score\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "iris = load_digits()\n", + "X = iris.data\n", + "y = iris.target\n", + "\n", + "X_train, X_test, y_train, y_test = train_test_split(\n", + " X,\n", + " y,\n", + " test_size=0.2,\n", + " random_state=42\n", + ")\n", + "\n", + "bag_clf = BaggingClassifier(\n", + " DecisionTreeClassifier(),\n", + " n_estimators=500,\n", + " max_samples=100,\n", + " bootstrap=True,\n", + " n_jobs=-1)\n", + "\n", + "bag_clf.fit(X_train, y_train)\n", + "y_pred = bag_clf.predict(X_test)\n", + "\n", + "accuracy_score(y_test, y_pred)" + ] + }, + { + "cell_type": "markdown", + "id": "58547b38-4209-450c-bfac-7f9a19657e1d", + "metadata": {}, + "source": [ + "#### Случайный лес\n", + "\n", + "Такой ансамбль деревьев принятия решений называется `случайным лесом (random forest)` и, несмотря на свою простоту, является довольно мощным алгоритмов.\n", + "\n", + "Что случайного в случайном лесе:\n", + "\n", + " 1. Обучающие выборки, сформированные методом бутстрап\n", + " 2. Признаки для условий в каждом узле дерева (вместо поиска лучшего из лучших признаков при расщеплении узла он ищет наилучший признак в случайном поднаборе признаков)" + ] + }, + { + "cell_type": "markdown", + "id": "79b7b3e9-3a46-497a-b19b-b383848f87f9", + "metadata": {}, + "source": [ + "Вместо построения экземпляра `BaggingClassifier` и его передачи экземпляру `DecisionTreeClassifier` вы можете применить класс `RandomForestClassifier`, который является более удобным и оптимизированным для деревьев принятия решений (аналогичным образом имеется класс `RandomForestRegressor` для задач регрессии). \n", + "\n", + "Показанный ниже код обучает классификатор на основе случайного леса с `500` деревьями (каждое ограничено максимум `16` узлами), используя все доступные процессорные ядра:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "03d6f940-3325-4bb8-afa5-e8472f74a48e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.975" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.ensemble import RandomForestClassifier\n", + "from sklearn.datasets import load_digits\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.metrics import accuracy_score\n", + "\n", + "\n", + "iris = load_digits()\n", + "X = iris.data\n", + "y = iris.target\n", + "\n", + "X_train, X_test, y_train, y_test = train_test_split(\n", + " X,\n", + " y,\n", + " test_size=0.2,\n", + " random_state=42\n", + ")\n", + "\n", + "rnd_clf = RandomForestClassifier(n_jobs=-1)\n", + "rnd_clf.fit(X_train, y_train)\n", + "\n", + "y_pred_rf = rnd_clf.predict(X_test)\n", + "\n", + "accuracy_score(y_test, y_pred_rf)" + ] + }, + { + "cell_type": "markdown", + "id": "62646b21-ee00-4836-893b-ddf57a9ab76b", + "metadata": {}, + "source": [ + "#### Градиентный бустинг" + ] + }, + { + "cell_type": "markdown", + "id": "4f157161-1635-47df-8dd1-e906e28ce095", + "metadata": {}, + "source": [ + "**Бустинг** — это техника построения ансамблей, в которой модели построены не независимо, а последовательно.\n", + "\n", + "**Градиентный бустинг** — это техника машинного обучения для задач классификации и регрессии, которая строит модель предсказания в форме ансамбля слабых предсказывающих моделей, обычно деревьев решений." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "15fd3ead-d29b-4fb4-b386-bcb9db0b4acc", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.datasets import make_regression\n", + "import pandas as pd" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5b369f91-871a-483b-aa0e-2b5f66ec05bc", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "X, y = make_regression(\n", + " n_samples=100,\n", + " n_features=3,\n", + " n_informative=2,\n", + " noise=10\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "91fa6840-4fff-498d-9fc7-7a722af03411", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "df = pd.DataFrame(X)\n", + "df['y_true'] = y" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "4d707117-4a54-4a8a-8a31-405ac2ed7435", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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DecisionTreeRegressor(max_depth=1)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "DecisionTreeRegressor(max_depth=1)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.tree