mirror of https://github.com/TheAlgorithms/C
77 lines
1.8 KiB
C
77 lines
1.8 KiB
C
/**
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* @file
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* \brief Find approximate solution for \f$f(x) = 0\f$ using
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* Newton-Raphson interpolation algorithm.
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*
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* \author [Krishna Vedala](https://github.com/kvedala)
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*/
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#include <complex.h> /* requires minimum of C99 */
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#include <limits.h>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#define ACCURACY 1e-10 /**< solution accuracy */
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/**
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* Return value of the function to find the root for.
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* \f$f(x)\f$
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*/
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double complex func(double complex x)
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{
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return x * x - 3.; /* x^2 = 3 - solution is sqrt(3) */
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// return x * x - 2.; /* x^2 = 2 - solution is sqrt(2) */
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}
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/**
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* Return first order derivative of the function.
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* \f$f'(x)\f$
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*/
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double complex d_func(double complex x) { return 2. * x; }
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/**
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* main function
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*/
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int main(int argc, char **argv)
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{
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double delta = 1;
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double complex cdelta = 1;
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/* initialize random seed: */
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srand(time(NULL));
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/* random initial approximation */
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double complex root = (rand() % 100 - 50) + (rand() % 100 - 50) * I;
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unsigned long counter = 0;
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/* iterate till a convergence is reached */
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while (delta > ACCURACY && counter < ULONG_MAX)
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{
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cdelta = func(root) / d_func(root);
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root += -cdelta;
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counter++;
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delta = fabs(cabs(cdelta));
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#if defined(DEBUG) || !defined(NDEBUG)
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if (counter % 50 == 0)
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{
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double r = creal(root);
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double c = cimag(root);
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printf("Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n", counter,
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r, c >= 0 ? '+' : '-', c >= 0 ? c : -c, delta);
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}
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#endif
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}
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double r = creal(root);
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double c = fabs(cimag(root)) < ACCURACY ? 0 : cimag(root);
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printf("Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n", counter, r,
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c >= 0 ? '+' : '-', c >= 0 ? c : -c, delta);
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return 0;
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}
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