/**************************************************
* Chebyshev Approximation of a user defined real  *
* function FUNC(X) in double precision.           *
* ----------------------------------------------- *
* SAMPLE RUN:                                     *
* (Approximate derivative of sin(x) from x=0 to   *
*  x=PI).                                         *
*                                                 *
*      X          Chebyshev Eval.     COS(X)      *
*                 of derivative                   *
* ----------------------------------------------  *
*  0.00000000      0.99999707      1.00000000     *
*  0.15707963      0.98768900      0.98768834     *
*  0.31415927      0.95105644      0.95105652     *
*  0.47123890      0.89100611      0.89100652     *
*  0.62831853      0.80901694      0.80901699     *
*  0.78539816      0.70710708      0.70710678     *
*  0.94247780      0.58778552      0.58778525     *
*  1.09955743      0.45399047      0.45399050     *
*  1.25663706      0.30901672      0.30901699     *
*  1.41371669      0.15643421      0.15643447     *
*  1.57079633     -0.00000000      0.00000000     *
*  1.72787596     -0.15643421     -0.15643447     *
*  1.88495559     -0.30901672     -0.30901699     *
*  2.04203522     -0.45399047     -0.45399050     *
*  2.19911486     -0.58778552     -0.58778525     *
*  2.35619449     -0.70710708     -0.70710678     *
*  2.51327412     -0.80901694     -0.80901699     *
*  2.67035376     -0.89100611     -0.89100652     *
*  2.82743339     -0.95105644     -0.95105652     *
*  2.98451302     -0.98768900     -0.98768834     *
*  3.14159265     -0.99999707     -1.00000000     *
*                                                 *
*               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   CHDER(double,double,double *,double *,int);
    
    double X0,X1, COEFF[NMAX], CDER[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 derivative of FUNC(x)
  CHDER(X0,X1,COEFF,CDER,N);

  NPTS=21;
  DX=(X1-X0)/(NPTS-1);
  X=X0-DX;

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

}

// end of file Tchebder.cpp