Mikkel Meyer Andersen |
February 25, 2010 at 07:05 (UTC) |
No Comments »
API, Google Wave, Latex, MathML, Python, Watexy, WatexyML I’ve been working on a robot just like Watexy, but instead of converting Latex to images, it should convert to MathML-fonts. And I’m actually quite far with the robot, so I assume that something will be ready within a couple of days (or maybe a week). Stay tuned!
Oh – and I removed the ads on the site. They was indeed annoying! I hope that you will help the development and server expenses by donating a bit if you can afford it. And thanks to those who already donated – it’s much appreciated!
Mikkel Meyer Andersen |
November 14, 2009 at 23:15 (UTC) |
31 Comments »
API, Google Wave, Latex, Python, Watexy Now version 14 of watexy@appspot.com is released.
$ $x$ $ makes an inline equation (with the $-signs immediately following each other and not with a space as here).
\[ 4 + 5 \] makes an equation in “display math mode”, i.e. centred on its own line. Edit by clicking at the equation (the image).
There are still a few misbehaviours/new feature suggestions:
I’m of course still working to fix these things, but it might not be solved until January because I’m going to travel the rest of the year.
Thanks a lot for your support and all the feedback. Please continue to comment on how the robot is made, bugs, and suggestions! I’m also on Twitter at http://twitter.com/mikldk.
A last request: If you can afford, please donate money to support my work and expenses. You’ll find the donate-button in the upper right corner of this page.
Mikkel Meyer Andersen |
November 13, 2009 at 01:45 (UTC) |
13 Comments »
API, Google Wave, Latex, Python, Watexy I’m a new version of Watexy with the possibility to edit equations and fixes the bug with < and > not working.
The testing-robot is:
watexy-test@appspot.com
It only works in wave.google.com and not in wavesandbox.com for some reason.
I hope you’ll take the time to give it a try and some feedback to improve it.
Mikkel Meyer Andersen |
November 11, 2009 at 00:00 (UTC) |
7 Comments »
API, Google Wave, Latex, Python, Watexy First of all, thanks for the feed-back in [1].
I’ve now fixed three things:
1) It’s now possible to put more than one equation in a blip, and they all get nicely/properly displayed, thanks to Michael, post 18 in [1] for a possible solution
2) Instead of using http://www.forkosh.dreamhost.com/mathtex.cgi , I’ve now installed the program on one of my own servers (thanks a lot for both the software and the service)
3) Multi-line is supported, such that the equation can be written over multiple lines and still be matched correctly
Please do not hesitate to comment this version as well!
By the way, I’m sorry for the delay with this new version. My life as an exchange student in Australia has been a bit hectic with all the travelling besides the studies.
[1]: http://www.scienco.org/2009/watexy-latex-robot-for-google-wave/
The new code is as follows:
# Python reference: # http://wave-robot-python-client.googlecode.com/svn/trunk/pydocs/index.html # Shortcut to the important OpBasedDocument # http://wave-robot-python-client.googlecode.com/svn/trunk/pydocs/waveapi.ops.OpBasedDocument-class.html __author__ = 'mikl@mikl.dk (Mikkel Meyer Andersen)' import re from waveapi import events from waveapi import model from waveapi import robot from waveapi import document def OnRobotAdded(properties, context): """Invoked when the robot has been added.""" root_wavelet = context.GetRootWavelet() root_wavelet.CreateBlip().GetDocument().SetText("Hi. My name is Watexy and I'm here to help you presenting Latex in waves. Just put the latex between $$ and $$, e.g. $$2+2=5$$.") def reversed_iterator(iter): return reversed(list(iter)) def OnBlipSubmitted(properties, context): """Invoked when a blip has been added.""" blip = context.GetBlipById(properties['blipId']) blip_text_view = blip.GetDocument() matches = re.finditer('\$\$(.+?)\$\$', blip_text_view.GetText(), re.DOTALL) """ Reverse list such that the last items will be changed first, such that the positions for the first items doesn't change """ matches = reversed_iterator(matches) for m in matches: """ The +/- 2 is because of the length of the $$'s. If not removed, the loop will run infintely! """ blip_text_view.DeleteRange(document.Range(m.start(1)-2, m.end(1)+2)) image = document.Image('http://meyer.fm/cgi-bin/mathtex.cgi?' + m.group(1), caption=m.group(1)) blip_text_view.InsertElement(m.start(1)-2, image) if __name__ == '__main__': myRobot = robot.Robot('watexy', image_url='http://watexy.appspot.com/assets/icon.png', version='12', profile_url='http://watexy.appspot.com/') myRobot.RegisterHandler(events.WAVELET_SELF_ADDED, OnRobotAdded) myRobot.RegisterHandler(events.BLIP_SUBMITTED, OnBlipSubmitted) myRobot.Run()
I’ve updated the qqmultinorm.R script a bit so that it’s now capable of picking a more optimal plot size (less unused space).
