23 Feb
This is a stepbystep tutorial for this assignment and an explanation of the basics of how it works for those that are having a difficult time understanding or just are stuck somewhere. To view the assignment click here.
So for this assignment we are going to be doing a lot of math calculations so we are going to need the include the both the iostream and the cmath libraries. We will also need the value of pi.
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#include <iostream>
#include <cmath>
#define PI 3.14159
or
const double PI = 3.14159;

Defining the Coordinate Class
For the coordinate class we need 2 private variables x and y, 3 constructors, and 11 member functions.
The way you do the constructors and member functions can be done 2 different ways. You can either do them inside the class, or you can define them inside the class, like you do prototypes, and then have the actual functions at the bottom of your code. I like to define them and then put the functions at the bottom, making the code a little bit easier to read so that is the way that I'll show you, but if you want to do it the other way then just do it how you normally would with a regular function.
So here is what your class should look like (keep in mind that this all goes at the top before the main function):
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class coordinate
{
private:
double x; // x value of the coordinate point
double y; // y value of the coordinate point
public:
coordinate(); // 1st constructor requiring that no arguments are passed
coordinate(double ); // 2nd constructor requiring that only 1 argument is passed
coordinate(double , double ); // 3rd constructor requiring that 2 arguments are passed
void set(double , double ); // sets both values and requires 2 arguments to be passed
void setx(double ); // sets x value and requires 1 argument to be passed
void sety(double ); // sets y value and requires 1 argument to be passed
void read(); // allows user to input both x and y values
void print(); // prints out the coordinate point in "(x, y)" form
double distancezero(); // calculates distance of point from zero and returns the value
double distancetwo(coordinate ); // calculates distance between 2 points (current instance and coordinate value passed) and returns the value
double ranglezero(); // calculates the angle of the coordinate in radians and returns the value
double danglezero(); // calculates the angle of the coordinate in degrees and returns the value
int quadrant(); // find what quadrant the coordinate is in and returns the value
void midpoint(coordinate ); // calculates the midpoint between 2 points (current instance and coordinate value passed) and prints the value as a coordinate
};

Writing the Actual Functions for the Coordinate Class
Since we are not actually writing the functions in the same place we are doing the class we will write them at the bottom after the main function. However, to do this we will need a little more than what we would with regular functions. For member functions we have to define what class the function is actually a member of. To do this we have to do coordinate::[function]().
For example, here are the 3 constructors for the coordinate class:
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// takes no arguments and sets x and y to 0
coordinate::coordinate()
{
x = y = 0;
}
// takes 1 argument and sets x and y to that value
coordinate::coordinate(double a)
{
x = y = a;
}
// takes 2 arguments and sets the corresponding x and y to those values
coordinate::coordinate(double a, double b)
{
x = a;
y = b;
}

Next, we have the member functions. The first 3 are the set functions. These allow the user to set the values of either the x or the y or both together.
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// take 2 arguments and sets the corresponding x and y to those values
void coordinate::set(double a, double b)
{
x = a;
y = b;
}
// takes 1 argument and sets the x to that value
void coordinate::setx(double a)
{
x = a;
}
// takes 1 argument and sets the y to that value
void coordinate::sety(double b)
{
y = b;
}

Next, is the read and print functions. All we want the read to do is to do a cin of the 2 values (x and y). The print is just the opposite. All it does is do a cout of the x and y values in the (x, y) format.
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// takes no arguments and reads in the x and y values from the screen
void coordinate::read()
{
cin >> x >> y;
}
// takes no arguments and prints the x and y values in (x, y) format
void coordinate::print()
{
cout << "(" << x << ", " << y << ")";
}

Next, we have the distance functions. distanczero calculates the distance of the current instance coordinate from 0. distancetwo calculates the distance between 2 points (the current instance and the coordinate passed in).
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// takes no arguments and returns the distance of the current instance from zero
double coordinate::distancezero()
{
return sqrt(x * x + y * y);
}
// take 1 argument and calculates the distance between them
double coordinate::distancetwo(coordinate pt)
{
return sqrt(pow(x  pt.x, 2.0) + pow(y  pt.y, 2.0));
}

