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Tutorial outline. • Random facts about NCSA systems, GPUs, and CUDA. – QP & Lincoln cluster configurations. – Tesla S1070 architecture. – Memory alignment for GPU. – CUDA APIs. • Matrix-matrix multiplication example. – K1: 27 GFLOPS. – K2: 44 GFLOPS. – K3: 43 GFLOPS. – K4: 169 GFLOPS. – K3+K4: 173 GFLOPS.
Intro. to Fin. Maths I. A matrix is an array of numbers, written within a set of [ ] brackets, and arranged into a pattern of rows and columns. For example: [ 1 2 3 . Matrix Multiplication. The rule for multiplying matrices can be represented as follows: AB = row 1 of A ? col 1 of B row 1 of A ? col 2 of B row 1 of A ? col 3
Matrix Multiplication. 7.2. Introduction. When we wish to multiply matrices together we have to ensure that the operation is possible and this is not always so. Also, unlike This matrix product is easily generalised to other row and column matrices. For example if C is a 1 ? 4 row matrix and D is a 4 ? 1 column matrix: C =.
D. For two matrices to be multiplied, their dimensions need to be analyzed to determine if it is possible. The number of columns of the first matrix MUST EQUAL the number of rows of the second matrix. Example: [. ] [. ] 3 x 2 and 2 x 5. They are the same so we can multiply these two matrices. The outside numbers tell the
2 Feb 2012 As an example, consider Strassen's algorithm for multiplying two 2?2 matrices, as copied from. Wikipedia: called tensoring, is the basic tool used in matrix multiplication algorithms. 1Not really Here ?, also known as the exponent of matrix multiplication, is defined as the infimum of all ? such that two n
Multiplying matrices. Introduction. One of the most important operations carried out with matrices is matrix multiplication. At first sight this is done in a rather strange way. The reason for this only becomes apparent when matrices are used to solve equations. 1. Some simple examples. To multiply ( 3 7 ) by ( 2. 9 perform the
Add and subtract matrices and multiply matrices Equality of Matrices. Two matrices A = [a ij. ] and B = [b ij. ] are equal if they have the same order (m ? n) and a ij. = b ij for 1 ? i ? m and. 1 ? j ? n. In other words, two matrices are equal if their corresponding entries are equal. Page 6. 6. Example 1 – Equality of Matrices.
2 Nov 2005 Matrix Multiplication. R Horan & M Lavelle. The aim of this document is to provide a short, self assessment programme for students who wish to learn how to multiply tion and subtraction of matrices, as well as scalar multiplication, were Example 1 In each of the following cases, find the product AB.
Matrices Review. Matrix Multiplication : When the number of columns of the first matrix is the same as the number of rows in the second matrix then matrix multiplication can be performed. Here is an example of matrix multiplication for two 2x2 matrices. Here is an example of matrices multiplication for a 3x3 matrix. When A
1 6. 9 3 ][. 0 ?1. ?1 2 ]= [. ?6 11. ?3 ?3 ] for example, to get 1,1 entry of product: C11 = A11B11 + A12B21 = (1)(0) + (6)(?1) = ?6 example 2: [. 0 ?1. ?1 2 ][. 1 6. 9 3 ]= [. ?9 ?3. 17. 0 ] these examples illustrate that matrix multiplication is not (in general) commutative: we don't (always) have AB = BA. Matrix Operations. 2–7

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February 2018