The idea refers to deciding the sides (dimensions) of a rectangle if the areal (number of plots) is known i.e., optimising the dimensions of a rectangle given the areal. We want the perimeter as small as possible (for better viewing), preferably wider than longer if square isn’t possible. A given number n is factorised in to numbers within a given error. For example if the allowed error is 2, then 7 gets factorised in (1,7), (2, 4), (4, 2), and (7, 1) (here redundant factorisation is included). Although 2*4 = 8, but abs(7-8) = 1 <= 2, so it's acceptable. Actually the default error is 10% of the input areal.
The way the proper factorisations is chosen, is by ordering the pairs by ascending the difference of the components i.e, how much the width and height differs. And then ordered ascending by height so that the plot gets wide screen-like instead of poster-like.
The new script is a follows (only find.optimal.mfrow.size(...) and a bit logic in qqmultinorm(...) added):
# File name: qqmultinorm.R
# Version: 1.1
# Last updated: 2009-08-28
#
# This R-code is made by:
# Mikkel Meyer Andersen, Denmark
# mikl [funny-a] math [.] aau [.] dk or
# mikl [funny-a] mikl [.] dk
#
# Licence: GPLv2
#
# Feel free to use it, but if you do I'll like to hear about it (just for fun).
# If you make corrections, please submit them back so others can enjoy them as well.
qqchisq <- function(y, main, df=2, continuity.correction = 0.5)
{
n <- length(y)
y <- sort(y)
c <- numeric(n)
for (i in 1:n)
c[i] <- qchisq((i-continuity.correction)/n, df=df)
plot(c, y, xlab="Theoretical Quantiles", ylab="Sample Quantiles", main=main)
lines(c(c[1], c[n]), c(c[1], c[n]), type="l")
}
dec2bin <- function(x)
{
if (!is.vector(x) || length(x) != 1 || x < 0)
stop("x must be a non-negative integer")
N <- length(x)
ndigits <- floor(log2(x)) + 1
bin <- numeric(ndigits)
for (i in (ndigits-1):0)
{
tmp <- 2^i
if (x %/% tmp >= 1)
{
bin[i+1] <- 1
x <- x - tmp
}
}
return(rev(bin))
}
# Returns the power set without the empty set
power.set <- function(v)
{
n <- length(v)
N <- 2^n - 1
ps <- vector("list", N)
for (i in 1:(N-1))
{
Nbin <- dec2bin(i)
Nbin <- c(numeric(n-length(Nbin)), Nbin)
Nbin <- rev(Nbin)
ps[[i]] <- v[which(Nbin == 1)]
}
ps[[N]] <- v
return(ps)
}
# Input: n
# - here the number of plots
# Returns c(h, w)
# - the optimal choice of rows and cols to use in in mfrow
find.optimal.mfrow.size <- function(n)
{
w0 <- ceiling(sqrt(n))
# The area can at max contain of 10% unused space
max.error <- round(n*0.1)
n.minus.error <- n - max.error
n.plus.error <- n + max.error
# If n is a square, fine!
if (w0^2 == n)
return(c(w0, w0))
# Col 1 and 2: w and h
# Col 3: The difference between w and h: this should be as small as possible
candidates <- matrix(ncol=3)
for (w in w0:1)
{
h <- ceiling(n / w)
n0 <- w*h
# Because of ceiling we know that n0 >= n
if (n0 <= n.plus.error)
candidates <- rbind(candidates, c(h, w, abs(w-h)))
}
# First row is NA
candidates <- candidates[-1,]
# Uups, something went wront - well, don't panic
if (nrow(candidates) == 0)
return(c(w0, w0))
# First order by abs(w-h) and then by h to get a widescreen-look
# instead of a poster-look
candidates <- candidates[order(candidates[,3], candidates[,1]), ]
return(candidates[1, c(1,2)])
}
# dataset: variables in columns and observations as rows
# subset.min.size, subset.max.size: inclusive limits
# filename: if specified, the plot are saved as a png file with this filename
qqmultinorm <- function(dataset, subset.min.size = 1, subset.max.size = 4, filename = NULL, use.optimale.size = F)
{
p <- ncol(dataset)
n <- nrow(dataset)
if (subset.min.size < 1) stop("subset.min.size < 1")
if (subset.min.size > p) stop("subset.min.size > p")
if (subset.max.size < 1) stop("subset.max.size < 1")
if (subset.max.size > p) stop("subset.max.size > p")
if (subset.min.size > subset.max.size) stop("subset.min.size > subset.max.size")
if (is.null(colnames(dataset)))
