I am trying to read data available and write it to a NetCDF file.
Say, I am reading temperature along different time, depth, latitude and longitude values, I will have to create a whole 4D grid of time, depth, latitude and longitude as dimensions.
However, the data I am recording has values at very few points. For example, in one of the cases, I had data at 155 points, while the grid was of 50x16x16x18 along time, depth latitude and longitude respectively. Thus I had data in only 155 points out of a grid having 230400 cells. Rest all points had fill values.
It seemed quite useless to have so many fill values. Is it possible to write a legitimate netCDF file with only the points that had data or maybe fewer use of fill values?
I am using NetCDF Java library for the process.
Thank you so much in advance.
It should be possible to represent the data at each grid point using one of the discrete sampling geometries (DSG) outlined by the CF Conventions (here are some examples). Perhaps one of these representations would work for your case (maybe timeSeries or timeSeriesProfile)? The DSGs are often talked about in the context of observational data, but they should apply to sub-sampled model output as well.
Any N-dimensional sparse array can be represented as a list (or 1-D array) of tuples, where each tuple has N coordinate value, and one data value.
If the array is sufficiently sparse, the list-based representation occupies less space ... on disk, and in memory.
Now the simple list-based representation is NOT good for random access because you need to scan through list to access the value at any point in the original array. You can improve on this (in the in-memory version):
If you order the list based on the coordinates and use an ArrayList, you can perform a binary search to find the value for a set of coordinates. This gives O(log N) indexing, with no additional memory overhead.
If you use a HashMap<Coords, Value>, you can get O(1) lookup. However, this comes at a significant addition memory cost. Probably around 50 to 80 additional bytes per entry compared to using an ArrayList representation.
Related
I am working with a very large netCDF file in three dimensions (lat/lon/time). The resolution is 300 meters and the time variable has 25 steps, which leads to 64800x129600x25 cells.
The one variable contained in the file is an integer (ranging from -36 to 120) but represents an underlying factor, which is the problem.
It is a land cover data set, so for example: -20 means the cell is of the land type Forest or 10 means the cell is covered by water.
I want to reshape the netCDF file such that there is an additional dimension which represents every factor level of the original variable. And the variable would then be just a 1 or 0 per cell indicating the presence of every factor level at a certain lat/lon/time.
The dimensions would then be lat/lon/time/land type.
Here is an example data set, that does not concern land type but is small enough that it can be used for testing. And here is some code to read it in:
library(ncdf4)
# Download the data
download.file("http://schubert.atmos.colostate.edu/~cslocum/code/air.sig995.2012.nc",
mode="wb", destfile = "test.nc")
test.ncdf <- nc_open("test.nc", write=TRUE)
# See the lon,lat,time dimensions
print(test.ncdf)
tmp.array <- ncvar_get(test.ncdf, varid="air")
I'm not sure if the raster package is better more suited for this task. For very small netCDF-files I have managed the intended result to some extent, by extracting the data and then stacking it as a data.frame.
Any help or pointing in the right direction would be greatly appreciated.
Thanks in advance.
If I understand correctly, you want to have a set of fields for each type that are 1 or 0 as a function of lat/long/time. e.g. if you are looking a forest you want an array which is 1 when the factor=20 and 0 otherwise.
I know you want to do this in a 4 dimensional array, for that you will need to use R I expect as you tagged the question. But if you don't mind to have a series of 3D arrays for types, a quick and easy way to do this is to use CDO to process the integer array
cdo eqc,-20 air.sig995.2012.nc test.nc
The issue with this is that the output variable still has the same name
(you don't say what it is called, so I refer to it as sfctype), and so you would need to change the meta data with nco.
Therefore a better way would be to use expr in cdo.
cdo expr,"forest=sfctype==-20" air.sig995.2012.nc forest.nc
This makes a new variable called forest which is 1 or 0.
You could now process all the types you want, and then merge them into one file:
cdo expr,"forest=(sfctype==-20)" air.sig995.2012.nc type_forest.nc
cdo expr,"forest=(sfctype==10)" air.sig995.2012.nc type_water.nc
...etc...
cdo merge type_*.nc combined_file.nc
(I don't think you need the curly brackets, but it is a clearer syntax)
...almost what you wanted in a few lines, but not quite... I am not sure how to "stack" these new variables into a 4D array if you really need that, but perhaps nco can do it.
