Example C++ Program Demonstrating Usage of a Pointer to a Function in the Call to Another Function

Transcription

1 ME 5241 Computer Aided Engineering Tom Chase Fall 2000 Example C++ Program Demonstrating Usage of a Pointer to a Function in the Call to Another Function The sample code below implements the Newton s Method function used to illustrate pseudo-code in lecture. The program will compile and run as shown. While it is written in C++, it will work equally well in C if the cin and cout statements utilized in the mainline are replaced with scanf and printf statements. Utilizing pointers to functions is useful because: The same function can be used to process many different functions within the same program. For example, newton is utilized to solve only one function, test fcn, in the example program shown below. However, a more complicated program may need to solve many different nonlinear equations within the same program. If newton were not told which function to solve by sending it a pointer, it could not be used to solve more than a single function. This structure enables you to assign very descriptive names to the functions being solved without changing the generic name used within function newton. / HEADER FILES * Note: To compile this program on an SGI, use the Irix C++ compiler: % CC -lm newton.c "iostream.h" is required to use "cin" and "cout" in C++ #include<iostream.h> "math.h" is required to use cos, fabs and pow in C #include<math.h> double test_fcn( double x ) AUTHOR: TRC DATE: 10/10/00 PURPOSE Implement the example equation used to illustrate Newton s Method for solving a single nonlinear equation in lecture INPUT x: Abscissa where equation is to be evaluated OUTPUT test_fcn: Value of equation at x 1

2 DESCRIPTION OF LOCAL VARIABLES None FUNCTIONS CALLED None START OF EXECUTABLE CODE This equation has no physical interpretation; it is simply an example return cos( x ) * pow( x, 3 ); double test_deriv( double x ) AUTHOR: TRC DATE: 10/10/00 PURPOSE Implement the derivative of the example equation used to illustrate Newton s Method for solving a single nonlinear equation in lecture NOTE: This function is only valid for the equation: f(x) = cos x - 3 x^3 INPUT x: Abscissa where equation is to be evaluated OUTPUT test_deriv: Value of derivative at x DESCRIPTION OF LOCAL VARIABLES None FUNCTIONS CALLED None START OF EXECUTABLE CODE This derivative has no physical interpretation; it is simply an example return - sin( x ) * x * x; int newton( double xinit, double (*fx)( double x ), double (*dfdx)( double x ), double tol, double* root ) 2

3 AUTHOR: TRC DATE: 10/10/00 PURPOSE Implement Newton s First Order Method for solving a single nonlinear equation INPUT xinit: Starting guess for the root fx: Name of the function containing the equation being solved dfdx: Name of the function containing the derivative of the function being solved Note: It is the responsibility of the user to ensure that fx and dfdx are compatible tol: Absolute or relative tolerance allowed for the root OUTPUT root: Root of the equation newton: Successful completion flag DESCRIPTION OF LOCAL VARIABLES chgmag: Magnitude of the change in the root from the previous iteration to the current denom: Denominator expression for Newton s iteration formula iter: Iteration counter oldroot: Value of the root from the previous iteration FUNCTIONS CALLED dfdx: Evaluate the derivative of the function being solved fx: Evaluate the function being solved LOCAL DECLARATIONS double chgmag, denom, oldroot; int iter; START OF EXECUTABLE CODE Initialize the root at the input guess *root = xinit; Start of main iteration loop for ( iter = 1; iter = 20; iter++ ) Ensure that the derivative is not zero before attempting to divide by it denom = (*dfdx)( *root ); if ( denom == 0.0 ) return 0; 3

4 Save most recent value of root for comparison with updated value oldroot = *root; Apply Newton s iteration formula *root += - (*fx)( *root ) / denom; Determine how much the root has changed between the previous and current iterations chgmag = fabs( *root - oldroot ); Check for either absolute or relative convergence. If either is satisfied, stop iterating. if ( ( chgmag < tol ) ( chgmag < fabs( tol * (*root) ) ) ) return 1; If the loop is completed, the answer has not converged after the maximum allowed number of iterations. Indicate a problem to the calling function. return 0; int main( ) AUTHOR: TRC DATE: 10/10/00 PURPOSE Test program to demonstrate the Newton s Method function DESCRIPTION OF LOCAL VARIABLES root: The root to the test equation userguess: Starting guess for x requested from the user FUNCTIONS CALLED newton: Implement Newton s First Order method for solving a single nonlinear equation. LOCAL DECLARATIONS double root, userguess; START OF EXECUTABLE CODE 4

5 Print title and desription of program cout << " \nnewton s Method Demonstration Progam\n\n"; cout << " This program attempts to solve the equation:\n"; cout << " cos x - 3 x^3 = 0\n\n"; Obtain starting guess from user cout << " Please input starting guess (in radians): "; cin >> userguess; Echo starting guess cout << " Starting guess =" << userguess << " rad\n\n"; Attempt to find root if (!newton( userguess, test_fcn, test_deriv,.001, &root ) ) If root was not found, provide informative message to the user. cout << " Sorry, Newton s Method did not converge!\n"; return 1; If root was found, print it. cout << " Root found at x = " << root << " rad\n"; return 1; 5