I am currently converting MATLAB to C++ with armadillo. I have a somewhat large cx_cube, 900x251x64, and I have uvec, "index", that I would like to use to index into the cube like so:
data(index,:,:);//matlab version
Looking at armadillo syntax I've thought about these 2.
Q.subcube(first_row,first_col,first_slice,last_row,last_col, last_slice); //"index" may or may not be continuous so won't work
Q.rows(index); // not proper syntax
It looks like my only 2 options would be
Q.elem( vector_of_indices )
Q( vector_of_indices )
but I am not too sure on how they would work to grab the numbers that I need.
Usually when converting MATLAB code to C++ with armadillo you want to reorder dimensions according to how you want to access it.
The api for non-contiguous views for cubes only includes individual element access with Q.elem( vector_of_indices ) and Q( vector_of_indices ), or individual slices access with Q.slices( vector_of_slice_indices ).
From your MATLAB code you seem to want to access individual matrices contained in the 3D array using you vector of indexes. In that case the non-contiguous view specifying slice indexes will work. All you need to do is using the third dimension instead of the first one when converting your MATLAB code to armadillo. That is, if the cube has dimension 251x64x900 you can easily access matrices with 251x64 dimension as slices.
Related
Edited...
Thanks for every one to try to help me!!!
i am trying to make a Finite Element Analysis in Mathemetica.... We can obtain all the local stiffness matrices that has 8x8 dimensions. I mean there are 2000 matrices they are similar but not same. every local stiffness matrix shown like a function that name is KK. For example KK[1] is first element local stiffness matrix
i am trying to assemble all the local matrices to make global stiffness matrix. To make it easy:
Do[K[e][i][j]=KK[[e]][[i]][[j]],{e,2000},{i,8},{j,8}]....edited
Here is my question.... this equality can affect the analysis time...If yes what can i do to improve this...
in matlab this is named as 3d array but i don't know what is called in Mathematica
what are the advantages and disadvantages of this explanation type in Mathematica...is t faster or is it easy way
Thanks for your help...
It is difficult to understand what your question is, so you might want to reformulate it.
As others have mentioned, there is no advantage to be expected from a switch from a 3D array to DownValues or SubValues. In fact you will then move from accessing data-structures to pattern matching, which is powerful and the real strength of Mathematica but not very efficient for what you plan to do, so I would strongly suggest to stay in the realm of ordinary arrays.
There is another thing that might not be clear for someone more familiar with matlab than with Mathematica: In Mathematica the "default" for arrays behave a lot like cell arrays in matlab: each entry can contain arbitrary content and they don't need to be rectangular (as High Performance Mark has mentioned they are just expressions with a head List and can roughly be compared to matlab cell arrays). But if such a nested list is a rectangular array and every element of it is of the same type such arrays can be converted to so called PackedArrays. PackedArrays are much more memory efficient and will also speed up many calculations, they behave in many respect like regular ("not-cell") arrays in matlab. This conversion is often done implicitly from functions like Table, which will oten return a packed array automatically. But if you are interested in efficiency it is a good idea to check with Developer`PackedArrayQ and convert explicitly with Developer`ToPackedArray if necessary. If you are working with PackedArrays speed and memory efficiency of many operations are much better and usually comparable to verctorized operations on normal matlab arrays. Unfortunately it can happen that packed arrays get "unpacked" by some operations, so if calculations become slow it is usually a good idea to check if that has happend.
Neither "normal" arrays nor PackedArrays are restricted in the rank (called Depth in Mathematica) they can have, so you can of course create and use "3D arrays" just as you can in matlab. I have never experienced or would know of any efficiency penalties when doing so.
It probably is of interest that newer versions of Mathematica (>= 10) bring the finite element method as one of the solver methods for NDSolve, so if you are not doing this as an exercise you might want to have a look what is available already, there is quite excessive documentation about it.
A final remark is that you can instead of kk[[e]][[i]][[j]] use the much more readable form kk[[e,i,j]] which is also easier and less error prone to type...
extended comment i guess, but
KK[e][[i]][[j]]
is not the (e,i,j) element of a "3d array". Note the single
brackets on the e. When you use the single brackets you are not denoting an array or list element but a DownValue, which is quite different from a list element.