Next, we have the angle functions. ranglezero uses the function in the math library atan()(arc tangent) to find the angle in radians from the positive x axis. danglezero does the same thing but converts the value from radians to degrees. To convert from radians to degrees you multiply the value by 180 / pi
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// takes no arguments and returns the angle of the coordinate from the positive x axis in radians
double coordinate::ranglezero()
{
double angle; // angle of coordinate from positive x axis
if(x == 0) // if x == 0 then you will get a domain error so compute angle manually
{
if(y > 0) return PI / 2;
if(y < 0) return PI / 2;
if(y == 0) return 0;
}
angle = atan(y / x);
if(x < 0 and y >= 0)
return PI  abs(angle);
if(x < 0 and y < 0)
return (PI  abs(angle));
return angle;
}
// takes no arguments and returns the angle of the coordinate from the positive x axis in degrees
double coordinate::danglezero()
{
double angle; // angle of coordinate from positive x axis
if(x == 0) // if x == 0 then you will get a domain error so compute angle manually
{
if(y > 0) return 90;
if(y < 0) return 90;
if(y == 0) return 0;
}
angle = atan(y / x) * 180 / PI;
if(x < 0 and y >= 0)
return 180  abs(angle);
if(x < 0 and y < 0)
return (180  abs(angle));
return angle;
}

Next, we have the quadrant function. This looks at whether the x and y values are positive or negative to determine which quadrant the coordinate is in. It will return the number of the quadrant as an integer 14 and 0 if the coordinate is (0, 0)
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int coordinate::quadrant()
{
if(x > 0 && y >= 0)
return 1; // return quadrant 1
if(x <= 0 && y > 0)
return 2; // return quadrant 2
if(x < 0 && y <= 0)
return 3; // return quadrant 3
if(x >= 0 && y < 0)
return 4; // return quadrant 4
return 0; // return 0 if point is (0, 0)
}

Last, we have the midpoint function. you will need to pass this function a coordinate instance and it will calculate the midpoint between the current instance and the passed instance and print the coordinate instance.
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void coordinate::midpoint(coordinate pt)
{
coordinate np; // new coordinate point
np.x = (x + pt.x) / 2.0;
np.y = (y + pt.y) / 2.0;
np.print();
}

Now all you have to do is test each constructor and member function to make sure that everything is working properly.
11 Feb
Update: Bloggity does not require the Engines plugin to run if you are using Rails 2.3 or above (where the Engines plugin is baked in).  Noted below by Bill.
Update: Added the plugin to github  simple_blog. It is not production ready or really all that usable quite yet.
Ok, so this a rant and I am sorry for that  but as simple as it is, I have been looking for a blog plugin lately. The problem with the plugins I find is that I don't want to have to deal with the engines plugin or have the controllers, models, views, etc ... all extracted into my applications code. I want it all external (hence a plugin) but let it be minimally configurable.
So in my recent search for a blog plugin for rails, I came across two that look very useful, but each with their flaws:
1) bloget  Everything is extracted to my code space. Why? Yes, I realize that it is most likely because I will want to override things, but get out of my space and keep to yourself!
Provide me a way to override things that I would need to (there really shouldn't be too many), after all it is ruby.
2) bloggity  Uses the engines plugin! I have nothing against the engines plugin (I think it is well written and documented) but for a freaking blog plugin?!? Why?
Is there a third option?
Glad you asked  yes, there is a third option  I hate to say it, but do it right! There's your third option.
Ok, but really, if there is a third option (a third plugin), I would love to hear about it.
Ok, so all that to lead up to a little plugin tutorial? Well, it got your attention didn't it?
Starting from scratch
Ok, I guess I will start from scratch. So let's get started.
Creating a plugin
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pullmonkey$ ./script/generate plugin simple_blog
create vendor/plugins/simple_blog/lib
create vendor/plugins/simple_blog/tasks
create vendor/plugins/simple_blog/test
create vendor/plugins/simple_blog/README
create vendor/plugins/simple_blog/MITLICENSE
create vendor/plugins/simple_blog/Rakefile
create vendor/plugins/simple_blog/init.rb
create vendor/plugins/simple_blog/install.rb
create vendor/plugins/simple_blog/uninstall.rb
create vendor/plugins/simple_blog/lib/simple_blog.rb
create vendor/plugins/simple_blog/tasks/simple_blog_tasks.rake
create vendor/plugins/simple_blog/test/simple_blog_test.rb
create vendor/plugins/simple_blog/test/test_helper.rb

