We have an R package for a certain purpose. The basic data structure is a correlation function which is a real/complex valued function for a smallish (100) number (T) of time slices. We have multiple measurements (N) of it, so at its core it is a N×T matrix. But then there are more things that it can become:
One can bootstrap it with R samples such that it becomes an R×T matrix. However we want to keep the original data, so there is a field for the R×T matrix and another for the N×T matrix.
It can be symmetrized which will cut T in half and also alter various other functions that work with those objects.
Also it can be shifted which takes the difference between consecutive elements and therefore drops one time slice. The first column in the matrix then corresponds to t = 1 and not t = 0 any more, which becomes important in fits to the data.
Correlation functions may have an imaginary part, this is stored as a second real matrix. But they might not.
When doing non-linear operations with the data, we do that once with the average of the original data and each bootstrap sample. If the result is another correlation function, that object will not have “original data” but only the average.
So basically we have a class that can have various fields and only the average of the original data is really common.
To make things worse, there is no formal documentation for the possible members and the invariants associated with them. Coming from C++ where a concise class definition allows me do encapsulation, The S3 class system in R seems like an invitation for inconsistencies.
This surfaced a few times when some function taking such a correlation function as argument and expected some field to be present while it was not. The code is riddled with lines that just add another field to the class when performing an operation.
Long story short: Is there some automatically enforcable way in the S3 class system to have an exhaustive list of all the fields that a class can have? Right now I only see the possibility to document (in English) in the constructor function and just hope nobody missed a line where fields were added.
Related
Working with code that describes a poisson cluster process in spatstat. Breaking down each line of code one at a time to understand. Easy to begin.
library(spatstat)
lambda<-100
win<-owin(c(0,1),c(0,1))
n.seeds<-lambda*win$xrange[2]*win$yrange[2]
Once the window is defined I then generate my points using a random generation function
x=runif(min=win$xrange[1],max=win$xrange[2],n=pmax(1,n.seeds))
y=runif(min=win$yrange[1],max=win$yrange[2],n=pmax(1,n.seeds))
This can be plotted straight away I know using the ppp function
seeds<-ppp(x=x,
y=y,
window=win)
plot(seeds)
The next line I add marks to the ppp object, it is apparently describing the angle of rotation of the points, I don't understand how this works right now but that is okay, I will figure out later.
marks<-data.frame(angles=runif(n=pmax(1,n.seeds),min=0,max=2*pi))
seeds1<-ppp(x=x,
y=y,
window=win,
marks=marks)
The first problem I encounter is that an objects called pops, describing the populations of the window, is added to the ppp object. I understand how the values are derived, it is a poisson distribution given the input value mu, which can be any value and the total number of observations equal to points in the window.
seeds2<-ppp(x=x,
y=y,
window=win,
marks=marks,
pops=rpois(lambda=5,n=pmax(1,n.seeds)))
My first question is, how is it possible to add a variable that has no classification in the ppp object? I checked the ppp documentation and there is no mention of pops.
The second question I have is about using double variables, the next line requires an sapply function to define dimensions.
dim1<-pmax(1,sapply(seeds1$marks$pops, FUN=function(x)rpois(n=1,sqrt(x))))
I have never seen the $ function being used twice, and seeds2$marks$pop returns $ operator is invalid for atomic vectors. Could you explain what is going on here?
Many thanks.
That's several questions - please ask one question at a time.
From your post it is not clear whether you are trying to understand someone else's code, or developing code yourself. This makes a difference to the answer.
Just to clarify, this code does not come from inside the spatstat package; it is someone's code using the spatstat package to generate data. There is code in the spatstat package to generate simulated realisations of a Poisson cluster process (which is I think what you want to do), and you could look at the spatstat code for rPoissonCluster to see how it can be done correctly and efficiently.
The code you have shown here has numerous errors. But I will start by answering the two questions in your title.
The rules for creating ppp objects are set out in the help file for ppp. The help says that if the argument window is given, then unmatched arguments ... are ignored. This means that in the line seeds2<-ppp(x=x,y=y,window=win,marks=marks,pops=rpois(lambda=5,n=pmax(1,n.seeds)))
the argument pops will be ignored.
The idiom sapply(seeds1$marks$pops, FUN=f) is perfectly valid syntax in R. If the object seeds1 is a structure or list which has a component named marks, which in turn is a structure or list which has a component named pops, then the idiom seeds1$marks$pops would extract it. This has nothing particularly to do with sapply.
Now turning to errors in the code,
The line n.seeds<-lambda*win$xrange[2]*win$yrange[2] is presumably meant to calculate the expected number of cluster parents (cluster seeds) in the window. This would only work if the window is a rectangle with bottom left corner at the origin (0,0). It would be safer to write n.seeds <- lambda * area(win).
