Instructor MATLAB Files for Essentials of MATLAB Programming 3rd Edition by Stephen J. Chapm

solution_files/Ex1.1/Ex1.1.png

solution_files/Ex1.1/test.m x = 0:0.1:10; y = 2 * exp( -0.2 * x); plot(x,y);

solution_files/Ex1.9/Ex1.9.png

solution_files/Ex1.9/test2.m % Create an input array from 2*pi to 2*pi t = -2*pi:pi/10:2*pi; % Calculate |sin(t)| x = abs(sin(t)); % Plot result plot(t,x);

solution_files/Ex2.1/array1.dat Data/auxiliary file.

solution_files/Ex2.1/array1.mat Data/auxiliary file.

solution_files/Ex2.10/Ex2.10.png

solution_files/Ex2.10/ball.m % Script file: ball.m % % Purpose: % To calculate and display the trajectory of a ball % thrown upward at a user-specified height and speed. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/03/15 S. J. Chapman Original code % % Define variables: % g -- Acceleration due to gravity (m/s^2) % h -- Height (m) % h0 -- Initial height (m) % t -- Time (s) % v -- Vertical Speed (m/s) % v0 -- Initial Vertical Speed (m/s)

% Initialize the acceleration due to gravity g = -9.81; % Prompt the user for the initial velocity. v0 = input('Enter the initial velocity of the ball: '); % Prompt the user for the initial height h0 = input('Enter the initial height of the ball: '); % We will calculate the speed and height for the first % 10 seconds of flight. (Note that this program can be % refined further once we learn how to use loops in a % later chapter. For now, we don't know how to detect % the point where the ball passes through the ground % at height = 0.) t = 0:0.5:10; h = zeros(size(t)); v = zeros(size(t)); h = 0.5 * g * t .^2 + v0 .* t + h0; v = g .* t + v0;

solution_files/Ex2.11/dist2d.m % Script file: dist2d.m % % Purpose: % To calculate the distance between two points on a % Cartesian plane. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/03/15 S. J. Chapman Original code % % Define variables: % dist -- Distance between points % x1, y1 -- Point 1 % x2, y2 -- Point 2 % Prompt the user for the input points

x1 = input('Enter x1: '); y1 = input('Enter y1: '); x2 = input('Enter x2: '); y2 = input('Enter y2: '); % Calculate distance dist = sqrt((x1-x2)^2 + (y1-y2)^2); % Tell user disp (['The distance is ' num2str(dist)]);

solution_files/Ex2.12/dist3d.m % Script file: dist3d.m % % Purpose: % To calculate the distance between two points on a % three-dimensional Cartesian plane. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/03/15 S. J. Chapman Original code % % Define variables: % dist -- Distance between points % x1, y1, z1 -- Point 1 % x2, y2, z2 -- Point 2 % Prompt the user for the input points x1 = input('Enter x1: '); y1 = input('Enter y1: '); z1 = input('Enter z1: '); x2 = input('Enter x2: '); y2 = input('Enter y2: '); z2 = input('Enter z2: '); % Calculate distance dist = sqrt((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2); % Tell user

disp (['The distance is ' num2str(dist)]);

solution_files/Ex2.13/db_plot.m % Script file: db_plot.m % % Purpose: % To plot power in watts vs power in dBm on a linear and % log scale. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/03/15 S. J. Chapman Original code % % Define variables: % dBm -- Power in dBm % pin -- Power in watts % Create array of power in watts pin = 1:2:100; % Calculate power in dBm dBm = 10 * log10( pin / 1.0e-3 ); % Plot on linear scale figure(1); plot(dBm,pin); title('Plot of power in watts vs power in dBm'); xlabel('Power (dBm)'); ylabel('Power (watts)'); grid on; % Plot on semilog scale figure(2); semilogy(dBm,pin); title('Plot of power in watts vs power in dBm'); xlabel('Power (dBm)'); ylabel('Power (watts)'); grid on;

solution_files/Ex2.13/decibel.m % Script file: decibel.m % % Purpose: % To calculate the dBm corresponding to a user-supplied % power in watts. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/03/15 S. J. Chapman Original code % % Define variables: % dBm -- Power in dBm % pin -- Power in watts % Prompt the user for the input power. pin = input('Enter the power in watts: '); % Calculate dBm dBm = 10 * log10( pin / 1.0e-3 ); % Tell user disp (['Power = ' num2str(dBm) ' dBm']);

solution_files/Ex2.13/linear.png

solution_files/Ex2.13/semilog.png

solution_files/Ex2.14/P_dBW.png

solution_files/Ex2.14/p_resistor.m % Script file: p_resistor.m % % Purpose: % To plot the power consumed by a resistor as a function % of the voltage across the resistor on both a linear and % a log scale. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/03/15 S. J. Chapman Original code % % Define variables: % ir -- Current in the resistor (A) % pr -- Power in the resistor (W) % r -- Resistance of resistor (ohms) % vr -- Voltage across the resistor (V) % vr_db -- Voltage across the resistor (dBW)

% Set the resistance r = 1000; % Create array of voltage across the resistor vr = 1:200; % Calculate the current flow through the resistor ir = vr / r; % Calculate the power consumed by the resistor in watts pr = ir .* vr; % Calculate the power consumed by the resistor in dBW pr_db = 10 * log10(pr); % Plot linear power figure(1); plot(vr,pr); title('Plot of power in watts vs voltage in volts'); xlabel('Voltage (V)'); ylabel('Power (watts)');

solution_files/Ex2.14/p_watts.png

solution_files/Ex2.15/rect2spherical.m % Script file: rect2spherical.m % % Purpose: % To calculate the spherical coordinates of a vector given % the 3D rectangular coordinates. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/04/15 S. J. Chapman Original code % % Define variables: % x, y, z -- Rectangular coordinates of vector % r -- Length of vector % theta -- Direction of vector (x,y) plane, in degrees % phi -- Elevation angle of vector, in degrees % Prompt the user for the input points x = input('Enter x: '); y = input('Enter y: '); z = input('Enter z: '); % Calculate polar coordinates. Note that "180/pi" converts % from radians to degrees. r = sqrt(x^2 + y^2 + z^2); theta = atan2(y,x) * 180/pi; phi = atan2(z,sqrt(x^2 + y^2)) * 180/pi; % Tell user disp ('The spherical coordinates are:'); disp (['r = ' num2str(r)]); disp (['theta = ' num2str(theta)]); disp (['phi = ' num2str(phi)]);

solution_files/Ex2.15/spherical2rect.m % Script file: spherical2rect.m %

% Purpose: % To calculate the 3D rectangular coordinates of a vector % given the spherical coordinates. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/04/15 S. J. Chapman Original code % % Define variables: % x, y, z -- Rectangular coordinates of vector % r -- Length of vector % theta -- Direction of vector (x,y) plane, in degrees % phi -- Elevation angle of vector, in degrees % Prompt the user for the input points r = input('Enter vector length r: '); theta = input('Enter plan view angle theta in degrees: '); phi = input('Enter elevation angle phi in degrees: '); % Calculate spherical coordinates. Note that "pi/180" converts % from radians to degrees. x = r * cos(phi * pi/180) * cos(theta * pi/180); y = r * cos(phi * pi/180) * sin(theta * pi/180); z = r * sin(phi * pi/180); % Tell user disp ('The 3D rectangular coordinates are:'); disp (['x = ' num2str(x)]); disp (['y = ' num2str(y)]); disp (['z = ' num2str(z)]);

solution_files/Ex2.16/rect2spherical.m % Script file: rect2spherical.m % % Purpose: % To calculate the spherical coordinates of a vector given % the 3D rectangular coordinates. %

% Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/04/15 S. J. Chapman Original code % 1. 03/04/15 S. J. Chapman Modified to use cart2sph % % Define variables: % x, y, z -- Rectangular coordinates of vector % r -- Length of vector % theta -- Direction of vector (x,y) plane, in degrees % phi -- Elevation angle of vector, in degrees % Prompt the user for the input points x = input('Enter x: '); y = input('Enter y: '); z = input('Enter z: '); % Calculate polar coordinates. Note that "180/pi" converts % from radians to degrees. [theta,phi,r] = cart2sph(x,y,z); theta = theta * 180/pi; phi = phi * 180/pi; % Tell user disp ('The spherical coordinates are:'); disp (['r = ' num2str(r)]); disp (['theta = ' num2str(theta)]); disp (['phi = ' num2str(phi)]);

solution_files/Ex2.16/spherical2rect.m % Script file: spherical2rect.m % % Purpose: % To calculate the 3D rectangular coordinates of a vector % given the spherical coordinates. % % Record of revisions: % Date Programmer Description of change % ==== ========== =====================

% 03/04/15 S. J. Chapman Original code % 1. 03/04/15 S. J. Chapman Modified to use sph2cart % % Define variables: % x, y, z -- Rectangular coordinates of vector % r -- Length of vector % theta -- Direction of vector (x,y) plane, in degrees % phi -- Elevation angle of vector, in degrees % Prompt the user for the input points r = input('Enter vector length r: '); theta = input('Enter plan view angle theta in degrees: '); phi = input('Enter elevation angle phi in degrees: '); % Calculate spherical coordinates. Note that "pi/180" converts % from radians to degrees. [x,y,z] = sph2cart(theta*pi/180,phi*pi/180,r); % Tell user disp ('The 3D rectangular coordinates are:'); disp (['x = ' num2str(x)]); disp (['y = ' num2str(y)]); disp (['z = ' num2str(z)]);

solution_files/Ex2.17/cosh1.m % Script file: cosh1.m % % Purpose: % To calculate the hyperbolic cosine of x. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/04/15 S. J. Chapman Original code % % Define variables: % x -- Input value % res1 -- cosh(x) from the definition % res2 -- cosh(x) from the MATLAB function

% Prompt the user for the input power. x = input('Enter x: '); % Calculate cosh(x) res1 = ( exp(x) + exp(-x) ) / 2; res2 = cosh(x); % Tell user fprintf('Result from definition = %14.10f\n',res1); fprintf('Result from function = %14.10f\n',res2);

solution_files/Ex2.17/cosh_plot.m % Script file: cosh_plot.m % % Purpose: % To plot cosh x vs x. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/04/15 S. J. Chapman Original code % % Define variables: % x -- input values % coshx -- cosh(x) % Create array of power in input values x = -3:0.1:3; % Calculate cosh(x) coshx = cosh(x); % Plot on linear scale plot(x,coshx); title('Plot of cosh(x) vs x'); xlabel('x'); ylabel('cosh(x)'); grid on;

solution_files/Ex2.17/cosh_plot.png

solution_files/Ex2.18/spring.m % Script file: spring.m % % Purpose: % To calculate the energy stored in a spring. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/04/15 S. J. Chapman Original code % % Define variables: % energy -- Stored energy (J) % f -- Force on spring (N) % k -- Spring constant (N/m) % x -- Displacement (m) % Prompt the user for the input force and spring constant. f = input('Enter force on spring (N): '); k = input('Enter spring constant (N/m): ');

% Calculate displacement x x = f/k; % Calculate stored energy energy = 0.5 * k * x^2; % Tell user fprintf('Displacement = %.3f meters\n',x); fprintf('Stored energy = %.3f joules\n',energy);

solution_files/Ex2.19/radio.m % Script file: radio.m % % Purpose: % To calculate the resonant frequency of a radio. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/05/15 S. J. Chapman Original code % % Define variables: % c -- Capacitance (F) % freq -- Resonant frequency (Hz) % l -- Inductance (H) % Prompt the user for the input force and spring constant. l = input('Enter inductance in henrys: '); c = input('Enter capacitance in farads: '); % Calculate resonant frequency freq = 1 / ( 2 * pi * sqrt(l*c) ); % Tell user fprintf('Resonant frequency = %.1f Hz\n',freq);

solution_files/Ex2.20/radio2.m % Script file: radio2.m % % Purpose:

% To plot the frequency response of a radio receiver. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/05/15 S. J. Chapman Original code % % Define variables: % c -- Capacitance (F) % freq -- Resonant frequency (Hz) % l -- Inductance (H) % r -- resistance (ohms) % v -- output viltage (V) % v0 -- input voltage (V) % w -- Angular frequency (rad/s) % Initialise values c = 0.1e-9; l = 0.25e-3; r = 50; v0 = 10e-3; % Create an array of frequencies centered on 1 MHz, % which is the resonant frequency freq = (0.7:0.001:1.3) * 1e6; % Calculate w w = 2 * pi * freq; % Calculate output voltage v = v0 .* r ./ sqrt( r^2 + (w.*l - 1./(w.*c)).^2 ); % Plot on linear scale plot(freq,v); title('Plot of output voltage vs frequency'); xlabel('Frequency (Hz)'); ylabel('Voltage (V)');

solution_files/Ex2.20/radio2.png

solution_files/Ex2.21/radio3.m % Script file: radio3.m % % Purpose: % To calculate the output power of a radio receiver. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/05/15 S. J. Chapman Original code % % Define variables: % c -- Capacitance (F) % freq -- Resonant frequency (Hz) % l -- Inductance (H) % r -- resistance (ohms) % p -- output power (W) % v -- output viltage (V) % v0 -- input voltage (V) % w -- Angular frequency (rad/s)

% Initialise values c = 0.1e-9; l = 0.25e-3; r = 50; % Get voltage and frequency v0 = input('Enter voltage (V): '); freq = input('Enter frequency (Hz): '); % Calculate w w = 2 * pi * freq; % Calculate output voltage v = v0 .* r ./ sqrt( r^2 + (w.*l - 1./(w.*c)).^2 ); % Calculate output power (=v^2/r) p = v^2 / r; % Tell user fprintf('Output power = %f W\n',p);

solution_files/Ex2.22/turning.m % Script file: turning.m % % Purpose: % To calculate the turning radius of an aircraft flying % in a circle, based on speed and max g. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/05/15 S. J. Chapman Original code % % Define variables: % g -- Max acceleration (g) % grav -- Acceleration of gravity (9.81 m/s2) % mach1 -- Speed of sound (340 m/s) % radius -- Turning radius (m) % speed -- Aircraft speed in Mach % Initialise values

grav = 9.81; mach1 = 340; % Get speed and max g speed = input('Enter speed (Mach): '); g = input('Enter max acceleration (g): '); % Calculate radius radius = (speed * mach1).^ 2 / ( g * grav ); % Tell user fprintf('Turning radius = %f m\n',radius);

solution_files/Ex2.22/turning2.m % Script file: turning2.m % % Purpose: % To plot the turning radius of an aircraft as a function % of speed. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/05/15 S. J. Chapman Original code % % Define variables: % g -- Max acceleration (g) % grav -- Acceleration of gravity (9.81 m/s2) % mach1 -- Speed of sound (340 m/s) % max_speed -- Maximum speed in Mach numbers % min_speed -- Minimum speed in Mach numbers % radius -- Turning radius (m) % speed -- Aircraft speed in Mach % Initialise values grav = 9.81; mach1 = 340; % Get speed and max g min_speed = input('Enter min speed (Mach): ');

max_speed = input('Enter min speed (Mach): '); g = input('Enter max acceleration (g): '); % Calculate range of speeds speed = min_speed:(max_speed-min_speed)/20:max_speed; % Calculate radius radius = (speed * mach1).^ 2 / ( g * grav ); % Plot the turning radius versus speed plot(speed,radius/1000); title('Plot of turning radius versus speed'); xlabel('Speed (Mach)'); ylabel('Turning radius (km)');

solution_files/Ex2.22/turning2.png

solution_files/Ex2.22/turning3.m % Script file: turning3.m % % Purpose: % To plot the turning radius of an aircraft as a function

% of centripetal acceleration. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/05/15 S. J. Chapman Original code % % Define variables: % g -- Acceleration (g) % grav -- Acceleration of gravity (9.81 m/s2) % mach1 -- Speed of sound (340 m/s) % max_g -- Maximum accleration in g's % min_g -- Minimum accleration in g's % radius -- Turning radius (m) % speed -- Aircraft speed in Mach % Initialise values grav = 9.81; mach1 = 340; % Get speed and max g speed = input('Enter speed (Mach): '); min_g = input('Enter min acceleration (g): '); max_g = input('Enter min acceleration (g): '); % Calculate range of accelerations g = min_g:(max_g-min_g)/20:max_g; % Calculate radius radius = (speed * mach1).^ 2 ./ ( g * grav ); % Plot the turning radius versus speed plot(g,radius/1000); title('Plot of turning radius versus acceleration'); xlabel('Centripetal acceleration (g)'); ylabel('Turning radius (km)');

solution_files/Ex2.22/turning3.png

solution_files/Ex2.4/array1.dat Data/auxiliary file.

solution_files/Ex2.4/array1.mat Data/auxiliary file.

solution_files/Ex2.6/data.mat Data/auxiliary file.

solution_files/Ex2.9/test.m a = [ -2.0 5.0 1.0 3.0 4.0 -1.0; ...

2.0 -1.0 -5.0 -2.0 6.0 4.0; ...

-1.0 6.0 -4.0 -5.0 3.0 -1.0; ...

4.0 3.0 -6.0 -5.0 -2.0 -2.0; ...

-3.0 6.0 4.0 2.0 -6.0 4.0; ...

2.0 4.0 4.0 4.0 5.0 -4.0 ]; b = [ 0.0; 1.0; -6.0; 10.0; -6.0; -2.0];

a\b

solution_files/Ex3.1/plot_function.fig Data/auxiliary file.

solution_files/Ex3.1/plot_functions.m % Get the point spacings x = linspace(0, 10, 100); % Calculate first function y1 = exp(-0.5.*x) .* sin(2.*x); % Plot the first function plot(x,y1,'b-', 'LineWidth', 2); hold on; % Calculate the second function y2 = exp(-0.5.*x) .* cos(2.*x); % Plot the second function plot(x,y2,'r--', 'LineWidth', 3); hold off; % Finish the plot title('\bfPlot of \ity(x) = e^{-2x} sin 2x \rm\bfand \ity(x) = e^{-2x} cos 2x'); xlabel('\bf\itx'); ylabel('\bf\ity(x)'); legend('Function 1','Function 2'); grid on;

solution_files/Ex3.1/resulting_plot.png

solution_files/Ex3.11/plot_function.m % Script file: plot_function.m % % Purpose: % This program plots amplitude and phase of a complex % function as amp and phase vs time on two subplots. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/15/15 S. J. Chapman Original code % % Define variables: % amp -- Amplitude of complex function % fn -- Output of complex function % phase -- Phase of complex function % t -- Independent variable % Calculate function t = 0:0.1:4;

fn = (1.0 + 0.25*i) .* t - 2; % Get amplitude and phase amp = abs(fn); phase = angle(fn); % Plot amplitude and phase vs time figure(1) subplot(2,1,1); plot (t,amp,'r-','LineWidth',2); title ('\bfAmplitude versus time'); xlabel('\bfTime'); ylabel('\bfAmplitude'); subplot(2,1,2); plot (t,phase,'r-','LineWidth',2); title ('\bfPhase versus time'); xlabel('\bfTime'); ylabel('\bfPhase');

solution_files/Ex3.11/resulting_plot.fig Data/auxiliary file.

solution_files/Ex3.11/resulting_plot.png

solution_files/Ex3.12/linspace.png

solution_files/Ex3.12/linspace_vs_logspace.m

% Script file: linspace_vs_logspace.m % % Purpose: % This program compares data point distribution using % linspace with data point distribution using logspace.. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/15/15 S. J. Chapman Original code % % Define variables: % x -- Independt points to plot % y -- Output values of fuction at x % Calculate function using linspace x = linspace(1,100,100); y = 20*log10(2*x); % Plot data figure(1) semilogx (x,y,'b-','LineWidth',2); hold on; semilogx (x,y,'ro'); hold off; title ('\bfPlot using linspace'); xlabel('\bfx'); ylabel('\bfy(x)'); % Calculate function using logspace x = logspace(0,2,100); y = 20*log10(2*x); % Plot data figure(2) semilogx (x,y,'r-','LineWidth',2); hold on; semilogx (x,y,'k*'); hold off; title ('\bfPlot using logspace');

solution_files/Ex3.12/logspace.png

solution_files/Ex3.13/errorbar_plot.fig Data/auxiliary file.

solution_files/Ex3.13/errorbar_plot.m % Script file: errorbar_plot.m % % Purpose: % To display mean temperature data with.extremes shown with % error bars. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/15/15 S. J. Chapman Original code % % Define variables: % temp -- Input data (col1 =,month; col2 = mean; % col3 = high; col4 = low)

% high -- Max temp above the mean value (deg) % low -- Min temp below the mean value (deg) % Get the data load temp.dat; % Calculate the upper limits of the errorbar high = temp(:,3) - temp(:,2); % Calculate the lower limits of the errorbar low = temp(:,2) - temp(:,4); % Plot data with error bars figure(1); errorbar(temp(:,1), temp(:,2), low, high, 'b-'); y = exp(-x) .* sin(x); title('\bfTemperature Plot with Error Bars'); xlabel('\bfMonth'); ylabel('\bfTemp (\circ F)');

solution_files/Ex3.13/errorbar_plot.png

solution_files/Ex3.13/temp.dat

Data/auxiliary file.

solution_files/Ex3.14/spiral.fig Data/auxiliary file.

solution_files/Ex3.14/spiral.m % Script file: spiral.m % % Purpose: % This program plots the spiral of Archimedes. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/16/15 S. J. Chapman Original code % % Define variables: % r -- Amplitude of function % theta -- Angle from antenna axis % Calculate gain versus angle theta = 0:pi/20:6*pi; r = 0.5 * theta; % Plot gain figure(1) polar (theta,r,'b-'); title ('\bfPlot of \itr \rm\bf = 0.5 \it\theta');

solution_files/Ex3.14/spiral.png

solution_files/Ex3.15/motor_power.fig Data/auxiliary file.

solution_files/Ex3.15/motor_power.m % Script file: motor_power.m % % Purpose: % This program plots torque, speed, and power output % from a motor versus time. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/16/15 S. J. Chapman Original code % % Define variables: % power -- output power (watts) % r -- Amplitude of function % speed -- Speed (rad/s)

% t -- Time (s) % torque -- Torque (N-m) % Calculate torque and speed vs time t = 0:0.1:10; speed = 188.5 * (1 - exp(-0.2*t)); torque = 10 * exp(-0.2*t); % Calculate power power = torque .* speed; % Plot torque, speed, and power versus time figure(1) subplot(3,1,1) plot(t,torque,'b-','LineWidth',2); title ('\bfPlot of Motor Output Torque, Speed, and Power vs Time'); ylabel('\bf\it\tau\rm\bf_{IND} (N-m)'); grid on; subplot(3,1,2) plot(t,speed,'b-','LineWidth',2); ylabel('\bf\it\omega_{m} \rm\bf(rad/s)'); grid on; subplot(3,1,3) plot(t,power,'b-','LineWidth',2); xlabel('\bfTime (s)');

solution_files/Ex3.15/motor_power.tif Data/auxiliary file.

solution_files/Ex3.16/orbits.m % Script file: orbits.m % % Purpose: % This program plots orbits with various eccentricities. % % Record of revisions: % Date Programmer Description of change % ==== ========== =====================

% 03/16/15 S. J. Chapman Original code % % Define variables: % e -- Eccentricity % p -- Size of orbit % r -- Range to satellite % theta -- Angle of orbit (radians) % Initialise values theta = 0:pi/20:2*pi; p = 1000; % Calculate orbits for e = 0 e = 0.0; r = p ./ ( 1 - e .* cos(theta) ); % Plot orbit figure(1) polar (theta,r,'b-'); title ('\bfOrbit for eccentricity = 0'); % Calculate orbits for e = 0.25 e = 0.25; r = p ./ ( 1 - e .* cos(theta) ); % Plot orbit figure(2) polar (theta,r,'b-'); title ('\bfOrbit for eccentricity = 0.25'); % Calculate orbits for e = 0.5 e = 0.5;

solution_files/Ex3.16/orbits_0.fig Data/auxiliary file.

solution_files/Ex3.16/orbits_0.png

solution_files/Ex3.16/orbits_25.fig Data/auxiliary file.

solution_files/Ex3.16/orbits_25.png

solution_files/Ex3.16/orbits_5.fig Data/auxiliary file.

