INTRODUCTION TO MATLAB | Custom PHD Thesis

Please read all the instructions carefully. Deadline: This assignment is due end of the day on Monday Feb. 29th (11:59 PM). This assignment will contribute 42% towards your overall mark of this component. Do not collaborate, inspire, copy, or copy and then modify, code from another student. This assignment must be done aloneóno lab partners. Departmental penalty rules will be applied for late submissions and plagiarism/collusion cases.

Using random numbers to calculate p

Consider the square with sides of length 1 and the circle with radius 1 that can be inscribed within

the square. The ratio of their areas is Areacircle square

= p .

Uniformly distributed points in the square can be drawn by using two independent uniform random

numbers (one for the x-coordinate and one for the y-coordinate). The fraction f of the points that fall within the inscribed circle is also the ratio of the areas f ò p . As the number of points increases,

the magnitude of the difference 4f – p decreases.

Please, write a very short script and produce some plots in MATLAB to demonstrate the concept described above.

ï (A-1) Draw 1000 points uniformly distributed in the unit square. To make your results consis- tent with your classmates, in the line before generating the random numbers set the random number generators seed via rng(171172).

ï (A-2,A-3) Compute a running average of f , the fraction of points falling within the inscribed

circle (the circle has a center of [ 1 , 1 ] and radius of 1 ). The running average should start

2 2 2

with the first point and continue to the 1000th point (fraction of the one-thousand points).

Hint: Use ones, cumsum twice, and ./ to calculate a running average.

ï (A-4) Create a plot showing the running average

ñ Plot a black horizontal line at y = p from 1 to 1000.

ñ Plot the value of running average of 4f as blue ◊ís.

ñ Create a title and label the axes

ï (A-5) Report the normalized percentage difference 100 4f -p % using 10, 50, 100, 500, and

1000 points in a table. Use 2 decimal points.

ï (A-6) Create a two-dimensional scatter plot that shows the first 500 points and differentiates the points within the circle from those outside the circle.

ñ Indicate points within the circle using red circle markers

ñ Indicate points outside the circle using blue square markers

ñ The plot area should be a square

ñ The plot should have a legend indicating which markers are within the circle

Temperature analysis

You are provided with a dataset consisting of the daily mean, maximum, and minimum temperatures at a Liverpool weather station in 2015 (the data is publicly available from Wunderground.com). The file is available on VITAL in MATLABís binary format and is called assign1.mat.

For this part of the assignment, you are tasked with calculating the average daily high and low for each month. (There was no recording for the 25th of December so its row has NaN, please remove this row before any calculations.) The values are recorded in Celsius, but please convert the monthly averages to Fahrenheit also. Report all values with one decimal point (for example, 4.2) in a table where each column is a month starting with January and there are 4 rows: first two rows are in Celsius,

2 ELEC171/172 ó INTRODUCTION TO MATLAB ó ASSIGNMENT 1

the first row is the average daily high and the second row is the daily low. The third and fourth rows correspond to the first two rows but the values are in Fahrenheit.

Example use of the dataset.

load(íassign1.matí,ídate_arrayí,ídata_valsí);

% date_array is a 365 by 3 matrix

% Columns correspond to year, month, day

% so you will only need the 2nd and possibly the 3rd columns

% data_vals is a 365 by 5 matrix

% Columns correspond to:

%MeanTemperatureC,MinTemperatureC,MaxTemperatureC,MeanWindSpeedKmh,MaxWindSpeedKmh figure(1),clf %create figure and clear it h1=plot(1:365,data_vals(:,1),íkoí,ímarkersizeí,8);

hold all %allows you to plot more than one h2=plot(1:365,data_vals(:,2),íbví,ímarkersizeí,8); h3=plot(1:365,data_vals(:,3),írsí,ímarkersizeí,8); set(gca,ífontsizeí,12) %change font size title(íDaily temperatures in Liverpoolí) xlabel(íDay of the yearí)

ylabel(íTemperature (C)í)

legend([h3 h1 h2],íHighí,íAverageí,íLowí)

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