dbfqad.f
SUBROUTINE DBFQAD (F, T, BCOEF, N, K, ID, X1, X2, TOL, QUAD, IERR,
+ WORK)
C***BEGIN PROLOGUE DBFQAD
C***PURPOSE Compute the integral of a product of a function and a
C derivative of a K-th order B-spline.
C***LIBRARY SLATEC
C***CATEGORY H2A2A1, E3, K6
C***TYPE DOUBLE PRECISION (BFQAD-S, DBFQAD-D)
C***KEYWORDS INTEGRAL OF B-SPLINE, QUADRATURE
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C Abstract **** a double precision routine ****
C
C DBFQAD computes the integral on (X1,X2) of a product of a
C function F and the ID-th derivative of a K-th order B-spline,
C using the B-representation (T,BCOEF,N,K). (X1,X2) must be a
C subinterval of T(K) .LE. X .LE. T(N+1). An integration rou-
C tine, DBSGQ8 (a modification of GAUS8), integrates the product
C on subintervals of (X1,X2) formed by included (distinct) knots
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 Description of Arguments
C Input F,T,BCOEF,X1,X2,TOL are double precision
C F - external function of one argument for the
C integrand BF(X)=F(X)*DBVALU(T,BCOEF,N,K,ID,X,INBV,
C WORK)
C T - knot array of length N+K
C BCOEF - coefficient array of length N
C N - length of coefficient array
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 in
C T(K) .LE. X .LE. T(N+1)
C TOL - desired accuracy for the quadrature, suggest
C 10.*DTOL .LT. TOL .LE. .1 where DTOL is the maximum
C of 1.0D-18 and double precision unit roundoff for
C the machine = D1MACH(4)
C
C Output QUAD,WORK are double precision
C QUAD - integral of BF(X) on (X1,X2)
C IERR - a status code
C IERR=1 normal return
C 2 some quadrature on (X1,X2) does not meet
C the requested tolerance.
C WORK - work vector of length 3*K
C
C Error Conditions
C Improper input is a fatal error
C Some quadrature fails to meet the requested tolerance
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 D1MACH, DBSGQ8, DINTRV, XERMSG
C***REVISION HISTORY (YYMMDD)
C 800901 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 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 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DBFQAD