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## Plotting Tick Data with ggplot2

Here are some examples of using ggplot2 and kdb+ together to produce some simple graphs of data stored in kdb+. I am using the qserver extension for R (http://code.kx.com/wsvn/code/cookbook_code/r/) to connect to a running kdb+ instance from within R.

First, lets create a dummy data set: a set of evenly-spaced timestamps and a random walk price series:

ONE_SEC:long$1e9 tab:([]time:.z.P+ONE_SEC * (til 1000);price:sums?[1000?1.<0.5;-1;1]) Then import the data into R: [source lang="r"]>tab <- execute(h,'select from tab')[/source] Then plot a simple line graph - remember ggplot2 works natively with data frames: [source lang="r"]>library(ggplot2) >ggplot(tab, aes(x=time, y=price)) + geom_line() + ggtitle("Stock Price Evolution")[/source] This will produce a line graph similar to the one below: Next, we can do a simple bin count / histogram on the price series: [source lang="r"]ggplot(tab, aes(x=(price))) + geom_histogram()[/source] Which will produce a graph like the following: We can adjust the bin width to get a more granular graph using the binwidth parameter: [source lang="r"]> ggplot(tab, aes(x=(price))) + geom_histogram(position="identity", binwidth=1)[/source] We can also make use of some aesthetic attributes, e.g. fill color - we can shade the histogram by the number of observations in each bin: [source lang="r"]ggplot(tab, aes(x=(price), fill=..count..)) + geom_histogram(position="identity", binwidth=1)[/source] Which results in: Some other graphs: Say I have a data frame with a bunch of currency tick data (bid/offer/mid prices). The currencies are interspersed. Here is a sample: [source lang="r"] > head(ccys) sym timestamp bid ask mid 1 AUDJPY 2013-01-15 11:00:16.127 94.485 94.496 94.4905 2 AUDJPY 2013-01-15 11:00:22.592 94.486 94.496 94.4910 3 AUDJPY 2013-01-15 11:00:30.117 94.498 94.505 94.5015 4 AUDJPY 2013-01-15 11:00:30.325 94.498 94.506 94.5020 5 AUDJPY 2013-01-15 11:00:37.118 94.499 94.507 94.5030 6 AUDJPY 2013-01-15 11:00:47.348 94.526 94.536 94.5310 [/source] I want to add a column containing the log-returns calculated separately for each currency: [source lang="r"] log.ret <- function(x) do.call("rbind", lapply(seq_along(x), function(i) cbind(x[[i]],lr=c(0, diff(log(x[[i]]$mid))))))
ccys <- log.ret(split(ccys, f=ccys$sym)) [/source] Then I can plot a simple line chart of the log returns using the lovely facets feature in ggplot to split out a separate panel per symbol: [source lang="r"] ggplot(ccys, aes(x=timestamp, y=lr)) + geom_line() + facet_grid(sym ~ .) [/source] Which produces the following: Another nice graph - display a visual summary of the tick frequency by time. This one uses a dummy column that represents a tick arrival. Note in the following graph I have reduced the line width and set the alpha value to a tiny value (creating a large transparency effect) as otherwise the density of tick lines is too great. The overall effect is visually pleasing: [source lang="r"] ccys <- cbind(ccys, dummy=rep(1,nrow(ccys))) ggplot(ccys, aes(x=timestamp,y=dummy, ymin=0, ymax=1)) + geom_linerange(alpha=1/2,size=.01,width=.01) + facet_grid(sym ~ .) + theme(axis.text.y=element_blank()) + xlab("ticks") + ylab("time") + ggtitle("Tick Density") [/source] Which results in: Next time (time permitting) - covariance matrices and bivariate density plots.. Categories ## Rmathlib and kdb+ part 3: Utility Functions In the first two parts of this series, I looked at the basics of the interface I created between rmathlib and kdb+. In this post, I’ll go through some of the convenience functions I wrote to emulate some basic R functionality. NOTE: I wrote these functions as a learning exercise to familiarise myself with q/kdb+ a