colnames(dataset) <- 1:p
# We have p variables. If all is to be checked against each other,
# then we have a power-set with 2^p subsets (including the empty set)
# Here we get subset containing indexes of the variables to include
# Note that power.set doesn't include the empty set.
subsets <- power.set(1:p)
subsets.len <- length(subsets)
# To get the plots with the fewest variables first, we do a litte trick:
# While we find out which plots to include, we build a list
# where each element of a list is the index of the subset,
# and the index of the element is the size of the subset.
# (The +1 is because the limits are includesive!)
s.included <- vector("list", subset.max.size - subset.min.size + 1)
plots <- 0
for (i in 1:subsets.len)
{
s <- subsets[[i]]
s.len <- length(s)
if (s.len >= subset.min.size && s.len <= subset.max.size)
{
plots <- plots + 1
s.included[[s.len - subset.min.size + 1]] <- c(s.included[[s.len - subset.min.size + 1]], i)
}
}
# Now it's possible to build the subset index vector;
# we disregard the size of each subset; no more need to know it.
s.indexes <- c()
for (s in s.included)
{
s.indexes <- c(s.indexes, s)
}
# We want the best view
plot.per.row <- ceiling(plots^(1/2))
plot.per.column <- ceiling(plots^(1/2))
if (use.optimale.size)
{
mfrow.parameters <- find.optimal.mfrow.size(plots)
plot.per.row <- mfrow.parameters[1]
plot.per.column <- mfrow.parameters[2]
}
plot.width <- 300
plot.height <- 200
if (!is.null(filename))
png(file=paste(filename, ".png", sep=""), bg="white", width = plot.per.row * plot.width, height = plot.per.column * plot.height)
par(mfrow = c(plot.per.row, plot.per.column))
# There's no need to calculate a whole lot several times:
ybar <- as.vector(colMeans(dataset))
S <- as.matrix(var(dataset))
current <- 1
for (i in s.indexes)
{
s <- subsets[[i]]
s.len <- length(s)
if (s.len > subset.max.size)
next
cat("Processing subset no.", current, "out of", plots, "\n")
# Container for our values
squared.dist <- numeric(n)
# qr.solve(A) = A^(-1)
Sinv <- qr.solve(S[s,s])
# Then calculate the squared distance for each datapoint
for (i in 1:n)
{
c <- dataset[i,s] - ybar[s]
squared.dist[i] <- t(c) %*% Sinv %*% c
}
# Finding the order statistic
squared.dist <- sort(squared.dist)
qqchisq(squared.dist, paste(colnames(dataset)[s], collapse=", "), s.len)
current <- current + 1
}
if (!is.null(filename))
dev.off()
}
# Example:
A <- matrix(rnorm(2000, mean=3, sd=2), ncol=8)
qqmultinorm(A, 2, 2, "multinorm-optimal.size", use.optimale.size = T)
qqmultinorm(A, 2, 2, "multinorm", use.optimale.size = F)I wrote a R-script that can be used to evaluate for multivariate normality of a sample. It’s a kind of generalisation to the qqnorm, but this one just uses sums of the squared statistical distance which is then chi squared distributed with degrees of freedom equalling the number of squared statistical distance summed.
The useful thing about this script, is that it’s able to plot all possible combinations of the variables. It’s possible to specify the minimum number of variables to compare and the maximum number of variables to compare. All possible combinations are found by calculating the power set (using binary representation through the decimal to binary conversion, dec2bin, because if a set has k elements, then its power set has 2^k elements, and the binary representation of the numbers from 1 to 2^k are then used to pick out the subsets in the power set).
Please notice that it’s possible to specify a filename so that the plots are written to a png file. This is by far the easiest thing – and only possibility – if there’s more than a few plots.
I haven’t wrote a lot of documentation besides this, but feel free to ask if in doubt of anything!
