double standard_deviation(const std::vector<double> & v)
{
double avg_value = average_value(v);
std::vector<double> diff(v.size());
std::transform(v.begin(), v.end(), diff.begin(), std::bind2nd(std::minus<double>(), avg_value));
double sq_sum = std::inner_product(diff.begin(), diff.end(), diff.begin(), 0.0);
return std::sqrt(sq_sum / v.size());
}
void a1(void)
{
int N = 3,
M = 1;
data *dat = (data*) malloc(N*sizeof(data));
dat[0] = (data) { .val = 299793.0, .delta = 2.0 };
dat[1] = (data) { .val = 299792.0, .delta = 4.5 };
dat[2] = (data) { .val = 299782.0, .delta = 25.0 };
double avg = average_value(N, dat),
sig_i = sigma_square_intern(N, dat),
sig_e = sigma_square_extern(M, N, dat);
printf("c_avg = %f\n", avg);
printf("sigma_i = %f\n", sqrt(sig_i));
printf("sigma_e = %f\n", sqrt(sig_e));
}
void a2(void)
{
int N;
measurement *m = read_measurements("dat/a2.txt", &N);
double a, b, sig_a, sig_b, chi;
printf("\nLinear regression I = b*U:\n");
linear_regression(N, m, NULL, &b, NULL, &sig_b);
chi = chi_square_(N, m, 0, b);
printf("b = %f +/- %f, chi = %f\n", b, sqrt(sig_b)/2, sqrt(chi));
printf("\nLinear regression I = a + b*U:\n");
linear_regression(N, m, &a, &b, &sig_a, &sig_b);
chi = chi_square_(N, m, a, b);
printf("a = %f +/- %f, b = %f +/- %f, chi = %f\n", a, sqrt(sig_a)/2, b, sqrt(sig_b)/2, sqrt(chi));
}
void a3(void)
{
// order of polynoms + 1
int N[5] = {3, 5, 9, 13, 17};
// output function (%i = current N)
char *output_p_gp = "results/a3/poly-%i.gp",
*output_p_txt = "results/a3/poly-%i.txt",
*output_l_dat = "results/a3/legendre-%i.dat",
*output_l_txt = "results/a3/legendre-%i.txt";
// read data
matrix dat = read_data("dat/a3.txt");
int i;
for (i = 0; i < sizeof(N)/sizeof(int); i++)
{
//
// use polynoms
//
matrix F = init_F(dat, N[i], &polynom);
vector b = init_b(dat, N[i], &polynom);
// solve system of linear equations
vector x = solve_gauss(F,b);
char fp[100];
// parameter output
snprintf(fp, sizeof(fp), output_p_txt, N[i]-1);
printf("Opening file %s...\n", fp);
FILE *file = fopen(fp, "w+");
vector_fprint(file, x);
fclose(file);
// gnuplot output
snprintf(fp, sizeof(fp), output_p_gp, N[i]-1);
printf("Opening file %s...\n", fp);
file = fopen(fp, "w+");
fprintf(file, "plot ");
int k;
for (k = 0; k < x.N; k++)
{
fprintf(file, "%e * x**%i", VectorGET(x,k), k);
if (k < x.N-1)
fprintf(file, " + ");
}
fprintf(file, "\n");
fclose(file);
//
// Use legendre polynoms
//
F = init_F(dat, N[i], &legendre_polynom);
b = init_b(dat, N[i], &legendre_polynom);
// solve system of linear equations
x = solve_gauss(F,b);
// parameter output
snprintf(fp, sizeof(fp), output_l_txt, N[i]-1);
printf("Opening file %s...\n", fp);
file = fopen(fp, "w+");
vector_fprint(file, x);
// "plot" data for legendre polynoms
snprintf(fp, sizeof(fp), output_l_dat, N[i]-1);
printf("Opening file %s...\n", fp);
file = fopen(fp, "w+");
double r = -1.0,
dr = 0.01;
while (r <= 1.0)
{
double sum = 0;
for (k = 0; k < x.N; k++)
{
sum += VectorGET(x,k) * legendre_polynom(k,r);
}
fprintf(file, "%f %e\n", r, sum);
r += dr;
}
fclose(file);
file = NULL;
}
}
int main()
{
//a1();
//a2();
a3();
return 0;
}
void main(void)
{
printf("The average of 100, 133, and 155 is %f\n",
average_value(100, 133, 155));
}