473 lines
No EOL
14 KiB
C
473 lines
No EOL
14 KiB
C
#include "math.h"
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#include "solve.h"
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#include <stdio.h> // УБРАТЬ
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inline int sravn_el(double x1, double x2){
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double eps = 1e-16;
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return fabs(x1 - x2) <= eps * fmax(fabs(x1), fabs(x2));
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}
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int task01(double (*f)(double), double a, double b, double eps, int m, double* x){
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int it, mon;
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double c = (a + b) / 2;
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double dlina_otrezka;
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double znach_a, znach_b, znach_c;
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znach_a = f(a);
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znach_b = f(b);
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mon = 1;
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if (znach_a > znach_b){
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mon = -1;
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}
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dlina_otrezka = b - a;
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if ((znach_a > 0 && znach_b > 0) || (znach_a < 0 && znach_b < 0)){
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return -1;
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}
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for (it = 1; it <= m; it++){
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if (dlina_otrezka < fmin(EPS, eps)){ // Считаем, ято метод не применим
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return -1;
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}
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dlina_otrezka *= 0.5;
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c = a + dlina_otrezka;
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znach_c = f(c);
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if (fabs(znach_c) < eps){
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*x = c;
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return it;
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}
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if (znach_c * mon > 0){
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b = c;
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znach_b = znach_c;
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}
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else {
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a = c;
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znach_a = znach_c;
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}
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}
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return -1; // За все итерации ничего путного
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}
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int task02(double (*f)(double), double (*df)(double), double x0, double eps, int m, double* x){
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int it;
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double znach_x0;
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double znach_pr_x0;
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double dop_x0;
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znach_x0 = f(x0);
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znach_pr_x0 = df(x0);
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for (it = 1; it <= m; it++){
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// УСЛОВИЯ ЗАВЕРШЕНИЯ
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if (fabs(znach_x0) < eps){ // Если значение в точке ~ноль
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*x = x0;
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return it;
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}
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dop_x0 = x0 - (znach_x0 / znach_pr_x0);
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if (fabs(dop_x0 - x0) < fmin(EPS, eps)){ // Считаем, что метод не применим
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return -1;
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}
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if (sravn_el(znach_pr_x0, 0)){ // Если значение произвдной 0, то метод не применим
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return -1;
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}
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x0 = dop_x0;
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znach_x0 = f(x0);
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znach_pr_x0 = df(x0);
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}
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return -1; // За все итерации ничего путного
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}
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int task03(double (*f)(double), double a, double b, double eps, int m, double* x){ // Если что-то не работает, то это метод не очень :)
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int it, mon;
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double c;
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double znach_c;
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double znach_a = f(a);
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double znach_b = f(b);
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mon = 1;
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if (znach_a > znach_b){
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mon = -1;
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}
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if ((znach_a > 0 && znach_b > 0) || (znach_a < 0 && znach_b < 0)){
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return -1;
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}
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for (it = 1; it <= m; it++){
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if (sravn_el(znach_b - znach_a, 0)){
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return -1;
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}
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if (fabs(b - a) < fmin(eps, EPS)){
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return -1;
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}
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c = a - (f(a) * (b - a) / (znach_b - znach_a));
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znach_c = f(c);
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if (c < a || c > b){ // c за пределами отрезка
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return -1;
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}
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if (znach_c < eps){
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*x = c;
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return it;
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}
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if (znach_c * mon > 0){ // С помощью значения "монотонности" проще написать проверку
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b = c;
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znach_b = znach_c;
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}
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else {
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a = c;
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znach_a = znach_c;
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}
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}
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return -1; // За все итерации ничего путного
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}
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int task04(double (*f)(double), double a, double b, double eps, int m, double* x){
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int it;
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double znach_c;
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double c;
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double znach_a = f(a);
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double znach_b = f(b);
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for (it = 1; it <= m; it++){
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//printf("a: %e f(a): %e\n", a, znach_a);
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//printf("b: %e f(b): %e\n", b, znach_b);
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if (sravn_el(znach_b - znach_a, 0)){
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return -1;
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}
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c = b - (znach_b * (b - a) / (znach_b - znach_a));
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znach_c = f(c);
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if (fabs(znach_c) < eps){
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*x = b;
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return it;
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}
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if (fabs(b - a) < fmin(EPS, eps)){
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return -1;
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}
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a = b;
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znach_a = znach_b;
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b = c;
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znach_b = znach_c;
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}
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return -1; // За все итерации ничего путного
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}
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int task05(double (*f)(double), double a, double c, double eps, int m, double* x){
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double w;
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double b, d;
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double razd_razn;
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double podkor_vyr;
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double znach_a, znach_b, znach_c, znach_d;
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int znak, it;
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b = (a + c) / 2;
