SUBROUTINE DBSQAD(T,BCOEF,N,K,X1,X2,BQUAD,WORK)
C***BEGIN PROLOGUE  DBSQAD
C***DATE WRITTEN   800901   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  H2A2A1,E3,K6
C***KEYWORDS  B-SPLINE,DATA FITTING,DOUBLE PRECISION,INTERPOLATION,
C             QUADRATURE,SPLINE
C***AUTHOR  AMOS, D. E., (SNLA)
C***PURPOSE  Computes the integral on (X1,X2) of a K-th order
C            B-spline using the B-representation.
C***DESCRIPTION
C
C     Written by D. E. Amos, June, 1979.
C
C      Reference
C         SAND-79-1825
C
C     Abstract    **** a double precision routine ****
C
C         DBSQAD computes the integral on (X1,X2) of a K-th order
C         B-spline using the B-representation (T,BCOEF,N,K).  Orders
C         K as high as 20 are permitted by applying a 2, 6, or 10
C         point Gauss formula on subintervals of (X1,X2) which are
C         formed by included (distinct) knots.
C
C         If orders K greater than 20 are needed, use DBFQAD with
C         F(X) = 1.
C
C         The maximum number of significant digits obtainable in
C         DBSQAD is the smaller of 18 and the number of digits
C         carried in double precision arithmetic.
C
C         DBSQAD calls DINTRV, DBVALU, XERROR
C
C     Description of Arguments
C         Input      T,BCOEF,X1,X2 are double precision
C           T      - knot array of length N+K
C           BCOEF  - B-spline coefficient array of length N
C           N      - length of coefficient array
C           K      - order of B-spline, 1 .LE. K .LE. 20
C           X1,X2  - end points of quadrature interval in
C                    T(K) .LE. X .LE. T(N+1)
C
C         Output     BQUAD,WORK are double precision
C           BQUAD  - integral of the B-spline over (X1,X2)
C           WORK   - work vector of length 3*K
C
C     Error Conditions
C         Improper input is a fatal error
C***REFERENCES  D.E. AMOS, *QUADRATURE SUBROUTINES FOR SPLINES AND
C                 B-SPLINES*, SAND79-1825, SANDIA LABORATORIES,
C                 DECEMBER 1979.
C***ROUTINES CALLED  DBVALU,DINTRV,XERROR
C***END PROLOGUE  DBSQAD