I would like to translate some existing Matlab code that quite naturally uses a lot of multidimensional arrays and I wonder what are the possible options. I want the containers to have copy constructors, default constructors, if possible clear error messages at compilation, access via A[i][j] and in general not to be troublesome. Preferably, they should use the std::move operation for speed.
As far as I can see the options boils down to:
std::vector iterated. It sure works, but it seems stupid to write std::vector<std::vector<std::vector<double> > >for a 3D array. I am also concerned with the overhead in speed and memory.
The boost::multiarray and blitz::Array offer most of the functionality but fails at the copy constructor (see stackoverflow) at runtime. It is unclear to me if there are valid reasons for that.
The Eigen library seems to be very fast but it does not allow copy at all, and has no default constructor, which means that another container has to be used.
The std::array has the disadvantage that the size has to be known when the object is created, so there is no default constructors.
Is there a simpler multidimensional container satisfying all the requests but more frugal than iterated std::vector?
There is good linear algebra package called Armadillo
http://arma.sourceforge.net/
used it with R, happy user
I am not sure this can answer all your needs but I myself had to handle multi-dimensional arrays for creating meshes/grid and wanted to create my own class for that.
My class let's call it MultiArray uses a a one-dimension vector as container.
For instance, writing MultiArray<4, float, 10, 15, 10, 18> A() would create a multi array A[10][15][10][18] in a vector of size 10*15*10*18.
I can access to elements by single index A(i) or by coordinates A[i][j][k][l] by calling A({i,j,k,l}). For performance purpose I have precomputed in the constructor the product of the dimensions in order to compute fastly coordinates->index or index->coordinates.
The code is generic for N dimensions. I can detail some parts if you want.
You have missed another option:
std::valarray
Depending on what your requirements are it could be useful.
http://www.cplusplus.com/reference/valarray/
I've created my own Matrix class were inside the class the information regarding the Matrix is stored in a STL vector. I've notice that while searching the web some people work with a vector of vectors to represent the Matrix information. My best guess tells me that so long as the matrix is small or skinny (row_num >> column_num) the different should be small, but what about if the matrix is square or fat (row_num << column_num)? If I were to create a very large matrix would I see a difference a run time? Are there other factors that need to be considered?
Thanks
Have you considered using an off-the-shelf matrix representation such as boost's instead of reinventing the wheel?
If you have a lot of empty rows for example, using the nested representation could save a lot of space. Unless you have specific information in actual use cases showing one way isn't meeting your requirements, code the way that's easiest to maintain and implement properly.
There are too many variables to answer your question.
Create an abstraction so that your code does not care how the matrix is represented. Then write your code using any implementation. Then profile it.
If your matrix is dense, the "vector of vectors" is very unlikely to be faster than a single big memory block and could be slower. (Chasing two pointers for random access + worse locality.)
If your matrices are large and sparse, the right answer to your question is probably "neither".
So create an abstract interface, code something up, and profile it. (And as #Mark says, there are lots of third-party libraries you should probably consider.)
If you store everything in a single vector, an iterator will traverse the entire matrix. If you use a vector of vectors, an iterator will only traverse a single dimension.
Is it okay to initialize a 2D vector like this (here all values in a 5x4 2D vectro are initialized to 3)?
std::vector<std::vector<int> > foo(5, std::vector<int>(4, 3));
This seems to behave okay, but everywhere I look on the web people seem to recommend initializing such a vector with for loops and push_back(). I was initially afraid that all rows here would point to the same vector, but that doesn't seem to be the case. Am I missing something?
This is perfectly valid - You'll get a 2D vector ([5, 4] elements) with every element initialized to 3.
For most other cases (where you e.g. want different values in different elements) you cannot use any one-liner - and therefore need loops.
Well, the code is valid and it indeed does what you want it to do (assuming I understood your intent correctly).
However, doing it that way is generally inefficient (at least in the current version of the language/library). The above initialization creates a temporary vector and then initializes individual sub-vectors by copying the original. That can be rather inefficient. For this reason in many cases it is preferrable to construct the top-level vector by itself
std::vector<std::vector<int> > foo(5);
and then iterate over it and build its individual sub-vectors in-place by doing something like
foo[i].resize(4, 3);
i want to store some kind of distance-matrix (2D), where each entry has some alternatives (different coordinates). So i want to access the distance for example x=1 with x_alt=3 and y=3 with y_alt=1, looking in a 4-dim multi-array with array[1][3][3][1].
The important thing to notice is the following: the 2 most inner arrays/vectors don't have the same size for different values of the outer ones.
After a first init step, where i calculate the values, no more modifying is needed!
