Matlab代写-B126
时间:2022-03-30
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MZB126
Engineering omputation Problem Solving Task A, 202
Problem Solving Task Part A
Weight:
1
3
of 50%
Due: 11:59PM, Friday 8th of April
Submit via the MZB126 Blackboard site.
Sharing this document or parts of it online, or asking for solutions online, constitutes academic
misconduct which could lead to failing this unit or suspension of enrolment.
FOR AT: This is an almost completely MATLAB-based task, paired with a small amount of
writing. You should upload your answer as MATLAB functions (.m files) in a .zip file, together
with your answer for the written component. Upload your solution even if it is not fully func-
tional, as marks are assigned for individual components (see final page).
Running Cables
As part of a development project, the different sites in the development must all be connected to
the main electricity supply with cables. Sites can also be connected to one another, so long as they
all connect back to the main supply one way or another. The company wants to minimise th cost
of the job, which means minimising the length of cable used.
Rather than plan out each development job separately, management wants a solution they can
apply to every job. In their big meeting on the topic, they came up with two different strategies
for laying the cables (and then argued a lot about which was better). Example cable networks
produced by the two algorithms are shown in Figure 1.
Algorithm 1
1. Select a random site that is not yet connected to electricity
2. Lay a new connection between the site selected in Step 1 and th closest site already con-
nected to power (including the power supply)
3. Repeat from Step 1 until all sites are connected to the mains supply
Algorithm 2
1. Select a random site that is connected to electricity (including the pow r supply)
2. Lay a new connection between the site selected in Step 1 and the closest site not yet con-
nected to power
3. Repeat from Step 1 until all sites are connected to the mains supply
CRICOS No. 00213J 1
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MZB126
Engineering omputation Problem Solving Task A, 202
Algorithm One Algorithm Two
Figure 1: Plans for connecting the different sites (marked with flags) to the main power supply
(marked with lightning), as produced by the two different algorithms proposed by management.
The Task
Unfortunately, despite coming up with the two algorithms, management doesn’t know how to
implement them as computer code. Your task is to create MATLAB implementations of the two
algorithms, that will work for any development job (so any number of sites in any locations).
[90 marks] Write two functions that take the form
[start_x, end_x, tart_y, end_y, L_tot]
= cable_de ign1(supply_x, supply_y, sites_x, ites_y)
[ tart_x, end_x, start_y, end_y, L_tot]
= cable_design2(supply_x, supply_y, sites_x, ites_y)
where supply_x and supply_y specify the x and y co-ordinates of the power supply, and
sites_x and sites_y are both vectors listing the x and y co-ordinates of all the sites that
need power. Your functions ust output the start and end co-ordinates for each cable (start_x,
end_x, start_y, end_y), as well as the total length of cable required (L_tot).
[10 marks] Try out both algorithms on a variety of problems. Briefly comment on which you
would recommend to manage ent, and why (this can be scanned writing, or anything as simple as a
.txt file included with your .zip).
Code for generating the visualisation is provided alongside this problem solving task. Test
scenarios will also be provided so you can verify your code, and the code skeletons on Black-
board hav some hints that may help you.
CRICOS No. 00213J 2
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MZB126
Engineering omputation Problem Solving Task A, 202
You may approach the task in any way you wish, but please ensure that your base functions for
the two algorithms use the inputs, and generate the outputs, specified above.
In order to assist you in this task, you may wish to take guidance from the suggested program
design on the following pages. For those following this design, please also download the pro-
vided .m files on the Problem Solving Task A page on Blackboard (under Assessment). These will
provide you a template to start from, and also a set of functions you can use to test the component
pieces of your code.
Possible Program Design
1. Create a MATLAB function that computes the distances d between a chosen location speci-
fied by x_c and y_c, and the locations of another set of points as listed in the input vectors x
and y:
d = compute_distances(x_c, y_c, x, y)
Recall that the formula for the distance betw en two points at locations (x1, y1) and (x2, y2) is:
d =
√
(x1 − x2)2 + (y1 − y )2.
Example: For given location (2,−1) and set of three sites with co-ordinates x = [0, 2, -1]
and y = [1, -1, 3], the output of this function should be
d = compute_distances(2,-1,x,y)
d =
2.8284 0 5
You can test your implementation of this function using test_comput _distances.m that will
be supplied on Blackboard.
2. Create a MATLAB functio that selects a random element from a list of values in a vector,
values:
value = select_random_value(values)
(Hint: You may find the M TLAB built-in function randi useful here.)
CRICOS No. 00213J 3
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MZB126
Engineering omputation Problem Solving Task A, 202
Example: For input values = [2, 6, 7], the output of his function should either be 2, 6,
or 7, sel cted with equal chance of each.
value = select_random_value([2,6,7])
value
= 6
value = select_random_value([2,6,7])
value
= 7
You can test your implementation of this function using test_ra dom_selection.m that will
be supplied on Blackboard.
3. Create a MATLAB function that given a site (current_sit ), selects the closest site from a
list of other sites (site_list) and also returns the distance to that site,
[chosen_site, L] = select_closest_site( current_ ite, site_list, x, y )
Note that the function also takes inputs x and y, the co-ordinates of all sites. (Hint: Your function
should use the function from step 1, compute_distances in order to achieve this)
Example: Consider the list of four sites, with locations x = [3, 1, 2, 2] and
y = [5, 2, 4, 6]. Given current_site = 4 and site_list = [1, 3], the func-
tion should consider which of sites 1 and 3 i closer to site 4, then select site 1 as it is closer.
The function should also report the distance to that site,
√
2:
x = [3, 1, 2, 2]
y = [5, 2, 4, 6]
[chosen_site, L] = select_closest_site(4, [1 3], x, y)
chosen_site
= 1
L
= 1.4142
You can test your implementation of this function using test_select_closest.m that will be
supplied on Blackboard.
CRICOS No. 00213J 4
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MZB126
Engineering omputation Problem Solving Task A, 202
4. Create the main functions that satisfy the task. Recall the form:
[start_x, end_x, start_y, e d_y, L_tot]
= cable_design1(supply_x, supply_y, sites_x, sites_y)
(Hint: Your function should use the functio s created in answering 2. and 3. above as appropriate in order
to achieve this. The algorithm involves repeating an action, so think about using a loop in MATLAB.)
Marking Sch me
10% – The code calculates distances between points correctly
15% – The code correctly selects sites at random where the algorithm requires this
20% – The code corr ctly follows the given algorithm to select the next point
15% – The code mak s correct use of a for or while loop
10% – he code outputs the correct path according to the algorithm
10% – he main function calculates the total distance correctly
10% – Both algorithms implemented corr ctly
10% – Reasonable comment on the behaviour of the two algorithms
CRICOS No. 00213J 5