BFQAD(3)

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

NAME
bfqad - Compute the integral of a product of a function and a derivative of a B-spline.

LIBRARY
SLATEC

CATEGORY
H2A2A1, E3, K6

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

KEYWORDS
INTEGRAL OF B-SPLINE, QUADRATURE

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract BFQAD 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 routine BSGQ8 (a modification of GAUS8), integrates the product on sub- intervals of (X1,X2) formed by included (distinct) knots. Description of Arguments Input F - external function of one argument for the integrand BF(X)=F(X)*BVALU(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.*STOL .LT. TOL .LE. 0.1 where STOL is the single precision unit roundoff for the machine = R1MACH(4) Output 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 X1 or X2 not in T(K) .LE. X .LE. T(N+1) is a fatal error. TOL not greater than the single precision unit roundoff or less than 0.1 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
BSGQ8, INTRV, R1MACH, 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)