8. Modules And Functions

8.1 Taking a top-down approach to programming by using modules

8.2 Writing and using general-purpose functions

8.3 Getting multiple outputs from functions

8.4 Giving multiple inputs to functions

8.5 Creating subfunctions

8.6 Calling functions properly

8.7 Drawing on previously defined functions versus creating your own

8.8 Practicing modules and functions

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8.1 Taking a top-down approach to programming by using modules

Code 8.1.1:

% College_Admissions_04

% Assuming that SATs and GPAs are related to IQs,

% this program generates dummy data for SATs, GPAs,

% Extra- curriculars (EC), and distance (Dist) from the

% college, giving larger scores to greater distance from % the college (for geographical diversity).

% The SATS and GPAs are summed, each of the student's

% three new scores (Acad, EC, and Dist) are normed, and

% then the min required score for admission is gradually % increased until the number admitted no longer exceeds

% max_admits_allowed.

% Clear variables, clear and open the commandwindow

clear all

clc

commandwindow

% Set constants

applications = 30;

max_admits_allowed = 10;

IQmean = 110;

IQsd = 20;

SATQsd = 10;

SATVsd = 10;

ECsd = 10;

GPAsd = 10;

Required_Score_Increase = .05;

% Generate dummy scores to test the program

for a = 1:applications

IQ(a) = IQmean + abs(randn)*IQsd;

SATQ(a) = IQ(a) + abs(randn)*SATQsd;

SATV(a) = IQ(a) + abs(randn)*SATVsd;

GPA(a) = IQ(a) + abs(randn)*GPAsd;

Acad(a) = SATQ(a) + SATV(a) + GPA(a);

EC(a) = abs(randn)*ECsd;

Dist(a) = abs(randn);

end

% Normalize the scores

Acad = (Acad - min(Acad)) ./ (max(Acad)-min(Acad));

EC = (EC -min(EC)) ./(max(EC)-min(EC));

Dist = (Dist - min(Dist)) ./(max(Dist)-min(Dist));

% Create a Scores matrix, including, in the final column,

% each student's total score

Scores = [Acad' EC' Dist'];

Total_Scores = sum(Scores');

Scores = [Scores Total_Scores'];

% Increase min_Required_Score until

% Students_Accepted <= max_admits_allowed

min_Required_Score = min(Scores(:,end));

Students_Accepted = inf; % To ensure entering while

while Students_Accepted > max_admits_allowed

min_Required_Score = min_Required_Score + Required_Score_Increase;

Students_Accepted = 0;

for a = 1:applications

Acceptance(a) = 0;

if Scores(a,end) > min_Required_Score

Acceptance(a) = 1;

Students_Accepted = Students_Accepted + 1;

end

% Display the results

disp('Student Number, Academics, EC, Distance, Total Score, Acceptance')

disp(' ')

Scores_And_Acceptances = [Scores Acceptance'];

[r,c] = size(Scores_And_Acceptances);

for i = 1:r

fprintf('%4d',i)

fprintf('%6.2f',Scores_And_Acceptances(i,1:end-1))

fprintf('%4d',Scores_And_Acceptances(i,end))

fprintf('\r')

end

Students_Accepted

min_Required_Score

Output 8.1.1:

