112 lines
3.4 KiB
C
112 lines
3.4 KiB
C
#include <stdio.h>
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#include <math.h>
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typedef float(*function)(float);
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//(-2, -1.5) (-1.5, -1) (-1, -0.5) (-0.5, 0)
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float f(float x) {
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return 8*x*x*x*x + 32*x*x*x + 40*x*x + 16*x + 1;
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}
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int signF(float x)
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{
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return f(x)==0 ? 0 : (f(x) < 0 ? -1:+1);
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}
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float rootFindLineSearch(float xl, float xr, float eps, function f) {
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float x, minx = xl, nextstep;
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nextstep = fabs(xr-xl)/(1/eps); //разбиваем на отрезки интервал
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int stepcount=0;
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for(x=xl; x<xr; x += nextstep, stepcount++) {
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if( fabs(f(x)) < fabs(f(minx)) )
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minx = x;
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}
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printf("Find Line Search root for %d steps\n",stepcount);
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return minx;
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}
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float rootFindDiv(float xl, float xr, float eps, function f) {
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int stepcount=0; //число шагов
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float xm;
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while(fabs(xr-xl)>eps) { //вещественный модуль разницы или floatabs
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stepcount++;
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xm=(xl+xr)/2; // середина отрезка
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if(signF(xl) != signF(xm)) //если знак отличается
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xr=xm;
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else
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xl=xm;
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}
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printf("Find Div Search root for %d steps\n",stepcount); //статистика
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return (xl+xr)/2;
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}
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float rootFindDiv2(float xl, float xr, float eps, function f) {
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int stepcount=0; //число шагов
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float xm;
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while(fabs(xr-xl)>eps) { //вещественный модуль разницы
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stepcount++;
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xm=(xl+xr)/2; // середина отрезка
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if(f(xr)==0) { // нашли решение на правой границе
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printf("Find root for %d steps\n",stepcount);
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return xr;
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}
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if(f(xl)==0) { // нашли решение на левой границе
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printf("Find root for %d steps\n",stepcount);
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return xl;
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}
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if(signF(xl) != signF(xm)) //если знак отличается
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xr=xm;
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else
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xl=xm;
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}
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printf("Find root for %d steps\n",stepcount); //статистика
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return (xl+xr)/2;
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}
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float rootFindChord(float xl, float xr, float eps, function f) {
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int stepcount=0;
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while(fabs(xr - xl) > eps) {
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xl = xr - (xr - xl) * f(xr) / (f(xr) - f(xl));
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xr = xl - (xl - xr) * f(xl) / (f(xl) - f(xr));
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stepcount++;
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}
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printf("Find Chord Search root for %d steps\n",stepcount);
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return xr;
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}
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float rootFindTangent(float xn, float eps, function f, function df ) {
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float x1 = xn - f(xn)/df(xn);
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float x0 = xn;
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int stepcount=0;
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while(fabs(x0-x1) > eps) {
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x0 = x1;
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x1 = x1 - f(x1)/df(x1);
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stepcount++;
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}
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printf("Find Tangent Search root for %d steps\n",stepcount);
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return x1;
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}
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float df(float x) {
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return 32*x*x*x + 96*x*x + 80*x + 16;
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}
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int main()
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{
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float points[4][2] = {{-2, -1.5},{-1.5, -1},{-0.7, 0.5},{-0.01, 0}};
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for(int i=0;i<4;i++)
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{
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printf("------------------Root%d----------------------\n",i);
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printf("Find Line Search root = %f\n", rootFindLineSearch(points[i][0],points[i][1],0.001,f));
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printf("Find Div Search root = %f\n", rootFindDiv(points[i][0],points[i][1],0.001,f));
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printf("Find Chord Search root = %f\n", rootFindChord(points[i][0],points[i][1],0.001,f));
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printf("Find Find Tangent root = %f\n", rootFindTangent(points[i][0],0.001,f,df));
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}
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return 0;
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}
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