task_sem2_4.1

#include <stdio.h>
#include <math.h>

double t_4[4][2];
double t_6[6][2];
double t_11[11][2];
double t_16[16][2];
double t_21[21][2];

double p(double x, double t[][2], int n) {
    double s = 0.0;

    for (int k = 0; k <= n; k++) {
        double m = t[k][1];
        for (int j = 0; j <= n; j++)
            if (j != k)
                m *= ((x - t[j][0]) / (t[k][0] - t[j][0]));
        s += m;
    }

    return s;
}

int main(int argc, char *argv[]) {
    extern double t_4[4][2];
    extern double t_6[6][2];
    extern double t_11[11][2];
    extern double t_16[16][2];
    extern double t_21[21][2];

    // populate our tables
    for (int i = 0; i < 4; i++) {
        t_4[i][0] = i / 3.0;
        t_4[i][1] = sqrt(t_4[i][0]);
    }

    for (int i = 0; i < 6; i++) {
        t_6[i][0] = i / 5.0;
        t_6[i][1] = sqrt(t_6[i][0]);
    }

    for (int i = 0; i < 11; i++) {
        t_11[i][0] = i / 10.0;
        t_11[i][1] = sqrt(t_11[i][0]);
    }

    for (int i = 0; i < 16; i++) {
        t_16[i][0] = i / 15.0;
        t_16[i][1] = sqrt(t_16[i][0]);
    }

    for (int i = 0; i < 21; i++) {
        t_21[i][0] = i / 20.0;
        t_21[i][1] = sqrt(t_21[i][0]);
    }

    FILE *f;

    f = fopen("p_3.dat", "w");
    for (double x = 0.0; x <= 1.0; x += 0.01) {
        printf("x = %g; P_3(x) = %e; sqrt(x) = %e; r(x) = %e\n", x, p(x, t_4, 3), sqrt(x), sqrt(x) - p(x, t_4, 3));
        fprintf(f, "%e\t%e\n", x, sqrt(x) - p(x, t_4, 3));
    }
    fclose(f);
    getchar();

    f = fopen("p_5.dat", "w");
    for (double x = 0.0; x <= 1.0; x += 0.01) {
        printf("x = %g; P_5(x) = %e; sqrt(x) = %e; r(x) = %e\n", x, p(x, t_6, 5), sqrt(x), sqrt(x) - p(x, t_6, 5));
        fprintf(f, "%e\t%e\n", x, sqrt(x) - p(x, t_6, 5));
    }
    fclose(f);
    getchar();


    f = fopen("p_10.dat", "w");
    for (double x = 0.0; x <= 1.0; x += 0.01) {
        printf("x = %g; P_10(x) = %e; sqrt(x) = %e; r(x) = %e\n", x, p(x, t_11, 10), sqrt(x), sqrt(x) - p(x, t_11, 10));
        fprintf(f, "%e\t%e\n", x, sqrt(x) - p(x, t_11, 10));
    }
    fclose(f);
    getchar();

    f = fopen("p_15.dat", "w");
    for (double x = 0.0; x <= 1.0; x += 0.01) {
        printf("x = %g; P_15(x) = %e; sqrt(x) = %e; r(x) = %e\n", x, p(x, t_16, 15), sqrt(x), sqrt(x) - p(x, t_16, 15));
        fprintf(f, "%e\t%e\n", x, sqrt(x) - p(x, t_16, 15));
    }
    fclose(f);
    getchar();

    f = fopen("p_20.dat", "w");
    for (double x = 0.0; x <= 1.0; x += 0.01) {
        printf("x = %g; P_20(x) = %e; sqrt(x) = %e; r(x) = %e\n", x, p(x, t_21, 20), sqrt(x), sqrt(x) - p(x, t_21, 20));
        fprintf(f, "%e\t%e\n", x, sqrt(x) - p(x, t_21, 20));
    }
    fclose(f);

    return 0;
}