solution_files/Ex3.16/orbits_5.png

solution_files/Ex3.2/After editing.png

solution_files/Ex3.2/Click here to edit plot.png

solution_files/Ex3.2/Editing the figure.png

solution_files/Ex3.2/plot_function.fig

Data/auxiliary file.

solution_files/Ex3.2/plot_functions.m % Get the point spacings x = linspace(0, 10, 100); % Calculate first function y1 = exp(-0.5.*x) .* sin(2.*x); % Plot the first function plot(x,y1,'b-', 'LineWidth', 2); hold on; % Calculate the second function y2 = exp(-0.5.*x) .* cos(2.*x); % Plot the second function plot(x,y2,'r--', 'LineWidth', 3); hold off; % Finish the plot title('\bfPlot of \ity(x) = e^{-2x} sin 2x \rm\bfand \ity(x) = e^{-2x} cos 2x'); xlabel('\bf\itx'); ylabel('\bf\ity(x)'); legend('Function 1','Function 2'); grid on;

solution_files/Ex3.2/resulting_plot.png

solution_files/Ex3.3/plot_functions.m % Get the point spacings x = logspace(-2, 1, 100); % Calculate first function y1 = exp(-0.5.*x) .* sin(2.*x); % Plot the first function semilogx(x,y1,'b-', 'LineWidth', 2); hold on; % Calculate the second function y2 = exp(-0.5.*x) .* cos(2.*x); % Plot the second function semilogx(x,y2,'r--', 'LineWidth', 3); hold off; % Finish the plot title('\bfPlot of \ity(x) = e^{-2x} sin 2x \rm\bfand \ity(x) = e^{-2x} cos 2x'); xlabel('\bf\itx'); ylabel('\bf\ity(x)'); legend('Function 1','Function 2');

grid on;

solution_files/Ex3.3/resulting_plot.fig Data/auxiliary file.

solution_files/Ex3.3/resulting_plot.png

solution_files/Ex3.4/bar_plot.fig Data/auxiliary file.

solution_files/Ex3.4/bar_plot.png

solution_files/Ex3.4/plot_function.m % Get the point spacings x = linspace(0, 10, 100); % Calculate the function y1 = exp(-0.5.*x) .* sin(2.*x); % Plot the function bar(x,y1); % Finish the plot title('\bfPlot of \ity(x) = e^{-2x} sin 2x \rm\bfand \ity(x) = e^{-2x} cos 2x'); xlabel('\bf\itx'); ylabel('\bf\ity(x)'); grid on;

solution_files/Ex3.5/plot_function.m % Get the point spacings theta = (0:0.01:2)*pi;

% Calculate the function r = sin(2.*theta) .* cos(theta); % Plot the function polar(theta,r); % Finish the plot title('\bfPlot of \itr(\it\theta\rm\bf) = sin(\it2\theta\rm\bf) * cos(\it\theta\rm\bf)'); grid on;

solution_files/Ex3.5/polar_plot.fig Data/auxiliary file.

solution_files/Ex3.5/polar_plot.png

solution_files/Ex3.6/plot_function.m % Get the point spacings x = linspace(-6, 6, 100); % Calculate the function f = x.^4 - 3*x.^3 + 10*x.^2 - x - 2;

% Plot the function plot(x,f,'k-', 'LineWidth', 2); hold on; % Finish the plot title('\bfPlot of \itf(x) = x\rm\bf^{4} - 3\itx\rm\bf^{3} + 10\itx\rm\bf^{2} - \itx\rm\bf - 2'); xlabel('\bf\itx'); ylabel('\bf\itf(x)'); grid on;

solution_files/Ex3.6/resulting_plot.fig Data/auxiliary file.

solution_files/Ex3.6/resulting_plot.png

solution_files/Ex3.7/plot_function.m % Get the point spacings x = linspace(-2, 8, 200);

% Calculate the function f = (x.^2 - 6*x + 5) ./ (x - 3); % Plot the function plot(x,f,'b-', 'LineWidth', 2); set(gca,'YLim',[-10 10]); hold on; % Finish the plot title('\bfPlot of function'); xlabel('\bf\itx'); ylabel('\bf\itf(x)'); grid on;

solution_files/Ex3.7/resulting_plot.fig Data/auxiliary file.

solution_files/Ex3.7/resulting_plot.png

solution_files/Ex3.8/pie_plot.fig Data/auxiliary file.

solution_files/Ex3.8/pie_plot.m % Create a pie plot figure(1); contrib = [15 5 10 5 15]; pie(contrib); title('\bfContributions to Gift'); legend('George', 'Sam', 'Betty', 'Charlie', 'Suzie');

solution_files/Ex3.8/pie_plot.png

solution_files/Ex3.9/bar_plot.png

solution_files/Ex3.9/compass_plot.png

solution_files/Ex3.9/horizontal_bar_plot.png

solution_files/Ex3.9/linear_plot.png

solution_files/Ex3.9/log-linear_plot.png

solution_files/Ex3.9/stair_plot.png

solution_files/Ex3.9/stem_plot.png

solution_files/Ex3.9/test_plots.m % Script file: test_plots.m % % Purpose: % To create 7 plot types. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/15/15 S. J. Chapman Original code % % Define variables: % x -- Independent variable % y -- Dependent variable % Define data x = 0:0.1:4; y = exp(-x) .* sin(x); % Create a linear plot figure(1);

plot(x,y); title('\bfLinear plot'); xlabel('\bfx'); ylabel('\bfy'); % Create a log-linear plot figure(2); semilogx(x,y); title('\bfLog-linear plot'); xlabel('\bfx'); ylabel('\bfy'); % Create a stem plot figure(3); stem(x,y); title('\bfStem plot'); xlabel('\bfx'); ylabel('\bfy'); % Create a stair plot

solution_files/Ex4.10/ideal_gas3.fig Data/auxiliary file.

solution_files/Ex4.10/ideal_gas3.m % Script file: ideal_gas3.m % % Purpose: % This program plots the pressure versus temperature of an % ideal gas in a specific container. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % P1 -- Pressure at 0 deg C (kPa)

% P2 -- Pressure at another temperature (kPa) % T1 -- Reference temperature 0 deg C = 273 K (K) % T2 -- Temperature to calculate pressure for (K) % Set reference temperature and pressure T1 = 273; P1 = 200; % Create array of input tempreatures (K) T2 = (0:10:200) + 273; % Calculate pressures P2 = (T2 ./ T1) * P1; % Create plot figure(1); plot( T2, P2, 'r-', 'LineWidth', 2 ); title('\bfPressure vs Temperature in an Ideal Gas'); xlabel('\bfTemperature (K)'); ylabel('\bfPressure (kPa)'); grid on;

solution_files/Ex4.10/ideal_gas3.png

solution_files/Ex4.11/van der waals.fig Data/auxiliary file.

solution_files/Ex4.11/van der waals.png

solution_files/Ex4.11/van_der_waals.m % Script file: van_der_waals.m % % Purpose: % This program plots the pressure versus volume of an % ideal gas according to the Ideal Gas Law and according % to the van der Waals equation. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % n -- Number of atoms (mol)

% P1 -- Array of pressures (Ideal Gass Law) (kPa) % P2 -- Array of pressures (van der Waals) (kPa) % R -- Ideal gas constant (L kPa/mol K) % T -- Temperature (K) % V1 -- volume (L) % Initialize abnRTV a = 0.396; % kPa-L b = 0.0427; % L/mol n = 1; % Moles of atoms R = 8.314; % Ideal gas constant T = 273; % Temperature (K) V = 30; % Volume (L) % Create array of input volumes. Note that this % array must be quite dense to catch the major % changes in volume at low pressures.

V1 = logspace(-1,2,100); % Calculate volumes according to Ideal Gas Law P1 = (n * R * T) ./ V1; % Calculate volumes according to van der Waals equation P2 = ((n * R * T) ./ (V1 - n*b)) - (n^2*a./V1.^2); % Create plot

solution_files/Ex4.14/ant_gain.fig Data/auxiliary file.

solution_files/Ex4.14/ant_gain.m % Script file: ant_gain.m % % Purpose: % This program plots an antenna gain pattern. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code

% % Define variables: % gain -- Gain as a function of angle % theta -- Angle from antenna axis % Calculate gain versus angle g = 0.5; theta = -pi/2:pi/40:pi/2; gain = abs(sin(4*theta)./(4*theta)); % Note that we must fix up the point where theta==0, % since sinc(0) = 1, but numerically it becomes NaN. gain(21) = 1; % Plot gain polar (theta,gain,'r-'); title ('\bfAntenna gain versus angle \theta');

solution_files/Ex4.14/ant_gain.png

solution_files/Ex4.15/calc_tax_2009.m % Script file: calc_tax_2009.m

% % Purpose: % To calculate Australian income taxes for 2009. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code % % Define variables: % income -- Income in dollars % tax -- Tax owed in dollars % Prompt the user for the input power. income = input('Taxible income: $'); % Calculate basic tax if income <= 6000 tax = 0; elseif income <= 34000 tax = 0.15 * (income - 6000); elseif income <= 80000 tax = 4200 + 0.30 * (income - 34000); elseif income <= 180000 tax = 18000 + 0.40 * (income - 80000); else tax = 58000 + 0.45 * (income - 180000); end % Add Medicare Levy tax = tax + 0.015 * income; % Tell user fprintf('Total tax for 2009 = $%.2f\n',tax);

solution_files/Ex4.16/calc_tax_difference.m % Script file: calc_tax_difference.m % % Purpose: % To calculate Australian income taxes for 2002

% and 2009, and compare the difference. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code % % Define variables: % income -- Income in dollars % tax2002 -- Tax 2002 owed in dollars % tax2009 -- Tax 2009 owed in dollars % Prompt the user for the input power. income = input('Taxible income: $'); % Calculate 2009 basic tax if income <= 6000 tax2009 = 0; elseif income <= 34000 tax2009 = 0.15 * (income - 6000); elseif income <= 80000 tax2009 = 4200 + 0.30 * (income - 34000); elseif income <= 180000 tax2009 = 18000 + 0.40 * (income - 80000); else tax2009 = 58000 + 0.45 * (income - 180000); end % Add Medicare Levy tax2009 = tax2009 + 0.015 * income; % Calculate 2002 basic tax if income <= 6000 tax2002 = 0; elseif income <= 20000

solution_files/Ex4.17/refraction.m % Script file: refraction.m %

% Purpose: % To calculate the angle of incidence at which a light ray % is refracted when passing from a medium with index of % refraction n1 into a medium with index of refraction n2. % The light ray is assumed to have an angle of incidence % theta1 in the first medium, and the program calculates % the angle of incidence theta2 in the second medium. Also, % plot the incident and reflected rays. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code % % Define variables: % arg -- Argument of asin function % n1 -- Index of refraction in medium 1 % n2 -- Index of refraction in medium 2 % theta1 -- Angle of incidence in medium 1 % theta2 -- Angle of incidence in medium 2 % Prompt the user for n1 n1 = input ('Enter index of refraction for medium 1: '); % Prompt the user for n2 n2 = input ('Enter index of refraction for medium 2: '); % Prompt the user for the angle of incidence in medium 1 theta1 = input ('Enter angle of incidence in medium 1 (degrees): '); % Calculate the argument of the arcsin function arg = ( n1 / n2 ) * sin( theta1 * pi/180 ); % Check for total reflection. if abs(arg) > 1.0 % Tell user. disp('This light ray is totally reflected.');

solution_files/Ex4.17/refraction_plot.fig Data/auxiliary file.

solution_files/Ex4.17/refraction_plot.png

solution_files/Ex4.18/highpass_filter.m % Script file: highpass_filter.m % % Purpose: % This program plots amplitude and phase response % of a highpass filter. It uses two subplots, on % for amplitude and one for phase. The amplitude % plot is log-log, and the phase plot is semilogx. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code % % Define variables: % amp -- Amplitude of complex function % c -- Capacitance (farads)

% f -- Frequency (Hz) % phase -- Phase of complex function % r -- Resistance (ohms) % vres -- Voltage response % Initialise filter values r = 16000; % Resistance (ohms) c = 1e-6; % Capacitance (farads) % Calculate frequency response f = 1:100; vres = (j*2*pi*f*r*c) ./ (1 + j*2*pi*f*r*c); % Get amplitude and phase. Express phase in degrees. amp = abs(vres); phase = angle(vres) * 100/pi; % Plot amplitude and phase vs frequency figure(1) subplot(2,1,1); loglog (f,amp,'r-','LineWidth',2); title ('\bfAmplitude and Phase versus frequency'); xlabel('\bfFrequency (Hz)'); ylabel('\bfAmplitude');

solution_files/Ex4.18/highpass_filter_plot.fig Data/auxiliary file.

solution_files/Ex4.18/highpass_filter_plot.png

solution_files/Ex4.19/datafile.mat Data/auxiliary file.

solution_files/Ex4.19/read_file.m % Script file: read_file.m % % Purpose: % This program prompts a user for a MAT file name, and % reads data from that file. The file open lies in a % try / catch structure to catch any errors, and allow % the user to try again. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code % % Define variables: % filename -- Capacitance (farads)

% Clear any old data clear all; try % Get the file name filename = input('Enter file name: ','s'); % Read the file load(filename) catch % If we get here, the file read failed. Tell user. disp('File read failed. Try again...'); end % If successful, display the names of the variables loaded whos

solution_files/Ex4.19/read_file_2.m % Script file: read_file.m % % Purpose: % This program prompts a user for a MAT file name, and % reads data from that file. The file open lies in a % try / catch structure to catch any errors, and allow % the user to try again. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/20/15 S. J. Chapman Original code % % Define variables: % data_read -- Data read flag % filename -- Capacitance (farads) % Clear any old data clear all; % Loop until data is read

data_read = false; while(~data_read) try % Get the file name filename = input('Enter file name: ','s'); % Read the file load(filename) % If successful, set the data_read flag so we will get out data_read = true; catch % If we get here, the file read failed. Tell user. disp('File read failed. Try again...');

solution_files/Ex4.4/mail.m % Script file: mail.m % % Purpose: % To calculate the cost of mail a parcel. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % cost -- cost in dollars % weight -- Weight of package (lbs) % Prompt the user for the input power. weight = input('Enter weight of parcel, in lbs: '); % Calculate cost if weight > 100 % Not mailable disp('Packages heavier than 100 pounds cannot be mailed!');

else if weight <= 2 cost = 15; else cost = 15 + (weight-2) * 5.00; end % Apply penalty if weight > 70 cost = cost + 15; end % Display weight fprintf('Cost = $%.2f\n',cost); end

solution_files/Ex4.5/funxy.m % Script file: funxy.m % % Purpose: % This program solves the function f(x,y) for a % user-specified x and y, where f(x,y) is defined as: %_ %| % | x + y x >= 0 and y >= 0 % | x + y**2 x >= 0 and y < 0 % f(x,y) = | x**2 + y x < 0 and y >= 0 % | x**2 + y**2 x < 0 and y < 0 % |_ % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 01/03/14 S. J. Chapman Original code % 1. 03/18/15 S. J. Chapman Modified for nested ifs % % Define variables: % x -- First independent variable

% y -- Second independent variable % fun -- Resulting function % Prompt the user for the values x and y x = input ('Enter the x coefficient: '); y = input ('Enter the y coefficient: '); % Calculate the function f(x,y) based upon % the signs of x and y. if x >= 0 if y >= 0 fun = x + y; else fun = x + x^2; end else if y >= 0 fun = x^2 + y; else

solution_files/Ex4.6/eval_fn.m % Script file: eval_fn.m % % Purpose: % This program evaluates a function, first checking % to ensure that the input argument is legal. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % x -- First independent variable % fun -- Resulting function % Prompt the user for the value x x = input ('Enter x: '); % Calculate the function

if x < 1 fun = log( 1 / (1-x) ); disp(['log( 1 / (1-x) ) = ' num2str(fun)]); else disp('x must be < 1!'); end

solution_files/Ex4.7/day_of_week.m % Script file: day_of_week.m % % Purpose: % To convert a string containing a day of week into the % corresponding number. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % day -- Day of week (string) % day_no -- Number of day % Get name of day day = input('Enter name of day: ','s'); % Convert to number switch (day) case {'Sunday'}, day_no = 1; case {'Monday'}, day_no = 2; case {'Tuesday'}, day_no = 3; case {'Wednesday'}, day_no = 4; case {'Thursday'}, day_no = 5;

case {'Friday'}, day_no = 6; case {'Saturday'}, day_no = 7; otherwise, disp(['Illegal day name: ' day '!']); day_no = 0; end % Tell user

solution_files/Ex4.8/select_course.m % Script file: select_course.m % % Purpose: % To convert make a selection from a list of courses. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % course -- Course name (string) % Get name of day course = input('Select course ("English", "History", "Astronomy", or "Literature"): ','s'); % Convert to number switch (course) case {'English'}, disp('English selected.'); case {'History'}, disp('History selected.'); case {'Astronomy'}, disp('Astronomy selected.'); case {'Literature'}, disp('Literature selected.'); otherwise,

disp(['Illegal course selected: ' course '!']); end

solution_files/Ex4.9/ideal_gas2.fig Data/auxiliary file.

solution_files/Ex4.9/ideal_gas2.m % Script file: ideal_gas2.m % % Purpose: % This program plots the pressure versus temperature of an % ideal gas. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/18/15 S. J. Chapman Original code % % Define variables: % n -- Number of atoms (mol) % P -- Pressure (kPa) % R -- Ideal gas constant (L kPa/mol K) % T -- Temperature (K) % V -- volume (L) % Initialize nRT n = 1; % Moles of atoms R = 8.314; % Ideal gas constant V = 10; % Volume of gas (L) % Create array of input tempreatures.

T = 250:10:400; % Calculate pressures P = (n * R * T) ./ V; % Create plot figure(1); plot( T, P, 'r-', 'LineWidth', 2 );

title('\bfPressure vs Temperature in an Ideal Gas'); xlabel('\bfTemperature (K)'); ylabel('\bfPressure (kPa)'); grid on;

solution_files/Ex4.9/ideal_gas2.png

solution_files/Ex5.1/eval_loop.fig Data/auxiliary file.

solution_files/Ex5.1/eval_loop.m % Script file: eval_loop.m % % Purpose: % This program evaluates the specified function over % the range -9 to 9 in steps of 0.5, using loops. % % Record of revisions: % Date Programmer Description of change % ==== ========== =====================

% 03/25/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % t -- Independent variable % y -- Dependent variable % Evaluate with loops % t = -9:0.5:9; y = zeros(size(t)); for ii = 1:length(t) if t(ii) >= 0 y(ii) = -3 * t(ii)^2 + 5; else y(ii) = 3 * t(ii)^2 + 5; end end % % Diplay result % plot(t,y,'LineWidth',2); xlabel('\bf\itt'); ylabel('\bf\ity'); grid on;

solution_files/Ex5.1/eval_loop.png

solution_files/Ex5.11/ball.m % Script file: ball.m % % Purpose: % This program calculates the distance traveled by a ball % thrown at a specified angle "theta" and a specified % velocity "vo" from a point on the surface of the Earth, % ignoring air friction and the Earth's curvature. It % calculates the angle yielding maximum range, and also % plots selected trajectories. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 01/30/14 S. J. Chapman Original code % 1. 03/27/15 S. J. Chapman Vectorized inner loops % % Define variables: % conv -- Degrees to radians conv factor % gravity -- Accel. due to gravity (m/s^2)

% ii, jj -- Loop index % index -- Location of maximum range in array % maxangle -- Angle that gives maximum range (deg) % maxrange -- Maximum range (m) % range -- Range for a particular angle (m) % time -- Time (s) % theta -- Initial angle (deg) % traj_time -- Total trajectory time (s) % vo -- Initial velocity (m/s) % vxo -- X-component of initial velocity (m/s) % vyo -- Y-component of initial velocity (m/s) % x -- X-position of ball (m) % y -- Y-position of ball (m) % Constants conv = pi / 180; % Degrees-to-radians conversion factor g = -9.81; % Accel. due to gravity vo = 20; % Initial velocity %Create an array to hold ranges range = zeros(1,91);

solution_files/Ex5.12/ball.m % Script file: ball.m % % Purpose: % This program calculates the distance traveled by a ball % thrown at a specified angle "theta" and a specified % velocity "vo" from a point on the surface of the Earth, % ignoring air friction and the Earth's curvature. It % calculates the angle yielding maximum range, and also % plots selected trajectories. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 01/30/14 S. J. Chapman Original code % 1. 03/27/15 S. J. Chapman Modified to read g

% % Define variables: % conv -- Degrees to radians conv factor % gravity -- Accel. due to gravity (m/s^2) % ii, jj -- Loop index % index -- Location of maximum range in array % maxangle -- Angle that gives maximum range (deg) % maxrange -- Maximum range (m) % range -- Range for a particular angle (m) % time -- Time (s) % theta -- Initial angle (deg) % traj_time -- Total trajectory time (s) % vo -- Initial velocity (m/s) % vxo -- X-component of initial velocity (m/s) % vyo -- Y-component of initial velocity (m/s) % x -- X-position of ball (m) % y -- Y-position of ball (m) % Constants conv = pi / 180; % Degrees-to-radians conversion factor vo = 20; % Initial velocity % Get acceleration due to gravity g = input('Enter g (m/s^2): ');

solution_files/Ex5.13/ball.m % Script file: ball.m % % Purpose: % This program calculates the distance traveled by a ball % thrown at a specified angle "theta" and a specified % velocity "vo" from a point on the surface of the Earth, % ignoring air friction and the Earth's curvature. It % calculates the angle yielding maximum range, and also % plots selected trajectories. % % Record of revisions: % Date Programmer Description of change

% ==== ========== ===================== % 01/30/14 S. J. Chapman Original code % 1. 03/27/15 S. J. Chapman Read initial velocity % % Define variables: % conv -- Degrees to radians conv factor % gravity -- Accel. due to gravity (m/s^2) % ii, jj -- Loop index % index -- Location of maximum range in array % maxangle -- Angle that gives maximum range (deg) % maxrange -- Maximum range (m) % range -- Range for a particular angle (m) % time -- Time (s) % theta -- Initial angle (deg) % traj_time -- Total trajectory time (s) % vo -- Initial velocity (m/s) % vxo -- X-component of initial velocity (m/s) % vyo -- Y-component of initial velocity (m/s) % x -- X-position of ball (m) % y -- Y-position of ball (m) % Constants conv = pi / 180; % Degrees-to-radians conversion factor g = -9.81; % Accel. due to gravity % Get initial velocity vo = input('Enter vo (m/s): ');

solution_files/Ex5.14/lsqfit.m % Script file: lsqfit.m % % Purpose: % To perform a least-squares fit of an input data set % to a straight line, and print out the resulting slope % and intercept values. % % Record of revisions: % Date Programmer Description of change

% ==== ========== ===================== % 01/30/14 S. J. Chapman Original code % 1. 03/27/15 S. J. Chapman Modified to use a while loop % % Define variables: % ii -- Loop index % n_points -- Number in input [x y] points % slope -- Slope of the line % sum_x -- Sum of all input x values % sum_x2 -- Sum of all input x values squared % sum_xy -- Sum of all input x*y yalues % sum_y -- Sum of all input y values % temp -- Variable to read user input % x -- Array of x values % x_bar -- Average x value % y -- Array of y values % y_bar -- Average y value % y_int -- y-axis intercept of the line disp('This program performs a least-squares fit of an '); disp('input data set to a straight line.'); % Read the input data n_points = 0; temp = input('Enter [x y] pair: '); while ~isempty(temp) n_points = n_points + 1; x(n_points) = temp(1); y(n_points) = temp(2); temp = input('Enter [x y] pair: '); end

solution_files/Ex5.15/input1.dat Data/auxiliary file.

solution_files/Ex5.15/input1a.dat Data/auxiliary file.

solution_files/Ex5.15/input1b.dat Data/auxiliary file.