Student Number, Academics, EC, Distance, Total Score, Acceptance

1 0.53 0.60 0.38 1.51 1

2 0.26 0.19 0.93 1.38 1

3 0.65 0.00 0.44 1.08 0

4 1.00 0.38 0.67 2.05 1

5 0.17 0.92 0.89 1.98 1

6 0.35 0.07 0.51 0.93 0

7 0.02 0.28 0.15 0.44 0

8 0.35 0.03 0.20 0.57 0

9 0.52 0.44 0.24 1.20 0

10 0.33 0.85 0.36 1.54 1

11 0.29 0.21 0.17 0.67 0

12 0.54 0.27 0.53 1.33 1

13 0.15 0.21 0.00 0.36 0

14 0.14 0.04 0.17 0.35 0

15 0.21 0.18 0.82 1.21 0

16 0.18 0.50 0.24 0.92 0

17 0.22 0.29 0.41 0.92 0

18 0.06 0.37 0.01 0.44 0

19 0.19 0.02 0.08 0.29 0

20 0.37 0.18 0.10 0.65 0

21 0.26 0.69 0.11 1.06 0

22 0.79 1.00 0.48 2.27 1

23 0.15 0.97 0.62 1.74 1

24 0.26 0.68 0.05 0.99 0

25 0.25 0.10 0.26 0.62 0

26 0.00 0.69 0.22 0.91 0

27 0.21 0.13 0.32 0.66 0

28 0.66 0.63 0.26 1.55 1

29 0.34 0.20 1.00 1.54 1

30 0.42 0.14 0.34 0.91 0

Students_Accepted =

min_Required_Score =

1.2392

Code 8.12:

% College_Admissions_Main.m

Clear_Start;

Set_Constants;

Generate_Dummy_Scores;

Normalize_Scores;

Create_Scores_Matrix;

Select_Students;

Display_Results;

Code 8.1.3:

% Clear_Start.m

% Called by College_Admissions_Main.m

clear all

clc

commandwindow

Code 8.1.4:

% Set_Constants.m

% Called by College_Admissions_Main.m

applications = 30;

max_admits_allowed = 10;

IQmean = 110;

IQsd = 20;

SATQsd = 10;

SATVsd = 10;

ECsd = 10;

GPAsd = 10;

Required_Score_Increase = .05;

Code 8.1.5:

% Generate_Dummy_Scores.m

% Called by College_Admissions_Main.m

for a = 1:applications

IQ(a) = IQmean + abs(randn)*IQsd;

SATQ(a) = IQ(a) + abs(randn)*SATQsd;

SATV(a) = IQ(a) + abs(randn)*SATVsd;

GPA(a) = IQ(a) + abs(randn)*GPAsd;

Acad(a) = SATQ(a) + SATV(a) + GPA(a);

EC(a) = abs(randn)*ECsd;

Dist(a) = abs(randn);

end

Code 8.1.6:

% Normalize_Scores.m

% Called by College_Admissions_Main.m

Acad = (Acad - min(Acad)) ./ (max(Acad)-min(Acad));

EC = (EC -min(EC)) ./(max(EC)-min(EC));

Dist = (Dist - min(Dist)) ./(max(Dist)-min(Dist));

Code 8.1.7:

% Create_Scores_Matrix.m

% Called by College_Admissions_Main.m

% Create a Scores matrix, including, in final column, each student's

% total score

Scores = [Acad' EC' Dist'];

Total_Scores = sum(Scores');

Scores = [Scores Total_Scores'];

Code 8.1.8:

% Select_Students.m

% Called by College_Admissions_Main.m

% Increase min_Required_Score until

% Students_Accepted <= max_admits_allowed

min_Required_Score = min(Scores(:,end));

Students_Accepted = inf; %To ensure entering while loop

while Students_Accepted > max_admits_allowed

min_Required_Score = min_Required_Score + ...
Required_Score_Increase;

Students_Accepted = 0;

for a = 1:applications

Acceptance(a) = 0;

if Scores(a,end) > min_Required_Score

Acceptance(a) = 1;

Students_Accepted = Students_Accepted + 1;

end

Code 8.1.9:

% Display_Results.m

% Called by College_Admissions_Main.m

disp('Student Number, Academics, EC, Distance, Total Score, Acceptance')

disp(' ')

Scores_And_Acceptances = [Scores Acceptance'];

[r,c] = size(Scores_And_Acceptances);

for i = 1:r

fprintf('%4d',i)

fprintf('%6.2f',Scores_And_Acceptances(i,1:end-1))

fprintf('%4d',Scores_And_Acceptances(i,end))

fprintf('\r')

end

Students_Accepted

min_Required_Score

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8.2 Writing and using general-purpose functions

