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3521972c8d
| Author | SHA1 | Date |
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 Ivan I. Ovchinnikov
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3521972c8d | |
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Ivan I. Ovchinnikov
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5cf682954c | |
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Ivan I. Ovchinnikov
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4749a6beca | |
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Ivan I. Ovchinnikov
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68f426bd51 |
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@ -919,5 +919,78 @@ decision_function_shape='ovr', break_ties=False, random_state=None)
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\subsection{}
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\subsection{}
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\newpage
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\appendix
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\setcounter{secnumdepth}{0}
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\section*{Приложения}
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\addcontentsline{toc}{section}{Приложения}
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\renewcommand{\thesubsection}{\Asbuk{subsection}}
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\subsection{Задачи с РК}
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ловушка, 3 неразличимых выхода, 1вых 3ч 2вых 2ч ведёт обратно, 3 вых 1ч ведётобратно
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шанс с первого раза Мо1-1/3
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\begin{equation*}
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\begin{gathered}
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M = 1/3*3+1/3(1+M)+1/3(2+M)\\
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M-1/3M-1/3M=1+1/3+2/3\\
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1/3M = 2\\
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M=6
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\end{gathered}
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\end{equation*}
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$x \in [0,1]$, плотность распределения $f(x) = 1/2e^{-|x|}$, найти мат. ожидание и дисперсию
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ChatGPT says:
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Математическое ожидание:
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$$
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\mathbb{E}(X) = \int_{-\infty}^{\infty}xf(x)dx =
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\int_{-1}^{0}\frac{x}{2}e^{x}dx + \int_{0}^{1}\frac{x}{2}e^{-x}dx
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$$
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Интегрируем первое слагаемое по частям:
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$$
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\int_{-1}^{0}\frac{x}{2}e^{x}dx =
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\left[\frac{x}{2}e^{x}\right]_{-1}^{0} -
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\int_{-1}^{0}\frac{1}{2}e^{x}dx = \frac{1}{2} - \frac{1}{2e}
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$$
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Интегрируем второе слагаемое:
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$$
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\int_{0}^{1}\frac{x}{2}e^{-x}dx =
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-\left[\frac{x}{2}e^{-x}\right]_{0}^{1} +
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\int_{0}^{1}\frac{1}{2}e^{-x}dx = \frac{1}{2} - \frac{1}{2e}
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$$
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Суммируем:
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$$
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\mathbb{E}(X) = \frac{1}{2} - \frac{1}{2e} + \frac{1}{2} -
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\frac{1}{2e} = 1 - \frac{1}{e} \approx 0.632
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$$
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Дисперсия:
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$$
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\mathbb{E}(X^2) = \int_{-\infty}^{\infty}x^2f(x)dx =
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\int_{-1}^{0}\frac{x^2}{2}e^{x}dx +
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\int_{0}^{1}\frac{x^2}{2}e^{-x}dx
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$$
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Интегрируем по частям:
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$$
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\int_{-1}^{0}\frac{x^2}{2}e^{x}dx =
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\left[\frac{x^2}{2}e^{x}\right]_{-1}^{0} - \int_{-1}^{0}xe^{x}dx =
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-\frac{1}{2} - \frac{1}{e}
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$$
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$$
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\int_{0}^{1}\frac{x^2}{2}e^{-x}dx =
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-\left[\frac{x^2}{2}e^{-x}\right]_{0}^{1} + \int_{0}^{1}xe^{-x}dx
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= \frac{1}{2} - \frac{3}{2e}
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$$
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Суммируем:
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$$
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\mathbb{E}(X^2) = -\frac{1}{2} - \frac{1}{e} + \frac{1}{2} -
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\frac{3}{2e} = 1 - \frac{5}{2e} \approx 0.472
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$$
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Используем формулу для дисперсии:
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$$
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\text{Var}(X) = \mathbb{E}(X^2) - (\mathbb{E}(X))^2 \approx 0.472
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- (0.632)^2 \approx 0.109
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$$
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\end{document}
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\end{document}
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@ -585,13 +585,16 @@ $N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (пе
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\item параллельные
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\item параллельные
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\end{itemize}
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\end{itemize}
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Основной элемент -- это компаратор.
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Основной элемент -- это компаратор. Усилитель, триггер шмидта, иногда стробирование и классический цифровой триггер.
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\begin{figure}[H]
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\begin{figure}[H]
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\centering
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\centering
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\fontsize{12}{1}\selectfont
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-compare.svg}
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\includesvg[scale=1.01]{pics/04-cedd-00-compare.svg}
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\end{figure}
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\end{figure}
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Это однобитный квантователь, перед ним стоит УВХ.
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Это однобитный квантователь, перед ним стоит УВХ.
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\paragraph{АЦП параллельного преобразования}
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Flash-ADC
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\begin{figure}[H]
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\begin{figure}[H]
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\centering
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\centering
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\fontsize{12}{1}\selectfont
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\fontsize{12}{1}\selectfont
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@ -599,9 +602,260 @@ $N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (пе
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\end{figure}
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\end{figure}
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получаем 255 уровней квантования. на выходе 255-разрядный (позиционный, температурный) код.
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получаем 255 уровней квантования. на выходе 255-разрядный (позиционный, температурный) код.
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Приоритетный шифратор формирует N-разрядный код. Слишком много компараторов (дорого, размер, потребление), зависит от точности резисторов (интегральная нелинейность), разброс задержек компараторов (решается цифровыми средствами), паразитные ёмкости.
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Приоритетный шифратор формирует N-разрядный код. Часто накручивают логику дальше, например, коды Грея, чтобы избежать эффекта пузырька (паразитная единицка среди ноликов).
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Слишком много компараторов (дорого, размер, потребление), зависит от точности резисторов (интегральная нелинейность), разброс задержек компараторов (решается цифровыми средствами), паразитные ёмкости.
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УВХ часто помогает стробировать сигнал и избавиться от части метастабильностей компараторов.
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\paragraph{Последовательного приближения}
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ЦАП делать проще. проблем с реализацией логики никогда не было, регистр последовательного приближения даже выпускался отдельной схемой.
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с ЦАП даём опорное на компаратор, 10000000 это половина шкалы, сравниваем, далее компаратор говорит больше или меньше, 8 итераций, и регистр выдаёт сигнал данные готовы.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-1-seq-zoom.svg}
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\end{figure}
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Ушли от резисторов, пришли к конденсаторной логике (C-DAC). Компаратор линейный, нелинейности будут формироваться ЦАПоп, разрядность 10-12 бит, скорость до 1мгц. Самое важное, что мы занимаем место.
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Основные используемые элементы
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\begin{itemize}
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\item транзисторы с тремя схемами включения
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\item усилитель
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\item дифференциальный усилитель
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\item токовое зеркало
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\item двухтактный выходной каскад
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\item ячейка гильберта (умножитель)
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\end{itemize}
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-2-diff-us.svg}
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\caption{Усилитель и дифференциальный усилитель}
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\end{figure}
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Стоимость микросхемы определяется размером кремниевого камня (поэтому борятся за минимизацию).
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\paragraph{АЦП с интерполяцией}
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Interpolation ADC Один из самых актуальных классов АЦП на сегодня
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-3-common.svg}
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\end{figure}
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Колическтво защёлок в компараторах не изменить, а усилители возможно
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-4-interpol.svg}
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\end{figure}
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К=2 фактор интерполяции, нужные уровни интерполируем на резисторах, больше 4 не делают потому что резистор не идеальный элемент и формирует нелинейности, дргуих особых минусов нет.
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\paragraph{Folding ADC}
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АЦП со сворачиванием
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-5-folding.svg}
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\end{figure}
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старшие преобразуются напрямую 3 или 4 бита. младшие передаются на folding усилитель.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-6-folding-idea.svg}
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\end{figure}
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то есть входной сигнал сворачивается в один и тот же диапазон, и нам нужно много меньше компараторов, выигрыш в 8 раз. Реализовано на дифференциальных усилителях и верной коммутации их нагрузок. За счёт небольшой аналоговой обработки компараторы переиспользуются.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-7-cross.svg}
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\end{figure}
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прямые подключаются только по нечётным, накрест - чётные. получается точный сигнал мы получим только с первого резистора, иногда только его и берут, это zero-crossing.
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\paragraph{folding and interpolating ADC}
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-8-MagAmp.svg}
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\end{figure}
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проблемы с линейностью остаются. фактически все высокоскоростные АЦП сделаны так, потому что это на основе параллельного преобразования.
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\paragraph{Time interleaving}
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АЦП со временным перемежением.
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Параллельно включаем несколько АЦП и на выходе мультплексируем.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-9-multiplexing.svg}
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\end{figure}
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В лоб засинхронизировать не получится, если работать только по фронтам то надо в 4 раза быстрее, нужно фазировать.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-10-timing.svg}
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\end{figure}
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Ошибки у АЦП с перемежением
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\begin{itemize}
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\item смещения \includesvg[scale=1.01]{pics/04-cedd-00-11-diffzero.svg} разные нули
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\item усиления \includesvg[scale=1.01]{pics/04-cedd-00-12-diffamp.svg}
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\item временные \includesvg[scale=1.01]{pics/04-cedd-00-13-jitter.svg} джиттер, приведёт к амплитудной ошибке
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\end{itemize}
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\subsection{Конвейерные АЦП}
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Pipeline ADC
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-14-seq.svg}
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\end{figure}
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Десятки (до сотен МГц) 1024 компаратора против 48 компараторов. На порядок снижается потребление. Набегают погрешности АЦП и ЦАП. Для некоторых задач может быть критичным, что существует конвейерная задержка.
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\subsection{Сигма-дельта}
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$\Sigma-\Delta ADC$
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-15-sigdel.svg}
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\end{figure}
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Сумматор или вычитатель можно реализовать на вычитающем опреационном усилителе, интегратор это тоже ОУ, компаратор
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-16-dac.svg}
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\end{figure}
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$$SNR = 6,02N+1,76dB = 7,78$$
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для 24-рязрядного нужно 144дБ.
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\begin{enumerate}
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\item передискретизация (частоту берём в К раз больше) для Д-С-АЦП может быть в сотни или тысячи раз.
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\item интегратор постоянно стремится минимизировать ошибку квантования (noise shaping)
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\end{enumerate}
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принципиально отсутствует нелинейность.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-17-second.svg}
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\end{figure}
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ДСМ второго порядка
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За счёт обратной связи происходит перенос спектра шума.
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\section{Методы построения ЦАП}
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У источника напряжения (ЭДС) внутреннее сопротивление стремится к нулю, а у источника тока стремится к бесконечности.
