SLATEC Routines --- PCHIA ---
*DECK PCHIA
REAL FUNCTION PCHIA (N, X, F, D, INCFD, SKIP, A, B, IERR)
C***BEGIN PROLOGUE PCHIA
C***PURPOSE Evaluate the definite integral of a piecewise cubic
C Hermite function over an arbitrary interval.
C***LIBRARY SLATEC (PCHIP)
C***CATEGORY E3, H2A1B2
C***TYPE SINGLE PRECISION (PCHIA-S, DPCHIA-D)
C***KEYWORDS CUBIC HERMITE INTERPOLATION, NUMERICAL INTEGRATION, PCHIP,
C QUADRATURE
C***AUTHOR Fritsch, F. N., (LLNL)
C Lawrence Livermore National Laboratory
C P.O. Box 808 (L-316)
C Livermore, CA 94550
C FTS 532-4275, (510) 422-4275
C***DESCRIPTION
C
C PCHIA: Piecewise Cubic Hermite Integrator, Arbitrary limits
C
C Evaluates the definite integral of the cubic Hermite function
C defined by N, X, F, D over the interval [A, B].
C
C To provide compatibility with PCHIM and PCHIC, includes an
C increment between successive values of the F- and D-arrays.
C
C ----------------------------------------------------------------------
C
C Calling sequence:
C
C PARAMETER (INCFD = ...)
C INTEGER N, IERR
C REAL X(N), F(INCFD,N), D(INCFD,N), A, B
C REAL VALUE, PCHIA
C LOGICAL SKIP
C
C VALUE = PCHIA (N, X, F, D, INCFD, SKIP, A, B, IERR)
C
C Parameters:
C
C VALUE -- (output) value of the requested integral.
C
C N -- (input) number of data points. (Error return if N.LT.2 .)
C
C X -- (input) real array of independent variable values. The
C elements of X must be strictly increasing:
C X(I-1) .LT. X(I), I = 2(1)N.
C (Error return if not.)
C
C F -- (input) real array of function values. F(1+(I-1)*INCFD) is
C the value corresponding to X(I).
C
C D -- (input) real array of derivative values. D(1+(I-1)*INCFD) is
C the value corresponding to X(I).
C
C INCFD -- (input) increment between successive values in F and D.
C (Error return if INCFD.LT.1 .)
C
C SKIP -- (input/output) logical variable which should be set to
C .TRUE. if the user wishes to skip checks for validity of
C preceding parameters, or to .FALSE. otherwise.
C This will save time in case these checks have already
C been performed (say, in PCHIM or PCHIC).
C SKIP will be set to .TRUE. on return with IERR.GE.0 .
C
C A,B -- (input) the limits of integration.
C NOTE: There is no requirement that [A,B] be contained in
C [X(1),X(N)]. However, the resulting integral value
C will be highly suspect, if not.
C
C IERR -- (output) error flag.
C Normal return:
C IERR = 0 (no errors).
C Warning errors:
C IERR = 1 if A is outside the interval [X(1),X(N)].
C IERR = 2 if B is outside the interval [X(1),X(N)].
C IERR = 3 if both of the above are true. (Note that this
C means that either [A,B] contains data interval
C or the intervals do not intersect at all.)
C "Recoverable" errors:
C IERR = -1 if N.LT.2 .
C IERR = -2 if INCFD.LT.1 .
C IERR = -3 if the X-array is not strictly increasing.
C (VALUE will be zero in any of these cases.)
C NOTE: The above errors are checked in the order listed,
C and following arguments have **NOT** been validated.
C IERR = -4 in case of an error return from PCHID (which
C should never occur).
C
C***REFERENCES (NONE)
C***ROUTINES CALLED CHFIE, PCHID, XERMSG
C***REVISION HISTORY (YYMMDD)
C 820730 DATE WRITTEN
C 820804 Converted to SLATEC library version.
C 870707 Corrected double precision conversion instructions.
C 870813 Minor cosmetic changes.
C 890411 Added SAVE statements (Vers. 3.2).
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890703 Corrected category record. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 930503 Corrected to set VALUE=0 when IERR.lt.0. (FNF)
C 930504 Changed CHFIV to CHFIE. (FNF)
C***END PROLOGUE PCHIA