Each statement is ended by a semi-colon (;). The formatting is free.

Transcription

1 Example 1 cout << "Give initial guess " << endl; cin >> x; double err, tol=1e-12, x1; int it, maxit=100; it = 0; err = tol + 1; while( err > tol && it < maxit ) x1 = x - (x-cos(x))/(1+sin(x)); err = fabs( x1 - x ); x = x1; it++; if( err <= tol ) cout << "The root is " << x << endl; else cout << "Error, no convergence \n"; The program solves the equation cos(x) = x, using Newton-Raphson s method, x k+1 = x k f(x k )/f (x k ). Note the following. Lines beginning with # are not part of the C++ language. They are commands to a preprocessor, which processes the file before it is compiled by the C++ compiler. Each statement is ended by a semi-colon (;). The formatting is free. Braces, are used to group several statements together. Variables can be declared anywhere in the program. They are defined from the point of declaration and downwards in the code. Variables can be given an initial value in the declaration statement. 1

2 cout and cin are standard output and input respectively. They are defined in the file iostream.h, which must be included when cout and cin are used. endl is a special object, outputing it means that a line feed is performed, and the output buffer is flushed. The same effect is achieved by outputting the string n, except that the output buffer is not necessarily flushed. The mathematical functions sin, cos, and fabs are defined in math.h. fabs is the absolute value of a floating point number. Warning: The function abs is made for integers, and will always return an integer. The logical and is obtained as &&. The operator & is the bitwise and operation. The main program is always declared as, if input from the command line is wanted, the form int main( int argc, char** argv ) is also possible. Example of compiling and running the program. The code is put into afilenamednr.c na20.nada.kth.se 848) g++ nr.c na20.nada.kth.se 849)./a.out Give initial guess 3 The root is na20.nada.kth.se 850) Example 2 #include <iostream> #include <cmath> using namespace std; cout << "Give initial guess " << endl; cin >> x; double err, tol=1e-12, x1; int it, maxit=100; 2

3 it = 0; err = tol + 1; while( err > tol && it < maxit ) x1 = x - (x-cos(x))/(1+sin(x)); err = fabs( x1 - x ); x = x1; it++; if( err <= tol ) cout << "The root is " << x << endl; else cout << "Error, no convergence \n"; Example 2 shows the same code as Example 1, but with the modern version of C++, using the namespace concept. Both Example 1 and Example 2 compiles with the g++ compiler. The include files are now written without the extension.h, and the namespace std must explicitly be given in order to use cout and cin. Example 3 // Compute the sum of 1/k^3 with n terms. cout << "Give number of terms "; int n; cin >> n; double sum = 0; for( int i=1 ; i <= n ; i++ ) sum += 1.0/(i*i*i); cout << "The sum is " << sum << endl; The example shows the computation of the sum n i=1 where n is input by the user. Note the following 1 i 3 3

4 The for statement, has three expressions: Initialization i=1, continuation condition i <= n, and statement to do at each iteration i++. These statements are separated by semi-colon. The loop variable i, can be declared directly in the for statement. It is then usually defined only in the statements inside the for iteration, but some older versions of C++ defines it all the way past the end of the for statement. Most C++ compilers has some flag to change this behavior of variables declared inside for statements. It is necessary to use 1.0 in the divide for summation terms. 1 would have given integer division, and all terms except the first would have been zero. Example from executing the program: na20.nada.kth.se 868)./a.out Give number of terms 40 The sum is na20.nada.kth.se 869)./a.out Give number of terms 400 The sum is na20.nada.kth.se 870)./a.out Give number of terms 4000 The sum is Infinity To think about: Why is it not working with 4000 terms? The sum is convergent. Example 4 char a; int i; a = A ; i = a; cout << i << endl; for( char ch = A ; ch <= Z ; ch++ ) cout << ch ; cout << endl; for( int i = 40 ; i <= 100 ; i++ ) a = i; cout << a; 4

5 cout << endl; This example shows manipulations with the character data type. The example shows that char often can be treated in the same way as int. Each character is represented by an internal integer code in the computer. As seen in the example A has the value 65. Also non-printable characters, such as line-feed have integer codes. Example from compiling and executing the program na20.nada.kth.se 873) g++ chartest.c na20.nada.kth.se 874)./a.out 65 ABCDEFGHIJKLMNOPQRSTUVWXYZ ()*+,-./ :;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_ abcd Strings, i.e., consisting of more than one character, are enclosed in double quotes, as in the expression cout << "Hello there "; which could equally well have been printed by cout << H << e << l << l << o << << t << h << e << r << e ; double f( double x ) return x - cos(x); double df( double x ) return 1 + sin(x); cout << "Give initial guess " << endl; cin >> x; double err, tol=1e-12, x1; int it, maxit=100; Example 5 it = 0; err = tol + 1; 5

6 while( err > tol && it < maxit ) x1 = x - f(x)/df(x); err = fabs( x1 - x ); x = x1; it++; if( err <= tol ) cout << "The root is " << x << endl; else cout << "Error, no convergence \n"; This example shows again the Newton-Raphson iteration of Example 1, but now with use of functions. x is a formal parameter in the function declaration. The functions f and df are defined before they are used. If we want to define them elsewhere, for example on another file, it is necessary to declare them before they are used, as in the example below. double f( double x ); double df( double x ); cout << "Give initial guess " << endl; cin >> x; double err, tol=1e-12, x1; int it, maxit=100; it = 0; err = tol + 1; while( err > tol && it < maxit ) x1 = x - f(x)/df(x); err = fabs( x1 - x ); x = x1; it++; if( err <= tol ) cout << "The root is " << x << endl; else cout << "Error, no convergence \n"; 6

7 The functions are now declared but not defined. We put the functions on another file as done below double f( double x ) return x - cos(x); double df( double x ) return 1 + sin(x); If the main program is on a file called main.c, and the functions are on another file called fcns.c, we compile the program by listing both files to the compile command, g++ main.c fcns.c A file a.out is produced, as usual. Example 6 #include <iostream> using namespace std; void fcn1( int i, double y ) i++; cout << " y = " << y << endl; void fcn2( int& i, double x ) i++; cout << " y = " << y << endl; int nr_print = 0; x = 1.0/3.0; fcn1( nr_print, x ); cout << nr_print << endl; fcn2( nr_print, x ); cout << nr_print << endl; fcn2( nr_print, x ); cout << nr_print << endl; fcn1( nr_print, x ); cout << nr_print << endl; 7

8 In the example above two functions are defined. Both increments the value of i by one, but fcn1 uses call-by-value as parameter passing mechanism and fcn2 uses call-by-reference. call-by-value means that a local copy of the variable is created in fcn1, the local copy is incremented by one. It will not affect the actual parameter in the calling program (nr print). call-by-value is used for input of values to the function. call-by-reference means that the variable i in fcn2 refers to the same variable as the actual parameter in the calling program, (nr print), so that when i is incremented in fcn2 it will also affect the value of the actual parameter. Call-by-reference is used when the parameter should transfer a value from the function (output parameter). Note also that When no return value is used, the function return type can be declared void. The underscore character canbeusedinvariablenames. InC ++ it has the same status as a letter. Example from running the program is na20.nada.kth.se 883)./a.out y = y = y = y = Example 7 double scprod( int n, double x[], double y[] ); double x[10], y[10]; for( int i = 0 ; i < 10 ; i++ ) x[i] = i; y[i] = sin(x[i]); 8