solution_files/Ex5.15/lsqfit.m % Script file: lsqfit.m % % Purpose: % To perform a least-squares fit of an input data set % to a straight line, and print out the resulting slope % and intercept values. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 01/30/14 S. J. Chapman Original code % 1. 03/27/15 S. J. Chapman Modified to read from input1.dat % % Define variables: % ii -- Loop index % n_points -- Number in input [x y] points % slope -- Slope of the line % sum_x -- Sum of all input x values % sum_x2 -- Sum of all input x values squared % sum_xy -- Sum of all input x*y yalues % sum_y -- Sum of all input y values % temp -- Variable to read user input % x -- Array of x values % x_bar -- Average x value % y -- Array of y values % y_bar -- Average y value % y_int -- y-axis intercept of the line disp('This program performs a least-squares fit of an '); disp('input data set to a straight line.'); % Read the input data load input1.dat x = input1(:,1);

y = input1(:,2); n_points = length(x); % Accumulate statistics sum_x = 0; sum_y = 0;

solution_files/Ex5.16/input1a.dat Data/auxiliary file.

solution_files/Ex5.16/input1b.dat Data/auxiliary file.

solution_files/Ex5.16/lsqfit.m % Script file: lsqfit.m % % Purpose: % To perform a least-squares fit of an input data set % to a straight line, and print out the resulting slope % and intercept values. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 01/30/14 S. J. Chapman Original code % 1. 03/27/15 S. J. Chapman Modified to read from user file % % Define variables: % filename -- Input file anme % ii -- Loop index % n_points -- Number in input [x y] points % slope -- Slope of the line % sum_x -- Sum of all input x values % sum_x2 -- Sum of all input x values squared % sum_xy -- Sum of all input x*y yalues % sum_y -- Sum of all input y values

% temp -- Variable to read user input % x -- Array of x values % x_bar -- Average x value % y -- Array of y values % y_bar -- Average y value % y_int -- y-axis intercept of the line disp('This program performs a least-squares fit of an '); disp('input data set to a straight line.'); % Get the file name to read filename = input('Enter file name: ','s'); % Read the input data in_data = textread(filename); x = in_data(:,1); y = in_data(:,2); n_points = length(x);

solution_files/Ex5.18/gen_data.m x = 0:0.05:4; y = x.^2 - 4*x + 4; for ii = 1:length(y) y(ii) = y(ii) + 0.1 * randn; end figure(1) plot(x,y);

solution_files/Ex5.18/input3.dat Data/auxiliary file.

solution_files/Ex5.18/running_ave.m % Script file: running_ave.m % % Purpose: % To perform a running average filter on an input data set. %

% Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/30/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % filename -- Input data file % n_ave -- Number of points to average % n_per_side -- Number of points to average per side % n_points -- Number of points in data set % x -- Array of input values % y -- Array of filtered values disp('This program performs a running average filter on an '); disp('input data set.'); filename = input('Enter the filename containing the data: ','s'); n_ave = input('Enter the number of samples to average: '); % Get the number of samples on either side of the sample % being averaged, dropping any fractional part. n_per_side = (n_ave-1) / 2; n_per_side = floor(n_per_side); % Read the input data x = textread(filename,'%f'); n_points = length(x); % Now perform the running average for ii = 1:n_points % Check to see how many points we can use on either side % of the point being averaged. n_low = min([ (ii-1) n_per_side]); n_high = min([ (n_points-ii) n_per_side]);

solution_files/Ex5.18/running_average_filter.fig Data/auxiliary file.

solution_files/Ex5.18/running_average_filter.png

solution_files/Ex5.19/input3.dat Data/auxiliary file.

solution_files/Ex5.19/median_filter.fig Data/auxiliary file.

solution_files/Ex5.19/median_filter.m % Script file: median_filter.m % % Purpose: % To perform a median filter on an input data set. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/30/15 S. J. Chapman Original code % % Define variables:

% ii -- Loop index % filename -- Input data file % n_ave -- Number of points to average % n_per_side -- Number of points to average per side % n_points -- Number of points in data set % slope -- Slope of the line % x -- Array of input values % y -- Array of filtered values disp('This program performs a median filter on an input data set.'); filename = input('Enter the filename containing the data: ','s'); n_ave = input('Enter the number of samples to average: '); % Get the number of samples on either side of the sample % being averaged, dropping any fractional part. n_per_side = (n_ave-1) / 2; n_per_side = floor(n_per_side); % Read the input data x = textread(filename,'%f'); n_points = length(x); % Now perform the running average for ii = 1:n_points % Check to see how many points we can use on either side % of the point being averaged. n_low = min([ (ii-1) n_per_side]); n_high = min([ (n_points-ii) n_per_side]);

solution_files/Ex5.19/median_filter.png

solution_files/Ex5.2/eval_vector.fig Data/auxiliary file.

solution_files/Ex5.2/eval_vector.m % Script file: eval_vector.m % % Purpose: % This program evaluates the specified function over % the range -9 to 9 in steps of 0.5, using vectors. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/25/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % t -- Independent variable % test -- Logical array for masking

% y -- Dependent variable % Evaluate with vectors % t = -9:0.5:9; test = t > 0; y(test) = -3 * t(test).^2 + 5; y(~test) = 3 * t(~test).^2 + 5; % % Diplay result % plot(t,y,'LineWidth',2); xlabel('\bf\itt'); ylabel('\bf\ity'); grid on;

solution_files/Ex5.2/eval_vector.png

solution_files/Ex5.20/fourier_series.fig Data/auxiliary file.

solution_files/Ex5.20/fourier_series.m % Script file: fourier_series.m % % Purpose: % To plot 3, 5, and 10 terms of a Fourier series approximation % to a square wave. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/30/15 S. J. Chapman Original code % % Define variables: % x -- Array of x values % y3 -- Three-term approimation % y5 -- Five-term approimation % y10 -- Ten-term approimation % Get the input data points x = -2:0.001:2; % Calculate the Fourier series approximation to 3 terms y3 = zeros(size(x)); for n = 1:2:5 y3 = y3 + (1/n) .* sin(n*pi*x); end % Calculate the Fourier series approximation to 5 terms y5 = zeros(size(x)); for n = 1:2:9 y5 = y5 + (1/n) .* sin(n*pi*x); end % Calculate the Fourier series approximation to 10 terms y10 = zeros(size(x)); for n = 1:2:19 y10 = y10 + (1/n) .* sin(n*pi*x); end % Plot the approximations

plot(x,y3,'r-','LineWidth',2);

solution_files/Ex5.20/fourier_series.png

solution_files/Ex5.21/doy.m % Script file: doy.m % % Purpose: % This program calculates the day of year corresponding % to a specified date. It illustrates the use switch and % for constructs. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 01/27/14 S. J. Chapman Original code % 1. 03/30/15 S. J. Chapman Modified to check for validity % % Define variables: % day -- Day (dd)

% day_of_year -- Day of year % ii -- Loop index % leap_day -- Extra day for leap year % max_day -- Last day in a month % month -- Month (mm) % year -- Year (yyyy) % Get day, month, and year to convert disp('This program calculates the day of year given the '); disp('current date.'); month = input('Enter current month (1-12): '); day = input('Enter current day(1-31): '); year = input('Enter current year(yyyy): '); % Check for leap year, and add extra day if necessary if mod(year,400) == 0 leap_day = 1; % Years divisible by 400 are leap years elseif mod(year,100) == 0 leap_day = 0; % Other centuries are not leap years elseif mod(year,4) == 0 leap_day = 1; % Otherwise every 4th year is a leap year else leap_day = 0; % Other years are not leap years end

solution_files/Ex5.22/eval_fn.m % Script file: eval_fn.m % % Purpose: % This program evaluates a function, first checking % to ensure that the input argument is legal. Evaluate % this function repeatedly until an illegal value is % entered. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/30/15 S. J. Chapman Original code

% % Define variables: % x -- Independent variable % fun -- Resulting function % Prompt the user for the value x x = input ('Enter x: '); % Calculate the function while x < 1 fun = log( 1 / (1-x) ); disp(['log( 1 / (1-x) ) = ' num2str(fun)]); x = input ('Enter x: '); end disp('Ending...');

solution_files/Ex5.23/fibonacci.m % Script file: fibonacci.m % % Purpose: % This program evaluates the nth Fibonacci number. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/30/15 S. J. Chapman Original code % % Define variables: % fn -- Fibonacci number % n -- The item in the sequence to calculate % Get n n = input('Enter the Fibonacci number n to evaluate (n>2): '); % Check to see that n is an integer greater than two if n <= 2 disp('Error--n must greater than two!'); elseif round(n) ~= n disp('Error--n must be an integer!');

else % Calculate fn fn = zeros(1,n); fn(1) = 1; fn(2) = 2; ii = 3; while ii <= n; fn(ii) = fn(ii-1) + fn(ii-2); ii = ii + 1; end % Display result disp(['The ' int2str(n) 'th Fibonacci number = ' int2str(fn(n))]);

solution_files/Ex5.24/diode.fig Data/auxiliary file.

solution_files/Ex5.24/diode.m % Script file: diode.m % % Purpose: % This program calculates and plots the current flowing % through a diode as a function of the voltage across it. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/01/15 S. J. Chapman Original code % % Define variables: % i0 -- Leakage current (A) % id -- Diode current (A) % k -- Boltzmann's constant (joule/K) % q -- Charge on an electron (coul) % temp_f -- Temperature (deg F) % temp_k -- Temperature (K) % vd -- Diode voltage (V)

% Initial values i0 = 2.0e-6; % amps k = 1.38e-23; % joule/K q = 1.602e-19; % Coulombs vd = -1.0:0.01:0.6; % Volts temp_f = [75 100 125]; % def F for ii = 1:length(temp_f) % Convert temperature to kelvins. temp_k = (5/9) * (temp_f(ii) - 32) + 273.15; % Calculate currents id = i0 .* ( exp((q*vd)/(k*temp_k)) - 1 ); % Plot line in various colors if ii == 1 plot(vd,id,'b-','LineWidth',2); hold on;

solution_files/Ex5.24/diode.png

solution_files/Ex5.25/cable.fig

Data/auxiliary file.

solution_files/Ex5.25/cable.m % Script file: cable.m % % Purpose: % To calculate the connection point that results in % minimum tension on a cable. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/01/15 S. J. Chapman Original code % % Define variables: % dist -- Distance to attachment (m) % lc -- Cable length (m) % ii -- index variable % lp -- Pole length (m) % saved_dist -- Save attachment distance % saved_tension -- Saved tension % tension -- Tension on cable % weight -- Weight of object (kg) % Initial values lc = 2; lp = 2; weight = 100; clear dist tension % Calculate tension at 0.3 m dist(1) = 0.3; tension(1) = weight * lc * lp ... / ( dist(1) * sqrt(lp^2 - dist(1)^2) ); % Save these initial values for comparision saved_dist = dist; saved_tension = tension; % Calculate for other values between 0.4 and 1.8 m

jj = 1; for ii = 0.4:0.1:1.8

solution_files/Ex5.25/cable.png

solution_files/Ex5.26/cable.fig Data/auxiliary file.

solution_files/Ex5.26/cable.m % Script file: cable.m % % Purpose: % To calculate the range of connection points that result % in cable tension within 10% of the minimum value. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/01/15 S. J. Chapman Original code

% % Define variables: % dist -- Distance to attachment (m) % lc -- Cable length (m) % ii -- index variable % jj -- index variable % lp -- Pole length (m) % max_dist -- Max distance within 10% of min tension % min_dist -- Min distance within 10% of min tension % saved_dist -- Save attachment distance % saved_index -- Index of minimum tension value % saved_tension -- Saved tension % tension -- Tension on cable % weight -- Weight of object (kg) % Initial values lc = 2; lp = 2; weight = 100; clear dist tension % Calculate tension at 0.3 m dist(1) = 0.3; tension(1) = weight * lc * lp ... / ( dist(1) * sqrt(lp^2 - dist(1)^2) ); % Save these initial values for comparision saved_dist = dist; saved_tension = tension;

solution_files/Ex5.26/cable.png

solution_files/Ex5.27/parallelogram.m % Script file: parallelogram.m % % Purpose: % To calculate the area of a parallelogram defined by two % vectors representing adjacent sides. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/01/15 S. J. Chapman Original code % % Define variables: % a -- First vector % area -- Area of parallelogram % b -- Second vector disp('This program calculates the area of a parallelogram defined.'); disp('by vectors representing two adjacent sides.'); a = input('Enter vector representing side A (three dimensions): ');

b = input('Enter vector representing side B (three dimensions): '); % Calculate area area = abs(cross(a,b)); % Tell user disp(['The area is ' num2str(area)]);

solution_files/Ex5.28/area_of_rectangle.m % Script file: area_of_rectangle.m % % Purpose: % To calculate the larges area possible for a rectangle % of perimeter 10. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/02/15 S. J. Chapman Original code % % Define variables: % area -- Area of rectange % h -- Height of rectangle % w -- Width of rectangle % saved_area -- Saved area of rectange % saved_h -- Saved height of rectangle % saved_w -- Saved width of rectangle % Get an array of widths w = 0:0.1:5; % Calculate heights h = (10 - 2.*w) ./ 2; % Calculate the aera of the rectanges area = w .* h; % Find the maximum area saved_area = 0; saved_w = 0; saved_h = 0;

for ii = 1:length(w) if area(ii) > saved_area saved_area = area(ii); saved_w = w(ii); saved_h = h(ii); end end

solution_files/Ex5.28/area_vs_width.fig Data/auxiliary file.

solution_files/Ex5.28/area_vs_width.png

solution_files/Ex5.29/bacteria.m % Script file: bacteria.m % % Purpose: % Program to calculate rate of bacterial growth in % different culture media.

% % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/02/15 S. J. Chapman Original code % % Define variables: % double_time_1 -- Doubling time of medium 1 (hrs) % double_time_2 -- Doubling time of medium 2 (hrs) % ii -- index variable % n_bact_1 -- Number of bacterial in medium 1 % n_bact_2 -- Number of bacterial in medium 2 % time -- Time (hrs) % Initial values double_time_1 = 1.0; double_time_2 = 1.5; % Print heading. disp('The rates of colony growth are: '); disp(' Time Colony 1 Colony 2'); disp(' ==== ======== ========'); % Calculate the sizes of each colony for ii = 1:9 % Set time time(ii) = 3 *(ii-1); % Calculate colony size n_bacteria_1(ii) = 2.0 ^ ( time(ii) / double_time_1); n_bacteria_2(ii) = 2.0 ^ ( time(ii) / double_time_2); % Tell user fprintf(' %6.1f%12.1f%12.1f\n',time(ii), ...

solution_files/Ex5.29/bacteria_linear.fig Data/auxiliary file.

solution_files/Ex5.29/bacteria_linear.png

solution_files/Ex5.29/bacteria_semilogy.fig Data/auxiliary file.

solution_files/Ex5.29/bacteria_semilogy.png

solution_files/Ex5.3/squares.m % Script file: squares.m % % Purpose: % This program creates a table of the squares of all even % numbers between 0 and 50. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/25/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % square -- Squares % Create headings fprintf(' Value Square \n'); fprintf(' ====== =========\n'); % Create and print squares

for ii = 0:2:50 square = ii^2; fprintf(' %3d %6d\n',ii,square); end

solution_files/Ex5.30/decibel2.m % Script file: decibel2.m % % Purpose: % To calculate the decibels referenced to 1 W for input % powers of 1 to 20 W. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/02/15 S. J. Chapman Original code % % Define variables: % dBW -- Power in dBW (dB referenced to 1 watt) % pin -- Power in watts % Get input power pin = 1:1:20; % Calculate dBm dBW = 10 * log10( pin / 1.0 ); % Plot dBW vs power figure(1); semilogx(pin,dBW,'b-','LineWidth',2); title('\bfPlot of dBW vs input power'); xlabel('\bfInput Power (W)'); ylabel('\bfdBW'); grid on;

solution_files/Ex5.30/decibel2.png

solution_files/Ex5.31/geometric_mean.m % Script file: geometric_mean.m % % Purpose: % To calculate the geometric mean of a set of positive % numbers. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/02/15 S. J. Chapman Original code % % Define variables: % x -- Input values % g -- Geometric mean % nvals -- Number of input values % prod -- Product of input values % Initialize product and nvals prod = 1;

nvals = 0; % Read the first number x = input('Enter first number: '); % Read the remaining numbers while x > 0 prod = prod * x; nvals = nvals + 1; x = input('Enter next number: '); end % Calculate geometric mean g = prod ^ (1/nvals); % Tell user fprintf('The geometric mean is %.4f\n',g);

solution_files/Ex5.32/rms_average.m % Script file: rms_average.m % % Purpose: % To calculate the rms average of a set of numbers. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/02/15 S. J. Chapman Original code % % Define variables: % nvals -- Number of inout values % rms -- Rms average % sum2 -- Sum of input values squared % x -- Input values % Initialize sum sum2 = 0; % Read the number of input values nvals = input('Enter number of values: '); % Read the numbers

for ii = 1:nvals x = input('Enter number: '); sum2 = sum2 + x^2; end % Calculate rms average rms = sqrt( sum2 / nvals ); % Tell user fprintf('The rms average is %.4f\n',rms);

solution_files/Ex5.33/harmonic_mean.m % Script file: harmonic_mean.m % % Purpose: % To calculate the harmonic mean of a set of numbers. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % % Define variables: % hmean -- Harmonic mean % nvals -- Number of input values % sumr -- Sum of reciprocals of the input values % x -- Input values % Initialize sum sumr = 0; % Read the number of input values nvals = input('Enter number of values: '); % Read the numbers for ii = 1:nvals x = input('Enter number: '); sumr = sumr + 1/x; end % Calculate harmonic mean

hmean = nvals / sumr; % Tell user fprintf('The harmonic mean is %.4f\n',hmean);

solution_files/Ex5.34/all_means.m % Script file: all_means.m % % Purpose: % To calculate the average (arithmetic mean), rms average, % geometric mean, and harmonic mean of a set of numbers. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % % Define variables: % ave -- average % g -- Geometric mean % hmean -- Harmonic mean % nvals -- Number of input values % prod -- Product of input values % rms -- Rms average % sum -- Sum of input values % sum2 -- Sum of input values squared % sumr -- Sum of reciprocals of the input values % x -- Input values % Initialize sums prod = 1; sum = 0; sumr = 0; sum2 = 0; % Read the number of input values nvals = input('Enter number of values: '); % Read the numbers for ii = 1:nvals

x = input('Enter number: '); prod = prod * x; sum = sum + x; sum2 = sum2 + x^2; sumr = sumr + 1/x; end

solution_files/Ex5.35/mtbf.m % Script file: mtbf.m % % Purpose: % To calculate the MTBF of a system based on the MTBFs % of its components. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % % Define variables: % mtbf -- Mean time between failure for overall system % mtbfi -- MTBF for individual subsystems % nvals -- Number of input values % sumr -- Sum of reciprocals of the input values % Initialize sum sumr = 0; % Read the number of input values nvals = input('Enter number of subsystems: '); % Read the numbers for ii = 1:nvals mtbfi = input(['Enter MTBF of Subsystem ' int2str(ii) ': ']); sumr = sumr + 1/mtbfi; end % Calculate overall MTBF mtbf = 1 / sumr;

% Tell user fprintf('The overall system MTBF is %.4f hours.\n',mtbf);

solution_files/Ex5.4/calc_function.m % Script file: calc_function.m % % Purpose: % This program calculates the equation y(x) = x^2 - 3*x + 2 % for values of x between -1 and 3. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/25/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % square -- Squares % Calculate in a for loop for ii = 1:41 x(ii) = (ii-11)/10; y(ii) = x(ii)^2 - 3*x(ii) + 2; end % Calculate as vectors x = -1:0.1:3; y = x.^2 - 3*x + 2; % Plot function figure(1); plot( x, y, 'r--', 'LineWidth',3); title('\bfPlot of \ity(x) \rm\bf vs \itx'); xlabel('\bf\itx'); ylabel('\bf\ity(x)');

solution_files/Ex5.4/calc_function_plot.fig Data/auxiliary file.

solution_files/Ex5.4/calc_function_plot.png

solution_files/Ex5.5/factorial.m % Script file: factorial.m % % Purpose: % This program evaluates N!. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 03/25/15 S. J. Chapman Original code % % Define variables: % fact -- n! % n -- Input value % Get n n = input('Enter n: '); % Check to see that n is a positive integer if n < 0

disp('Error--n must be non-negative!'); elseif round(n) ~= n disp('Error--n must be an integer!'); else % Calculate n! if n == 0 fact = 1; else fact = 1; for ii = 1:n fact = fact * ii; end end % Display result disp([int2str(n) '! = ' int2str(fact)]);

solution_files/Ex5.7/ex5_7a.m ires = 0; for index = -10:10 ires = ires + 1; end

solution_files/Ex5.7/ex5_7b.m ires = 0; for index = 10:-2:4 if index == 6 continue; end ires = ires + index; end

solution_files/Ex5.7/ex5_7c.m ires = 0; for index = 10:-2:4

if index == 6 break; end ires = ires + index; end

solution_files/Ex5.7/ex5_7d.m ires = 0; for index1 = 10:-2:4 for index2 = 2:2:index1 if index2 == 6 break end ires = ires + index2; end end

solution_files/Ex5.8/ex5_8a.m ires = 1; while mod(ires,10) ~= 0 ires = ires + 1; end disp(num2str(ires));

solution_files/Ex5.8/ex5_8b.m ires = 2; while ires <= 200 ires = ires^2; end disp(num2str(ires));

solution_files/Ex5.8/ex5_8c.m ires = 2; while ires > 200 ires = ires^2;

end disp(num2str(ires));

solution_files/Ex5.9/ex5_9a.m arr1 = [1 2 3 4; 5 6 7 8; 9 10 11 12]; mask = mod(arr1,2) == 0; arr1(mask) = -arr1(mask); arr1

solution_files/Ex5.9/ex5_9b.m arr1 = [1 2 3 4; 5 6 7 8; 9 10 11 12]; arr2 = arr1 <= 5; arr1(arr2) = 0; arr1(~arr2) = arr1(~arr2).^2; arr1

solution_files/Ex6.10/inductance.m function ind = inductance(r, D, length) %INDUCTANCE Calculate the inductance of a transmission line % Function INDUCTANCE calculates the inductance of a % single-phase two-wire transmission line. % % Calling sequence: % ind = inductance(r, D, length) % % where % r = the radius of the conductors in meters % D = the distance between the two lines in meters % length = Length of transmission line in meters % Define variables: % ind_per_m -- Inductance per meter % Record of revisions: % Date Programmer Description of change % ==== ========== =====================

% 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Constants mu0 = pi * 4e-7; % H/m % Calculate the inductance ind_per_m = mu0 / pi * (1/4 + log(D/r)); % Get the inductance ind = ind_per_m * length;

solution_files/Ex6.12/capacitance.m function cap = capacitance(r, D, length) %CAPACITANCE Calculate the capacitance of a transmission line % Function CAPACITANCE calculates the capacitance of a % single-phase two-wire transmission line. % % Calling sequence: % cap = capacitance(r, D, length) % % where % r = the radius of the conductors in meters % D = the distance between the two lines in meters % length = Length of transmission line in meters % Define variables: % cap_per_m -- Capacitance per meter % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Constants

e0 = pi * 4e-7; % F/m % Calculate the capacitance cap_per_m = pi * e0 / log((D-r)/r); % Get the capacitance cap = cap_per_m * length;

solution_files/Ex6.14/compare_sorts.m % Script file: compare_sorts.m % % Purpose: % To compare the sort function from Example 6.2 and the % built-in MATLAB sort % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % % Define variables: % data1 -- Array to sort % data2 -- Copy of array to sort % elapsed_time1 -- Elapsed time for ssort % elapsed_time2 -- Elapsed time for sort % Constants SIZE = 100000; % Number of values to sort % Set seed seed(123456); % Create a sample data set to sort. data1 = random0(1,SIZE); % Sort using ssort data2 = data1; tic; out = ssort(data2); elapsed_time1 = toc; % Sort using sort

data2 = data1; tic; out = sort(data2); elapsed_time2 = toc; % Display the relative times disp(['Sort time using ssort = ' num2str(elapsed_time1)]);

solution_files/Ex6.14/random0.m function ran = random0(m,n) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(m) -- Generate an m x m array % random0(m,n) -- Generate an m x n array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % Declare global values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If the n argument is missing, set it to m.

