commit e06634dcfe24f90f628dd1e6d600b9f43ba93db5
parent efb623a3630a0692cd686e6bf9ee3f53d7fdc558
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Wed, 20 Jun 2018 15:38:09 +0300
Add main ARMA slide.
Diffstat:
2 files changed, 182 insertions(+), 160 deletions(-)
diff --git a/arma-slides.org b/arma-slides.org
@@ -54,7 +54,7 @@
Недостатки: периодичность, вероятностная сходимость, линейная теория волн.
-** Цель и задачи
+** Постановка задачи
Разработать /без предположений линейной теории волн/
- трехмерную имитационную модель морского волнения,
@@ -62,22 +62,83 @@
- программный комплекс для систем с общей и распределенной памятью.
* Трехмерная модель АРСС
-** Основные формулы
+
+** Процесс АРСС
+
\begin{equation*}
- \zeta_{i,j,k} =
+ \rectemph{zeta1}{\zeta_{i,j,k}} =
\sum\limits_{l=0}^{p_1}
\sum\limits_{m=0}^{p_2}
\sum\limits_{n=0}^{p_3}
- \Phi_{l,m,n} \zeta_{i-l,j-m,k-n}
+ \rectemph{phi}{\Phi_{l,m,n}} \rectemph{zeta2}{\zeta_{i-l,j-m,k-n}}
+
\sum\limits_{l=0}^{q_1}
\sum\limits_{m=0}^{q_2}
\sum\limits_{n=0}^{q_3}
- \Theta_{l,m,n} \epsilon_{i-l,j-m,k-n}
- ,
- \label{eq:arma-process}
+ \rectemph{theta}{\Theta_{l,m,n}} \rectemph{eps}{\epsilon_{i-l,j-m,k-n}}
\end{equation*}
+#+BEAMER: \vspace{0.5cm}
+
+#+begin_src dot :exports results :file build/arma-pipeline-ru.pdf
+digraph G {
+
+ node [fontname="Open Sans",fontsize=10,margin="0.055,0",shape=box,bgcolor="E5E6E5",style="filled",height="0.37"]
+ graph [nodesep="0.25",ranksep="0.30",rankdir="LR" margin=0]
+ edge [arrowsize=0.66]
+ bgcolor="#F5F6F5"
+
+ acf [label="АКФ"]
+ yule_walker_equations [label="Уравнения\nЮла—Уокера"]
+ nonlinear_equations [label="Нелинейные\nуравнения"]
+ ar_process [label="Процесс\nАР"]
+ ma_process [label="Процесс\nСС"]
+ arma_process [label="Процесс\nАРСС"]
+
+ acf->yule_walker_equations->ar_process->arma_process
+ acf->nonlinear_equations->ma_process->arma_process
+
+}
+#+end_src
+
+#+RESULTS:
+[[file:build/arma-pipeline-ru.pdf]]
+
+#+begin_export latex
+\begin{tikzpicture}[remember picture,overlay]
+\node[fill=none,baseline,anchor=south west,xshift=1.1cm,yshift=-1.75cm]
+ (zetaLabel) at (current page.north west)
+ {\scriptsize{}подъем взволнованной поверхности};
+\node[fill=none,anchor=south east,xshift=-2cm,yshift=-1.75cm]
+ (epsLabel) at (current page.north east)
+ {\scriptsize{}белый шум};
+\node[fill=none,baseline,anchor=north west,below=of phi,yshift=0.2cm]
+ (phiLabel)
+ {\scriptsize{}коэф. АР};
+\node[fill=none,baseline,anchor=north west,below=of theta,yshift=0.2cm]
+ (thetaLabel)
+ {\scriptsize{}коэф. СС};
+\path[->,thick] (zetaLabel.south -| zeta1.north) edge (zeta1.north);
+\path[->,thick] (zetaLabel.south -| zeta2.north west)
+ edge [transform canvas={xshift=2mm}]
+ (zeta2.north west);
+\path[->,thick] (epsLabel.south -| eps.north west)
+ edge [transform canvas={xshift=2mm}]
+ (eps.north west);
+\path[->,thick] (phiLabel.north -| phi.south west)
+ edge [transform canvas={xshift=2.5mm}]
+ (phi.south west);
+\path[->,thick] (thetaLabel.north -| theta.south west)
+ edge [transform canvas={xshift=2.5mm}]
+ (theta.south west);
+\end{tikzpicture}
+#+end_export
+
+*** Note
+:PROPERTIES:
+:BEAMER_ENV: note
+:END:
+
По сравнению с моделью ЛХ
- высоко-производительная,
- непериодическая,
@@ -87,101 +148,19 @@
- трехмерная,
- исследуются трехмерные АКФ, а не спектры.