This should be easily possible with the use of stl-vectors:
vector<vector<vector<vector<double> > > >`extended_distance_matrix;
where i can dynamically iterate over the outer 2 dimensions and fill only as much alternatives to the inner 2 dimensions as i need (e.g. with push_back()).
Questions:
Is this kind of data-structure definition possible with Boost.MultiArray? How?
Is it a good idea to use Boost.MultiArray instead of the nested vectors? Performance (especially lookups! (Memory-layout))? Easy of use?
Thanks for any input!
sascha
PS: The boost documentation didn't help me. Maybe one can use multi_array_ref to get already sized arrays into the whole 4D-structure?
Edit:
At the moment i'm thinking of another approach: flattening the alternatives -> one bigger matrix with all the distances between the alternatives. Then i only need to calc the number of alternatives per node, build up the prefix sum (which is describing the matrix position/shift) and can then access the information in a 2-step-way.
But my questions are still open.
it sounds like you need:
multi_array<ublas::matrix<type>,2>
Boost.MultiArray deals with contiguous memory (arranged logically in many dimensions) so it is difficult to add elements in the inner dimensions. MultiArrays can be dynamically resized, e.g. to add elements in any dimension, but this is a costly operation that almost certainly need (internally) reallocation and copying.
Because of that requirement MultiArray is not the best option. But from what you say it looks like a combination of the two would be appropriate to you.
boost::multi_array<std::vector<std::vector<type>>, 2> data
The very nice thing is that the indexing interface doesn't change with respect to boost::multi_array<type, 4>. For example data[1][2][3][4] still makes sense.
I don't know from your post how you handle the inner dimension but it could even make sense to use this:
boost::multi_array<boost::multi_array<type>, 2>, 2> data
In any case, unless you really need to do linear algebra I would stay away from boost::ublas::array, or at most use it for the internal array if type is numeric. boost::multi_array<boost::ublas::array<type>, 2> data which is mentioned in the other answer.
This is my little big question about containers, in particular, arrays.
I am writing a physics code that mainly manipulates a big (> 1 000 000) set of "particles" (with 6 double coordinates each). I am looking for the best way (in term of performance) to implement a class that will contain a container for these data and that will provide manipulation primitives for these data (e.g. instantiation, operator[], etc.).
There are a few restrictions on how this set is used:
its size is read from a configuration file and won't change during execution
it can be viewed as a big two dimensional array of N (e.g. 1 000 000) lines and 6 columns (each one storing the coordinate in one dimension)
the array is manipulated in a big loop, each "particle / line" is accessed and computation takes place with its coordinates, and the results are stored back for this particle, and so on for each particle, and so on for each iteration of the big loop.
no new elements are added or deleted during the execution
First conclusion, as the access on the elements is essentially done by accessing each element one by one with [], I think that I should use a normal dynamic array.
I have explored a few things, and I would like to have your opinion on the one that can give me the best performances.
As I understand there is no advantage to use a dynamically allocated array instead of a std::vector, so things like double** array2d = new ..., loop of new, etc are ruled out.
So is it a good idea to use std::vector<double> ?
If I use a std::vector, should I create a two dimensional array like std::vector<std::vector<double> > my_array that can be indexed like my_array[i][j], or is it a bad idea and it would be better to use std::vector<double> other_array and acces it with other_array[6*i+j].
Maybe this can gives better performance, especially as the number of columns is fixed and known from the beginning.
If you think that this is the best option, would it be possible to wrap this vector in a way that it can be accessed with a index operator defined as other_array[i,j] // same as other_array[6*i+j] without overhead (like function call at each access) ?
Another option, the one that I am using so far is to use Blitz, in particular blitz::Array:
typedef blitz::Array<double,TWO_DIMENSIONS> store_t;
store_t my_store;
Where my elements are accessed like that: my_store(line, column);.
I think there are not much advantage to use Blitz in my case because I am accessing each element one by one and that Blitz would be interesting if I was using operations directly on array (like matrix multiplication) which I am not.
Do you think that Blitz is OK, or is it useless in my case ?
These are the possibilities I have considered so far, but maybe the best one I still another one, so don't hesitate to suggest me other things.
Thanks a lot for your help on this problem !
Edit:
From the very interesting answers and comments bellow a good solution seems to be the following:
Use a structure particle (containing 6 doubles) or a static array of 6 doubles (this avoid the use of two dimensional dynamic arrays)
Use a vector or a deque of this particle structure or array. It is then good to traverse them with iterators, and that will allow to change from one to another later.
In addition I can also use a Blitz::TinyVector<double,6> instead of a structure.