import DecisionTreeRegressor\n", + "\n", + "tree_1 = DecisionTreeRegressor(max_depth=1)\n", + "tree_1.fit(df[[0,1,2]], df[['residual_0']])" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "a133c7a3-44ca-4371-b163-90395ed05e2f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "df['tree_pred_1'] = tree_1.predict(df[[0,1,2]])" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "e8c8c5d9-fb94-46cf-b939-49e33a9e2369", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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012y_truey_pred_0residual_0tree_pred_1
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" + ], + "text/plain": [ + " 0 1 2 y_true y_pred_0 residual_0 \\\n", + "0 -0.135456 -1.013084 -1.430305 -37.673161 31.267689 -68.940850 \n", + "1 1.883766 0.568611 0.391718 184.487726 31.267689 153.220037 \n", + "2 0.428091 0.781200 -0.438449 40.129650 31.267689 8.861961 \n", + "3 1.613016 -0.746272 1.112609 178.316824 31.267689 147.049135 \n", + "4 -0.285830 0.899955 0.390032 -18.258000 31.267689 -49.525689 \n", + ".. ... ... ... ... ... ... \n", + "95 -1.184045 0.025689 -0.321175 -118.370507 31.267689 -149.638196 \n", + "96 -0.515505 0.315502 -1.474370 -64.266387 31.267689 -95.534076 \n", + "97 -0.382320 -1.635677 0.070134 -32.789144 31.267689 -64.056833 \n", + "98 0.891264 -0.674273 -1.349810 70.299484 31.267689 39.031795 \n", + "99 0.994868 0.685481 -0.526537 75.109633 31.267689 43.841944 \n", + "\n", + " tree_pred_1 \n", + "0 -84.433122 \n", + "1 81.122019 \n", + "2 81.122019 \n", + "3 81.122019 \n", + "4 -84.433122 \n", + ".. ... \n", + "95 -84.433122 \n", + "96 -84.433122 \n", + "97 -84.433122 \n", + "98 81.122019 \n", + "99 81.122019 \n", + "\n", + "[100 rows x 7 columns]" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "markdown", + "id": "b8abd1de-75ea-4b29-b872-f6eb0a2c76e7", + "metadata": {}, + "source": [ + "Теперь забустим наше первоначальное предсказание. Для этого полученные предсказания первого дерева нужно умножить на learning rate и прибавить к константному предсказанию. Таким образом мы приблизимся на шаг и истинным значениям." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "669f9a1b-10bd-4c4e-9af6-0310813bcede", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "lr = 0.1\n", + "df['y_pred_1'] = df['y_pred_0'] + lr * df['tree_pred_1']" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "dc0ceec8-9334-4198-97d7-c1d8e88aaa5c", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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012y_truey_pred_0residual_0tree_pred_1y_pred_1
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" + ], + "text/plain": [ + " 0 1 2 y_true y_pred_0 residual_0 \\\n", + "0 -0.135456 -1.013084 -1.430305 -37.673161 31.267689 -68.940850 \n", + "1 1.883766 0.568611 0.391718 184.487726 31.267689 153.220037 \n", + "2 0.428091 0.781200 -0.438449 40.129650 31.267689 8.861961 \n", + "3 1.613016 -0.746272 1.112609 178.316824 31.267689 147.049135 \n", + "4 -0.285830 0.899955 0.390032 -18.258000 31.267689 -49.525689 \n", + ".. ... ... ... ... ... ... \n", + "95 -1.184045 0.025689 -0.321175 -118.370507 31.267689 -149.638196 \n", + "96 -0.515505 0.315502 -1.474370 -64.266387 31.267689 -95.534076 \n", + "97 -0.382320 -1.635677 0.070134 -32.789144 31.267689 -64.056833 \n", + "98 0.891264 -0.674273 -1.349810 70.299484 31.267689 39.031795 \n", + "99 0.994868 0.685481 -0.526537 75.109633 31.267689 43.841944 \n", + "\n", + " tree_pred_1 y_pred_1 \n", + "0 -84.433122 22.824377 \n", + "1 81.122019 39.379891 \n", + "2 81.122019 39.379891 \n", + "3 81.122019 39.379891 \n", + "4 -84.433122 22.824377 \n", + ".. ... ... \n", + "95 -84.433122 22.824377 \n", + "96 -84.433122 22.824377 \n", + "97 -84.433122 22.824377 \n", + "98 81.122019 39.379891 \n", + "99 81.122019 39.379891 \n", + "\n", + "[100 rows x 8 columns]" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "markdown", + "id": "be1eda59-4685-42d2-bed3-0d2c1f25bb53", + "metadata": { + "tags": [] + }, + "source": [ + "Посчитаем ошибку и убедимся что она уменьшилась:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "8dc0f80c-e85a-4dfd-817a-fa1ff7e8a8e8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Было: 83.64294087330029\n", + "Стало: 76.18633734863174\n" + ] + } + ], + "source": [ + "print(f\"Было: {mean_absolute_error(df['y_true'], df['y_pred_0'])}\")\n", + "print(f\"Стало: {mean_absolute_error(df['y_true'], df['y_pred_1'])}\")" + ] + }, + { + "cell_type": "markdown", + "id": "7ba9c503-88ff-4d72-8204-6cc6239f7524", + "metadata": {}, + "source": [ + "Таким образом, мы забустили константное предсказание.\n", + "\n", + "Далее алгоритм для следующего дерева такой же:\n", + "- Посчитать разницу между последним предсказанием и истинным значением\n", + "- Обучить новое дерево на этой разнице\n", + "- Предсказываем значения на новом дереве\n", + "- Делаем шаг от прошлого предсказания в сторону истинных значений\n", + " \n", + "Обернем все в цикл:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "97a1cbbf-56da-4e23-b828-cc87d5552515", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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012y_truey_pred
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" + ], + "text/plain": [ + " 0 1 2 y_true y_pred\n", + "0 -0.135456 -1.013084 -1.430305 -37.673161 31.267689\n", + "1 1.883766 0.568611 0.391718 184.487726 31.267689\n", + "2 0.428091 0.781200 -0.438449 40.129650 31.267689\n", + "3 1.613016 -0.746272 1.112609 178.316824 31.267689\n", + "4 -0.285830 0.899955 0.390032 -18.258000 31.267689\n", + ".. ... ... ... ... ...\n", + "95 -1.184045 0.025689 -0.321175 -118.370507 31.267689\n", + "96 -0.515505 0.315502 -1.474370 -64.266387 31.267689\n", + "97 -0.382320 -1.635677 0.070134 -32.789144 31.267689\n", + "98 0.891264 -0.674273 -1.349810 70.299484 31.267689\n", + "99 0.994868 0.685481 -0.526537 75.109633 31.267689\n", + "\n", + "[100 rows x 5 columns]" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "train = df[[0,1,2,'y_true']].copy()\n", + "train['y_pred'] = train['y_true'].mean()\n", + "train" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "d79bc2fe-bd41-4336-b2fa-ea464c0c5561", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Дерево 1: MAE=76.18633734863174\n", + "Дерево 2: MAE=69.78839469511819\n", + "Дерево 3: MAE=65.23121406231614\n", + "Дерево 4: MAE=59.80214563570313\n", + "Дерево 5: MAE=55.92610812568657\n", + "Дерево 6: MAE=52.97726287762965\n", + "Дерево 7: MAE=49.89017878618041\n", + "Дерево 8: MAE=47.449637517710016\n", + "Дерево 9: MAE=44.10842265940846\n", + "Дерево 10: MAE=41.8402034112005\n" + ] + } + ], + "source": [ + "n_trees = 10\n", + "lr = 0.1\n", + "\n", + "trees = []\n", + "for i in range(n_trees):\n", + " train['residual'] = train['y_true'] - train['y_pred']\n", + " tree = DecisionTreeRegressor(max_depth=1)\n", + " tree.fit(train[[0,1,2]], train[['residual']])\n", + " trees.append(tree)\n", + " train['y_pred'] += lr * tree.predict(train[[0,1,2]])\n", + " print(f\"Дерево {i + 1}: MAE={mean_absolute_error(train['y_true'], train['y_pred'])}\")\n", + " \n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "809d87c5-c9b8-46b9-9ebd-f995f6ca8960", + "metadata": {}, + "source": [ + "Таким образом мы обучили наши деревья, давайте напишем инференс(сделаем предсказание) по ним.\n", + "\n", + "Чтобы сделать предсказание, нужно так же сначала сделать констатное предсказание." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "ad38fdcb-72f0-45f1-abcf-5aef77ed52eb", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MAE: 41.8402034112005\n" + ] + } + ], + "source": [ + "test = df[[0,1,2,'y_true']].copy()\n", + "test['y_pred'] = test['y_true'].mean()\n", + "\n", + "for tree in trees:\n", + " test['y_pred'] += lr * tree.predict(df[[0,1,2]])\n", + " \n", + "print(f\"MAE: {mean_absolute_error(test['y_true'], test['y_pred'])}\")" + ] + }, + { + "cell_type": "markdown", + "id": "a643006a-2854-469b-9292-4e52e32d2f50", + "metadata": {}, + "source": [ + "#### Популярные библиотеки для градиентного