-** Определение коэффициентов :noexport:
-#+begin_export latex
-\framesubitile{Модель АР}
- \small%
- Решить СЛАУ (трехмерные уравнения Юла---Уокера) относительно $\Phi$:
- \begin{equation*}
- \Gamma
- \left[
- \begin{array}{l}
- \Phi_{0,0,0}\\
- \Phi_{0,0,1}\\
- \vdotswithin{\Phi_{0,0,0}}\\
- \Phi_{p_1,p_2,p_3}
- \end{array}
- \right]
- =
- \left[
- \begin{array}{l}
- K_{0,0,0}-\Var{\epsilon}\\
- K_{0,0,1}\\
- \vdotswithin{K_{0,0,0}}\\
- K_{p_1,p_2,p_3}
- \end{array}
- \right],
- \qquad
- \Gamma=
- \left[
- \begin{array}{llll}
- \Gamma_0 & \Gamma_1 & \cdots & \Gamma_{p_1} \\
- \Gamma_1 & \Gamma_0 & \ddots & \vdotswithin{\Gamma_0} \\
- \vdotswithin{\Gamma_0} & \ddots & \ddots & \Gamma_1 \\
- \Gamma_{p_1} & \cdots & \Gamma_1 & \Gamma_0
- \end{array}
- \right],
- \end{equation*}
- \begin{equation*}
- \Gamma_i =
- \left[
- \begin{array}{llll}
- \Gamma^0_i & \Gamma^1_i & \cdots & \Gamma^{p_2}_i \\
- \Gamma^1_i & \Gamma^0_i & \ddots & \vdotswithin{\Gamma^0_i} \\
- \vdotswithin{\Gamma^0_i} & \ddots & \ddots & \Gamma^1_i \\
- \Gamma^{p_2}_i & \cdots & \Gamma^1_i & \Gamma^0_i
- \end{array}
- \right]
- \qquad
- \Gamma_i^j=
- \left[
- \begin{array}{llll}
- K_{i,j,0} & K_{i,j,1} & \cdots & K_{i,j,p_3} \\
- K_{i,j,1} & K_{i,j,0} & \ddots &x \vdotswithin{K_{i,j,0}} \\
- \vdotswithin{K_{i,j,0}} & \ddots & \ddots & K_{i,j,1} \\
- K_{i,j,p_3} & \cdots & K_{i,j,1} & K_{i,j,0}
- \end{array}
- \right].
- \end{equation*}
-#+end_export
-
-** Определение коэффициентов :noexport:
-#+begin_export latex
-\framesubitile{Модель СС}
- \small%
- Solve non-linear system of equations for $\Theta$:
- \begin{equation*}
- K_{i,j,k} =
- \left[
- \displaystyle
- \sum\limits_{l=i}^{q_1}
- \sum\limits_{m=j}^{q_2}
- \sum\limits_{n=k}^{q_3}
- \Theta_{l,m,n}\Theta_{l-i,m-j,n-k}
- \right]
- \Var{\epsilon}
- \end{equation*}
- via fixed-point iteration method:
- \begin{equation*}
- \theta_{i,j,k} =
- -\frac{K_{0,0,0}}{\Var{\epsilon}}
- +
- \sum\limits_{l=i}^{q_1}
- \sum\limits_{m=j}^{q_2}
- \sum\limits_{n=k}^{q_3}
- \Theta_{l,m,n} \Theta_{l-i,m-j,n-k}.
- \end{equation*}
-#+end_export
+** АКФ морской поверхности
-** Критерии выбора моделей АР и СС
-Использовать модель АР для стоячих волн и модель СС для прогрессивных.
-#+latex: \newline\newline
-Экспериментальный результат:
-- модели расходятся, если делать наоборот;
-- характеристики взволнованной поверхности соответствуют реальным.
