gibson:teaching:fall-2014:math445:lecture9-diary
====== Differences ====== This shows you the differences between two versions of the page.
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gibson:teaching:fall-2014:math445:lecture9-diary [2014/10/13 19:40] gibson created |
gibson:teaching:fall-2014:math445:lecture9-diary [2014/10/15 12:45] (current) gibson [example: solving a nonlinear equation] |
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| A ''for'' loop repeats a given action a fixed number of times. The general form of a ''for'' loop is | A ''for'' loop repeats a given action a fixed number of times. The general form of a ''for'' loop is | ||
| <code matlab> | <code matlab> | ||
| - | for value = vector | + | for value = vector |
| - | action | + | action |
| - | end | + | end |
| - | </code> | + | </code> |
| The ''action'' will be performed ''length(vector)'' times, with ''value'' set to each element of | The ''action'' will be performed ''length(vector)'' times, with ''value'' set to each element of | ||
| ''vector'' successively. It's probably clearer to see this by example. | ''vector'' successively. It's probably clearer to see this by example. | ||
| **example 1:** Print the numbers from 1 to 10. | **example 1:** Print the numbers from 1 to 10. | ||
| + | <code matlab> | ||
| + | for n = 1:10 | ||
| + | fprintf('The value of n is %i\n', n); | ||
| + | end | ||
| + | </code> | ||
| - | **example 2:** Print the numbers from 10 to 1. | + | **example 2:** Print the numbers from 10 to 0. |
| + | <code matlab> | ||
| + | for n = 10:-1:0 | ||
| + | fprintf('%i '); | ||
| + | end | ||
| + | fprintf('blast off!\n'); | ||
| + | </code> | ||
| **example 3:** Write a ''mysum'' function that computes the sum of the elements of a vector. | **example 3:** Write a ''mysum'' function that computes the sum of the elements of a vector. | ||
| + | <code matlab> | ||
| + | function s = mysum(x) | ||
| + | % return the sum of the components of vector x | ||
| + | | ||
| + | s = 0; % start with partial sum s = 0 | ||
| + | for i = 1:length(x) % loop over all elements in x | ||
| + | s = s + x(i); % add x(i) to the previously computed partial sum | ||
| + | end | ||
| + | | ||
| + | end | ||
| + | </code> | ||
| **example 4:** Write a function that computes the factorial of //n//. | **example 4:** Write a function that computes the factorial of //n//. | ||
| + | |||
| + | <code matlab> | ||
| + | function p = factorial(n) | ||
| + | % return the factorial of n (assume n is a positive integer) | ||
| + | | ||
| + | p = 1; % start with partial product p = 1 | ||
| + | for k = 1:n % loop k over all integers from 1 to n | ||
| + | p = p*k; % multiply previous partial product by k | ||
| + | end | ||
| + | | ||
| + | end | ||
| + | </code> | ||
| **The for loop is probably the single most important programming construct in numerical mathematics.** | **The for loop is probably the single most important programming construct in numerical mathematics.** | ||
| Line 28: | Line 62: | ||
| A ''while'' loop repeats a given action as long as its condition is true. The general form is | A ''while'' loop repeats a given action as long as its condition is true. The general form is | ||
| <code matlab> | <code matlab> | ||
| - | while condition | + | while condition |
| - | action | + | action |
| - | end | + | end |
| </code> | </code> | ||
| + | In order for the ''while'' loop to terminate, the action must modify variables in the condition. | ||
| + | For example, the factorial function above could also be written this way... | ||
| + | |||
gibson/teaching/fall-2014/math445/lecture9-diary.1413254445.txt.gz · Last modified: 2014/10/13 19:40 by gibson
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