Create the app directories for your plugin
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pullmonkey$ cd vendor/plugins/simple_blog/ # pretty important
pullmonkey$ ls
init.rb install.rb lib MITLICENSE Rakefile README tasks test uninstall.rb
pullmonkey$ mkdir app
pullmonkey$ mkdir p app/models
pullmonkey$ mkdir p app/controllers
pullmonkey$ mkdir p app/views
pullmonkey$ mkdir p app/helpers
pullmonkey$ ls app/
controllers helpers models views

Well that was easy, so let's move on.
Models, Views, Controllers and Helpers  Living as one in my plugin
Models
Ok, so we have a clear path for where our models, controllers, views, and helpers should live, right?
For simplicity, let's just have a post and comment model  you have all seen this a billion times.
Models: vendor/plugins/simple_blog/app/models/post.rb
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class Post < ActiveRecord::Base
has_many :comments
end

Models: vendor/plugins/simple_blog/app/models/comment.rb
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class Comment < ActiveRecord::Base
belongs_to :post
end

And there you have it.
So what do you do to tell your rails application about your models?
Simple  inside vendor/plugins/simple_blog/init.rb  add these lines
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model_path = File.join(directory, 'app', 'models')
$LOAD_PATH << model_path
ActiveSupport::Dependencies.load_paths << model_path

Ok, so let's test it out.
Step 1  we will need some default migrations for the model to use.
Post migration:
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pullmonkey$ ./script/generate migration post
# This is what mine looks like
class Post < ActiveRecord::Migration
def self.up
create_table :posts do t
t.string :subject
t.text :body
t.timestamps
end
end
def self.down
drop_table :posts
end
end

And then the comment migration:
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pullmonkey$ ./script/generate migration comment
# This is what mine looks like
def self.up
create_table :comments do t
t.string :username
t.text :body
t.references :post
t.timestamps
end
end
def self.down
drop_table :comments
end

Run the migrations:

pullmonkey$ rake db:migrate

That was all just setup  now for the actual testing:
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pullmonkey$ ./script/console
Loading development environment (Rails 2.2.2)
>> Comment.new
=> #<Comment id: nil, username: nil, body: nil, post_id: nil, created_at: nil, updated_at: nil>
>> Post.new
=> #<Post id: nil, subject: nil, body: nil, created_at: nil, updated_at: nil>
>> p = Post.create(:subject => "Test 1", :body => "My Body")
=> #<Post id: 1, subject: "Test 1", body: "My Body", created_at: "20090211 19:09:25", updated_at: "20090211 19:09:25">
>> p.body
=> "My Body"
>> p.subject
=> "Test 1"
>> p.new_record?
=> false
>> p.comments
=> []
>> c = Comment.create(:username => 'pullmonkey', :body => "this is simple")
=> #<Comment id: 1, username: "pullmonkey", body: "this is simple", post_id: nil, created_at: "20090211 19:10:01", updated_at: "20090211 19:10:01">
>> p.comments << c
=> [#<Comment id: 1, username: "pullmonkey", body: "this is simple", post_id: 1, created_at: "20090211 19:10:01", updated_at: "20090211 19:10:06">]
>> p.comments
=> [#<Comment id: 1, username: "pullmonkey", body: "this is simple", post_id: 1, created_at: "20090211 19:10:01", updated_at: "20090211 19:10:06">]
>> Post.first.comments
=> [#<Comment id: 1, username: "pullmonkey", body: "this is simple", post_id: 1, created_at: "20090211 19:10:01", updated_at: "20090211 19:10:06">]

