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References

- C++ Programming Language, Bjarne Stroustrup, Addison-Wesley
- C++ and Object-Oriented Numeric Computing for Scientists and Engineers, Daoqi Yang, Springer
- Scientific and Engineering C++, John J. Barton and Lee R. Nackman, Addison-Wesley

Rational Class Mechanics

- Goal: Design and test a class, Rational, for manipulating rational numbers
- Components:
- rational.h – header file with definition of the class including member data and functions
- rational.cpp – implementation of member functions
- testrat.cpp – a small program to test the class definition

Access

- Keywords: private (default), public, protected, friend
- private – members can accessed only by other member functions or operators of the class
- public – members can be used directly by client programs
- protected – members can be used only by other member functions or operators of the class or derived classes
- friend – complete access to all class members, use with caution

Client Program Example - Revisited

#include <iostream>

#include <string>

#include “rational.h”

using namespace std;

int main() {

Rational r(3/4), s(2/3);

Rational t(r);

Rational Sum = r + s;

Rational Product = r * s;

cout << r << “+” << s << “=“ << Sum << endl;

return(0);

}

Statements not permissible due to access restrictions

Rational r(3,4);

r.ImaginaryValue = 6; //illegal – data is private

int a = GetNumerator(r) //illegal – function is protected

r.SetNumerator(b); //illegal – function is protected

Constructors

- Rational ();
- use in external program or function:
- Rational b; //data not initialized
- Rational (int numer, int denom=1);
- Use in external program or function:
- Rational b(3,4); //data is ¾
- Rational c(4); //denominator defaults to 1

const qualifier

- Objects may also be declared as constants, e.g.
- const Rational OneHalf(1,2);
- const objects require const member functions
- const member functions can be used with both const and non-const objects
- Example:
- Rational Add(const Rational &r) const;
- Object is passed by reference (&r), const qualifier prevents modification
- const member function will not modify any of object's data members

Inspectors

- Note: protected not accessible to main or external functions
- Used to retrieve member data
- int GetNumerator() const;
- int GetDenominator() const;
- const qualifier permits use with const objects

Mutators

- Modify member data
- Protected access
- void SetNumerator(int numer);
- void SetDenominator(int denom);

Arithmetic Functions

- Rational Add(const Rational &r) const;
- Public member functions – accessible in main and other functions
- Example usage:
- Rational r(3,4);
- Rational s(2,5);
- Rational t =r.Add(s);
- Explanation: r is a rational object invoking its public member function Add with the rational object s as an argument. The result is another Rational object which is assigned to t

Stream Facilitators

- public access
- void Insert(ostream &sout) const;
- inserts a representation of the object into the output stream referenced by &sout
- void Extract(istream &sin) const;
- extracts a representation of the object from the input stream referenced by &sin

Stream use examples

Rational r:

Rational s;

cout << “Enter rational number (a/b): “;

r.Extract(cin);

cout << “Enter rational number (a/b): “;

s.Extract(cin);

Rational t = r.Add(s);

t.Insert(cout);

cout << endl;

//note: illustrations of use are based only on the

//definitions. These member functions still have to be

//implemented

Overloaded Operators

- Rational operator+(const Rational &r, const Rational &s);
- reserved word operator indicates operator overloading
- returns a Rational object

Implementation

- use a .cc or .cpp file
- Syntax for member function implementation header:
- <return-type> <classname>::<functionname>(<parameters>)
- Example:
- void Rational::SetNumerator(int numer) {
- NumeratorValue=numer;
- }

Constructors - Implementation

//default constructor

Rational::Rational() {

SetNumerator(0);

SetDenominator(1);

}

//numer, denom constructor

Rational::Rational(int numer, int denom) {

SetNumerator(numer);

SetDenominator(denom);

}

//Notice: both constructors are invoking protected

member functions SetNumerator and SetDenominator

Inspector Implementations

//get numerator

int Rational::GetNumerator() const {

return NumeratorValue;

}

//get denominator

int Rational::GetDenominator() const {

return DenominatorValue;

