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docstring cleanups
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jacobwilliams committed Jan 27, 2024
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2 changes: 1 addition & 1 deletion LICENSE.txt
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PCHIP: Piecewise Cubic Hermite Interpolation Package
https://github.com/jacobwilliams/PCHIP

Copyright (c) 2019-2022, Jacob Williams
Copyright (c) 2019-2024, Jacob Williams
All rights reserved.

Redistribution and use in source and binary forms, with or without modification,
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2 changes: 1 addition & 1 deletion ford.md
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project: PCHIP
project_dir: ./src
src_dir: ./src
output_dir: ./doc
media_dir: ./media
project_github: https://github.com/jacobwilliams/PCHIP
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2 changes: 1 addition & 1 deletion fpm.toml
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Expand Up @@ -2,7 +2,7 @@ name = "pchip"
version = "1.1.0"
author = "Jacob Williams"
maintainer = "Jacob Williams"
copyright = "Copyright (c) 2019-2022, Jacob Williams"
copyright = "Copyright (c) 2019-2024, Jacob Williams"
license = "BSD-3"
description = "Piecewise Cubic Hermite Interpolation Package"
homepage = "https://github.com/jacobwilliams/PCHIP"
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100 changes: 50 additions & 50 deletions src/pchip_module.f90
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Expand Up @@ -52,7 +52,7 @@ end function dpchsd
!>
! Check a single cubic for monotonicity
!
! Called by [[DPCHCM]] to determine the monotonicity properties of the
! Called by [[dpchcm]] to determine the monotonicity properties of the
! cubic with boundary derivative values D1,D2 and chord slope DELTA.
!
!### Cautions
Expand Down Expand Up @@ -135,10 +135,10 @@ end function dchfcm
!
! Evaluate a cubic polynomial given in Hermite form and its
! first derivative at an array of points. While designed for
! use by [[DPCHFD]], it may be useful directly as an evaluator
! use by [[dpchfd]], it may be useful directly as an evaluator
! for a piecewise cubic Hermite function in applications,
! such as graphing, where the interval is known in advance.
! If only function values are required, use [[DCHFEV]] instead.
! If only function values are required, use [[dchfev]] instead.
!
! Evaluates the cubic polynomial determined by function values
! F1,F2 and derivatives D1,D2 on interval (X1,X2), together with
Expand Down Expand Up @@ -228,7 +228,7 @@ end subroutine dchfdv
! Cubic Hermite Function Evaluator
!
! Evaluate a cubic polynomial given in Hermite form at an
! array of points. While designed for use by [[DPCHFE]], it may
! array of points. While designed for use by [[dpchfe]], it may
! be useful directly as an evaluator for a piecewise cubic
! Hermite function in applications, such as graphing, where
! the interval is known in advance.
Expand Down Expand Up @@ -312,7 +312,7 @@ end subroutine dchfev
!>
! Cubic Hermite Function Integral Evaluator
!
! Called by [[DPCHIA]] to evaluate the integral of a single cubic (in
! Called by [[dpchia]] to evaluate the integral of a single cubic (in
! Hermite form) over an arbitrary interval (A,B).
!
!@note There is no error return from this routine because zero is
Expand Down Expand Up @@ -402,7 +402,7 @@ end function dchfie
! but it works on all systems on which DPCHBS has been tested.
!
!### See Also
! * [[DPCHIC]], [[DPCHIM]], or [[DPCHSP]] can be used to determine an interpolating
! * [[dpchic]], [[dpchim]], or [[dpchsp]] can be used to determine an interpolating
! PCH function from a set of data.
! * The B-spline routine `DBVALU` can be used to evaluate the
! B-representation that is output by DPCHBS.
Expand Down Expand Up @@ -516,16 +516,16 @@ end subroutine dpchbs

