DPFQAD(3)

SYNOPSIS
SUBROUTINE DPFQAD (F, LDC, C, XI, LXI, K, ID, X1, X2, TOL, QUAD, + IERR)

NAME
dpfqad - Compute the integral on (X1,X2) of a product of a function F and the ID-th derivative of a B-spline, (PP-representation).

LIBRARY
SLATEC

CATEGORY
H2A2A1, E3, K6

TYPE
DOUBLE PRECISION (PFQAD-S, DPFQAD-D)

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

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract **** a double precision routine **** DPFQAD computes the integral on (X1,X2) of a product of a function F and the ID-th derivative of a B-spline, using the PP-representation (C,XI,LXI,K). (X1,X2) is normally a sub- interval of XI(1) .LE. X .LE. XI(LXI+1). An integration routine, DPPGQ8 (a modification of GAUS8), integrates the product on subintervals of (X1,X2) formed by the included break points. Integration outside of (XI(1),XI(LXI+1)) is permitted provided F is defined. 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,C,XI,X1,X2,TOL are double precision F - external function of one argument for the integrand PF(X)=F(X)*DPPVAL(LDC,C,XI,LXI,K,ID,X, INPPV) 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 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, normally in XI(1) .LE. X .LE. XI(LXI+1) TOL - desired accuracy for the quadrature, suggest 10.*DTOL .LT. TOL .LE. 0.1 where DTOL is the maximum of 1.0D-18 and double precision unit roundoff for the machine = D1MACH(4) Output QUAD is double precision QUAD - integral of PF(X) on (X1,X2) IERR - a status code IERR=1 normal return 2 some quadrature does not meet the requested tolerance Error Conditions Improper input is a fatal error. Some quadrature does not 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, DINTRV, DPPGQ8, 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)