SLATEC Routines --- DBVALU ---

*DECK DBVALU
      DOUBLE PRECISION FUNCTION DBVALU (T, A, N, K, IDERIV, X, INBV,
     +   WORK)
C***BEGIN PROLOGUE  DBVALU
C***PURPOSE  Evaluate the B-representation of a B-spline at X for the
C            function value or any of its derivatives.
C***LIBRARY   SLATEC
C***CATEGORY  E3, K6
C***TYPE      DOUBLE PRECISION (BVALU-S, DBVALU-D)
C***KEYWORDS  DIFFERENTIATION OF B-SPLINE, EVALUATION OF B-SPLINE
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         DBVALU is the BVALUE function of the reference.
C
C         DBVALU evaluates the B-representation (T,A,N,K) of a B-spline
C         at X for the function value on IDERIV=0 or any of its
C         derivatives on IDERIV=1,2,...,K-1.  Right limiting values
C         (right derivatives) are returned except at the right end
C         point X=T(N+1) where left limiting values are computed.  The
C         spline is defined on T(K) .LE. X .LE. T(N+1).  DBVALU returns
C         a fatal error message when X is outside of this interval.
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         DBVALU calls DINTRV
C
C     Description of Arguments
C
C         Input      T,A,X are double precision
C          T       - knot vector of length N+K
C          A       - B-spline coefficient vector of length N
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          IDERIV  - order of the derivative, 0 .LE. IDERIV .LE. K-1
C                    IDERIV = 0 returns the B-spline value
C          X       - argument, T(K) .LE. X .LE. T(N+1)
C          INBV    - an initialization parameter which must be set
C                    to 1 the first time DBVALU is called.
C
C         Output     WORK,DBVALU are double precision
C          INBV    - INBV contains information for efficient process-
C                    ing after the initial call and INBV must not
C                    be changed by the user.  Distinct splines require
C                    distinct INBV parameters.
C          WORK    - work vector of length 3*K.
C          DBVALU  - value of the IDERIV-th derivative at X
C
C     Error Conditions
C         An 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  DINTRV, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   800901  DATE WRITTEN
C   890831  Modified array declarations.  (WRB)
C   890911  Removed unnecessary intrinsics.  (WRB)
C   890911  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  DBVALU