}

Mutator Implementation

//set numerator

void Rational::SetNumerator(int numer) {

NumeratorValue = numer;

}

//set denominator

void Rational::SetDenominator(int denom) {

if (denom != 0) {

DenominatorValue = denom;

}

else {

cerr << “Illegal denominator: “ << denom << “using 1” << endl;

DenominatorValue = 1;

}

}

Arithmetic Function Implementation

One example will suffice:

Rational Rational::Add(const Rational &r ) const {

int a = GetNumerator();

int b = GetDenominator();

int c = r.GetNumerator();

int d = r.GetDenominator();

return Rational(a*d + b*c, b*d);

}

//Note that the return invokes the constructor

Stream Insertion and Extraction - Implement

//Inserting a Rational

void Rational::Insert(ostream &sout) const {

//output as a/b

sout << GetNumerator() << '/' << GetDenominator();

return;

}

//Extracting a Rational

void Rational::Extract(istream &sin) {

//input a/b

int numer;

int denom;

char slash;

sin >> numer >> slash >> denom;

SetNumerator(numerb);

SetDenominator(denom);

}

Operator implementation

Again, one example:

Rational operator+(const Rational &r, const Rational &s)

{

return r.Add(s);

}

Automatic member functions

C++ automatically makes copy constructor available:

e.g.

Rational r(1,2);

Rational s(r); //s is copy constructed from r

C++ also automatically makes assignment available,

e.g.

Rational t = r;

C++ automatically makes destructor member function

available, ~Rational()

-Restrictions: no parameters, no return value

Explicit Implementation

//Rational copy constructor

Rational::Rational(const Rational &r) {

int a = r.getDenominator();

int b = r.getNumerator();

SetNumerator(b);

SetDenominator(a);

}

//Rational: destructor

Rational::~Rational()

{ }

//Rational: assignment operator

Rational& Rational::operator=(const Rational &r) {

int a = r.GetDenominator();

int b = r.GetNumerator();

SetNumerator(b);

SetDenominator(a);

return *this;

}

What is *this ?

this is a keyword for the address of the object whose

member function is being invoked

* is the dereferencing operator

*this is the value of the object at that address

Putting it all together

1. Create rational.h file with class definitions

2. Create rational.cpp file with implementations for

member functions

3. Compile:

g++ -c rational.cpp

4. Create a simple driver program using the class,

e.g. call example program, testrat.cpp

5. Compile the driver

g++ -c testrat.cpp

5. Link the driver to the class module:

g++ -o testrat testrat.o rational.o

Other possible member functions for Rational class

- operator += (and other op=)
- operator ==
- ++, --

MyComplex Class

- Using example of Rational Class, walk through construction of user-defined Complex Class

Point Class

- 2 dimensional point
- attributes: x,y
- methods:
- Constructor (s)
- move –

parameters1 : x,y coordinates,

parameters 2: another point

- draw – for now, just print out
- ?? Other functions

Integral Class

- ref: Yang
- evaluate definite integrals
- attributes:
- lower and upper bounds
- pointer to a function

Integral Class

typedef double (*pfn)(double); //defining a function ptr

class integral {

double lower;

double upper;

pfn integrand; //integrand function

public:

integral(double a, double b, pfn f) {

lower = a; upper = b; integrand = f;

}

double lowbd() const {return lower;};

double upbd() const {return upper;}

void changebd(double, double);

double trapezoidal(int) const;

friend double simpson(integral, int);

}

;

Integral Class Use Example

int main() {

integral di(0,5, sin);

double result = di.trapezoidal(100);

cout << result << endl;

//change bounds

di.changebd(3,7);

result = di.trapezoidal(100);

cout << result << endl;

result = simpson(di, 200);

cout << result << endl;

}

Class MyVector

Class MyVector: a vector

Data: plain array

Functions: subscripting, change length, assignment to another

vector, inner product with another vector, ...