bit more – they are very simplistic and I am sure there are much better ways to do them (I know the very nice qml project does a lot of this stuff, plus interfaces to external BLAS libraries). Some basics: load the library: q)\l rmath.q ### seq – sequence function The first convenience function is seq, which is like R’s seq() or Numpy’s arange() in that it takes a start and end point, and generates a range of numbers. q)seq[1;100] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26... The function is just a curried wrapper around seqn, which also takes a step size: q)seqn[1;10;.5] 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10  This is handy when working with some of the probability generation functions shown last time. For instance the commands below calculate the normal distribution (cdf) values for evenly spaced points from -3 to 3: q)each[{pnorm[x;0;1]}] seqn[-3;3;.5] 0.001349898 0.006209665 0.02275013 0.0668072...  ### table – Symbol Tabulation R provides a handy function to show summary count tables of factor levels. In q, this can be used as follows: q)t:([] sym:1000?ABCD) q)table[sym;t] B| 241 A| 244 C| 256 D| 259 This tabulates the column sym from the table t. The summary is ordered by increasing frequency count. NOTE: this has really no advantage over the standard q)x xasc select count i by sym from t sym| x ---| --- B | 241 A | 244 C | 256 D | 259 except some slight brevity. ### range – Min/Max The range function simply returns the boundaries of a set of values: q)x:rnorm[10000] q)range[x] -3.685814 4.211363 q)abs (-) . range[x] / absolute range 7.897177 ### summary – Min/Max/Mean/Median/IQR The summary function provides summary stats, a la R’s summary() function: q)x:norm[10000;3;2] q)summary x min | -4.755305 1q | 1.59379 median| 2.972523 mean | 2.966736 3q | 4.336589 max | 10.00284 ### quantile – Quantile Calculations A very simple quantile calc: q)x:norm[10000;3;2] q)quantile[x;.5] 2.973137 ### hist – Bin Count Very crude bin count – specify the data and the number of bins: q)hist[x;10] -4.919383| 14 -3.279589| 101 -1.639794| 601 0 | 1856 1.639794 | 3043 3.279589 | 2696 4.919383 | 1329 6.559177 | 319 8.198972 | 40 9.838766 | 1 ### diag – Identity Matrix Generation q)diag 10 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 ### Scale functions Sometimes its very useful to scale an input data set – e.g. when feeding multiple inputs into a statistical model, large differences between the relative scales of the inputs combined with finite-precision computer arithmetic can result in some inputs being dwarfed by others. The scale function just adjusts the input as follows: $$X_{s}=(X-\mu)/\sigma$$. The example below scales two inputs with different ranges: q)x:norm[10;0;1]; y:norm[10;5;3] q)x 1.920868 -1.594028 -0.02312519 1.079606 -0.5310111 0.2762119 0.1218428 0.9584264 -0.4244091 -0.7981221 q)y 10.69666 2.357529 8.93505 3.65696 5.218461 3.246216 5.971919 7.557135 1.412827 1.246241 q)range x -1.594028 1.920868 q)range y 1.246241 10.69666 q)range scale x -1.74507 1.878671 q)range scale y -1.232262 1.845551 There are other useful scaling measures, including the min/max scale: $$\frac{x-min(x)}{max(x)-min(x)}$$. This is implemented using the minmax function: q)minmax x 1 0 0.4469273 0.760658 0.302432 0.5320897 0.4881712 0.726182 0.3327606 0.226438 range minmax x 0 1f  There are other functions which are useful for scaling, e.g. the RMSD (root-mean-square deviation): $$\sqrt{\frac{\sum{x_i^2}}{N}}$$: q)x:rnorm 1000 q)rms x 1.021065 ### nchoosek – Combinations The nchoosek function calculates the number of combinations of N items chosen k at a time (i.e. $${N}\choose{k}$$: q)nchoosek[100;5] 7.528752e+07 q)each[{nchoosek[10;x]}] seq[1;10] 10 45 120 210 252 210 120 45 10 1f The source file is