Does anyone know how to modify the following string in order to display the two-lines bracket?
str = '$$c_i =\{\begin{array}{l l} 1 \quad L\left(Q_i\right) < 0 \\ 0 \quad L\left(Q_i\right) \geq 0 \\ \end{array}$$';
The current output is the following:
The sign '{' has to embrace both rows (1 and 0).
$$c_i =\begin{cases} 1 & L\left(Q_i\right) < 0 \\
0 & L\left(Q_i\right) \geq 0
\end{cases}$$
The tex file should have \usepackage{amsmath} in the preamble.
This is derived from Niall Murphy's answer, "tidied up" a bit:
\[
c_i =
\begin{cases}
1 & L (Q_i) < 0 \\
0 & L (Q_i) \geq 0
\end{cases}
\]
Note that the "\" becomes "\\", and I've removed the \left and \right parenthesis modifiers, which introduce unwanted (I think) space between L and (.
Try add \left before \{ and \rigth. at the end.
It should look like
$$\alpha_t = \left \{ {{\sqrt{\frac1N},\; t = 0 } \atop {\sqrt{\frac2N},\; t \ne 0 } } \right.$$
or
$$
\left\{\begin{tabular}{l} \textbf{Y} = 0,299\textbf{R} + 0,587\textbf{G} + 0,114\textbf{B} \\ \textbf{Cb} = 128 + 0,5\textbf{R} - 0,418688\textbf{G} - 0,081312\textbf{B} \\ \textbf{Cr} = 128 - 0,168736\textbf{R} - 0,331264\textbf{G} - 0,53\textbf{B} \end{tabular} \right.
$$
Related
I wrote a wrapped equation in overleaf:
\begin{equation}
\begin{aligned}
\y & = \argmin_{\y'} \sum_{i,j}\W_{ij}||\y'_i - \y'_j||_2^2 \\
& = \argmin_{\y'} \sum_{i,j}(\y'_i - \y'_j)^2\W_{ij} \\
& = \argmin_{\y'} \sum_{i,j}(\y'_i^2 + \y'_j^2 - 2\y'_i\y'_j)\W_{ij} \\
& = \argmin_{\y'} \sum_{i,j}\y'_i^2\W_{ij} + \sum_{i,j}\y'_j^2\W_{ij} - 2\sum_{i,j}\y'_i\y'_j\W_{ij} \\ & = \argmin_{\y'} \sum_{i}\y'_i^2D_{ii} + \sum_{j}\y'_j^2D_{jj} - 2\sum_{i,j}\y'_i\y'_j\W_{ij} \\ & = \argmin_{\y'} 2 (\sum_{i}\y'_i^2D_{ii} - \sum_{i,j}\y'_i\y'_j\W_{ij}) \\
& = \argmin_{\y'} 2 {\y'}^\top \L{\y'} \\
\end{aligned}
\end{equation}
The overleaf shows that there are three "double superscript" error in this code, what is that and how can I fix this (although I can compile it successfully)?
I expect to find the solution to this problem.
A double sub-/superscript error occurs when you have more than one sub-/superscript associated with an element. An example is $x^2^2$ which can be interpreted in two ways: ${x^2}^2$ or $x^{2^2}$. Mathematically they mean the same, but from a typesetting point of view they are interpreted differently:
The first - ${x^2}^2$ - sets both exponents in \scriptstyle (so they're the same size) while the second sets the exponents in staggering (reducing) sizes (first one uses \scriptstyle while the second uses \scriptscriptstyle). This difference in typesetting is rather pushed to the user to fix to avoid confusion or misinterpreting what the result should look like. A similar concept holds for subscripts (like $x_2_2$) and combinations of scripts (like `$x_2^2_2$).
What is hidden in your is the use of a prime (like $y'$) which is similar to $y^\prime$:
$x' = x^\prime \neq x\prime$
As such, $y'^2$ is similar to $y^\prime^2$ which is interpreted as a double superscript, causing the error you see.