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Идеальная индуктивность сопротивление стремится к нулю
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Идеальный конденсатор, параллельно подключенное сопротивление стремится к бесконечности
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Максимально быстродействующий -- параллельный.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-18-parallel.svg}
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\end{figure}
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основная задача задать пороги источников тока, они формируют дифференциальную нелинейность
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\subsection{Сигма-Дельта ЦАП}
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\begin{figure}[H]
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\centering
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||||||
|
\fontsize{12}{1}\selectfont
|
||||||
|
\includesvg[scale=1.01]{pics/04-cedd-00-18-ds-dac.svg}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\subsection{ЦАП поразрядного уравновешивания}
|
||||||
|
на резистивной матрице.
|
||||||
|
|
||||||
|
(1) используют до 16 бит
|
||||||
|
|
||||||
|
делают как с токовым выходом так и с выходным напряжением, обычно интегрируют в схему и дают выбор использования. Сопротивление матрицы постоянно и равно R. Рассогласование R дифференциальная нелинейность, интегральная нелинейность если все Р ушли в одну сторону.
|
||||||
|
|
||||||
|
$$I = \frac{U_o}{R}$$
|
||||||
|
|
||||||
|
схема может работать как умнажающий ЦАП (вместо источника опорного напряжения включают Iвход). Выполняются по биполярной и КМОП технологиям.
|
||||||
|
|
||||||
|
$$I = I_i * D$$
|
||||||
|
|
||||||
|
(2)
|
||||||
|
Реализация цифрового потенциометра, подстройки, управление амплитудами, управляемое кодом цифровое сопротивление, и так далее.
|
||||||
|
|
||||||
|
\subsection{ЦАП на переключаемых конденсаторах}
|
||||||
|
ЦАП на коммутируемых конденсаторах (C-DAC). Binary weight charge redistribution.
|
||||||
|
(3)
|
||||||
|
|
||||||
|
\begin{equation*}
|
||||||
|
\begin{gathered}
|
||||||
|
C_k = 2^kC_0\\
|
||||||
|
g = V_o\sum_{k-0}^{n-1}c_kd_k = V_oc_0\sum_{k-0}^{n-1}2^kd_k=V_oc_0D\\
|
||||||
|
U_{out} = -(g/c) = -U_o\frac{c_0}{c}D
|
||||||
|
\end{gathered}
|
||||||
|
\end{equation*}
|
||||||
|
|
||||||
|
Соответственно, ёмкости растут в два раза. Часто особенно на старых платах ёмкость подложки бывает сопоставима с общими ёмкостями. Источники опорного напряжения могут быть интегрированы. Точно сделать ёмкость проще. DNL - разница между соседними ёмкостями, INL например ёмкость подложки.
|
||||||
|
|
||||||
|
\section{Синтез сигналов}
|
||||||
|
Схемы формирования тактовых сигналов.
|
||||||
|
|
||||||
|
Кварцевый генератор - высокодобротный колебательный контур.
|
||||||
|
\subsection{Схемы прямого синтеза}
|
||||||
|
|
||||||
|
(4)
|
||||||
|
|
||||||
|
если нужно несколько частот -- можно сделать два генератора и их как-то коммутировать.
|
||||||
|
5, 6
|
||||||
|
|
||||||
|
стабильность $10^{-5} - 10^{-7}$ ($10^{-8} - 10^{-9}$ термостабильные)
|
||||||
|
1 контур 1-20МГц
|
||||||
|
до 100мгц
|
||||||
|
|
||||||
|
генератор -- колебательный контур
|
||||||
|
(7)
|
||||||
|
очень нестабильные $10^{-3} - 10^{-4}$. чтобы управлять таким генератором электронно нужен варикап
|
||||||
|
(8)
|
||||||
|
чтобы сделать меандр нужно в конце поставить компаратор. Самый стабильный генератор -- генерирует синус.
|
||||||
|
|
||||||
|
\subsection{Схемы косвенного синтеза}
|
||||||
|
на основе ФАПЧ (PLL -- phase lock loop) система с обратной связью (главный недостаток)
|
||||||
|
(9)
|
||||||
|
|
||||||
|
\begin{equation*}
|
||||||
|
\begin{gathered}
|
||||||
|
f_o = f_i*M\\
|
||||||
|
\Delta f = \frac{f_i}{N}
|
||||||
|
\end{gathered}
|
||||||
|
\end{equation*}
|
||||||
|
|
||||||
|
чтобы делать делитель на любые частоты нужен счётчик с предустановкой.
|
||||||
|
|
||||||
|
ФД формирует выходное напряжение по разности фаз. если фаза = 0 выход = 0, если максимум (360) то максимальное напряжение. ФД это умножитель. схема гильберта.
|
||||||
|
$$\cos\omega_1t\cdot\cos\omega_2t = \cos(\omega_1+\omega_2)t + \cos(\omega_1-\omega_2)t $$
|
||||||
|
для цифровых схем нужно сигналы проксорить, далее ФНЧ как раз сравнивает сигнал. в низкоскоростных -- рц цепочка, в высокоскоростных используют пропорционально интегрирующий фильтр (10).
|
||||||
|
|
||||||
|
Часто делитель не может работать на нужных частотах поэтому используют специальную микросхему prescaler (делитель, обычно на 2, 5, 10).
|
||||||
|
|
||||||
|
можно использовать фапч для демодуляции частотно манипулированного сигнала (не нужен делитель). снимаем сигнал с напряжения управления.
|
||||||
|
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|
||||||
|
осциллограф с режимом стробоскопа. логический анализатор с функцией вычисления и последовательными протоколами
|
||||||
|
|
||||||
|
частотно-компенсируемый делитель
|
||||||
|
|
|
||||||
|
|
@ -507,7 +507,19 @@ compose написан на python, конфигурация в yaml-файла
|
||||||
|
|
||||||
докер-композ ямл - описывает процесс загрузки и настройки контейнеров.
|
докер-композ ямл - описывает процесс загрузки и настройки контейнеров.
|
||||||
|
|
||||||
Основные команды
|
\subsection{Основные команды}
|
||||||
|
К основным командам docker можно отнести:
|
||||||
|
\begin{itemize}
|
||||||
|
\item docker pull-скачивает образ
|
||||||
|
\item docker run - запускает контейнер на основе образа
|
||||||
|
\item docker ps - вызывает список запущенных контейнеров
|
||||||
|
\item docker exec - позволяет выполнять команды в контейнере
|
||||||
|
\item docker stop - останавливает контейнер
|
||||||
|
\item docker rm-удаляет контейнер
|
||||||
|
\item docker rmi - удаляет образ
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
docker-compose
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
\item build -- сборка
|
\item build -- сборка
|
||||||
\item up -- запуск
|
\item up -- запуск
|
||||||
|
|
@ -522,19 +534,753 @@ compose написан на python, конфигурация в yaml-файла
|
||||||
Оркестраторы управляют ЖЦ контейнеров микросервисных приложений. Задачи оркестратора:
|
Оркестраторы управляют ЖЦ контейнеров микросервисных приложений. Задачи оркестратора:
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
\item подготовка инфраструктуры и развёртывание -- установка приложения и его зависимостей на сервер, включая подготовку этого сервера -- установку библиотек, служб, и так далее.
|
\item подготовка инфраструктуры и развёртывание -- установка приложения и его зависимостей на сервер, включая подготовку этого сервера -- установку библиотек, служб, и так далее.
|
||||||
\item Разделение ресурсов -- Для развёртывания в кластере требуется...
|
\item Разделение ресурсов -- Для развертывания приложения кластере разработки требуется B выделить вычислительные ресурсы сервера для различных процессов: это объемы памяти (RAM) центрального процессора (CPU). И Устанавливаются запрашиваемые и предельные параметры, правила при достижении контейнерами ресурсных лимитов, различные ограничения. Это важно для поддержания приложения в рабочем состоянии и сведения затрат к минимуму.
|
||||||
\item Масштабирование контейнеров на основе рабочих нагрузок -- простой излишних ресурсов приводит к издержкам, а недостаток -- к нестабильно йработе приложения. Регулировать объёмы используемых ресурсов позволяет масштабирование, основанное на анализе нагрузок. Может быть ручным или автоматизированным.
|
\item Масштабирование контейнеров на основе рабочих нагрузок -- простой излишних ресурсов приводит к издержкам, а недостаток -- к нестабильно йработе приложения. Регулировать объёмы используемых ресурсов позволяет масштабирование, основанное на анализе нагрузок. Может быть ручным или автоматизированным.
|
||||||
\item Балансировка нагрузок -- автоматический анализ и распределение рабочих нагрузок на сервер целиком и контейнеры в частности. Балансировка оптимизирует использование ресурсов, увеличивает пропускную способность каналов связи,...
|
\item Балансировка нагрузок -- Автоматический анализ и распределение рабочих нагрузок на сервер целиком и контейнеры в частности. Балансировка оптимизирует использование ресурсов, увеличивает пропускную способность каналов связи, минимизирует Время отклика и помогает избежать перегрузки отдельных ресурсов.
|
||||||
\item Маршрутизация трафика
|
\item Маршрутизация трафика -- Чтобы приложение было доступно из интернета, нужно настроить правильное распределение трафика из внешней сети по контейнерам и нужным сервисам.
|
||||||
\item Мониторинг состояния контейнеров -- позволяет видеть какие контейнеры и образы запущены
|
\item Мониторинг состояния контейнеров -- Эта функция позволяет видеть, какие контейнеры и их образы запущены и где, какие команды используются в контейнерах, какие контейнеры потребляют слишком много ресурсов и почему.
|
||||||
\item Обеспечение безопасного взаимодействия между контейнерами -- на основе непрерывной оценки кластеров, узлов и реестра контейнеров...
|
\item Обеспечение безопасного взаимодействия между контейнерами -- На основе непрерывной оценки кластеров, узлов и реестра контейнеров предоставляются данные о неверных конфигурациях и других уязвимостях, которые могут представлять угрозу, а также рекомендации по устранению Выявленных угроз.
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
|
|
||||||
\subsection{Kubernetes}
|
\subsection{Системы оркестрации контейнеров}
|
||||||
Считается отраслевым стандартом
|
\subsubsection{Kubernetes (k8s)}
|
||||||
|
|
||||||
|
Эта платформа открытым исходным кодом считается отраслевым C стандартом. Позволяет автоматизировать масштабирование, развертывание с помощью шаблонов управление рабочей нагрузкой сервисами и контейнеров. Поддерживает ОС: Windows, macOS, Linux.
|
||||||
|
|
||||||
|
Предлагает:
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
\item мониторинг сервисов
|
\item мониторинг сервисов и распределение нагрузки,
|
||||||
\item
|
\item автомонтирование гибкой системы хранения,
|
||||||
|
\item автоматизированные откаты и развертывания,
|
||||||
|
\item автораспределение нагрузки,
|
||||||
|
\item горизонтальное автомасштабирование,
|
||||||
|
\item автоперезапуск, замена и завершение работы отказавших контейнеров,
|
||||||
|
\item управление конфигурацией и конфиденциальной информацией, самовосстановление.
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
|
|
||||||
|
\subsection{OpenShift Container Platform}
|
||||||
|
Платформа в формате PaaS для разработки, развертывания и управления не только контейнерными, но классическими приложениями И И их компонентами в режиме самообслуживания. Позволяет автоматизировать их в физических, виртуальных и общедоступных, частных и гибридных облачных средах. Поддержка ОС: Linux.
|
||||||
|
|
||||||
|
Предлагает:
|
||||||
|
\begin{itemize}
|
||||||
|
\item встроенные средства кластеризации и оркестрации;
|
||||||
|
\item автомасштабирование;
|
||||||
|
\item балансировку нагрузки;
|
||||||
|
\item совместимость созданных на платформе приложений с любыми другими платформами, поддерживающими контейнеры Docker.
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\subsection{Nomad}
|
||||||
|
Легкий в поддержке, гибкий оркестратор для развертывания и управления контейнерными и классическими приложениями в физической или облачной среде. Поддерживает ОС: Linux, Windows, macOS. B основном Nomad управляет развертыванием и перезапускает контейнеры при обнаружении ошибок. Этого часто оказывается достаточно для небольших проектов.
|
||||||
|
|
||||||
|
Предлагает:
|
||||||
|
\begin{itemize}
|
||||||
|
\item простое управление,
|
||||||
|
\item хорошую экосистему встроенную интеграцию с другими продуктами (например, Terraform),
|
||||||
|
\item автоматизацию переноса приложения из монолитной в микросервисную архитектуру,
|
||||||
|
\item масштабируемость,
|
||||||
|
\item возможность развернуть все кластерное приложение с несколькими контейнерами с помощью плагина из каталога одним щелчком мыши.
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\subsection{Docker Swarm}
|
||||||
|
Это «родная», базовая система кластеризации и оркестрации контейнеров Docker. **Docker Swarm** - базовая система кластеризации и оркестрации контейнеров Docker. Взаимодействие с кластером происходит через команды Docker, a управление действиями - через менеджер Swarm. Поддержка ОС: \textbf{Windows, macOS, Linux}.
|
||||||
|
|
||||||
|
Кластер \textbf{Swarm (Docker Swarm Cluster)} состоит из узлов (нод), которые делят на два типа:
|
||||||
|
\begin{itemize}
|
||||||
|
\item управляющая нода (\textbf{manager}). Это нода, которая принимает запросы и распределяет задачи между всеми нодами в кластере.
|
||||||
|
\item рабочие (\textbf{worker}) ноды (узлы)
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\textbf{Docker Swarm} - \textbf{встроенное} в Docker решение по контейнерной оркестрации. Более легкое в освоении, чем Kubernetes.
|
||||||
|
Swarm - стандартный оркестратор для Docker контейнеров, доступный вам, если у вас установлен сам Docker.
|
||||||
|
|
||||||
|
Что потребуется для освоения:
|
||||||
|
\begin{itemize}
|
||||||
|
\item Иметь опыт работы с Docker и Docker Compose.
|
||||||
|
\item Настроенный Docker registry.
|
||||||
|
\item Swarm не очень любит работать с локальными образами.
|
||||||
|
\item Несколько виртуальных машин для создания кластера, хотя по факту кластер может состоять из одной ВМ, но так будет нагляднее.
