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