I need to find the derivative wrt ${X}$ of:  $$ f({X}) = \operatorname{tr}( B^{T}X^{T}A^{T}CXD )$$  To make this simpler, I let $E = A^{T}C$, then I have:  $$ f({X}) = \operatorname{tr}( B^{T}X^{T}EXD ) = \operatorname{tr}( DB^{T}X^{T}EX )$$  We can rewrite this using the Frobenius inner product:  $$ f({X}) = XBD^{T}:EX$$  So we can calculate the differential easily now:  $$ df = (dX)BD^{T}:EdX$$  Unfortunately this is where I am stuck.    Perhaps we can rewrite this as:  $$ df = BD^{T}:(dX)^{T} E dX$$  But how do we isolate the dX value?    Edits:  I tried: $(dX)^{T} E dX = \operatorname{tr}( dXdX^{T}E) = \operatorname{tr}( EdXdX^{T}) $ but that isn't getting me anywhere either...
How is the derivative of $\mbox{Trace}\left\{ X^T A X B\right\}$ with respect to matrix $X$ equal to $AXB + A^TXB^T$?  \begin{align}   \nabla_X \ \textrm{Trace}\left\{ X^T A X B\right\} = AXB + A^TXB^T \end{align}  where $A$ and $B$ matrices are given.
Get a resource using getResource() Requirements for a clan war? I am currently in a clan with three members. When we tried to initiate a clan war it said we had insufficient clan requirements. Does anyone know what the full requirements are? Is there a minimum clan member requirement? After a botched upgrade from Ubuntu 14.04 to Ubuntu 16.04 I had to wipe my system and start all over. This time I decided to go with a much less CPU intensive desktop environment and installed Lubuntu 16.04-1.  My problem: when I run Steam from the menu shortcut it acts like it is doing nothing. However it does show up in the task manager. If I just type steam in the terminal I get the following.  michael@michael-HP-Pavilion-dm1-Notebook-PC:~$ steam Running Steam on ubuntu 16.04 64-bit STEAM_RUNTIME is enabled automatically grep: symbol lookup error: grep: undefined symbol: pcre_jit_stack_alloc grep: symbol lookup error: grep: undefined symbol: pcre_jit_stack_alloc /bin/bash: /home/michael/.local/share/Steam/ubuntu12_32/steam-runtime/amd64/lib/x86_64-linux-gnu/libtinfo.so.5: no version information available (required by /bin/bash) grep: symbol lookup error: grep: undefined symbol: pcre_jit_stack_alloc awk: /home/michael/.local/share/Steam/ubuntu12_32/steam-runtime/amd64/lib/x86_64-linux-gnu/libtinfo.so.5: no version information available (required by /lib/x86_64-linux-gnu/libreadline.so.6) Installing breakpad exception handler for appid(steam)/version(1468023329) libGL error: unable to load driver: r600_dri.so libGL error: driver pointer missing libGL error: failed to load driver: r600 libGL error: unable to load driver: swrast_dri.so libGL error: failed to load driver: swrast   Then nothing happens including steam doesn't show up in the task manager. Now I did find the command.  LD_PRELOAD='/usr/$LIB/libstdc++.so.6' DISPLAY=:0 steam   This does run Steam but it is not a real solution in my eyes. How can I fix it? What characters do I need to escape when using sed in a sh script? Take the following script:  #!/bin/sh sed 's/(127\.0\.1\.1)\s/\1/' [some file]   If I try to run this in sh (dash here), it'll fail because of the parentheses, which need to be escaped. But I don't need to escape the backslashes themselves (between the octets, or in the \s or \1). What's the rule here? What about when I need to use {...} or [...]? Is there a list of what I do and don't need to escape? If we're implementing , why don't we also require that users have at least 1.5 times the amount of reputation needed to ask their current question in order to answer their current question?  I believe this would really reduce the amount of non-answers that should have been edits to the original question, or perhaps a comment under another answer.  