suggested using various matrix multiplication characteristics to predict. Improving Performance of Sparse Matrix-Vector Multiplication Ali Pınar Michael T. Fleury University of Essex, Department of Electronic Systems Engineering, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom e-mail: [email protected] MATMUL, a C program which compares various methods for computing the matrix product. Using standard multiplication, execution takes a minute. General matrix-matrix multiplication (GEMM) is a fundamental operation in many scientific, engineering, and machine learning applications and is one of the key routines in the BLAS (basic linear algebra subprograms) domain. March 30, 2009. For that purpose I can't use your code because (1) it rolls out own centralized scheduling via own channel, (2) parallel for will cause bottleneck on memory throughput so it can't potentially scale. sources are made by Cedric Nugteren, errors by. Heath Department of Computer Science and Center of Simulation of Advanced Rockets University of Illinois at Urbana-Champaign Abstract Sparse matrix-vector multiplication (SpMxV) is one of the most important computational kernels in scientiﬁc computing. Anatomy of High-Performance Matrix Multiplication KAZUSHIGE GOTO and ROBERT A. After compilation, use. TMS320C6748: Matrix multiplication benchmark. 7 ) ms with 10 runs performed a=rand(1000,1000); b=rand(1000,1000); c=rand(1000,1000); tic for i=1:100 c=a*b; end toc/100 2) Python performance ( %timeit a. Time complexity of matrix multiplication is O(n^3) using normal matrix multiplication. For special cases such as sparse matrices, you can write specialized algorithms. Performance comparison of matrix-matrix multiplication (GEMM)s on Tesla V100 (Volta) using Tensor Cores versus Tesla P100 (Pascal). That is, better performance will require architec-tural changes. Sep 14, 2005 · The program provided by the link on the top performs a matrix/vector multiplication. See full list on mathsisfun. Since there is very little data dependency, this function is the perfect. The matrix multiplication function was selected as a benchmark because of the abundance of matrix operations in DSP applications. This post provides an review of efficiency for basic sparse matrix data structures in the context of sparse matrix-vector multiplication (SpMV) on GPU. They show how a comparison of υTC with υTAB and Cω with ABω can detect and correct errors introduced in matrix C (where υT and ω are checksum vectors). A Matrix Multiplication Benchmark. In this article, we explain how to design and measure of the performance using Intel MKL SGEMM, and outline about 7 tips to help developers to perform performance tests and quickly evaluate the floating pointing computing capability (FLOPS) on a. A Matrix Multiplication Benchmark MATMUL is a C program which compares various methods for computing the matrix product A * B = C. 0 benchmark. MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!) There are many algorithms built in, including the simple triple DO loop. Sparse Matrix-Matrix Multiplication Benchmark Code for Intel Xeon and Xeon Phi. It is assumed that the student is familiar with C programming, but no other background is assumed. point addition and multiplication execute in one clock cycle, so the savings from this method are not expected to be large. The orginal version is a simple code doing the multilication in an intuitive way, with 3 nested loops to perform the sum of products for each A[i][j] term. I changed everything to incorporate floats, and now there is a problem. It would be good if someone could give some benchmark about multiplication of two 3000by3000 matrices by using GPU and mention the model of his/her GPU. The obvious thing to do is to pick say M x values of x from the interval [ 0, A] and M y values of y from the interval [ 0, B], then form two matrices X = { X i ( x j) }, 1 ≤ i ≤ N and 1 ≤ j ≤ M x, and Y = { Y i ( y j) }, 1 ≤ i ≤ N and 1 ≤ j ≤ M y, and finally multiply them as X ⊤ Y or Y ⊤ X using Mathematica's Dot function. TMS320C6748: Matrix multiplication benchmark. Computing matrix products is a central part of computational applications. first row, first column). Matrix Multiplication Benchmarks¶. Sep 17, 2020 · Sparse Matrix-Vector Multiplication The need to accelerate this operation comes from its application in Krylov methods on large sparse matrices, whose SpMVs are performed iteratively. cronin • 4 years ago. It also displays the matrix and the two vectors (multiplication and result). 0 client JVM comes out on top over GCC with full optimizations. Matrix multiplication on big-data processing framework. In the single core benchmarks, Blaze 3. TMS320C6748: Matrix multiplication benchmark. Insired by this StackOverflow question I decided to run my own benchmarks to compare frameworks like Numpy, Blas and Eigen3 in computational speed. If somehow the matrix multiplication function does not account for the cache limitation when the matrix size grows large and ends up causing a lot of cache thrashing, then really there is no easy way to do large matrix multiplication effectively on the DSP using the function as is. To show some real-live application results, I develop a Matrix Structural Analysis. C - for bubble sort, IBM's 1. files listed here. matrix-matrix multiplication (when performed with a tiling algorithm) would be more memory bandwidth efficient that. Let's replicate the result in Python. 2 days ago · High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. Matrix multiplication is a function of linear algebra that allows you to produce a matrix from two matrices that represents a composition. There are two papers that I know of that go into detail about this, one by McKellar in 1969 and another by Prokop in 1999. dot: If both a and b are 1-D (one dimensional) arrays -- Inner product of two vectors (without complex conjugation) If both a and b are 2-D (two dimensional) arrays -- Matrix. uk Abstract itself contributed to the performance of the algorithm. Implementing SpMM e ciently on throughput-oriented processors, such as the graphics processing unit (GPU), requires. We like building things on level 3 BLAS routines. Program re-ordering for improved L2 cache hit rate. 2 days ago · High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. You will specifically learn about: Block-level matrix multiplications. Multi-dimensional pointer arithmetic. Matrix multiplication, also known as matrix product and the multiplication of two matrices, produces a single matrix. I am trying to find out how long a matrix multiplication takes on different processors. For that purpose I can't use your code because (1) it rolls out own centralized scheduling via own channel, (2) parallel for will cause bottleneck on memory throughput so it can't potentially scale. Matrix Multiplication Revisited. Design decisions are jus-. The following instructions are for *nix-based systems. Raw benchmark numbers in CSV format are available here and the benchmark source code for each language can be found in the perf. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!) There are many algorithms built in, including the simple triple DO. matrix-matrix multiplication (when performed with a tiling algorithm) would be more memory bandwidth efficient that. In this post, I’m going to discuss the efficiency of block sparse matrix-vector multiplication on GPU. The result of this dot product is the element of resulting matrix at position [0,0] (i. For multiplying two matrices, use the dot method. Iterative algorithm. Depending on what I set BLOCK_SIZE, the results become unpredictable. C - for bubble sort, IBM's 1. Matrix multiplication is a traditionally intense mathematical operation for most processors. High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. Our first assignment is to write a benchmark in C/C++. The first step is the dot product between the first row of A and the first column of B. Mar 7, 2016. matrix-matrix multiplication (when performed with a tiling algorithm) would be more memory bandwidth efficient that. To show some real-live application results, I develop a Matrix Structural Analysis. Optimizing Sparse Matrix-Matrix Multiplication for the GPU Steven Daltony Nathan Bellz Luke N. See full list on quantstart. Mar 12, 2021 · NumPy Multiplication Matrix. 0, SuanShu has implemented an advanced algorithm for even faster matrix multiplication. 2 days ago · High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. Let us create a Thread class that implements Runnable Interface. rand ( i , i ). WebGL2-compute vs. Existing solutions achieve good performance for certain types of matrices, but fail to accelerate all kinds of matrices in the same manner. Sep 14, 2005 · The program provided by the link on the top performs a matrix/vector multiplication. uk Abstract itself contributed to the performance of the algorithm. Fleury University of Essex, Department of Electronic Systems Engineering, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom e-mail: [email protected]x. We quickly describe naive and optimized CPU algorithms and then delve more deeply into solutions for a GPU. The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries c i j = ∑ k = 1 m a i k b k j. From the data he provided, matrix multiplication using C# is two to three times slower than using C++ in comparable. This repo evaluates different matrix multiplication implementations given two large square matrices (2000-by-2000 in the following example): To compile the evaluation program: or omit the CBLAS setting you don't have it. Improving Performance of Sparse Matrix-Vector Multiplication Ali Pınar Michael T. Matrix multiplication on big-data processing framework. dot in numpy. Therefore we have decided to present (almost) all examples in two versions. In this study, the matrix multiplication, which is a common and time-consuming. Nevertheless, I found that there were some limitations in Hotspot's. We quickly describe naive and optimized CPU algorithms and then delve more deeply into solutions for a GPU. The ordinary matrix multiplication A B can be performed by setting α to one and C to an all-zeros matrix of the appropriate size. We can see that the CLAPACK multiplication of an identity matrix is faster ( x14) than the MKL. Nov 14, 2003 · SNAP matrix benchmark - Java vs. In the above image, 19 in the (0,0) index of the outputted matrix is the dot product of the 1st row of the 1st matrix and the 1st column of the 2nd matrix. In this article, we explain how to design and measure of the performance using Intel MKL SGEMM, and outline about 7 tips to help developers to perform performance tests and quickly evaluate the floating pointing computing capability (FLOPS) on a. Build and Run. 9 GHz) dgemm (GOTO) dgemm (ESSL) dgemm (ATLAS) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 1 2 3 4 5 6 m=n. See full list on martin-thoma. We like building things on level 3 BLAS routines. Consolidating the comments: No, you are very unlikely to beat a typical BLAS library such as Intel's MKL, AMD's Math Core Library, or OpenBLAS. The setting. MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!) There are many algorithms built in, including the simple triple DO. The obvious thing to do is to pick say M x values of x from the interval [ 0, A] and M y values of y from the interval [ 0, B], then form two matrices X = { X i ( x j) }, 1 ≤ i ≤ N and 1 ≤ j ≤ M x, and Y = { Y i ( y j) }, 1 ≤ i ≤ N and 1 ≤ j ≤ M y, and finally multiply them as X ⊤ Y or Y ⊤ X using Mathematica's Dot function. The main reason why I wrote this article - and the code - is the poor performance of the clBlas library on NVIDIA GPUs. OpenGL ES Compute shaders are similar to OpenCL kernels and scripts are matched almost one-to-one (i. This paper shows that performance significantly improves when different optimization techniques are applied. A common operation on sparse matrices is to multiply them by a dense vector. To show some real-live application results, I develop a Matrix Structural Analysis. Anatomy of High-Performance Matrix Multiplication KAZUSHIGE GOTO and ROBERT A. 2 days ago · High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. In this section, we shall therefore restrict ourselves to the programming problem of improving the performance of matrix multiplication by code modiﬁcations that imple-ment the standard O(N3) algorithm. Figure 1: A simple finite element mesh model. This repository contains the benchmark code supplementing my blog post on a matrix-matrix multiplication benchmark on Intel Xeon and Xeon Phi. They show how a comparison of υTC with υTAB and Cω with ABω can detect and correct errors introduced in matrix C (where υT and ω are checksum vectors). Also included in Level 3 are routines for computing B ← α T − 1 B , {\displaystyle {\boldsymbol {B}}\leftarrow \alpha {\boldsymbol {T}}^{-1}{\boldsymbol {B}},}. cronin • 4 years ago. 99 C++ (ms) 6137. This benchmark is a classical example to demonstrate the importance of code transformations like blocking (tiling) for scientific numerical codes computing on large arrays. and Marlin proposed an algorithm to predict matrix multiplication performance of Apache Spark. Multiplication of two matrices involves dot products between rows of first matrix and columns of the second matrix. 20 functions; the rest are pure Python implementations. General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block of a number of high-level algorithms and real-world applications. I'm trying to show my boss how the GPU improves matrix multiplication by a great amount. matrix multiplication performance tests in CPU and GPU. 1807 views. the example of Matrix Multiplication to introduce the basics of GPU computing in the CUDA environment. We consider both optimized “naïve” matrix multiplication with cubic complexity, as well as the Strassen multiplication algorithm which has a lower asymptotic run-time complexity. After compilation, use. See full list on martin-thoma. 