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\subsection{Устройство}
|
||||||
|
Основу кластера Docker Swarm представляют управляющие (manager) и рабочие (worker) узлы
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=12cm]{04-telematics-ustr.png}
|
||||||
|
\end{figure}
|
||||||
|
Docker Swarm состоит из менеджеров и воркеров. Менеджеры определяют, на каких воркерах и как будут работать контейнеры.
|
||||||
|
|
||||||
|
\subsection{Термины}
|
||||||
|
Для того чтобы пользоваться Docker Swarm надо запомнить несколько типов сущностей:
|
||||||
|
\textbf{Node} - это BM, на которых установлен Docker. Есть manager и worker ноды.
|
||||||
|
\textbf{Manager нода} управляет worker нодами. Она отвечает за workers a также за их создание/обновление/удаление сервисов на workers, масштабирование и поддержку в требуемом состоянии. Worker ноды используются только для выполнения поставленных задач и не могут управлять кластером.
|
||||||
|
\textbf{Stack} - это набор сервисов, которые логически связаны между собой. По сути это набор сервисов, которые мы описываем в обычном compose файле. Части Stack (services) могут располагаться как на одной ноде, так и на разных.
|
||||||
|
\textbf{Service} это как раз то, из чего состоит Stack. Service является описанием - того, какие контейнеры будут создаваться. Как Docker-compose.yaml. Кроме стандартных полей Docker B режиме Swarm поддерживает ряд дополнительных, большинство из которых находятся внутри секции deploy.
|
||||||
|
\textbf{Task} - это непосредственно созданный контейнер, который Docker создал на основе той информации, которую мы указали при описании Service. Swarm будет следить за состоянием контейнера и при необходимости его перезапускать или перемещать на другую ноду.
|
||||||
|
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=12cm]{04-telematics-swarm.png}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\subsection{Создание кластера}
|
||||||
|
Для того чтобы кластер работал корректно, необходимо:
|
||||||
|
\begin{itemize}
|
||||||
|
\item IP-адрес управляющей ноды должен быть назначен сетевому интерфейсу, доступному операционной системе хоста. Все ноды в Swarm должны подключаться к менеджеру по IP-адресу.
|
||||||
|
\item Открытые протоколы и порты между хостами
|
||||||
|
\item Должны быть доступны следующие порты. В некоторых системах они открыты по умолчанию.
|
||||||
|
\begin{itemize}
|
||||||
|
\item \textbf{ТСР-порт 2377} для управления кластером.
|
||||||
|
\item \textbf{Порт ТСР и UDP 7946} для связи между узлами.
|
||||||
|
\item \textbf{UDP-порт 4789} для оверлейного сетевого трафика.
|
||||||
|
\end{itemize}
|
||||||
|
\end{itemize}
|
||||||
|
\textbf{docker swarm init} необходимо выполнить на всех worker node, чтобы присоединить их в только что созданный кластер. Если все прошло успешно:
|
||||||
|
|
||||||
|
\textbf{docker node ls} Ha manager Hоде в консоли, вы увидите что-то подобное:
|
||||||
|
|
||||||
|
Чтобы убрать ноду из кластера, необходимо зайти на ВМ, которая является ею, и выполнить команду: \textbf{docker swarm leave}
|
||||||
|
|
||||||
|
Если затем зайти на manager ноду и выполнить docker node ls, вы заметите, что статус у нее поменялся с Ready на Down (это может занять некоторое время). Swarm больше не будет использовать данную ноду для размещения контейнеров.
|
||||||
|
|
||||||
|
Для того чтобы окончательно удалить ноду, надо выполнить (на manager node): \textbf{docker node rm stage}
|
||||||
|
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=12cm]{04-telematics-stack.png}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
В начале необходимо достать image из registry и только затем развернуть в наш кластер:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
docker pull docker-registry.ru:5000/ptm:stage;
|
||||||
|
docker stack deploy --with-registry-auth \
|
||||||
|
-c ./docker-compose.stage.yaml stage;*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Команды выполняются на manager node. Флаг --with-registry-auth позволяет передать авторизационные данные на worker ноды, для того чтобы использовался один и тот же образ из регистра. Stage это имя нашего стэка. Посмотреть список стэков можно с помощью:
|
||||||
|
|
||||||
|
docker stack ls Список сервисов внутри стэка:
|
||||||
|
|
||||||
|
docker stack services stage
|
||||||
|
|
||||||
|
Удалить стэк можно следующим образом: docker stack rm stage
|
||||||
|
|
||||||
|
Можно запускать и отдельно взятые сервисы, например:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
docker service create --name nginx --replicas 3 nginx:alpine;
|
||||||
|
docker service ps nginx;
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
В данном примере мы запустили сервис nginx в виде 3 экземпляров, которые Swarm раскидал по 3 нодам.
|
||||||
|
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=12cm]{04-telematics-ps.png}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
Удалить сервис можно следующим образом: docker service rm nginx
|
||||||
|
|
||||||
|
Для того чтобы увидеть более подробную информацию по сервису в виде JSON: \verb|docker service inspect stage_back|. Тут также можно увидеть, какие порты слушает сервис, в каких сетях участвует, какой у него статус и т.д.
|
||||||
|
|
||||||
|
\textbf{Label Swarm} по умолчанию развертывает сервисы на любой доступной ноде/нодах, но как правило нам необходимо развертывать их на конкретной ноде или на специфической группе. Для этого нужны labels. Например, у нас есть stage и prod окружение. Stage используется для внутренней демонстрации продукта, а prod группой разработки.
|
||||||
|
|
||||||
|
Для каждого из окружений у есть compose файл: docker-compose.stage.yaml и docker-compose.prod.yaml. По умолчанию Swarm будет раскидывать service произвольно по нодам. А нам нужно, чтобы сервис для stage запускался только на stage BM и аналогично для prod.
|
||||||
|
|
||||||
|
В начале, добавим еще одну ноду в кластер, в качестве worker
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
# заходим по ssh на еще одну виртуальную
|
||||||
|
# машину и добавляем ее в кластер
|
||||||
|
docker swarm join --token \
|
||||||
|
SWMTKN-1-54k2k418tw2jejuwm3inq6crp4ow6xogswihcc5azg7oc
|
||||||
|
# выполняем команду на manager ноде:
|
||||||
|
docker node ls
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Затем необходимо разметить ноды:
|
||||||
|
\begin{verbatim}
|
||||||
|
docker node update --label-add TAG=stage stage
|
||||||
|
docker node update --label-add TAG=prod prod-1
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Используя hostname виртуальных машин, мы ставим label. Для того чтобы убедиться, что все прошло успешно, необходимо выполнить команду: docker node inspect stage. Ищем раздел Spec. Labels, где мы должны увидеть label, который добавили:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
"Spec": {
|
||||||
|
"Labels": {
|
||||||
|
"TAG": "stage"
|
||||||
|
},
|
||||||
|
"Role": "worker",
|
||||||
|
"Availability": "active"
|
||||||
|
}
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
После чего в compose файл необходимо добавить директиву placement, где прописывается условие, которое указывает, на каких нодах разворачивать данный сервис: Для docker-compose.prod.yaml будет аналогично, но с тэгом prod (однако для внешнего мира надо использовать другой порт, например 4004). После развертывания данных Stacks сервисы разворачиваются только на нодах с определенным тэгом.
|
||||||
|
|
||||||
|
docker-compose.stage.yaml
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
version: "3.9"
|
||||||
|
services:
|
||||||
|
back:
|
||||||
|
image: docker-registry.ru:5000/pta:stage
|
||||||
|
ports:
|
||||||
|
-"4003:4083"
|
||||||
|
environment:
|
||||||
|
12: "Europe/Moscow"
|
||||||
|
extra_hosts:
|
||||||
|
- host docker. internal:host-gateway command: make server_start volumes:
|
||||||
|
- /p/ptm/config/config-yaml:/p/ptm/config/config.yaml
|
||||||
|
- /p/ptm/stat/web:/p/ptm/stat/web.
|
||||||
|
#swarm deploy:
|
||||||
|
placement:
|
||||||
|
constraints:
|
||||||
|
- "node.labels. TAG==stage”
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
\subsection{Маршрутизация}
|
||||||
|
В данный момент у нас 3 ноды: manager нода, нода для stage версии приложения и еще одна для разработки.
|
||||||
|
|
||||||
|
docker node ls
|
||||||
|
|
||||||
|
Если развернуть наш стэк для docker-compose.prod.yaml на том же 4003 порту, что и для уже запущенного стэка docker-compose.stage.yaml, то получим ошибку, связанную с тем, что порт уже занят.
|
||||||
|
|
||||||
|
Почему это произошло? И более того, если мы зайдем на ВМ prod-1 и Сделаем curl 127.0.0.1:4003, то увидим, что наш сервис доступен, хотя на этой ноде мы еще не успели ничего развернуть?
|
||||||
|
|
||||||
|
Связано это с тем, что у Swarm имеется ingress сеть, которая используется для маршрутизации траффика между нодами. Если у сервиса есть публичный порт, то Swarm слушает его и в случае поступления запроса на него делает следующее: определяет есть ли контейнер на этой хост машине и если нет, то находит ноду, на которой запущен контейнер для данного сервиса, и перенаправляет запрос туда.
|
||||||
|
|
||||||
|
В данном примере используется внешний балансировщик, который балансирует запросы между тремя ВМ, а дальше Swarm перенаправляет запросы в соответствующие контейнеры.
|
||||||
|
|
||||||
|
?ФОТО
|
||||||
|
|
||||||
|
Поэтому для docker-compose.prod.yaml нужно использовать любой другой публичный порт, отличный от того, который указан в docker-compose.stage.yaml.
|
||||||
|
|
||||||
|
Отключить автоматическую маршрутизацию трафика можно с помощью mode: host при декларации ports:
|
||||||
|
|
||||||
|
В данном случае запрос, который придет на порт 4004, Swarm будет направлять только на контейнер текущей ноде никуда И больше.
|
||||||
|
|
||||||
|
Настройка mode (напрямую это не относится к маршрутизации). Она может принимать следующие значения: global или replicated (по умолчанию):
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*deploy:
|
||||||
|
mode: global
|
||||||
|
deploy:
|
||||||
|
mode: replicated
|
||||||
|
replicas: A*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Если global это означает, что данный сервис будет запущен ровно в одном экземпляре на всех возможных нодах. A replicated означает, что п-ое кол-во контейнеров для данного сервиса будет запущено на всех доступных нодах.
|
||||||
|
|
||||||
|
\textbf{Zero downtime deployment} Это возможность организовать «бесшовную» смену контейнеров во время развертывания. Это возможно и в Docker-compose, но надо держать дополнительную реплику контейнера (даже, если по нагрузке требуется всего одна) и на уровне балансировщика переключать трафик с одного контейнера на другой. C Docker Swarm это все не нужно, необходимо лишь немного скорректировать конфигурацию сервиса. Для начала нужно добавить директиву healthcheck:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*healthcheck:
|
||||||
|
test: curl -ss http://127.0.0.1:4004/ptm/api/healthcheck ||
|
||||||
|
echo 1
|
||||||
|
interval: 30s
|
||||||
|
timeout: 3s
|
||||||
|
retries: 12*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Она предназначена, чтобы Docker мог определить, корректно ли работает контейнер. test - результат исполнения этой команды Docker использует для определения корректно
|
||||||
|
ли работает контейнер.
|
||||||
|
*interval* - с какой частотой проверять состояние. В данном случае каждые 30 секунд.
|
||||||
|
*timeout* - таймаут для ожидания выполнения команды.
|
||||||
|
*retries* - количество попыток для проверки состояния сервера внутри контейнера.
|
||||||
|
|
||||||
|
После добавления директивы healthcheck в compose file мы увидим в Status информацию о состоянии контейнера:
|
||||||
|
**docker container Is**
|
||||||
|
|
||||||
|
После развертывания стэка контейнер сначала имеет статус **starting** (сервер внутри нашего контейнера запускается), а через некоторое время получит статус **healthy** (сервер запустился), в противном случае **unhealthy**.
|
||||||
|
**Docker** в режиме **Swarm** не просто отслеживает жизненное состояние контейнера, но и в случае перехода в состояние **unhealthy** попытается пересоздать контейнер.
|
||||||
|
|
||||||
|
**Настройки для обновления контейнера:**
|
||||||
|
**replicas** - количество контейнеров, которые необходимо запустить
|
||||||
|
для данного сервиса.
|
||||||
|
Директива \verb|update_config| описывает каким образом сервис должен обновляться:
|
||||||
|
**parallelism** количество контейнеров для одновременного - обновления. По умолчанию данный параметр имеет значение 1 - контейнеры будут обновляться по одному. 0 - обновить сразу все контейнеры. В большинстве случаев это число должно быть меньше, чем общее количество реплик сервиса.