That's probably good enough. We have a working model and relationships. The best part is that all the code is still in the plugin.
What does my code space contain?
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pullmonkey$ ls l app/**
app/controllers:
total 4
rwrwr 1 pullmonkey pullmonkey 720 Feb 11 11:00 application.rb
app/helpers:
total 4
rwrwr 1 pullmonkey pullmonkey 115 Feb 11 11:00 application_helper.rb
app/models:
total 0
app/views:
total 4
drwxrwxrx 2 pullmonkey pullmonkey 4096 Feb 11 11:00 layouts

Just the defaults  neat
Controllers
In much the same way as models, we can easily use controllers from our plugin. No extracting, no engines plugin.
Controllers: vendor/plugins/simple_blog/app/controllers/posts_controller.rb
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class PostsController < ApplicationController
def index
@posts = Post.all
end
def show
@post = Post.find(params[:id])
end
def new
@post = Post.new
end
def create
if @post = Post.create(params[:post])
flash[:notice] = "Post Created"
redirect_to :action => 'index'
else
flash[:error] = "Post Not Created"
render :action => 'new'
end
end
#.... more code
end

Controllers: vendor/plugins/simple_blog/app/controllers/comments_controller.rb
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class CommentsController < ApplicationController
def index
@comments = Comment.find_all_by_post_id(params[:post_id])
end
#.... more code
end

Now, to register the controllers, add the following to vendor/plugins/simple_blog/init.rb:
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controller_path = File.join(directory, 'app', 'controllers')
$LOAD_PATH << controller_path
ActiveSupport::Dependencies.load_paths << controller_path
config.controller_paths << controller_path

Ok, before we can really test this we will need to do the views, so keep going.
Views
Create your view directories:
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pullmonkey$ mkdir p app/views/posts
pullmonkey$ mkdir p app/views/comments

Create your views:
For this example, I will just create one, then we will test it.
Views: vendor/plugins/simple_blog/app/views/posts/index.html.erb
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<h1>Posts</h1>
<% @posts.each do post %>
<h2><%= h post.subject %></h2>
<%= post.body %>
<h3>Comments</h3>
<% post.comments.each do comment %>
<b>by <%= comment.username %></b><br/>
<%= comment.body %><br/>
<br/>
<% end %>
<% end %>

Append your view paths:
If you don't do this next step, you will very likely see an error message like this:
Missing template posts/index.erb in view path /home/pullmonkey/rails_projects/simple_blog/app/views:
So let's add it.
There are at least two ways to do this. 1) Added to your controllers individually or 2) Add to application controller globally.
I prefer the less obtrusive, so let's go with number 1.
For this test, we will just work with the posts controller, so open it up again and add this line:

self.append_view_path(File.join(File.dirname(__FILE__), '..', 'views'))

So your file should look like this now:
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class PostsController < ApplicationController
self.append_view_path(File.join(File.dirname(__FILE__), '..', 'views'))
def index
@posts = Post.all
end
def show
@post = Post.find(params[:id])
end
def new
@post = Post.new
end
def create
if @post = Post.create(params[:post])
flash[:notice] = "Post Created"
redirect_to :action => 'index'
else
flash[:error] = "Post Not Created"
render :action => 'new'
end
end
end