0, SuanShu has implemented an advanced algorithm for even faster matrix multiplication. During the development of some linear algebra/QM · Without seeing the implementations, there's very little. This thesis presents a toolkit called Sparsity for the automatic optimization of sparse matrix-vector multiplication. In a recent post, I took a look at matrix multiplication in pure Java, to see if it can go faster than reported in SIMD Intrinsics on Managed Language Runtimes. Each cell in the output matrix is the result of the multiplication of a row from m1 against a column from m2. Using standard multiplication, execution takes a minute. I measured the elapsed time of the multiplication of two 2400x2400 matrices consisting of uniformly distributed random numbers between 0 and 10 ("DGEMM2400"). I'm trying to show my boss how the GPU improves matrix multiplication by a great amount. Multiplication of two matrices involves dot products between rows of first matrix and columns of the second matrix. There are two papers that I know of that go into detail about this, one by McKellar in 1969 and another by Prokop in 1999. It is a type of binary operation. To achieve higher performance, the GPU needs to perform higher-level operations. In the programming guide, I coded in the matrix multiplication without shared memory access for integers, and it worked perfectly. MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!) There are many algorithms built in, including the simple triple DO. Google Scholar; Mehmet Deveci, Christian Trott, and Sivasankaran Rajamanickam. Anatomy of High-Performance Matrix Multiplication KAZUSHIGE GOTO The University of Texas at Austin and ROBERT A. This is the speed determining factor in my applications - if DGEMM runs N times faster, my programs will also run N times faster. (although I've heard from similar results in c++) struct mat4 { float[4][4] m; mat4 opMul(in mat4 _m); } mat4 mul(in mat4 m1, in mat4 m2); I've tested this 2 multiplication functions (overloaded and free). In this post, I'm going to discuss the efficiency of block sparse matrix-vector multiplication on GPU. This benchmark is a classical example to demonstrate the importance of code transformations like blocking (tiling) for scientific numerical codes computing on large arrays. Raw benchmark numbers in CSV format are available here and the benchmark source code for each language can be found in the perf. first row, first column). In modern video games, the 4x4 matrix multiplication is an important cornerstone. To show some real-live application results, I develop a Matrix Structural Analysis. SuanShu v3. Performance-Portable Sparse Matrix-Matrix Multiplication for Many-Core Architectures Mehmet Deveci, Christian Trott, and Sivasankaran Rajamanickam Sandia National Laboratories, Albuquerque, NM fmndevec,crtrott,[email protected] point addition and multiplication execute in one clock cycle, so the savings from this method are not expected to be large. Hello, I'm trying to develop an application in C# for Windows Mobile, which needs two big matrices to be multiplicated (100x15000 and 15000x1). See full list on karlrupp. To show some real-live application results, I develop a Matrix Structural Analysis. The versions of the packages used for the benchmarks. See full list on martin-thoma. sources are made by Cedric Nugteren, errors by. Olsonx Abstract Sparse matrix-matrix multiplication (SpMM) is a key operation in numerous ar-eas from information to the physical sciences. time (); x. 2 days ago · High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. 1 Ò CPU and GPU structure. Here is the result on my machines:. Jan 11, 2016 · Improve cache performance: matrix multiplication as an example It is surprising to see mul1() is 10 times slower than mul2(). Matrix multiplication is one of the most well-known and widely-used linear algebra operations, and is frequently used to demonstrate the high-performance computing capabilities of GPUs. This tool can be used by users to select the best library for their application and by developers for identifying bugs and weaknesses. Hi everyone. Anatomy of High-Performance Matrix Multiplication KAZUSHIGE GOTO and ROBERT A. Matrix-Matrix. Matrix multiplication, also known as matrix product and the multiplication of two matrices, produces a single matrix. Multithreading code for matrix multiplication To optimize the performance of this program, we have to use the advantage of multi-cores. Parallel Matrix Multiplication. Analysing the performance of GPUs in different application scenarios helps to improve computing performance. It makes some operations 100x times faster those of our competitors! The new benchmark can be found here. The code should also work on Windows, but is not tested. Feb 02, 2014 · Matrix Multiplication Benchmark. If A and B are the two matrices, then the product of the two matrices A and B are denoted by: X = AB. Anatomy of High-Performance Matrix Multiplication · 3 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 1 2 3 4 5 6 7 m=n GFLOPS/sec Pentium4 (3. to see the available options. 2 days ago · High Performance GPU Code Generation for Matrix-Matrix Multiplication using MLIR: Some Early Results | Navdeep Katel, Vivek Khandelwal, Uday Bondhugula | Code generation, Computer science, CUBLAS, CUDA, HPC, Matrix multiplication, nVidia, nVidia GeForce RTX 3090, Package. randn (size, size), dtype = np. This repo evaluates different matrix multiplication implementations given two large square matrices (2000-by-2000 in the following example): To compile the evaluation program: or omit the CBLAS setting you don't have it. Matrix Multiplication Revisited. astype ( np. Performance-Portable Sparse Matrix-Matrix Multiplication for Many-Core Architectures Mehmet Deveci, Christian Trott, and Sivasankaran Rajamanickam Sandia National Laboratories, Albuquerque, NM fmndevec,crtrott,[email protected] This post provides an review of efficiency for basic sparse matrix data structures in the context of sparse matrix-vector multiplication (SpMV) on GPU. Nov 01, 2017 · Several algorithms have been studied in the past for this foundational kernel. Matrix Multiplication Performance on Commodity Shared-Memory Multiprocessors G. It makes some operations 100x times faster those of our competitors! The new benchmark can be found here. VAN DE GEIJN The University of Texas at Austin We present the basic principles that underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. First we demonstrate a traditional version with explicit data copying be-. high-performance matrix multiplication. See full list on mathsisfun. 