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
deploy:
|
||||||
|
replicas: 1
|
||||||
|
update_config:
|
||||||
|
parallelism: 1
|
||||||
|
order: start-first
|
||||||
|
failure_action: rollback
|
||||||
|
delay: 10s
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
order - порядок обновления контейнеров. По умолчанию ptop-first, сначала текущий контейнер останавливается, а затем запускается новый. Для «бесшовного» обновления нужно использовать start- first. В этом случае вначале запускается новый контейнер, а затем выключается старый.
|
||||||
|
\verb|failure_action| - стратегия в случае сбоя. Вариантов несколько: continue, rollback, или pause (по умолчанию).
|
||||||
|
delay - задержка между обновлением группы контейнеров.
|
||||||
|
|
||||||
|
**Docker secrets**
|
||||||
|
Swarm предоставляет хранилище для приватных данных (secrets), которые необходимы контейнерам. Это используется для хранения логинов, паролей, ключей шифрования и токенов доступа от внешних систем, БД и т.д.
|
||||||
|
**Создадим yaml файл с «секретным» токеном:**
|
||||||
|
* example.yaml
|
||||||
|
\begin{verbatim}
|
||||||
|
token: sfsjksajflsf_secret*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
В данный момент у нас 3 ноды: manager нода, нода для stage версии приложения и еще одна для разработки.
|
||||||
|
**docker node 1s**
|
||||||
|
|
||||||
|
Если развернуть наш стэк для docker-compose.prod.yaml на том же 4003 порту, что и для уже запущенного стэка docker-compose.stage.yaml, то получим ошибку, связанную с тем, что порт уже занят.
|
||||||
|
|
||||||
|
Почему это произошло? И более того, если мы зайдем на ВМ prod-1 и Сделаем curl 127.0.0.1:4003, то увидим, что наш сервис доступен, хотя на этой ноде мы еще не успели ничего развернуть?
|
||||||
|
|
||||||
|
Связано это с тем, что у Swarm имеется ingress сеть, которая используется для маршрутизации траффика между нодами. Если у сервиса есть публичный порт, то Swarm слушает его и в случае поступления запроса на него делает следующее: определяет есть ли контейнер на этой хост машине и если нет, то находит ноду, на которой запущен контейнер для данного сервиса, и перенаправляет запрос туда.
|
||||||
|
|
||||||
|
В данном примере используется внешний балансировщик, который балансирует запросы между тремя ВМ, а дальше Swarm перенаправляет запросы в соответствующие контейнеры.
|
||||||
|
|
||||||
|
? ФОТО
|
||||||
|
|
||||||
|
Поэтому для docker-compose.prod.yaml нужно использовать любой другой публичный порт, отличный от того, который указан в docker-compose.stage.yaml.
|
||||||
|
Отключить
|
||||||
|
автоматическую маршрутизацию трафика можно с помощью mode: host при декларации ports:
|
||||||
|
В данном случае запрос, который придет на порт 4004, Swarm будет направлять только на контейнер текущей ноде никуда И больше.
|
||||||
|
|
||||||
|
Настройка **mode** (напрямую это не относится к маршрутизации). Она может принимать следующие значения: global или replicated (по умолчанию):
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*deploy:
|
||||||
|
mode: global
|
||||||
|
deploy:
|
||||||
|
mode: replicated
|
||||||
|
replicas: A*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Если global это означает, что данный сервис будет запущен ровно в одном экземпляре на всех возможных нодах. A replicated означает, что п-ое кол-во контейнеров для данного сервиса будет запущено на всех доступных нодах.
|
||||||
|
|
||||||
|
**Zero downtime deployment**
|
||||||
|
Это возможность организовать «бесшовную» смену контейнеров во время развертывания.
|
||||||
|
Это возможно и в Docker-compose, но надо держать дополнительную реплику контейнера (даже, если по нагрузке требуется всего одна) и на уровне балансировщика переключать трафик с одного контейнера на другой.
|
||||||
|
C **Docker Swarm** это все не нужно, необходимо лишь немного скорректировать конфигурацию сервиса.
|
||||||
|
Для начала нужно добавить директиву healthcheck:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*healthcheck:
|
||||||
|
test: curl -ss http://127.0.0.1:4004/ptm/api/healthcheck ||
|
||||||
|
echo 1
|
||||||
|
interval: 30s
|
||||||
|
timeout: 3s
|
||||||
|
retries: 12*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Она предназначена, чтобы Docker мог определить, корректно ли работает контейнер. test - результат исполнения этой команды Docker использует для определения корректно
|
||||||
|
ли работает контейнер.
|
||||||
|
*interval* - с какой частотой проверять состояние. В данном случае каждые 30 секунд.
|
||||||
|
*timeout* - таймаут для ожидания выполнения команды.
|
||||||
|
*retries* - количество попыток для проверки состояния сервера внутри контейнера.
|
||||||
|
|
||||||
|
После добавления директивы healthcheck в compose file мы увидим в Status информацию о состоянии контейнера:
|
||||||
|
**docker container Is**
|
||||||
|
|
||||||
|
После развертывания стэка контейнер сначала имеет статус **starting** (сервер внутри нашего контейнера запускается), а через некоторое время получит статус **healthy** (сервер запустился), в противном случае **unhealthy**.
|
||||||
|
**Docker** в режиме **Swarm** не просто отслеживает жизненное состояние контейнера, но и в случае перехода в состояние **unhealthy** попытается пересоздать контейнер.
|
||||||
|
|
||||||
|
**Настройки для обновления контейнера:**
|
||||||
|
**replicas** - количество контейнеров, которые необходимо запустить
|
||||||
|
для данного сервиса.
|
||||||
|
Директива \verb|update_config| описывает каким образом сервис должен обновляться:
|
||||||
|
**parallelism** количество контейнеров для одновременного - обновления. По умолчанию данный параметр имеет значение 1 - контейнеры будут обновляться по одному. 0 - обновить сразу все контейнеры. В большинстве случаев это число должно быть меньше, чем общее количество реплик сервиса.
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
deploy:
|
||||||
|
replicas: 1
|
||||||
|
update_config:
|
||||||
|
parallelism: 1
|
||||||
|
order: start-first
|
||||||
|
failure_action: rollback
|
||||||
|
delay: 10s
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
order - порядок обновления контейнеров. По умолчанию ptop-first, сначала текущий контейнер останавливается, а затем запускается новый. Для «бесшовного» обновления нужно использовать start- first. В этом случае вначале запускается новый контейнер, а затем выключается старый.
|
||||||
|
\verb|failure_action| - стратегия в случае сбоя. Вариантов несколько: continue, rollback, или pause (по умолчанию).
|
||||||
|
delay - задержка между обновлением группы контейнеров.
|
||||||
|
|
||||||
|
**Маршрутирзация**
|
||||||
|
|
||||||
|
В данный момент у нас 3 ноды: manager нода, нода для stage версии приложения и еще одна для разработки.
|
||||||
|
**docker node 1s**
|
||||||
|
Если развернуть наш стэк для docker-compose.prod.yaml на том же 4003 порту, что и для уже запущенного стэка docker-compose.stage.yaml, то получим ошибку, связанную с тем, что порт уже занят.
|
||||||
|
Почему это произошло? И более того, если мы зайдем на ВМ prod-1 и Сделаем curl 127.0.0.1:4003, то увидим, что наш сервис доступен, хотя на этой ноде мы еще не успели ничего развернуть?
|
||||||
|
Связано это с тем, что у Swarm имеется ingress сеть, которая используется для маршрутизации траффика между нодами. Если у сервиса есть публичный порт, то Swarm слушает его и в случае поступления запроса на него делает следующее: определяет есть ли контейнер на этой хост машине и если нет, то находит ноду, на которой запущен контейнер для данного сервиса, и перенаправляет запрос туда.
|
||||||
|
|
||||||
|
В данном примере используется внешний балансировщик, который балансирует запросы между тремя ВМ, а дальше Swarm перенаправляет запросы в соответствующие контейнеры.
|
||||||
|
|
||||||
|
Поэтому для docker-compose.prod.yaml нужно использовать любой другой публичный порт, отличный от того, который указан в docker-compose.stage.yaml.
|
||||||
|
Отключить
|
||||||
|
автоматическую маршрутизацию трафика можно с помощью mode: host при декларации ports:
|
||||||
|
В данном случае запрос, который придет на порт 4004, Swarm будет направлять только на контейнер текущей ноде никуда И больше.
|
||||||
|
|
||||||
|
Настройка **mode** (напрямую это не относится к маршрутизации). Она может принимать следующие значения: global или replicated (по умолчанию):
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*deploy:
|
||||||
|
mode: global
|
||||||
|
deploy:
|
||||||
|
mode: replicated
|
||||||
|
replicas: A*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Если global это означает, что данный сервис будет запущен ровно в одном экземпляре на всех возможных нодах. A replicated означает, что п-ое кол-во контейнеров для данного сервиса будет запущено на всех доступных нодах.
|
||||||
|
|
||||||
|
**Zero downtime deployment**
|
||||||
|
Это возможность организовать «бесшовную» смену контейнеров во время развертывания.
|
||||||
|
Это возможно и в Docker-compose, но надо держать дополнительную реплику контейнера (даже, если по нагрузке требуется всего одна) и на уровне балансировщика переключать трафик с одного контейнера на другой.
|
||||||
|
C **Docker Swarm** это все не нужно, необходимо лишь немного скорректировать конфигурацию сервиса.
|
||||||
|
Для начала нужно добавить директиву healthcheck:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*healthcheck:
|
||||||
|
test: curl -ss http://127.0.0.1:4004/ptm/api/healthcheck ||
|
||||||
|
echo 1
|
||||||
|
interval: 30s
|
||||||
|
timeout: 3s
|
||||||
|
retries: 12*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Она предназначена, чтобы Docker мог определить, корректно ли работает контейнер. test - результат исполнения этой команды Docker использует для определения корректно
|
||||||
|
ли работает контейнер.
|
||||||
|
*interval* - с какой частотой проверять состояние. В данном случае каждые 30 секунд.
|
||||||
|
*timeout* - таймаут для ожидания выполнения команды.
|
||||||
|
*retries* - количество попыток для проверки состояния сервера внутри контейнера.
|
||||||
|
|
||||||
|
После добавления директивы healthcheck в compose file мы увидим в Status информацию о состоянии контейнера:
|
||||||
|
**docker container Is**
|
||||||
|
|
||||||
|
После развертывания стэка контейнер сначала имеет статус **starting** (сервер внутри нашего контейнера запускается), а через некоторое время получит статус **healthy** (сервер запустился), в противном случае **unhealthy**.