бустинга\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "ae6631b3-d2f2-4cc4-a7f0-f28d3dbbee76", + "metadata": { + "tags": [] + }, + "source": [ + "- [CatBoost](https://catboost.ai/en/docs/)\n", + "- [LightGBM](https://lightgbm.readthedocs.io/en/v3.3.2/#)\n", + "- [XGBoost](https://xgboost.readthedocs.io/en/stable/#)\n", + "\n", + "CatBoost, LightGBM и XGBoost - это три популярные библиотеки градиентного бустинга, которые широко используются для решения задач машинного обучения. Вот несколько основных различий между ними:\n", + "\n", + "1. Обработка категориальных признаков: CatBoost и LightGBM предоставляют встроенные механизмы для автоматической обработки категориальных признаков, в то время как в XGBoost необходимо предварительно выполнять преобразования для кодирования категориальных признаков в числовые значения.\n", + "\n", + "2. Оптимизация памяти и скорость обучения: LightGBM и CatBoost изначально были разработаны с акцентом на оптимизацию памяти и производительность. Они используют различные алгоритмы для сжатия данных и оптимизации работы с памятью, что делает их более эффективными на больших наборах данных и быстрее в обучении моделей, по сравнению с XGBoost.\n", + "\n", + "3. Поддержка работы с категориальными признаками не только в деревьях, но и в линейных моделях: CatBoost позволяет использовать категориальные признаки не только в деревьях, но и в линейных моделях, что может быть полезно в некоторых задачах. LightGBM также поддерживает использование категориальных признаков в линейных моделях, но XGBoost поддерживает только использование категориальных признаков в деревьях.\n", + "\n", + "4. Автоматическая обработка пропущенных значений: CatBoost автоматически обрабатывает пропущенные значения в данных без необходимости предварительной обработки, в то время как LightGBM и XGBoost требуют явного заполнения пропущенных значений перед обучением моделей.\n", + "\n", + "5. Работа с несбалансированными данными: CatBoost и XGBoost предлагают встроенные механизмы для работы с несбалансированными данными, такими как автоматическое балансирование классов, в то время как LightGBM требует явного указания параметров модели для работы с несбалансированными данными." + ] + }, + { + "cell_type": "markdown", + "id": "b9f76cfa-75f2-4133-b521-a0686050b3b2", + "metadata": {}, + "source": [ + "### CatBoost\n", + "\n", + "Библиотека CatBoost – это градиентный бустинговый фреймворк с открытым исходным кодом, разработанный компанией Yandex." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "46c1ea73-eee7-4bb1-8127-31dc96facf4c", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# !pip install catboost" + ] + }, + { + "cell_type": "markdown", + "id": "bf28abb0-b5ef-449b-876d-5d46805bd148", + "metadata": {}, + "source": [ + "В этом примере мы использовали функцию `make_regression` из библиотеки `scikit-learn` для генерации синтетических данных для задачи регрессии. Затем мы создали и обучили модель `CatBoostRegressor`, указав индексы категориальных признаков в параметре `cat_features`. Наконец, мы оценили качество модели на тестовом наборе данных с помощью среднеквадратичной ошибки (`MSE`)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e4f2aa8e-fdfc-4759-81e3-cf7bcde33999", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "from sklearn.datasets import make_regression\n", + "from sklearn.model_selection import train_test_split\n", + "from catboost import CatBoostRegressor\n", + "\n", + "# Генерация синтетических данных\n", + "X, y = make_regression(n_samples=1000, n_features=5, n_informative=3, random_state=42)\n", + "X = np.round(X) # Округление признаков до целых чисел\n", + "X = X.astype(int) # Преобразование признаков в целочисленный тип данных\n", + "cat_features = [0, 2, 4] # Индексы категориальных признаков\n", + "\n", + "# Разделение данных на обучающий и тестовый наборы\n", + "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", + "\n", + "# Создание и обучение модели CatBoostRegressor\n", + "model = CatBoostRegressor(iterations=1000, # Количество итераций\n", + " learning_rate=0.1, # Скорость обучения\n", + " depth=6, # Глубина дерева\n", + " cat_features=cat_features, # Индексы