0, SuanShu has implemented an advanced algorithm for even faster matrix multiplication. Anatomy of High-Performance Matrix Multiplication KAZUSHIGE GOTO The University of Texas at Austin and ROBERT A. Jan 11, 2016 · Improve cache performance: matrix multiplication as an example It is surprising to see mul1() is 10 times slower than mul2(). C++ for matrix multiplication ; Nine-Language Performance Round-Up - math and file I/O performance among nine languages ; Performance comparison C++, C# and Java - similar results as mine, mostly ; Java vs. Sparse Matrix-Matrix Multiplication Benchmark Code for Intel Xeon and Xeon Phi. dot( a, b, out=None) Few specifications of numpy. Let’s replicate the result in Python. Matrix Multiplication Benchmarks¶. Matrix multiplication (MM) of two matrices is one of the most fundamental operations in linear algebra. Anatomy of High-Performance Matrix Multiplication KAZUSHIGE GOTO and ROBERT A. Depending on what I set BLOCK_SIZE, the results become unpredictable. matrix-matrix multiplication (when performed with a tiling algorithm) would be more memory bandwidth efficient that. Understanding the performance of sparse matrix-vector multiplication. SuanShu v3. This post provides an review of efficiency for basic sparse matrix data structures in the context of sparse matrix-vector multiplication (SpMV) on GPU. First we demonstrate a traditional version with explicit data copying be-. Matrix multiplication is a traditionally intense mathematical operation for most processors. However, to complete the matrix-by-matrix multiplication, we must execute three more iterations, using values y4 to yF in registers q1 to q3. In this post, I'm going to discuss the efficiency of block sparse matrix-vector multiplication on GPU. We can note an acceleration multipliy by 84 between the MKL and CLAPACK dense matrix multiplication. Build and Run. Implementations of Matrix-Matrix Multiplication We consider the problem of computing the product,C =AB, of two large, dense, N N matrices. The code should also work on Windows, but is not tested. When I perform matrix multiplication with MATLAB, 2048x2048 and even bigger matrices are almost instantly multiplied. 13 Apr 2017. A Benchmark of matrix multiplication between C and Python Motivation After a Python convention in my city (Python Brasil) me, a unqualified newbie and a friend of mine from the comp. Performance-portable sparse matrix-matrix multiplication for many-core architectures. Optimizing Sparse Matrix-Matrix Multiplication for the GPU Steven Daltony Nathan Bellz Luke N. General matrix-matrix multiplication (GEMM) is a fundamental operation in many scientific, engineering, and machine learning applications and is one of the key routines in the BLAS (basic linear algebra subprograms) domain. Starting version 3. Part I was about simple matrix multiplication algorithms and Part II was about the Strassen algorithm. Two benchmarks are performed - the first is multiplication of two random matrices and the second is multiplication of identity matrices. A Matrix Multiplication Benchmark MATMUL is a C program which compares various methods for computing the matrix product A * B = C. Matrix multiplication, also known as matrix product and the multiplication of two matrices, produces a single matrix. academia discussed with a few colleagues about the potential advantages of python, including its application in the scientific field for numerical applications. 4k-by-4k Matrix Multiplication Version Implementation Running time (s) GFLOPS Absolute speedup Relative speedup Fraction of peak 1 Python 25,552. In contrast to ATLAS [20], which utilizes register tiling, cache blocking and instruction scheduling to achieve high performance on pipelined processor. Consolidating the comments: No, you are very unlikely to beat a typical BLAS library such as Intel's MKL, AMD's Math Core Library, or OpenBLAS. I've wrote the code below and it runs successfully. sources are made by Cedric Nugteren, errors by. Nov 01, 2017 · Several algorithms have been studied in the past for this foundational kernel. Since normal matrix multiplication is an O(n³) time algorithm with O(n²) output elements, a reasonable hypothesis could be that those times increase linearly with the size. 0 benchmark. Results (in microseconds per output element):. size = 20000. 1 Ò CPU and GPU structure. Sep 14, 2005 · The program provided by the link on the top performs a matrix/vector multiplication. VAN DE GEIJN The University of Texas at Austin We present the basic principles that underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. It is not possible (or, at least, very hard) to do significantly better (on a CPU). See full list on baeldung. In the single core benchmarks, Blaze 3. Iterative algorithm. First we demonstrate a traditional version with explicit data copying be-. 4k-by-4k Matrix Multiplication Version Implementation Running time (s) GFLOPS Absolute speedup Relative speedup Fraction of peak 1 Python 25,552. The function multiplies two 4x4 matricies (a and b) and stores the result in a product matrix. Thus, not only is the availability of a fault-tolerant matrix-matrix multiplication an important ﬁrst step towards cre-ating fault-tolerant linear algebra libraries, but there is an inherent opportunity for adding fault-tolerance to matrix-matrix multiplication while retaining high-performance. 2 Case Study with Matrix Multiplication • An important kernel in many problems • Optimization ideas can be used in other problems • The most-studied algorithm in high performance computing. For matrix multiplication the simple O(n^3) algorithm, properly optimized with the tricks above, are often faster than the sub-cubic ones for reasonable matrix sizes, but sometimes they win. Multiplication of two matrices involves dot products between rows of first matrix and columns of the second matrix. It would be much better to compare the results with Matlab of course. Multi-dimensional pointer arithmetic. In this post, I’m going to discuss the efficiency of block sparse matrix-vector multiplication on GPU. The Python implementations of matrix_statistics and matrix_multiply use NumPy v1. dot( a, b, out=None) Few specifications of numpy. I measured the elapsed time of the multiplication of two 2400x2400 matrices consisting of uniformly distributed random numbers between 0 and 10 ("DGEMM2400"). For matrix multiplication the simple O(n^3) algorithm, properly optimized with the tricks above, are often faster than the sub-cubic ones for reasonable matrix sizes, but sometimes they win. In a recent post, I took a look at matrix multiplication in pure Java, to see if it can go faster than reported in SIMD Intrinsics on Managed Language Runtimes. After compilation, use. Matrix-Matrix. SuanShu was already the fastest in matrix multiplication and hence linear algebra per our benchmark. Rows of the 1st matrix with columns of the 2nd; Example 1. It displays the time spent in the C++ function and the time spent in the assembly function. General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block of a number of high-level algorithms and real-world applications. Implementations of Matrix-Matrix Multiplication We consider the problem of computing the product,C =AB, of two large, dense, N N matrices. We focus on finding a new format for SpMV on the GPU because existing formats do not achieve good performance on large and unstructured matrices such as those. 