FUNCTION BVALU(T,A,N,K,IDERIV,X,INBV,WORK)
C***BEGIN PROLOGUE  BVALU
C***DATE WRITTEN   800901   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  E3,K6
C***KEYWORDS  B-SPLINE,DATA FITTING,INTERPOLATION,SPLINE
C***AUTHOR  AMOS, D. E., (SNLA)
C***PURPOSE  Evaluates the B-representation of a B-spline at X for the
C            function value or any of its derivatives.
C***DESCRIPTION
C
C     Written by Carl de Boor and modified by D. E. Amos
C
C     Reference
C         SIAM J. Numerical Analysis, 14, No. 3, June, 1977, pp.441-472.
C
C     Abstract
C         BVALU is the BVALUE function of the reference.
C
C         BVALU 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).  BVALU 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         BVALU calls INTRV
C
C     Description of Arguments
C         Input
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 BVALU is called.
C
C         Output
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          BVALU   - value of the IDERIV-th derivative at X
C
C     Error Conditions
C         An improper input is a fatal error
C***REFERENCES  C. DE BOOR, *PACKAGE FOR CALCULATING WITH B-SPLINES*,
C                 SIAM JOURNAL ON NUMERICAL ANALYSIS, VOLUME 14, NO. 3,
C                 JUNE 1977, PP. 441-472.
C***ROUTINES CALLED  INTRV,XERROR
C***END PROLOGUE  BVALU