+*** Columns
+:PROPERTIES:
+:BEAMER_env: columns
+:END:
-** АКФ морской поверхности
+**** Column 1
+:PROPERTIES:
+:BEAMER_col: 1.00
+:END:
+#+latex: \vspace{-0.5cm}
#+begin_src dot :exports results :file build/acf-pipeline-ru.pdf
digraph G {
@@ -207,6 +186,20 @@ digraph G {
#+RESULTS:
[[file:build/acf-pipeline-ru.pdf]]
+**** Column 2 :noexport:
+:PROPERTIES:
+:BEAMER_col: 0.37
+:END:
+
+\begin{equation*}
+\hat{\gamma} = |\hat{\zeta}|^2
+\end{equation*}
+
+*** Separator
+:PROPERTIES:
+:BEAMER_env: ignoreheading
+:END:
+
*** Columns
:PROPERTIES:
:BEAMER_env: columns
@@ -218,7 +211,6 @@ digraph G {
:BEAMER_col: 0.30
:END:
-#+latex: \vspace{-1cm}
#+header: :width 1.7 :height 1.2 :bg #F5F6F5 :font sans
#+begin_src R :file build/acf-propagating-plain-wave-ru.pdf
source(file.path("R", "common.R"))
@@ -250,7 +242,6 @@ arma.wavy_plot(df, 0, zlim=c(0,0.5), expand=0.5, border=NA)
:BEAMER_col: 0.35
:END:
-#+latex: \vspace{-1cm}
#+header: :width 1.7 :height 1.2 :bg #F5F6F5 :font sans
#+begin_src R :file build/acf-standing-plain-wave-ru.pdf
source(file.path("R", "common.R"))
@@ -281,7 +272,6 @@ arma.wavy_plot(df, 0, zlim=c(-0.05,0.05), expand=0.5, border=NA)
:BEAMER_col: 0.30
:END:
-#+latex: \vspace{-1cm}
#+header: :width 1.7 :height 1.2 :bg #F5F6F5 :font sans
#+begin_src R :file build/acf-propagating-stokes-wave-ru.pdf
source(file.path("R", "common.R"))
@@ -310,66 +300,97 @@ arma.acf_plot(df, 0, zlim=c(0,1.0), expand=0.5, border=NA)
#+RESULTS:
[[file:build/acf-propagating-stokes-wave-ru.pdf]]
-** АКФ морской поверхности :noexport:
+** Определение коэффициентов :noexport:
#+begin_export latex
-\small
-\begin{tikzpicture}[remember picture,overlay]
- \node[fill=spbuWhite2,text width=2.3cm,xshift=1cm,yshift=1.5cm,anchor=west] (waveProfile) at (current page.west) {Формула профиля волны или спектра};
- \node[fill=spbuWhite2,text width=2.0cm,yshift=1.5cm] (bigPoly) at (current page.center) {Полином высокой степени};
- \node[fill=spbuWhite2,text width=2.0cm,xshift=-1cm,yshift=1.5cm,anchor=east] (acfApprox) at (current page.east) {Формула АКФ};
- \draw[->,thick] (waveProfile) to node[above] {\scriptsize теорема} node[below] {\scriptsize Винера---Хинчина} (bigPoly);
- \draw[->,thick] (bigPoly) to node[above] {\scriptsize аппроксимация} node[below] {\scriptsize модельной функцией} (acfApprox);
-\end{tikzpicture}
-\only<1>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-0}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-00}};
-\end{tikzpicture}
-}
-\only<2>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-1}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-00}};
-\end{tikzpicture}
-}
-\only<3>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-3}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-00}};
-\end{tikzpicture}
-}
-\only<4>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-4}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-00}};
-\end{tikzpicture}
-}
-\only<5>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-4}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-00}};
-\end{tikzpicture}
-}
-\only<6>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-4}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-01}};
-\end{tikzpicture}
-}
-\only<7>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-4}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-03}};
-\end{tikzpicture}