0 benchmark. Matrix-vector multiply: n2 data, 2n2 ﬂops 3. If somehow the matrix multiplication function does not account for the cache limitation when the matrix size grows large and ends up causing a lot of cache thrashing, then really there is no easy way to do large matrix multiplication effectively on the DSP using the function as is. Java Matrix Benchmark. Matrix-vector multiplication is entirely memory bandwidth bound, so once you have sorted the coalescing, you are close to optimal performance. Sparse Matrix-Matrix Multiplication Benchmark Code for Intel Xeon and Xeon Phi. VAN DE GEIJN The University of Texas at Austin We present the basic principles which underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. 1024x1024 2048x2048 4096x4096 ----- ----- ----- CUDA C (ms) 43. 1 Ò CPU and GPU structure. This post provides an review of efficiency for basic sparse matrix data structures in the context of sparse matrix-vector multiplication (SpMV) on GPU. sources are made by Cedric Nugteren, errors by. You'll measure and report observed performance on the Stampede system located at TACC. We quickly describe naive and optimized CPU algorithms and then delve more deeply into solutions for a GPU. Hi everyone. Nov 15, 2019 · New matrix multiplication algorithm pushes the performance to the limits. TMS320C6748: Matrix multiplication benchmark. In the above image, 19 in the (0,0) index of the outputted matrix is the dot product of the 1st row of the 1st matrix and the 1st column of the 2nd matrix. and OpenBLAS v0. In this post, I'm going to discuss the efficiency of block sparse matrix-vector multiplication on GPU. Multi-dimensional pointer arithmetic. Since normal matrix multiplication is an O(n³) time algorithm with O(n²) output elements, a reasonable hypothesis could be that those times increase linearly with the size. Proper tensorflow benchmark (You'll find execution times match or are better than GPU skcuda on a Tesla K80): import numpy as np. Analysing the performance of GPUs in different application scenarios helps to improve computing performance. It makes some operations 100x times faster those of our competitors! The new benchmark can be found here. I am trying to find out how long a matrix multiplication takes on different processors. In his article, he compared the performance between C# and C++ in matrix multiplication. Intel® Math Kernel Library (Intel® MKL) provides highly optimized and extensively threaded general matrix-matrix multiplication (GEMM) functions. The amount of compute that we need to perform is 1024 ^ 3 * 2, which is about 2. Heath Department of Computer Science and Center of Simulation of Advanced Rockets University of Illinois at Urbana-Champaign Abstract Sparse matrix-vector multiplication (SpMxV) is one of the most important computational kernels in scientiﬁc computing. For special cases such as sparse matrices, you can write specialized algorithms. You can find two ways to proceed this operation (one in C++ and another in assembler). This forum may not be the best place for a discussion of the many issues involved in performance number-crunching, but I'd very much appreciate comments, suggestions, etc. SuanShu was already the fastest in matrix multiplication and hence linear algebra per our benchmark. The goal of this module is to show the student how to o oad parallel computations to the. The library exploits opportunities to overcome the unique challenges of matrix multiplication at lower precision with bandwidth-bound pre- and post. Matrix Multiplication Performance on Commodity Shared-Memory Multiprocessors G. Matrix-matrix multiplication is implemented as sgemm in cblas, and as np. ies automatic generation of high-performance matrix mul-tiplication on graphics hardware, as matrix multiplication is the most important building block for a variety of nu-merical libraries. Nov 01, 2017 · Several algorithms have been studied in the past for this foundational kernel. 0 (released August, 24th, 2016) is compared to the following third party libraries: MTL4, version 4. It is not possible (or, at least, very hard) to do significantly better (on a CPU). Intel® Math Kernel Library (Intel® MKL) provides highly optimized and extensively threaded general matrix-matrix multiplication (GEMM) functions. Matrix-vector multiplication is entirely memory bandwidth bound, so once you have sorted the coalescing, you are close to optimal performance. point addition and multiplication execute in one clock cycle, so the savings from this method are not expected to be large. This multiplication work is inherently embarrassingly parallel. I found faster implementations than the paper's benchmarks implied was possible. Moreover, the difference of the time consumption during the muliplication of a dense*denseT and an identity matrix is very slim. Let’s replicate the result in Python. SuanShu v3. I changed everything to incorporate floats, and now there is a problem. Mar 12, 2021 · NumPy Multiplication Matrix. first row, first column). Tsilikas and M. Since there is very little data dependency, this function is the perfect. Here is the result on my machines:. Matrix-matrix multiplication is implemented as sgemm in cblas, and as np. Depending on what I set BLOCK_SIZE, the results become unpredictable. Moreover, the difference of the time consumption during the muliplication of a dense*denseT and an identity matrix is very slim. Nov 08, 2018 · It is a low-precision, high-performance matrix-matrix multiplications and convolution library that enables large-scale production servers to run the most powerful deep learning models efficiently. Matrix-Matrix. first row, first column). 0 benchmark. In this article, we explain how to design and measure of the performance using Intel MKL SGEMM, and outline about 7 tips to help developers to perform performance tests and quickly evaluate the floating pointing computing capability (FLOPS) on a. Results (in microseconds per output element):. 