So is it a good idea to use std::vector<double> ?
Usually, a std::vector should be the first choice of container. You could use either std::vector<>::reserve() or std::vector<>::resize() to avoid reallocations while populating the vector. Whether any other container is better can be found by measuring. And only by measuring. But first measure whether anything the container is involved in (populating, accessing elements) is worth optimizing at all.
If I use a std::vector, should I create a two dimensional array like std::vector<std::vector<double> > [...]?
No. IIUC, you are accessing your data per particle, not per row. If that's the case, why not use a std::vector<particle>, where particle is a struct holding six values? And even if I understood incorrectly, you should rather write a two-dimensional wrapper around a one-dimensional container. Then align your data either in rows or columns - what ever is faster with your access patterns.
Do you think that Blitz is OK, or is it useless in my case?
I have no practical knowledge about blitz++ and the areas it is used in. But isn't blitz++ all about expression templates to unroll loop operations and optimizing away temporaries when doing matrix manipulations? ICBWT.
First of all, you don't want to scatter the coordinates of one given particle all over the place, so I would begin by writing a simple struct:
struct Particle { /* coords */ };
Then we can make a simple one dimensional array of these Particles.
I would probably use a deque, because that's the default container, but you may wish to try a vector, it's just that 1.000.000 of particles means about a single chunk of a few MBs. It should hold but it might strain your system if this ever grows, while the deque will allocate several chunks.
WARNING:
As Alexandre C remarked, if you go the deque road, refrain from using operator[] and prefer to use iteration style. If you really need random access and it's performance sensitive, the vector should prove faster.
The first rule when choosing from containers is to use std::vector. Then, only after your code is complete and you can actually measure performance, you can try other containers. But stick to vector first. (And use reserve() from the start)
Then, you shouldn't use an std::vector<std::vector<double> >. You know the size of your data: it's 6 doubles. No need for it to be dynamic. It is constant and fixed. You can define a struct to hold you particle members (the six doubles), or you can simply typedef it: typedef double particle[6]. Then, use a vector of particles: std::vector<particle>.
Furthermore, as your program uses the particle data contained in the vector sequentially, you will take advantage of the modern CPU cache read-ahead feature at its best performance.
You could go several ways. But in your case, don't declare astd::vector<std::vector<double> >. You're allocating a vector (and you copy it around) for every 6 doubles. Thats way too costly.
If you think that this is the best option, would it be possible to wrap this vector in a way that it can be accessed with a index operator defined as other_array[i,j] // same as other_array[6*i+j] without overhead (like function call at each access) ?
(other_array[i,j] won't work too well, as i,j employs the comma operator to evaluate the value of "i", then discards that and evaluates and returns "j", so it's equivalent to other_array[i]).
You will need to use one of:
other_array[i][j]
other_array(i, j) // if other_array implements operator()(int, int),
// but std::vector<> et al don't.
other_array[i].identifier // identifier is a member variable
other_array[i].identifier() // member function getting value
other_array[i].identifier(double) // member function setting value
You may or may not prefer to put get_ and set_ or similar on the last two functions should you find them useful, but from your question I think you won't: functions are prefered in APIs between parts of large systems involving many developers, or when the data items may vary and you want the algorithms working on the data to be independent thereof.
So, a good test: if you find yourself writing code like other_array[i][3] where you've decided "3" is the double with the speed in it, and other_array[i][5] because "5" is the the acceleration, then stop doing that and give them proper identifiers so you can say other_array[i].speed and .acceleration. Then other developers can read and understand it, and you're much less likely to make accidental mistakes. On the other hand, if you are iterating over those 6 elements doing exactly the same things to each, then you probably do want Particle to hold a double[6], or to provide an operator[](int). There's no problem doing both:
struct Particle
{
double x[6];
double& speed() { return x[3]; }
double speed() const { return x[3]; }
double& acceleration() { return x[5]; }
...
};
BTW / the reason that vector<vector<double> > may be too costly is that each set of 6 doubles will be allocated on the heap, and for fast allocation and deallocation many heap implementations use fixed-size buckets, so your small request will be rounded up t the next size: that may be a significant overhead. The outside vector will also need to record a extra pointer to that memory. Further, heap allocation and deallocation is relatively slow - in you're case, you'd only be doing it at startup and shutdown, but there's no particular point in making your program slower for no reason. Even more importantly, the areas on the heap may just around in memory, so your operator[] may have cache-faults pulling in more distinct memory pages than necessary, slowing the entire program. Put another way, vectors store elements contiguously, but the pointed-to-vectors may not be contiguous.