if nargin < 2 n = m; end % Initialize the output array ran = zeros(m,n); % Now calculate random values for ii = 1:m

solution_files/Ex6.14/seed.m function seed(new_seed) %SEED Set new seed for function RANDOM0 % Function SEED sets a new seed for function % RANDOM0. The new seed should be a positive % integer. % Define variables: % ISEED -- Random number seed (global) % new_seed -- New seed % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/02/14 S. J. Chapman Original code % % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Save seed new_seed = round(new_seed); ISEED = abs(new_seed);

solution_files/Ex6.14/ssort.m function out = ssort(a) %SSORT Selection sort data in ascending order

% Function SSORT sorts a numeric data set into % ascending order. Note that the selection sort % is relatively inefficient. DO NOT USE THIS % FUNCTION FOR LARGE DATA SETS. Use MATLAB's % "sort" function instead. % Define variables: % a -- Input array to sort % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable % nvals -- Number of values in "a" % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/02/14 S. J. Chapman Original code % Get the length of the array to sort nvals = length(a); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii) through a(n) iptr = ii; for jj = ii+1:nvals if a(jj) < a(iptr) iptr = jj; end end % iptr now points to the minimum value, so swap a(iptr) % with a(ii) if ii ~= iptr. if ii ~= iptr temp = a(ii);

solution_files/Ex6.15/compare_sorts.m % Script file: compare_sorts.m

% % Purpose: % To compare the sort function from Example 6.2 and the % built-in MATLAB sort % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % % Define variables: % data1 -- Array to sort % data2 -- Copy of array to sort % elapsed_time1 -- Elapsed time for ssort % elapsed_time2 -- Elapsed time for sort % Set seed seed(123456); % Create a sample data set to sort nsamp = 10000; data1 = random0(1,nsamp); % Sort using ssort data2 = data1; tic; out = ssort(data2); elapsed_time1 = toc; % Sort using sort data2 = data1; tic; out = sort(data2); elapsed_time2 = toc; % Display the relative times disp(['Sort time for ' int2str(nsamp) ' using ssort = ' num2str(elapsed_time1)]); disp(['Sort time for ' int2str(nsamp) ' using sort = ' num2str(elapsed_time2)]);

solution_files/Ex6.15/random0.m

function ran = random0(m,n) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(m) -- Generate an m x m array % random0(m,n) -- Generate an m x n array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % Declare global values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If the n argument is missing, set it to m. if nargin < 2 n = m; end % Initialize the output array ran = zeros(m,n); % Now calculate random values for ii = 1:m

solution_files/Ex6.15/seed.m

function seed(new_seed) %SEED Set new seed for function RANDOM0 % Function SEED sets a new seed for function % RANDOM0. The new seed should be a positive % integer. % Define variables: % ISEED -- Random number seed (global) % new_seed -- New seed % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/02/14 S. J. Chapman Original code % % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Save seed new_seed = round(new_seed); ISEED = abs(new_seed);

solution_files/Ex6.15/ssort.m function out = ssort(a) %SSORT Selection sort data in ascending order % Function SSORT sorts a numeric data set into % ascending order. Note that the selection sort % is relatively inefficient. DO NOT USE THIS % FUNCTION FOR LARGE DATA SETS. Use MATLAB's % "sort" function instead. % Define variables: % a -- Input array to sort % ii -- Index variable % iptr -- Pointer to min value

% jj -- Index variable % nvals -- Number of values in "a" % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/02/14 S. J. Chapman Original code % Get the length of the array to sort nvals = length(a); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii) through a(n) iptr = ii; for jj = ii+1:nvals if a(jj) < a(iptr) iptr = jj; end end % iptr now points to the minimum value, so swap a(iptr) % with a(ii) if ii ~= iptr. if ii ~= iptr temp = a(ii);

solution_files/Ex6.16/random0.m function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(n) -- Generate an n x n array % random0(n,m) -- Generate an n x m array % Define variables: % ii -- Index variable

% ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % 1. 04/05/15 S. J. Chapman Modified for 0 arguments % Declare global values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end

solution_files/Ex6.16/seed.m function seed(new_seed) %SEED Set new seed for function RANDOM0 % Function SEED sets a new seed for function % RANDOM0. The new seed should be a positive % integer. % Define variables: % ISEED -- Random number seed (global) % new_seed -- New seed

% Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Save seed new_seed = round(new_seed); ISEED = abs(new_seed);

solution_files/Ex6.17/random0.m function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(n) -- Generate an n x n array % random0(n,m) -- Generate an n x m array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code

% 1. 04/05/15 S. J. Chapman Modified to provide initial seed % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If the m argument is missing, set it to n. if nargin < 2 m = n; end % Initialize the output array ran = zeros(n,m); % Test for missing seed, and supply a default if necessary.

solution_files/Ex6.17/seed.m function seed(new_seed) %SEED Set new seed for function RANDOM0 % Function SEED sets a new seed for function % RANDOM0. The new seed should be a positive % integer. % Define variables: % ISEED -- Random number seed (global) % new_seed -- New seed % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Save seed

new_seed = round(new_seed); ISEED = abs(new_seed);

solution_files/Ex6.18/dice.fig Data/auxiliary file.

solution_files/Ex6.18/dice.m function result = dice() %DICE Return a random integer between 1 and 6 % Function DICE simulates the throw of a fair % die. It returns a random integer between 1 % and 6. % Define variables: % result -- Resulting integer % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(0,0,nargin); error(msg); % The value "6*random0(1,1)" returns a value % in the range [0,6). The "floor" function % returns {0,1,2,3,4,5} with equal probability, % so "result" returns 1-6. result = floor( 6 * random0(1,1) ) + 1;

solution_files/Ex6.18/dice.png

solution_files/Ex6.18/random0.m function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(n) -- Generate an n x n array % random0(n,m) -- Generate an n x m array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % Record of revisions: % Date Programmer Description of change

% ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % 1. 04/05/15 S. J. Chapman Modified to provide initial seed % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If the m argument is missing, set it to n. if nargin < 2 m = n; end % Initialize the output array ran = zeros(n,m); % Test for missing seed, and supply a default if necessary.

solution_files/Ex6.18/seed.m function seed(new_seed) %SEED Set new seed for function RANDOM0 % Function SEED sets a new seed for function % RANDOM0. The new seed should be a positive % integer. % Define variables: % ISEED -- Random number seed (global) % new_seed -- New seed % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,1,nargin);

error(msg); % Save seed new_seed = round(new_seed); ISEED = abs(new_seed);

solution_files/Ex6.18/test_dice.m % Script file: test_dice.m % % Purpose: % To test the function dice. This function calls dice % 10,000 times, and examines the distribution of the % resulting values. They should be roughly uniform. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % % Define variables: % ii -- index variable % result -- Array of results % Initial values result = zeros(1,100000); for ii = 1:100000; result(ii) = dice; end % Display the first 30 values. fprintf('The first 30 values are:\n'); for ii = 1:30 fprintf('%d ',result(ii)); end fprintf('\n'); % Now calculate a histogram to determine the overall % distribution of numbers. hist(result,6); title('\bfHistogram of values returned from function "dice"');

xlabel('\bfValue'); ylabel('\bfCount');

solution_files/Ex6.19/poisson.fig Data/auxiliary file.

solution_files/Ex6.19/poisson.m function result = poisson(k, t, lamda) %POISSON Return a random integer between 1 and 6 % Function POISSON calculates a sample value from % the Poisson distribution for specific values of % k, t, and lamda. % Define variables: % fact -- k! (k-factorial) % result -- Resulting value from distribution % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Calculate k! fact = factorial(k); % Calculate value from Poisson distribution. result = exp(-lamda*t) * (lamda*t) ^ k / fact;

solution_files/Ex6.19/poisson.png

solution_files/Ex6.19/traffic.m % Script file: traffic.m % % Purpose: % To calculate the probability of a given number of cars % passing a particular point on a highway in a given time. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % % Define variables: % k -- Actual number of cars in time t % lamda -- Expected number of cars per minute % prob -- Probability array % t -- Period of time (minutes) % Get initial values lamda = input('Enter expected number of cars/minute: ');

t = input('Enter period of time in minutes: '); % Calculate values. Note that k runs from 0 to 5, while the % minimum value for a MATLAB array is 1, so we must index into % the MATLAB array using "k+1" instead of "k". for k = 0:5 prob(k+1) = poisson(k, t, lamda); end % Display results disp(['The probability of k cars passing in ' num2str(t) ' minutes is:']); for k = 0:5 fprintf(' %3d %12.7f\n',k,prob(k+1)); end % Now plot the distribution. figure(1); plot(0:5,prob,'bo','LineWidth',2); title('\bfPoisson Distribution'); xlabel('\bfValue'); ylabel('\bfProbability');

solution_files/Ex6.20/cosh1.fig Data/auxiliary file.

solution_files/Ex6.20/cosh1.m function out = cosh1(x) %COSH1 Calculate hyperbolic cosine function % Function COSH1 calculates the hyperbolic cosine function % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin);

error(msg); % Calculate value out = (exp(x) + exp(-x))/2;

solution_files/Ex6.20/cosh1.png

solution_files/Ex6.20/sinh.m function out = sinh(x) %SIND Calculate hyperbolic sine function % Function SINH calculates the hyperbolic sine function % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin);

error(msg); % Calculate value out = (exp(x) - exp(-x))/2;

solution_files/Ex6.20/sinh1.fig Data/auxiliary file.

solution_files/Ex6.20/sinh1.m function out = sinh1(x) %SINH1 Calculate hyperbolic sine function % Function SINH1 calculates the hyperbolic sine function % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value out = (exp(x) - exp(-x))/2;

solution_files/Ex6.20/sinh1.png

solution_files/Ex6.20/tanh1.fig Data/auxiliary file.

solution_files/Ex6.20/tanh1.m function out = tanh1(x) %TANH1 Calculate hyperbolic tangent function % Function TANH1 calculates the hyperbolic tangent function % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value

out = (exp(x) - exp(-x)) ./ (exp(x) + exp(-x));

solution_files/Ex6.20/tanh1.png

solution_files/Ex6.20/test_hyperbolic_functions.m % Script file: test_hyperbolic_functions.m % % Purpose: % To plot the hyperbolic functions sinh, cosh, abd tanh. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % % Define variables: % out_cosh -- Hyperbolic cosine % out_sinh -- Hyperbolic sine % out_tanh -- Hyperbolic tangent % Calculate results

x = -5:0.05:5; out_cosh = cosh1(x); out_sinh = sinh1(x); out_tanh = tanh1(x); % Display results figure(1); plot(x,out_cosh); title('\bfHyperbolic cosine'); xlabel('\bfx'); ylabel('\bfcosh(x)'); grid on; figure(2); plot(x,out_sinh); title('\bfHyperbolic sine'); xlabel('\bfx'); ylabel('\bfsinh(x)'); grid on; figure(3); plot(x,out_cosh); title('\bfHyperbolic tangent');

solution_files/Ex6.21/gen_data.m x = 0:0.05:4; y = x.^2 - 4*x + 4; for ii = 1:length(y) y(ii) = y(ii) + 0.1 * randn; end figure(1) plot(x,y);

solution_files/Ex6.21/input3.dat Data/auxiliary file.

solution_files/Ex6.21/running_ave.m

function y = running_ave(x,n_ave) %RUNNING_AVE Function to perform a running average filter % Function RUNNING_AVE performs a running average filter % % Calling sequence: % y = running_ave(x, n_ave) % % where: % n_ave -- Number of points to average % x -- Array of input values % y -- Array of filtered values % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % Define local variables: % ii -- Loop index % n_per_side -- Number of points to average per side % n_points -- Number of points in data set % slope -- Slope of the line % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % Set a default number of points to average if this value % is undefined. if nargin < 2 n_ave = 7; end % Get the number of samples on either side of the sample % being averaged, dropping any fractional part. n_per_side = (n_ave-1) / 2; n_per_side = floor(n_per_side); % Get the number of points in the input structure

solution_files/Ex6.21/running_average_filter.fig

Data/auxiliary file.

solution_files/Ex6.21/running_average_filter.png

solution_files/Ex6.21/test_running_ave.m % Script file: test_running_ave.m % % Purpose: % To perform test the running average filter function. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % filename -- Input data file % n_ave -- Number of points to average % n_per_side -- Number of points to average per side

% n_points -- Number of points in data set % x -- Array of input values % y -- Array of filtered values disp('This program performs a running average filter on an '); disp('input data set.'); filename = input('Enter the filename containing the data: ','s'); n_ave = input('Enter the number of samples to average: '); % Get the number of samples on either side of the sample % being averaged, dropping any fractional part. n_per_side = (n_ave-1) / 2; n_per_side = floor(n_per_side); % Read the input data x = textread(filename,'%f'); n_points = length(x); % Get running average y = running_ave(x,n_ave); % Plot the data points as blue circles with no % connecting lines. plot(x,'bo'); hold on;

solution_files/Ex6.22/input3.dat Data/auxiliary file.

solution_files/Ex6.22/median_filter.fig Data/auxiliary file.

solution_files/Ex6.22/median_filter.m function y = median_filter(x,n_ave) %RUNNING_AVE Function to perform a median filter % Function RUNNING_AVE performs a median filter % % Calling sequence: % y = median_filter(x, n_ave)

% % where: % n_ave -- Number of points to average % x -- Array of input values % y -- Array of filtered values % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % Define local variables: % ii -- Loop index % n_per_side -- Number of points to average per side % n_points -- Number of points in data set % slope -- Slope of the line % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % Set a default number of points to average if this value % is undefined. if nargin < 2 n_ave = 7; end % Get the number of samples on either side of the sample % being averaged, dropping any fractional part. n_per_side = (n_ave-1) / 2; n_per_side = floor(n_per_side); % Get the number of points in the input structure

solution_files/Ex6.22/median_filter.png

solution_files/Ex6.22/test_median_filter.m % Script file: test_median_filter.m % % Purpose: % To test the median filter function. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % filename -- Input data file % n_ave -- Number of points to average % n_per_side -- Number of points to average per side % n_points -- Number of points in data set % slope -- Slope of the line % x -- Array of input values % y -- Array of filtered values

disp('This program performs a median filter on an input data set.'); filename = input('Enter the filename containing the data: ','s'); n_ave = input('Enter the number of samples to average: '); % Get the number of samples on either side of the sample % being averaged, dropping any fractional part. n_per_side = (n_ave-1) / 2; n_per_side = floor(n_per_side); % Read the input data x = textread(filename,'%f'); n_points = length(x); % Now perform the median filter y = median_filter(x,n_ave); % Plot the data points as blue circles with no % connecting lines. plot(x,'bo'); hold on;

solution_files/Ex6.23/sort_with_carry.m function [out1, out2] = sort_with_carry(a,b) %SORT_WITH_CARRY Selection sort with carry in ascending order % Function SORT_WITH_CARRY sorts a numeric data set a into % ascending order, carrying along array b. Note that the % selection sort is relatively inefficient. DO NOT USE THIS % FUNCTION FOR LARGE DATA SETS. % Define variables: % a -- Input array to sort % b -- Input array to carry along % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable % nvals -- Number of values in "a" and "b" % out -- Sorted output array % out2 -- Carried output array % temp -- Temp variable for swapping % Record of revisions:

% Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Check for a legal length. Both a and b must be % the same length. if length(a) ~= length(b) error('Vectors a and b must be the same length'); end % Get the length of the array to sort nvals = length(a); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii) through a(n)

solution_files/Ex6.23/test_sort_with_carry.m % Script file: test_sort_with_carry.m % % Purpose: % To read in an input data set a and sort it into % ascending order while carrying along array b. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % % Define variables: % a -- Input data array to sort % b -- Input data array to carry % ii -- Index variable % nvals -- Number of input values % out1 -- Sorted data array

% out2 -- Carried data array % Input arrays a = [ 1, 11, -6, 17, -23, 0, 5, 1, -1]; b = [ 31,101, 36,-17, 0, 10, -8, -1, -1]; % Now sort the data [out1, out2] = sort_with_carry(a,b); % Display the sorted result. fprintf('\nSorted data:\n'); for ii = 1:length(a) fprintf(' %8.4f %8.4f\n',out1(ii),out2(ii)); end

solution_files/Ex6.24/test_sortrows.m % Script file: test_sortrows.m % % Purpose: % To read in an input data set a and sort it into % ascending order while carrying along array b. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % % Define variables: % a -- Input data array to sort % b -- Input data array to carry % c -- Compislte matrix % ii -- Index variable % nvals -- Number of input values % out1 -- Sorted data array % out2 -- Carried data array % Input arrays a = [ 1, 11, -6, 17, -23, 0, 5, 1, -1]; b = [ 31,101, 36,-17, 0, 10, -8, -1, -1]; c = [a' b'];

% Now sort the data c = sortrows(c); % Display the sorted result. fprintf('\nSorted data:\n'); for ii = 1:length(a) fprintf(' %8.4f %8.4f\n',c(ii,1),c(ii,2)); end

solution_files/Ex6.25/compare_sort_with_carry.m % Script file: compare_sort_with_carry.m % % Purpose: % To compare function sort_with_carry with function % sortrows. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % % Define variables: % a -- Input data array to sort % array -- Input data for sortrows % b -- Input data array to carry % ii -- Index variable % nvals -- Number of input values % out -- Output data for sortrows % out1 -- Sorted data array % out2 -- Carried data array % Create random arrays array = rand(25000,2); % Make copy for sort_with_carry a = array(:,1); b = array(:,2); % Sort using sort_with_carry tic;

[out1, out2] = sort_with_carry(a,b); disp(['sort_with_carry time = ',num2str(toc)]); % Sort using sortrows tic; out = sortrows(array,1); disp(['sortrows time = ',num2str(toc)]);

solution_files/Ex6.25/sort_with_carry.m function [out1, out2] = sort_with_carry(a,b) %SORT_WITH_CARRY Selection sort with carry in ascending order % Function SORT_WITH_CARRY sorts a numeric data set a into % ascending order, carrying along array b. Note that the % selection sort is relatively inefficient. DO NOT USE THIS % FUNCTION FOR LARGE DATA SETS. % Define variables: % a -- Input array to sort % b -- Input array to carry along % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable % nvals -- Number of values in "a" and "b" % out -- Sorted output array % out2 -- Carried output array % temp -- Temp variable for swapping % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/08/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Check for a legal length. Both a and b must be % the same length. if length(a) ~= length(b) error('Vectors a and b must be the same length');

end % Get the length of the array to sort nvals = length(a); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii) through a(n)

solution_files/Ex6.26/range_bearing.m function [r2, phi2] = range_bearing(x1,y1,theta1,r1,phi1, ... x2,y2,theta2) %RANGE_BEARING Calculate the range and bearing of a target from a ship % Function RANGE_BEARING calculates the range and bearing of a % target from a ship, given the location, range, and bearing of % the target from another ship. % Define variables: % phi1 -- Bearing of target from Ship 1 (degrees) % phi2 -- Bearing of target from Ship 2 (degrees) % r1 -- Range of target from Ship 1 % r2 -- Range of target from Ship 2 % theta1 -- Heading of Ship 1 (degrees) % theta2 -- Heading of Ship 2 (degrees) % x -- x-pos of target in global coordinate system % x1 -- x-pos of Ship 1 % x2 -- x-pos of Ship 2 % y -- y-pos of target in global coordinate system % y1 -- y-pos of Ship 1 % y2 -- y-pos of Ship 2 % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/09/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(8,8,nargin); error(msg); % Convert input angles to radians for use with trig functions

theta1 = theta1 * pi/180; theta2 = theta2 * pi/180; phi1 = phi1 * pi/180; % Calculate the (x,y) position of the target in the % coordinate system. x = x1 + r1 * cos( theta1 + phi1 ); y = y1 + r1 * sin( theta1 + phi1 );

solution_files/Ex6.26/test_range_bearing.m % Script file: test_range_bearing.m % % Purpose: % To test function range_bearing.m % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/09/15 S. J. Chapman Original code % % Define variables: % phi1 -- Bearing of target from Ship 1 (degrees) % phi2 -- Bearing of target from Ship 2 (degrees) % r1 -- Range of target from Ship 1 % r2 -- Range of target from Ship 2 % theta1 -- Heading of Ship 1 (degrees) % theta2 -- Heading of Ship 2 (degrees) % x1 -- x-pos of Ship 1 % x2 -- x-pos of Ship 2 % y1 -- y-pos of Ship 1 % y2 -- y-pos of Ship 2 % Get location of Ship 1 (x,y,theta): x1 = input('x-pos of Ship 1: '); y1 = input('y-pos of Ship 1: '); theta1 = input('Heading of Ship 1 (deg): '); % Get location of Ship 2 (x,y,theta): x2 = input('x-pos of Ship 2: ');

y2 = input('y-pos of Ship 2: '); theta2 = input('Heading of Ship 2 (deg): '); % Get location of target as seen by Ship 1 r1 = input('Range to target from Ship 1: '); phi1 = input('Bearing to target from Ship 1: '); % Calculate range and bearing from Ship 2 [r2, phi2] = range_bearing( x1, y1, theta1, r1, phi1, ... x2, y2, theta2 );

solution_files/Ex6.27/lsqfit.fig Data/auxiliary file.

solution_files/Ex6.27/lsqfit.m function [slope, yint] = lsqfit(x, y) %LSQFIT Calculate the linear least squares fit to a data set. % Function LSQFIT calculates the linear least squares fit line % to an input data set. Note that vectors x and y must be % the same length, and must contain at least two elements. % % The calling sequence is: % [slope,yint] = lsqfit(x,y); % % where % slope = the slope of the fitted line % yint = y-intercept of the fitted line % x = Input x values % y = Input y values % Define variables: % sum_x -- Sum of values in x % sum_x2 -- Sum of values in x.^2 % sum_xy -- Sum of values in x.*y % sum_y -- Sum of values in y % xbar -- Average of x % ybar -- Average of y % Record of revisions:

% Date Programmer Description of change % ==== ========== ===================== % 04/09/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Check to make sure that the two vectors are the same length if length(x) ~= length(y) error('Vectors x and y must be the same length!'); end % Check to ensure that there are at least two elements if length(x) < 2 error('Vectors x and y must be at least 2 elements long!');

solution_files/Ex6.27/lsqfit.png

solution_files/Ex6.27/test_lsqfit.m % Script file: test_lsqfit.m %

% Purpose: % To test the function lsqfit. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/09/15 S. J. Chapman Original code % % Define variables: % slope -- Slope of fitted line % x -- Input x values % x1 -- x values of fitted line % y -- Input y values % y1 -- y values of fitted line % yint -- Y-intercept of fitted line % Input data values x = [-4.91 -3.84 -2.41 -2.62 -3.78 -0.52 -1.83 ...

-2.01 0.28 1.08 -0.94 0.59 0.69 3.04 ...

1.01 3.60 4.53 5.13 4.43 4.12 ]; y = [-8.18 -7.49 -7.11 -6.15 -5.62 -3.30 -2.05 ...

-2.83 -1.16 0.52 0.21 1.73 3.96 4.26 ...

5.75 6.67 7.70 7.31 9.05 10.95 ]; % Get fitted line [slope, yint] = lsqfit(x,y); x1(1) = min(x); x1(2) = max(x); y1 = slope*x1 + yint; % Tell user fprintf('\n%s\n','Using lsqfit.m:'); fprintf('%s%7.3f\n','Slope = ',slope); fprintf('%s%7.3f\n','Intercept = ',yint); % Plot points and the fitted line figure(1); plot(x,y,'bo','LineWidth',2);

solution_files/Ex6.28/lsqfit.fig

Data/auxiliary file.

solution_files/Ex6.28/lsqfit.m function [slope, yint] = lsqfit(x, y) %LSQFIT Calculate the linear least squares fit to a data set. % Function LSQFIT calculates the linear least squares fit line % to an input data set. Note that vectors x and y must be % the same length, and must contain at least two elements. % % The calling sequence is: % [slope,yint] = lsqfit(x,y); % % where % slope = the slope of the fitted line % yint = y-intercept of the fitted line % x = Input x values % y = Input y values % Define variables: % sum_x -- Sum of values in x % sum_x2 -- Sum of values in x.^2 % sum_xy -- Sum of values in x.*y % sum_y -- Sum of values in y % xbar -- Average of x % ybar -- Average of y % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/09/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Check to make sure that the two vectors are the same length if length(x) ~= length(y) error('Vectors x and y must be the same length!'); end

% Check to ensure that there are at least two elements if length(x) < 2 error('Vectors x and y must be at least 2 elements long!');

solution_files/Ex6.28/lsqfit.png

solution_files/Ex6.28/residuals.fig Data/auxiliary file.

solution_files/Ex6.28/residuals.png

solution_files/Ex6.28/test_lsqfit.m % Script file: test_lsqfit.m % % Purpose: % To test the function lsqfit. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/09/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % slope -- Slope of fitted line % x -- Input x values % x1 -- x values of fitted line % y -- Input y values % y1 -- y values of fitted line % yint -- Y-intercept of fitted line

% Input data values x = [-4.91 -3.84 -2.41 -2.62 -3.78 -0.52 -1.83 ...