However, the variable n.seeds is used later as it it were the number of cluster parents (cluster seeds). The author has forgotten that the number of seeds is random with a Poisson distribution. So, the more correct calculation would be n.seeds <- rpois(1, lambda * area(win))
However this is still not correct because cluster parents (seed points) outside the window can also generate offspring points inside the window. So, seed points must actually be generated in a larger window obtained by expanding win. The appropriate command used inside spatstat to generate the cluster parents is bigwin <- grow.rectangle(Frame(win), cluster_diameter) ; Parents <- rpoispp(lambda, bigwin)
The author apparently wants to assign two mark values to each parent point: a random angle and a random number pops. The correct way to do this is to make the marks a data frame with two columns, for example marks(seeds1) <- data.frame(angles=runif(n.seeds, max=2*pi), pops=rpois(n.seeds, 5))
I connect Tableau to R and execute an R function for recommending products. When R ends, the return value is a string which will have all products details, like below:
ID|Existing_Prod|Recommended_Prod\nC001|NA|PROD008\nC002|PROD003|NA\nF003|NA|PROD_ABC\nF004|NA|PROD_ABC1\nC005|PROD_ABC2|NA\nC005|PRODABC3|PRODABC4
(Each line separated by \n indicating end of line)
On Tableau, I display the calculated field which is as below:
ID|Existing_Prod|Recommended_Prod
C001|NA|PROD008
C002|PROD003|NA
F003|NA|PROD_ABC
F004|NA|PROD_ABC1
C005|PROD_ABC2|NA
C005|PRODABC3|PRODABC4
Above data reaches Tableau through a calculated field as a single string which I want to split based on pipeline ('|'). Now, I need to split this into three columns, separated by the pipeline.
I used Split function on the calculated field :
SPLIT([R_Calculated_Field],'|',1)
SPLIT([R_Calculated_Field],'|',2)
SPLIT([R_Calculated_Field],'|',3)
But the error says "SPLIT function cannot be applied on Table calculations", which is self explanatory. Are there any alternatives to solve this ?? I googled to check for best practices to handle integration between R and Tableau and all I could find was simple kmeans clustering codes.
Make sure you understand how partitioning and addressing work for table calcs. Table calcs pass vectors of arguments to the R script, and receive a single vector in response. The cardinality of those vectors depends on the partitioning of the table calc. You can view that by editing the table calc, clicking specific dimensions. The fields that are not checked determine the partitioning - and thus the cardinality of the arguments you send and receive from R
This means it might be tricky to map your problem onto this infrastructure. Not necessarily impossible. It was designed to send a series of vector arguments with one cell per partitioning dimension, say, Manufacturer and get back one vector with one result per Manufacturer (or whatever combination of fields partition your data for the table calc). Sounds like you are expecting an arbitrary length list of recommendations. It shouldn’t be too hard to have your R script turn the string into a vector before returning, but the size of the vector has to make sense.
As an example of an approach that fits this model more easily, say you had a Tableau view that had one row per Product (and you had N products) - and some other aggregated measure fields in the view per Product. (In Tableau speak, the view’s level of detail is at the Product level.)
It would be straightforward to pass those measures as a series of argument vectors to R - each vector having N values, and then have R return a vector of reals of length N where the value returned at each location was a recommender score for the product at that position. (Which is why the ordering aka addressing of the vectors also matters)
Then you could filter out low scoring products from the view and visually distinguish highly recommended products.
So the first step to understanding R integration is to understand how table calcs operate with partitioning and addressing and to think in terms of vectors of fixed lengths passed in both directions.
If this model doesn’t support your use case well, you might be able to do something useful with URL actions or the JavaScript API.
I am currently attempting to implement a trading idea that I have been playing around with. It consists of 50+ securities and has a strategy very similar to this one. (Current package I am using is quantmod).
http://www.r-bloggers.com/backtesting-a-simple-stock-trading-strategy/
For those who aren't interested in clicking, it is a strategy that will look at the pass X days( in his case 200 ) and enter a position depending on the peak reached in the stock. I understand how to do this strategy for my idea, but I cannot grasp how to aggregate my data into one summary.
Is there a way I can consolidate the summary for all the positions I have entered into one larger portfolio summary and chart that against the S&P 500?
Any advice on where I can find resources or being lead to the information. I have looked at portfolio analysis package for R and I do not believe that will be much help to me.
Thank you in advance.
