DBSQAD(3)

SYNOPSIS
SUBROUTINE DBSQAD (T, BCOEF, N, K, X1, X2, BQUAD, WORK)

NAME
dbsqad - Compute the integral of a K-th order B-spline using the B-representation.

LIBRARY
SLATEC

CATEGORY
H2A2A1, E3, K6

TYPE
DOUBLE PRECISION (BSQAD-S, DBSQAD-D)

KEYWORDS
INTEGRAL OF B-SPLINES, QUADRATURE

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract **** a double precision routine **** DBSQAD computes the integral on (X1,X2) of a K-th order B-spline using the B-representation (T,BCOEF,N,K). Orders K as high as 20 are permitted by applying a 2, 6, or 10 point Gauss formula on subintervals of (X1,X2) which are formed by included (distinct) knots. If orders K greater than 20 are needed, use DBFQAD with F(X) = 1. 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 T,BCOEF,X1,X2 are double precision T - knot array of length N+K BCOEF - B-spline coefficient array of length N N - length of coefficient array K - order of B-spline, 1 .LE. K .LE. 20 X1,X2 - end points of quadrature interval in T(K) .LE. X .LE. T(N+1) Output BQUAD,WORK are double precision BQUAD - integral of the B-spline over (X1,X2) WORK - work vector of length 3*K Error Conditions Improper input is a fatal error

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

ROUTINES CALLED
DBVALU, 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)