# dppqad.f

          SUBROUTINE DPPQAD (LDC, C, XI, LXI, K, X1, X2, PQUAD)
    C***BEGIN PROLOGUE  DPPQAD
    C***PURPOSE  Compute the integral on (X1,X2) of a K-th order B-spline
    C            using the piecewise polynomial (PP) representation.
    C***LIBRARY   SLATEC
    C***CATEGORY  H2A2A1, E3, K6
    C***TYPE      DOUBLE PRECISION (PPQAD-S, DPPQAD-D)
    C***KEYWORDS  B-SPLINE, DATA FITTING, INTERPOLATION, QUADRATURE, SPLINES
    C***AUTHOR  Amos, D. E., (SNLA)
    C***DESCRIPTION
    C
    C     Abstract    **** a double precision routine ****
    C         DPPQAD computes the integral on (X1,X2) of a K-th order
    C         B-spline using the piecewise polynomial representation
    C         (C,XI,LXI,K).  Here the Taylor expansion about the left
    C         end point XI(J) of the J-th interval is integrated and
    C         evaluated on subintervals of (X1,X2) which are formed by
    C         included break points.  Integration outside (XI(1),XI(LXI+1))
    C         is permitted.
    C
    C     Description of Arguments
    C         Input      C,XI,X1,X2 are double precision
    C           LDC    - leading dimension of matrix C, LDC .GE. K
    C           C(I,J) - right Taylor derivatives at XI(J), I=1,K , J=1,LXI
    C           XI(*)  - break point array of length LXI+1
    C           LXI    - number of polynomial pieces
    C           K      - order of B-spline, K .GE. 1
    C           X1,X2  - end points of quadrature interval, normally in
    C                    XI(1) .LE. X .LE. XI(LXI+1)
    C
    C         Output     PQUAD is double precision
    C           PQUAD  - integral of the PP representation over (X1,X2)
    C
    C     Error Conditions
    C         Improper input is a fatal error
    C
    C***REFERENCES  D. E. Amos, Quadrature subroutines for splines and
    C                 B-splines, Report SAND79-1825, Sandia Laboratories,
    C                 December 1979.
    C***ROUTINES CALLED  DINTRV, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   800901  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (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  DPPQAD