I am asking this here because I couldn't find the answer I am looking for elsewhere and I don't know where else I could ask this. I hope someone can reply without saying that the question is irrelevant to the forum. I have a biology background and I am currently using bioinformatics. I need to understand in lay language hash tables and suffix trees. Something simple, I don't get the O(n) concepts and all that stuff, I think they are both kind of the same: a way to store string data? But I would like to understand better the differences. This will help enormously to other people like me. We are a lot in this field now!
Thanks in advance.
OK, lets use bioinformatics to help illustrate the differences.
Let's say you have several DNA sequences that are pretty long. If we want to store these sequences in a datastructure.
If we want to use a hashtable
A Hashtable is a useful way to store a bunch of objects but very quickly search the datastructure to see if we already contain a particular object.
One bioinformatics usecase that we can solve with a hashtable is de-duping a large sequence set. Let's say we have a huge dataset of next-gen sequenced data and we want to de-duplicate it before we assemble. We can use a hashtable to store the unique sequences. Before inserting any sequences into the hashtable, we can first check to see if it already exists in the hashtable and if it does we skip that read. Only if it is not yet in the hashtable do we add it. Then when we are done the elements in the hash will be the unique sequences.
Hashtables are basically an array of LinkedLists. Each cell in the array we will call a "bin". When we insert or search for something in the hashtable, we have to first know what bin it is in. The way we determine which bin to use is by a hash algorithm.
We have to come up with a hash algorithm. Something that will convert our sequence into a number. A requirement of this equation is the same sequence must always evaluate to the same number. It's OK if different sequences evaluate to the same number (which is called as hash collision) since there are an infinite number of possible sequences and we will only have a limited range of possible number values in our hash.
A simple hash algorithm is to assign a value to each base A =1 G =2 C = 3 T =4 (assume no ambiguities) then we can just sum up the bases in our sequence. This would mean that any sequences with the same number of As, Cs Gs and Ts will have the same hash value. If we wanted, we could also have a more complicated algorithm that also takes position into account so to get the same number we would have to also have the same sequence in the same order.
Once we have our hash algorithm. We can make a hash table by binning the sequences by their hash values. The more bins we have in our table, the fewer hash values per bin. Hashtables are often implemented by an array of LinkedLists. This is a very fast lookup because to see if a sequence is in our hashtable or to add a new sequence to our hash table, we just compute the hash value for the sequence to see what bin it is in, then we only have to look at the values inside that bin. We can ignore the rest of the bins.
suffix tree
A Suffix Tree is a different datastructure which is a graph where each node is (in this case) a residue in our sequence. Edges in the graph will point to the next node etc. So for example if our sequence was ACGT the path in the graph will be A->C->G->T->$. If we had another sequence ACTT the path will be A->C->T->T->$.
We can combine consecutive nodes if there is only 1 path so in the previous example since both sequence start with AC then the paths will be AC->G->T->$and AC->T->T->$.
In bioinformatics this is really useful for substring matching (like finding repetitive regions or primer binding sites etc) since we can easily see where there are subpaths in our graph that match our motif.
Hope that helps
I want to analyse angles in movement of animals. I have tracking data that has 10 recordings per second. The data per recording consists of the position (x,y) of the animal, the angle and distance relative to the previous recording and furthermore includes speed and acceleration.
I want to analyse the speed an animal has while making a particular angle, however since the temporal resolution of my data is so high, each turn consists of a number of minute angles.
I figured there are two possible ways to work around this problem for both of which I do not know how to achieve such a thing in R and help would be greatly appreciated.
The first: Reducing my temporal resolution by a certain factor. However, this brings the disadvantage of losing possibly important parts of the data. Despite this, how would I be able to automatically subsample for example every 3rd or 10th recording of my data set?
The second: By converting straight movement into so called 'flights'; rule based aggregation of steps in approximately the same direction, separated by acute turns (see the figure). A flight between two points ends when the perpendicular distance from the main direction of that flight is larger than x, a value that can be arbitrarily set. Does anyone have any idea how to do that with the xy coordinate positional data that I have?
It sounds like there are three potential things you might want help with: the algorithm, the math, or R syntax.