|
||||||
|
**Docker** в режиме **Swarm** не просто отслеживает жизненное состояние контейнера, но и в случае перехода в состояние **unhealthy** попытается пересоздать контейнер.
|
||||||
|
|
||||||
|
**Настройки для обновления контейнера:**
|
||||||
|
**replicas** - количество контейнеров, которые необходимо запустить
|
||||||
|
для данного сервиса.
|
||||||
|
Директива \verb|update_config| описывает каким образом сервис должен обновляться:
|
||||||
|
**parallelism** количество контейнеров для одновременного - обновления. По умолчанию данный параметр имеет значение 1 - контейнеры будут обновляться по одному. 0 - обновить сразу все контейнеры. В большинстве случаев это число должно быть меньше, чем общее количество реплик сервиса.
|
||||||
|
**order** - порядок обновления контейнеров. По умолчанию ptop-first, сначала текущий контейнер останавливается, а затем запускается новый. Для «бесшовного» обновления нужно использовать start- first. В этом случае вначале запускается новый контейнер, а затем выключается старый.
|
||||||
|
\verb|failure_action| - стратегия в случае сбоя. Вариантов несколько: continue, rollback, или pause (по умолчанию).
|
||||||
|
**delay** - задержка между обновлением группы контейнеров.
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
deploy:
|
||||||
|
replicas: 1
|
||||||
|
update_config:
|
||||||
|
parallelism: 1
|
||||||
|
order: start-first
|
||||||
|
failure_action: rollback
|
||||||
|
delay: 10s
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
**Docker secrets**
|
||||||
|
|
||||||
|
**Swarm** предоставляет хранилище для приватных данных (secrets), которые необходимы контейнерам. Это используется для хранения логинов, паролей, ключей шифрования и токенов доступа от внешних систем, БД и т.д.
|
||||||
|
**Создадим yaml файл с «секретным» токеном:**
|
||||||
|
* example.yaml
|
||||||
|
\begin{verbatim}
|
||||||
|
token: sfsjksajflsf_secret*
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Создадим **secret** с именем \verb|back_config|:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
docker secret create back_config example.yaml
|
||||||
|
nys6v16j4d8ymmi f8755305
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
docker secret is
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
*#inspect specific secret*
|
||||||
|
docker secret inspect back_config
|
||||||
|
"ID": "nys6v16j4d8ynnif875q6305",
|
||||||
|
"Version": [
|
||||||
|
"Index"; 24683
|
||||||
|
"CreatedAt": "2022-04-13715:19:14.4746056842", "UpdatedAt": "2022-04-13T15:19:14.4746086842",
|
||||||
|
"Spec": {
|
||||||
|
"Name": "back_config",
|
||||||
|
"Labels": {}
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
**docker ps**
|
||||||
|
Чтобы просмотреть все контейнеры во всех состояниях, передайте аргумент - а. Docker автоматически настраивает локальный реестр образов на компьютере. Про- смотреть образы в реестре с помощью команды: docker images
|
||||||
|
Удалить образ из локального реестра Docker с помощью команды docker rmi. Указывается имя или ID образа, который требуется удалить. Допустим, удалим образ с именем temp-Ubuntu:version-1.0:
|
||||||
|
**docker rmi temp-Ubuntu:version-1.0**
|
||||||
|
Если образ используется контейнером, удалить его нельзя. Команда docker rmi возвращает сообщение об ошибке, в котором указывается контейнер, использующий
|
||||||
|
образ. Для удаления контейнера служит команда docker rm
|
||||||
|
\begin{verbatim}
|
||||||
|
docker rm happy_wilbur
|
||||||
|
\end{verbatim}
|
||||||
|
После удаления контейнера все данные В нем уничтожаются. При планировании хранения данных важно учитывать, что контейнеры являются временными.
|
||||||
|
Для перезапуска контейнера используется команда docker restart
|
||||||
|
\begin{verbatim}
|
||||||
|
docker restart happy_wilbur
|
||||||
|
\end{verbatim}
|
||||||
|
Так контейнер получает команду stop, а затем команду start.
|
||||||
|
Приостанавливает контейнер команда docker pause.
|
||||||
|
\begin{verbatim}
|
||||||
|
docker pause happy_wilbur
|
||||||
|
\end{verbatim}
|
||||||
|
Приостановка контейнера приводит к приостановке всех процессов. Эта команда позволяет контейнеру продолжить процессы в дальнейшем. Команда docker unpause отменяет приостановку всех процессов в указанных контейнерах.
|
||||||
|
**2.7 Флаги команды docker run**
|
||||||
|
Если перед флагом стоит два тире то это его полная форма, флаг с одним тире
|
||||||
|
- это сокращённый вариант некоего флага. Действуют они одинаково. Например, -р - это сокращённая форма флага рort:-1(--interactive) поток STDIN под- держивается в открытом состоянии даже если контейнер к STDIN не подключён; -t (--tty)-соединяет используемый терминал с потоками STDIN и STDOUT контей- нера.
|
||||||
|
Для того чтобы получить возможность взаимодействия с контейнером через тер- минал нужно совместно использовать флаги -i и -t.
|
||||||
|
**docker run -it tmp-ubuntu**
|
||||||
|
Запускает контейнер команда docker run. Для запуска контейнера из образа нужно просто указать его имя или идентификатор.
|
||||||
|
**docker run -d tmp-ubuntu**
|
||||||
|
Здесь для запуска контейнера в фоновом режиме следует добавить флаг -. -р (--port) порт это интерфейс, благодаря которому контейнер взаимодей- ствует с внешним миром. Например: конструкция 1000: 8000 перенаправляет порт Docker 8000 на порт 1000 компьютера, на котором выполняется контейнер. Если в контейнере работает некое приложение, способное выводить что-то в браузер, то, для того, чтобы к нему обратиться, в нашем случае можно перейти в браузере по адресу localhost:1000.
|
||||||
|
-d (--detach) запуск контейнер в фоновом режиме. Это позволяет использовать
|
||||||
|
|
||||||
|
**Docker Swarm** несложный оркестратор для контейнеров, который - доступен для пользователей **Docker**.
|
||||||
|
Преимущества:
|
||||||
|
низкий порог вхождения, простота использования
|
||||||
|
Недостатки:
|
||||||
|
- уступает **Kubernetes** в широте администрирования
|
||||||
|
- отсутствует автомасштабирование
|
||||||
|
- функционал сильно уступает Kubernetes
|
||||||
|
|
||||||
|
**Основы безопасности в Docker**
|
||||||
|
|
||||||
|
5 основных правил:
|
||||||
|
|
||||||
|
1) Регулярно устанавливайте обновления
|
||||||
|
|
||||||
|
2) Ограничьте доступ к сокету службы Docker
|
||||||
|
|
||||||
|
3) Используйте непривилегированного пользователя внутри контейнера
|
||||||
|
|
||||||
|
4) Не запускайте контейнер с повышенными привилегиями
|
||||||
|
|
||||||
|
5) Используйте инструменты проверки docker-image на уязвимости
|
||||||
|
|
||||||
|
**Основы безопасности в Docker**
|
||||||
|
**Правило 1:** Регулярно устанавливайте обновления
|
||||||
|
Регулярные обновление хостовой машины и Docker позволят вам:
|
||||||
|
- Защититься от уязвимостей
|
||||||
|
Получать новый функционал
|
||||||
|
Продлевать поддержку производителя ПО
|
||||||
|
Быть в курсе имеющихся проблем у производителя Осваивать новые технологии
|
||||||
|
Помните, что контейнеры используют ядро совместно с хостом.
|
||||||
|
Эксплойт, запущенный внутри контейнера напрямую выполняются в ядре хоста.
|
||||||
|
|
||||||
|
**Правило 2:** Ограничьте доступ к сокету службы Docker
|
||||||
|
**Docker daemon** использует UNIX сокет /var/run/docker.sock для входящих соединений API. **Владельцем данного ресурса должен быть пользователь root.** И никак иначе. Изменение прав доступа к этому сокету по сути равносильно предоставлению root-доступа к хостовой системе.
|
||||||
|
Не используйте **Docker TCP** сокет без защиты (авторизации, шифрования):
|
||||||
|
***Expose daemon on tcp://localhost:2375 without TLS**
|
||||||
|
Exposing daemon on TCP without TLS helps legacy clients connect to the daemon. It also makes yourself vulnerable to remote code execution attacks. Use with caution.*
|
||||||
|
|
||||||
|
**Правило 3:** Настройка контейнера на
|
||||||
|
использование
|
||||||
|
непривилегированного
|
||||||
|
пользователя.
|
||||||
|
Это лучший способ избежать атаки на повышение привилегий.
|
||||||
|
Это можно сделать различными способами:
|
||||||
|
|
||||||
|
1. Используя флаг и команды docker run:
|
||||||
|
**docker run -u 4000 alpine**
|
||||||
|
|
||||||
|
2. Во время сборки образа:
|
||||||
|
|
||||||
|
\begin{verbatim}
|
||||||
|
FROM alpine
|
||||||
|
**RUN groupadd-r myuser && useradd-r-g myuser myuser
|
||||||
|
<Здесь ещё можно выполнять команды от root-пользователя, например, ставить пакеты>
|
||||||
|
USER myuser**
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
3. Включить поддержку «user namespace» (пользовательского окружения) в Docker daemon:
|
||||||
|
|
||||||
|
**Правило 4** Избегайте запуска контейнеров с файлом - - privileged
|
||||||
|
docker run - -privileged -p 127.0.0.1:3306:3306 —name mariadb
|
||||||
|
|
||||||
|
**Правило 5:** Используйте инструменты проверки docker-image
|
||||||
|
|
||||||
|
на уязвимости
|
||||||
|
|
||||||
|
Используйте команду docker scan для сканирования образов:
|
||||||
|
|
||||||
|
Package manager: deb
|
||||||
|
project name: docker-image|mariadb
|
||||||
|
Docker image: mariadb
|
||||||
|
Platform: linux/amd64
|
||||||
|
Base image: ubuntu:20.04
|
||||||
|
|
||||||
|
Tested 185 dependencies for known vulnerabilities, found 19 vulnerabilities.
|
||||||
|
|
||||||
|
\section{Kubernetes}
|
||||||
|
Kubernetes (k8s)
|
||||||
|
|
||||||
|
**Kubernetes** работает по принципу «ведущий - ведомый».
|
||||||
|
Управление системой основано на двух подходах
|
||||||
|
**декларативном** - разработчик задает цели, а не пути их достижения, - которые система автоматически выбирает сама
|
||||||
|
**императивном** - разработчик может распоряжаться ресурсами с помощью команд «Создать», «Изменить», «Удалить>>
|
||||||
|
|
||||||
|
\subsection{Как работает Kubernetes}
|
||||||
|
|
||||||
|
**Kubectl** модуль **Kubernetes** для управления кластером (все - команды управления посылаются на **Master ноду**).
|
||||||
|
https://kubernetes.io/docs/tasks/tools/install-kubectl-windows
|
||||||
|
|
||||||
|
**Minikube** для создания **Kubernetes кластера Single-Node**, - оптимизированного для тестов и учебы (Master и Worker B одном).
|
||||||
|
|
||||||
|
Итак, мультиконтейнерное приложение запущено на сервере
|
||||||
|
Контейнеров несколько, задача настроить их совместную работу так, чтобы
|
||||||
|
они не отбирали друг у друга ресурсы аппаратной платформы
|
||||||
|
эффективно их расходовали
|
||||||
|
периодически следить за корректной работой и исправлять ошибки.
|
||||||
|
Kubernetes позволяет автоматизировать большинство процессов
|
||||||
|
|
||||||
|
\subsection{Возможности Kubernetes:}
|
||||||
|
|
||||||
|
• мониторинг сервисов и распределения нагрузки • автомонтирование гибкой системы хранения,
|
||||||
|
• автоматизированные откаты и развертывания, • автораспределение нагрузки,
|
||||||
|
горизонтальное автомасштабирование,
|
||||||
|
автоперезапуск, замена и завершение работы отказавших контейнеров, управление конфигурацией и конфиденциальной информацией.
