/**************************************************
* Chebyshev Approximation of a user defined real  *
* function FUNC(X) in double precision.           *
* ----------------------------------------------- *
* SAMPLE RUN:                                     *
* (Approximate integral of sin(x) from x=0 to     *
*  x=PI).                                         *
*                                                 *
*      X          Chebyshev Eval.   -COS(X)+1     *
*                  of integral                    *
* ----------------------------------------------  *
*  0.00000000      -0.00000000      0.00000000    *
*  0.15707963       0.01231166      0.01231166    *
*  0.31415927       0.04894348      0.04894348    *
*  0.47123890       0.10899348      0.10899348    *
*  0.62831853       0.19098301      0.19098301    *
*  0.78539816       0.29289321      0.29289322    *
*  0.94247780       0.41221474      0.41221475    *
*  1.09955743       0.54600950      0.54600950    *
*  1.25663706       0.69098301      0.69098301    *
*  1.41371669       0.84356554      0.84356553    *
*  1.57079633       1.00000000      1.00000000    *
*  1.72787596       1.15643446      1.15643447    *
*  1.88495559       1.30901699      1.30901699    *
*  2.04203522       1.45399050      1.45399050    *
*  2.19911486       1.58778526      1.58778525    *
*  2.35619449       1.70710679      1.70710678    *
*  2.51327412       1.80901699      1.80901699    *
*  2.67035376       1.89100652      1.89100652    *
*  2.82743339       1.95105651      1.95105652    *
*  2.98451302       1.98768834      1.98768834    *
*  3.14159265       2.00000000      2.00000000    *
*                                                 *
*               C++ Release By J-P Moreau, Paris. *
*                      (www.jpmoreau.fr)          *
**************************************************/
// To link with Chebyshe.cpp
#include <stdio.h>
#include <math.h>

#define  NMAX  51
#define  HALF  0.5
#define  ONE   1.0
#define  TWO   2.0
#define  ZERO  0.0
#define  PI    4.0*atan(1.0)


    void   CHEBFT(double, double, double *, int);
    double CHEBEV(double, double, double *, int, double);
    void   CHINT(double,double,double *,double *,int);
    
    double X0,X1, COEFF[NMAX], CINT[NMAX];
    double DX, X;
    int I,N,NPTS;

    // user defined function
    double FUNC(double x) {
      return (sin(x));
    }

void main() {

  N=10;
  X0=ZERO; X1=PI;

// calculate Chebyshev coefficients of FUNC(x)
  CHEBFT(X0,X1,COEFF,N);

// calculate Chebyshev coefficients of integral of FUNC(x)
  CHINT(X0,X1,COEFF,CINT,N);

  NPTS=2*N+1;
  DX=(X1-X0)/(NPTS-1);
  X=X0-DX;

  printf("      X        Chebyshev Eval.   -COS(X)+1   \n");
  printf("                of integral                  \n");
  printf(" --------------------------------------------\n");
  for (I=1; I<=NPTS; I++) {
    X += DX;
    printf("%11.8f %15.8f %15.8f\n", X, CHEBEV(X0,X1,CINT,N,X), -cos(X)+ONE);
  }

}

// end of file Tchebint.cpp