категориальных признаков\n", + " random_state=42) # Задаем случайное начальное состояние для воспроизводимости\n", + "\n", + "model.fit(X_train, y_train, verbose=100) # Обучение модели с выводом прогресса на каждой 100-й итерации\n", + "\n", + "# Прогнозирование на тестовом наборе данных\n", + "y_pred = model.predict(X_test)\n", + "\n", + "# Оценка качества модели\n", + "mse = np.mean((y_test - y_pred) ** 2) # Среднеквадратичная ошибка\n", + "print(f\"Mean Squared Error: {mse:.4f}\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "9d40af0a-89a9-467e-98e6-e7853f12e311", + "metadata": {}, + "source": [ + "#### LightGBM\n", + "\n", + "LightGBM - это эффективная библиотека градиентного бустинга, разработанная Microsoft, которая обладает высокой производительностью благодаря оптимизации памяти и быстрым алгоритмам обучения." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5de56b14-4056-4e13-a12f-b4578597862d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# !pip install lightgbm" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "86316bc6-4315-4cec-8386-59e758d407a3", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from sklearn.datasets import make_regression\n", + "from sklearn.model_selection import train_test_split\n", + "import lightgbm as lgb\n", + "\n", + "# Генерация синтетических данных\n", + "X, y = make_regression(n_samples=1000, n_features=5, n_informative=3, random_state=42)\n", + "X = np.round(X) # Округление признаков до целых чисел\n", + "\n", + "# Создание DataFrame из массивов NumPy\n", + "df = pd.DataFrame(X, columns=[f\"feature_{i}\" for i in range(X.shape[1])])\n", + "df[\"cat_feature\"] = np.random.choice([\"A\", \"B\", \"C\"], size=X.shape[0]) # Добавление категориального признака\n", + "df['cat_feature'] = df['cat_feature'].astype('category')\n", + "cat_features = [\"cat_feature\"] # Список категориальных признаков\n", + "\n", + "# Разделение данных на обучающий и тестовый наборы\n", + "X_train, X_test, y_train, y_test = train_test_split(df, y, test_size=0.2, random_state=42)\n", + "\n", + "# Создание и обучение модели LGBMRegressor\n", + "model = lgb.LGBMRegressor(num_leaves=31, # Количество листьев в дереве\n", + " learning_rate=0.1, # Скорость обучения\n", + " n_estimators=100, # Количество деревьев\n", + " categorical_feature=cat_features, # Список категориальных признаков\n", + " random_state=42) # Задаем случайное начальное состояние для воспроизводимости\n", + "model.fit(X_train, y_train, verbose=10) # Обучение модели с выводом прогресса на каждой 10-й итерации\n", + "\n", + "# Прогнозирование на тестовом наборе данных\n", + "y_pred = model.predict(X_test)\n", + "\n", + "# Оценка качества модели\n", + "mse = np.mean((y_test - y_pred) ** 2) # Среднеквадратичная ошибка\n", + "print(f\"Mean Squared Error: {mse:.4f}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "35896ec9-b40e-4885-bc3b-e5fcc5d97f6b", + "metadata": {}, + "source": [ + "В этом примере мы использовали функцию `make_regression` из библиотеки `scikit-learn` для генерации синтетических данных для задачи регрессии. Затем мы создали `DataFrame` из массивов `NumPy`, добавили категориальный признак в `DataFrame` с помощью библиотеки `pandas`, и указали его в параметре `categorical_feature` при создании и обучении модели `LGBMRegressor`. Наконец, мы оценили качество модели на тестовом наборе данных с помощью среднеквадратичной ошибки (`MSE`)." + ] + }, + { + "cell_type": "markdown", + "id": "c6d4294c-d241-46e3-8391-87d321752ff9", + "metadata": {}, + "source": [ + "#### XGBoost\n", + "\n", + "Библиотека XGBoost была разработана и представлена в 2014 году Даниэлем Ченом (Daniel Chen) - исследователем в области машинного обучения и анализа данных. Он разработал XGBoost в рамках своей докторской диссертации на университете Вашингтона (University of Washington), и с тех пор библиотека стала одним из наиболее популярных инструментов машинного обучения, широко применяемых в индустрии и академическом сообществе. В настоящее время XGBoost поддерживается и развивается открытым сообществом разработчиков." