PFQAD(3)

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

NAME
pfqad - 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
SINGLE PRECISION (PFQAD-S, DPFQAD-D)

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

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract PFQAD 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 rou- tine, PPGQ8(a modification of GAUS8), integrates the product on sub-intervals of (X1,X2) formed by the included break points. Integration outside of (XI(1),XI(LXI+1)) is permitted provided F is defined. Description of Arguments Input F - external function of one argument for the integrand PF(X)=F(X)*PPVAL(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.*STOL .LT. TOL .LE. 0.1 where STOL is the single precision unit roundoff for the machine = R1MACH(4) Output 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 TOL not greater than the single precision unit roundoff or less than 0.1 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
INTRV, PPGQ8, 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)