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znach_a = f(a);
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znach_b = f(b);
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znach_c = f(c);
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for (it = 1; it <= m; it++){
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//printf("a: %lf b: %lf c: %lf\n", a, b, c);
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//printf("f(a): %lf f(b): %lf f(c): %lf\n", znach_a, znach_b, znach_c);
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if (fabs(b - c) < EPS || fabs(a - c) < EPS || fabs(a - b) < EPS){
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return -1;
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}
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w = (znach_b - znach_c) / (b - c) + (znach_a - znach_c) / (a - c) - (znach_a - znach_b) / (a - b);
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if (w < 0){
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znak = -1;
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}
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else{
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znak = 1;
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}
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razd_razn = ((znach_a - znach_b) / (a - b) - (znach_b - znach_c) / (b - c)) / (a - c);
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podkor_vyr = w * w - 4 * razd_razn;
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if (podkor_vyr < 0) podkor_vyr = 0;
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d = c - 2 * znach_c / (w + znak * sqrt(podkor_vyr));
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znach_d = f(d);
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//printf("d: %lf f(d): %lf\n", d, znach_d);
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if (fabs(znach_d) < eps){
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*x = d;
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return it;
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}
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if (fabs(d - c) < fmin(EPS, eps)){
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return -1;
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}
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a = b;
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znach_a = znach_b;
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b = c;
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znach_b = znach_c;
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c = d;
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znach_c = znach_d;
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}
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return -1; // За все итерации ничего путного
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}
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int task06(double (*f)(double), double deg, double* d, double a, double b, double eps, int m, double* x){ // Недоделана
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(void)f;
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(void)deg;
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(void)d;
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(void)a;
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(void)b;
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(void)eps;
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(void)m;
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(void)x;
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return -1;
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}
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double task04_09(double x0, int n, double* x, double* y, double* d, double*znach){ // Недоделана
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int i, m;
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double p;
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double pred_el, razn, tek_el;
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int double_n = 2 * n;
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(void)x0;
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(void)n;
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(void)x;
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(void)y;
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(void)d;
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(void)*znach;
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(void)m;
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/*
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printf("y:\n");
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for (i = 0; i<n;i++){
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printf("%lf\n", y[i]);
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}
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printf("d:\n");
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for (i = 0; i<n;i++){
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printf("%lf\n", d[i]);
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}
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*/
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pred_el = y[n - 1];
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m = 1;
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for (i = n - 1; i > 0; i--){
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if (2 * i - 2 >= n){
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d[(2 * i) % n] = (d[(2 * i) % n] - d[(2 * i - 2) % n]) / (x[i % n] - x[(i - 1) % n]);
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}
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else if (2 * i >= n && 2 * i - 2 < n){
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d[(2 * i) % n] = (d[(2 * i) % n] - y[2 * i - 2]) / (x[i % n] - x[(i - 1) % n]);
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}
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else{
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y[2 * i] = (y[2 * i] - y[2 * i - 2]) / (x[i] - x[i - 1]);
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}
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}
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for (m = 2; m < double_n; m++){
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// printf("----\n");
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for (i = double_n - 1; i >= m; i--){
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if (i - 1 >= n){
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pred_el = d[i % n];
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tek_el = d[(i - 1) % n];
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razn = x[(i - m) / 2] - x[i / 2];
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if (sravn_el(razn, 0)) return 1;
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d[i % n] = (pred_el - tek_el) / razn;
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}
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else if (i == n){
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pred_el = d[i % n];
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tek_el = y[i - 1];
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razn = x[(i - m) / 2] - x[i / 2];
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if (sravn_el(razn, 0)) return 1;
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d[i % n] = (pred_el - tek_el) / razn;
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}
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else{
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pred_el = y[i];
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tek_el = y[i - 1];
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razn = x[(i - m) / 2] - x[i / 2];
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if (sravn_el(razn, 0)) return 1;
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y[i] = (pred_el - tek_el) / razn;
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}
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}
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p = 0;
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for (i = double_n - 1; i >= 1; i--){
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if (i >= n){
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p = (p + d[i % n]) * (x0 - x[(i - 1) / 2]);
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}
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else{
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p = (p + y[i]) * (x0 - x[(i - 1) / 2]);
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}
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}
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p = p + y[0];
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*znach = p;
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return 0;
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}
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/*
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printf("y:\n");
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for (i = 0; i < n; i++){
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printf("%lf\n", y[i]);
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}
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*/
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// Пересчитываем первичную фазу
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return 0;
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}
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int task07(double (*f)(double), double x0, double eps, int m, double* x){
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int it;
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double znach_x0 = x0;
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for (it = 1; it <= m; it++){
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printf("x0: %lf\n", x0);
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znach_x0 = f(x0);
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if (fabs(znach_x0 - x0) < eps){
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*x = x0;
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return it;
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}
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x0 = znach_x0;
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}
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return -1;
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}
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int task08(double (*f)(double), double a, double b, double eps, int m, double* x){ // ЧЕРЕЗ ****, НО ВРОДЕ РАБОТАЕТ
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// ДОПИСАТЬ ВЫВОД ЗНАЧЕНИЯ ПОСЛЕ ИНТЕРАЦИЙ эт про чо?
