Transcendent math functions

Functions
int DSPL_API	bessel_i0 (double *x, int n, double *y)
	Modified Bessel Function of the First Kind – \( I_0(x)\) [1]. More...
int DSPL_API	sine_int (double *x, int n, double *si)
	Sine integral function \(\textrm{Si}(x)\) for the real vector x. More...

Detailed Description

Function Documentation

bessel_i0()

int bessel_i0	(	double *	x,
		int	n,
		double *	y
	)

Modified Bessel Function of the First Kind – \( I_0(x)\) [1].

---

Parameters

[in]	x	Pointer to the function argument vector \( x \). Vector size is [n x 1]. Input vector must contain nonnegative values.
[in]	n	Input vector size x.
[out]	y	Pointer to \( I_0(x)\) function vector. Vector size is [n x 1]. Memory must be allocated.

Returns

RES_OK if function calculated successfully.
Else code error.

Note

[1] Rational Approximations for the Modified Bessel Function of the First Kind – I0(x) for Computations with Double Precision by PAVEL HOLOBORODKO on NOVEMBER 11, 2015

Example:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dspl.h"
 
#define N 50
 
 
 
/******************************************************************************
 * Main function
 ******************************************************************************/
int main(int argc, char* argv[])
{
 
    void* hdspl;    /* DSPL handle */
    void* hplot;    /* GNUPLOT handle */
    double x[N], y[N];
 
    /* Load DSPL function */
    hdspl = dspl_load();
 
    /* x in [0, 3] */
    linspace(0.0, 3.0, N, DSPL_SYMMETRIC, x);
 
    /* Bessel I0(x) function */
    bessel_i0(x, N, y);
 
    /* Write calculated values to the dat/dat0.txt file */
    writetxt(x, y, N, "dat/dat0.txt");
 
 
    /* plotting by GNUPLOT */
    gnuplot_create(argc, argv, 560, 380, "img/bessel_i0.png", &hplot);
    gnuplot_cmd(hplot, "set grid");
    gnuplot_cmd(hplot, "set xlabel 'x'");
    gnuplot_cmd(hplot, "set key left top");
    gnuplot_cmd(hplot, "set ylabel 'I_0(x)'");
    gnuplot_cmd(hplot, "set yrange [0:5]");
    gnuplot_cmd(hplot, "plot 'dat/dat0.txt' with lines");
    gnuplot_close(hplot);
 
 
    /* free dspl handle */
    dspl_free(hdspl);
 
    return 0;
}
 

Program calcultes \( I_0(x)\) function for x in \([0 \ 3]\) interval. Data saved if dat/dat0.txt file and shows on the plot

Author

Sergey Bakhurin www.dsplib.org

Definition at line 116 of file bessel_i0.c.

sine_int()

int sine_int	(	double *	x,
		int	n,
		double *	si
	)

Sine integral function \(\textrm{Si}(x)\) for the real vector x.

---

\[ \textrm{Si}(x) = \int_{0}^{x} \frac{\sin(x)}{x} \, dx\]

This function uses Padé approximants of the convergent Taylor series.

Parameters

[in]	x	Pointer to the input vector \( x \). Vector size is [n x 1]. Memory must be allocated.
[in]	n	Size of input vector x.
[out]	si	Pointer to the Si function vector. Vector size is [n x 1]. Memory must be allocated.

Returns

RES_OK if function calculated successfully.
Else code error.
Example:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dspl.h"
 
#define N 400
 
int main(int argc, char* argv[])
{
    void* hdspl;           /* DSPL handle        */
    void* hplot;           /* GNUPLOT handle     */
    hdspl = dspl_load();   /* Load DSPL function */
 
    double x[N], y[N];
 
    linspace(-6*M_PI, 6*M_PI, N, DSPL_PERIODIC, x);
 
    sine_int(x, N, y);
    writetxt(x, y, N, "dat/dat0.txt");
 
    sinc(x, N, 1.0, y);
    writetxt(x, y, N, "dat/dat1.txt");
 
    /* plotting by GNUPLOT */
    gnuplot_create(argc, argv, 560, 280, "img/sine_int.png", &hplot);
    gnuplot_cmd(hplot, "set grid");
    gnuplot_cmd(hplot, "set xlabel 'x'");
    gnuplot_cmd(hplot, "set lmargin at screen 0.10");
    gnuplot_cmd(hplot, "set key left top");
    gnuplot_cmd(hplot, "set ylabel 'Si(x), sinc(x)'");
    gnuplot_cmd(hplot, "set yrange [-2:2]");
    gnuplot_cmd(hplot, "plot   'dat/dat0.txt' with lines title 'Si(x)', \\");
    gnuplot_cmd(hplot, "       'dat/dat1.txt' with lines title 'sinc(x)'");
    gnuplot_close(hplot);
 
    dspl_free(hdspl);      // free dspl handle
 
    return 0;
}

This program calcultes sine integral \(\textrm{Si}(x)\) and \(\textrm{sinc}(x)\) functions for input x vector in interval \([-6\pi \ 6\pi]\). Functions values saved to th
dat/dat0.txt and dat/dat1.txt files and showed on the figure:

Author

Sergey Bakhurin www.dsplib.org

Definition at line 114 of file sine_int.c.