0, SuanShu has implemented an advanced algorithm for even faster matrix multiplication. Java Matrix Benchmark (JMatBench) is a tool for evaluating Java linear algebra libraries for speed, stability, and memory usage. A common operation on sparse matrices is to multiply them by a dense vector. Hi everyone. A Matrix Multiplication Benchmark. You can find two ways to proceed this operation (one in C++ and another in assembler). Multiplication is the dot product of rows and columns. This repository contains the benchmark code supplementing my blog post on a matrix-matrix multiplication benchmark on Intel Xeon and Xeon Phi. MATMULcan do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!). With a rapid increase of simulation resolution and precision in fields like quantum chemistry, solid state physics, medicine, and machine learning, fast parallel algorithms become essential for the efficient utilization of powerful, GPU-accelerated supercomputers. Sparse general matrix-matrix multiplication on GPUs is challenging due to the varying sparsity patterns of sparse matrices. Nevertheless, I found that there were some limitations in Hotspot's. The algorithm for MM is very simple, it could be easily implemented in any programming language. Hi everyone. Understanding the performance of sparse matrix-vector multiplication. Mar 12, 2021 · NumPy Multiplication Matrix. Each cell in the output matrix is the result of the multiplication of a row from m1 against a column from m2. Matrix-Matrix. Two benchmarks are performed - the first is multiplication of two random matrices and the second is multiplication of identity matrices. The Python implementations of matrix_statistics and matrix_multiply use NumPy v1. VAN DE GEIJN The University of Texas at Austin We present the basic principles which underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. 6 GHz) dgemm (GOTO) dgemm (MKL) dgemm (ATLAS) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 2 3 4 5 6 7 m=n Power 5 (1. The library exploits opportunities to overcome the unique challenges of matrix multiplication at lower precision with bandwidth-bound pre- and post. Intel® Math Kernel Library (Intel® MKL) provides highly optimized and extensively threaded general matrix-matrix multiplication (GEMM) functions. The NESL code for taking the dot-product of a sparse row with a dense vector x is: sum ( {v * x [i] : (i,v) in row}); This code takes each index-value pair (i,v. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:. 1) Matlab performance: time= (14. You'll measure and report observed performance on the Stampede system located at TACC. files listed here. Each cell in the output matrix is the result of the multiplication of a row from m1 against a column from m2. MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!) There are many algorithms built in, including the simple triple DO. Jan 11, 2016 · Improve cache performance: matrix multiplication as an example It is surprising to see mul1() is 10 times slower than mul2(). I've created a simple 4x4 Matrix struct and have made some tests, with surprising results. Related Papers. 93 C# (ms) 10509. From the data he provided, matrix multiplication using C# is two to three times slower than using C++ in comparable. Raw benchmark numbers in CSV format are available here and the benchmark source code for each language can be found in the perf. For special cases such as sparse matrices, you can write specialized algorithms. A Benchmark of matrix multiplication between C and Python Motivation After a Python convention in my city (Python Brasil) me, a unqualified newbie and a friend of mine from the comp. I'm trying to show my boss how the GPU improves matrix multiplication by a great amount. A Matrix Multiplication Benchmark MATMUL, a C program which compares various methods for computing the matrix product A * B = C. When I perform matrix multiplication with MATLAB, 2048x2048 and even bigger matrices are almost instantly multiplied. Our first assignment is to write a benchmark in C/C++. Since there is very little data dependency, this function is the perfect. Sparse matrix-matrix multiplication (SpGEMM) is a key kernel in many applications in High Performance Computing such as algebraic multigrid solvers and graph analytics. The orginal version is a simple code doing the multilication in an intuitive way, with 3 nested loops to perform the sum of products for each A[i][j] term. The results show that a conventional Xeon system provides the best performance with 1. This forum may not be the best place for a discussion of the many issues involved in performance number-crunching, but I'd very much appreciate comments, suggestions, etc. You can find two ways to proceed this operation (one in C++ and another in assembler). Multiplication of two matrices involves dot products between rows of first matrix and columns of the second matrix. Implementations of Matrix-Matrix Multiplication We consider the problem of computing the product,C =AB, of two large, dense, N N matrices. The following instructions are for *nix-based systems. Matrix-matrix multiply: 2n2 data, 2n2 ﬂops These are examples of level 1, 2, and 3 routines in Basic Linear Algebra Subroutines (BLAS). Since there is very little data dependency, this function is the perfect. This repository contains the benchmark code supplementing my blog post on a matrix-matrix multiplication benchmark on Intel Xeon and Xeon Phi. WebGL2-compute vs. not high because many computing cores are not fully utilised and. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:. The goal of this module is to show the student how to o oad parallel computations to the. first row, first column). We will create a thread for each row in a matrix that does the multiplication in parellel and reduce the processing time. small-scale matrix calculation, the parallelism degree of the GPU is. Since its main component was a dense single-precision matrix-multiplication, I made a call to the SGEMM routine of clBlas. TMS320C6748: Matrix multiplication benchmark. The matrix multiplication function was selected as a benchmark because of the abundance of matrix operations in DSP applications. Matrix-matrix multiplication is implemented as sgemm in cblas, and as np. 99 C++ (ms) 6137. dot (x); print. Part I: Performance of Matrix multiplication in Python, Java and C++. 20 functions; the rest are pure Python implementations. However, for the purposes of this post, single threaded performance. First we demonstrate a traditional version with explicit data copying be-. The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. To show some real-live application results, I develop a Matrix Structural Analysis. first row, first column). Analysing the performance of GPUs in different application scenarios helps to improve computing performance. In the above image, 19 in the (0,0) index of the outputted matrix is the dot product of the 1st row of the 1st matrix and the 1st column of the 2nd matrix. 