If you do for example,
f[1]=0
f[2]=2
...
the resulting f appears similar to an array, but is actually more akin to an overloaded function in some other language. It is convenient because the indices need not be contiguous or even integers, but there is a significant performance drawback if you ever want to operate on the structure as a list.
Your 'do' loop example would almost certainly be better written as:
kk = Table[ k[e][i][j] ,{e,2000},{i,8},{j,8} ]
( Your loop wont even work as-is unless you previously "initialized" each of the kk[e] as an 8x8 array. )
Note now the list elements are all double bracketed, ie kk[[e]][[i]][[j]] or kk[[e,i,j]]
I have a 4x4x1250 matrix in MATLAB. I want to find a way to move through the 4x4 matrices slice by slice in order to find the condition of the 4x4 matrices individually.
I don't want to do it in a loop because I want to do this on the GPU and would like it to be indexed.
I saw "squeeze", but I don't think it works for 3D arrays...
I kind of want to use arrayfun, but I don't know how to indicate the specific dimension that I'm interested in.
Any ideas?
Edit: I thought the details I gave are sufficient, nevertheless:
I have a matrix A, size 4x4x1250.
I am interested in the conditions of the 1250 4x4 matrices that make up A. So lets say B = A(:,:,1).
I want to calculate cond(B), but in reality I want 1250 of these calculations.
If I do arrayfun, I don't know how to specify the specific dimension of A along which to slice.
ARRAYFUN disregards the shape of the input, and operates in a purely element-wise fashion. There's also PAGEFUN on the GPU which operates on pages of an array - however, PAGEFUN only really offers an advantage if you're using one of the functions explicitly supported - otherwise it operates in an element-wise fashion.
Is there a way to work with C-ordered or non-contiguous arrays natively in Julia?
For example, when using NumPy, C-ordered arrays are the default, but I can initialize a Fortran ordered array and do computations with that as well.
One easy way to do this was to take the Transpose of a matrix.
I can also work with non-contiguous arrays that are made via slicing.
I have looked through the documentation, etc. and can't find a way to make, declare, or work with a C-ordered array in Julia.
The transpose appears to return a copy.
Does Julia allow a user to work with C-ordered and non-contiguous arrays?
Is there currently any way to get a transpose or a slice without taking a copy?
Edit: I have found how to do slicing.
Currently it is available as a different type called a SubArray.
As an example, I could do the following to get the first row of a 100x100 array A
sub(A, 1, 1:100)
It looks like there are plans to improve this, as can be seen in https://github.com/JuliaLang/julia/issues/5513
This still leaves open the question of C-ordered arrays.
Is there an interface for C-ordered arrays?
Is there a way to do a transpose via a view instead of a copy?
Naturally, there's nothing that prevents you from working with row-major arrays as a chunk of memory, and certain packages (like Images.jl) support arbitrary ordering of arbitrary-dimensional arrays.
Presumably the main issue you're wondering about is linear algebra. Currently I don't know of anything out-of-the-box, but note that matrix multiplication in Julia is implemented through a series of functions with names like A_mul_B, At_mul_B, Ac_mul_Bc, etc, where t means transpose and c means conjugate. The parser replaces expressions like A'*b with Ac_mul_B(A, b) without actually taking the transpose.
Consequently, you could implement a RowMajorMatrix <: AbstractArray type yourself, and set up special multiplication rules:
A_mul_B(A::RowMajorMatrix, B::RowMajorMatrix) = At_mul_Bt(A, B)
A_mul_B(A::RowMajorMatrix, B::AbstractArray) = At_mul_B(A, B)
A_mul_B(A::AbstractArray, B::RowMajorMatrix) = A_mul_Bt(A, B)
etc. In addition to these two-argument versions, there are 3-argument versions (like A_mul_B!) that store the result in a pre-allocated output; you'd need to implement those, too. Finally, you'd also have to set up appropriate show methods (to display them appropriately), size methods, etc.
Finally, Julia's transpose function has been implemented in a cache-friendly manner, so it's quite a lot faster than the naive
for j = 1:n, i = 1:m
At[j,i] = A[i,j]
end
Consequently there are occasions where it's not worth worrying about creating custom implementations of algorithms, and you can just call transpose.