-}
-\only<8>{
-\begin{tikzpicture}[remember picture,overlay]
- \node[xshift=-3cm,yshift=-1.5cm,anchor=center] (acf1) at (current page.center) {\includegraphics[scale=0.7]{standing-acf-4}};
- \node[xshift=3cm,yshift=-1.5cm,anchor=center] (acf2) at (current page.center) {\includegraphics[scale=0.7]{propagating-acf-04}};
-\end{tikzpicture}
-}
+\framesubitile{Модель АР}
+ \small%
+ Решить СЛАУ (трехмерные уравнения Юла---Уокера) относительно $\Phi$:
+ \begin{equation*}
+ \Gamma
+ \left[
+ \begin{array}{l}
+ \Phi_{0,0,0}\\
+ \Phi_{0,0,1}\\
+ \vdotswithin{\Phi_{0,0,0}}\\
+ \Phi_{p_1,p_2,p_3}
+ \end{array}
+ \right]
+ =
+ \left[
+ \begin{array}{l}
+ K_{0,0,0}-\Var{\epsilon}\\
+ K_{0,0,1}\\
+ \vdotswithin{K_{0,0,0}}\\
+ K_{p_1,p_2,p_3}
+ \end{array}
+ \right],
+ \qquad
+ \Gamma=
+ \left[
+ \begin{array}{llll}
+ \Gamma_0 & \Gamma_1 & \cdots & \Gamma_{p_1} \\
+ \Gamma_1 & \Gamma_0 & \ddots & \vdotswithin{\Gamma_0} \\
+ \vdotswithin{\Gamma_0} & \ddots & \ddots & \Gamma_1 \\
+ \Gamma_{p_1} & \cdots & \Gamma_1 & \Gamma_0
+ \end{array}
+ \right],
+ \end{equation*}
+ \begin{equation*}
+ \Gamma_i =
+ \left[
+ \begin{array}{llll}
+ \Gamma^0_i & \Gamma^1_i & \cdots & \Gamma^{p_2}_i \\
+ \Gamma^1_i & \Gamma^0_i & \ddots & \vdotswithin{\Gamma^0_i} \\
+ \vdotswithin{\Gamma^0_i} & \ddots & \ddots & \Gamma^1_i \\
+ \Gamma^{p_2}_i & \cdots & \Gamma^1_i & \Gamma^0_i
+ \end{array}
+ \right]
+ \qquad
+ \Gamma_i^j=
+ \left[
+ \begin{array}{llll}
+ K_{i,j,0} & K_{i,j,1} & \cdots & K_{i,j,p_3} \\
+ K_{i,j,1} & K_{i,j,0} & \ddots &x \vdotswithin{K_{i,j,0}} \\
+ \vdotswithin{K_{i,j,0}} & \ddots & \ddots & K_{i,j,1} \\
+ K_{i,j,p_3} & \cdots & K_{i,j,1} & K_{i,j,0}
+ \end{array}
+ \right].
+ \end{equation*}
#+end_export
+** Определение коэффициентов :noexport:
+#+BEAMER: \framesubitile{Модель СС}
+#+BEAMER: \small
+Решить систему нелинейных уравнений
+\begin{equation*}
+ K_{i,j,k} =
+ \left[
+ \displaystyle
+ \sum\limits_{l=i}^{q_1}
+ \sum\limits_{m=j}^{q_2}
+ \sum\limits_{n=k}^{q_3}
+ \Theta_{l,m,n}\Theta_{l-i,m-j,n-k}
+ \right]
+ \Var{\epsilon}
+\end{equation*}
+относительно \(\Theta\) с помощью метода простой итерации:
+\begin{equation*}
+ \theta_{i,j,k} =
+ -\frac{K_{0,0,0}}{\Var{\epsilon}}
+ +
+ \sum\limits_{l=i}^{q_1}
+ \sum\limits_{m=j}^{q_2}
+ \sum\limits_{n=k}^{q_3}
+ \Theta_{l,m,n} \Theta_{l-i,m-j,n-k}.
+\end{equation*}
+
+** Критерии выбора моделей АР и СС :noexport:
+Использовать модель АР для стоячих волн и модель СС для прогрессивных.
+#+latex: \newline\newline
+Экспериментальный результат:
+- модели расходятся, если делать наоборот;
+- характеристики взволнованной поверхности соответствуют реальным.
+
** Верификация модели АРСС
*** Стоячие волны
diff --git a/slides-preamble.tex b/slides-preamble.tex
@@ -16,6 +16,7 @@
\usepackage{colortbl}
\usepackage{tikz}
\usetikzlibrary{shapes}
+\usetikzlibrary{positioning}
\graphicspath{{build/}{graphics/slides/}}
@@ -45,7 +46,7 @@
\newcommand*{\rectemph}[2]{%
\begin{tikzpicture}[baseline=(#1tmp.base),remember picture]
\node[fill=none,inner sep=0mm] (#1tmp) {$\displaystyle\phantom{#2}$};%
- \node[overlay,rectangle,fill=none,ultra thick,draw=markBlue, inner xsep=0.5mm, inner ysep=1mm] (#1) at (#1tmp) {$\displaystyle#2$};%
+ \node[overlay,rectangle,fill=none,ultra thick,draw=none, inner xsep=0.5mm, inner ysep=1mm] (#1) at (#1tmp) {$\displaystyle#2$};%
\end{tikzpicture}
}
