SLATEC Routines --- DPCHSP ---
*DECK DPCHSP
SUBROUTINE DPCHSP (IC, VC, N, X, F, D, INCFD, WK, NWK, IERR)
C***BEGIN PROLOGUE DPCHSP
C***PURPOSE Set derivatives needed to determine the Hermite represen-
C tation of the cubic spline interpolant to given data, with
C specified boundary conditions.
C***LIBRARY SLATEC (PCHIP)
C***CATEGORY E1A
C***TYPE DOUBLE PRECISION (PCHSP-S, DPCHSP-D)
C***KEYWORDS CUBIC HERMITE INTERPOLATION, PCHIP,
C PIECEWISE CUBIC INTERPOLATION, SPLINE INTERPOLATION
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 DPCHSP: Piecewise Cubic Hermite Spline
C
C Computes the Hermite representation of the cubic spline inter-
C polant to the data given in X and F satisfying the boundary
C conditions specified by IC and VC.
C
C To facilitate two-dimensional applications, includes an increment
C between successive values of the F- and D-arrays.
C
C The resulting piecewise cubic Hermite function may be evaluated
C by DPCHFE or DPCHFD.
C
C NOTE: This is a modified version of C. de Boor's cubic spline
C routine CUBSPL.
C
C ----------------------------------------------------------------------
C
C Calling sequence:
C
C PARAMETER (INCFD = ...)
C INTEGER IC(2), N, NWK, IERR
C DOUBLE PRECISION VC(2), X(N), F(INCFD,N), D(INCFD,N), WK(NWK)
C
C CALL DPCHSP (IC, VC, N, X, F, D, INCFD, WK, NWK, IERR)
C
C Parameters:
C
C IC -- (input) integer array of length 2 specifying desired
C boundary conditions:
C IC(1) = IBEG, desired condition at beginning of data.
C IC(2) = IEND, desired condition at end of data.
C
C IBEG = 0 to set D(1) so that the third derivative is con-
C tinuous at X(2). This is the "not a knot" condition
C provided by de Boor's cubic spline routine CUBSPL.
C < This is the default boundary condition. >
C IBEG = 1 if first derivative at X(1) is given in VC(1).
C IBEG = 2 if second derivative at X(1) is given in VC(1).
C IBEG = 3 to use the 3-point difference formula for D(1).
C (Reverts to the default b.c. if N.LT.3 .)
C IBEG = 4 to use the 4-point difference formula for D(1).
C (Reverts to the default b.c. if N.LT.4 .)
C NOTES:
C 1. An error return is taken if IBEG is out of range.
C 2. For the "natural" boundary condition, use IBEG=2 and
C VC(1)=0.
C
C IEND may take on the same values as IBEG, but applied to
C derivative at X(N). In case IEND = 1 or 2, the value is
C given in VC(2).
C
C NOTES:
C 1. An error return is taken if IEND is out of range.
C 2. For the "natural" boundary condition, use IEND=2 and
C VC(2)=0.
C
C VC -- (input) real*8 array of length 2 specifying desired boundary
C values, as indicated above.
C VC(1) need be set only if IC(1) = 1 or 2 .
C VC(2) need be set only if IC(2) = 1 or 2 .
C
C N -- (input) number of data points. (Error return if N.LT.2 .)
C
C X -- (input) real*8 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*8 array of dependent variable values to be
C interpolated. F(1+(I-1)*INCFD) is value corresponding to
C X(I).
C
C D -- (output) real*8 array of derivative values at the data
C points. These values will determine the cubic spline
C interpolant with the requested boundary conditions.
C The value corresponding to X(I) is stored in
C D(1+(I-1)*INCFD), I=1(1)N.
C No other entries in D are changed.
C
C INCFD -- (input) increment between successive values in F and D.
C This argument is provided primarily for 2-D applications.
C (Error return if INCFD.LT.1 .)
C
C WK -- (scratch) real*8 array of working storage.
C
C NWK -- (input) length of work array.
C (Error return if NWK.LT.2*N .)
C
C IERR -- (output) error flag.
C Normal return:
C IERR = 0 (no errors).
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 IERR = -4 if IBEG.LT.0 or IBEG.GT.4 .
C IERR = -5 if IEND.LT.0 of IEND.GT.4 .
C IERR = -6 if both of the above are true.
C IERR = -7 if NWK is too small.
C NOTE: The above errors are checked in the order listed,
C and following arguments have **NOT** been validated.
C (The D-array has not been changed in any of these cases.)
C IERR = -8 in case of trouble solving the linear system
C for the interior derivative values.
C (The D-array may have been changed in this case.)
C ( Do **NOT** use it! )
C
C***REFERENCES Carl de Boor, A Practical Guide to Splines, Springer-
C Verlag, New York, 1978, pp. 53-59.
C***ROUTINES CALLED DPCHDF, XERMSG
C***REVISION HISTORY (YYMMDD)
C 820503 DATE WRITTEN
C 820804 Converted to SLATEC library version.
C 870707 Corrected XERROR calls for d.p. name(s).
C 890206 Corrected XERROR calls.
C 890411 Added SAVE statements (Vers. 3.2).
C 890703 Corrected category record. (WRB)
C 890831 Modified array declarations. (WRB)
C 891006 Cosmetic changes to prologue. (WRB)
C 891006 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 920429 Revised format and order of references. (WRB,FNF)
C***END PROLOGUE DPCHSP