4k-by-4k Matrix Multiplication Version Implementation Running time (s) GFLOPS Absolute speedup Relative speedup Fraction of peak 1 Python 25,552. General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block of a number of high-level algorithms and real-world applications. VAN DE GEIJN The University of Texas at Austin We present the basic principles that underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. Build and Run. Tsilikas and M. astype ( np. implements matrix multiplication based on CUDA and Tensorflow and performance test analysis. Example of Matrix Multiplication 6. The first step is the dot product between the first row of A and the first column of B. randn (n, n) a = time. See full list on medium. performance is the main reason for using GPUs in matrix computations. I'm contemplating porting my single-precision numerical CUDA code to ATI/AMD platform. and OpenBLAS v0. General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block of a number of high-level algorithms and real-world applications. Starting version 3. A Matrix Multiplication Benchmark. astype ( np. Analysing the performance of GPUs in different application scenarios helps to improve computing performance. Performance is also highly dependent on the nonzero structure of the sparse matrix, the organization of the data and its computation, and the exact parameters of the hardware memory system. 2 Case Study with Matrix Multiplication • An important kernel in many problems • Optimization ideas can be used in other problems • The most-studied algorithm in high performance computing. Depending on what I set BLOCK_SIZE, the results become unpredictable. Sparse general matrix-matrix multiplication on GPUs is challenging due to the varying sparsity patterns of sparse matrices. matrix-matrix multiplication (when performed with a tiling algorithm) would be more memory bandwidth efficient that. The code should also work on Windows, but is not tested. point addition and multiplication execute in one clock cycle, so the savings from this method are not expected to be large. dot in numpy. Understanding the performance of sparse matrix-vector multiplication. 99 C++ (ms) 6137. The Python implementations of matrix_statistics and matrix_multiply use NumPy v1. The matrix multiplication function was selected as a benchmark because of the abundance of matrix operations in DSP applications. For special cases such as sparse matrices, you can write specialized algorithms. import tensorflow as tf. Moreover, the difference of the time consumption during the muliplication of a dense*denseT and an identity matrix is very slim. MATMULcan do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!). Optimizing SpGEMM on modern. C - for bubble sort, IBM's 1. Sparse matrix-matrix multiplication (SpGEMM) is a key kernel in many applications in High Performance Computing such as algebraic multigrid solvers and graph analytics. Performance is also highly dependent on the nonzero structure of the sparse matrix, the organization of the data and its computation, and the exact parameters of the hardware memory system. Since its main component was a dense single-precision matrix-multiplication, I made a call to the SGEMM routine of clBlas. WebGL We can compare performance of Shader 6 with SSBuffers benchmark WebGL2-compute TensorFlow. I'm trying to show my boss how the GPU improves matrix multiplication by a great amount. For that purpose I can't use your code because (1) it rolls out own centralized scheduling via own channel, (2) parallel for will cause bottleneck on memory throughput so it can't potentially scale. For example, I’m. The matrix multiplication function was selected as a benchmark because of the abundance of matrix operations in DSP applications. 1 These not only use vectorization, but also (at least for the major functions) use kernels that are hand-written in architecture-specific assembly language in order to optimally exploit available vector extensions (SSE, AVX), multiple cores, and cache. Multi-dimensional pointer arithmetic. randn (size, size), dtype = np. A Matrix Multiplication Benchmark. A common operation on sparse matrices is to multiply them by a dense vector. Sep 17, 2020 · Sparse Matrix-Vector Multiplication The need to accelerate this operation comes from its application in Krylov methods on large sparse matrices, whose SpMVs are performed iteratively. After compilation, use. Charles Ung92 Intellectual 440 points Part Number: TMS320C6748 Other Parts Discussed in Thread: PROCESSOR-SDK-OMAPL138. from this group of knowledgeable programmers on the data shown below. Matrix Multiplication CPS343 Parallel and High Performance Computing Spring 2020 CPS343 (Parallel and HPC) Matrix Multiplication Spring 2020 1/32. With a rapid increase of simulation resolution and precision in fields like quantum chemistry, solid state physics, medicine, and machine learning, fast parallel algorithms become essential for the efficient utilization of powerful, GPU-accelerated supercomputers. The performance of these algorithms depend on the data structures used in them. Google Scholar; Mehmet Deveci, Christian Trott, and Sivasankaran Rajamanickam. 99 C++ (ms) 6137. We can note an acceleration multipliy by 84 between the MKL and CLAPACK dense matrix multiplication. I’m trying to show my boss how the GPU improves matrix multiplication by a great amount. I found this link which gave me some basic numbers for 16x16 timing. By Sidi Mahmoudi. Nov 08, 2018 · It is a low-precision, high-performance matrix-matrix multiplications and convolution library that enables large-scale production servers to run the most powerful deep learning models efficiently. Figure 3 shows the comparative performance of GP100 (Pascal) to GV100 (Volta) hardware. Charles Ung92 Intellectual 440 points Part Number: TMS320C6748 Other Parts Discussed in Thread: PROCESSOR-SDK-OMAPL138. Moreover, the difference of the time consumption during the muliplication of a dense*denseT and an identity matrix is very slim. Matrix Multiplication Performance on Commodity Shared-Memory Multiprocessors G. For example, I’m. Your starting point is a naive CUDA implementation, plus, for comparison purposes, a high performance multicore implementation. SuanShu was already the fastest in matrix multiplication and hence linear algebra per our benchmark. rand ( i , i ). import tensorflow as tf. Feb 02, 2014 · Matrix Multiplication Benchmark. The goal of this module is to show the student how to o oad parallel computations to the. Now > we are back at the situation that a person who is doing this work > really should just understand how matrix multiplication works and what. import time. See full list on karlrupp. Also included in Level 3 are routines for computing B ← α T − 1 B , {\displaystyle {\boldsymbol {B}}\leftarrow \alpha {\boldsymbol {T}}^{-1}{\boldsymbol {B}},}. js matrix multiplication benchmark WebGL SGEMM with FLOAT RGBA32F textures Demo with HALF_FLOAT RGBA16F textures. Sparse Matrix-Matrix Multiplication Benchmark Code for Intel Xeon and Xeon Phi. Tsilikas and M. The code should also work on Windows, but is not tested. Here is the result on my machines:. Moreover, the difference of the time consumption during the muliplication of a dense*denseT and an identity matrix is very slim. Today, we take a step back from finance to introduce a couple of essential topics, which will help us to write more advanced (and efficient!) programs in the future. The function multiplies two 4x4 matricies (a and b) and stores the result in a product matrix. For that purpose I can't use your code because (1) it rolls out own centralized scheduling via own channel, (2) parallel for will cause bottleneck on memory throughput so it can't potentially scale. In recent years, several efficient SpGEMM algorithms have been proposed for many-core processors such as GPUs. March 30, 2009. Depending on what I set BLOCK_SIZE, the results become unpredictable. See full list on baeldung. Matrix-vector multiplication is entirely memory bandwidth bound, so once you have sorted the coalescing, you are close to optimal performance. 