# File name: qqmultinorm.R
#
# This R-code is made by:
# Mikkel Meyer Andersen, Denmark
# mikl [funny-a] math [.] aau [.] dk or
# mikl [funny-a] mikl [.] dk
#
# Licence: GPLv2
#
# Feel free to use it, but if you do I'll like to hear about it (just for fun).
# If you make corrections, please submit them back so others can enjoy them as well.
qqchisq <- function(y, main, df=2, continuity.correction = 0.5)
{
n <- length(y)
y <- sort(y)
c <- numeric(n)
for (i in 1:n)
c[i] <- qchisq((i-continuity.correction)/n, df=df)
plot(c, y, xlab="Theoretical Quantiles", ylab="Sample Quantiles", main=main)
lines(c(c[1], c[n]), c(c[1], c[n]), type="l")
}
dec2bin <- function(x)
{
if (!is.vector(x) || length(x) != 1 || x < 0)
stop("x must be a non-negative integer")
N <- length(x)
ndigits <- floor(log2(x)) + 1
bin <- numeric(ndigits)
for (i in (ndigits-1):0)
{
tmp <- 2^i
if (x %/% tmp >= 1)
{
bin[i+1] <- 1
x <- x - tmp
}
}
return(rev(bin))
}
# Returns the power set without the empty set
power.set <- function(v)
{
n <- length(v)
N <- 2^n - 1
ps <- vector("list", N)
for (i in 1:(N-1))
{
Nbin <- dec2bin(i)
Nbin <- c(numeric(n-length(Nbin)), Nbin)
Nbin <- rev(Nbin)
ps[[i]] <- v[which(Nbin == 1)]
}
ps[[N]] <- v
return(ps)
}
# dataset: variables in columns and observations as rows
# subset.min.size, subset.max.size: inclusive limits
# filename: if specified, the plot are saved as a png file with this filename
qqmultinorm <- function(dataset, subset.min.size = 1, subset.max.size = 4, filename = NULL)
{
p <- ncol(dataset)
n <- nrow(dataset)
if (subset.min.size < 1) stop("subset.min.size < 1")
if (subset.min.size > p) stop("subset.min.size > p")
if (subset.max.size < 1) stop("subset.max.size < 1")
if (subset.max.size > p) stop("subset.max.size > p")
if (subset.min.size > subset.max.size) stop("subset.min.size > subset.max.size")
if (is.null(colnames(dataset)))
colnames(dataset) <- 1:p
# We have p variables. If all is to be checked against each other,
# then we have a power-set with 2^p subsets (including the empty set)
# Here we get subset containing indexes of the variables to include
# Note that power.set doesn't include the empty set.
subsets <- power.set(1:p)
subsets.len <- length(subsets)
# To get the plots with the fewest variables first, we do a litte trick:
# While we find out which plots to include, we build a list
# where each element of a list is the index of the subset,
# and the index of the element is the size of the subset.
# (The +1 is because the limits are includesive!)
s.included <- vector("list", subset.max.size - subset.min.size + 1)
plots <- 0
for (i in 1:subsets.len)
{
s <- subsets[[i]]
s.len <- length(s)
if (s.len >= subset.min.size && s.len <= subset.max.size)
{
plots <- plots + 1
s.included[[s.len - subset.min.size + 1]] <- c(s.included[[s.len - subset.min.size + 1]], i)
}
}
# Now it's possible to build the subset index vector;
# we disregard the size of each subset; no more need to know it.
s.indexes <- c()
for (s in s.included)
{
s.indexes <- c(s.indexes, s)
}
# We want a squared view
plot.per.row <- ceiling(plots^(1/2))
plot.per.column <- ceiling(plots^(1/2))
plot.width <- 200
plot.height <- 200
if (!is.null(filename))
png(file=paste(filename, ".png", sep=""), bg="white", width = plot.per.row * plot.width, height = plot.per.column * plot.height)
par(mfrow = c(plot.per.row, plot.per.column))
# There's no need to calculate a whole lot several times:
ybar <- as.vector(colMeans(dataset))
S <- as.matrix(var(dataset))
current <- 1
for (i in s.indexes)
{
s <- subsets[[i]]
s.len <- length(s)
if (s.len > subset.max.size)
next
cat("Processing subset no.", current, "out of", plots, "\n")
# Container for our values
squared.dist <- numeric(n)
# qr.solve(A) = A^(-1)
Sinv <- qr.solve(S[s,s])
# Then calculate the squared distance for each datapoint
for (i in 1:n)
{
c <- dataset[i,s] - ybar[s]
squared.dist[i] <- t(c) %*% Sinv %*% c
}
# Finding the order statistic
squared.dist <- sort(squared.dist)
qqchisq(squared.dist, paste(colnames(dataset)[s], collapse=", "), s.len)
current <- current + 1
}
if (!is.null(filename))
dev.off()
}
# Example:
A <- matrix(rnorm(2000, mean=3, sd=2), ncol=8)
qqmultinorm(A, 1, 3, "multinorm-1-3")
#qqmultinorm(A, 4, 4, "multinorm-4")
#qqmultinorm(A, 5, 5, "multinorm-5")
#qqmultinorm(A, 6, 8, "multinorm-6-8")
multinorm-1-3
Sometimes when I export MySQL to files, I end up having one huge query on one line. It can be quite annoying! I’d rather want it on several lines; in that way it easier to just copy out a fragment of the query. And it also seems that some editors handle several lines better than one huge. Well, in this case my line looked like this:
INSERT INTO TABLE VALUES (...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...),(...);
With this sed-command, every entry got its own line:
sed s/\),\(/\),\\n\(/g export.sql > one-per-line.sql
Mikkel Meyer Andersen |
July 30, 2009 at 00:06 (UTC) |
34 Comments »
API, Google Wave, Latex, Python, Watexy I finally got access to a Google Wave sandbox account, making it possible to start experimenting. The first thing I made was a Latex robot. By adding the robot, it’s possible to write Latex in Waves. Afterwards, simply by putting Latex between two $’s:
$$\lim_{n \to \infty} \frac{1}{n} = 0$$Watexy then changes the Wave and inserts the Latex as an image instead of the text.