The algorithm you need may depend on the specifics of your data. For example, how much data do you have? What format is it in? Is it in 2D or 3D? One possibility is to iterate through your data set. With each new point, you need to check all the previous points to see if they fall within your desired column. If the data set is large, however, this might be really slow. Worst case scenario, all the data points are in a single flight segment, meaning you would check the first point the same number of times as you have data points, the second point one less, etc. The means n + (n-1) + (n-2) + ... + 1 = n(n-1)/2 operations. That's O(n^2); the operating time could have quadratic growth with respect to the size of your data set. Hence, you may need something more sophisticated.
The math to check whether a point is within your desired column of x is pretty straightforward, although maybe more sophisticated math could help inform a better algorithm. One approach would be to use vector arithmetic. To take an example, suppose you have points A, B, and C. Your goal is to see if B falls in a column of width x around the vector from A to C. To do this, find the vector v orthogonal to C, then look at whether the magnitude of the scalar projection of the vector from A to B onto v is less than x. There is lots of literature available for help with this sort of thing, here is one example.
I think this is where I might start (with a boolean function for an individual point), since it seems like an R function to determine this would be convenient. Then another function that takes a set of points and calculates the vector v and calls the first function for each point in the set. Then run some data and see how long it takes.
I'm afraid I won't be of much help with R syntax, although it is on my list of things I'd like to learn. I checked out the manual for R last night and it had plenty of useful examples. I believe this is very doable, even for an R novice like myself. It might be kind of slow if you have a big data set. However, with something that works, it might also be easier to acquire help from people with more knowledge and experience to optimize it.
Two quick clarifying points in case they are helpful:
The above suggestion is just to start with the data for a single animal, so when I talk about growth of data I'm talking about the average data sample size for a single animal. If that is slow, you'll probably need to fix that first. Then you'll need to potentially analyze/optimize an algorithm for processing multiple animals afterwards.
I'm implicitly assuming that the definition of flight segment is the largest subset of contiguous data points where no "sub" flight segment violates the column rule. That is to say, I think I could come up with an example where a set of points satisfies your rule of falling within a column of width x around the vector to the last point, but if you looked at the column of width x around the vector to the second to last point, one point wouldn't meet the criteria anymore. Depending on how you define the flight segment then (e.g. if you want it to be the largest possible set of points that meet your condition and don't care about what happens inside), you may need something different (e.g. work backwards instead of forwards).
Trying to create an array from an xyz data file. The data file is arranged so that x,y,z of each atom is on a new line and I want the array to reflect this.
Then to use this array to find find the distance from each atom in the list with all the others.
To do this the array has been copied such that atom1 & atom2 should be identical to the input file.
length is simply the number of atoms in the list.
The write statement: WRITE(20,'(3F12.9)') atom1 actually gives the matrix wanted but when I try to find individual elements they're all wrong!
Any help would be really appreciated!
Thanks guys.
DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE ::atom1,atom2'
ALLOCATE(atom1(length,3),atom2(length,3))
READ(10,*) ((atom1(i,j), i=1,length), j=1,3)
atom2=atom1
distn=0
distc=0
DO n=1,length
x1=atom1(n,1)
y1=atom1(n,2) !1st atom
z1=atom1(n,3)
DO m=1,length
x2=atom2(m,1)
y2=atom2(m,2) !2nd atom
z2=atom2(m,3)`
Your READ statement reads all the x coordinates for all atoms from however many records, then all the y coordinates, then all the z coordinates. That's inconsistent with your description of the input file. You have the nesting of the io-implied-do's in the READ statement around the wrong way - it should be ((atom1(i,j),j=1,3),i=1,length).
Similarly, as per the comment, your diagnostic write mislead you - you were outputting all x ordinates, followed by all y ordinates, etc. Array element order of a whole array reference varies the first (leftmost) dimension fastest (colloquially known as column major order).
(There are various pitfalls associated with list directed formatting that mean I wouldn't recommend it for production code (or perhaps for input specifically written with the knowledge of and defence against those pitfalls). One of those pitfalls is that the READ under list directed formatting will pull in as many records as it requires to satisfy the input list. You may have detected the problem earlier if you were using an explicit format that nominated the number of fields per record.)
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 ?