99 C++ (ms) 6137. To show some real-live application results, I develop a Matrix Structural Analysis. Design decisions are. 1 These not only use vectorization, but also (at least for the major functions) use kernels that are hand-written in architecture-specific assembly language in order to optimally exploit available vector extensions (SSE, AVX), multiple cores, and cache. the example of Matrix Multiplication to introduce the basics of GPU computing in the CUDA environment. See full list on gist. I am making some benchmarks with CUDA, C++, C#, Java, and using MATLAB for verification and matrix generation. A Matrix Multiplication Benchmark MATMUL is a C program which compares various methods for computing the matrix product A * B = C. To show some real-live application results, I develop a Matrix Structural Analysis. For example, I'm. Performance evaluation of the sparse matrix-vector multiplication on modern architectures. Optimizing Sparse Matrix-Matrix Multiplication for the GPU Steven Daltony Nathan Bellz Luke N. We focus on finding a new format for SpMV on the GPU because existing formats do not achieve good performance on large and unstructured matrices such as those. A Matrix Multiplication Benchmark MATMUL is a FORTRAN90 program which compares various methods for computing the matrix product A * B = C. The result of this dot product is the element of resulting matrix at position [0,0] (i. This repo evaluates different matrix multiplication implementations given two large square matrices (2000-by-2000 in the following example): To compile the evaluation program: or omit the CBLAS setting you don't have it. We will create a thread for each row in a matrix that does the multiplication in parellel and reduce the processing time. Nov 14, 2003 · SNAP matrix benchmark - Java vs. It would be much better to compare the results with Matlab of course. Matrix multiplication is one of the most well-known and widely-used linear algebra operations, and is frequently used to demonstrate the high-performance computing capabilities of GPUs. Your starting point is a naive CUDA implementation, plus, for comparison purposes, a high performance multicore implementation. Implementations of Matrix-Matrix Multiplication We consider the problem of computing the product,C =AB, of two large, dense, N N matrices. For special cases such as sparse matrices, you can write specialized algorithms. A Matrix Multiplication Benchmark MATMUL, a C program which compares various methods for computing the matrix product A * B = C. General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block of a number of high-level algorithms and real-world applications. Four precisions (real single, real double, complex single, and complex double) of GEMM exist. We consider both optimized “naïve” matrix multiplication with cubic complexity, as well as the Strassen multiplication algorithm which has a lower asymptotic run-time complexity. Multiplication of two matrices involves dot products between rows of first matrix and columns of the second matrix. In this section, we shall therefore restrict ourselves to the programming problem of improving the performance of matrix multiplication by code modiﬁcations that imple-ment the standard O(N3) algorithm. It makes some operations 100x times faster those of our competitors! The new benchmark can be found here. Heath Department of Computer Science and Center of Simulation of Advanced Rockets University of Illinois at Urbana-Champaign Abstract Sparse matrix-vector multiplication (SpMxV) is one of the most important computational kernels in scientiﬁc computing. Sep 14, 2005 · The program provided by the link on the top performs a matrix/vector multiplication. Java Matrix Benchmark. Depending on what I set BLOCK_SIZE, the results become unpredictable. Matrix-Matrix Multiplication on the GPU with Nvidia CUDA In the previous article we discussed Monte Carlo methods and their implementation in CUDA, focusing on option pricing. MATMUL, a C program which compares various methods for computing the matrix product. See full list on quantstart. This thesis presents a toolkit called Sparsity for the automatic optimization of sparse matrix-vector multiplication. Two benchmarks are performed - the first is multiplication of two random matrices and the second is multiplication of identity matrices. randn (size, size), dtype = np. You can find two ways to proceed this operation (one in C++ and another in assembler). The following instructions are for *nix-based systems. This repo evaluates different matrix multiplication implementations given two large square matrices (2000-by-2000 in the following example): To compile the evaluation program: or omit the CBLAS setting you don't have it. implements matrix multiplication based on CUDA and Tensorflow and performance test analysis. A few days ago, I ran across this article by Dmitri Nesteruk. In this article, we explain how to design and measure of the performance using Intel MKL SGEMM, and outline about 7 tips to help developers to perform performance tests and quickly evaluate the floating pointing computing capability (FLOPS) on a. Matrix multiplication performance. academia discussed with a few colleagues about the potential advantages of python, including its application in the scientific field for numerical applications. I worked on a project that required acceleration of code on an NVIDIA Tesla K40m GPU using OpenCL. Matrix multiplication in WebGL2-compute Matrix multiplication C = A x B (SGEMM) tuning for Nvidia GPU (low-end really) demos are based on Tutorial: OpenCL SGEMM tuning for Kepler by Cedric Nugteren (see his test results on Tesla below). MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!) There are many algorithms built in, including the simple triple DO loop. Matrix-matrix multiply: 2n2 data, 2n2 ﬂops These are examples of level 1, 2, and 3 routines in Basic Linear Algebra Subroutines (BLAS). 2 Case Study with Matrix Multiplication • An important kernel in many problems • Optimization ideas can be used in other problems • The most-studied algorithm in high performance computing. For example, I’m. Performance is also highly dependent on the nonzero structure of the sparse matrix, the organization of the data and its computation, and the exact parameters of the hardware memory system.