DPPQAD(3)

SYNOPSIS
SUBROUTINE DPPQAD (LDC, C, XI, LXI, K, X1, X2, PQUAD)

NAME
dppqad - Compute the integral on (X1,X2) of a K-th order B-spline using the piecewise polynomial (PP) representation.

LIBRARY
SLATEC

CATEGORY
H2A2A1, E3, K6

TYPE
DOUBLE PRECISION (PPQAD-S, DPPQAD-D)

KEYWORDS
B-SPLINE, DATA FITTING, INTERPOLATION, QUADRATURE, SPLINES

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract **** a double precision routine **** DPPQAD computes the integral on (X1,X2) of a K-th order B-spline using the piecewise polynomial representation (C,XI,LXI,K). Here the Taylor expansion about the left end point XI(J) of the J-th interval is integrated and evaluated on subintervals of (X1,X2) which are formed by included break points. Integration outside (XI(1),XI(LXI+1)) is permitted. Description of Arguments Input C,XI,X1,X2 are double precision LDC - leading dimension of matrix C, LDC .GE. K C(I,J) - right Taylor derivatives at XI(J), I=1,K , J=1,LXI XI(*) - break point array of length LXI+1 LXI - number of polynomial pieces K - order of B-spline, K .GE. 1 X1,X2 - end points of quadrature interval, normally in XI(1) .LE. X .LE. XI(LXI+1) Output PQUAD is double precision PQUAD - integral of the PP representation over (X1,X2) 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
DINTRV, XERMSG

REVISION HISTORY (YYMMDD)
800901 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890911 Removed unnecessary intrinsics. (WRB)
890911 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)
920501 Reformatted the REFERENCES section. (WRB)