DPCHIA(3)

SYNOPSIS
DOUBLE PRECISION FUNCTION DPCHIA (N, X, F, D, INCFD, SKIP, A, B, + IERR)

NAME
dpchia - Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

LIBRARY
SLATEC (PCHIP)

CATEGORY
E3, H2A1B2

TYPE
DOUBLE PRECISION (PCHIA-S, DPCHIA-D)

KEYWORDS
CUBIC HERMITE INTERPOLATION, NUMERICAL INTEGRATION, PCHIP, QUADRATURE

AUTHOR
Fritsch, F. N., (LLNL) Lawrence Livermore National Laboratory P.O. Box 808 (L-316) Livermore, CA 94550 FTS 532-4275, (510) 422-4275

DESCRIPTION
DPCHIA: Piecewise Cubic Hermite Integrator, Arbitrary limits Evaluates the definite integral of the cubic Hermite function defined by N, X, F, D over the interval [A, B]. To provide compatibility with DPCHIM and DPCHIC, includes an increment between successive values of the F- and D-arrays. ---------------------------------------------------------------------- Calling sequence: PARAMETER (INCFD = ...) INTEGER N, IERR DOUBLE PRECISION X(N), F(INCFD,N), D(INCFD,N), A, B DOUBLE PRECISION VALUE, DPCHIA LOGICAL SKIP VALUE = DPCHIA (N, X, F, D, INCFD, SKIP, A, B, IERR) Parameters: VALUE -- (output) value of the requested integral. N -- (input) number of data points. (Error return if N.LT.2 .) X -- (input) real*8 array of independent variable values. The elements of X must be strictly increasing: X(I-1) .LT. X(I), I = 2(1)N. (Error return if not.) F -- (input) real*8 array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I). D -- (input) real*8 array of derivative values. D(1+(I-1)*INCFD) is the value corresponding to X(I). INCFD -- (input) increment between successive values in F and D. (Error return if INCFD.LT.1 .) SKIP -- (input/output) logical variable which should be set to preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed (say, in DPCHIM or DPCHIC). SKIP will be set to .TRUE. on return with IERR.GE.0 . A,B -- (input) the limits of integration. NOTE: There is no requirement that [A,B] be contained in [X(1),X(N)]. However, the resulting integral value will be highly suspect, if not. IERR -- (output) error flag. Normal return: IERR = 0 (no errors). Warning errors: IERR = 1 if A is outside the interval [X(1),X(N)]. IERR = 2 if B is outside the interval [X(1),X(N)]. IERR = 3 if both of the above are true. (Note that this means that either [A,B] contains data interval or the intervals do not intersect at all.) "Recoverable" errors: IERR = -1 if N.LT.2 . IERR = -2 if INCFD.LT.1 . IERR = -3 if the X-array is not strictly increasing. (VALUE will be zero in any of these cases.) NOTE: The above errors are checked in the order listed, and following arguments have **NOT** been validated. IERR = -4 in case of an error return from DPCHID (which should never occur).

REFERENCES
(NONE)

ROUTINES CALLED
DCHFIE, DPCHID, XERMSG

REVISION HISTORY (YYMMDD)
820730 DATE WRITTEN
820804 Converted to SLATEC library version.
870707 Corrected XERROR calls for d.p. name(s).
870707 Corrected conversion to double precision.
870813 Minor cosmetic changes.
890206 Corrected XERROR calls.
890411 Added SAVE statements (Vers. 3.2).
890531 Changed all specific intrinsics to generic. (WRB)
890703 Corrected category record. (WRB)
890831 Modified array declarations. (WRB)
891006 Cosmetic changes to prologue. (WRB)
891006 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)
930503 Corrected to set VALUE=0 when IERR.lt.0. (FNF)
930504 Changed DCHFIV to DCHFIE. (FNF)