SUBROUTINE PFQAD(F,LDC,C,XI,LXI,K,ID,X1,X2,TOL,QUAD,IERR)
C***BEGIN PROLOGUE  PFQAD
C***DATE WRITTEN   800901   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  H2A2A1,E3,K6
C***KEYWORDS  B-SPLINE,DATA FITTING,INTERPOLATION,QUADRATURE,SPLINE
C***AUTHOR  AMOS, D. E., (SNLA)
C***PURPOSE  Computes the integral on (X1,X2) of a product of a function
C            F and the ID-th derivative of a B-spline,
C            (PP-representation).
C***DESCRIPTION
C
C     Written by D. E. Amos, June, 1979.
C
C     Reference SAND-79-1825
C
C     Abstract
C         PFQAD computes the integral on (X1,X2) of a product of a
C         function F and the ID-th derivative of a B-spline, using the
C         PP-representation (C,XI,LXI,K). (X1,X2) is normally a sub-
C         interval of XI(1) .LE. X .LE. XI(LXI+1).  An integration rou-
C         tine, PPGQ8(a modification of GAUS8), integrates the product
C         on sub-intervals of (X1,X2) formed by the included break
C         points.  Integration outside of (XI(1),XI(LXI+1)) is permitted
C         provided F is defined.
C
C         PFQAD calls INTRV, PPVAL, PPGQ8, R1MACH, XERROR
C
C     Description of Arguments
C         Input
C           F      - external function of one argument for the
C                    integrand PF(X)=F(X)*PPVAL(LDC,C,XI,LXI,K,ID,X,
C                    INPPV)
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           ID     - order of the spline derivative, 0 .LE. ID .LE. K-1
C                    ID=0 gives the spline function
C           X1,X2  - end points of quadrature interval, normally in
C                    XI(1) .LE. X .LE. XI(LXI+1)
C           TOL    - desired accuracy for the quadrature, suggest
C                    10.*STOL .LT. TOL .LE. 0.1 where STOL is the single
C                    precision unit roundoff for the machine = R1MACH(4)
C
C         Output
C           QUAD   - integral of PF(X) on (X1,X2)
C           IERR   - a status code
C                    IERR=1 normal return
C                         2 some quadrature does not meet the
C                           requested tolerance
C
C     Error Conditions
C         TOL not greater than the single precision unit roundoff or
C         less than 0.1 is a fatal error.
C         Some quadrature does not meet the requested tolerance.
C***REFERENCES  D.E. AMOS, *QUADRATURE SUBROUTINES FOR SPLINES AND
C                 B-SPLINES*, SAND79-1825, SANDIA LABORATORIES,
C                 DECEMBER 1979.
C***ROUTINES CALLED  INTRV,PPGQ8,R1MACH,XERROR
C***END PROLOGUE  PFQAD