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# vectorize_code - Tech-Note 1109 How Do I Vectorize My Code...

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Tech-Note 1109: How Do I Vectorize My Code? 1109 How Do I Vectorize My Code? Revison: 1.3 Last Date Modified: 31-August-2000 This technical note provides an introduction to vectorization techniques. In order to understand some of the tricks available, an introduction to MATLAB indexing is provided. Then several vectorization techniques are discussed, in order of simplest to most complicated. There are two aspects to this presentation. Knowledge of all the techniques available is only half of the battle. The other half is knowing when to use them -- recognizing situations where this approach or that one is likely to yield a better (quicker, cleaner) algorithm. Each section provides an example, which proceeds from a description of the problem to a final solution. We hope that illustrating the process by example achieves both of these goals. 1. MATLAB Subscripting A powerful feature of MATLAB is the ability to select subsets of an array or matrix. There are two types of subscripting available in MATLAB. In indexed subscripting , the values of the subscript are the indices of the matrix where the matrix's values are desired. Thus, if A = 1:5, then A([3,5]) denotes the third and fifth elements of matrix A: » A = 1:5; » A([3,5]) ans = 3 5 The second type of subscripting is logical subscripting . With this type of subscripting, the subscript is a matrix the same size as A containing only 0's http://www.mathworks.com/support/tech-notes/1100/1109.shtml (1 of 13) [4/25/2002 2:47:46 PM]

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Tech-Note 1109: How Do I Vectorize My Code? and 1's. The elements of A that are selected have a '1' in the corresponding position of the subscripting matrix. For example, if A = 1:5, then A(logical([0 0 1 0 1])) denotes the third and fifth elements of A: » A = 1:5; » A(logical([0 0 1 0 1])) ans = 3 5 This second type of subscripting is very powerful, and we use it frequently in the following sections. For more information on subscripting, see the Using MATLAB manual. 2. Basic Array Operations: y(i) = fcn(x1(i), x2(i), . ..) The simplest type of vector operations in MATLAB can be thought of as bulk processing . In this approach, the same operation is performed for each corresponding element in a data set (which may include more than one matrix). Suppose you have some data from an experiment. The data measurements are the length L, width W, height H, and mass M of an object, and you want to find the density D of the object. If you had run the experiment once, you would just have one value for each of the four observables (i.e., L, W, H, and M are scalars). Here is the calculation you want to run: D = M/(L*W*H) Now, suppose that you actually run the experiment 20 times. Now L, W, H, and M are vectors of length 20, and you want to calculate the corresponding vector D, which represents the density for each run. In most programming languages, you would set up a loop, the equivalent of the
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vectorize_code - Tech-Note 1109 How Do I Vectorize My Code...

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