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int i, it;
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double h;
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double tek_tochka, tek_znach, sled_tochka = 0, sled_znach = 0;
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double t_kr, znach_kr;
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h = b - a;
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tek_tochka = a;
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tek_znach = f(tek_tochka);
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if (tek_znach > f(b)){
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znach_kr = tek_znach;
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t_kr = a;
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}
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else{
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znach_kr = f(b);
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t_kr = b;
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}
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for (it = 0; it < m / 10; it++){
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if (it % 2 == 0){
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h = h * 0.1;
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//printf("h_c: %e\n", h);
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if (fabs(h) < eps){
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if (tek_znach > sled_znach){
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if (tek_znach > znach_kr){
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*x = tek_tochka;
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}
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else{
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*x = t_kr;
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}
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}
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else{
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if (sled_znach > znach_kr){
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*x = sled_tochka;
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}
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else {
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*x = t_kr;
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}
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}
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return it + 1;
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}
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for (i = 1; i <= 10; i++){
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//printf("tek: %lf %lf\n", tek_tochka, tek_znach);
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sled_tochka = a + i * h;
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sled_znach = f(sled_tochka);
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if (tek_znach > sled_znach){
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break;
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}
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if (i == 10) break;
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tek_tochka = sled_tochka;
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tek_znach = sled_znach;
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}
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a = tek_tochka;
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b = sled_tochka;
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//printf("new a: %lf b: %lf\n", a, b);
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//printf("---------\n");
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}
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else {
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h = h * 0.1;
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//printf("h_n: %e\n", h);
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if (fabs(h) < eps){
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if (tek_znach > sled_znach){
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if (tek_znach > znach_kr){
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*x = tek_tochka;
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}
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else{
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*x = t_kr;
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}
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}
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else{
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if (sled_znach > znach_kr){
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*x = sled_tochka;
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}
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else {
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*x = t_kr;
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}
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}
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return it + 1;
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}
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for (i = 1; i <= 10; i++){
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//printf("tek: %lf %lf\n", tek_tochka, tek_znach);
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tek_tochka = b - i * h;
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tek_znach = f(sled_tochka);
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if (tek_znach < sled_znach){
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break;
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}
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sled_tochka = tek_tochka;
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sled_znach = tek_znach;
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}
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a = tek_tochka;
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b = sled_tochka;
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//printf("new a: %lf b: %lf\n", a, b);
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//printf("---------\n");
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}
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}
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*x = (a + b) / 2;
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return it + 1;
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}
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int task09(double (*f)(double), double a, double b, double eps, int m, double* x){ // ПРОТЕСТИРОВАТЬ
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double znach_x1, znach_x2;
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double x1, x2;
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int it;
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double razn;
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//double golden_ratio = (1 + sqrt(5)) / 2; // не пригодилося :)
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for (it = 1; it <= m; it++){
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razn = 0.5 * (sqrt(5) - 1) * (b - a);
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x1 = b - razn;
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x2 = a + razn;
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znach_x1 = f(x1);
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znach_x2 = f(x2);
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if (znach_x1 < znach_x2) a = x1;
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else b = x2;
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if (fabs(a - b) < eps){
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*x = (a + b) / 2;
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return it;
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}
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}
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*x = (a + b) / 2;
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return it;
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}
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int task10(double (*f)(double), double a, double c, double eps, int m, double* x){ // НЕ РАБОТАЕТ
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double w;
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double b, d;
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double razd_razn;
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double podkor_vyr;
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double znach_a, znach_b, znach_c, znach_d;
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int znak, it;
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b = (a + c) / 2;
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znach_a = -fabs(f(a));
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znach_b = -fabs(f(b));
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znach_c = -fabs(f(c));
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for (it = 1; it <= m; it++){
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//printf("a: %lf b: %lf c: %lf\n", a, b, c);
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//printf("f(a): %lf f(b): %lf f(c): %lf\n", znach_a, znach_b, znach_c);
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if (fabs(b - c) < EPS || fabs(a - c) < EPS || fabs(a - b) < EPS){
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return -1;
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}
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w = (znach_b - znach_c) / (b - c) + (znach_a - znach_c) / (a - c) - (znach_a - znach_b) / (a - b);
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if (w < 0){
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znak = -1;
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}
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else{
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znak = 1;
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}
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razd_razn = ((znach_a - znach_b) / (a - b) - (znach_b - znach_c) / (b - c)) / (a - c);
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podkor_vyr = w * w - 4 * razd_razn;
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if (podkor_vyr < 0) podkor_vyr = 0;
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d = c - 2 * znach_c / (w + znak * sqrt(podkor_vyr));
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znach_d = -fabs(f(d));
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//printf("d: %lf f(d): %lf\n", d, znach_d);
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if (fabs(znach_d) < eps){
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*x = d;
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return it;
|
||
}
|
||
if (fabs(d - c) < EPS){
|
||
*x = d;
|
||
return it;
|
||
}
|
||
a = b;
|
||
znach_a = znach_b;
|
||
b = c;
|
||
znach_b = znach_c;
|
||
c = d;
|
||
znach_c = znach_d;
|
||
}
|
||
// ВОЗМОЖНО, УБРАТЬ!!!
|
||
*x = c;
|
||
return it;
|
||
} |