|
||||||
|
Kubernetes - это широкие возможности по автоматизированной оркестрации мультиконтейнерных приложений, но необходима предварительная подготовка и настройка
|
||||||
|
|
||||||
|
Поднятие простого Kubernetes кластера на Windows
|
||||||
|
|
||||||
|
Minikube для создания Kubernetes кластера Single-Node, - оптимизированного для тестов и учебы (Master и Worker B одном).
|
||||||
|
|
||||||
|
\subsection{Кластер Kubernetes}
|
||||||
|
|
||||||
|
Компоненты кластера Kubernetes
|
||||||
|
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=12cm]{04-telematics-kub-cluster.png}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\subsection{Nodes (ноды, узлы)}
|
||||||
|
|
||||||
|
Это физические или виртуальные машины. на которых развертываются и запускаются контейнеры с приложениями.
|
||||||
|
Совокупность Kubernetes нод образует кластер Kubernetes
|
||||||
|
Nodes бывают двух типов:
|
||||||
|
**Master** (мастер-нода) - узел, управляющий
|
||||||
|
всем кластером.
|
||||||
|
**Worker** (рабочие ноды) - узлы, на которых работают контейнеры
|
||||||
|
|
||||||
|
\subsection{Pods (Поды)}
|
||||||
|
Pods - базовые модули управления приложениями состоящие из одного или нескольких контейнеров
|
||||||
|
Контейнеры в поде запускаются и работают вместе имеют общие сетевые ресурсы и хранилище
|
||||||
|
Под и все его контейнеры функционируют на одном узле и находятся там до завершения работы
|
||||||
|
Обычно Kubernetes сам создает поды
|
||||||
|
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
\begin{subfigure}[b]{0.48\textwidth}
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=\textwidth]{04-telematics-kub-pods.png}
|
||||||
|
\end{subfigure}
|
||||||
|
\hfill
|
||||||
|
\begin{subfigure}[b]{0.48\textwidth}
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=\textwidth]{04-telematics-kub-01.png}
|
||||||
|
\caption{Компоненты master-ноды кластера Kubernetes}
|
||||||
|
\end{subfigure}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
Поднятие простого Kubernetes кластера на Windows
|
||||||
|
|
||||||
|
Проще всего воспользоваться готовой реализацией - **Minikube**. Нам потребуется установить 3 приложения:
|
||||||
|
**VirtualBox
|
||||||
|
Kubectl
|
||||||
|
Minikube**
|
||||||
|
Другие модули **Kubernetes: kubeadm** (создание и настройка кластеров), **kubelet** (их запуск на хостах), **kubectl** (настройка компонентов, входящих в кластер - управление кластером).
|
||||||
|
|
||||||
|
Kubectl - модуль Kubernetes для управления кластером (все команды управления посылаются на Master ноду).
|
||||||
|
https://kubernetes.io/docs/tasks/tools/install-kubectl-windows/
|
||||||
|
|
||||||
|
Далее в терминале запускаем кластер:
|
||||||
|
minikube start
|
||||||
|
"minikube ans Windows Home minikube start --no-vtx-check-cpusx-memory-gb-d-e-Ig
|
||||||
|
|
||||||
|
**Поднятие простого Kubernetes кластера на Windows**
|
||||||
|
Далее в терминале видим, если все прошло успешно:
|
||||||
|
**Done! kubectl is now configured to use "minikube"**
|
||||||
|
Конфигурационный файл **«config» kubectl расположен в:
|
||||||
|
\begin{verbatim}
|
||||||
|
C:\Users\User\.kube**
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Конфигурационный файл «config» kubectl расположен
|
||||||
|
\begin{verbatim}
|
||||||
|
C:\Users\User.kube
|
||||||
|
\end{verbatim}
|
||||||
|
|
||||||
|
Работа с Kubectl
|
||||||
|
|
||||||
|
Что такое Kubectl?
|
||||||
|
Kubectl - это инструмент командной строки для управления кластерами Kubernetes.
|
||||||
|
Kubectl ищет файл config в директории /.kube
|
||||||
|
|
||||||
|
Синтаксис Kubectl
|
||||||
|
|
||||||
|
Синтаксис для выполнения команд kubectl в терминале
|
||||||
|
|
||||||
|
**kubectl [command] [TYPE] [NAME] [flags]**
|
||||||
|
|
||||||
|
- command: определяет выполняемую операцию с одним или несколькими ресурсами, например, create, get, delete.
|
||||||
|
- TYPE: определяет тип ресурса.
|
||||||
|
- NAME: определяет имя ресурса.
|
||||||
|
- flags: определяет дополнительные флаги.
|
||||||
|
|
||||||
|
Простая инструкция по работе с k8s-кластером
|
||||||
|
Базовые команды по работе с k8s-кластером, используя утилиту rubectl:
|
||||||
|
**kubectl cluster-info** - информация о кластере
|
||||||
|
**kubectl get nodes** - получить все доступные ноды в кластере
|
||||||
|
**kubectl get pods** - получение списка развернутых подов
|
||||||
|
**kubectl run** - запуск пода на основе докер-образа (архаичный вариант запуска, обычно используются специально подготовленные манифесты в формате yaml).
|
||||||
|
**kubectl expose pod** - создание службы для межподового/межконтейнерного взаимодействия (архаичный вариант, обычно используются специально подготовленные манифесты в формате yaml)
|
||||||
|
|
||||||
|
**Поднятие простого Kubernetes кластера на Windows**
|
||||||
|
|
||||||
|
**Управление созданным Single-Node кластером**
|
||||||
|
|
||||||
|
**minikube start** - запуск кластера minikube
|
||||||
|
|
||||||
|
**minikube pause** - приостановка кластера minikube, не затрагивая развернутые приложения.
|
||||||
|
|
||||||
|
**minikube unpause** - возобновление работы приостановленного экземпляра
|
||||||
|
|
||||||
|
**minikube stop** - остановка.
|
||||||
|
|
||||||
|
**minikube delete** - удаление кластера minikube.
|
||||||
|
|
||||||
|
Работа внутри minikube: **minikube ssh**
|
||||||
|
|
||||||
|
Установка «Dashboard» - панели управления Kubernetes
|
||||||
|
|
||||||
|
**Установка «Dashboard» - панели управления Kubernetes**
|
||||||
|
**Dashboard** - панель управления Kubernetes
|
||||||
|
|
||||||
|
**Dashboard** - это веб-интерфейс пользователя Kubernetes.
|
||||||
|
|
||||||
|
**Dashboard** удобен для:
|
||||||
|
|
||||||
|
- развертывания контейнерных приложений в кластере Kubernetes,
|
||||||
|
- устранения неполадок в контейнерном приложении
|
||||||
|
- управления ресурсами кластера.
|
||||||
|
Dashboard не устанавливается по умолчанию.
|
||||||
|
|
||||||
|
**Dashboard** также предоставляет информацию о состоянии ресурсов
|
||||||
|
**Kubernetes** в кластере и об возникших ошибках.
|
||||||
|
|
||||||
|
Dashboard - панель управления Kubernetes
|
||||||
|
|
||||||
|
Команды для установки на:
|
||||||
|
|
||||||
|
[https://kubernetes.io/docs/tasks/access-application-cluster/web-ui-dashboard/](https://kubernetes.io/docs/tasks/access-application-cluster/web-ui-dashboard/)
|
||||||
|
|
||||||
|
Интерактивное руководство - создание кластера Kubernetes
|
||||||
|
|
||||||
|
[https://kubernetes.io/docs/tutorials/kubernetes-basics/create-cluster/cluster-interactive/](https://kubernetes.io/docs/tutorials/kubernetes-basics/create-cluster/cluster-)
|
||||||
|
|
||||||
|
Интерактивное руководство - работа с кластером Docker Swarm
|
||||||
|
|
||||||
|
[https://labs.play-with-docker.com/](https://labs.play-with-docker.com/)
|
||||||
|
|
||||||
|
\section{git}
|
||||||
|
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|
|
||||||
|
|
@ -586,6 +586,47 @@ Var(\xi_t) = E(\xi_t^2-E\xi_t)
|
||||||
\end{equation*}
|
\end{equation*}
|
||||||
В основном рассматриваются процессы прогнозирующие изменения доходности ARCH, GARCH.
|
В основном рассматриваются процессы прогнозирующие изменения доходности ARCH, GARCH.
|
||||||
|
|
||||||
|
\section{Многомерные параметрические модели временных рядов}
|
||||||
|
Какие ряды следует включать в модель? Включаются только те, которые являются «причинными по Грейнджеру». Факторы должны иметь тот же порядок интеграции. То есть если изъятие информации о факторе меняет условное матожидание ряда.
|
||||||
|
|
||||||
|
$$E(Y_{t+1}|Y_t, Y_{t-1} X_t, ...) = E(Y_{t+1}|Y_t, Y_{t-1})$$
|
||||||
|
|
||||||
|
Связь должна быть односторонняя, то есть если Х объясняет У, а У объясняет Х -- они не подходят. Тест проверяет, может ли фактор Х улучшить прогноз У.
|
||||||
|
|
||||||
|
\begin{equation*}
|
||||||
|
\begin{gathered}
|
||||||
|
X_t = \alpha_0+\alpha_1X_{t-1}+\beta Y_{t-1} + \xi_t\\
|
||||||
|
Y_t = \gamma_0+\gamma_1Y_{t-1}+\delta Y_{t-1} + \xi_t
|
||||||
|
\end{gathered}
|
||||||
|
\end{equation*}
|
||||||
|
|
||||||
|
$Y_t$ причинная по грейнджеру для $X_t$
|
||||||
|
$$
|
||||||
|
\begin{cases}
|
||||||
|
H_0 \beta_1 = 0 \text{отвергнута}\\
|
||||||
|
H_0 \delta_1 = 0 \text{не может быть отвергнута}\\
|
||||||
|
\end{cases}
|
||||||
|
$$
|
||||||
|
|
||||||
|
Если вероятность ошибиться меньше 0,05 -- принимаем гипотезу.
|
||||||
|
|
||||||
|
\subsection{Ложная регрессия}
|
||||||
|
|
||||||
|
\subsection{Коинтеграция}
|
||||||
|
Если наблюдаемые ряды принадлежат к классы DS процессов, то при определённых условиях между ними может существовать связь, проявляющаяся в том, что для них существует стационарная линейная комбинация.
|
||||||
|
|
||||||
|
\subsection{Стационарные ряды}
|
||||||
|
|
||||||
|
\subsection{Модель коррекции ошибками ECM}
|
||||||
|
\begin{equation*}
|
||||||
|
\begin{gathered}
|
||||||
|
Y_t = \mu + \alpha_2 Y_{t-1}+\beta_0 X_t + \beta_1 X_{t-1} + \xi_t\\
|
||||||
|
Y_t - Y_{t-1} = \mu -(1-\alpha_1) * Y_{t-1}+\beta_0 X_t + \beta_1 X_{t-1} + \xi_t\\
|
||||||
|
\Delta Y_t = \beta_0 \Delta X_t -(1-\alpha_1)(Y_{t-1} - \frac{\beta_0+\beta_1}{1-\alpha_1}X_{t-1} - \frac{\mu}{1-\alpha_1}) + \xi_t
|
||||||
|
\end{gathered}
|
||||||
|
\end{equation*}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\appendix
|
\appendix
|
||||||
\setcounter{secnumdepth}{0}
|
\setcounter{secnumdepth}{0}
|
||||||
|
|
@ -655,7 +696,110 @@ r = число параметров модели, N - объём выборки.
|
||||||
|
|
||||||
SARIMA(p,d,q)(P,D,Q,S) -- учёт сезонности.
|
SARIMA(p,d,q)(P,D,Q,S) -- учёт сезонности.
|
||||||
|
|
||||||
|
\section{РК2}
|
||||||
|
Для того, чтобы определить, является ли процесс обратимым, необходимо проверить, существует ли такая последовательность коэффициентов $\{ \psi_i \}$, что процесс можно представить в виде:
|
||||||
|
$$
|
||||||
|
X_t = \sum_{i=1}^{\infty} \psi_i \varepsilon_{t-i}
|
||||||
|
$$
|
||||||
|
где $\varepsilon_t$ - белый шум.
