SLATEC Routines --- DBSPEV ---

*DECK DBSPEV
      SUBROUTINE DBSPEV (T, AD, N, K, NDERIV, X, INEV, SVALUE, WORK)
C***BEGIN PROLOGUE  DBSPEV
C***PURPOSE  Calculate the value of the spline and its derivatives from
C            the B-representation.
C***LIBRARY   SLATEC
C***CATEGORY  E3, K6
C***TYPE      DOUBLE PRECISION (BSPEV-S, DBSPEV-D)
C***KEYWORDS  B-SPLINE, DATA FITTING, INTERPOLATION, SPLINES
C***AUTHOR  Amos, D. E., (SNLA)
C***DESCRIPTION
C
C     Written by Carl de Boor and modified by D. E. Amos
C
C     Abstract    **** a double precision routine ****
C         DBSPEV is the BSPLEV routine of the reference.
C
C         DBSPEV calculates the value of the spline and its derivatives
C         at X from the B-representation (T,A,N,K) and returns them in
C         SVALUE(I),I=1,NDERIV, T(K) .LE. X .LE. T(N+1).  AD(I) can be
C         the B-spline coefficients A(I), I=1,N) if NDERIV=1.  Otherwise
C         AD must be computed before hand by a call to DBSPDR (T,A,N,K,
C         NDERIV,AD).  If X=T(I),I=K,N), right limiting values are
C         obtained.
C
C         To compute left derivatives or left limiting values at a
C         knot T(I), replace N by I-1 and set X=T(I), I=K+1,N+1.
C
C         DBSPEV calls DINTRV, DBSPVN
C
C     Description of Arguments
C
C         Input      T,AD,X, are double precision
C          T       - knot vector of length N+K
C          AD      - vector of length (2*N-NDERIV+1)*NDERIV/2 containing
C                    the difference table from DBSPDR.
C          N       - number of B-spline coefficients
C                    N = sum of knot multiplicities-K
C          K       - order of the B-spline, K .GE. 1
C          NDERIV  - number of derivatives, 1 .LE. NDERIV .LE. K.
C                    NDERIV=1 gives the zero-th derivative =
C                    function value
C          X       - argument, T(K) .LE. X .LE. T(N+1)
C          INEV    - an initialization parameter which must be set
C                    to 1 the first time DBSPEV is called.
C
C         Output     SVALUE,WORK are double precision
C          INEV    - INEV contains information for efficient process-
C                    ing after the initial call and INEV must not
C                    be changed by the user.  Distinct splines require
C                    distinct INEV parameters.
C          SVALUE  - vector of length NDERIV containing the spline
C                    value in SVALUE(1) and the NDERIV-1 derivatives
C                    in the remaining components.
C          WORK    - work vector of length 3*K
C
C     Error Conditions
C         Improper input is a fatal error.
C
C***REFERENCES  Carl de Boor, Package for calculating with B-splines,
C                 SIAM Journal on Numerical Analysis 14, 3 (June 1977),
C                 pp. 441-472.
C***ROUTINES CALLED  DBSPVN, DINTRV, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   800901  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   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DBSPEV