# include # include # include # include # include # include # include "zero_itp.h" int main ( ); void zero_itp_example ( double f ( double x ), double a, double b, double epsi, double k1, double k2, int n0, bool verbose, char *title ); double f_01 ( double x ); double f_02 ( double x ); double f_03 ( double x ); double f_04 ( double x ); double f_05 ( double x ); double f_06 ( double x ); void timestamp ( ); /******************************************************************************/ int main ( ) /******************************************************************************/ /* Purpose: zero_itp_test() tests zero_itp(). Licensing: This code is distributed under the MIT license. Modified: 02 March 2024 Author: John Burkardt */ { double a; double b; double epsi; double k1; double k2; int n0; char *title; bool verbose; timestamp ( ); printf ( "\n" ); printf ( "zero_itp_test():\n" ); printf ( " C version\n" ); printf ( " Test zero_itp(), which seeks a root of a function F(X)\n" ); printf ( " in an interval [A,B].\n" ); a = 1.0; b = 2.0; epsi = sqrt ( DBL_EPSILON ); k1 = 1.0 / ( b - a ) / 5.0; k2 = 2.0; n0 = 1; title = "f_01(x) = sin ( x ) - x / 2"; verbose = false; zero_itp_example ( f_01, a, b, epsi, k1, k2, n0, verbose, title ); a = 0.0; b = 1.0; epsi = sqrt ( DBL_EPSILON ); k1 = 1.0 / ( b - a ) / 5.0; k2 = 2.0; n0 = 1; title = "f_02(x) = 2 * x - exp ( - x )"; verbose = false; zero_itp_example ( f_02, a, b, epsi, k1, k2, n0, verbose, title ); a = -1.0; b = 0.5; epsi = sqrt ( DBL_EPSILON ); k1 = 1.0 / ( b - a ) / 5.0; k2 = 2.0; n0 = 1; title = "f_03(x) = x * exp ( - x )"; verbose = false; zero_itp_example ( f_03, a, b, epsi, k1, k2, n0, verbose, title ); a = 0.0001; b = 20.0; epsi = sqrt ( DBL_EPSILON ); k1 = 1.0 / ( b - a ) / 5.0; k2 = 2.0; n0 = 1; title = "f_04(x) = exp ( x ) - 1 / ( 100 * x * x )"; verbose = false; zero_itp_example ( f_04, a, b, epsi, k1, k2, n0, verbose, title ); a = -5.0; b = 2.0; epsi = sqrt ( DBL_EPSILON ); k1 = 1.0 / ( b - a ) / 5.0; k2 = 2.0; n0 = 1; title = "f_05(x) = (x+3) * (x-1) * (x-1)"; verbose = false; zero_itp_example ( f_05, a, b, epsi, k1, k2, n0, verbose, title ); a = 1.0; b = 2.0; epsi = 0.0005; k1 = 1.0 / ( b - a ) / 5.0; k2 = 2.0; n0 = 1; title = "f_06(x) = x^3 - x - 2"; verbose = true; zero_itp_example ( f_06, a, b, epsi, k1, k2, n0, verbose, title ); /* Terminate. */ printf ( "\n" ); printf ( "zero_itp_test():\n" ); printf ( " Normal end of execution.\n" ); printf ( "\n" ); timestamp ( ); return 0; } /******************************************************************************/ void zero_itp_example ( double f ( double x ), double a, double b, double epsi, double k1, double k2, int n0, bool verbose, char *title ) /******************************************************************************/ /* Purpose: zero_itp_example() tests zero_itp() on one test function. Licensing: This code is distributed under the MIT license. Modified: 31 May 2021 Author: John Burkardt Input: double F ( double x ), the name of a user-supplied function which evaluates the function whose zero is being sought. double A, B, the endpoints of the change of sign interval. char *TITLE, a title for the problem. bool verbose: true if extra output is desired from zero_itp(); */ { int calls; double fa; double fb; double fz; double z; zero_itp ( f, a, b, epsi, k1, k2, n0, verbose, &z, &fz, &calls ); fa = f ( a ); fb = f ( b ); printf ( "\n" ); printf ( " %s\n", title ); printf ( "\n" ); printf ( " A Z B\n" ); printf ( " F(A) F(Z) F(B)\n" ); printf ( "\n" ); printf ( " %14f %14f %14f\n", a, z, b ); printf ( " %14e %14e %14e\n", fa, fz, fb ); printf ( " Number of calls to F = %d\n", calls ); return; } /******************************************************************************/ double f_01 ( double x ) /******************************************************************************/ /* Purpose: f_01() evaluates sin ( x ) - x / 2. Licensing: This code is distributed under the MIT license. Modified: 13 April 2008 Author: John Burkardt Input: double X, the evaluation point. Output: double F_01, the value of the function at X. */ { double value; value = sin ( x ) - 0.5 * x; return value; } /******************************************************************************/ double f_02 ( double x ) /******************************************************************************/ /* Purpose: f_02() evaluates 2*x-exp(-x). Licensing: This code is distributed under the MIT license. Modified: 13 April 2008 Author: John Burkardt Input: double X, the evaluation point. Output: double F_02, the value of the function at X. */ { double value; value = 2.0 * x - exp ( - x ); return value; } /******************************************************************************/ double f_03 ( double x ) /******************************************************************************/ /* Purpose: f_03() evaluates x*exp(-x). Licensing: This code is distributed under the MIT license. Modified: 13 April 2008 Author: John Burkardt Input: double X, the evaluation point. Output: double F_03, the value of the function at X. */ { double value; value = x * exp ( - x ); return value; } /******************************************************************************/ double f_04 ( double x ) /******************************************************************************/ /* Purpose: f_04() evaluates exp(x) - 1 / (100*x*x). Licensing: This code is distributed under the MIT license. Modified: 13 April 2008 Author: John Burkardt Input: double X, the evaluation point. Output: double F_04, the value of the function at X. */ { double value; value = exp ( x ) - 1.0 / 100.0 / x / x; return value; } /******************************************************************************/ double f_05 ( double x ) /******************************************************************************/ /* Purpose: f_05() evaluates (x+3)*(x-1)*(x-1). Licensing: This code is distributed under the MIT license. Modified: 13 April 2008 Author: John Burkardt Input: double X, the evaluation point. Output: double F_05, the value of the function at X. */ { double value; value = ( x + 3.0 ) * ( x - 1.0 ) * ( x - 1.0 ); return value; } /******************************************************************************/ double f_06 ( double x ) /******************************************************************************/ /* Purpose: f_06() evaluates x^3 - x - 2. Licensing: This code is distributed under the MIT license. Modified: 02 March 2024 Author: John Burkardt Input: double X, the evaluation point. Output: double F_06, the value of the function at X. */ { double value; value = x * x * x - x - 2; return value; } /******************************************************************************/ void timestamp ( ) /******************************************************************************/ /* Purpose: timestamp() prints the current YMDHMS date as a time stamp. Example: 31 May 2001 09:45:54 AM Licensing: This code is distributed under the MIT license. Modified: 24 September 2003 Author: John Burkardt */ { # define TIME_SIZE 40 static char time_buffer[TIME_SIZE]; const struct tm *tm; time_t now; now = time ( NULL ); tm = localtime ( &now ); strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm ); printf ( "%s\n", time_buffer ); return; # undef TIME_SIZE }