|
||||||
|
Для процесса с заданной автокорреляционной функцией $\rho_1 = 0.5$ и $\rho_k = 0, k \geq 2$ можно найти автоковариационную функцию:
|
||||||
|
$$
|
||||||
|
\gamma_k = \rho_1 \rho_{k-1} + \rho_2 \rho_{k-2} + ... + \rho_{k-1} \rho_1
|
||||||
|
$$
|
||||||
|
Так как $\rho_k = 0$ для $k \geq 2$, то $\gamma_k = 0$ для $k \geq 3$. Также, $\gamma_1 = \rho_1 = 0.5$ и $\gamma_2 = \rho_1 \rho_1 + \rho_2 \rho_0 = 0.5$. Таким образом, автоковариационная функция для данного процесса равна:
|
||||||
|
$$
|
||||||
|
\gamma_k =
|
||||||
|
\begin{cases}
|
||||||
|
0.5 & k = 1 \\
|
||||||
|
0.5 & k = 2 \\
|
||||||
|
0 & k \geq 3
|
||||||
|
\end{cases}
|
||||||
|
$$
|
||||||
|
Для того, чтобы процесс был обратимым, необходимо, чтобы $\gamma_k > 0$ для всех $k \geq 1$. В данном случае, $\gamma_3 = 0$, что означает, что процесс не является обратимым.
|
||||||
|
|
||||||
|
|
||||||
|
Да, возможно проверить обратимость процесса с заданной автокорреляционной функцией $\rho_1 = 0.5$ и $\rho_k = 0, k \geq 2$ с помощью теоремы Вольда.
|
||||||
|
Теорема Вольда утверждает, что стационарный процесс обратим тогда и только тогда, когда его спектральная плотность имеет нули только на одной точке.
|
||||||
|
Спектральная плотность для процесса с заданной автокорреляционной функцией может быть найдена с помощью преобразования Фурье. В данном случае, автокорреляционная функция имеет вид:
|
||||||
|
$$
|
||||||
|
\rho_1 = 0.5; \quad \rho_k = 0, k \geq 2
|
||||||
|
$$
|
||||||
|
С учетом свойства симметричности автокорреляционной функции, получаем:
|
||||||
|
$$
|
||||||
|
\rho_0 = 1, \quad \rho_1 = 0.5, \quad \rho_k = 0, k \geq 2
|
||||||
|
$$
|
||||||
|
Применяя преобразование Фурье, получаем спектральную плотность:
|
||||||
|
$$
|
||||||
|
f(\lambda) = \sum_{k=-\infty}^{\infty} \rho_k e^{-i \lambda k}
|
||||||
|
$$
|
||||||
|
В данном случае, $f(\lambda) = \rho_0 + \rho_1 e^{-i \lambda} = 1 + 0.5 e^{-i \lambda}$.
|
||||||
|
Спектральная плотность имеет нули тогда и только тогда, когда ее модуль равен нулю. Модуль спектральной плотности $|f(\lambda)| = \sqrt{1 + 0.5^2 - e^{-i \lambda}}$ не равен нулю ни в одной точке, следовательно, процесс является обратимым по теореме Вольда.
|
||||||
|
|
||||||
|
Теорема Вольда утверждает, что стационарный процесс обратим тогда и только тогда, когда его спектральная плотность имеет нули только на одной точке.
|
||||||
|
Спектральную плотность можно представить в виде:
|
||||||
|
$$
|
||||||
|
f(\lambda) = \sum_{k=-\infty}^{\infty} \rho_k e^{-i \lambda k}
|
||||||
|
$$
|
||||||
|
В данном случае, $\rho_1 = 0.5$ и $\rho_k = 0, k \geq 2$, следовательно:
|
||||||
|
$$
|
||||||
|
f(\lambda) = \rho_0 + \rho_1 e^{-i \lambda} = 1 + 0.5 e^{-i \lambda}
|
||||||
|
$$
|
||||||
|
Чтобы проверить, имеет ли спектральная плотность нули, необходимо решить уравнение:
|
||||||
|
$$
|
||||||
|
f(\lambda) = 1 + 0.5 e^{-i \lambda} = 0
|
||||||
|
$$
|
||||||
|
Умножим обе части на $e^{i \lambda}$:
|
||||||
|
$$
|
||||||
|
e^{i \lambda} + 0.5 = 0
|
||||||
|
$$
|
||||||
|
Отсюда получаем:
|
||||||
|
$$
|
||||||
|
e^{i \lambda} = -0.5
|
||||||
|
$$
|
||||||
|
Решение этого уравнения может быть найдено с помощью формулы Эйлера:
|
||||||
|
$$
|
||||||
|
e^{i \lambda} = \cos \lambda + i \sin \lambda
|
||||||
|
$$
|
||||||
|
Следовательно,
|
||||||
|
$$
|
||||||
|
\cos \lambda + i \sin \lambda = -0.5
|
||||||
|
$$
|
||||||
|
Отсюда можно найти значение $\lambda$:
|
||||||
|
$$
|
||||||
|
\lambda = \pi + 2n \pi, \quad n \in \mathbb{Z}
|
||||||
|
$$
|
||||||
|
Заметим, что полученное значение $\lambda$ соответствует нулю спектральной плотности только в одной точке. Следовательно, процесс является обратимым по теореме Вольда.
|
||||||
|
|
||||||
|
\subsection{1}
|
||||||
|
Чтобы найти прогноз на 1 и 2 шага вперед, нам нужно сначала представить модель процесса в виде линейного уравнения с лагами (ARMA) и затем использовать найденные значения для расчета прогноза.
|
||||||
|
|
||||||
|
Модель имеет вид:
|
||||||
|
$$(1 - 0,3L)y_t = 0,2 + (1 - 0,4L^2)\xi_t$$
|
||||||
|
|
||||||
|
Преобразуем уравнение, чтобы получить значение $y_t$:
|
||||||
|
$$y_t = (0,3L)y_t + 0,2 + \xi_t - 0,4L^2\xi_t$$
|
||||||
|
|
||||||
|
Теперь у нас есть линейное уравнение с лагами:
|
||||||
|
$$y_t = 0,3y_{t-1} + 0,2 + \xi_t - 0,4\xi_{t-2}$$
|
||||||
|
|
||||||
|
Теперь мы можем использовать это уравнение для прогнозирования на шаг вперед (t + 1) и на два шага вперед (t + 2).
|
||||||
|
|
||||||
|
Прогноз на 1 шаг вперед (t + 1):
|
||||||
|
$$y_{t+1|t} = 0,3y_{t} + 0,2 + \xi_{t+1} - 0,4\xi_{t-1}$$
|
||||||
|
|
||||||
|
Поскольку мы не знаем значения ошибок, мы предполагаем, что ожидаемое значение ошибки равно нулю ($E[\xi_t] = 0$):
|
||||||
|
|
||||||
|
$$y_{t+1|t} = 0,3y_{t} + 0,2$$
|
||||||
|
|
||||||
|
Прогноз на 2 шага вперед (t + 2):
|
||||||
|
$$y_{t+2|t} = 0,3y_{t+1} + 0,2 + \xi_{t+2} - 0,4\xi_{t}$$
|
||||||
|
|
||||||
|
Аналогично предыдущему шагу, предполагаем $E[\xi_t] = 0$:
|
||||||
|
|
||||||
|
$$y_{t+2|t} = 0,3(0,3y_{t} + 0,2) + 0,2$$
|
||||||
|
|
||||||
|
$$y_{t+2|t} = 0,09y_{t} + 0,26$$
|
||||||
|
|
||||||
|
Итак, прогноз на 1 шаг вперед равен $0,3y_{t} + 0,2$, а прогноз на 2 шага вперед равен $0,09y_{t} + 0,26$. Значения $y_t$ должны быть известны или предварительно рассчитаны для получения числовых прогнозов
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|
||||||
|
|
@ -38,10 +38,10 @@
|
||||||
\begin{gathered}
|
\begin{gathered}
|
||||||
1-2.5z+z^2=0\\
|
1-2.5z+z^2=0\\
|
||||||
z = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\
|
z = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\
|
||||||
z_1 = \frac{-2.5-\sqrt{-2.5^2-4}}{2}\\
|
z_1 = \frac{-2.5-\sqrt{2.5^2-4}}{2}\\
|
||||||
z_1 = 1.25 + \sqrt{1.5625-1} \approx 2\\
|
z_1 = 1.25 + \sqrt{6.25-4} = 1.25 + 1.5 \approx 2.75\\
|
||||||
z_2 = \frac{-2.5+\sqrt{-2.5^2-4}}{2}\\
|
z_2 = \frac{-2.5+\sqrt{2.5^2-4}}{2}\\
|
||||||
z_2 = 1.25 - \sqrt{1.5625-1} \approx 0.5
|
z_2 = 1.25 - \sqrt{6.25-4} = 1.25 - 1.5 \approx -0.25
|
||||||
\end{gathered}
|
\end{gathered}
|
||||||
\end{equation*}
|
\end{equation*}
|
||||||
Только один корень уравнения по модулю больше, поэтому процесс \textbf{не является обратимым}.
|
Только один корень уравнения по модулю больше, поэтому процесс \textbf{не является обратимым}.
|
||||||
|
|
@ -72,6 +72,37 @@ z_2 = 1.25 - \sqrt{1.5625-1} \approx 0.5
|
||||||
\end{equation*}
|
\end{equation*}
|
||||||
|
|
||||||
\subsection{Процесс ARMA(1, 1)}
|
\subsection{Процесс ARMA(1, 1)}
|
||||||
|
Для того чтобы процесс ARMA(1,1) был стационарным, необходимо выполнение следующих условий:
|
||||||
|
\begin{itemize}
|
||||||
|
\item Корни характеристического уравнения $1 - \alpha z = 0$ должны быть по модулю больше единицы. Характеристическое уравнение имеет вид $z = \frac{1}{\alpha}$, поэтому условие стационарности может быть записано как $|\frac{1}{\alpha}| > 1$, что эквивалентно $|\alpha| < 1$.
|
||||||
|
\item Веса авторегрессии и скользящего среднего должны быть ограничены, то есть $|\alpha| < 1$ и $|1 - \beta| < 1$, где $\beta$ - коэффициент скользящего среднего.
|
||||||
|
Таким образом, из условия 1 получаем, что $|\alpha| < 1$. Из условия 2 следует, что $|1 - \alpha| < 1$, что эквивалентно $0 < \alpha < 2$.
|
||||||
|
\end{itemize}
|
||||||
|
Таким образом, все значения $\alpha$ из интервала $(0, 1)$ удовлетворяют условиям стационарности процесса ARMA(1,1).
|
||||||
|
|
||||||
|
Процесс ARMA(1, 1) может быть записан как
|
||||||
|
$$
|
||||||
|
y_t = \alpha y_{t-1} + \xi_t - 0.5 \xi_{t-1}
|
||||||
|
$$
|
||||||
|
Для того чтобы процесс был обратимым, необходимо чтобы любое значение $y_t$ можно было выразить через прошлые значения ошибок $\xi_t, \xi_{t-1}, \xi_{t-2}, \dots$.
|
||||||
|
Рассмотрим процесс $y_{t-1}$:
|
||||||
|
$$
|
||||||
|
y_{t-1} = \alpha y_{t-2} + \xi_{t-1} - 0.5 \xi_{t-2}
|
||||||
|
$$
|
||||||
|
Теперь можем выразить $y_t$ через прошлые значения ошибок:
|
||||||
|
$$
|
||||||
|
\begin{aligned}
|
||||||
|
y_t &= \alpha y_{t-1} + \xi_t - 0.5 \xi_{t-1} \\
|
||||||
|
&= \alpha (\alpha y_{t-2} + \xi_{t-1} - 0.5 \xi_{t-2}) + \xi_t - 0.5 \xi_{t-1} \\
|
||||||
|
&= \alpha^2 y_{t-2} + \alpha \xi_{t-1} - 0.5 \alpha \xi_{t-2} + \xi_t - 0.5 \xi_{t-1}
|
||||||
|
\end{aligned}
|
||||||
|
$$
|
||||||
|
Продолжая этот процесс, получаем:
|
||||||
|
$$
|
||||||
|
\begin{aligned}
|
||||||
|
y_t &= \alpha^t y_0 + \sum_{i=0}^{t-1} \alpha^i \xi_{t-i-1} - 0.5 \sum_{i=1}^{t-1} \alpha^{i-1} \xi_{t-1-i} \\
|
||||||
|
&= \alpha^t y_0 + \sum_{i=0}^{t-1} \alpha^i \xi_{t-i-1} - 0.5 \sum_{i=0}^{t-2} \alpha^i \xi_{t-i-2}
|
||||||
|
\end{aligned}
|
||||||
|
$$
|
||||||
|
Теперь мы можем выразить любое значение $y_t$ через прошлые значения ошибок, поэтому процесс будет обратимым для любого $\alpha$.