The way around it is to appropriately group the elements to denote the way you want it represented in output. In your case, this is most likely ${y'}^2$. I've done that below, with some adjustments to other elements:
\documentclass{article}
\usepackage{mathtools}
% https://tex.stackexchange.com/q/5223/5764
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclarePairedDelimiter{\norm}{\|}{\|}
\newcommand{\y}{\mathcal{Y}}
\newcommand{\W}{\mathcal{W}}
\begin{document}
\begin{equation}
\begin{aligned}
\y & = \argmin_{\y'} \sum_{i, j} \W_{ij} \norm[\big]{ \y'_i - \y'_j }_2^2 \\
& = \argmin_{\y'} \sum_{i, j} \bigl(\y'_i - \y'_j \bigr)^2 \W_{ij} \\
& = \argmin_{\y'} \sum_{i, j} \bigl( {\y'}_i^2 + {\y'}_j^2 - 2 \y'_i \y'_j \bigr) \W_{ij} \\
& = \argmin_{\y'} \sum_{i, j}{\y'}_i^2 \W_{ij} + \sum_{i, j} {\y'}_j^2 \W_{ij} - 2\sum_{i, j} \y'_i \y'_j \W_{ij} \\
& = \argmin_{\y'} \sum_i {\y'}_i^2 D_{ii} + \sum_j {\y'}_j^2 D_{jj} - 2 \sum_{i, j} \y'_i \y'_j \W_{ij} \\
& = \argmin_{\y'} 2 \biggl( \sum_i {\y'}_i^2 D_{ii} - \sum_{i, j} \y'_i \y'_j \W_{ij} \biggr) \\
& = \argmin_{\y'} 2 {\y'}^\top \L \y'
\end{aligned}
\end{equation}
\end{document}
I want the variables and signs aligned in a set of equations.
Desired output:
What I am trying in Mathjax:
\[
\begin{align}
2&x_1 - x_2 &+ 1.5&x_3 &= 8 \\
&x_1 &- 4&x_3 &= -1
\end{align}
\]
What I got:
So, what do I have to do to have the same alignment as in the "desired output" image?
There are a number of ways to achieve this. Below I use an array (with appropriate stretch and spacing), alignat and align coupled with eqparbox for measuring similarly-tagged boxes (this latter approach requires two compilations with every change in the largest element associated with every <tag>):
\documentclass{article}
\usepackage{amsmath,eqparbox}
%\usepackage{xparse}% If you have LaTeX2e < 2020-10-01
% https://tex.stackexchange.com/a/34412/5764
\makeatletter
% \eqmathbox[<tag>][<align>]{<math>}
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
\IfValueTF{#1}
{\def\eqmathbox###1##2{\eqmakebox[#1][#2]{$##1##2$}}}
{\def\eqmathbox###1##2{\eqmakebox{$##1##2$}}}
\mathpalette\eqmathbox#{#3}
}
\makeatother
\begin{document}
\[
\renewcommand{\arraystretch}{1.2}
\setlength{\arraycolsep}{0pt}
\begin{array}{ r c r c r c r }
2 x_1 & {}-{} & x_2 & {}+{} & 1.5 x_3 & {}={} & 8 \\
x_1 & & & {}-{} & 4 x_3 & {}={} & -7
\end{array}
\]
\begin{alignat*}{4}
2 x_1 & {}-{} & x_2 & {}+{} & 1.5 x_3 = {} && 8 \\
x_1 & & & {}-{} & 4 x_3 = {} && -7
\end{alignat*}
\begin{align*}
\eqmathbox[x1][r]{2 x_1} - \eqmathbox[x2][r]{x_2} + \eqmathbox[x3][r]{1.5 x_3} &= \eqmathbox[c][r]{8} \\
\eqmathbox[x1][r]{ x_1} \phantom{{}-{}} \eqmathbox[x2][r]{} - \eqmathbox[x3][r]{4 x_3} &= \eqmathbox[c][r]{-7}
\end{align*}
\end{document}
All yield similar output:
I have one flalign environment, so columns are aligned same way whole page. I need \subsections inside this flalign, so I used \intertext. And I need \label these \subsections. And thats where I failed. It \label first equation after \subsection but not \subsection itself or error occurs.
Image:
When I tried to use more flalign environments and place subsections between them they were not aligned same way and it looked terible.