Edit: In the link, at the bottom, there are 3 indexes that are FTSE, N225, DJIA. Could i combine those 3 summaries to show the same output as below, BUT combined
FTSE:
Me Index
Cumulative Return 3.56248582 3.8404476
Annual Return 0.05667121 0.0589431
Annualized Sharpe Ratio 0.45907768 0.3298633
Win % 0.53216374 0.5239884
Annualized Volatility 0.12344579 0.1786895
Maximum Drawdown -0.39653398 -0.5256991
Max Length Drawdown 1633.00000 2960.0000
Could I get that same output but for the 3 securities data combined? Is there a effective way of doing that. Thank you so much. Happy holidays
It's a little unclear to me what you mean by "combine" in this case. If you want a single column representing the combined returns from all three exchanges as if they were a single unified market, that's really tricky, because the exchanges trade in different currencies (British pounds; U.S. dollars, Japanese Yen, etc.). The underlying analysis would have to be modified substantially to take into account fluctuating daily foreign exchange rates.
I suspect that this is NOT want you want. Rather, you are simply asking how to take three sequential two-column outputs and turn them into a single parallel six-column output.
If that is indeed what you want, then you need to rewrite the testStrategy() function shown near the bottom of the link. As it's currently written, that function takes three inputs: an index name myStock (with allowed values of FTSE, DJIA, or N225), and two integer values, nHold and nHigh. You would need to change it so that it instead accepts five inputs; e.g., myStockA, myStockB and myStockC, plus the two integer values already mentioned. Then each of the lines currently referring to myStock would have to be replicated three times. Finally, the two cbind() lines that you see at the bottom would have to be modified so that instead of merging the data together into only two columns, you include all six.
For a good intro tutorial on how to write and modify your own R functions, please see this. To understand how to use the cbind() function, which you will have to call with six rather than two inputs, please see this.
I am trying my hand at learning Latent Component Analysis, while also learning R. I'm using the poLCA package, and am having a bit of trouble accessing the attributes. I can run the sample code just fine:
ds = read.csv("http://www.math.smith.edu/r/data/help.csv")
ds = within(ds, (cesdcut = ifelse(cesd>20, 1, 0)))
library(poLCA)
res2 = poLCA(cbind(homeless=homeless+1,
cesdcut=cesdcut+1, satreat=satreat+1,
linkstatus=linkstatus+1) ~ 1,
maxiter=50000, nclass=3,
nrep=10, data=ds)
but in order to make this more useful, I'd like to access the attributes within the objects created by the poLCA class as such:
attr(res2, 'Nobs')
attr(res2, 'maxiter')
but they both come up as 'Null'. I expect Nobs to be 453 (determined by the function) and maxiter to be 50000 (dictated by my input value).
I'm sure I'm just being naive, but I could use any help available. Thanks a lot!
Welcome to R. You've got the model-fitting syntax right, in that you can get a model out (don't know how latent component analysis works, so can't speak to the statistical validity of your result). However, you've mixed up the different ways in which R can store information pertaining to a model.
poLCA returns an object of class poLCA, which is
a list containing the following elements:
(. . .)
Nobs number of fully observed cases (less than or equal to N).
maxiter maximum number of iterations through which the estimation algorithm was set
to run.
Since it's a list, you can extract individual elements from your model object using the $ operator:
res2$Nobs # number of observations
res2$maxiter # maximum iterations
In some cases, there might be extractor functions to get this information without having to do low-level indexing. For example, many model-fitting functions will have a fitted method, which pulls out the vector of fitted values on the training data; and similarly residuals pulls out the vector of residuals. You should check whether there are such extractor functions provided by the poLCA package and use them if possible; that way, you're not making assumptions about the structure of the model object that might be broken in the future.
This is distinct to getting the attributes of an object, which is what you use attr for. Attributes in R are what you might call metadata: they contain R-specific information about an object itself, rather than information about whatever it is the object relates to. Examples of common attributes include class (the class of an object), dim (the dimensions of an array or matrix), names (names of individual elements of a vector/list/array) and so on.
I want to test some of the newer sparse linear solvers and I want to know if there is a fast way of filling in the matrix. The format I'm interested is CSR (http://goo.gl/hLXYd). Let's say the matrix, in CSR format, is given by:
values(num non-zero elements)
columns(num non-zero elements)
rowIndex(num rows + 1)
The sparse matrix under consideration derives from networks. So, I have thousands of nodes and some of them are connected between them by lines. So, the matrix is structurally symmetric. Each connection (i,j) adds something to the diagonal terms (i,i) and (j,j) and to the off-diagonal (i,j) and (j,i). I could have several connections between the same nodes (i,j,1), (i,j,2)... So, I might need to revisit the 2 diagonal and 2 off-diagonal elements more than once.
I know I can get the beginning of the row by doing rowIndex(i). Then, I would have to run through the elements columns(rowIndex(i):rowIndex(i+1)-1) to find where is j situated.
