![]() Implicit looping is everywhere in Matlab with all its other arithmetic and logical operators and the hundreds of built-in functions that handle array inputs and outputs. ![]() But matrix multiplication is just the beginning. The most obvious example of implicit looping in MATLAB is the matrix multiplication operator, in which one asterisk takes the place of three nested for loops, three index variables, eight indices, and scalar multiplication and addition operators that are required in our MATMOL function, for example. Moler's decision some 40 years ago to incorporate those operators directly in MATLAB forced him to incorporate the same implicit looping in the language itself, and it has had a huge impact on numerical programming. The notation of numerical computing included operations like matrix multiplication and matrix transposition each symbolized by single operator, with all the looping and indexing required to carry out those operations implied but not written out on the page. He was using the notation of that field everyday when it occurred to him that there should be a computer language that incorporated that notation. The inventor, Cleve Moler, was and still is an expert in the field of numerical computation. Decisions on implementation are especially important in MATLAB, which was invented expressly to work with matrices and arrays. Deciding which ones to use and how to combine them while coding a particular algorithm can have a profound effect on the speed of your program. All programming languages come with built-in operators and built-in functions. The reason for that is that there are many different ways to implement the same algorithm, an implementation can make a big difference. But what if you've settled on what you believe to be the ideal overall algorithm for your problem and yet your implementation is still too slow for your purposes, is there anything more you can do to improve it? Many times, the answer is yes. Find the sum of the odd numbers between 100 and 200.By now, I hope we have convinced you of the importance of the role of algorithms in programming and specifically in the efficiency of your programs.Create the vector of the previous question in decreasing order.Create a list of the whole numbers between 10 and 20 (inclusive), find their sum.Try out sequences with step-size \(\ne1\):.A column of increasing numbers (using transpose) (n:m)'.A column vector (manual): (notice the semicolons). ![]()
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