-2.01 0.28 1.08 -0.94 0.59 0.69 3.04 ...

1.01 3.60 4.53 5.13 4.43 4.12 ]; y = [-8.18 -7.49 -7.11 -6.15 -5.62 -3.30 -2.05 ...

-2.83 -1.16 0.52 0.21 1.73 3.96 4.26 ...

5.75 6.67 7.70 7.31 9.05 10.95 ]; % Get fitted line [slope, yint] = lsqfit(x,y); x1(1) = min(x); x1(2) = max(x); y1 = slope*x1 + yint; % Tell user fprintf('\n%s\n','Using lsqfit.m:'); fprintf('%s%7.3f\n','Slope = ',slope); fprintf('%s%7.3f\n','Intercept = ',yint); % Plot points and the fitted line figure(1);

solution_files/Ex6.29/random0.m function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(n) -- Generate an n x n array % random0(n,m) -- Generate an n x m array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array

% % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % 1. 04/05/15 S. J. Chapman Modified for 0 arguments % Declare global values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end

solution_files/Ex6.29/random1.m function ran = random1(n,m) %RANDOM1 Generate uniform random numbers in [1,1) % Function RANDOM1 generates an array of uniform % random numbers in the range [1,1). The usage % is: % % random1() -- Generate a single value % random1(n) -- Generate an n x n array % random1(n,m) -- Generate an n x m array % Define variables: % m -- Number of columns % n -- Number of rows % ran -- Output array % Record of revisions:

% Date Programmer Description of change % ==== ========== ===================== % 04/06/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end % Initialize the output array ran = 2 * random0(n,m) - 1;

solution_files/Ex6.29/seed.m function seed(new_seed) %SEED Set new seed for function RANDOM0 % Function SEED sets a new seed for function % RANDOM0. The new seed should be a positive % integer. % Define variables: % ISEED -- Random number seed (global) % new_seed -- New seed % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % % Declare globl values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(1,1,nargin);

error(msg); % Save seed new_seed = round(new_seed); ISEED = abs(new_seed);

solution_files/Ex6.30/gaussian.fig Data/auxiliary file.

solution_files/Ex6.30/gaussian.png

solution_files/Ex6.30/random_normal.m function res = random_normal(n,m) %RANDOM_NORMAL Return samples from a normal distribution. % Function RANDOM_NORMAL generates an array of gaussian % normal random numbers. The usage is: % % random_normal() -- Generate a single value % random_normal(n) -- Generate an n x n array % random_normal(n,m) -- Generate an n x m array

% % Define variables: % ii, jj -- Loop index % m -- Number of row % n -- Number of columns % r -- sqrt of v1^2 + v2^2 % res -- Results % v1, v2 -- Uniform random variables in [-1,1) % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end % Calculate data res = zeros(n,m); for ii = 1:n for jj = 1:m

solution_files/Ex6.30/test_random_normal.m % Script file: test_random_normal.m % % Purpose: % To test function random_normal by getting 1000 random % normal values, calculating the mean and standard % deviation, and plotting a histogram of the values.

% % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % % Define variables: % ave -- Average (mean) of distribution % dist -- Distribution % sd -- Standard deviation of distribution % Get 1000 values dist = random_normal(1,1000); % Calculate mean and standard deviation ave = mean(dist); sd = std(dist); % Tell user fprintf('Average = %.4f\n',ave); fprintf('Std Dev = %.4f\n',sd); % Create histogram hist(dist,9); title('\bfHistogram of random values'); xlabel('\bfValue'); ylabel('\bfCount');

solution_files/Ex6.31/gravity.m function force = gravity(range,m1,m2) %GRAVITY Return force of gravity between two masses. % Function GRAVITY calculates the gravitation force % between two objects separated by a specified range. % The usage is: % % force = gravity(range,m1,m2); % where % range -- range in meters % m1 -- Mass of object 1 in kilograms % m2 -- Mass of object 2 in kilograms

% force -- Force in newtons % Define local variables: % gravc -- Gravitational constant % m -- Number of row % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Gravitational constant gravc = 6.672E-11; % Calculate force force = gravc .* m1 .* m2 ./ range.^2;

solution_files/Ex6.31/test_gravity.m % Script file: test_gravity.m % % Purpose: % To test the gravitational force calculation. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % % Define variables: % m1 -- Mass of body 1, in kg % m2 -- Mass of body 2, in kg % range -- Distance between objects, in m % Get input values m1 = input('Enter mass of object 1 (kg): '); m2 = input('Enter mass of object 2 (kg): '); range = input('Enter range between objects (m): ');

% Calculate force fprintf('The force due to gravity is %0.4f N.\n', ... gravity(range,m1,m2));

solution_files/Ex6.32/random_rayleigh.m function res = random_rayleigh(n,m) %RANDOM_RAYLEIGH Return samples from a Rayleigh distribution. % Function RANDOM_RAYLEIGH generates an array of Rayleigh% distributed random numbers. The usage is: % % random_rayleigh() -- Generate a single value % random_rayleigh(n) -- Generate an n x n array % random_rayleigh(n,m) -- Generate an n x m array % % Define variables: % arr1 -- Normally-distributed array % arr2 -- Normally-distributed array % res -- Results % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/07/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end % Calculate data arr1 = randn(n,m);

arr2 = randn(n,m); res = sqrt( arr1.^2 + arr2.^2 );

solution_files/Ex6.32/rayleigh.fig Data/auxiliary file.

solution_files/Ex6.32/rayleigh.png

solution_files/Ex6.32/test_random_rayleigh.m % Script file: test_random_rayleigh.m % % Purpose: % To test function random_rayleigh by getting 20,000 % values, calculating the mean and standard % deviation, and plotting a histogram of the values. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/07/15 S. J. Chapman Original code

% % Define variables: % ave -- Average (mean) of distribution % dist -- Distribution % sd -- Standard deviation of distribution % Get 20,000 values dist = random_rayleigh(1,20000); % Calculate mean and standard deviation ave = mean(dist); sd = std(dist); % Tell user fprintf('Average = %.4f\n',ave); fprintf('Std Dev = %.4f\n',sd); % Create histogram hist(dist,21); title('\bfHistogram of random values'); xlabel('\bfValue'); ylabel('\bfCount');

solution_files/Ex6.4/ssort1.m function out = ssort1(a,dir) %SSORT1 Selection sort data in ascending or descending order % Function SSORT1 sorts a numeric data set into ascending % or descending order, depending on the value of the % second parameter. If the parameter is 'up', then it % sorts the data in ascending order. If the parameter is % 'down', then it sorts the data in descending order. The % default value is 'up'. Note that 'up' and 'down' may % be abbreviated to 'u' and 'd', if desired. % % Note that the selection sort is relatively inefficient. % DO NOT USE THIS FUNCTION FOR LARGE DATA SETS. Use MATLAB's % "sort" function instead. % Define variables: % a -- Input array to sort

% ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable % nvals -- Number of values in "a" % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If the direction argument is missing, set it to 'up'. if nargin < 2 dir = 'up'; end % Check for the direction of the sort if dir(1) == 'u' | dir(1) == 'U' sort_up = 1;

solution_files/Ex6.4/test_ssort1.m % Script file: test_ssort1.m % % Purpose: % To read in an input data set, sort it into ascending % order using the selection sort algorithm, and to % write the sorted data to the Command window. This % program calls function "ssort1" to do the actual % sorting. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code %

% Define variables: % array -- Input data array % ii -- Index variable % nvals -- Number of input values % sorted1 -- Sorted data array (up) % sorted2 -- Sorted data array (down) % Prompt for the number of values in the data set nvals = input('Enter number of values to sort: '); % Preallocate array array = zeros(1,nvals); % Get input values for ii = 1:nvals % Prompt for next value string = ['Enter value ' int2str(ii) ': ']; array(ii) = input(string); end % Now sort the data in ascending order sorted1 = ssort1(array,'up'); % Display the sorted result.

solution_files/Ex6.5/acosd.m function out = acosd(x) %ACOSD Calculate acos(x), where the output is in degrees % Function ACOSD calculates acos(x), where the output is in degrees % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg);

% Calculate value out = 180/pi * acos(x);

solution_files/Ex6.5/asind.m function out = asind(x) %ASIND Calculate asin(x), where the output is in degrees % Function ASIND calculates asin(x), where the output is in degrees % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value out = 180/pi * asin(x);

solution_files/Ex6.5/atan2d.m function out = atan2d(y,x) %ATAN2D Four quadrant inverse tangent, where the output is in degrees % Function ATAN2D calculates the Four quadrant inverse tangent, where % the output is in degrees. % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg);

% Calculate value out = 180/pi * atan2(y,x);

solution_files/Ex6.5/atand.m function out = atand(x) %ATAND Calculate atan(x), where the output is in degrees % Function ATAND calculates atan(x), where the output is in degrees % % Define variables: % x -- Input value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value out = 180/pi * atan(x);

solution_files/Ex6.5/cosd.m function out = sind(x) %COSD Calculate cos(x), where x is in degrees % Function COSD calculates cos(x), where x is in degrees % % Define variables: % x -- Angle in degrees % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg);

% Calculate value out = cos(pi/180*x);

solution_files/Ex6.5/sind.m function out = sind(x) %SIND Calculate sin(x), where x is in degrees % Function SIND calculates sin(x), where x is in degrees % % Define variables: % x -- Angle in degrees % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value out = sin(pi/180*x);

solution_files/Ex6.5/tand.m function out = tand(x) %TAND Calculate tan(x), where x is in degrees % Function TAND calculates tan(x), where x is in degrees % % Define variables: % x -- Angle in degrees % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg);

% Calculate value out = tan(pi/180*x);

solution_files/Ex6.5/test_functions.m % Script file: test_functions.m % % Purpose: % To perform a median filter on an input data set. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/03/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % filename -- Input data file % n_ave -- Number of points to average % n_per_side -- Number of points to average per side % n_points -- Number of points in data set % slope -- Slope of the line % x -- Array of input values % y -- Array of filtered values disp('This program tests the trig functions that return answers in degrees.'); % Set the angle theta = 30 degrees, and try the forward trig functions disp(' '); disp(['Testing forward trig functions:']); disp(['sind(30) = ' num2str(sind(30))]); disp(['cosd(30) = ' num2str(cosd(30))]); disp(['tand(30) = ' num2str(tand(30))]); disp(['sind(45) = ' num2str(sind(45))]); disp(['cosd(45) = ' num2str(cosd(45))]); disp(['tand(45) = ' num2str(tand(45))]); % Test the inverse trig functions disp(' '); disp(['Testing inverse trig functions:']);

disp(['asind(0) = ' num2str(asind(0))]); disp(['asind(1/sqrt(2)) = ' num2str(asind(1/sqrt(2)))]); disp(['asind(1) = ' num2str(asind(1))]); disp(['acosd(0) = ' num2str(acosd(0))]); disp(['acosd(1/sqrt(2)) = ' num2str(acosd(1/sqrt(2)))]);

solution_files/Ex6.6/f_to_c.m function deg_c = f_to_c(deg_f) %F_TO_C Convert degrees Fahrenheit to degrees Celsius % Function F_TO_C converts degrees Fahrenheit to degrees Celsius %% % Calling sequence: % deg_c = f_to_c(deg_f) % Define variables: % deg_f -- Input in degrees Fahrenheit % deg_c -- Output in degrees Celsius % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value deg_c = 5/9 * (deg_f - 32);

solution_files/Ex6.7/c_to_f.m function deg_f = c_to_f(deg_c) %C_TO_F Convert degrees Celsius to degrees Fahrenheit % Function C_TO_F converts degrees Celsius to degrees Fahrenheit %% % Calling sequence: % deg_f = c_to_f(deg_c) % Define variables: % deg_c -- Input in degrees Celsius

% deg_f -- Output in degrees Fahrenheit % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value deg_f = 9/5 * deg_c + 32;

solution_files/Ex6.7/f_to_c.m function deg_c = f_to_c(deg_f) %F_TO_C Convert degrees Fahrenheit to degrees Celsius % Function F_TO_C converts degrees Fahrenheit to degrees Celsius %% % Calling sequence: % deg_c = f_to_c(deg_f) % Define variables: % deg_f -- Input in degrees Fahrenheit % deg_c -- Output in degrees Celsius % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate value deg_c = 5/9 * (deg_f - 32);

solution_files/Ex6.8/area2d.m function area = area2d(x1, y1, x2, y2, x3, y3) %AREA2D Calculate the area of a triangle specified by three vertices

% Function AREA2D calculates the area of a triangle specified by % three vertices % % Calling sequence: % area = area2d(x1, y1, x2, y2, x3, y3) % Define variables: % x1, y1 -- Location of vertex 1 % x2, y2 -- Location of vertex 2 % x3, y3 -- Location of vertex 3 % area -- Area of triangle % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(6,6,nargin); error(msg); % Calculate value area = 0.5 * (x1*(y2-y3) - x2*(y1-y3) + x3*(y1-y2));

solution_files/Ex6.9/area2d.m function area = area2d(x1, y1, x2, y2, x3, y3) %AREA2D Calculate the area of a triangle specified by three vertices % Function AREA2D calculates the area of a triangle specified by % three vertices % % Calling sequence: % area = area2d(x1, y1, x2, y2, x3, y3) % Define variables: % x1, y1 -- Location of vertex 1 % x2, y2 -- Location of vertex 2 % x3, y3 -- Location of vertex 3 % area -- Area of triangle % Record of revisions: % Date Programmer Description of change

% ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(6,6,nargin); error(msg); % Calculate value area = 0.5 * (x1*(y2-y3) - x2*(y1-y3) + x3*(y1-y2));

solution_files/Ex6.9/area_polygon.m function area = area_polygon(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6) %AREA_POLYGON Calculate the area of a polygon specified by its vertices % Function AREA_POLYGON calculates the area of a polygon specified by % its vertices % % Calling sequence: % area = area_polygon(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6) % Define variables: % ii -- Loop index % n_vertices -- Number of vetices in polygon % x1, y1 -- Location of vertex 1 % x2, y2 -- Location of vertex 2 % x3, y3 -- Location of vertex 3 % x4, y4 -- Location of vertex 4 % x5, y5 -- Location of vertex 5 % x6, y6 -- Location of vertex 6 % area -- Area of polygon % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/05/15 S. J. Chapman Original code % Check for a legal number of input arguments. % There must be at least 3 vertices, and no more than 6. msg = nargchk(6,12,nargin); error(msg); % Get the number of vertices

n_vertices = nargin / 2; % Save vertices in arrays x = zeros(1,n_vertices); y = zeros(1,n_vertices); % Save values x(1) = x1; y(1) = y1; x(2) = x2;

solution_files/Ex7.1/random1.m function ran = random1(n,m) %RANDOM1 Generate uniform random numbers in [1,1) % Function RANDOM1 generates an array of uniform % random numbers in the range [1,1). The usage % is: % % random1() -- Generate a single value % random1(n) -- Generate an n x n array % random1(n,m) -- Generate an n x m array % Define variables: % m -- Number of columns % n -- Number of rows % ran -- Output array % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1;

elseif nargin < 2 m = n; end % Initialize the output array ran = 2 * random0(n,m) - 1; function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage

solution_files/Ex7.10/extremes.m function [xmin,min_value,xmax,max_value] = ... extremes(first_value,last_value,num_steps,func) %EXTREMES Locate the extreme values of a function on an interval % Function EXTREMES searches a user-supplied function over % a user-suppled interval, and returns the minimum and maximum % values found, as well as their locations. % % The calling sequence is: % [xmin,min_value,xmax,max_value] = ... % extremes(first_value,last_value,num_steps,func); % % where % first_value = the start of the interval to search % last_value = the end of the interval to search % num_steps = the number of steps to use in search % func = the function to evaluate % % The output values are: % xmin = location of smallest value found % min_value = smallest value found % xman = location of largest value found % max_value = largest value found % Define variables: % dx -- Step size % x -- Input values to evaluate fun at

% y -- Function output % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(4,4,nargin); error(msg); % Create array of values to evaluate the function at dx = (last_value - first_value) / (num_steps - 1); x = first_value:dx:last_value;

solution_files/Ex7.11/extremes.m function [xmin,min_value,xmax,max_value] = ... extremes(first_value,last_value,num_steps,func) %EXTREMES Locate the extreme values of a function on an interval % Function EXTREMES searches a user-supplied function over % a user-suppled interval, and returns the minimum and maximum % values found, as well as their locations. % % The calling sequence is: % [xmin,min_value,xmax,max_value] = ... % extremes(first_value,last_value,num_steps,func); % % where % first_value = the start of the interval to search % last_value = the end of the interval to search % num_steps = the number of steps to use in search % func = the function to evaluate % % The output values are: % xmin = location of smallest value found % min_value = smallest value found % xman = location of largest value found % max_value = largest value found % Define variables:

% dx -- Step size % x -- Input values to evaluate fun at % y -- Function output % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(4,4,nargin); error(msg); % Create array of values to evaluate the function at dx = (last_value - first_value) / (num_steps - 1); x = first_value:dx:last_value;

solution_files/Ex7.11/fun.m function y = fun(x) %FUN Function to test extremes % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code y = x.^3 - 5*x.^2 + 5*x +2;

solution_files/Ex7.11/test_extremes.m % Script file: test_extremes.m % % Purpose: % To test function extremes. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % % Define variables:

% max_value -- Maximum value % min_value -- Minimum value % xmax -- Location of maximum value % xmin -- Location of minimum value % Call extremes [xmin,min_value,xmax,max_value] = extremes(-1,3,201,'fun'); % Display results fprintf('The maximum value is %.4f at %.2f\n',max_value,xmax); fprintf('The minimum value is %.4f at %.2f\n',min_value,xmin);

solution_files/Ex7.12/find_zeros.m % Script file: find_zeros.m % % Purpose: % To find the zeros of the function f(x) = (cos (x))^2 - 0.25 % between 0 and 2*PI. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % % Define variables: % x -- Input values to examine % y -- Value of the function at x % zero_index -- Index into the zero array % zero_loc -- Location of zeros % Create function hndl = @ (x) cos(x).^2 - 0.25; % Evaluate the function at 50 points between 0 and 2*PI. x = linspace(0,2*pi,50); y = hndl(x); % Check for a sign change zero_loc = []; zero_index = 0;

for ii = 1:length(x)-1 if y(ii)*y(ii+1) <= 0 % Find zeros zero_index = zero_index + 1; zero_loc(zero_index) = fzero(hndl,[x(ii) x(ii+1)]); % Display results disp(['There is a zero at at ' num2str(zero_loc(zero_index))]); end end

solution_files/Ex7.12/plot.fig Data/auxiliary file.

solution_files/Ex7.12/plot.png

solution_files/Ex7.13/eval_and_plot_fn.m % Script file: eval_and_plot_fn.m %

% Purpose: % To find the zeros of the function f(x) = (cos (x))^2 - 0.25 % between 0 and 2*PI. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % % Define variables: % hndl -- Function handle % x -- Input values to examine % y -- Value of the function at x % Create function handle hndl = @ fun; % Evaluate the function at 50 points between 0 and 2*PI. x = linspace(0,2*pi,200); y = feval(hndl,x); % Now plot the function figure(1); plot(x,y,'b-','LineWidth',2); title('\bfPlot of function'); xlabel('\bfx'); ylabel('\bfy'); grid on;

solution_files/Ex7.13/fun.m function y = fun(x) %FUN Function to evaluate and plot % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code y = tan(x).^2 + x - 2;

solution_files/Ex7.13/plot1.fig Data/auxiliary file.

solution_files/Ex7.13/plot1.png

solution_files/Ex7.13/plot2.fig Data/auxiliary file.

solution_files/Ex7.13/plot2.png

solution_files/Ex7.14/find_radar_targets.m % Script file: find_radar_targets.m % % Purpose: % This program detects potential targets in the range / % velocity space. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % % Define variables: % amp_levels -- Amplitude level of each bin % noise_power -- Power level of peak noise % nvals -- Number of samples in each bin % Load the data load rd_space.mat % Calculate histogram

[nvals, amp_levels] = hist(amp(:), 31); % Get location of peak [max_val, max_loc] = max(nvals); % Get the power level of that bin noise_power = amp_levels(max_loc); % Now look for targets. A potential target is a point that % is higher than all of the points around it. fprintf(' Range Vel Amp SNR\n'); for ii = 2:length(velocity)-1 for jj = 2:length(range)-1 % Is this point bigger than the surrounding ones? if (amp(ii,jj) > amp(ii+1,jj)) && ... (amp(ii,jj) > amp(ii-1,jj)) && ... (amp(ii,jj) > amp(ii,jj+1)) && ... (amp(ii,jj) > amp(ii,jj-1))

solution_files/Ex7.14/rd_space.mat Data/auxiliary file.

solution_files/Ex7.15/derivative.fig Data/auxiliary file.

solution_files/Ex7.15/derivative.m function der = derivative(vector,dx,nsamp) %DERIVATIVE Take the derivative of a function stored as a vector % Function DERIVATIVE takes the derivative of a functions stored % as an input vector if nsamp samples with a spacing of dx between % samples. % % The calling sequence is: % der = derivative(vector,dx,nsamp); % % where % vector = the input function

% dx = step size between elements of the input vector % nsamp = the number of elements in the vector % Define variables: % dx -- Step size % x -- Input values to evaluate fun at % y -- Function output % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Check for a positive step size if dx <= 0 error('dx must be positive!'); end % Create array of values to evaluate the function at der = diff(vector(1:nsamp)/dx);

solution_files/Ex7.15/derivative.png

solution_files/Ex7.15/test_derivative.m % Script file: test_derivative.m % % Purpose: % To test the function derivative. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % % Define variables: % cosx -- cos(x) % der -- derivative of sin(x) % dx -- Step size % sinx -- sin(x) % x -- Input values % Calculate sin(x) dx = 0.05;

x = 0:dx:99*dx; sinx = sin(x); % Calculate cos(x) cosx = cos(x); % Calculate derivative of sin(x) der = derivative(sinx,dx,length(sinx)); % Plot sin(x), cos(x), and the derivative figure(1); plot(x,sinx,'b--','LineWidth',2); hold on; plot(x,cosx,'k-','LineWidth',2); % Since the derivative is 1 shorter than the % other vectors, it must be plotted versus % a shorter x vector. x1 = x(1:length(x)-1); plot(x1,der,'r:','LineWidth',2); legend ('sin(x)','cos(x)','derivative');

solution_files/Ex7.16/derivative.m function der = derivative(vector,dx,nsamp) %DERIVATIVE Take the derivative of a function stored as a vector % Function DERIVATIVE takes the derivative of a functions stored % as an input vector if nsamp samples with a spacing of dx between % samples. % % The calling sequence is: % der = derivative(vector,dx,nsamp); % % where % vector = the input function % dx = step size between elements of the input vector % nsamp = the number of elements in the vector % Define variables: % dx -- Step size % x -- Input values to evaluate fun at

% y -- Function output % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Check for a positive step size if dx <= 0 error('dx must be positive!'); end % Create array of values to evaluate the function at der = diff(vector(1:nsamp)/dx);

solution_files/Ex7.16/derivative_with_noise.fig Data/auxiliary file.