Thanks for help.
\begin{flalign}
&\text{Značení: } &&X\sim \text{Exp($\lambda$)} &&
\\
&\text{Parametry: } &&\lambda > 0 &&
\\
&\text{Nosič: } &&X \in (0,\infty) &&
\\
&\text{Hustota: } &&f(x)=
\begin{cases}
\lambda e^{-\lambda x} & x>0
\\
0 & x\leq 0
\end{cases}
\\
&\text{Distribuční funkce: } &&F(x)=
\begin{cases}
1-e^{-\lambda x} & x>0
\\
0 & x\leq 0
\end{cases} &&
\\
&\text{Střední hodnota: } && \E X = \frac{1}{\lambda} &&
\\
&\text{Rozptyl: } && \var X = \frac{1}{\lambda^2} &&
\\
\intertext{\subsection{Weibullovo rozdělení}}\label{priloha:weibdist}
&\text{Značení: } &&X\sim \text{Weib($\alpha$, $\beta$)}&&
\\
&\text{Parametry: } &&\text{$\alpha$, $\beta>0$}&&
\\
&\text{Nosič: } &&X \in \langle 0,\infty)&&
\\
&\text{Hustota: } &&f(x)=
\begin{cases}
\alpha \beta^\alpha x^{\alpha-1} e^{-(\beta x)^\alpha} & x\geq 0
\\
0 & x< 0
\end{cases}&&
\\
&\text{Distribuční funkce: } &&F(x)=
\begin{cases}
1-e^{-(\beta x)^\alpha} & x\geq 0
\\
0 & x< 0
\end{cases}
\\
&\text{Střední hodnota: } &&\E X = \frac{1}{\beta} \Gamma\left(1+\frac{1}{\alpha}\right)
\\
&\text{Rozptyl: } &&\var X = \frac{1}{\beta^2} \left\lbrace\Gamma \left(1+\frac{2}{\alpha}\right)-\left[\Gamma\left(1+\frac{1}{\alpha}\right)\right]^2\right\rbrace
\\
\intertext{\subsection{Gama rozdělení}}\label{priloha:gammadist}
&\text{Značení: } &&X\sim \Gamma(\alpha,\;\beta)&&
\\
&\text{Parametry: } &&\alpha,\; \beta > 0
\\
&\text{Nosič: } &&X \in (0,\infty)
\\
&\text{Hustota: } &&f(x)=
\begin{cases}
\frac{\alpha^\beta}{\Gamma(\beta)}x^{\beta-1}e^{-\alpha x} & x>0
\\
0 & x\leq 0
\end{cases}
\\
&\text{Střední hodnota: } && \E X = \frac{\beta}{\alpha}
\\
&\text{Rozptyl: } && \var X = \frac{\beta}{\alpha^2}
\end{flalign}
From the images you show, I would suggest to use a tabular with a fixed width instead. This will allow you to break for things like subsections:
\documentclass[12pt,fleqn]{article}
\usepackage{amsmath}
\usepackage{array}
\begin{document}
\subsection{First part}
\noindent%
{%
\abovedisplayskip=-\baselineskip
\belowdisplayskip=-.5\baselineskip
\begin{tabular}{#{}p{.3\textwidth}#{}p{.7\textwidth}#{}}
First equation: & \begin{equation} a+b+c=d \end{equation}\\
Second equation: & \begin{equation} a+b+c=d \end{equation}\\
\end{tabular}
}
\subsection{Second part}
\label{sub:1}
\noindent%
{%
\abovedisplayskip=-\baselineskip
\belowdisplayskip=-.5\baselineskip
\begin{tabular}{#{}m{.3\textwidth}#{}m{.7\textwidth}#{}}
Next equation: & \begin{equation} a+b+c+45867+ddlk=d \end{equation}\\
Another equation: & \begin{equation} a+b+c+sdfsdf+565=d \end{equation}\\
\end{tabular}
}
Here alignment is working, but labeling not. Second part is \ref{sub:1}. It referes to 3th equation instead of subsection.
\end{document}
Today I see a beautiful equation:
(Sorry for cannot put the pic directly, I'm new here.)
