/***************************************************
*   Program to demonstrate Cheby_Ser() Function    *
* ------------------------------------------------ *
* Reference: BASIC Scientific Subroutines, Vol. II *
* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
*                                                  *
*             C++ Version By J.-P. Moreau, Paris.  *
*                     (www.jpmoreau.fr)            *
* ------------------------------------------------ *
* SAMPLE RUN:                                      *
*                                                  *
* Chebyshev polynomial coefficients for degree 2   *
*    A(0) = -1                                     *
*    A(1) = 0                                      *
*    A(2) = 2                                      *
*                                                  *
* Chebyshev polynomial coefficients for degree 3   *
*    A(0) = 0                                      *
*    A(1) = -3                                     *
*    A(2) = 0                                      *
*    A(3) = 4                                      *
*                                                  *
* Chebyshev polynomial coefficients for degree 4   *
*    A(0) = 1                                      *
*    A(1) = 0                                      *
*    A(2) = -8                                     *
*    A(3) = 0                                      *
*    A(4) = 8                                      *
*                                                  *
* Chebyshev polynomial coefficients for degree 5   *
*    A(0) = 0                                      *
*    A(1) = 5                                      *
*    A(2) = 0                                      *
*    A(3) = -20                                    *
*    A(4) = 0                                      *
*    A(5) = 16                                     *
*                                                  *
* Chebyshev polynomial coefficients for degree 6   *
*    A(0) = -1                                     *
*    A(1) = 0                                      *
*    A(2) = 18                                     *
*    A(3) = 0                                      *
*    A(4) = -48                                    *
*    A(5) = 0                                      *
*    A(6) = 32                                     *
*                                                  *
* Chebyshev polynomial coefficients for degree 7   *
*    A(0) = 0                                      *
*    A(1) = -7                                     *
*    A(2) = 0                                      *
*    A(3) = 56                                     *
*    A(4) = 0                                      *
*    A(5) = -112                                   *
*    A(6) = 0                                      *
*    A(7) = 64                                     *
*                                                  *
* Chebyshev polynomial coefficients for degree 8   *
*    A(0) = 1                                      *
*    A(1) = 0                                      *
*    A(2) = -32                                    *
*    A(3) = 0                                      *
*    A(4) = 160                                    *
*    A(5) = 0                                      *
*    A(6) = -256                                   *
*    A(7) = 0                                      *
*    A(8) = 128                                    *
*                                                  *
* Chebyshev polynomial coefficients for degree 9   *
*    A(0) = 0                                      *
*    A(1) = 9                                      *
*    A(2) = 0                                      *
*    A(3) = -120                                   *
*    A(4) = 0                                      *
*    A(5) = 432                                    *
*    A(6) = 0                                      *
*    A(7) = -576                                   *
*    A(8) = 0                                      *
*    A(9) = 256                                    *
*                                                  *
* Chebyshev polynomial coefficients for degree 10  *
*    A(0) = -1                                     *
*    A(1) = 0                                      *
*    A(2) = 50                                     *
*    A(3) = 0                                      *
*    A(4) = -400                                   *
*    A(5) = 0                                      *
*    A(6) = 1120                                   *
*    A(7) = 0                                      *
*    A(8) = -1280                                  *
*    A(9) = 0                                      *
*    A(10) = 512                                   *
*                                                  *
***************************************************/
#include <stdio.h>
#include <math.h>

#define SIZE  10

double B[SIZE+1][SIZE+1];

int    i, n;


/*******************************************************
* Chebyshev series coefficients evaluation subroutine  *
* ---------------------------------------------------- *
* The order of the polynomial is n. The coefficients   *
* are returned in the array B[i,j), i is the degree of *
* the polynomial, j is the coefficient order.          *
*******************************************************/
void Cheby_Ser()  {
  int i, j;
  // Establish t0 and t1 coefficients
  B[0][0] = 1; B[1][0] = 0; B[1][1] = 1;
  // Return if order is less than two
  if (n < 2) return;
  for (i = 2; i < n+1; i++)  {
    for (j = 1; j < i+1; j++)
      // Basic recursion relation
      B[i][j] = 2 * B[i - 1][j - 1] - B[i - 2][j];
    B[i][0] = -B[i - 2][0];
  }
}


void main()  {
  printf("\n");
  for (n = 2; n < SIZE+1; n++) {
    Cheby_Ser();
    printf(" Chebyshev polynomial coefficients for degree %d\n\n",n);
    for (i = 0; i < n+1; i++)
      printf("  A(%d) = %5.0f\n",i,B[n][i]); 
    if (n < SIZE) getchar();
  }
  printf("\n");
}


// End of file chebyser.cpp