Added simpified polynomial coefficients computation

main.c

@@ -1,12 +1,16 @@
 #include "./polynominal_interpolation.h"
 
+/*
+ Newton interpolation polynomial
+*/
+
 /* Divided difference is evaluated for:
    array y stands for f(x)
    array x stands for x
    number i stands for index of evaluated difference (from 0)
    number d stands for order of difference (from 0)
    example: https://shorturl.at/tBCPS */
-double div_diff(double *y, double *x, int i, int d)
+double div_diff(double *y, double *x, unsigned int i, unsigned int d)
 {
   return (y[i] - y[i - 1]) / (x[i] - x[i - d]);
 }
@@ -14,7 +18,7 @@ double div_diff(double *y, double *x, int i, int d)
 /* Evaluates divided differences of n values - array of some kind of derivatives with big enough dx
    Example: https://shorturl.at/tBCPS
    Warning: result is evaluated in `double *y` array */
-double *div_diff_es(double *x, double *y, int n)
+double *div_diff_es(double *x, double *y, unsigned int n)
 {
   for (int i = 1; i < n; i++)        // first element remains unchanged
     for (int j = n - 1; j >= i; j--) // evaluate from the end of array, decreacing number of step every repeation
@@ -23,8 +27,78 @@ double *div_diff_es(double *x, double *y, int n)
   return y;
 }
 
+/*
+ Coeficients of simplified polynomial computation
+*/
+
+void simplify_polynomial(double *res, double *rev_el_coef, double *x, unsigned int n)
+{
+  for (int i = 0; i < n; i++)
+    if (rev_el_coef[i])
+      for (int j = 0; j <= i; j++)
+        res[i - j] += (j % 2 ? -1 : 1) * rev_el_coef[i] * compute_sum_of_multiplications_of_k(x, j, i);
+}
+
+double compute_sum_of_multiplications_of_k(double *arr, unsigned int k, unsigned int n)
+{
+  if (k == 0)
+    return 1;
+
+  if (k == 1 && n == 1)
+    return arr[0];
+
+  unsigned int *selected = (unsigned int *)malloc(sizeof(unsigned int) * k); // Indexes of selected for multiplication elements
+
+  int i = 0, // index of `arr` array
+      j = 0; // index of `selected` array
+
+  double sum = 0;
+
+  while (j >= 0)
+  {
+    if (i <= (n + (j - k)))
+    {
+      selected[j] = i;
+
+      if (j == k - 1)
+      {
+        sum += mult_by_indexes(arr, selected, k);
+        i++;
+      }
+      else
+      {
+        i = selected[j] + 1;
+        j++;
+      }
+    }
+    else
+    {
+      j--;
+      if (j >= 0)
+        i = selected[j] + 1;
+    }
+  }
+
+  free(selected);
+
+  return sum;
+}
+
+double mult_by_indexes(double *arr, unsigned int *indexes, unsigned int size)
+{
+  double res = 1;
+  for (int i = 0; i < size; i++)
+    res *= arr[indexes[i]];
+
+  return res;
+}
+
+/*
+ User Interface 
+*/
+
 /* Prints interpolation polynomial in Newton notation */
-void print_newton_poly(double *f, double *x, int n)
+void print_newton_poly(double *f, double *x, unsigned int n)
 {
   for (int i = 0; i < n; i++)
   {
@@ -60,6 +134,18 @@ void insert_coords(double *xes, double *yes, unsigned int n)
   }
 }
 
+void print_array(double *arr, unsigned int n)
+{
+  for (int i = 0; i < n; i++)
+    printf("%lf ", arr[i]);
+
+  printf("\n");
+}
+
+/* 
+ Main
+*/
+
 int main()
 {
   unsigned n = insert_n();
@@ -69,5 +155,15 @@ int main()
 
   insert_coords(x, y, n);
 
-  print_newton_poly(div_diff_es(x, y, n), x, n);
+  double *f = div_diff_es(x, y, n);
+
+  print_newton_poly(f, x, n);
+
+  double *coeficients = (double *)malloc(sizeof(double) * n);
+
+  simplify_polynomial(coeficients, f, x, n);
+
+  print_array(coeficients, n);
+
+  return 0;
 }

polynominal_interpolation.h

@@ -8,15 +8,24 @@
  Business logic
 */
 
-double div_diff(double *y, double *x, int i, int d);
+double div_diff(double *y, double *x, unsigned int i, unsigned int d);
-double *div_diff_es(double *x, double *y, int n);
+double *div_diff_es(double *x, double *y, unsigned int n);
 
 /*
  User interface
 */
 
 unsigned int insert_n();
-void print_newton_poly(double *f, double *x, int n);
+void print_newton_poly(double *f, double *x, unsigned int n);
 void insert_coords(double *x, double *y, unsigned int n);
+void print_array(double *arr, unsigned int n);
+
+/*
+ Coeficients of simplified polynomial computation
+*/
+
+void simplify_polynomial(double *res, double *rev_el_coef, double *x, unsigned int n);
+double compute_sum_of_multiplications_of_k(double *x, unsigned int k, unsigned int n);
+double mult_by_indexes(double *arr, unsigned int *indexes, unsigned int size);
 
 #endif