solution_files/Ex7.16/derivative_with_noise.png

solution_files/Ex7.16/random0.m function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(n) -- Generate an n x n array % random0(n,m) -- Generate an n x m array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % 1. 04/05/15 S. J. Chapman Modified for 0 arguments % Declare global values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2

m = n; end

solution_files/Ex7.16/test_derivative2.m % Script file: test_derivative2.m % % Purpose: % To test the function derivative in the presence of noise. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/12/15 S. J. Chapman Original code % % Define variables: % der -- derivative of sin(x) % dern -- derivative of sin(x) plus noise % dx -- Step size % sinx -- sin(x) % sinxn -- sin(x) plus noise % x -- Input values % Calculate sin(x) dx = 0.05; x = 0:dx:99*dx; sinx = sin(x); % Calculate sin(x) plus noise noise = 0.04 * random0(1,length(sinx)) - 0.02; sinxn = sinx + noise; % Calculate derivative of sin(x) der = derivative(sinx,dx,length(sinx)); % Calculate derivative of sin(x) plus noise dern = derivative(sinxn,dx,length(sinx)); % Plot sin(x) and the derivative figure(1); plot(x,sinx,'b-','LineWidth',2);

hold on; plot(x,sinxn,'k--','LineWidth',2); % Since the derivative is 1 shorter than the

solution_files/Ex7.17/find_roots.m % Script file: find_roots.m % % Purpose: % To find the roots of the function y(x) = 2 * exp(-0.5*x) - 0.2 % between 0 and 7. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/13/15 S. J. Chapman Original code % % Define variables: % root_index -- Index into the root array % root_loc -- Location of roots % x -- Input values to examine % y -- Value of the function at x % Create anonymous functions f = @ (x) 2 * exp(-0.5*x) - 0.2; % Evaluate the function at 50 points between 0 and 7. x = linspace(0,7,50); y = f(x); % Check for a sign change root_loc = []; root_index = 0; for ii = 1:length(x)-1 if y(ii)*y(ii+1) <= 0 % Find roots root_index = root_index + 1; root_loc(root_index) = fzero(f,[x(ii) x(ii+1)]); % Display results

disp(['There is a root at at ' num2str(root_loc(root_index))]); end end

solution_files/Ex7.17/plot_of_function.fig Data/auxiliary file.

solution_files/Ex7.17/plot_of_function.png

solution_files/Ex7.18/fact.m function result = fact(n) %FACT Calculate the factorial function % Function FACT calcualates the factorial function % by recursively calling itself. % Define variables: % n -- Non-negative integer input % result -- Result of calculation % % Record of revisions:

% Date Programmer Description of change % ==== ========== ===================== % 07/07/14 S. J. Chapman Original code % 1. 04/13/15 S. J. Chapman CHeck for invalid input % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Make sure n is a non-negative integer if (round(n) ~= n) || (n < 0) error('n must be a non-negative integer'); else % Calculate value. if n >= 1 result = n * factorial(n-1); else result = 1; end end

solution_files/Ex7.19/fibonacci.m function fn = fibonacci(n) %FIBONACCI evaluates the nth Fibonacci number % Function FIBONACCI evaluates the nth Fibonacci number % recursively, where n is >= 0. % Define variables: % fn -- Fibonacci number % n -- The item in the sequence to calculate % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/13/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg);

% Make sure n is a non-negative integer if (round(n) ~= n) || (n < 0) error('n must be a non-negative integer'); else % Calculate value. if n == 0 fn = 0; elseif n == 1 fn = 1; else fn = fibonacci(n-1) + fibonacci(n-2); end end

solution_files/Ex7.2/private/random0.m function ran = random0(n,m) %RANDOM0 Generate uniform random numbers in [0,1) % Function RANDOM0 generates an array of uniform % random numbers in the range [0,1). The usage % is: % % random0(n) -- Generate an n x n array % random0(n,m) -- Generate an n x m array % Define variables: % ii -- Index variable % ISEED -- Random number seed (global) % jj -- Index variable % m -- Number of columns % msg -- Error message % n -- Number of rows % ran -- Output array % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/04/14 S. J. Chapman Original code % 1. 04/05/15 S. J. Chapman Modified for 0 arguments

% Declare global values global ISEED % Seed for random number generator % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end

solution_files/Ex7.2/randomn.m function ran = randomn(n,m,low,high) %RANDOMN Generate uniform random numbers in [low,high) % Function RANDOM1 generates an array of uniform % random numbers in the range [low,high), where low % and high are optional parameters supplied by the user. % If not supplied, low and high default to 0 and 1, % respectively. The usage is: % % random1(n) -- Generate an n x n array % random1(n,m) -- Generate an n x m array % Define variables: % high -- Upper end of range % low -- Lower end of range % m -- Number of columns % n -- Number of rows % ran -- Output array % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 07/15/11 S. J. Chapman Original code

% Check for a legal number of input arguments. msg = nargchk(1,4,nargin); error(msg); % If arguments are missing, supply the default values. if nargin < 2 m = n; low = 0; high = 1; elseif nargin < 3 low = 0; high = 1; elseif nargin < 4 high = 1; end % Check that low < high

solution_files/Ex7.20/Birthday.fig Data/auxiliary file.

solution_files/Ex7.20/Birthday.png

solution_files/Ex7.20/birthday.m function prob = birthday(n) %BIRTHDAY Calculate the prob of 2 or more of n people having the same birthday. % This function calculates the probability of two or more of % n people having the same birthday, where "n" is a calling % parameter. % % The calling sequence is: % prob = birthday(n); % % where % prob = Probability of 2 or more people having the same birthday % n = Number of people in group % Define variables: % birthdays -- Array of birthdays % ii -- Loop index % jj -- Loop index % n_matches -- Number of matches that have occurred % n_trials -- The number of trials to perform % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/13/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Check to make sure that there are at least 2 people if n < 2 error('There must be at least two people in the group!'); end % Set the number of trials to try n_trials = 100000; % Reset the number of matches

n_matches = 0;

solution_files/Ex7.20/test_birthday.m % Script file: test_birthday.m % % Purpose: % To calculate the probability of 2 or more of n people % having the same birthday, where "n" is a number between % 2 and 40. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/13/15 S. J. Chapman Original code % % Define variables: % ii -- Number of people in group % prob -- Probability of 2 or more with same birthday % Calculate and display probabilities fprintf(' n prob\n'); fprintf(' = ====\n'); for ii = 2:40 prob(ii) = birthday(ii); fprintf(' %2d %0.4f\n',ii,prob(ii)); end % Plot probabilities plot(2:40,prob(2:40),'b-','LineWidth',2); title('\bfProbability of 2 or more people with same birthday'); xlabel('\bfNumber of people in group'); ylabel('\bfProbability'); grid on;

solution_files/Ex7.21/calc_cfar.m % Script file: calc_cfar.m %

% Purpose: % To calculate the rate of false detections in a radar receiver % as a function of detection threshold setting. The detection % threshold is expressed as a ratio in dB. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/13/15 S. J. Chapman Original code % % Define variables: % count -- Number of threshold crossings for each threshold % ii -- Loop index % mean_noise -- Mean noise amplitude % n_samples -- Number of samples % sample -- Samples of random noise % thresh_db -- Threshold level expressed in dB % thresh_v -- Threshold level expressed in volts % Initialize threshold levels n_samples = 10000000; mean_noise = 10; thresh_db = [ 5., 6., 7., 8., 9., 10., 11., 12., 13. ]; thresh_v = mean_noise .* 10.0 .^(thresh_db/20.); % Calculate an array of 1,000,000 Rayleigh-distributed samples % Get Rayleigh-distributed samples with a mean amplitude of 10 volts. % Note from the previous problem that the function random_rayleigh has % a mean amplitude of 1.25, so to get the desired amplitude of % "mean_noise", we must multiply the output by mean_noise/1.25. sample = mean_noise / 1.25 * random_rayleigh(1,n_samples); % Count the number of threshold crossings for each threshold level. for ii = 1:length(thresh_v) count(ii) = sum( sample > thresh_v(ii) ); end % Tell user about result.

solution_files/Ex7.21/random_rayleigh.m

function res = random_rayleigh(n,m) %RANDOM_RAYLEIGH Return samples from a Rayleigh distribution. % Function RANDOM_RAYLEIGH generates an array of Rayleigh% distributed random numbers. The usage is: % % random_rayleigh() -- Generate a single value % random_rayleigh(n) -- Generate an n x n array % random_rayleigh(n,m) -- Generate an n x m array % % Define variables: % arr1 -- Normally-distributed array % arr2 -- Normally-distributed array % res -- Results % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/23/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end % Calculate data arr1 = randn(n,m); arr2 = randn(n,m); res = sqrt( arr1.^2 + arr2.^2 );

solution_files/Ex7.22/gen_func.m function hndl = gen_func(a, b, c)

%GEN_FUNC Generate a polynomial function. % Function GEN_FUNC generates a polynomial function % of the form f(x) = a*x^2 + b*x + c, and returns a % function handle to a function that evaluates the % polynomial at a specific value of x. % Define variables: % a -- Coefficient of x^2 % b -- Coefficient of x % c -- Constant coefficient % hndl -- Handle to function "eval_func" % msg -- Error message % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Return function handle hndl = @eval_func; % Nested function eval_func. This function evaluates % the polynomial f(x) = a*x^2 + b*x + c for the specified % values of a, b, c, and x. function y = eval_func(x) y = a*x.^2 + b*x + c; end % function eval_func end % function gen_func

solution_files/Ex7.22/plot_func.m function plot_func(hndl, x1, x2) %PLOT_FUNC Plot a function specified by a function handle. % Function PLOT_FUNC plots the function specifed in the % function handle between the limits [x1 x2]. % Define variables:

% hndl -- Handle to function "eval_func" % msg -- Error message % str -- Title string % x -- X values to plot % x1 -- Starting value to plot % x2 -- Ending value to plot % y -- Y values to plot % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(3,3,nargin); error(msg); % Get the x values to plot x = x1:0.1:x2; % Get the y values to plot y = hndl(x); % Plot the function plot(x,y,'LineWidth',2); str = ['\bfPlot of polynomial between ' num2str(x1) ' and ' num2str(x2)]; title(str); xlabel('\bfx'); ylabel('\bfy'); grid on; end % function plotfunc

solution_files/Ex7.22/poly1.fig Data/auxiliary file.

solution_files/Ex7.22/poly1.png

solution_files/Ex7.22/poly2.fig Data/auxiliary file.

solution_files/Ex7.22/poly2.png

solution_files/Ex7.22/test_gen_func.m % Script file: test_gen_func.m % % Purpose: % To test function gen_func. This program creates % handles to two polynomials, and then plots them % between specified limits using the function handle. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % % Define variables: % h1 -- Handle to function f(x) = x^2 + 2*x + 1 % h2 -- Handle to function f(x) = x^2 + 4*x + 3 clear all % Create polynomial function f(x) = x^2 + 2*x + 1 h1 = gen_func(1,2,1);

% Create polynomial function f(x) = x^2 + 4*x + 3 h2 = gen_func(1,4,3); % Plot the first function between -3 and 3 figure(1); plot_func(h1,-3,3); % Plot the first function between -3 and 3 figure(2); plot_func(h2,-3,3);

solution_files/Ex7.23/derivative_fn.m function yprime = derivative_fn(t,y) %DERIVATIVE_FN Calculates the derivative of the output voltage. % Define variables: % t -- Time (in days) % y -- Vector of states (voltage) % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % Set decay constant. r = 1.0e6; % ohms c = 1.0e-6; % farads lambda = 1 / (r * c); % Calculate derivative yprime = lambda * vin(t) - lambda * y;

solution_files/Ex7.23/rc_circuit.m % Script file: rc_circuit.m % % Purpose: % To calculate the ouput voltage from a simple RC % circuit being driven by a square wave input voltage. %

% Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % % Define variables: % odefun_handle -- Handle to function that defines the derivative % tspan -- Duration to solve equation for % yo -- Initial condition for equation % t -- Array of solution times % y -- Array of solution values % Get a handle to the function that defines the % derivative. odefun_handle = @derivative_fn; % Solve the equation over the period 0 to 10 seconds tspan = [0 10]; % Set the initial conditions y0 = 0; % Call the differential equation solver. [t,y] = ode45(odefun_handle,tspan,y0); % Plot the result figure(1); plot(t,y,'b-','LineWidth',2); grid on; title('\bfOutput Voltage'); xlabel('\bfTime (s)'); ylabel('\bf\itv_{out}');

solution_files/Ex7.23/vin.m function result = vin(t) %VIN Calculates the input voltage vs time. % Define variables: % t -- Time % result -- Input voltage

% % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % Calculate derivative if t >= 0 % Voltage is 1 for seconds starting on an even number, and % 0 for seconds starting on an odd number. if mod(floor(t),2) == 0 result = 1; else result = -1; end else % Before time 0 result = 0; end

solution_files/Ex7.23/vout_vs_time.fig Data/auxiliary file.

solution_files/Ex7.23/vout_vs_time.png

solution_files/Ex7.24/fun1.m function yprime = fun1(t,y) yprime = -y + vin(t);

solution_files/Ex7.24/ode45_soln.m % Script file: ode45_soln.m % % Purpose: % This program solves a differential equation of the % form dy/dt + 2 * y = 0, with the initial condition % y(0) = 1. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % % Define variables: % odefun_handle -- Handle to function that defines the derivative

% tspan -- Duration to solve equation for % yo -- Initial condition for equation % t -- Array of solution times % y -- Array of solution values % Get a handle to the function that defines the % derivative. odefun_handle = @fun1; % Solve the equation over the period 0 to 5 seconds tspan = [0 10]; % Set the initial conditions y0 = 0; % Call the differential equation solver. [t,y] = ode45(odefun_handle,tspan,y0); % Plot the result figure(1); plot(t,y,'b-','LineWidth',2); grid on; title('\bfSolution of Differential Equation'); xlabel('\bfTime (s)'); ylabel('\bf\itv(t)');

solution_files/Ex7.24/v.fig Data/auxiliary file.

solution_files/Ex7.24/v.png

solution_files/Ex7.24/vin.m function result = vin(t) % Define variables: % t -- Time % result -- Input voltage % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/20/15 S. J. Chapman Original code % Calculate derivative if (t >= 0) & (t <= 5) result = t; else result = 0; end

solution_files/Ex7.25/random_rayleigh.m

function res = random_rayleigh(n,m) %RANDOM_RAYLEIGH Return samples from a Rayleigh distribution. % Function RANDOM_RAYLEIGH generates an array of Rayleigh% distributed random numbers. The usage is: % % random_rayleigh() -- Generate a single value % random_rayleigh(n) -- Generate an n x n array % random_rayleigh(n,m) -- Generate an n x m array % % Define variables: % arr1 -- Normally-distributed array % arr2 -- Normally-distributed array % res -- Results % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/23/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(0,2,nargin); error(msg); % If both arguments are missing, set to 1. % If the m argument is missing, set it to n. if nargin < 1 m = 1; n = 1; elseif nargin < 2 m = n; end % Calculate data arr1 = randn(n,m); arr2 = randn(n,m); res = sqrt( arr1.^2 + arr2.^2 );

solution_files/Ex7.25/rayleigh.fig Data/auxiliary file.

solution_files/Ex7.25/rayleigh.png

solution_files/Ex7.25/test_random_rayleigh.m % Script file: test_random_rayleigh.m % % Purpose: % To test function random_rayleigh by getting 20,000 % values, calculating the mean and standard % deviation, and plotting a histogram of the values. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/23/15 S. J. Chapman Original code % % Define variables: % ave -- Average (mean) of distribution % dist -- Distribution % sd -- Standard deviation of distribution % Get 20,000 values

dist = random_rayleigh(1,20000); % Calculate mean and standard deviation ave = mean(dist); sd = std(dist); % Tell user fprintf('Average = %.4f\n',ave); fprintf('Std Dev = %.4f\n',sd); % Create histogram hist(dist,21); title('\bfHistogram of random values'); xlabel('\bfValue'); ylabel('\bfCount');

solution_files/Ex7.3/hyperbolic.m function result = hyperbolic(fun,x) % HYPERBOLIC Calculate the hyperbolic sine of x % Function HYPERBOLIC calculates the value of a hyperbolic % sin, cos, or tan, depending on its its input parameter. % Define variables: % fun -- Function to evaluate % x -- Input value % result -- Result of calculation % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Calculate function switch (fun) case 'sinh', result = sinh(x); case 'cosh', result = cosh(x);

case 'tanh', result = tanh(x); otherwise, msg = ['Invalid input function: ' fun]; error(msg); end function result = sinh1(x) %SINH1 Calculate the hyperbolic sine of x % Function SINH1 calculates the hyperbolic sine of % its input parameter. % Define variables: % x -- input value

solution_files/Ex7.4/plot.fig Data/auxiliary file.

solution_files/Ex7.4/plot.png

solution_files/Ex7.4/test_anonymous.m

% Script file: test_anonymous.m % % Purpose: % To create three anonymous functions, and then create a % plot using them. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code % % Define variables: % f -- Function handle % g -- Function handle % h -- Function handle % x -- Input data samples % Create anonymous functions f = @ (x) 10 * cos(x); g = @ (x) 5 * sin(x); h = @ (a,b) sqrt(a.^2 + b.^2); % Plot the functiion h(f(x),g(x)) x = -10:0.1:10; plot(x,h(f(x),g(x)));

solution_files/Ex7.5/plot.fig Data/auxiliary file.

solution_files/Ex7.5/plot.png

solution_files/Ex7.5/plot_fn.m fplot(@(x) 1/sqrt(x), [0.1 10]); title('Plot of f(x) = 1 / sqrt(x)'); xlabel('\bfx'); ylabel('\bff(x)'); grid on;

solution_files/Ex7.6/plot.fig Data/auxiliary file.

solution_files/Ex7.6/plot.png

solution_files/Ex7.6/test_fminbnd.m % Script file: test_fminbnd.m % % Purpose: % To test function fminbnd using an anonymous function % as an input fucntion. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code % % Define variables: % minloc -- Location of minimum % minval -- Value at minimum % y -- Function handle % x -- Input data samples % Create anonymous function y = @ (x) x.^4 - 3*x.^2 + 2*x;

% Find the minimum of the function in the range % 0.5 <= x <= 1.5. [minloc,minval] = fminbnd(y,0.5,1.5); disp(['The minimum is at location ' num2str(minloc)]); % Plot the function z = linspace(-4,4,100); plot(z,y(z)); grid on; xlabel('\bfx'); ylabel('\bfy'); grid on;

solution_files/Ex7.7/plot.fig Data/auxiliary file.

solution_files/Ex7.7/plot.png

solution_files/Ex7.7/test_fminbnd.m % Script file: test_fminbnd.m

% % Purpose: % To test function fminbnd using an anonymous function % as an input fucntion. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code % % Define variables: % minloc -- Location of minimum % minval -- Value at minimum % y -- Function handle % x -- Input data samples % Create anonymous function y = @ (x) x.^4 - 3*x.^2 + 2*x; % Find the minimum of the function in the range % -2 < x < 2. [minloc,minval] = fminbnd(y,-2.0,2.0); disp(['The minimum in the range (-2,2) is at location ' num2str(minloc)]); % Find the minimum of the function in the range % -1.5 < x < 0.5. [minloc,minval] = fminbnd(y,-1.5,0.5); disp(['The minimum in the range (-1.5,0.5) is at location ' num2str(minloc)]); % Plot the function z = linspace(-2.5,2.5,100); plot(z,y(z)); grid on; xlabel('\bfx'); ylabel('\bfy'); grid on;

solution_files/Ex7.8/plot.fig Data/auxiliary file.

solution_files/Ex7.8/plot.png

solution_files/Ex7.8/test_randn.m % Script file: test_randn.m % % Purpose: % To create a histogram of 100,000 samples from a random % normal distribution. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code % % Define variables: % dist -- Samples % Get 100,000 values dist = randn(1,100000); % Create histogram hist(dist,21);

title('\bfHistogram of random values'); xlabel('\bfValue'); ylabel('\bfCount');

solution_files/Ex7.9/plot.fig Data/auxiliary file.

solution_files/Ex7.9/plot.png

solution_files/Ex7.9/test_rose.m % Script file: test_rose.m % % Purpose: % To create a rose plot of 100,000 samples from a random % normal distribution. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/10/15 S. J. Chapman Original code

% % Define variables: % dist -- Samples % Get 100,000 values dist = randn(1,100000); % Create histogram rose(dist,21); title('\bfRose Plot of random values'); xlabel('\bfValue'); ylabel('\bfCount');

solution_files/Ex8.1/to_polar.m function [mag,theta] = to_polar(c) %TO_POLAR Converts a complex number into polar form. % Function TO_POLAR accepts a single complex number % and returns the magnitude and the angle in degrees. % % Usage: % [mag,theta] = to_polar(c) % % Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate answer mag = abs(c); theta = angle(c) * 180 / pi;

solution_files/Ex8.10/plot3_plot.fig Data/auxiliary file.

solution_files/Ex8.10/plot3_plot.m figure(1); t = 0:0.1:10; v = 10 * exp((-0.2+j*pi).*t); figure(1); plot3(real(v),imag(v),t); grid on;

solution_files/Ex8.10/plot3_plot.png

solution_files/Ex8.11/euler_plot.m theta = 0:pi/20:2*pi; value = cos(theta) + 1i*sin(theta); figure(1); plot(value,'LineWidth',2);

axis equal; grid on; figure(2) plot3(real(value),imag(value),theta); hndl = plot3(real(value),imag(value),theta); set(hndl,'LineWidth',2); grid on;

solution_files/Ex8.11/plot1.fig Data/auxiliary file.

solution_files/Ex8.11/plot1.png

solution_files/Ex8.11/plot2.fig Data/auxiliary file.

solution_files/Ex8.11/plot2.png

solution_files/Ex8.12/contour_plot.fig Data/auxiliary file.

solution_files/Ex8.12/contour_plot.png

solution_files/Ex8.12/mesh_plot.fig Data/auxiliary file.

solution_files/Ex8.12/mesh_plot.m % Script file: mesh_plot.m % % Purpose: % To plot a text function with mesh, surface, and % contour plots. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % x -- Independent variable % y -- Independent variable % z -- Function result

% Define mesh grid [x,y] = meshgrid(-1:0.05:1,-2*pi:pi/20:2*pi); % Calculate function z = exp(x + 1i.*y); % Create mesh plot figure(1); mesh(x,y,real(z)); title('\bfMesh plot of real(\itz\rm\bf), where \it z = e^{x+iy}'); xlabel('\bfx'); ylabel('\bfy'); zlabel('\bfz'); % Create surface plot figure(2); surf(x,y,real(z)); title('\bfSurface plot of real(\itz\rm\bf), where \it z = e^{x+iy}'); xlabel('\bfx'); ylabel('\bfy'); zlabel('\bfz'); % Create contour plot figure(3);

solution_files/Ex8.12/mesh_plot.png

solution_files/Ex8.12/surface_plot.fig Data/auxiliary file.

solution_files/Ex8.12/surface_plot.png

solution_files/Ex8.13/calc_potential.m % Script file: calc_potential.m % % Purpose: % To calculate the electrostatic potential due to a set % of charges and various locations on a plane. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % qq -- magnitudes of charges % qx -- x locations of charges % qy -- y locations of charges % qz -- z locations of charges % v -- Array of potentials % x -- x grid locations to calculate potential at % y -- y grid locations to calculate potential at

% z -- z grid locations to calculate potential at % Create a grid of locations to calculate potential at various points on a plane x = -10:0.1:10; y = -10:0.1:10; z = 1; v = zeros(length(x),length(y)); % Create the locations of each charge, plus the amplitudes of the charges qx = [1 1 -1 -1]; qy = [1 -1 -1 1]; qz = [0 0 0 0]; qq = [1e-13 1e-13 -1e-13 1e-13]; % Sum up the potential at each point in the grid from each charge for ii = 1:length(x) for jj = 1:length(y) for kk = 1:4; % Get distance from charge to point r = sqrt( (x(ii)-qx(kk)).^2 + (y(jj)-qy(kk)).^2 + (z-qz(kk)).^2);

solution_files/Ex8.13/contour_plot.fig Data/auxiliary file.

solution_files/Ex8.13/contour_plot.png

solution_files/Ex8.13/mesh_plot.fig Data/auxiliary file.

