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Working with Arrays in MATLAB Chapter 3 MATLAB Fundamentals Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Review: Scalars and Arrays • In a spreadsheet, we do not need to name every variable: the cell address (row/column) defines the storage location Storage locations for time and displacement values Engineering Computation: An Introduction Using MATLAB and Excel Arrays • In MATLAB and other programming languages, the variables must be named and storage of results must be planned • An array is a variable that has multiple values • An array’s name is followed by an index (or indices, for multi-dimensional arrays) in parentheses Engineering Computation: An Introduction Using MATLAB and Excel Indices of Arrays • Think of the index value as an address • Important: Indices must be positive integers, and must start with one • Example: To store these results, we would define t(1) = 0, t(2) = 0.1, t(3) = 0.2… y(1) = 3, y(2) = 2.45016… Engineering Computation: An Introduction Using MATLAB and Excel Common Mistakes Using Indices with MATLAB • Using an index of zero: • Using an index not an integer: setting t(0.1) equal to a value results in the same error as above Engineering Computation: An Introduction Using MATLAB and Excel Common Mistakes Using Indices with MATLAB • Progressing indices by values other than 1. For example, if we take a temperature reading every 10 seconds, and set the first value as T(10), then zeros are filled in for the first nine values of T: (No error is reported, but this result is probably not what is desired) • All of these errors result from confusion between independent variables and indices. Thinking of indices as addresses helps avoid these errors Engineering Computation: An Introduction Using MATLAB and Excel Multi-Dimensional Arrays • A variable may have more than one index. A twodimensional array is similar to the data storage of a spreadsheet. Instead of a row number and a column letter, a two-dimensional array has two index numbers • Examples: t(1,5) R(3,3) temp(1,20) • Efficient way to store data: if both indices range from 1-10, then the number of values stored is 10 X 10 = 100 Engineering Computation: An Introduction Using MATLAB and Excel Matrices • One- and two-dimensional arrays are also called matrices • Many mathematical operations can be performed with matrices - the name MATLAB comes from “Matrix Laboratory” • The size of a matrix is defined by the numbers of rows and columns. Example; a 3 X 2 matrix: Engineering Computation: An Introduction Using MATLAB and Excel Vectors • One-dimensional matrices are referred to in MATLAB as vectors • Vectors can be classified as column vectors (all values arranged in a single column) or row vectors (all values arranged in a single row) • Caution: in mechanics classes, the term “vector” has a different definition: a vector is defined as a physical quantity which is defined by magnitude and direction Engineering Computation: An Introduction Using MATLAB and Excel Entering Arrays in MATLAB • Consider the matrix: • To enter this matrix in MATLAB: or Commas or spaces separate elements within a row, semicolons separate rows Engineering Computation: An Introduction Using MATLAB and Excel Arrays • We will work with matrix math later, with applications such as solving simultaneous equations • We will create large arrays of results using programming loops. Loops control the execution of repetitive calculations, and the results are often stored in arrays Engineering Computation: An Introduction Using MATLAB and Excel