DBFQAD(3)

SYNOPSIS
SUBROUTINE DBFQAD (F, T, BCOEF, N, K, ID, X1, X2, TOL, QUAD, IERR, + WORK)

NAME
dbfqad - Compute the integral of a product of a function and a derivative of a K-th order B-spline.

LIBRARY
SLATEC

CATEGORY
H2A2A1, E3, K6

TYPE
DOUBLE PRECISION (BFQAD-S, DBFQAD-D)

KEYWORDS
INTEGRAL OF B-SPLINE, QUADRATURE

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract **** a double precision routine **** DBFQAD computes the integral on (X1,X2) of a product of a function F and the ID-th derivative of a K-th order B-spline, using the B-representation (T,BCOEF,N,K). (X1,X2) must be a subinterval of T(K) .LE. X .LE. T(N+1). An integration rou- tine, DBSGQ8 (a modification of GAUS8), integrates the product on subintervals of (X1,X2) formed by included (distinct) knots The maximum number of significant digits obtainable in DBSQAD is the smaller of 18 and the number of digits carried in double precision arithmetic. Description of Arguments Input F,T,BCOEF,X1,X2,TOL are double precision F - external function of one argument for the integrand BF(X)=F(X)*DBVALU(T,BCOEF,N,K,ID,X,INBV, WORK) T - knot array of length N+K BCOEF - coefficient array of length N N - length of coefficient array K - order of B-spline, K .GE. 1 ID - order of the spline derivative, 0 .LE. ID .LE. K-1 ID=0 gives the spline function X1,X2 - end points of quadrature interval in T(K) .LE. X .LE. T(N+1) TOL - desired accuracy for the quadrature, suggest 10.*DTOL .LT. TOL .LE. .1 where DTOL is the maximum of 1.0D-18 and double precision unit roundoff for the machine = D1MACH(4) Output QUAD,WORK are double precision QUAD - integral of BF(X) on (X1,X2) IERR - a status code IERR=1 normal return 2 some quadrature on (X1,X2) does not meet the requested tolerance. WORK - work vector of length 3*K Error Conditions Improper input is a fatal error Some quadrature fails to meet the requested tolerance

REFERENCES
D. E. Amos, Quadrature subroutines for splines and B-splines, Report SAND79-1825, Sandia Laboratories, December 1979.

ROUTINES CALLED
D1MACH, DBSGQ8, DINTRV, XERMSG

REVISION HISTORY (YYMMDD)
800901 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890531 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)