# qcheb.f

          SUBROUTINE QCHEB (X, FVAL, CHEB12, CHEB24)
    C***BEGIN PROLOGUE  QCHEB
    ....
    ....
    Warning:   this routine is not intended to be user-callable.
    ....
    ....
    C***SUBSIDIARY
    C***PURPOSE  This routine computes the CHEBYSHEV series expansion
    C            of degrees 12 and 24 of a function using A
    C            FAST FOURIER TRANSFORM METHOD
    C            F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
    C            F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
    C            Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.
    C***LIBRARY   SLATEC
    C***TYPE      SINGLE PRECISION (QCHEB-S, DQCHEB-D)
    C***KEYWORDS  CHEBYSHEV SERIES EXPANSION, FAST FOURIER TRANSFORM
    C***AUTHOR  Piessens, Robert
    C             Applied Mathematics and Programming Division
    C             K. U. Leuven
    C           de Doncker, Elise
    C             Applied Mathematics and Programming Division
    C             K. U. Leuven
    C***DESCRIPTION
    C
    C        Chebyshev Series Expansion
    C        Standard Fortran Subroutine
    C        Real version
    C
    C        PARAMETERS
    C          ON ENTRY
    C           X      - Real
    C                    Vector of dimension 11 containing the
    C                    Values COS(K*PI/24), K = 1, ..., 11
    C
    C           FVAL   - Real
    C                    Vector of dimension 25 containing the
    C                    function values at the points
    C                    (B+A+(B-A)*COS(K*PI/24))/2, K = 0, ...,24,
    C                    where (A,B) is the approximation interval.
    C                    FVAL(1) and FVAL(25) are divided by two
    C                    (these values are destroyed at output).
    C
    C          ON RETURN
    C           CHEB12 - Real
    C                    Vector of dimension 13 containing the
    C                    CHEBYSHEV coefficients for degree 12
    C
    C           CHEB24 - Real
    C                    Vector of dimension 25 containing the
    C                    CHEBYSHEV Coefficients for degree 24
    C
    C***SEE ALSO  QC25C, QC25F, QC25S
    C***ROUTINES CALLED  (NONE)
    C***REVISION HISTORY  (YYMMDD)
    C   810101  DATE WRITTEN
    C   830518  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900328  Added TYPE section.  (WRB)
    C***END PROLOGUE  QCHEB