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9fbb2cb4-79b8-442b-a48c-6981567bd05a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# !pip install xgboost" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "de909c76-3e75-4502-99ae-c35854cad3b3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import xgboost as xgb\n", + "from sklearn.datasets import make_regression\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "# Создание синтетических данных с категориальными признаками\n", + "X, y = make_regression(n_samples=1000, n_features=5, n_informative=3, random_state=42)\n", + "X = np.round(X) # Округление признаков до целых чисел\n", + "X = X.astype(int) # Приведение типа данных к целочисленному\n", + "\n", + "# Разделение данных на обучающую и тестовую выборки\n", + "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", + "\n", + "# Создание объекта DMatrix для обучающей и тестовой выборок\n", + "dtrain = xgb.DMatrix(X_train, label=y_train)\n", + "dtest = xgb.DMatrix(X_test, label=y_test)\n", + "\n", + "# Определение параметров модели\n", + "params = {\n", + " 'booster': 'gbtree',\n", + " 'objective': 'reg:squarederror',\n", + " 'eval_metric': 'rmse',\n", + " 'max_depth': 3,\n", + " 'eta': 0.1,\n", + " 'subsample': 0.8,\n", + " 'colsample_bytree': 0.8,\n", + " 'alpha': 0.1,\n", + " 'lambda': 0.1,\n", + " 'min_child_weight': 1,\n", + " 'seed': 42\n", + "}\n", + "\n", + "# Обучение модели XGBoost\n", + "num_rounds = 100\n", + "model = xgb.train(params, dtrain, num_rounds)\n", + "\n", + "# Прогнозирование на тестовой выборке\n", + "y_pred = model.predict(dtest)\n", + "\n", + "# Оценка качества модели\n", + "rmse = np.sqrt(np.mean((y_pred - y_test) ** 2))\n", + "print(f'RMSE на тестовой выборке: {rmse:.4f}')\n" + ] + }, + { + "cell_type": "markdown", + "id": "0f713d2b-391e-42b3-a39b-2d6ba9d5a66b", + "metadata": {}, + "source": [ + "В данном примере мы создаем синтетические данные с категориальными признаками, разделяем их на обучающую и тестовую выборки, создаем объекты DMatrix для этих выборок, определяем параметры модели XGBoost, обучаем модель и оцениваем ее качество на тестовой выборке с помощью метрики RMSE (корень из среднеквадратической ошибки)." + ] + }, + { + "cell_type": "markdown", + "id": "f1f22246-ab30-4417-919a-06f7c01ff754", + "metadata": {}, + "source": [ + "### Как подобрать наилучшие гиперпараметры для модели" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2bc29d71-8ce6-4f21-98c2-e1ce75da126b", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from sklearn.datasets import make_regression\n", + "from sklearn.model_selection import train_test_split, GridSearchCV\n", + "from catboost import CatBoostRegressor\n", + "\n", + "# Генерация данных\n", + "X, y = make_regression(n_samples=1000, n_features=10, noise=0.1, random_state=42)\n", + "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", + "\n", + "# Создание модели CatBoostRegressor\n", + "model = CatBoostRegressor()\n", + "\n", + "# Определение гиперпараметров и их значений для подбора\n", + "param_grid = {\n", + " 'learning_rate': [0.01, 0.1, 0.2],\n", + " 'depth': [4, 6, 8],\n", + " 'iterations': [100, 200, 300]\n", + "}\n", + "\n", + "# Подбор гиперпараметров с использованием GridSearchCV\n", + "grid_search = GridSearchCV(model, param_grid, cv=3)\n", + "grid_search.fit(X_train, y_train)\n", + "\n", + "# Вывод наилучших параметров и значения метрик\n", + "print(\"Наилучшие параметры: \", grid_search.best_params_)\n", + "print(\"Наилучшее значение RMSE на тестовом наборе: \", np.sqrt(-grid_search.score(X_test, y_test)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2cdd7b0b-c60e-4086-9728-af6439587676", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "a6a79e09-5af5-40e9-afb0-3596ea6e1fe0", + "metadata": {}, + "source": [ + "## Лаб 4\n", + "\n", + "Узнать какой бустинг и с какими гиперпараметрами лучше работает на вашем наборе данных.\n", + "\n", + "Обучить простую модель и бустинг, сравнить модели по какой-нибудь метрике." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ed0f5b5a-ad97-4681-8459-d03df4f4820c", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}