Julia> nVector = 1000 # Usually varies between 1e4 and 2e5Ġ.080671 seconds (6 allocations: 53.406 MiB, 77.77% gc time)Ġ.132145 seconds (3.01 k allocations: 107.407 MiB, 46.73% gc time)Įventually he says he wants all of the matrices to be different sizes, in which case this won’t work. Julia> nMatrix = 1000 # Usually varies between 1e4 - 1e7, sometimes as high as 1e8 Your job can be expressed as a single matrix-matrix multiplication if you use the proper memory layout. You probably want to use the mighty GEMM. As mentioned in my comments on the first Julia code, the total number of matrices is usually very large (1e4 - 1e8) so I think I’d rather use shared memory so that I don’t have nProc * sizeof(M) from multiple processes with their own copies of the data. So not only is the code not “6-threads = ~6x faster” but it’s eating up alot of RAM too. #34.264 ms (2976 allocations: 106.60 MiB)Īnd tracking the julia.exe process in task manager shows >14GB RAM utilization (128GB available), plus takes about a minute to run. R = zeros(N1,nVector for i = 1:nMatrix # Iterate through the matrices But when I naively try to use multi-threading: # export JULIA_NUM_THREADS=6 I have a 12 physical-core workstation (and access to a 72-core node) and it sure would seem like I could parallelize across the matrices. Matlab 2018b Comparison LASTN = maxNumCompThreads(1) ĭisp()Īre there any thoughts on this? As a long-time Matlab user, that’s the Julia that seems most natural to me… but are there other things I’ve missed… preferably without completely obfuscating my code?Īssuming that I have mostly maxed out performance of Julia, I’ve looked into parallel computations. Which isn’t too shabby While not quite as fast as single-threaded Matlab 2018b, we’re on the same order of magnitude - so I chalk this up to different math libraries: R = M * V # Matrix-Matrix multiplication is equivalent to naive approach NVector = 1000 # Usually varies between 1e4 and 2e5įor i = 1:nMatrix # Iterate through the matricesįor j = 1:nVector # Iterate through the vectors NMatrix = 1000 # Usually varies between 1e4 - 1e7, sometimes as high as 1e8 Pseudocode: M(N1,N2,nMatrix) x D(N2,nVector) => R(N1,nVector,nMatrix) But for now I’m just trying to understand performant Julia on this “array of matrices” case. In Matlab I might think of this as a cell-array of matrices and a cell array of vectors. Each matrix is the same size (N1xN2) in my current form, but eventually I’d like to remove this requirement, so that each matrix-vector combination can have arbitrary size. Each matrix multiplies the same, entire list of vectors. Here we discuss how to perform matrix multiplication in Matlab along with the examples.I have a critical portion of code that essentially involves the multiplication of many pre-computed matrices by many pre-computed vectors. This is a guide to Matrix Multiplication in Matlab. Both the methods used for matrix multiplication are easy and simple to implement. Matrix multiplication is a very difficult and complex operation in mathematics but we implement the same in Matlab we can easily get the output without error. In the above example, the dimension of the first matrix are 3 rows and 4 columns and dimensions of the second matrix are 3 rows and 3 columns so a number of columns of the first matrix are not equal to the number of rows of the second matrix so multiplication cannot execute. Let us assume two matrices are mat1 and mat2, Let us consider two matrix mat1 and mat2, Here are some of the examples of matrix multiplication in Matlab which are given below: Example #1 Step 2: assign a 3 rd variable for output and give command mtimes.Įxamples to Implement Matrix Multiplication.A statement can be written as mtimes ( matrix 1, matrix 2 ) In this method, there is no need for operators we can give the direct command to the input matrix. Step 2: assign 3 rd variable for output and write a statement as matrix 1 * matrix 2.Step 1: accept two matrix by declaring two variables.Here are some of the steps that we need to follow as given below: we can directly declare the matrices or we can accept input from the user. To multiply two matrices first we need two matrix. There are two ways to multiply matrix one is by using multiplication ‘*’ operator. How to Perform Matrix Multiplication in Matlab? Let us assume first matrix dimensions are 2 rows and 3 columns and second matrix dimensions are 4 rows and 3 columns then we cannot perform multiplication because a number of columns in the first matrix and number of rows in the second matrix are not the same. If there are two matrices then a number of columns of the first matrix should be equal to the number of rows of the second column. There are some rules of matrix multiplication just like mathematics. Hadoop, Data Science, Statistics & others
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