Code 8.2.1:

r = [1:99];

mean_r = mean(r)

Output 8.2.1:

mean_r =

Code 8.2.2:

% normalize.m

function y = normalize(x)

y = (x - min(x)) ./ (max(x)-min(x));

Code 8.2.3:

x = [1:11];

normalized_values = normalize(x)

Output 8.2.3:

normalized_values =

Columns 1 through 8

0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

Columns 9 through 11

0.8000 0.9000 1.0000

Code 8.2.4:

clear normalized_values

a = [1:11];

normalized_values = normalize(a)

Output 8.2.4:

normalized_values =

Columns 1 through 8

0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

Columns 9 through 11

0.8000 0.9000 1.0000

Code 8.2.5:

a = [1:11];

normalize(a);

Output 8.2.5:

??? Undefined function or variable 'y'.

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8.3 Getting multiple outputs from functions

Code 8.3.1:

function [ly, uy] = normalize_split(x);

lx = [];

ux = [];

for j = 1:length(x)

if x(j) <= median(x)

lx = [lx x(j)];

else

ux = [ux x(j)];

end

uy = (ux - min(ux)) ./ (max(ux)-min(ux));

ly = (lx - min(lx)) ./ (max(lx)-min(lx));

Code 8.3.2:

a = logspace(20,22,10);

[lower_normed, upper_normed] = normalize_split(a)

Output 8.3.2:

lower_normed =

0 0.0991 0.2644 0.5401 1.0000

upper_normed =

0 0.0991 0.2644 0.5401 1.0000

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8.4 Giving multiple inputs to functions

Code 8.4.1:

% normalize_split_two_args.m

function [ly, uy] = normalize_split_two_args(x,i);

lx = [];

ux = [];

if i == 0 % median split

for j = 1:length(x)

if x(j) <= median(x)

lx = [lx x(j)];

else

ux = [ux x(j)];

end

elseif i == 1 % mean split

for j = 1:length(x)

if x(j) <= mean(x)

lx = [lx x(j)];

else

ux = [ux x(j)];

end

else % error feedback

disp('An error was made in the call to normalize_split');

end

ly = (lx - min(lx)) ./ (max(lx)- min(lx));

uy = (ux - min(ux)) ./ (max(ux)- min(ux));

Code 8.4.2:

a = logspace(20,22,10);

[median_based_lower_norm,median_based_upper_norm_mean] = ...

normalize_split_two_args(a,0)

[mean_based_lower_norm,mean_based_upper_norm] = ...

normalize_split_two_args(a,1)

[other_based_lower_norm,other_based_upper_norm_mean] = ...

normalize_split_two_args(a,3)

Output 8.4.2:

median_based_lower_norm =

0 0.0991 0.2644 0.5401 1.0000

median_based_upper_norm_mean =

0 0.0991 0.2644 0.5401 1.0000

mean_based_lower_norm =

0 0.0325 0.0868 0.1773 0.3282 0.5800 1.0000

mean_based_upper_norm =

0 0.3748 1.0000

An error was made in the call to normalize_split

other_based_lower_norm =

[]

other_based_upper_norm_mean =

[]

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8.5 Creating subfunctions

Code 8.5.1:

function [y,ty] = mean_and_trimmed_mean(x)

y = mean(x);

ty = mean(trimmed(x));

function yy = trimmed(x)

yy = [x(1):x(end-1)];

Code 8.5.2:

x = [1:5];

[a b] = mean_and_trimmed_mean(x)

Output 8.5.2:

a =

b =

2.5000

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8.6 Calling functions properly

Code 8.6.1:

mean_and_trimmed_mean(x)

c = mean_and_trimmed_mean(x)

[d e] = mean_and_trimmed_mean(x)

[f g h] = mean_and_trimmed_mean(x)

Output 8.6.1:

ans =

c =

d =

e =

2.5000

??? Error using ==> mean_and_trimmed_mean

Too many output arguments.