available here: https://github.com/rwinston/kdb-rmathlib/blob/master/rmath_aux.q. Categories ## Rmathlib and kdb+, part 2 – Probability Distribution Functions Following on from the last post on integrating some rmathlib functionality with kdb+, here is a sample walkthrough of how some of the functionality can be used, including some of the R-style wrappers I wrote to emulate some of the most commonly-used R commands in q. ## Loading the rmath library Firstly, load the rmathlib library interface: q)\l rmath.q ## Random Number Generation R provides random number generation facilities for a number of distributions. This is provided using a single underlying uniform generator (R provides many different RNG implementations, but in the case of Rmathlib it uses a Marsaglia-multicarry type generator) and then uses different techniques to generate numbers distributed according to the selected distribution. The standard technique is inversion, where a uniformly distributed number in [0,1] is mapped using the inverse of the probability distribution function to a different distribution. This is explained very nicely in the book “Non-Uniform Random Variate Generation”, which is availble in full here: http://luc.devroye.org/rnbookindex.html. In order to make random variate generation consistent and reproducible across R and kdb+, we need to be able to seed the RNG. The default RNG in rmathlib takes two integer seeds. We can set this in an R session as follows: [source lang=”R”] > .Random.seed[2:3]<-as.integer(c(123,456)) [/source] and the corresponding q command is: q)sseed[123;456] Conversely, getting the current seed value can be done using: q)gseed[] 123 456i The underlying uniform generator can be accessed using runif: q)runif[100;3;4] 3.102089 3.854157 3.369014 3.164677 3.998812 3.092924 3.381564 3.991363 3.369.. produces 100 random variates uniformly distributed between [3,4]. Then for example, normal variates can be generated: q)rnorm 10 -0.2934974 -0.334377 -0.4118473 -0.3461507 -0.9520977 0.9882516 1.633248 -0.5957762 -1.199814 0.04405314 This produces identical results in R: [source lang=”r”] > rnorm(10) [1] -0.2934974 -0.3343770 -0.4118473 -0.3461507 -0.9520977 0.9882516 1.6332482 -0.5957762 -1.1998144 [10] 0.0440531 [/source] Normally-distributed variables with a distribution of $$N(\mu,\sigma)$$ can also be generated: q)dev norm[10000;3;1.5] 1.519263 q)avg norm[10000;3;1.5] 2.975766 Or we can alternatively scale a standard normal $$X ~ N(0,1)$$ using $$Y = \sigma X + \mu$$: q)x:rnorm[1000] q) int$ (avg x; dev x) 0 1i q)y:(x*3)+5 q) int$(avg y; dev y) 5 3i ## Probability Distribution Functions As well as random variate generation, rmathlib also provides other functions, e.g. the normal density function: q)dnorm[0;0;1] 0.3989423 computes the normal density at 0 for a standard normal distribution. The second and third parameters are the mean and standard deviation of the distribution. The normal distribution function is also provided: q)pnorm[0;0;1] 0.5 computes the distribution value at 0 for a standard normal (with mean and standard deviation parameters). Finally, the quantile function (the inverse of the distribution function – see the graph below – the quantile value for .99 is mapped onto the distribution function value at that point: 2.32): q)qnorm[.99;0;1] 2.326348 We can do a round-trip via pnorm() and qnorm(): q)int$ qnorm[ pnorm[3;0;1]-pnorm[-3;0;1]; 0; 1] 3i

Thats it for the distribution functions for now – rmathlib provides lots of different distributions (I have just linked in the normal and uniform functions for now. There are some other functions that I have created that I will cover in a future post.

All code is on github: https://github.com/rwinston/kdb-rmathlib

[Check out part 3 of this series]