Edit  Inspired by marcog's excellent suggestion , perhaps it would make more sense to set a minimum amount of time that must pass before you can answer your own question. New users would need to wait in the neighborhood of six hours, while users with more reputation could answer their own question within minutes if they discovered the solution on their own.  This would get in the way of the behavior that we don't want, which is people posting answers that should have been edits while not annoying most. Let $x, y$ and $z$ be real numbers such that $x^2+ y^2+ z^2= 1$. Find the   maximum and minimum values of $2x + 3y + z$ .       How can I able to solve the problem? Thanks for your help. I am using QGIS and I created a vector grid on a crop field in order to cut it into plots. I want to save each grid cell into individual polygon shapefiles automatically.  Here is an example of a vector grid I would like to split into 117 shapefiles:    Eventually, I did it manually with the selection tool and "Save as" but it is really time-consuming when there are more than 100 plots to save.    Is there any way to do it faster and more automatically?  Each plot as an attribute named "Plot" that can discriminate against them (basically being id + 1). It's the attribute used here to label them. $x^{x^{x^{\dots}}}=2$, what is the value of $x$? I came up with this little simple exercise, stating:  $x^{x^{x^{\dots}}}$ infinite times is equal to $2$, find $x$.   As we're dealing with infinity, we can just separate the first $x$ and get $x^2=2 \implies x=\sqrt2$  But then I thought what if we change $2$ to $4$? Now we get $x^4=4 \implies x=\sqrt[4]4=\sqrt2$  Something went wrong, can someone explain? Turning live() into on() in jQuery BufferedWriter not writing everything to its output file Lat/Long co-ordinates are not plotting onto EPSG:3857 OSM basemap correctly Excuse me if this is a stupid question, but I've honestly tried to find the answer in a few threads here on SE, and I cannot seem to follow the suggested steps correctly.    Project is in  (WGS 84 / Pseudo-Mercator) BaseMap (OpenStreetMap) layer is set to EPSG:3857 Vector data has been imported from CSV, and has Lat/Long coordinates, set to EPSG:3857.    The layer appears right in the middle of the map, around 0,0 obviously.   Why is this, what am I doing wrong? So I need to compress a directory with max compression.   How can I do it with xz? I mean I will need tar too because I can't compress a directory with only xz. Is there a oneliner to produce e.g. foo.tar.xz? Maybe the concept, why it's used, and an example. Is it safe to cancel CHKDSK when it has been started without any parameters? I know that it is not a good idea to forcibly stop a chkdsk process that has been executed with parameters like /f and /r.   But is it safe to stop the process when it has been started simply by the chkdskcommand? Chkdsk prints out a lot of errors and is continuing very slowly.  I suppose it to should be safe to cancel the process since there should be only in read mode, correct? It always takes a  and money to find the next . Why is it so important to do this work and what is the application those numbers? Check if file is already open Is  structured data (in Microdata, JSON-LD, or RDFa) relevant for SEO?   