I  am trying to create a program in python where I have to calculate f(x) and the gradient of f(x) for N number of matrices. Let s assume that f(x) = 1/2 * transpose(x)*Q*x+transpose(q)*x  I remember that the gradient will be  Q*x+q  I vaguely remember that I can calculate the f(x) as the sum of the Q*x?? I remember there was a type i could use instead of f(x) = 1/2 * transpose(x)*Q*x+transpose(q)*x  Do I remember correctly?
It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$?
GNU find and masking the {} for some shells - which? The man page for GNU find states:    -exec command ;     [...] The  string `{}'  is  replaced  by the current      file name being processed everywhere it occurs in the      arguments to the command, not just in arguments where      it is alone, as in some  versions  of  find.     Both  of  these  constructions might need to be escaped      (with a `\') or quoted to protect them from expansion      by the shell.     That's from the man to find (GNU findutils) 4.4.2.   Now I tested this with bash and dash, and both don't need to have the {} being masked. Here is a simple test:  find /etc -name "hosts" -exec md5sum {} \;    Is there a shell, for which I really need to mask the braces? Note, that it doesn't depend upon whether the file found contains a blank (invoked from bash):   find ~ -maxdepth 1 -type d -name "U*" -exec ls -d {} \;  /home/stefan/Ubuntu One   This changes if the found file is passed to a subshell:  find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d {}' \;  ls: cannot access /home/stefan/Ubuntu: No such file or directory ls: cannot access One: No such file or directory   which can be solved by:  find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d "$0"' {} \;   in contrast to:   find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d "{}"' \;  /home/stefan/Ubuntu One   but that's not what the man page is talking about, is it? So which shell treats {} in a different way? Theorem. Let $(X,\mathcal B,\mu)$ a finite measure space, where $\mu$ is a positive measure. Let $\mathcal A\subset \mathcal B$ an algebra generating $\cal B$. Then for all $B\in\cal B$ and $\varepsilon&gt;0$, we can find $A\in\cal A$ such that $$\mu(A\Delta B)=\mu(A\cup B)-\mu(A\cap B)&lt;\varepsilon.$$  I don't think there is a proof in this site. It's a useful result for several reasons:  We know what the algebra generated by a collection of sets is, but not what the generated $\sigma$-algebra is. The map $\rho\colon \cal B\times\cal B\to \Bbb R_+$, $\rho(A,A')=\mu(A\Delta A')$ gives a pseudo-metric on $\cal B$. This makes a link between generating for an algebra and dense for the pseudo-metric. We say that a $\sigma$-algebra is separable if it's generated by a countable class of sets. In this case, the algebra generated by this class is countable. An with the mentioned result, we can show that $L^p(\mu)$ is separable for $1\leq p&lt;\infty$, which makes a link between the two notions. In ergodic theory, we have to test mixing conditions only an a generating algebra, not on all the $\sigma$-algebra. The result of ls * , ls ** and ls *** I know using the command ls will list all the directories. But what does the ls * command do ? I used it and it just lists the directories. Does the star in front of ls mean how deep it will list the directories? Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it... Is errno thread-safe? I have a netbook with an AZERTY layout. I've changed it to "bépo" to try it, but now I've reset it to a french layout.  While all the apps have taken the change into account, Ubuntu's login manager still uses bépo, making entering passwords a challenge. I've enabled the virtual keyboard for the time being so that I could login again.  I don't remember what I had done in the first place to switch the login screen to bépo, but now I can't switch it back.    EDIT : In the keyboard settings page, if I click "use system defaults", then everything is in bépo ! Where is this different keyboard layout set ?  ANOTHER EDIT : Here's what did not work :   Changing the layout in settings using the "use system defaults" checkbox in settings sudo dpkg-reconfigure keyboard-configuration changing it in Xconf adding a line in /etc/lightdm/lightdm.conf  sudo dpkg-reconfigure locales slaming head against desk dpkg-reconfigure lightdm sudo gsettings set org.gnome.libgnomekbd.keyboard layouts "['fr']" combinations of the above     Is it possible to relaunch the keyboard configuration tool that's in ubuntu's setup ? The thing has automatic layout detection and it changes the setting everywhere. Within 300 km of Tokyo: Where for flora, landscape, nature? Are there tips and tricks to overcome a fear of flying? Are there tips and tricks for people with fear of flying that can makes them have a more pleasant experience when flying? I know drugs can do magic, and . I'm ideally after official advice and recommendations, but other tips and tricks would be nice as well. Single word for floating dust visible in sunlight Is there a single word used in English for the visibility of dust particles floating in a stream of sunlight?     