mirror of https://github.com/TheAlgorithms/C
81 lines
2.3 KiB
C
81 lines
2.3 KiB
C
/**
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* @file
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* @brief [Secant Method](https://en.wikipedia.org/wiki/Secant_method) implementation. Find a
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* continuous function's root by using a succession of roots of secant lines to
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* approximate it, starting from the given points' secant line.
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* @author [Samuel Pires](https://github.com/disnoca)
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*/
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#include <assert.h> /// for assert
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#include <math.h> /// for fabs
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#include <stdio.h> /// for io operations
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#define TOLERANCE 0.0001 // root approximation result tolerance
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#define NMAX 100 // maximum number of iterations
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/**
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* @brief Continuous function for which we want to find the root
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* @param x Real input variable
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* @returns The evaluation result of the function using the input value
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*/
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double func(double x)
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{
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return x * x - 3.; // x^2 = 3 - solution is sqrt(3)
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}
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/**
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* @brief Root-finding method for a continuous function given two points
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* @param x0 One of the starting secant points
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* @param x1 One of the starting secant points
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* @param tolerance Determines how accurate the returned value is. The returned
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* value will be within `tolerance` of the actual root
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* @returns `root of the function` if secant method succeed within the
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* maximum number of iterations
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* @returns `-1` if secant method fails
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*/
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double secant_method(double x0, double x1, double tolerance)
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{
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int n = 1; // step counter
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while (n++ < NMAX)
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{
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// calculate secant line root
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double x2 = x1 - func(x1) * (x1 - x0) / (func(x1) - func(x0));
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// update values
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x0 = x1;
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x1 = x2;
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// return value if it meets tolerance
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if (fabs(x1 - x0) < tolerance)
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return x2;
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}
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return -1; // method failed (maximum number of steps exceeded)
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}
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/**
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* @brief Self-test implementations
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* @returns void
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*/
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static void test()
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{
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// compares root values found by the secant method within the tolerance
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assert(secant_method(0.2, 0.5, TOLERANCE) - sqrt(3) < TOLERANCE);
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assert(fabs(secant_method(-2, -5, TOLERANCE)) - sqrt(3) < TOLERANCE);
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assert(secant_method(-3, 2, TOLERANCE) - sqrt(3) < TOLERANCE);
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assert(fabs(secant_method(1, -1.5, TOLERANCE)) - sqrt(3) < TOLERANCE);
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printf("All tests have successfully passed!\n");
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main()
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{
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test(); // run self-test implementations
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return 0;
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}
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