You can try it yourself by adding watexy [this-funny-curly-a] appspot.com to your Wave-conversations. You can download the source here.
There’s still a quite big bug: It’s only the first Latex-image that gets substituted correctly. The following gets inserted some positions wrong, and the deletion of the text isn’t correct neither. But the images itself are correct, only the substitution isn’t working properly. But I’m working on that!
The more technical part: the robot is written in Python, hence using the Google Wave Python API. It’s the first time I’ve tried that (thought it was a good possibility to learn it). The robot basically works by getting triggered when a new blip is submitted. Then it searches for Latex-code in that and substitutes it with pictures. Although the code is quite simple, it shows some very basic concepts on how to alter/change the contents of Waves on-the-fly (deleting text and inserting images, but it could be other things as well) with robots. The Latex-source-to-image is done by the http://www.forkosh.dreamhost.com/source_mathtex.html#webservice service.
The core Python comprising the robot is this:
# Python reference: # http://wave-robot-python-client.googlecode.com/svn/trunk/pydocs/index.html # Shortcut to the important OpBasedDocument # http://wave-robot-python-client.googlecode.com/svn/trunk/pydocs/waveapi.ops.OpBasedDocument-class.html """ Known bugs: - From (and including) the second Latex-fragment, the positioning gets wrong > Probably the document needs some kind of updatering > Even though it's a bit strange since the re matches all the Latex correctly """ __author__ = 'mikl@mikl.dk (Mikkel Meyer Andersen)' import re from waveapi import events from waveapi import model from waveapi import robot from waveapi import document def OnRobotAdded(properties, context): """Invoked when the robot has been added.""" root_wavelet = context.GetRootWavelet() root_wavelet.CreateBlip().GetDocument().SetText("Hi. My name is Watexy and I'm here to help you presenting Latex in waves. Just put the latex between $$ and $$, e.g. $$2+2=5$$. This robot uses the http://www.forkosh.dreamhost.com/source_mathtex.html#webservice service.") def OnBlipSubmitted(properties, context): """Invoked when a blip has been added.""" blip = context.GetBlipById(properties['blipId']) blip_text_view = blip.GetDocument() latex_regex = re.compile('\$\$(.+?)\$\$') m = latex_regex.search(blip_text_view.GetText()) """ Only replace one Latex-fragment at a time, because replaceing one fragment changes the text positions in the rest. That's why re.finditer isn't used. """ while m != None: """ The +/- 2 is because of the length of the $$'s. If not removed, the loop will run infintely! """ blip_text_view.DeleteRange(document.Range(m.start(1)-2, m.end(1)+2)) image = document.Image('http://www.forkosh.dreamhost.com/mathtex.cgi?' + m.group(1), caption=m.group(1)) blip_text_view.InsertElement(m.start(1)-2, image) m = latex_regex.search(blip_text_view.GetText()) if __name__ == '__main__': myRobot = robot.Robot('watexy', image_url='http://watexy.appspot.com/assets/icon.png', version='9', profile_url='http://watexy.appspot.com/') myRobot.RegisterHandler(events.WAVELET_SELF_ADDED, OnRobotAdded) myRobot.RegisterHandler(events.BLIP_SUBMITTED, OnBlipSubmitted) myRobot.Run()