The question:
Is there a way of accessing the elements faster, while in CSR format, without having to do a search every time I want to update an element?
Some clarifications:
I just need to fill in the matrix from scratch. The matrix is structurally symmetric and not really symmetric. The values saved have to do with network data (impedances, resistances etc), they have real values. In general Value(i,j)<>Value(j,i). I have tuples of the form (name1,i1,j1,value1), (name2,i2,j2,value2) etc. These tuples are not sorted, and 2 tuples can refer to the same i,j values, meaning they need to be added
Thanks in advance!
What you have is so called triplet sparse format. Creation of CRS, including removing duplicate entries and summing the values, can be implemented very efficiently. Before programing it yourself, have a look at the SuiteSparse library. It is written in C, but I'm sure you will understand the principle. What interests you is the cholmod_triplet.c file, which implements the functionality you need.
Essentially, the conversion is performed using two phase bucket sort on your row and column indices. This algorithm has linear complexity, which is important if you are interested in processing large data sets.
Edit If you want to skip explicit creation of the triplet format all together, you can do that by generating the (row, col) connectivities on the fly and adding them to a dynamic sparse structure. I usually do it using insertion sort and sorted lists, which is in practice the fastest. It is also faster than triplet to CRS conversion, and uses much less memory. The method goes as follows:
if you know approximately, how many non-zero entries there are in every row, for every row you pre-allocate an array of (empty) column indices, and a separate array for the values (not linked list, but a simple array) of that size. Something like
static_lists_cols[row] = malloc(sizeof(int)*expected_number_of_non_zeros)
static_lists_vals[row] = malloc(sizeof(double)*expected_number_of_non_zeros)
If you do not know that, you choose an initial size and reallocate as needed (using some block size large enough to avoid reallocation overhead) when the row lists are full.
for every (row, col) pair you insert the col into the sorted list corresponding to row using insertion sort. For small (up to a few hundred) non-zeros per row linear search is the fastest. For larger number of non-zeros per row you can use bisection to locate the correct place to insert the col index.
col is inserted into rowth sorted list by moving the non-zero entries with higher column index in the sorted list. This is cache-friendly, since the rows are in practice small enough to fit into any cache nowadays.
After you finish you need to assemble the individual sorted lists into a valid CRS structure by copying the individual row lists into the final columns. The same with values.
You could actually avoid the last step by pre-allocating a static 'array of lists' if you are ok that some of the rows can have zero entries. You will hence have a constant number of entries per row, some of which might be zero. Sometimes that is ok.
This method is faster than using triplet to sparse conversion, at least for FEM models, for which I use it. The general reason is that memory bandwidth is the bottleneck here, and the above scheme uses much less memory:
creating the triplet format takes time, and you need to write the triplets to memory
conversion to CRS requires reading and writing the triplets at least once to sort them (actually a bit more than once, if you look at the algorithm. You sort twice, and you need auxiliary data structures.)
depending on the connectivity structure, you may end up having a large number of (row, col) duplicates in the triplet format, which are removed during the assembly by adding the corresponding values. This overhead does not exist in the method above - if the col already exists in the row list, you simply update the corresponding value.
updating the sorted lists can be done in parallel if you assign row ranges to individual workers. No communication, nor synchronization is needed. Assuring load balancing is another story...
Have a look at a performance comparison of using those two methods (Figure 1) for triangular elements in 2D. Note that the performance difference depends on the ratio of the number of entries in the triplet to assembled sparse matrix format (Table 2). But in general, the method is never worse than triplet to crs conversion, and triplets need to be created in the first place. You can also download a MATLAB MEX function sparse_create, which is a part of mutils package (see the downloads section).
Your question seems to confuse 2 rather different questions:
What is a fast way of creating a matrix in CSR form ?
Is there a faster way of reading values from a matrix already stored in CSR form ? (Faster, that is, than the straightforward approach you describe)
So here are 2 answers:
In general, read the network data from whatever form it is in into something like a dictionary of keys (other intermediate forms are available and may be more appealing to you for speed or other reasons); then turn that intermediate structure into the CSR form of the matrix. More on this below.
I don't believe so, not with a matrix stored in CSR form. This relative slowness of access is part of the price you pay for saving space. You've traded time for space, or space for time, depending on your point of view.
Your description of your input data suggests that you should consider devising your own intermediate form into which to marshal the raw data. Since your adjacency matrix is symmetric you only need to store, in any form, half of it. Further, you probably don't need to store the elements along the main diagonal -- I'm guessing either that node i is always connected to node i or never so that the nature of the network determines the value stored at (i,i). I'm a little uncertain of the information you want to store at each node of the matrix, is it the number of connections between i and j or something else ?