I was recently reading a paper and I came across this diagram in the paper:  It basically shows the precision of an approximation algorithm as x and y varies. Does anyone know what sort of package this is?
I have a huge amount of 2D-coordinates, associated with a value, e.g.:    x   |   y   | value 27.50   52.15   12.51 61.83   13.32   57.56 36.23   21.83   41.73 40.46   85.67   25.20 ...   The data is not tabular and I Want the points between two data-points to be interpolated in some way (which way is not really clear, yet)  I want to preset the data as heatmap like this:   Is there any ready-to-use package for PSTricks or TikZ to do it?
How do you sort du output by size? How do you sort du -sh /dir/* by size? I read one site that said use | sort -n but that's obviously not right. Here's an example that is wrong.  [~]# du -sh /var/* | sort -n 0       /var/mail 1.2M    /var/www 1.8M    /var/tmp 1.9G    /var/named 2.9M    /var/run 4.1G    /var/log 8.0K    /var/account 8.0K    /var/crash 8.0K    /var/cvs 8.0K    /var/games 8.0K    /var/local 8.0K    /var/nis 8.0K    /var/opt 8.0K    /var/preserve 8.0K    /var/racoon 12K     /var/aquota.user 12K     /var/portsentry 16K     /var/ftp 16K     /var/quota.user 20K     /var/yp 24K     /var/db 28K     /var/empty 32K     /var/lock 84K     /var/profiles 224M    /var/netenberg 235M    /var/cpanel 245M    /var/cache 620M    /var/lib 748K    /var/spool I am stuck in a question for Algebraic Structures:  I need to prove: If given any ring $R$, for any $a$ in $R$ $a\cdot a=0$ then $a+a=0$.  (of course $+$, $*$ and $0$ regarding $R$)  I didn't find any question regarding this question. Ubuntu 14.04.5/16.04 and newer on AMD graphics I have 14.04.5/16.04 or newer and an AMD GPU. I'm not getting the performance I want, and some programs say they need things like OpenCL.  I've heard about fglrx, but if I try to install it on my machine, it breaks and I have no GUI.  Is there anything I can do to get my AMD card working to its full potential? What are some of the rule changes that Pathfinder brings in comparison to D&amp;D 3.5?  I am curious what changes were made so I can explain to my group what it has to offer. Regard the diff equation:  $mϕ′′+aϕ′+(mg/L)ϕ=0$  $ϕ(0)=0.1$  $ϕ′(0)=0$  where $m=0.1,L=1,a=2,$  1) Rewrite the second order diff equation as a system of first order linear equations.  2) What is the matrix that comes from the rewritten equations? What is the smallest convex set includes all smooth unit curves? I try to understand: is there a smallest in area convex set that every smooth curve with length 1 can be placed inside it by translation and rotation?  I only have a upper bound $S \leq \frac14+\frac{\pi}{16}$ because of convex hull of two circles radius $\frac14$ and simple lower bound $S\geq\frac1{4\pi}$.  Does this set exist and what is its length? How to perform a true GIS clip of polygons layer using a polygon layer in R? I would like to do a true GIS Clip in R of soils polygons using a series of single boundary polygons, but I cannot find an R function to properly do it. It should work just like the clip function in ESRI's ArcMap. I've tried the over method in sp package but it doesn't seem to work for polys over polys.   One suggestion was to use the gIntersection in rgeos package as a clip using the following code:  #------------------------------------ library(rgeos) library(maptools)  #Read layers as SpatialPolygonsDataFrame (both the same Albers projection) Soils_poly = readShapePoly("Soils_polygons")  #Note - Has 400 polygons clipper_poly = readShapePoly("clipper_polygon")  #Note - Has 1 polygon  #Try gintersection as clip  Clipped_polys = gIntersection(Clipper_Tile_poly, Soils_poly)  #-----------------------------------   This takes 5 minutes to run (way too slow) and errors with this:     Error in RGEOSBinTopoFunc(spgeom1, spgeom2, byid, id, drop_not_poly, "rgeos_intersection") :      TopologyException: no outgoing dirEdge found at -721459.77681285271 2009506.5980877089   I also tried this code to check for overlap:  gIntersects(Clipper_Tile_poly, Soils_poly)   and the result was TRUE. clip function in ESRI ArcMap works fine for this data.   Anyone knows of an R function to properly do a clip on spatial polygons using spatial polygons? If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$ Let $a$, $b$, $c$ be the roots of $$x^3 - 6x^2 + 3x + 1 = 0$$ Find all possible values of $a^2 b + b^2 c + c^2 a$. Express all the possible values, in commas.  I've already tried to bash out all the roots, Vieta's Formula, and try to manipulate the equation to become easier to work with. However, Vieta's didn't get me anywhere, and I couldn't find a way to make the equation simpler or anything. Any hints to start this problem? Edited vs emitted - why one t vs two t's Why does "edited" have one "t" and  and "emitted" has two? "Edit" and "emit" are so similar in spelling and pronunciation.  I keep wanting to type "editted" for some reason. Prove the inequality $n! \geq 2^n$ by induction I'm having difficulty solving an exercise in my course.  The question is:      Prove that $n!\geq 2^n$.   We have to do this by induction. I started like this:   The lowest natural number where the assumption is correct is $4$ as: $4! \geq 2^4 \iff 24 \ge 16$. The assumption is: $n! \ge 2^n$.   Now proof for $(n+1)$ which brings me to: $(n+1)! \ge 2^{(n+1)}$  I think I can rewrite it somehow like this:  $$ {(n+1)} \times {n!}  \stackrel{\text{(definition of factorial)}}{\ge} 2^n \times 2 $$  $$ (n+1) \times 2^n \ge 2^n \times 2 $$  Then I think I can eliminate the $2^n$ and have something like this: $n+1 \ge 2$, or $n \ge 1$.  But I think I'm wrong here some where and was hoping somebody has some advice on this. How can I prove the above assumption?  Any help would be appreciated, kind regards. Problem with ListVectorPlot3D Minimum of $\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}$ What is the minimum of $$f(a,b,c):=\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}$$ where $a,b,c$ are positive real numbers?  When $a=b=c$, we have $f(a,b,c)=\dfrac{3}{\sqrt{2}}\approx 2.12$  When $a=1,b=c\rightarrow\infty$, we have $f(a,b,c)\rightarrow 2$. So the minimum is at most $2$. Which of these are acceptable? Is one preferable over the other?   "Chemically-deposited tourmaline is never periwinkle." "Chemically deposited tourmaline is never periwinkle."   Also, is the title to the this question asking what I'm trying to ask?  (I realize that there are other questions about hyphenation in similar contexts; I'm asking specifically about -ly adverbs.) For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$ trying to install libgraph Warning: preg_replace(): Unknown modifier How to connect to device via SSH over direct ethernet connection Is there a clear set of conditions under which lasso, ridge, or elastic net solution paths are monotone? The question  demonstrates solution paths for the lasso estimator that are not monotonic. That is, some of the cofficients grow in absolute value before they shrink.  I've applied these models to several different kinds of data sets and never seen this behavior "in the wild," and until today had assumed that they were always monotonic.  Is there a clear set of conditions under which the solution paths are guaranteed to be monotone? Does it affect the interpretation of the results if the paths change direction? Asking similar questions - process? How To Represent 0.1 In Floating Point Arithmetic And Decimal