Description

Introduction to Programming with MATLAB Lesson 7

• Unless otherwise indicated, your function should not print anything to the Command Window, but your function will not be counted incorrect if it does.
• Note that you are not required to use the suggested names of input variables and output variables, but you must use the specified function names.
• Also, read the instructions on the web page on how to test your functions with the auto-grader program provided, and what to submit to Coursera to get credit.
• Note that starred problems, marked by ***, are harder than usual, so do not get discouraged if you have difficulty solving them.
• You need MATLAB r2012a or newer or MATLAB Online to run the grader! Older versions are not supported.

1. Write a function called integerize that takes as its input a matrix A of integers of type double, and returns the name of the “smallest” signed integer class to which A can be converted without loss of information. If no such class exists, the text ‘NONE’ is returned. For example, if the smallest element of A is -100 and the largest is +100, then the function would return ‘int8’. As another example, if there is an element of A equal to -1e20, then the function would return ‘NONE’.
• The month field must contain a string with the name of the month (first letter capitalized).
• The day field must contain the three-letter abbreviation of the day chosen from this list: ‘Mon’, ‘Tue’, ‘Wed’, ‘Thu’, ‘Fri’, ‘Sat’, ‘Sun’.
For example, here is a call of the function followed by a command that shows the seventh element of the struct array that is returned by the function:
>> m = year2016(2);
>> m(7) ans =

3. *** A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Write a function that is called this way:
>> n = palin_product(dig,lim);
The function returns the largest palindrome smaller than lim that is the product of two dig digit numbers. If no such number exists, the function returns 0. (Inspired by Project Euler.)
4. Each number on telephone keypads, except 0 and 1, corresponds to a set of uppercase letters as shown in this list:
2 ABC, 3 DEF, 4 GHI, 5 JKL, 6 MNO, 7 PQRS, 8 TUV, 9 WXYZ
Hence, a phone-number specification can include uppercase letters and digits. Write a function called dial that takes as its input argument a char vector of length 16 or less that includes only these characters and returns as its output argument the telephone number as a uint64. Here is the input and output for one example of a call of the function:
Input: ‘1FUNDOG4YOU’
Output: 13863644968
You can assume that a phone number never starts with 0. If the input contains any illegal characters, the function returns 0. You are not allowed to use the built-in function strrep.
5. An n-by-n square logical matrix can be represented by a cell vector of n elements where the kth element corresponds to the kth row of the matrix. Each element of the cell vector is a row vector of positive integers in increasing order representing the column indexes of the logical true values in the given row of the matrix. All other elements in the given row of the logical matrix are false. Write a function called logiunpack that takes such a cell vector as its only input and returns the corresponding square logical matrix. For example, such a cell vector representation of a 100-by-100 logical matrix with the only true elements at indexes (10,20) and (10,75) would have only one non-empty element of the cell vector at index 10. That element is the vector [20 75].
6. Solve the inverse of the previous problem. That is, write a function called logipack that takes a square logical matrix as its only input argument and returns its cell vector representation as specified in the previous assignment. Note that empty array elements of the cell vector corresponding to rows with all false values must have a size of 0x0.
>> cent = centuries(1864);
will make cent equal to ‘XIX’.
2

8. Write the function find_zero that is defined like this function x = find_zero(f,x1,x2).
The first input argument is special. It is a “function handle”. A function handle is gotten by typing @
and the name of any function. For example,
x = find_zero(@sin,-1,1) will give f the
function handle for MATLAB’s built-in sin function. Then, inside find_zero, the statement y = f(-1) would set y = sin(-1). Note that
the @ sign is not used inside the function. Only the caller uses it. All other arguments to find_zero are scalar numbers, and x1 is less than x2. The
goal of the function is to find an x that lies in the range from x1 to x2 such that after the command, y = f(x), is executed inside the function find_zero, y is approximately zero as defined by abs(y) < 1e-10. All you know about the function f is that it has one scalar input and one scalar output, and a plot of its values crosses the x-axis exactly once between x1 and x2, as, for example, in the figure. It is the responsibility of the caller to call the function with arguments that obey these rules. Here are two sample runs:
>> find_zero(@sin,-2.5,2.3) % as shown in the figure ans =
-6.4000e-11
>> format long
>> find_zero(@cos,-2,1.3) ans =
-1.570796326871000

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