Time to test
Start your web server  ./script/server
Browse to http://localhost:3000/posts
You should see the post we created up above via Post.create(...) and its associated comment that we also created above.
Note:Feel free to overwrite any of the views. This can be done simply for the posts index view by creating the same file under RAILS_ROOT/app/views/posts/index.html.erb and doing what you'd like.
That's it for part 1
Ok, so that's part 1. The goal was to keep everything external and I think we succeeded (aside from migrations).
No offense to those that use engines or extract files into one's application's space, we all have our ways  the above is what I prefer.
Part 2 will consist mainly of filling this out a bit more and further discussion on adding helpers, routes and migrations to your plugin without interfering in the application's code space.
As always, have fun and good luck!
05 Feb
This is a stepbystep tutorial for this assignment and an explanation of the basics of how it works for those that are having a difficult time understanding or just are stuck somewhere. To view the assignment click here.
Part A
1. Create a structure (called point) that includes a time and y value (both doubles).
This is very simple using the typedef struct and listing your variables.
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typedef struct
{
double time;
double y;
} point;

2. Create a main program that has an array of 40 points (or structures), keeps track of the number of values in the array and has variables for each of the values needed to calculate above.
In the main program we will need an array of points p, an integer with the total number of points values, and 4 double variables, one for each of the functions (I used vert_shift, amp, freq, and phase_shift).
Then you will need to call each function and for testing I printed each value out to make sure everything was coming in right. It is short, simple, and to the point like all programming should be. Your main should look something like this:
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int main()
{
point p[40]; // array of points
int values = 0; // total number of values in the points array
double vert_shift=0; // vertical shift
double amp=0; // amplitude
double freq=0; // frequency
double phase_shift=0; // phase shift
values = read_data(p);
cout << "Values: " << endl;
for(lcv=0; lcv < values; lcv++)
cout << " " << p[lcv].time << " " << p[lcv].y << endl;
cout << "nTotal Number of values = " << values << endl;
vert_shift = vertical(p, values);
cout << "nVertical shift = " << vert_shift << endl;
amp = amplitude(p, values);
cout << "nAmplitude = " << amp << endl;
freq = frequency(p, values);
cout << "nFrequency = " << freq << endl;
phase_shift = pshift(p, values);
cout << "nPhase Shift = " << phase_shift << endl;
return 0;
}

3. The main program should then call the read_data function. This function will have one argument (the array of points  or structures  which will be passed as a pointer to the function) and will return the number of values in the array. It should read the data from the data file using a pointer and the arrow (>) operator.
First, we are going to be reading from a file in this function so we are going to need to include the fstream library.
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#inlcude <fstream> // reading from file

Next, we need to create the prototype for this function called read_data. This will go above the main. The read_data function will need the array of points and will return the total number of points as an integer. So it should look like this:
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int read_data(point *);

Now below the main we can create our function and lets call the array of points a. In this function we will need 2 more variables, an integer (total) for counting the number of points that we read from the file and an ifstream variable (f) for opening and closing the file.
First, we need to try to open the file using f.open("sp09prog1.txt"). Next, we need to test to make sure the file was opened and that we can read from it and if not then print out error message and exit. If the file was opened then we need to read in the values into the point array and count the number of points using the total integer variable. We do this until we read the end of the file and we find out if we are at the end of the file with f.eof(). Finally, we will want to return the total. It should look like this:
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int read_data(point *a)
{
ifstream f; // file streaming variable
int total=0; // counts the total number of points in file
f.open("sp09prog1.txt");
if(f.fail())
{
cout << "ERROR: File could not be opened" << endl;
exit(1);
}
while(!f.eof())
{
f >> a>time >> a>y;
total++;
a++;
}
return total  1;
}

