!-------------------------------------------------------------------------------
!> Summary: Computes the coefficients in the Chebychev expansion
!> Author:
!> Deprecated: False
!-------------------------------------------------------------------------------
!> see: p.80 in algorithms for the computation
!> of mathematical functions, y.l.luke, academic press,london 1977
!>
!> Computes the coefficients in the chebychev expansion of 0f1(;c;z)
!>
!> Description of variables:
!> cp input - parameter c in 0f1(;c;z)
!> w input - this is a preselected scale factor such that \(0 \leq z/w \leq 1\)
!> n input - two less than the number of coefficients to be generated
!> c output - a vector containing the n+2 Chebychev coefficients
!> sum output - the sum of the coefficients
!> all other variables are for internal use
!-------------------------------------------------------------------------------
MODULE MOD_CNWF011
CONTAINS
!-------------------------------------------------------------------------------
!> Summary: Computes the coefficients in the Chebychev expansion of 0f1(;c;z)
!> Author:
!> Date:
!> Category: KKRimp, special-functions, numerical-tools
!> Deprecated: False
!-------------------------------------------------------------------------------
SUBROUTINE CNWF011(CP,W,N,C,SUM)
c**********************************************************************
C .. Scalar Arguments ..
REAL*8 CP !! Parameter c in 0f1(;c;z)
REAL*8 SUM !! Sum of the coefficients
REAL*8 W !! Preselected scale factor such that \(0 \leq z/w \leq 1\)
INTEGER N !! Two less than the number of coefficients to be generated
C ..
C .. Array Arguments ..
REAL*8 C(*) !! Vector containing the n+2 Chebychev coefficients
C ..
C .. Local Scalars ..
REAL*8 A1,A2,A3,C1,DIVFAC,FOUR,ONE,P,RHO,START,TWO,X1,
+ Z1,ZERO
INTEGER I,K,L,N1,N2,NCOUNT
C ..
C .. Save statement ..
SAVE ZERO,ONE,TWO,FOUR,START
C ..
C .. Data statements ..
DATA ZERO,ONE,TWO,FOUR,START/0.D0,1.D0,2.D0,4.D0,1.D-20/
C ..
N1 = N + 1
N2 = N + 2
c
c ------- start computing coefficients by means of --------------
c ------- backward recurrence scheme --------------
A3 = ZERO
A2 = ZERO
A1 = START
Z1 = FOUR/W
NCOUNT = N2
C(NCOUNT) = START
X1 = N2
C1 = ONE - CP
DO 10 K = 1,N1
DIVFAC = ONE/X1
X1 = X1 - ONE
NCOUNT = NCOUNT - 1
C(NCOUNT) = X1* ((DIVFAC+Z1* (X1-C1))*A1+
+ (ONE/X1+Z1* (X1+C1+ONE))*A2-DIVFAC*A3)
A3 = A2
A2 = A1
A1 = C(NCOUNT)
10 CONTINUE
C(1) = C(1)/TWO
c
c --------- compute scale factor --------------
RHO = C(1)
SUM = RHO
P = ONE
DO 20 I = 2,N2
RHO = RHO - P*C(I)
SUM = SUM + C(I)
P = -P
20 CONTINUE
c
c ---------- scale coefficients ------------
DO 30 L = 1,N2
C(L) = C(L)/RHO
30 CONTINUE
SUM = SUM/RHO
END SUBROUTINE
END MODULE MOD_CNWF011
