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


typedef struct {
  int l; // length
  double * d; // data
} vector;

vector * new_vector(int length) {
  vector * v;
  v = calloc(1, sizeof(vector));
  v->l = length;
  v->d = calloc (length, sizeof(double));
  return v;
}


double scalar (vector * x, vector * y) {
  double s;
  int i;
  
  if (x->l != y->l) {
    fprintf(stderr, "error in scalar: vectors have different length.\n");
    exit(1);
  }
  s = 0;
  for (i=0; i< x->l; i++) {
    s += x->d[i] * y->d[i];
  }
  return s;
}

void scale (vector * x, double a) {
  int i; 
  for (i=0; i< x->l; i++) {
    x->d[i] *= a;
  }
}

double norm(vector * x) {
  double norm;
  
  norm = sqrt(scalar(x,x));
  
  return(norm);
}

double normalize(vector * x) {
  double n;
  
  n = norm(x);
  scale(x, 1./n);
  
  return(n);
}

// v = a*x+b*y
void combine(vector * v, double a, vector *x, double b, vector * y) {
  int i; 
  if (x->l != y->l || x->l != v->l) {
    fprintf(stderr, "error in combine: vectors have different length.\n");
    exit(1);
  }
  for (i=0; i< v->l; i++) {
    v->d[i] = a * x->d[i] + b * y->d[i];
  }
}
 
void gs(vector ** v, int m, double * norm) {
  double a;
  int i, j;
  
  for (i=0; i<m; i++) {
    for (j=0; j<i ; j++) {
      a = scalar(v[i], v[j]);
      combine(v[i], 1, v[i], -a, v[j]);
    }
    norm[i] = normalize(v[i]);
  }
}
  
  
  
  

int main () {
  int L=3; // dimension of vectors
  int m=3; // number of vectors 
  double *norm;
  vector **v;
  int i, j;
  
  norm = calloc(m, sizeof(double));
  v = calloc(m, sizeof(vector *));
  for (i=0; i<m; i++) {
    v[i] = new_vector(L);
    printf("vector %d = [", i);
    for (j=0; j<L; j++) {
      v[i]->d[j] = (int) (10*(2*drand48()-1));
      printf("%lf ,", v[i]->d[j]);
    }
    printf("]\n");
  }
  
  gs(v, m, norm);
  
  printf("vettori normalizzati:\n");
  for (i=0; i<m; i++) {
    printf("vector %d = [", i);
    for (j=0; j<L; j++) {
      printf("%lf ,", v[i]->d[j]);
    }
    printf("]\n");
  }


}