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Parallel Architectures
Published in Pranabananda Chakraborty, Computer Organisation and Architecture, 2020
The information being processed by a vector processor may not be in consecutive memory locations. But they are usually ordered to have a fixed distance that separates successive elements which are to be merged into a single vector. This distance is called stride. The stride for a vector expresses the address increment used to move from one element to the next at the time of vector access. Consider a two-dimensional vector, and assume that a program is written to access rows or columns of this vector. To accomplish this, the stride value is provided. The load unit uses this stride value to find these locations, and load them into the vector registers whenever required. For example, suppose a two-dimensional (2-D) vector of size 8 × 8 is stored in the main memory in a row-major order. If the stride is set to 1, then we can fetch a row of 8 elements. If the stride is set to 8, then we can fetch a column of 8 elements.
Introduction
Published in Randall L. Eubank, Ana Kupresanin, Statistical Computing in C++ and R, 2011
Randall L. Eubank, Ana Kupresanin
The list class provides another important R data structure where objects are obtained by combining elements from various classes. A function in R is allowed to return only one object as output. † As a result, lists turn out to be a key aspect of the language that provide a vehicle for bundling together different objects that might be produced in an analysis into a single object (namely, a list) that can be returned at the end of computation. The default choice of FALSE for byrows stems from the fact that matrices in R are stored in column major order. In contrast, C/C++ uses row major order. To see the difference, let a1,a2,…,amn be a sequence of numbers that comprise the elements of an m×n array. With column major order the (i,j) th element of the matrix will be a(j-1)m+i while for row major order it will be a(i-1)n+j.
Linear Systems
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Various high-level languages store numeric data in matrix-like arrays. If the storage pattern assumes that consecutive entries are elements in the same matrix row, the matrix is said to be in row-major order. On the other hand, if consecutive entries are items in the same column, the matrix is said to be in column-major order. The following are the storage schemes used by some high-level languages
Linear Algebra on Parallel Structures Using Wiedemann Algorithm to Solve Discrete Logarithm Problem
Published in IETE Journal of Research, 2022
K S Spoorthi, R. Padmavathy, S K Pal, S Ravi Chandra
First row major linked list is used to store the matrix. In row major order list the sparsity of the matrix is taken into consideration. Hence every row contains only non-zero columns. This contains two lists such as row list and column list. Rowlist has two links, one which points to the first non-zero column of the list, second one points to the next row, and a variable to store the row number. Columnlist contains a link that points to the next column and one variable which stores the column number and one variable to store the value of the column. Figures 7 and 8 show lists structure and matrix formed from the structures. The matrix structure is shown as ‘C’ language structure in the figures.
Sparktope: linear programs from algorithms
Published in Optimization Methods and Software, 2022
The variables in the LP are denoted as follows. They correspond to the values of variables in the source code at a given time t in the execution. Binary variables. represents the value of binary variable i after t steps of computation. For convenience we may group W consecutive bits together as an (unsigned) integer variablei. represents the value of the jth bit of integer variable i after t steps of computation. The bits are numbered from right (least significant) to left (most significant), the rightmost bit being numbered 1.Binary arrays A binary array is stored in consecutive binary variables from some base location α. The array index m is stored as a W-bit integer and so we must have .2-dimensional binary arrays A two-dimensional binary array , , is stored in row major order in consecutive binary variables , , from some base location α. The array indices m and c are stored as W-bit integers and so we must have . If v = W, the rows of may be addressed as W-bit integers.Step counter.Variable represents the instruction to be executed at time t. It takes value 1 if line i of the assembly code is being executed at time t and 0 otherwise.