solution_files/Ex8.13/mesh_plot.png

solution_files/Ex8.13/potential.m function v = potential(q,r) %POTENTIAL Calculate electrostatic potential from charge q at range r. % Function POTENTIAL calculates the electrostatic potential from % charge q at range r. % % Usage: % v = potential(q,r) % % Define variables: % q -- Charge in coulombs % r -- Distance from charge to point % v -- Resuling potential % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin);

error(msg); % Constant e0 = 8.85e-12; % Permeability of free space (F/m) % Calculate answer v = 1/(4*pi*e0) * q / r;

solution_files/Ex8.13/surface_plot.fig Data/auxiliary file.

solution_files/Ex8.13/surface_plot.png

solution_files/Ex8.14/character_count.m % Script file: character_count.m % % Purpose: % To accept a string from the user, and to count the % number of occurrences of a user-specified letter % within the string. %

% Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % % Define variables: % c -- character to check for % count -- Number of occurrences % str -- Input string % y -- Independent variable % z -- Function result % Get string str = input('Enter test string: ','s'); % Get character to check for c = input('Enter character to check for: ','s'); % Find the characters in the string that match count = 0; for ii = 1:length(str) if strncmp(str(ii),c,1) count = count + 1; end end % Tell user fprintf('The letter %c occurs %d times in the string.\n', ... c,count);

solution_files/Ex8.15/character_count.m % Script file: character_count.m % % Purpose: % To accept a string from the user, and to count the % number of occurrences of a user-specified letter % within the string. This version of the program is % case insensitive. % % Record of revisions:

% Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % 1. 05/01/15 S. J. Chapman Modified to be case insensitive % % Define variables: % c -- character to check for % count -- Number of occurrences % str -- Input string % y -- Independent variable % z -- Function result % Get string str = input('Enter test string: ','s'); % Get character to check for c = input('Enter character to check for: ','s'); % Find the characters in the string that match count = 0; for ii = 1:length(str) if strncmpi(str(ii),c,1) count = count + 1; end end % Tell user fprintf('The letter %c occurs %d times in the string.\n', ... c,count);

solution_files/Ex8.16/parse_string.m % Script file: parse_string.m % % Purpose: % To accept a string from the user, chop the string into % individual tokens, and print them out. % % Record of revisions: % Date Programmer Description of change % ==== ========== =====================

% 05/01/15 S. J. Chapman Original code % % Define variables: % c -- character to check for % count -- Number of occurrences % str -- Input string % y -- Independent variable % z -- Function result % Get string str = input('Enter test string: ','s'); % Chop string into tokens remainder = str; all_words = ''; while (any(remainder)) [chopped,remainder] = strtok(remainder); all_words = strvcat(all_words,chopped); end % Now sort the tokens using the matlab function % "sortrows". all_words = sortrows(all_words); % Print out the tokens fprintf('The sorted tokens are:\n'); for ii = 1:size(all_words,1) fprintf('%s\n',all_words(ii,:)); end

solution_files/Ex8.17/c_sort.m function out = c_sort(a) %C_SORT Selection sort character in ascending order % Function C_SORT sorts a set of strings into % ascending (alphabetical) order. The strings must % be contained in a character array, with one string % per row in the array. This function uses function % c_strcmp from Chapter 6 to perform the comparions. % % Usage:

% out = c_sort(a); % % where a is an array of strings, with one string % per row. % Define variables: % a -- Input array containing strings to sort % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable % nvals -- Number of rows in "a" (= number of strings) % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % Get the number of strings to sort nvals = size(a,1); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii,:) through a(nvals,:) iptr = ii; for jj = ii+1:nvals if c_strcmp(a(jj,:),a(iptr,:)) < 0 iptr = jj; end

solution_files/Ex8.17/c_strcmp.m function result = c_strcmp(str1,str2) %C_STRCMP Compare strings like C function "strcmp" % Function C_STRCMP compares two strings, and returns % a -1 if str1 < str2, a 0 if str1 == str2, and a % +1 if str1 > str2. % Define variables: % diff -- Logical array of string differences

% msg -- Error message % result -- Result of function % str1 -- First string to compare % str2 -- Second string to compare % strings -- Padded array of strings % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/25/14 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Check to see if the arguments are strings if ~(isstr(str1) & isstr(str2)) error('Both str1 and str2 must both be strings!') else % Pad strings strings = strvcat(str1,str2); % Compare strings diff = strings(1,:) ~= strings(2,:); if sum(diff) == 0 % Strings match, so return a zero! result = 0; else % Find first difference between strings ival = find(diff);

solution_files/Ex8.17/test_c_sort.m % Script file: test_c_sort.m % % Purpose: % To read in an set of input strings, sort them % into ascending order, and to write the sorted % data to the Command window. This program uses

% function "c_sort" to do the actual sorting. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % % Define variables: % array -- Input data array % ii -- Index variable % nvals -- Number of input values % sorted -- Sorted data array % temp -- temporary string % Prompt for the number of values in the data set nvals = input('Enter number of strings to sort: '); % Preallocate array array = ''; % Get input values for ii = 1:nvals % Prompt for next value string = ['Enter string ' int2str(ii) ': ']; temp = input(string,'s'); array = strvcat(array,temp); end % Now sort the data sorted = c_sort(array); % Display the sorted result. fprintf('\nSorted strings:\n');

solution_files/Ex8.18/c_sorti.m function out = c_sorti(a) %C_SORT Selection sort character in ascending order % Function C_SORTI sorts a set of strings into % ascending (alphabetical) order ignoring case. The % strings must be contained in a character array, with

% one string per row in the array. This function uses % fucntion c_strcmpi to perform the comparions. % % Usage: % out = c_sorti(a); % % where a is an array of strings, with one string % per row. % Define variables: % a -- Input array containing strings to sort % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable % nvals -- Number of rows in "a" (= number of strings) % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % Get the number of strings to sort nvals = size(a,1); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii,:) through a(nvals,:) iptr = ii; for jj = ii+1:nvals if c_strcmpi(a(jj,:),a(iptr,:)) < 0 iptr = jj; end

solution_files/Ex8.18/c_strcmpi.m function result = c_strcmpi(str1,str2) %C_STRCMPI Compare strings ignoring case like C function "strcmpi" % Function C_STRCMPI compares two strings ignoring case,

% and returns a -1 of str1 < str2, a 0 if str1 == str2, % and a +1 if str1 > str2. % Define variables: % diff -- Logical array of string differences % msg -- Error message % result -- Result of function % str1 -- First string to compare % str2 -- Second string to compare % strings -- Padded array of strings % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 02/25/14 S. J. Chapman Original code % 1. 05/01/15 S. J. Chapman Modified to ignore case % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Check to see if the arguments are strings if ~(isstr(str1) & isstr(str2)) error('Both str1 and str2 must both be strings!') else % Pad strings strings = strvcat(str1,str2); % Compare strings diff = upper(strings(1,:)) ~= upper(strings(2,:)); if sum(diff) == 0 % Strings match, so return a zero! result = 0; else % Find first difference between strings

solution_files/Ex8.18/test_c_sorti.m % Script file: test_c_sorti.m % % Purpose:

% To read in an set of input strings, sort them % into ascending order, and to write the sorted % data to the Command window. This program uses % function "c_sorti" to do the actual sorting. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % % Define variables: % array -- Input data array % ii -- Index variable % nvals -- Number of input values % sorted -- Sorted data array % temp -- temporary string % Prompt for the number of values in the data set nvals = input('Enter number of strings to sort: '); % Preallocate array array = ''; % Get input values for ii = 1:nvals % Prompt for next value string = ['Enter string ' int2str(ii) ': ']; temp = input(string,'s'); array = strvcat(array,temp); end % Now sort the data sorted = c_sorti(array); % Display the sorted result. fprintf('\nSorted strings:\n');

solution_files/Ex8.19/caps.m function out = caps(str) %CAPS Capitalise the words in a string

% Function CAPS capitalizes the first letter of each % word in an input string, while shifting a remaining % characters to lower case. % % Usage: % out = caps(str); % % where str is a string. % Define variables: % ii -- Index variable % nvals -- Number of rows in "a" (= number of strings) % out -- Output string % str -- Input string % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 11/26/07 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Get the length of the string nvals = length(str); % First, shift the entire string to lower case str = lower(str); % Now capitalize the first character. This will % cause no harm if it is a space or number, since % "upper" does nothing to them. str(1) = upper(str(1)); % Now capitalize the first letter of each word. % The start of a word can be found because the % previous character is a space and the current

solution_files/Ex8.19/test_caps.m % Script file: test_caps.m %

% Purpose: % To read in a string, and to capitalise the % words in the string. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % % Define variables: % string -- Input string % Prompt for the number of values in the data set string = input('Enter string: ','s'); % Display before and after capitalized fprintf('Before = %s\n',string); fprintf('After = %s\n',caps(string));

solution_files/Ex8.2/test_conversions.m % Script file: test_conversions.m % % Purpose: % To test the to_polar and to_complex conversions. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % c -- Complex number % mag -- Magnitude of number % theta -- Angle of number (deg) % Enter a complex number c = input('Enter a complex number: '); % Convert to polar and tell user [mag, theta] = to_polar(c);

fprintf('The magnitude of this number is %.4f.\n',mag); fprintf('The angle of this number is %.4f degrees.\n',theta); % Convert back to complex. Note that we are using "disp" % here, since "fprintf" will only display the real part of % a complex number. c = to_complex(mag,theta); disp(['The corresponding complex number is ' num2str(c) '.']);

solution_files/Ex8.2/to_complex.m function c = to_complex(mag,theta) %TO_COMPLEX Converts a magnitude and angle to a complex number. % Function TO_COMPLEX accepts a magnitude and an angle in % degrees and returns the corresponding complex number. % % Usage: % c = to_complex(mag,theta) % % Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. Note that % it is possible to supply only the magintude, in which % case the angle defaults to zero! msg = nargchk(1,2,nargin); error(msg); % Note that the magitude and angle should be real values. % It is an error if complex values are supplied. if ~isreal(mag) error('The magnitude must be a non-complex value!'); end

% Check for the presence of the angle, and supply a % default value if it is missing. Otherwise, make % sure that the angle is not a complex quantity. if nargin < 2 theta = 0; elseif ~isreal(theta) error('The angle must be a non-complex value!'); end

solution_files/Ex8.2/to_polar.m function [mag,theta] = to_polar(c) %TO_POLAR Converts a complex number into polar form. % Function TO_POLAR accepts a single complex number % and returns the magnitude and the angle in degrees. % % Usage: % [mag,theta] = to_polar(c) % % Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate answer mag = abs(c); theta = angle(c) * 180 / pi;

solution_files/Ex8.20/is_other.m function out = is_other(str)

%IS_OTHER Returns true if a character not alphanumeric or whitespace % Function IS_OTHER returns a true logical value if a % character is not alphanumeric and not whitespace, and a % false value otherwise. % % Usage: % out = is_other(str); % % where str is a string and out is a logical array. % Define variables: % out -- Output logical array % str -- Input string % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Now check for of characters that are NOT alphanumeric % and NOT whitespace. out = (~isstrprop(str,'alphanum')) & (~isstrprop(str,'wspace'));

solution_files/Ex8.21/is_vowel.m function out = is_vowel(str) %IS_VOWEL Returns true if a character is a vowel % Function IS_VOWEL returns a true logical value if a % character is a vowel, and a false value otherwise. % This function works correctly regardless of case. % % Usage: % out = is_vowel(str); % % where str is a string and out is a logical array. % Define variables:

% ii -- Index variable % nvals -- Number of rows in "a" (= number of strings) % out -- Output logical array % str -- Input string % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Get the length of the string nvals = length(str); % First, shift the entire string to lower case str = lower(str); % Now create output array out = logical(zeros(size(str))); % Now check for vowels, defined as "aeiou". Note that % we use "||" to allow partial expression evaluation. for ii = 1:nvals if (str(ii) == 'a') || (str(ii) == 'e') || ... (str(ii) == 'i') || (str(ii) == 'o') || ...

solution_files/Ex8.22/multiply.m function product = multiply(a,b) %MULTIPLY Multiplies an INT16 value by a SINGLE value % Function MULTIPLY multiplies an INT16 value by a % SINGLE value, and returns the result as a SINGLE. % % Usage: % product = multiply(a,b); % % Define variables: % a -- First argument % b -- First argument

% product -- SINGLE output value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/01/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Convert both variables to double a = double(a); b = double(b); product = single(a * b);

solution_files/Ex8.23/ellipsoid_of_revolution.fig Data/auxiliary file.

solution_files/Ex8.23/ellipsoid_of_revolution.m % Script file: ellipsoid_of_revolution.m % % Purpose: % This program plots an ellipsoid of revolution using % the surf function. % % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % a -- Radius of major axis % b -- Radius of minor axis % n -- Number of points in az and el to plot % phi -- meshgrid list of elevation values % Phi -- Array of elevation values to plot % theta -- meshgrid list of azimuth values

% Theta -- Array of azimuth values to plot % x -- Array of x point to plot % y -- Array of y point to plot % z -- Array of z point to plot % Define the number of angles on the sphere to plot % points at n = 20; % Calculate the points on the surface of the ellipsoid a = 2; b = 1; theta = linspace(-pi,pi,n); phi = linspace(-pi/2,pi/2,n); [theta,phi] = meshgrid(theta,phi); % Convert to (x,y,z) values x = a * cos(phi) .* cos(theta); y = b * cos(phi) .* sin(theta); z = b * sin(phi); % Plot the Elipsoid of Revolution

solution_files/Ex8.23/ellipsoid_of_revolution.png

solution_files/Ex8.24/sphere_and_ellipsoid.fig Data/auxiliary file.

solution_files/Ex8.24/sphere_and_ellipsoid.m % Script file: sphere_and_ellipsoid.m % % Purpose: % This program plots a sphere and an ellopsoid of % revolution on the same axes. % % Record of revisions: % Date Engineer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % a -- Radius of major axis of ellipsoid % b -- Radius of minor axis of ellopsoid % n -- Number of points in az and el to plot % r -- Radius of sphere % phi -- meshgrid list of elevation values % Phi -- Array of elevation values to plot % theta -- meshgrid list of azimuth values % Theta -- Array of azimuth values to plot % x -- Array of x point to plot % y -- Array of y point to plot % z -- Array of z point to plot % Define the number of angles on the sphere to plot % points at n = 20; % Calculate the points on the surface of the ellipsoid a = 1; b = 0.5; theta = linspace(-pi,pi,n);

phi = linspace(-pi/2,pi/2,n); [theta,phi] = meshgrid(theta,phi); % Convert to (x,y,z) values x = a * cos(phi) .* cos(theta); y = b * cos(phi) .* sin(theta); z = b * sin(phi);

solution_files/Ex8.24/sphere_and_ellipsoid.png

solution_files/Ex8.3/calc_current.m % Script file: calc_current.m % % Purpose: % To calculate the current flow through an impedance. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code %

% Define variables: % ia -- Complex current (amps) % ia_mag -- Current magnitude (amps) % ia_ang -- Curret phase (deg) % v -- Complex voltage (volts) % v_mag -- Voltage magnitude (volts) % v_ang -- Voltage phase (deg) % z -- Complex impedance (ohms) % z_mag -- Magnitude of impedance (ohms) % z_ang -- Phase of impedance (deg) % Enter the voltage across the impedance v_mag = ... input('Enter the magnitude of the voltage across the impedance (V): '); v_ang = ... input('Enter the phase of the voltage across the impedance (deg): '); v = to_complex(v_mag,v_ang); % Enter the impedance z_mag = ... input('Enter the magnitude of the impedance (ohms): '); z_ang = ... input('Enter the phase of the impedance (deg): '); z = to_complex(z_mag,z_ang); % Calculate current flow ia = v / z; % Convert to polar and tell user [ia_mag, ia_ang] = to_polar(ia);

solution_files/Ex8.3/to_complex.m function c = to_complex(mag,theta) %TO_COMPLEX Converts a magnitude and angle to a complex number. % Function TO_COMPLEX accepts a magnitude and an angle in % degrees and returns the corresponding complex number. % % Usage: % c = to_complex(mag,theta) %

% Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. Note that % it is possible to supply only the magintude, in which % case the angle defaults to zero! msg = nargchk(1,2,nargin); error(msg); % Note that the magitude and angle should be real values. % It is an error if complex values are supplied. if ~isreal(mag) error('The magnitude must be a non-complex value!'); end % Check for the presence of the angle, and supply a % default value if it is missing. Otherwise, make % sure that the angle is not a complex quantity. if nargin < 2 theta = 0; elseif ~isreal(theta) error('The angle must be a non-complex value!'); end

solution_files/Ex8.3/to_polar.m function [mag,theta] = to_polar(c) %TO_POLAR Converts a complex number into polar form. % Function TO_POLAR accepts a single complex number % and returns the magnitude and the angle in degrees. % % Usage: % [mag,theta] = to_polar(c)

% % Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate answer mag = abs(c); theta = angle(c) * 180 / pi;

solution_files/Ex8.4/complex_multiply.m % Script file: complex_multiply.m % % Purpose: % To multiply two complex numbers in polar form. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % a1 -- First number % a1_mag -- Magnitude of first number % a1_ang -- Angle of first number (deg) % a2 -- Second number % a2_mag -- Magnitude of second number % a2_ang -- Angle of second number (deg) % res -- Product % res_mag -- Magnitude of product

% res_ang -- Angle of product (deg) % Enter the first number a1 = input('Enter the first number: '); a2 = input('Enter the second number: '); % Calculate product [a1_mag, a1_ang] = to_polar(a1); [a2_mag, a2_ang] = to_polar(a2); res_mag = a1_mag * a2_mag; res_ang = a1_ang + a2_ang; res = to_complex(res_mag,res_ang); % Display answer disp(['The product using polar math is: ' num2str(res)]); disp(['The product MATLAB calculations is: ' num2str(a1*a2)]);

solution_files/Ex8.4/to_complex.m function c = to_complex(mag,theta) %TO_COMPLEX Converts a magnitude and angle to a complex number. % Function TO_COMPLEX accepts a magnitude and an angle in % degrees and returns the corresponding complex number. % % Usage: % c = to_complex(mag,theta) % % Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. Note that % it is possible to supply only the magintude, in which % case the angle defaults to zero! msg = nargchk(1,2,nargin);

error(msg); % Note that the magitude and angle should be real values. % It is an error if complex values are supplied. if ~isreal(mag) error('The magnitude must be a non-complex value!'); end % Check for the presence of the angle, and supply a % default value if it is missing. Otherwise, make % sure that the angle is not a complex quantity. if nargin < 2 theta = 0; elseif ~isreal(theta) error('The angle must be a non-complex value!'); end

solution_files/Ex8.4/to_polar.m function [mag,theta] = to_polar(c) %TO_POLAR Converts a complex number into polar form. % Function TO_POLAR accepts a single complex number % and returns the magnitude and the angle in degrees. % % Usage: % [mag,theta] = to_polar(c) % % Define variables: % c -- Complex value % mag -- Magnitude of number % theta -- Angle of number % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg);

% Calculate answer mag = abs(c); theta = angle(c) * 180 / pi;

solution_files/Ex8.5/Combined Plots.fig Data/auxiliary file.

solution_files/Ex8.5/Combined Plots.png

solution_files/Ex8.5/Current Mag vs Frequency linear.fig Data/auxiliary file.

solution_files/Ex8.5/Current Mag vs Frequency linear.png

solution_files/Ex8.5/Current Mag vs Frequency semilogx.fig Data/auxiliary file.

solution_files/Ex8.5/Current Mag vs Frequency semilogx.png

solution_files/Ex8.5/Current Phase vs Frequency linear.fig Data/auxiliary file.

solution_files/Ex8.5/Current Phase vs Frequency linear.png

solution_files/Ex8.5/Current Phase vs Frequency semilogx.fig Data/auxiliary file.

solution_files/Ex8.5/Current Phase vs Frequency semilogx.png

solution_files/Ex8.5/combined_plots.m % Plot on log-linear scale figure(1); subplot(2,1,1); semilogx(f,abs(io),'LineWidth',2); title('\bfPlot of amplitude of current flow vs frequency'); ylabel('\bfAumpitude (A)'); grid on; subplot(2,1,2); semilogx(f,phase,'LineWidth',2); title('\bfPlot of phase of current flow vs frequency'); xlabel('\bfFrequency (Hz)'); ylabel('\bfPhase (Deg)'); grid on;

solution_files/Ex8.5/rlc_circuit.m % Script file: rlc_circuit.m % % Purpose:

% To calculate the current flow out of a series RLC % circuit as a function of frequency. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % c -- Capacitance (F) % f -- Frequency of voltage source (Hz) % io -- output current (A) % l -- Inductance (H) % r -- resistance (ohms) % p -- output power (W) % vs -- input voltage (V) % w -- Angular frequency (rad/s) % Initialise values f = 100000:50000:10000000; vs = 120; c = 0.25e-9; l = 0.1e-3; r = 100; % Calculate w w = 2 * pi * f; % Calculate output current io = vs ./ (r + j*2*pi*f*l - j ./ (2*pi*f*c)); % Plot on linear scale figure(1); plot(f,abs(io)); title('\bfPlot of magnitude of current flow vs frequency'); xlabel('\bfFrequency (Hz)'); ylabel('\bfCurrent (A)');

solution_files/Ex8.5/rlc_circuit2.m % Script file: rlc_circuit2.m

% % Purpose: % To calculate the phase of the current flow out of % a series RLC circuit as a function of frequency. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables: % c -- Capacitance (F) % f -- Frequency of voltage source (Hz) % io -- output current (A) % l -- Inductance (H) % r -- resistance (ohms) % p -- output power (W) % phase -- phase of current vs frequency % vs -- input voltage (V) % w -- Angular frequency (rad/s) % Initialise values f = 100000:50000:10000000; vs = 120; c = 0.25e-9; l = 0.1e-3; r = 100; % Calculate w w = 2 * pi * f; % Calculate output current io = vs ./ (r + j*2*pi*f*l - j ./ (2*pi*f*c)); % Calculate phase phase = angle(io) * 180 / pi; % Plot on linear scale figure(1);

solution_files/Ex8.6/complex_point_plot.fig

Data/auxiliary file.

solution_files/Ex8.6/complex_point_plot.png

solution_files/Ex8.6/plot_complex.m function plot_complex(c) %PLOT_COMPLEX plots a complex value on a Cartesian plane % Function PLOT_COMPLEX plots a complex value on a % Cartesian plane. The usage is: % % plot_complex(c); % where % c -- Complex value % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/30/15 S. J. Chapman Original code % % Define variables:

% c -- Complex number % Plot cartesian axes plot([-abs(c) abs(c)], [0 0], 'k'); hold on; plot([0 0], [-abs(c) abs(c)], 'k'); % Plot a vector from the origin to the point. plot([0 real(c)],[0 imag(c)], 'b-', 'LineWidth',2); hold on; % Plot a marker at the location of the point plot(real(c),imag(c),'ro','LineWidth',2); % Titles, etc. title('\bfPlot of complex value in a Cartesian plane'); xlabel('\bfReal'); ylabel('\bfImaginary'); hold off;

solution_files/Ex8.7/plot.fig Data/auxiliary file.

solution_files/Ex8.7/plot.png

solution_files/Ex8.7/plot_function.m figure(1); t = 0:0.1:10; v = 10 * exp((-0.2+j*pi).*t); plot(t,v);

solution_files/Ex8.8/plot.fig Data/auxiliary file.

solution_files/Ex8.8/plot.png

solution_files/Ex8.8/plot_function.m figure(1); t = 0:0.1:10; v = 10 * exp((-0.2+j*pi).*t); plot(v);

solution_files/Ex8.9/polar_plot.fig Data/auxiliary file.

solution_files/Ex8.9/polar_plot.m figure(1); t = 0:0.1:10; v = 10 * exp((-0.2+j*pi).*t); r = abs(v); theta = angle(v); figure(1); polar(theta,r);

solution_files/Ex8.9/polar_plot.png

solution_files/Ex9.1/c_compare.m function res = c_compare(a,b) %C_COMPARE Compare two strings % Function C_COMPARE compares two strings for % lexographical order: % 1. If a < b, return -1. % 2. If a == b, return 0. % 3. If a > b, return 1. % % Usage: % res = c_compare(a,b); % Define variables: % a -- Input string 1 % b -- Input string 2 % ii -- Index variable % len_a -- Length of string a % len_b -- Length of string b % res -- Comparison result

% Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 5/02/15 S. J. Chapman Original code % Get the number of strings to sort len_a = length(a); len_b = length(b); % Compare strings res = 0; for ii = 1:max([len_a len_b]) % If string a has ended, string b is greater. % Return -1. if ii > len_a res = -1; break; % If string b has ended, string a is greater.

solution_files/Ex9.1/c_sort1.m function out = c_sort1(a) %C_SORT1 Selection sort character in ascending order % Function C_SORT1 sorts a set of strings into % ascending (alphabetical) order. The strings must % be contained in a cell array. This function uses % function c_compare to perform the comparions. % % Usage: % out = c_sort1(a); % % where a is a cell array of strings, with one string % per cell. % Define variables: % a -- Input cell array containing strings to sort % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable

% nvals -- Number of cells in "a" % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % Get the number of strings to sort nvals = length(a); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii) through a(nvals) iptr = ii; for jj = ii+1:nvals if c_compare(a{jj},a{iptr}) < 0 iptr = jj; end end

solution_files/Ex9.1/test_c_sort1.m % Script file: test_c_sort1.m % % Purpose: % To read in an set of input strings, sort them % into ascending order, and to write the sorted % data to the Command Window. This program uses % function "c_sort" to do the actual sorting. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % % Define variables: % array -- Input data array % ii -- Index variable

% nvals -- Number of input values % sorted -- Sorted data array % Prompt for the number of values in the data set nvals = input('Enter number of strings to sort: '); % Preallocate array to create cell array array = cell(1,1); % Get input values for ii = 1:nvals % Prompt for next value string = ['Enter string ' int2str(ii) ': ']; array{ii} = input(string,'s'); end % Now sort the data sorted = c_sort1(array); % Display the sorted result. fprintf('\nSorted strings:\n'); for ii = 1:nvals fprintf(' %s\n',sorted{ii});

solution_files/Ex9.10/dir_size.m function bytes = dir_size(dir_name) %DIR_SIZE Calculate the size of all files in a directory. % Function DIR_SIZE calculates the total size of all files % in a directory. % Define variables: % bytes -- Sum of all files sizes, in bytes % files -- Structure array of files % ii -- Index variable % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Check for a legal number of input arguments.

msg = nargchk(1,1,nargin); error(msg); % Get the file structure files = dir(dir_name); % Get the total size of all files bytes = 0; for ii = 1:length(files) if ~files(ii).isdir bytes = bytes + files(ii).bytes; end end

solution_files/Ex9.10/test_dir_size.m % Script file: test_dir_size.m % % Purpose: % To test function dir_size. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Define variables: % x -- Independent variable % y -- Dependent variable % Get the directory name dirname = input('Enter file name / path: ','s'); % Get the directory size bytes = dir_size(dirname); % Tell user fprintf('Directory %s size = %10.0f bytes\n', dirname, bytes);

solution_files/Ex9.11/dir_size.m function bytes = dir_size(dir_name)

%DIR_SIZE Calculate the size of all files in a directory. % Function DIR_SIZE calculates the total size of all files % in a directory, AND in all directories under it. % Define variables: % bytes -- Sum of all files sizes, in bytes % files -- Structure array of files % ii -- Index variable % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % 1. 05/03/15 S. J. Chapman Modified to make recursive % % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Get the file structure files = dir(dir_name); % Get the total size of all files bytes = 0; for ii = 1:length(files) if ~files(ii).isdir % Add in the size of this file bytes = bytes + files(ii).bytes; else % Add in the size of this subdirectory if ~strcmp(files(ii).name,'.') & ~strcmp(files(ii).name,'..') bytes = bytes + dir_size([dir_name '\' files(ii).name]); end end end

solution_files/Ex9.11/test_dir_size.m % Script file: test_dir_size.m

% % Purpose: % To test function dir_size. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Define variables: % x -- Independent variable % y -- Dependent variable % Get the directory name dirname = input('Enter file name / path: ','s'); % Get the directory size bytes = dir_size(dirname); % Tell user fprintf('Directory %s size = %10.0f bytes\n', dirname, bytes);

solution_files/Ex9.13/named_figure.fig Data/auxiliary file.

solution_files/Ex9.13/named_figure.m % Script file: named_figure.m % % Purpose: % To manipulate figure properties to assign a name to a % plot window. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/25/15 S. J. Chapman Original code % % Define variables:

% x -- Independent varible % y -- Function result % Create the plot figure(1); x = -2:0.1:2; y = exp(x); plot(x,y,'LineWidth',2); title('\bfPlot of \ity(x) = e^{x}'); xlabel('\bf\itx'); ylabel('\bf\ite^{x}'); grid on; % The "Name" property sets the name for a figure window, and % the "NumberTitle" property controls whether or not a number % is displayed in the Figure Window title bar. Set them now. set(gcf,'Name','Plot Window'); set(gcf,'NumberTitle','off');

solution_files/Ex9.13/named_figure.png

solution_files/Ex9.14/ellipse.fig

Data/auxiliary file.

solution_files/Ex9.14/ellipse.m % Script file: ellipse.m % % Purpose: % To demonstrate changing default properties in the % root graphics object. This program changes default % properties and then draws an ellipse to show that % the change was effective. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 11/28/07 S. J. Chapman Original code % % Define variables: % t -- Independent varible % x -- Function 1 result % y -- Function 2 result % Set the default properties. Note that orange can be % produced with the RGB vector [1.0 0.5 0.1]. set(groot,'DefaultFigureColor',[1.0 0.5 0.1]) set(groot,'DefaultLineLineWidth',3) % Create the plot figure(1); t = 0:pi/40:2*pi; x = 10 * cos(t); y = 6 * sin(t); plot(x,y); title('\bfEllipse'); xlabel('\bf\itx'); ylabel('\bf\ity'); grid on;

solution_files/Ex9.14/ellipse.png

solution_files/Ex9.15/drawlines.m % Script file: drawlines.m % % Purpose: % To allow the user to draw lines on a figure window % by successive mouse clicks. This program illustrates % how to accept mouse input in a MATLAB program. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/25/15 S. J. Chapman Original code % % Define variables: % new_x -- Current mouse click x position % new_y -- Current mouse click y position % prev_x -- Array of previous mouse click x positions % prev_y -- Array of previous mouse click y positions % res -- Result of key press or mouse click

% t -- Independent varible % x -- Function 1 result % y -- Function 2 result % Create the plot with blank axes figure(1); subplot(1,1,1); cla; title('\bfDemonstrate Drawing with Mouse Clicks'); axis([-1 1 -1 1]); % Set previous point information to null prev_x = []; prev_y = []; % Now wait for a mouse click or key press res = waitforbuttonpress; % If res == 0, then this was a mouse click. If res == 1 % then it was from the keyboard. while res == 0

solution_files/Ex9.15/drawlines.png

solution_files/Ex9.16/plotsinc.m % Script file: plotsinc.m % % Purpose: % This program illustrates the use of handle graphics % commands by creating a plot of sinc(x) from -3*pi to % 3*pi, and modifying the characteristics of the figure, % axes, and line using the "set" function. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 04/02/14 S. J. Chapman Original code % 1. 05/25/15 S. J. Chapman Use handle xyntax % % Define variables: % hndl -- Handle of line % x -- Independent variable % y -- sinc(x) % Calculate sinc(x) x = -3*pi:pi/10:3*pi; y = sin(x) ./ x; % Find the zero value and fix it up. The zero is % located in the middle of the x array. index = fix(length(y)/2) + 1; y(index) = 1; % Plot the function. hFig = figure(1); hAxes = subplot(1,1,1); hndl = plot(x,y); % Now modify the figure to create a pink background, % modify the axis to turn on y-axis grid lines, and % modify the line to be a 2-point wide orange line. hFig.Color = [1 0.8 0.8]; hAxes.YGrid = 'on'; hndl.Color = [1 0.5 0];

hndl.LineWidth = 3;

solution_files/Ex9.16/plotsinc_output.fig Data/auxiliary file.

solution_files/Ex9.16/plotsinc_output.png

solution_files/Ex9.17/drawlines.m % Script file: drawlines.m % % Purpose: % To allow the user to draw lines on a figure window % by successive mouse clicks. This program illustrates % how to accept mouse input in a MATLAB program. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/25/15 S. J. Chapman Original code % 1. 05/25/15 S. J. Chapman Modified to change line color/style

% % Define variables: % ch -- Current keyboard character % color -- Array of possible line colors % icolor -- Index to current line color % istyle -- Index to current line style % iwidth -- Index to current line width % linestyle -- Array of possible line styles % linewidth -- Array of possible line widths % new_x -- Current mouse click x position % new_y -- Current mouse click y position % res -- Result of key press or mouse click % t -- Independent varible % x -- X values to plot % y -- Y values to plot % Create the plot with blank axes figure(1); subplot(1,1,1); cla; title('\bfDemonstrate Drawing with Mouse Clicks'); axis([-1 1 -1 1]); % Color choices color = cell(1,5); color{1} = 'b'; color{2} = 'k';

solution_files/Ex9.17/drawlines_output.fig Data/auxiliary file.

solution_files/Ex9.17/drawlines_output.png

solution_files/Ex9.18/change_color.m % Script file: change_color.m % % Purpose: % To demonstrate selecting an object with the mouse % and changing the properties of that object. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/25/15 S. J. Chapman Original code % % Define variables: % c -- Array of color choices % res -- Result of key press or mouse click % obj_type -- Tye of object selected % t -- Independent varible % x1 -- Function 1 result % x2 -- Function 2 result

% Set up an array containing the color strings. Note that this % is a cell array, so potentially each element could contain either % a color character ('b') or a complete RGB vector ([0 0 255]). c{1} = 'r'; c{2} = 'g'; c{3} = 'b'; c{4} = 'y'; c{5} = 'c'; c{6} = 'm'; c{7} = 'k'; % Create the plot figure(1); t = -2:0.04:2; x1 = cos(t/pi); x2 = 2 * sin(t/(2*pi)); % Plot x1 with a random color selected from the array above index = floor( 7 * rand(1,1) ) + 1 plot(t,x1,c{index},'LineWidth',3); hold on;

solution_files/Ex9.18/figure.fig Data/auxiliary file.

solution_files/Ex9.18/figure.png

solution_files/Ex9.19/plot_line.fig Data/auxiliary file.

solution_files/Ex9.19/plot_line.m % Script file: plot_line.m % % Purpose: % To plot the function y = cos(2*pi*t - theta) % for various values of theta. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/25/15 S. J. Chapman Original code % % Define variables: % h1 -- Figure handle % ii -- Loop index % theta -- Phase delay (radians)

% t -- Independent varible % y -- Function result % Create the plot with blank axes figure(1); subplot(1,1,1); % Plot initial data t = -1:0.01:1; theta = 0; y = cos(2*pi*t - theta); h1 = plot(t,y,'LineWidth',2); title('\bfPlot of y = cos(2\pit - \theta) for various \theta'); grid on; % Now loop through changing theta for ii = 1:20 % Pause first pause(0.5); % Now plot new data theta = ii* (pi/10); y = cos(2*pi*t - theta);

solution_files/Ex9.19/plot_line.png

solution_files/Ex9.2/c_compare.m function res = c_compare(a,b) %C_COMPARE Compare two strings % Function C_COMPARE compares two strings for % lexographical order: % 1. If a < b, return -1. % 2. If a == b, return 0. % 3. If a > b, return 1. % % Usage: % res = c_compare(a,b); % Define variables: % a -- Input string 1 % b -- Input string 2 % ii -- Index variable % len_a -- Length of string a % len_b -- Length of string b % res -- Comparison result % Record of revisions:

% Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % 1. 05/02/15 S. J. Chapman Make case insensitive % Convert to uppercase a = upper(a); b = upper(b); % Get the number of strings to sort len_a = length(a); len_b = length(b); % Compare strings res = 0; for ii = 1:max([len_a len_b]) % If string a has ended, string b is greater. % Return -1. if ii > len_a

solution_files/Ex9.2/c_sort1.m function out = c_sort1(a) %C_SORT1 Selection sort character in ascending order % Function C_SORT1 sorts a set of strings into % ascending (alphabetical) order. The strings must % be contained in a cell array. This function uses % function c_compare to perform the comparions. % % Usage: % out = c_sort1(a); % % where a is a cell array of strings, with one string % per cell. % Define variables: % a -- Input cell array containing strings to sort % ii -- Index variable % iptr -- Pointer to min value % jj -- Index variable

% nvals -- Number of cells in "a" % out -- Sorted output array % temp -- Temp variable for swapping % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % Get the number of strings to sort nvals = length(a); % Sort the input array for ii = 1:nvals-1 % Find the minimum value in a(ii) through a(nvals) iptr = ii; for jj = ii+1:nvals if c_compare(a{jj},a{iptr}) < 0 iptr = jj; end end

solution_files/Ex9.2/test_c_sort1.m % Script file: test_c_sort1.m % % Purpose: % To read in an set of input strings, sort them % into ascending order, and to write the sorted % data to the Command Window. This program uses % function "c_sort" to do the actual sorting. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % % Define variables: % array -- Input data array % ii -- Index variable

% nvals -- Number of input values % sorted -- Sorted data array % Prompt for the number of values in the data set nvals = input('Enter number of strings to sort: '); % Preallocate array to create cell array array = cell(1,1); % Get input values for ii = 1:nvals % Prompt for next value string = ['Enter string ' int2str(ii) ': ']; array{ii} = input(string,'s'); end % Now sort the data sorted = c_sort1(array); % Display the sorted result. fprintf('\nSorted strings:\n'); for ii = 1:nvals fprintf(' %s\n',sorted{ii});

solution_files/Ex9.3/sum_args.m function out = sum_args(varargin) %SUM_ARGS Sums up the values of all input arguments % Function SUM_ARGS accepts an arbitrary number of % input arguments, and sums up the values of all % elements in the arguments. Each argument can be % either a scalar or an array, since MATLAB scalars % are just arrays of length 1. % % Usage: % out = sum_args(arg1, arg2, ...); % % where arg1, arg2, etc. are numeric arguments. % Define variables: % ii -- Index variable % jj -- Index variable

% nvals -- Number of input arguments % temp -- Temp variable for holding partial sums % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % Get the number of arguments to sum nvals = nargin; % Sum up the arguments out = 0; for ii = 1:nvals % Sum up all elements in each argument. Note that % this can be tricky, since each argument can be % an array of ANY dimension. For example, an array % can have 3, 4 or more subscripts. Fortunately, % the "sum" function can be used to add up all the % elements of a muntidimensional array. We must apply % the function once for each dimension in the array % to complete the sum.

solution_files/Ex9.3/test_sum_args.m % Script file: test_sum_args.m % % Purpose: % To test function sum_args. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % % Define variables: % total -- Sum of arguments % Define arguments clear all

a = 10; b = [4; -2; 2]; c = [1 0 3; -5 1 2; 1 2 0]; d = [1 5 -2]; % Calculate the sum of the a arguments total = sum_args(a,b,c,d); fprintf('The sum of the arguments is %.2f\n',total);

solution_files/Ex9.4/sum_args.m function out = sum_args(varargin) %SUM_ARGS Sums up the values of all input arguments % Function SUM_ARGS accepts an arbitrary number of % input arguments, and sums up the values of all % elements in the arguments. Each argument can be % either a scalar or an array, since MATLAB scalars % are just arrays of length 1. Note that this version % can also handle numeric arguments that are within % a cell array. % % Usage: % out = c_sort1(arg1, arg2, ...); % % where arg1, arg2, etc. are numeric arguments. % Define variables: % ii -- Index variable % jj -- Index variable % nvals -- Number of input arguments % temp -- Temp variable for holding partial sums % temp_cell -- Temp variable for a cell array argument % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % 1. 05/02/15 S. J. Chapman Modified to support cell inputs % Get the number of arguments to sum nvals = nargin;

% Sum up the arguments out = 0; for ii = 1:nvals if ~iscell(varargin{ii}) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% % This argument is an ordinary array or scalar. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%

solution_files/Ex9.4/test_sum_args.m % Script file: test_sum_args.m % % Purpose: % To test function sum_args. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % 1. 05/02/15 S. J. Chapman Modified to to test cell arrays % % Define variables: % total -- Sum of arguments % Define arguments clear all a = [1 4; -2 3]; b{1} = [1 5 2]; b{2} = [1 -2; 2 1]; % Calculate the sum of the a arguments total = sum_args(a,b); fprintf('The sum of the arguments is %.2f\n',total);

solution_files/Ex9.5/plot1.fig Data/auxiliary file.

solution_files/Ex9.5/plot1.png

solution_files/Ex9.5/plot2.fig Data/auxiliary file.

solution_files/Ex9.5/plot2.png

solution_files/Ex9.5/plot3.fig Data/auxiliary file.

solution_files/Ex9.5/plot3.png

solution_files/Ex9.5/plot_structure.m function out = plot_structure(plot_struct) %PLOT_STRUCTURE Plot a data set passed to the function as a structure % Function PLOT_STRUCTURE accepts an input structure % and creates a plot according to the data in the % structure. The elements in the structure should be:\ % % x_data -- Cell array containing x arrays to plot % y_data -- Cell array containing y arrays to plot % type -- Type of plot (a standard MATLAB function name) % title -- Title of plot % x_label -- X-axis label % y_label -- Y-axis label % x_range -- X-axis range % y_range -- Y-axis range % grid -- Grid status: 'ON' or 'OFF' % % Usage: % plot_structure(plot_struct); % where plot_struct is the plot structure

% Define variables: % ii -- Index variable % jj -- Index variable % nvals -- Number of input arguments % temp -- Temp variable for holding partial sums % temp_cell -- Temp variable for a cell array argument % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % First plot the data set(s) for ii = 1:length(plot_struct.x_data) % Get x and y data to plot x = plot_struct.x_data{ii}; y = plot_struct.y_data{ii}; % Create plot

solution_files/Ex9.5/test_plot_structure.m % Script file: test_plot_structure.m % % Purpose: % To test function plot_structure. This program creates % three different plot structures, and passes them to % function plot_structure for plotting % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/02/15 S. J. Chapman Original code % % Define variables: % plot_struct -- Plotting structure % t -- Independent variable % theta -- Independent variable clear all

% Create three plot structures. The first one will contain % sin(t) and cos(t) vs t, over the range -2*pi <= x <= 2*pi t = -2*pi:pi/20:2*pi; plot_struct(1).x_data{1} = t; % First line to plot plot_struct(1).y_data{1} = sin(t); plot_struct(1).x_data{2} = t; % Second line to plot plot_struct(1).y_data{2} = cos(t); plot_struct(1).type = 'plot'; % Linear plot plot_struct(1).title = '\bfPlot of sin(t) and cos(t) vs t'; plot_struct(1).x_label = '\bft'; plot_struct(1).y_label = '\bfsin(t) and cos(t)'; plot_struct(1).x_range = []; % Default plot ranges plot_struct(1).y_range = []; plot_struct(1).grid = 'on'; % Grid on % The second one will contain a plot of exp(-t/(2*pi)) * sin(t) % vs exp(-t/(2*pi)) * cos(t), over the range 0 <= x <= 4*pi t = 0:pi/20:4*pi; plot_struct(2).x_data{1} = exp(-t/(2*pi)) .* sin(t);

solution_files/Ex9.6/dist3.m function dis = dist3(point1, point2) %DIST3 Calculate distance between 2 point in a plane % Function DIST3 accepts two point structures and % calculate the difference between them. The elements % in a point structure should be: % % x -- Point x position % y -- Point y position % % Usage: % dis = dist3(point1, point2); % where point1 and point2 are point structures % Define variables: % point1 -- First point structure % point2 -- Second point structure % dis -- Distance between points

% Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Calculate the distance between the two points dis = sqrt( (point1.x - point2.x).^2 ... + (point1.y - point2.y).^2 );

solution_files/Ex9.6/test_dist3.m % Script file: test_dist3.m % % Purpose: % To test function dist3. This program creates two % point structures and calculates the distance between % them. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Define variables: % p1 -- First point structure % p2 -- Second point structure % dis -- Distance between points clear all % Create point structures p1.x = 3; p1.y = 4; p2.x = -4; p2.y = -3; % Get the distance between the two points

dis = dist3(p1,p2); % Tell user fprintf('Point 1 = (%.4f,%.4f) \n', p1.x, p1.y); fprintf('Point 2 = (%.4f,%.4f) \n', p2.x, p2.y); fprintf('Distance = %.4f\n',dis);

solution_files/Ex9.7/analyse_structure.m function [names, types] = analyse_structure(st) %ANALYSE_STRUCTURE Get element names and types from a structure % Function ANALYSE_STRUCTURE returns two cell arrays, one % containing the names of the fields in the strucure, and the % other containing the types of the data in the structure. % % Usage: % [names, types] = analyse_structure(st); % where st is a structure, names is a cell array containing % field names, and types is a cell array containing field types. % Define variables: % ii -- Loop index % temp1 -- The data in a field % temp2 -- "whos" output for "temp1" % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Check to see that "st" is a structure if ~isstruct(st) msg = ['Argument ' inputname(1) ' is not a structure']; error(msg); end % Get a list of fieldnames names = fieldnames(st);

% Create a cell array for the types types = cell(size(names)); % Now get the types of each field. We will extract each % field to a temporary array, and then using the "whos" % command recover the class (data type).

solution_files/Ex9.7/test_analyse_structure.m % Script file: test_analyse_structure.m % % Purpose: % To test function analyse_structure. This program creates % a structure, and then calls "analyse_structure" to analyse % its results. % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Define variables: % ii -- Loop index % names -- Cell array of field names % types -- Cell array of field types % st -- Test structure clear all % Create structure st.x = 3; st.y = 4; st.a = 'This is a test'; st.b = true; % Analyse the structure [names, types] = analyse_structure(st); % Tell user fprintf('The structure names and types are:\n'); fprintf(' Name Type \n') fprintf(' =============================\n')

for ii = 1:length(names) fprintf(' %10s %10s \n', names{ii}, types{ii}); end

solution_files/Ex9.8/calc_average.m function [student, class_ave] = calc_average(student) %CALC_AVERAGE Calculate the final average for each student. % Function CALC_AVERAGE calculates the final average for % each student in the class, and the overall average for % the class. Add the final average as a field in the % student structure. % Define variables: % class_ave -- Class average % ii -- Index variable % student -- Array of students % sums -- Running sum for final average % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Check for a legal number of input arguments. msg = nargchk(1,1,nargin); error(msg); % Calculate the final average for each student, and % create a running sum of grades to calculate the class % average. sums = 0; for ii = 1:length(student) % Calculate the average, and save it in a new field student(ii).final = sum(student(ii).exams) ... / length (student(ii).exams) % Include in running sums sums = sums + student(ii).final;

end % Calculate the final class average class_ave = sums / length(student);

solution_files/Ex9.8/student.mat Data/auxiliary file.

solution_files/Ex9.9/concat_fields.m function str = concat_fields(structure,field) %CONCAT_FIELDS Concatenate characters in the specified field. % Function CONCAT_FIELDS checks the specified field to ensure % that it is valid, and if it is a string, it concatenates all % of the characters together for all elements in the structure. % Define variables: % str -- Output string % ii -- Index variable % % Record of revisions: % Date Programmer Description of change % ==== ========== ===================== % 05/03/15 S. J. Chapman Original code % % Check for a legal number of input arguments. msg = nargchk(2,2,nargin); error(msg); % Is this a valid structure? if ~isstruct(structure) msg = ['Argument 1 (' inputname(1) ... ') is not a valid stucture']; error(msg); end % Is this field valid in the structure? if ~isfield(structure,field) msg = ['Argument 2 (' inputname(2) ... ') is not a valid field name'];

error(msg); end % Otherwise, concatenate all items of this field % containg strings. str = []; for ii = 1:length(structure) if isstr(structure(ii).(field)) str = [str structure(ii).(field)]; end

solution_files/Ex9.9/student.mat Data/auxiliary file.