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|
|
||||||
|
|
@ -389,6 +389,23 @@ $S_x$ -- размер одного пикселя светочувствител
|
||||||
|
|
||||||
\textbf{Детекторы} -- обнаружение. \textbf{Дескрипторы} -- обнаружение и описание. Мы всё будем называть детекторами. Хороший алгоритм должен быть инвариантен к шумам и деформациям.
|
\textbf{Детекторы} -- обнаружение. \textbf{Дескрипторы} -- обнаружение и описание. Мы всё будем называть детекторами. Хороший алгоритм должен быть инвариантен к шумам и деформациям.
|
||||||
|
|
||||||
|
\subsection{Характеристики хорошего детектора}
|
||||||
|
\begin{itemize}
|
||||||
|
\item инвариантность относительно преобразования изображения
|
||||||
|
\begin{enumerate}
|
||||||
|
\item смещения
|
||||||
|
\item поворота
|
||||||
|
\item к изменению масштаба (харрис-, харрис-лаплас+)
|
||||||
|
\item изменению яркости (моравец-, харрис+)
|
||||||
|
\item изменению точки положения камеры
|
||||||
|
\end{enumerate}
|
||||||
|
\item повторяемость (при изменении условийсъёмки)
|
||||||
|
\item локальность (при перекрытии объекта часть признаков должна остаться видимой, например если взять контур и его часть перекроется -- он перестанет детектироваться)
|
||||||
|
\item репрезентативность (кол-во признаков должно быть достаточным для детектировании даже на небольшом масштабе)
|
||||||
|
\item Точность
|
||||||
|
\item Эффективность (не требовательны к вычислительным ресурсам и времени)
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
\subsection{Детектор Моравеца}
|
\subsection{Детектор Моравеца}
|
||||||
Самый простой детектор углов на изображении.
|
Самый простой детектор углов на изображении.
|
||||||
\begin{figure}[H]
|
\begin{figure}[H]
|
||||||
|
|
@ -461,5 +478,86 @@ Features from Accelerated Test
|
||||||
Строим дерево решений. Множество которое соответствует узлу дерева разбивается на подмножества и на основе этих деревьев не рассматриваем всё, а проходим по дереву и находим характерные точки.
|
Строим дерево решений. Множество которое соответствует узлу дерева разбивается на подмножества и на основе этих деревьев не рассматриваем всё, а проходим по дереву и находим характерные точки.
|
||||||
|
|
||||||
\subsection{Детектор MSER}
|
\subsection{Детектор MSER}
|
||||||
|
Maximally stable extremal regions
|
||||||
|
|
||||||
|
не будут исчезать при изменении порогового значения. То есть превращаем изображение не в градации серого, а в ч/б (бинаризация). Варьируем порог и в итоге смотрим какие участки исчезают, а те что остались -- наиболее устойчивые.
|
||||||
|
$$ I_g(x,y) =
|
||||||
|
\begin{cases}
|
||||||
|
255, I(x,y)>g\\
|
||||||
|
0, I(x,y)\leq g
|
||||||
|
\end{cases}, g \in [0,255]
|
||||||
|
$$
|
||||||
|
g -- порог бинаризации. варьируем, строим дерево
|
||||||
|
(1)
|
||||||
|
светлая буква на тёмном фоне. Можем это изображение масштабировать. Если мы делаем маленький порог ($g=50$) всё изображение светлое, иногда только точки будут тёмные, увеличивая порог видим разное поведение характерных точек. Если точки совсем пропали - нет смысла ни масштабировать ни менять пороги. Плохо выраженные точки при изменённых порогах не попадут в стабильные характерные точки.
|
||||||
|
|
||||||
|
Применяется чаще всего для градаций серого, хотя цветные тоже иногда делят на компоненты и применяют этот метод.
|
||||||
|
|
||||||
|
\subsection{Дескрипторы}
|
||||||
|
\subsubsection{SIFT}
|
||||||
|
Scale Invariant Feature Transform. Размываем начальное изображение гауссовым ядром
|
||||||
|
$$\mathbb{G}(x, y, \sigma) = \frac{1}{2\pi\sigma^2}e^{\frac{-(x^2+y^2)}{2\pi^2}}$$
|
||||||
|
|
||||||
|
$$\mathbb{L}(x,y,\sigma) = I(x, y)*\mathbb{G}(x,y,\sigma)$$
|
||||||
|
|
||||||
|
размываем не всё изображение, а, например, окрестность 16х16 пикселей. Для каждого из пикселей определяем магнитуды и направление, задаём веса (чтобы какие-то учитывались больше, а какие-то меньше).
|
||||||
|
(2)
|
||||||
|
по каждому из пикселей таких квадратов вычисляем амплитуду градиента и направление, строим гистограммы по каждому квадрату. ориентация ключевой точки
|
||||||
|
$$m(x,y)=\sqrt{(L(x+1, y)-L(x-1, y))^2+(L(x, y+1)-L(x, y-1))^2}$$
|
||||||
|
направление ориентации можно вычислить как
|
||||||
|
$$\theta(x,y)=\arctan\left(\frac{L(x, y+1)-L(x, y-1)}{L(x+1, y)-L(x-1, y)}\right)$$
|
||||||
|
(3)
|
||||||
|
Выбираем порог, который отсеит маленькие значения (обычно берут 80\%) Всё что выше будет потенциальными характерными точками изображения. на основе гистаграммы можем построить некий усреднённый дескриптор квадратов 8х8 (можно отсортировать для ускорения). Квадраты 8х8 можем представить как набор градиентов
|
||||||
|
(4)
|
||||||
|
|
||||||
|
\begin{itemize}
|
||||||
|
\item [+] инвариантность относительно масштаба, поворота, смещения
|
||||||
|
\item [+] устойчивость к шуму
|
||||||
|
\item [+] вычислительная эффективность
|
||||||
|
\end{itemize}
|
||||||
|
\subsubsection{SURF}
|
||||||
|
speeded-up robust features
|
||||||
|
Также как и в предыдущем -- инвариантен к поворотам и масштабированию. Используется матрица гёссе - гессиан (вторые производные).
|
||||||
|
(5)
|
||||||
|
сигма - это не размытие, а масштаб. Использование гессиана позволяет определять характерные точки инвариантные к повороту и масштабированию, вычисляем точки, которые не будут меняться. Детерминант будет достигать экстремумов в точках с максимальным изменением яркости.
|
||||||
|
|
||||||
|
Делим изображение на квадраты (например, 8х8)
|
||||||
|
(6)
|
||||||
|
вычисляем для каждого квадрата градиент, можно использовать свёртку с примитивами Хаара и строим функцию различия (где наибольшее и где наименьшее). где меньше там примитив хаара хуже описывает объект. в итоге описываем отдельные части изображения.
|
||||||
|
|
||||||
|
\subsubsection{GLOH}
|
||||||
|
Gradient location orientation histogram -- модификация SIFT, но здесь окрестности не квадратные, а рассматриваются разные сектора.
|
||||||
|
(7)
|
||||||
|
и для каждого сектора делаем тоже самое про градиент как в СИФТ. радиусы 6, 11, 15 пикселей. В каждом таком секторе строим свой набор (карту) градиентов. Получается 17 шт. строим и определяем наибольшие с порогом 0,8 и суммируем те, которые прошли порог.
|
||||||
|
|
||||||
|
В отличие от сифт учитывает характерные точки, попавшие на границы разделения квадратами
|
||||||
|
|
||||||
|
\subsubsection{DAISY}
|
||||||
|
модификация SIFT рассматриваем окрестности в виде окружностей (не секторов как гло)
|
||||||
|
(8)
|
||||||
|
окрестности внахлёст и в некоторых задачах лучше подходит, но будет гораздо хуже по вычислительной сложности.
|
||||||
|
|
||||||
|
$$I(x,y)$$
|
||||||
|
|
||||||
|
\section{Вопросы к РК}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item Все детекторы
|
||||||
|
\item Методы отслеживания
|
||||||
|
\begin{enumerate}
|
||||||
|
\item рекурс
|
||||||
|
\item не рекурс
|
||||||
|
\item вычитание фона
|
||||||
|
\item многоуровн движения
|
||||||
|
\item параметрического движения
|
||||||
|
\begin{enumerate}
|
||||||
|
\item линейный сдвиг,
|
||||||
|
\item поворот,
|
||||||
|
\item приближение,
|
||||||
|
\item комбинации
|
||||||
|
\end{enumerate}
|
||||||
|
\item лукас-канаде
|
||||||
|
\end{enumerate}
|
||||||
|
\end{enumerate}
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|
||||||
|
|
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|
|
|
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|
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id="text1064-3"><tspan
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id="text1068-6"><tspan
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<text
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<path
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<path
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d="m 133.61458,25.135417 v 5.291666 h 11.90625 l 2.64583,-2.645834 -2.64583,-2.645832 h -11.90625"
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<path
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<path
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<path
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id="text1132-2"><tspan
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id="tspan1130-3"
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x="133.61458"
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style="stroke-width:0.264583">n</tspan></text>
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<text
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xml:space="preserve"
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style="font-size:4.9389px;line-height:1.25;font-family:'PT Astra Serif';-inkscape-font-specification:'PT Astra Serif';stroke-width:0.264583"
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x="144.19791"
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id="text1136-7"><tspan
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id="tspan1134-5"
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x="144.19791"
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y="37.041668"
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style="stroke-width:0.264583">4бит</tspan></text>
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<text
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xml:space="preserve"
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style="font-size:4.9389px;line-height:1.25;font-family:'PT Astra Serif';-inkscape-font-specification:'PT Astra Serif';stroke-width:0.264583"
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x="161.39583"
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id="text1068-6-9"><tspan
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|
x="161.39583"
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y="13.22917"
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style="stroke-width:0.264583">АЦП</tspan></text>
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<path
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style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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|
d="m 158.75,11.906249 2.64583,-2.645832 h 11.90625 v 5.291666 H 161.39583 L 158.75,11.906249"
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<path
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style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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|
d="m 178.53459,33.191244 -2.64583,-1.322919"
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id="path1128-0-9" />
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<text
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x="179.8575"
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y="33.191242"
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id="text1132-2-7"><tspan
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x="179.8575"
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y="33.191242"
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style="stroke-width:0.264583">n</tspan></text>
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xml:space="preserve"
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style="font-size:4.9389px;line-height:1.25;font-family:'PT Astra Serif';-inkscape-font-specification:'PT Astra Serif';stroke-width:0.264583"
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id="text1136-7-6"><tspan
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|
x="182.55045"
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style="stroke-width:0.264583">4бит</tspan></text>
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<path
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style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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d="M 154.78125,11.90625 H 158.75"
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id="path1326" />
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<path
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style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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d="m 173.30208,11.90625 h 3.96875 l 0,27.78125"
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<text
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xml:space="preserve"
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x="99.086113"
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id="text1332"><tspan
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id="tspan1330"
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x="99.086113"
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y="45.354336"
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style="stroke-width:0.264583">корректирующая логика</tspan></text>
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<rect
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<path
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<path
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Loading…
Reference in New Issue