cub_spline_integral
Computes the integral of a cubic spline.
Synopsis
#include <imsl.h>
float imsl_f_cub_spline_integral (float a, float b, Imsl_f_ppoly *ppoly)
The type double function is imsl_d_cub_spline_integral.
Required Arguments
float a (Input)
float b (Input)
Endpoints for integration.
Imsl_f_ppoly *ppoly (Input)
Pointer to the piecewise polynomial structure that represents the cubic spline.
Return Value
The integral from a to b of the cubic spline. If no value can be computed, then NaN is returned.
Description
The function imsl_f_cub_spline_integral computes the integral of a cubic spline from a to b.
Example
In this example, a cubic spline interpolant to a function f is computed. The values of the integral of this spline are then compared with the exact integral values. Since the default settings are used, the interpolant is determined by the “not-a-knot” condition (see de Boor 1978).
#include <imsl.h>
#include <stdio.h>
#include <math.h>
#define NDATA 21
/* Define function */
#define F(x) (float)(sin(15.0*x))
/* Integral from 0 to x */
#define FI(x) (float)((1.-cos(15.0*x))/15.)
int main()
{
int i;
float fdata[NDATA], xdata[NDATA], x, y;
Imsl_f_ppoly *pp;
/* Set up a grid */
for (i = 0; i < NDATA; i++) {
xdata[i] = (float)i /((float)(NDATA-1));
fdata[i] = F(xdata[i]);
}
/* Compute cubic spline interpolant */
pp = imsl_f_cub_spline_interp_e_cnd (NDATA, xdata, fdata, 0);
/* Print results */
printf(" x FI(x) Interpolant Integral Error\n");
for (i = NDATA/2; i < 3*NDATA/2; i++){
x = (float) i /(float)(2*NDATA-2);
y = imsl_f_cub_spline_integral(0.0, x, pp);
printf(" %6.3f %10.3f %10.3f %10.4f\n", x, FI(x), y,
fabs(FI(x)-y));
}
}
Output
x FI(x) Interpolant Integral Error
0.250 0.121 0.121 0.0001
0.275 0.104 0.104 0.0001
0.300 0.081 0.081 0.0001
0.325 0.056 0.056 0.0001
0.350 0.033 0.033 0.0001
0.375 0.014 0.014 0.0002
0.400 0.003 0.003 0.0002
0.425 0.000 0.000 0.0002
0.450 0.007 0.007 0.0002
0.475 0.022 0.022 0.0001
0.500 0.044 0.044 0.0001
0.525 0.068 0.068 0.0001
0.550 0.092 0.092 0.0001
0.575 0.113 0.113 0.0001
0.600 0.127 0.128 0.0001
0.625 0.133 0.133 0.0001
0.650 0.130 0.130 0.0001
0.675 0.118 0.118 0.0001
0.700 0.098 0.098 0.0001
0.725 0.075 0.075 0.0001
0.750 0.050 0.050 0.0001