Notice that we return total  1. This is because we increment total and then we find out it is the end of the file. So we incremented one too many times so we need to subtract 1 before returning it.
4. Main should then call the vertical function to calculate the vertical shift. This function has two arguments (the array of points  passed as a pointer  and the number of values in the array). It will calculate the vertical shift by finding the average of the maximum and minimum yvalues. You will need to search through the array of points to find these max and min values.
5. Next, main will call the amplitude function to calculate the amplitude. This function has two arguments (the array of points  passed as a pointer  and the number of values in the array; you must also use the arrow operator in this function) and will return the amplitude. To find the amplitude, you need to calculate half the difference between the maximum and minimum values of the yvalues (you will need to search through the array for the maximum and minimum values again).
The functions are both almost identical. The only difference is the equation at the end so we will do them at the same time.
First, we will create the prototypes. Both functions take the array of points and the integer total number of points and they both return a double. So the prototypes should look like this:
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double vertical(point *, int );
double amplitude(point *, int );

So lets call the point array p and the integer total.
To find the max and min values we need to create 2 double variables (max and min) and an integer (lcv) that we will use for the loop.
Next we will need to set both max and min to the first y element in the array of points. Then we will have a loop and start from 0 to total. Each time we run through this loop we need to do 3 things:
 1. Test if max is less than the current y value? If yes then set max to the current y
 2. Test if min is greater than the current y value? If yes then set min to the current y
 3. Increment a to the next position in the array. Because we are using a pointer to the array we can do this easily by doing a++
Next we will just return the result of the equation as a double. So your functions should look something like this:
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double vertical(point *a, int total)
{
double min; // minimum y value found in array
double max; // maximum y value found in array
int lcv; // loop control variable
max = min = a>y;
for(lcv=0; lcv < total; lcv++)
{
if(max < a>y)
max = a>y;
if(min > a>y)
min = a>y;
a++;
}
return (max + min) / 2.0;
}
double amplitude(point *a, int total)
{
double min; // minimum y value found in array
double max; // maximum y value found in array
int lcv; // loop control variable
max = min = a>y;
for(lcv=0; lcv < total; lcv++)
{
if(max < a>y)
max = a>y;
if(min > a>y)
min = a>y;
a++;
}
return (max  min) / 2.0;
}

6. The next function called by main is the frequency function that has two arguments (the array of points  passed as a pointer  and the number of values in the array; again using the arrow operator to access values) and will return the frequency. To calculate the frequency, find the period which is time difference between the maximum and minimum yvalues and multiply by 2. Then, divide to calculate the frequency. Please note that you are using the difference between time values, not the y values, to perform the overall computation.
7. Finally, main will call the pshift function that contains two arguments (the array of points  passed as a pointer  and the number of values in the array; again using the arrow operator to access values) and will return the phase shift or horizontal shift. This shift can be found by finding the average of the time values where the maximum and minimum yvalues occur; then subtracting it from half the period (see step 6 to find the period).
The functions for steps 6 and 7 are both almost identical expect for the equation at the end so we will do these both at the same time.
For the frequency function we will need to use the absolute value function in the cmath library. To include this you will need to do this at the top of your file.
Like the functions in step 4 and 5 they need to have the array of points and the integer total number of points and they both return a double. So the prototypes should look like this:
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double frequency(point *, int );
double pshift(point *, int );

So lets call the point array p and the integer total.
To find the max and min values we need to create 2 pointers to point variables (max and min) and an integer (lcv) that we will use for the loop.
Next we will need to set both max and min pointers to the same address as a points which is the first position in the array of points. Then we will have a loop and start from 0 to total. Each time we run through this loop we need to do 3 things:
 1. Test if max>y is less than the current a>y value? If yes then set max to the current a address.
 2. Test if min>y is greater than the current a>y value? If yes then set min to the current a address.
 3. Increment a to the next position in the array. Because we are using a pointer to the array we can do this easily by doing a++
Next we will just return the result of the equation as a double. So your functions should look something like this:
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double frequency(point *a, int total)
{
point *min; // minimum y value location found in array
point *max; // maximum y value location found in array
int lcv; // loop control variable
max = min = a;
for(lcv=0; lcv < total; lcv++)
{
if(max>y < a>y)
max = a;
if(min>y > a>y)
min = a;
a++;
}
return abs(PI / (max>time  min>time));
}
double pshift(point *a, int total)
{
point *min; // minimum y value location found in array
point *max; // maximum y value location found in array
int lcv; // loop control variable
max = min = a;
for(lcv=0; lcv < total; lcv++)
{
if(max>y < a>y)
max = a;
if(min>y > a>y)
min = a;
a++;
}
a = total;
return (2 * PI / frequency(a, total)) / 2  (max>time + min>time) / 2.0;
}