I don't know how to write it in Tex. I try my best to write like following:
\begin{equation}
\begin{aligned}
r_{t}=\left\{
\begin{array}{crl}
1+\dfrac{\bar{R}_{Q}(t+\Delta t)-R_{Q}(t)}{2\Delta t/T_{single}}\; &+0\qquad &if\,\bar{R}_{Q}(t+\Delta t)>0,\\
0 \; &-P\qquad &if\,R_{Q}(t)\neq 0\wedge R_{Q}(t+\Delta t)=0,\\
0\; &+0\qquad &if\,R_{Q}(t)=0
\label{rforProtRwd}
\end{array}
\right.
\\
\underbrace{\hspace{10em}}_{=:r_{t}^{(1)}}\hspace{1em}\underbrace{\hspace{2em}}_{=:r_{t}^{(2)}}\hspace{17em}
\end{aligned}
\end{equation}
It is obviously that the underbrace is a little far from the main part of the equation. And actually both the method I write and the result are ugle.
So I wonder if there are some better ways to write it.
Hoping someone can help.
Here is an accurate \underbrace that matches the content within a cases environment.
\documentclass{article}
\usepackage{mathtools,eqparbox}
\begin{document}
\begin{align}
r_t = \begin{cases}
\eqmakebox[LHS]{$1 + \dfrac{\bar{R}_Q(t + \Delta t) - R_Q(t)}{2 \Delta t / T_{\text{single}}}$}
+ 0 & \text{if $\bar{R}_Q(t + \Delta t) > 0$}, \\
\eqmakebox[LHS]{$0$}
- P & \text{if $R_Q(t) \neq 0 \wedge R_Q(t + \Delta t) = 0$}, \\
\eqmakebox[LHS]{$0$}
+ 0 & \text{if $R_Q(t) = 0$}
\end{cases} \\[-1.2\normalbaselineskip]
\underbrace{\eqmakebox[LHS]{\mathstrut}}_{=:r_t^{(1)}}
\underbrace{\mathstrut\phantom{{} - P}}_{\mathclap{=:r_t^{(2)}}}
\quad\phantom{\text{if $R_Q(t) \neq 0 \wedge R_Q(t + \Delta t) = 0$},} \nonumber
\end{align}
\end{document}
I want to left align a block of equations. The equations in the block itself are aligned, but that's not related at all to my question! I want to left align the equations rather than have them centered all the time, because it looks dumb with narrow centered equations.
Example, I want to left align this
\begin{align*}
|\vec a| &= \sqrt{3^{2}+1^{2}} = \sqrt{10} \\
|\vec b| &= \sqrt{1^{2}+23^{2}} = \sqrt{530} \\
\cos v &= \frac{26}{\sqrt{10} \cdot \sqrt{530}} \\
v &= \cos^{-1} \left(\frac{26}{\sqrt{10} \cdot \sqrt{530}}\right) \\
v &= \uuline{69.08...\degree}
\end{align*}
but also this
\begin{align*}
f(x) = -1.25x^{2} + 1.5x
\end{align*}
How is this done? If it's even possible.
Try to use the fleqn document class option.
\documentclass[fleqn]{article}
(See also http://en.wikibooks.org/wiki/LaTeX/Basics for a list of other options.)
You can use \begin{flalign}, like the example bellow:
\begin{flalign}
&f(x) = -1.25x^{2} + 1.5x&
\end{flalign}
Try this:
\begin{flalign*}
&|\vec a| = \sqrt{3^{2}+1^{2}} = \sqrt{10} & \\
&|\vec b| = \sqrt{1^{2}+23^{2}} = \sqrt{530} &\\
&\cos v = \frac{26}{\sqrt{10} \cdot \sqrt{530}} &\\
&v = \cos^{-1} \left(\frac{26}{\sqrt{10} \cdot \sqrt{530}}\right) &\\
\end{flalign*}
The & sign separates two columns, so an & at the beginning of a line means that the line starts with a blank column.
The fleqn option in the document class will apply left aligning setting in all equations of the document. You can instead use \begin{flalign}. This will align only the desired equations.