If you implement something like this, I'd encourage you to contribute it as a package, as it's likely that others may be interested.
I'm trying to develop a program in C to convert a sparse matrix file into a dense matrix. From what I've read, the best approach would be the use of linked lists but I have no experience with them and haven't found a good online resource explaining the subject. I'm not looking for a quick solution but rather a website or text source that can explain how the process works so I can apply it to this project. What resources I have seen, suggest using three arrays to handle the values in the matrix (The row, column, and individual value) and two arrays for the vector (one for the row, the other for the column). Thanks!
The file format you've specified is for a dense matrix. A 10x10 matrix with 100 elements is dense. A sparse matrix has fewer than n*m elements and all "missing" elements are assumed to be 0. The point of doing it this way is so that matrices that are almost all zero (which happens in a lot of applications) will use less space. But using a sparse matrix format to store a dense matrix will use far more space than just a plain array.
One common sparse matrix file format is called MatrixMarket and it looks very similar to what you described. The first line has three values, # of rows, # of columns, # of nonzero elements (called nnz). Then you have nnz lines of the actual elements in a triplet: (row #) (column #) (value)
If your sparse matrix is in a similar format then you don't need any sparse matrix in memory. Just scan the values and fill in your dense array directly.
If you do want to have a sparse matrix in memory then there are several options for how to store it. Triplets is the easiest, and it's just an in-memory version of the MatrixMarket file. 3 arrays, or 1 array of structs.
The most common structure for linear algebra operations is Compressed Sparse Columns (CSC) or Compressed Sparse Rows (CSR). I'll let you look that up, but if you want a C implementation to play with you should look at Tim Davis' CSparse. This is also how MatLAB stores sparse matrices, Tim was one of the people who wrote that part of MatLAB.
It sounds like a linked list may not be what you're looking for, but this site offers a pretty comprehensive tutorial on the subject. It may help shed some light on whether or not it would be appropriate for your problem... Good luck!
I went through the topic and found out this link quite useful and simple at the same time.
Storing matrices in a relational database
But can you please let me know if the way mentioned as
A B C D
E F G H
I J K L
[A B C D E F G H I J K L]
is the best and simple or even reliable way of storing the matrix elements in the database. Moreover I need to multiply two matrices and make the operation dynamic. So will the storage of data this create any problems for the task?
In postgresql you can actually have multidimensional arrays, define your own types and define your own functions on those types. For instance one could simply do:
CREATE TABLE tictactoe (
squares integer[3][3]
);
See The PostgreSQL manual for info on how to create your own types.
I think it pretty much depends on how you want to use the matrices in your application.
Is the DB only for persistence for the same application, speed is important, and sizes cannot be known in advance? Make your own serialization scheme, and save the binary blob.
Is the DB for sharing in between applications, with the size not known in advance? Use the comma delimited list.
Are you concerned with data integrity, type safety, and would like to query individual cells? Then use the (row, col, cell value) schema.
Do you know that your matrices are of fixed size and relatively small, for example 4X4 transformation matrices, and will have a 1 to 1 relationship to whatever element you have in the DB? Then you could actually have 16 rows in your table, layed out in line.
Think about your use cases, and experiment!
is the best and simple or even reliable way of storing the matrix elements in the database. Moreover I need to multiply two matrices and make the operation dynamic. So will the storage of data this create any problems for the task?
I'll start by saying both approaches are valid, but the second one is not sufficient as written by you. You have to have some other information, like the length of the rows or the (row, col) indexes of each element to store a matrix as a 1D array. This is commonly done for sparse matricies, where there are lots of zeros surrounding values clustered on either side of the diagonal.
Persisting the matrix in a database and operating on it in memory are two separate things.
Tasks like multiplying require (row, col) indexes. Storing the matrix as a 2D array means that you'll have them, so no other info is needed. The 1D array needs this info too, so you'll have to supply it.
The advantage swings to the 1D array for sparse matricies. You don't have to store zero values outside the bandwidth in that case, but your operations like addition and multiplication become more complex to code.