Notice how in the pshift function after the loop we do a = total. This is because a is currently pointing the last element in the array and if we want to call frequency and pass the address of the first element in the array of points then we need to set a back to the first element.
Also notice that the frequency function uses a variable called PI. This is the value of pi so at the top above the main you will need to define it as a constant. You can do this one of 2 ways:
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#define PI 3.14159
or
const double PI=3.14159;

Either way will work but I prefer to use the #define since it uses less memory and only takes more processing when you compile the program not in running it.
Outcome
Using the text file provided this is what I got when I ran the program:
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[scnaegle@egor ece231]$ ./a.out
Values:
1.5708 4
1.6791 3.3551
1.7875 2.7403
1.8958 2.1845
2.0041 1.7135
2.1125 1.3495
2.2208 1.1094
2.3291 1.0044
2.4374 1.0395
2.5458 1.2131
2.6541 1.5169
2.7624 1.9369
2.8708 2.4533
2.9791 3.0421
3.0874 3.6756
3.1958 4.3244
3.3041 4.9579
3.4124 5.5467
3.5208 6.0631
3.6291 6.4831
3.7374 6.7869
3.8457 6.9605
3.9541 6.9956
4.0624 6.8906
4.1707 6.6505
4.2791 6.2865
4.3874 5.8155
4.4957 5.2597
4.6041 4.6449
4.7124 4
Total Number of values = 30
Vertical shift = 4
Amplitude = 2.9956
Frequency = 1.93329
Phase Shift = 1.5166

Part B
Using MATLAB, you need to plot the original data using the data file sp09prog1.txt. To do this, load the file into MATLAB, then assign the first column to be the x values and the second column to be the y values. You can then use the plot command to plot these (you should only plot the points  not any connecting lines).
This is easy. Use the load() function to read in data from the file into a matrix.
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table = load('sp09prog1.txt')

Then we need to get the data into arrays of time and y. To do this use matrixvairable(row,column). Use a colon (:) to get everything in either the row or column. In this case we will want all rows in the first column for time and all rows and second column for y.
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time = table(: , 1)
y = table(: , 2)

Then plot the data using the plot() function. For this you will need to pass 3 things (x values, y values, and symbol). Our x values is the array time and our y values is array y.
Then, using the values you found in the C++ program for each of the four variables, create a cosine curve that can be plotted over the data. You will need to create a matrix of xvalues that run from 1 to 2π with an increment of π/100. Then, create a matrix of y values using the cosine equation: where vs is the vertical shift, ps is the phase shift, amp is the amplitude and freq is the frequency. Plot these x and y values using a red line.
This is just the same as the first part only we need to find the x and y values using equations. But first lets set all the values we will need for our calculations which we can get from Part A of the program.
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vs = 4
amp = 2.9956
freq = 1.93329
ps = 1.5166
PI = 3.14159

Next we will have to create the array x with all the x values. In this case we are going to go from 0 to 2pi and step by pi/100. To do this we have a colon (:) between each argument like this:
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x = 0 : PI / 100 : 2 * PI

Now, to create the array y with all the y values we use the equation we were given.
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y = vs + amp * (cos(freq * x  ps))

Now, all we need to do is plot it on the graph. However, we want to plot the new equation on the same plot as the last one. To do this we need to use the command hold on. We also want the new graph to look different so lets make it a full line 4px wide and the color be dark red. Like this:
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hold on
plot(x, y, '', 'LineWidth', 4, 'Color', [.6 0 0])

Now run it and see if your two line match up at all.