shutterstock.com Elevated command line prompt can't access shared drives I map a share from another machine using my user account. I launch an elevated command prompt (cmd.exe, right click, Run as administrator). Navigating to shared drive (Z:) results in:   The system cannot find the drive specified  Now if I open a non elevated command prompt, I can navigate to Z: just fine. Intuitive explanation of binomial coefficient formula Regarding the formula for binomial coefficients:  $$\binom{n}{k}=\frac{n(n-1)(n-2)\cdots(n-k+1)}{k!}$$  the professor described the formula as first choosing the $k$ objects from a group of $n$, where order matters, and then dividing by $k!$ to adjust for overcounting.  I understand the reasoning behind the numerator but don't understand why dividing by $k!$ is what's needed to adjust for overcounting. Can someone please help me understand how one arrives at $k!$? Thanks. How to plot stacked bar plot inside table? I have following code in Latex. Which plots only one data series (data2). I would like to plot staked bar plot inside table for both data1 and data2 with different colours.  Any ideas.?  Many thanks.  \documentclass{article} \usepackage{booktabs} \usepackage{multirow} \usepackage{pgfplotstable} \usepackage{filecontents}  % The data \begin{filecontents}{data.txt} accession,data1,data2 C1,150708.4564,481.0388003 C2,49652.53112,275.2190163 C3,37379.1284,58.85806921 C4,34165.85698,26.06571636 C5,30856.19158,35.96802428 C6,15204.22768,26.71594573 \end{filecontents}   \pgfplotstableread[col sep=comma]{data.txt}\data  \newcommand{\errplot}{% \begin{tikzpicture}[trim axis right] \begin{axis}[y=-\baselineskip,   scale only axis,   width=5cm,   enlarge y limits={abs=0.5},   axis y line*=middle,   ytick=\empty,   axis x line*=bottom,   xbar,   bar width=1.5ex,   xmin=0,   visualization depends on=x \as \rawx,   nodes near coords,   every node near coord/.style={   anchor=east,   shift={(axis direction cs:-\rawx,0)}   }  ] %   \addplot [draw=black, fill=red]  table [x=data2,y expr=\coordindex]{\data}; \end{axis} \end{tikzpicture}% }  \begin{document}  % Get number of rows in datafile  \pgfplotstablegetrowsof{\data} \let\numberofrows=\pgfplotsretval  % Print the table \pgfplotstabletypeset[columns={accession,data1,data2},   % Booktabs rules   every head row/.style={before row=\toprule,after row=\midrule},   every last row/.style={after row=[3ex]\bottomrule},   % Set header name   columns/accession/.style={string type,column type=l,column name=accession},   columns/data1/.style={string type,column type=l,column name=data1},    columns/data2/.style={     column name={Data2},     assign cell content/.code={% use \multirow for Z column:    \ifnum\pgfplotstablerow=0    \pgfkeyssetvalue{/pgfplots/table/@cell content}    {\multirow{\numberofrows}{6.5cm}{\errplot}}%    \else    \pgfkeyssetvalue{/pgfplots/table/@cell content}{}%    \fi   }  }, ]{\data} \end{document} Partition on sublists beginning with a certain marker elements I'm learning about private/public IPs, port forwarding and NAT, and still fail to see the answer to a simple question:  Suppose two users on the same network are communicating with a single server outside their network (say, me &amp; my wife send http requests to yahoo.com).  The server sees both users as a single public ip, and often - as in this case - communicating on the same port.  How does the router route the packets according to the two different connections? Is there any routing info inside the packet beyond ip/port?  Is there some 'session table' maintained somewhere? By whom and what exactly does it include? and is such interpretation the norm?  When something went from 4 units to 8 units, most authoritative sources seem to agree with the use of "a two-fold increase", even though what was actually increased is more like "one-fold", i.e. the original quantity.  But if the "two-fold increase" is the correct usage, why most people seem to interpret "a 100% increase" the same thing? Why bother with the dual problem when fitting SVM? How to delete file with this name on linux: -]???????q Somehow a file named -]???????q got created on my terminal. I tried  rm -f "-]???????q"  (in double quotes), but it did not get deleted. (Error::  rm: invalid option -- ]).  How do I delete it? How may I reference the script tag that loaded the currently-executing script? Overleaf does not compile after using Biblatex I have my PhD deadline on Monday and disaster has struck at the very last minute! Any assistance would be eternally appreciated.  I'm using Overleaf (v2) to write my thesis - it's a very large file tree containing multiple .tex files.  Everything was compiling fine, until I decided to experiment and use:  \usepackage{biblatex}   It compiled with this included but looked odd, so I deleted the line again. However, now it does not compile - despite the document being exactly the same as before the problem began. Are locks unnecessary in multi-threaded Python code because of the GIL? If you are relying on an implementation of Python that has a Global Interpreter Lock (i.e. CPython) and writing multithreaded code, do you really need locks at all?  If the GIL doesn't allow multiple instructions to be executed in parallel, wouldn't shared data be unnecessary to protect?  sorry if this is a dumb question, but it is something I have always wondered about Python on multi-processor/core machines.    same thing would apply to any other language implementation that has a GIL.