I know that structured data can provide benefits in other areas, but here I’m only asking about its significance for general web search engines. I have the message:   Error Broken count &gt;0 Check if you are using third party repositories. If so disable them, since they are a common source of problems. Furthermore run the following command in a Terminal: apt-get install -f Details: The following packages have unmet dependencies: firefox-globalmenu: Depends: firefox (= 19.0+build1-0ubuntu0.12.04.2) but 19.0+build1-0ubuntu0.12.04.1 is installed   Any suggestions? What are the differences between a pointer variable and a reference variable in C++? I know references are syntactic sugar, so code is easier to read and write. But what is the difference between a pointer variable and a reference variable? Comparing two logit or probit curves using a single parameter I've conducted a psychological experiment on the same subject, under two different condition. For each condition I've collected the number of correct and wrong answer for each stimulus (number of trials per stimulus = 10; number of stimulus = 15). From the data collected I fitted a psychometric curve (probit or logit curve), and now I want to compare the results.  Consider subject 1: His answers are collected in the following matrices  **COND_1**     correct cnt   Y  N   1   0 10   2   0 10   3   0 10   4   0 10   5   0 10   6   0 10   7   1  9   8   4  6   9   5  5   10  7  3   11  8  2   12  7  3   13 10  0   14 10  0   15 10  0  **COND_2**     correct cnt   Y  N   1   0 10   2   2  8   3   2  8   4   3  7   5   2  8   6   4  6   7   8  2   8  10  0   9   8  2   10 10  0   11  9  1   12 10  0   13 10  0   14 10  0   15 10  0  COND_1.1 &lt;- matrix(c(0, 2, 2, 3, 2, 4, 8, 10, 8, 10, 9, 10, 10, 10, 10, 10, 8, 8, 7, 8, 6, 2, 0, 2, 0, 1, 0, 0, 0, 0), byrow=F, ncol=2)  COND_1.2 &lt;- matrix(c(0, 0, 0, 0, 0, 0, 1, 4, 5, 7, 8, 7, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 6, 5, 3, 2, 3, 0, 0, 0), byrow=F, ncol=2)  cnt &lt;- seq(from=0, to=1.4, by=0.1)  ddprob.1.1 &lt;- glm(COND_1.1 ~ cnt, family = binomial(link = "probit"))  ddprob.2.1 &lt;- glm(COND_2.1 ~ cnt, family = binomial(link = "probit"))     Observing the plot, you can surely say that performance under condition 2 is better then the performance under condition 1. In fact if you compute some parameters like AUC, p25, p50, p75 (the value of the stimulus at which the number of correct answers are 25%, 50% and 75% each) [threshold parameters], you'll see that:  COND_1      COND_2 AUC    &lt;    AUC p25    &gt;    p25 p50    &gt;    p50 p75    &gt;    p75     Now consider subject 2:  COND_1     correct cnt   Y  N   1   0 10   2   0 10   3   0 10   4   0 10   5   3  7   6   3  7   7   4  6   8   5  5   9   9  1   10  9  1   11 10  0   12 10  0   13 10  0   14 10  0   15 10  0  COND_2     correct cnt   Y  N   1   0 10   2   1  9   3   0 10   4   4  6   5   2  8   6   6  4   7   4  6   8   7  3   9   4  6   10  7  3   11  7  3   12 10  0   13  9  1   14 10  0   15 10  0   COND_1.2 &lt;- matrix(c(0, 0, 0, 0, 3, 3, 4, 5, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 7, 6, 5, 1, 1, 0, 0, 0, 0, 0), byrow=F, ncol=2) COND_2.2 &lt;- matrix(c(0, 1, 0, 4, 2, 6, 4, 7, 4, 7, 7, 10, 9, 10, 10, 10, 9, 10, 6, 8, 4, 6, 3, 6, 3, 3, 0, 1, 0, 0), byrow=F, ncol=2) cnt &lt;- seq(from=0, to=1.4, by=0.1)  ddprob.1.1 &lt;- glm(COND_1.2 ~ cnt, family = binomial(link = "probit")) ddprob.2.1 &lt;- glm(COND_2.2 ~ cnt, family = binomial(link = "probit"))   The plotted curves are shown in the image below.    Can you say what performance is better? Under condition 1 or under condition 2? Extrapolating AUC, p25, p50, p75, you have:  COND_1      COND_2 AUC     &gt;   AUC p25     &gt;   p25 p50     =   p50 p75     &lt;   p75   So my question is: Is there a method to say that a generic curve (logit, probit or whatelse) is HIGHER then another? Is there a method to compare (a single number of "performance") that describe the differences of the two curves? My example shows that AUC, p25, p50, p75 are not good parameters. I'd like to compute a single numeric parameter for each curves, to make a simple t-paired test, extrapolated from the distribution seen.