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MA 310 - Homepage Mathematical Programming 2

Geoffrey Cox, PhD.

Section Homework 1

Before you begin ...
  • DO NOT use AI for any part of this problem.
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  • Review the Homework Policies before you begin.
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  • Follow the Submitting Work before you begin.
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  • Do not use any built-in MATLAB commands unless specified below.
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  • Exercises labeled as a “Function”, should use the Function Template.
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  • Exercises labeled as a “Script”, should use the Script Template.
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  • Name the file function_name.m, where each function_name is listed below.
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  • Upload each of these files to the homework page on Canvas. No zip files.
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  • The due date is specified on Canvas
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Permitted MATLAB Functions & Commands for Homework 1.

The following built-in MATLAB functions and commands are permitted for this assignment.
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Vector/Matrix
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Operations:
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round • mod • floor • ceil
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Size/Dimensions:
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length • numel • size • height • width
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Creation:
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zeros • ones • true • false
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Logical:
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all • any
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Flow Control
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Conditional:
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if • switch-case • try-catch
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Loops:
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for • while • continue • break • return
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Strings and Character Arrays
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Operations:
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join • replace
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Conversion:
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num2str • str2num • str2double • string • char
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Other
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Printing Text:
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fprintf • disp • display • input • assert
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Random Generators:
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rand • randi • rng
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Special Variables:
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nargin
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Type Detection:
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isnan • isfield • isempty
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Points will be deducted from any programs using functions outside this list.
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Subsection list_sum

Returns the sum of all the numbers in a list.
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Inputs:
list (1 x N) double vector.
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Outputs:
total_sum (1x1) double — sum of the values in list
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Details:
▸ Use numel, size, or length to get the number of values in the list.
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▸ Use a for or while loop to code this.
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▸ Do NOT use MATLAB’s sum command.
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Examples: 
S = list_sum([2 1 3 -1])
% should return S = 5

S = list_sum([-2 1 0 -8 10 9 0 3.22 9 -1 -100 9.54])
% should return S = -69.2400
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Subsection list_is_nonnegative

Returns true if a list contains no negative numbers. The list may have any length.
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Inputs:
list (1 x N) — list of numeric values (doubles)
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Outputs:
result (1x1) — true if list has no negative numbers
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Details:
▸ Use numel, size, or length to get the number of values in the list.
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▸ Use a for or while loop together with an if-statement.
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▸ No other built-in MATLAB commands are allowed.
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▸ Zero is a non-negative number.
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Examples: 
result = list_is_nonnegative([111 -90 20 66 -167 42])
% returns false (0)

result = list_is_nonnegative([1 1 1 0 1 2 3 9 7 5 0 9 9 4])
% returns true  (1)
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Subsection list_occurrences

Returns the number of times a number occurs in a given list of numbers.
Inputs:
list (1 x N) double vector
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num (1x1) double — number we are looking for in list
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Outputs:
num_count (1x1) integer — number of times num occurs in list
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Details:
▸ Use numel, size, or length to get the number of values in the list.
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▸ Use a for or while loop together with an if-statement.
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▸ No other built-in MATLAB commands are allowed.
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Examples: 
num_count = list_occurrences([1 1 1 -9 0 0 6 6 -1 6 7 1 2], 1)
% returns 4

num_count = list_occurrences([1 1 1 -9 0 0 6 6 -1 6 7 1 2], -6)
% returns 0
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Subsection list_sign_change_count

Returns the number of times consecutive numbers have a different sign in the list.
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Inputs:
list (1 x N) double vector
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Outputs:
count (1x1) integer — number of sign changes in list
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Details:
▸ Use length to get the number of values in the list.
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▸ Use a for or while loop together with an if-statement.
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▸ Changing from a positive or negative to a zero does not count as a change of sign.
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▸ Only count changes between adjacent numbers.
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Examples: 
count = list_sign_change_count([1 -1 1 -9 6 6 -1 -2 4])
% returns 6

count = list_sign_change_count([1 1 1 -9 0 0 6 6 -1 6 7 1 2])
% returns 3
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Subsection get_direction

Returns an object’s direction given two 2D positions \((x,y)\text{:}\) the initial position position_old and the final position position_new. The direction must be one of the eight cardinal directions:
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'N', 'S', 'E', 'W', 'NE', 'NW', 'SE', 'SW'.
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Inputs:
position_old (1 x 2) double vector — contains the (x, y)-coordinates of the initial position
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position_new (1 x 2) double vector — contains the (x, y)-coordinates of the final position
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Outputs:
direction (1x1) or (1 x 2) character vector — indicating the movement direction
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Details:
▸ If position_old equals position_new, return the empty string ''.
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▸ Any movement in a primary direction should be reflected (for example, moving 10 units north and only 0.1 units west should return 'NW')
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▸ Use an if-statement.
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Examples: 
direction = get_direction([2 1], [3 1])
% returns 'E'

direction = get_direction([-2 1], [0 -8])
% returns 'SE'

direction = get_direction([8 -2], [-2 5])
% returns 'NW'

direction = get_direction([0 -2], [0 -2])
% returns ''
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