dcsevl.f

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*DECK DCSEVL
      DOUBLE PRECISION FUNCTION dcsevl (X, CS, N)
C***BEGIN PROLOGUE  DCSEVL
C***PURPOSE  Evaluate a Chebyshev series.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C3A2
C***TYPE      DOUBLE PRECISION (CSEVL-S, DCSEVL-D)
C***KEYWORDS  CHEBYSHEV SERIES, FNLIB, SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C  Evaluate the N-term Chebyshev series CS at X.  Adapted from
C  a method presented in the paper by Broucke referenced below.
C
C       Input Arguments --
C  X    value at which the series is to be evaluated.
C  CS   array of N terms of a Chebyshev series.  In evaluating
C       CS, only half the first coefficient is summed.
C  N    number of terms in array CS.
C
C***REFERENCES  R. Broucke, Ten subroutines for the manipulation of
C                 Chebyshev series, Algorithm 446, Communications of
C                 the A.C.M. 16, (1973) pp. 254-256.
C               L. Fox and I. B. Parker, Chebyshev Polynomials in
C                 Numerical Analysis, Oxford University Press, 1968,
C                 page 56.
C***ROUTINES CALLED  D1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   770401  DATE WRITTEN
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   900329  Prologued revised extensively and code rewritten to allow
C           X to be slightly outside interval (-1,+1).  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DCSEVL
      DOUBLE PRECISION b0, b1, b2, cs(*), onepl, twox, x, d1mach
      LOGICAL first
      SAVE first, onepl
      DATA first /.true./
C***FIRST EXECUTABLE STATEMENT  DCSEVL
      IF (first) onepl = 1.0d0 + d1mach(4)
      first = .false.
      IF (n .LT. 1) CALL xermsg ('SLATEC', 'DCSEVL',
     +   .LE.'NUMBER OF TERMS  0', 2, 2)
      IF (n .GT. 1000) CALL xermsg ('SLATEC', 'DCSEVL',
     +   .GT.'NUMBER OF TERMS  1000', 3, 2)
      IF (abs(x) .GT. onepl) CALL xermsg ('SLATEC', 'DCSEVL',
     +   'X OUTSIDE THE INTERVAL (-1,+1)', 1, 1)
C
      b1 = 0.0d0
      b0 = 0.0d0
      twox = 2.0d0*x
      DO 10 i = 1,n
         b2 = b1
         b1 = b0
         ni = n + 1 - i
         b0 = twox*b1 - b2 + cs(ni)
   10 CONTINUE
C
      dcsevl = 0.5d0*(b0-b2)
C
      RETURN
      END