This example is for illustration only. A vector class is defined in the

Standard Template Library

MyVector - functionality

Create vectors of a specified length:

MyVector v(n);

Create a vector with zero length:

MyVector v;

Redimension a vector to length n:

v.redim(n);

Create a vector as a copy of another vector w:

MyVector v(w);

Extract the length of the vector:

const int n = v.size();

More functionality

Extract an entry:

double e = v(i);

Assign a number to an entry:

v(j) = e;

Set two vectors equal to each other:

w = v;

Take the inner product of two vectors:

double a = w.inner(v);

or alternatively

a = inner(w,v);

More functionality

Write a vector to the screen:

v.print(…);

Arithmetic operations with vectors…

It is assumed that the example syntax would be defined in the

MyVector class.

MyVector consists of the data in the vector, the length of the vector, as

well as a set of member functions for operating on the vector data

Users can only operate on the vector data using the member

Functions

MyVector class possible definition

class MyVector

{

private:

double* A; // vector entries (C-array)

int length;

void allocate (int n); // allocate memory, length=n

void deallocate(); // free memory

public:

MyVector (); // MyVector v;

MyVector (int n); // MyVector v(n);

MyVector (const MyVector& w); // MyVector v(w);

~MyVector (); // clean up dynamic memory

bool redim (int n); // v.redim(m);

MyVector& operator= (const MyVector& w);// v = w;

double operator() (int i) const; // a = v(i);

double& operator() (int i); // v(i) = a;

void print (ostream& o) const; // v.print(cout);

double inner (const MyVector& w) const; // a = v.inner(w);

int size () const { return length; } // n = v.size();

/ operators:

MyVector operator* (double a, const MyVector& v); // u = a*v;

MyVector operator* (const MyVector& v, double a); // u = v*a;

MyVector operator+ (const MyVector& a, const MyVector& b); // u = a+b;

Constructors - I

MyVector v; // declare a vector of length 0

// this actually means calling the function

MyVector::MyVector ()

{ A = NULL; length = 0; }

Constructors II

MyVector v(n); // declare a vector of length n

// means calling the function

MyVector::MyVector (int n)

{ allocate(n); }

void MyVector::allocate (int n)

{

length = n;

A = new double[n]; // create n doubles in memory

}

Destructor

A MyVector object is created (dynamically) at run time, but must

also be destroyed when it is no longer in use. The destructor

specifies how to destroy the object:

MyVector::~MyVector ()

{

deallocate();

}

// free dynamic memory:

void MyVector::deallocate ()

{

delete [] A;

}

Assignment Operator

Set a vector equal to another vector:

// v and w are MyVector objects

v = w;

means calling:

MyVector& MyVector::operator= (const MyVector& w)

// for setting v = w;

{

redim (w.size()); // make v as long as w

int i;

for (i = 0; i < length; i++) { // (C++ arrays start at 0)

A[i] = w.A[i];

return *this;

}

// return of *this, i.e. a MyVector&, allows nested

// assignments:

u = v = u_vec = v_vec;

Redimensioning Length

Change the length of an already allocated MyVector object:

v.redim(n); // make a v of length n

Implementation:

bool MyVector::redim (int n)

{

if (length == n)

return false; // no need to allocate anything

else {

if (A != NULL) {

/ "this" object has already allocated memory

deallocate();

} //end if

allocate(n);

return true; // the length was changed

} //end else

}

Copy Constructor

Create a new vector as a copy of an existing one:

MyVector v(w); // take a copy of w

MyVector::MyVector (const MyVector& w)

{

allocate (w.size()); // "this" object gets w’s length

*this = w; // call operator=

}

this is a pointer to the current (“this”) object, *this is the object

itself

Subscripting

// a and v are MyVector objects; want to set a(j) = v(i+1);

// the meaning of a(j) is defined by

inline double& MyVector::operator() (int i)

{

return A[i-1];

// base index is 1 (not 0 as in C/C++)

}

Inline functions: function body is copied to calling code, no overhead

of function call!

Note: inline is just a hint to the compiler; there is no guarantee that

the compiler really inlines the function

Why return a double reference?

double& MyVector::operator() (int i) { return A[i-1]; }

// returns a reference (‘‘pointer’’) directly to A[i-1]

// such that the calling code can change A[i-1]

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