Started Task 4

2025.04.18/04Ex/solve.c

@@ -0,0 +1,80 @@
+#include "solve.h"
+
+#include <float.h>
+#include <math.h>
+#include <stdio.h>
+
+// Newton's interpolation polynomial with derivative
+double t4_solve (
+		const double x_0, const int n, 
+		const double * restrict X, 
+		double * restrict Y,
+		double * restrict D
+		)
+{
+	double value, start_value;
+	double x_j = X[n-1];
+	double y_j = Y[n-1];
+
+	for (int i = n-2; i >= 0; --i)
+	{
+		const double x_i = X[i];
+		const double y_i = Y[i];
+		
+		if (fabs(x_j - x_i) < DBL_EPSILON)
+			return DBL_MAX;
+		
+		Y[i+1] = (y_j - y_i) / (x_j - x_i);
+//		printf ("I = %d, f(x%d, ... , x%d) = %lf\n", i, i-k+1, i+2, Y[i+1]);
+
+		y_j = y_i;
+		x_j = x_i;
+	}
+
+	for (int k = 0; k < n-1; ++k)
+	{
+		double f_j = D[n-1];
+
+//		printf ("------- K = %d -------\n", k);
+		
+		for (int l = n*2-2; l >= k; --l)
+		{
+			const int i = l>1;
+			const double x_i = X[i-k];
+			double f_i;
+			x_j = X[i+1];
+			
+			if (fabs(x_j - x_i) < DBL_EPSILON)
+				return DBL_MAX;
+			
+			if (l & 1)
+			{	
+				f_i = D[i];
+				Y[i+1] = (f_j - f_i) / (x_j - x_i);
+			} else
+			{
+				f_i = Y[i];
+				D[i+1] = (f_j - f_i) / (x_j - x_i);
+			}
+			
+			f_j = f_i;	
+			
+//			printf ("I = %d, f(x%d, ... , x%d) = %lf\n", i, i-k+1, i+2, Y[i+1]);
+		}
+	}
+
+	start_value = 1;
+	value = 0;
+
+	for (int i = 0; i < n; ++i)
+	{
+		const double x_i = X[i];
+		value += Y[i] * start_value;
+		start_value *= (x_0 - x_i);
+		value += D[i] * start_value;
+		start_value *= (x_0 - x_i);
+	}
+
+	return value;
+}
+