!***************************************************************************
!>
! Set boundary conditions for [[DPCHIC]]
! Set boundary conditions for [[dpchic]]
!
! Called by [[DPCHIC]] to set end derivatives as requested by the user.
! Called by [[dpchic]] to set end derivatives as requested by the user.
! It must be called after interior derivative values have been set.
!
! To facilitate two-dimensional applications, includes an increment
! between successive values of the D-array.
!
!### Programming notes
! 1. The function [[DPCHST]](ARG1,ARG2) is assumed to return zero if
! 1. The function [[dpchst]](ARG1,ARG2) is assumed to return zero if
! either argument is zero, +1 if they are of the same sign, and
! -1 if they are of opposite sign.
! 2. One could reduce the number of arguments and amount of local
Expand All @@ -547,7 +547,7 @@ subroutine dpchce (ic, vc, n, x, h, slope, d, incfd, ierr)
!! * IC(1) = IBEG, desired condition at beginning of data.
!! * IC(2) = IEND, desired condition at end of data.
!!
!! ( see prologue to [[DPCHIC]] for details. )
!! ( see prologue to [[dpchic]] for details. )
integer,intent(in) :: n !! number of data points. (assumes N>=2)
integer,intent(in) :: incfd !! increment between successive values in D.
!! This argument is provided primarily for 2-D applications.
Expand Down Expand Up @@ -707,7 +707,7 @@ end subroutine dpchce
!>
! Set interior derivatives for DPCHIC
!
! Called by [[DPCHIC]] to set derivatives needed to determine a monotone
! Called by [[dpchic]] to set derivatives needed to determine a monotone
! piecewise cubic Hermite interpolant to the data.
!
! Default boundary conditions are provided which are compatible
Expand All @@ -719,10 +719,10 @@ end subroutine dpchce
! between successive values of the D-array.
!
! The resulting piecewise cubic Hermite function should be identical
! (within roundoff error) to that produced by [[DPCHIM]].
! (within roundoff error) to that produced by [[dpchim]].
!
!### Programming notes
! 1. The function [[DPCHST]](ARG1,ARG2) is assumed to return zero if
! 1. The function [[dpchst]](ARG1,ARG2) is assumed to return zero if
! either argument is zero, +1 if they are of the same sign, and
! -1 if they are of opposite sign.
!
Expand Down Expand Up @@ -831,7 +831,7 @@ end subroutine dpchci
! Checks the piecewise cubic Hermite function defined by N,X,F,D
! for monotonicity.
!
! To provide compatibility with [[DPCHIM]] and [[DPCHIC]], includes an
! To provide compatibility with [[dpchim]] and [[dpchic]], includes an
! increment between successive values of the F- and D-arrays.
!
!### Cautions
Expand Down Expand Up @@ -984,14 +984,14 @@ end subroutine dpchcm
!>
! Monotonicity Switch Derivative Setter
!
! Called by [[DPCHIC]] to adjust the values of D in the vicinity of a
! Called by [[dpchic]] to adjust the values of D in the vicinity of a
! switch in direction of monotonicity, to produce a more "visually
! pleasing" curve than that given by [[DPCHIM]].
! pleasing" curve than that given by [[dpchim]].
!
!@warning This routine does no validity-checking of arguments.
!
!### Programming notes:
! 1. The function [[DPCHST]](ARG1,ARG2) is assumed to return zero if
! 1. The function [[dpchst]](ARG1,ARG2) is assumed to return zero if
! either argument is zero, +1 if they are of the same sign, and
! -1 if they are of opposite sign.

Expand All @@ -1007,7 +1007,7 @@ subroutine dpchcs (switch, n, h, slope, d, incfd, ierr)
!! * H(I) = X(I+1)-X(I),
!! * SLOPE(I) = (Y(I+1)-Y(I))/H(I), I=1(1)N-1.
real(wp),intent(inout) :: d(incfd,*) !! (input) array of derivative values at the data points,
!! as determined by [[DPCHCI]].
!! as determined by [[dpchci]].
!!
!! (output) derivatives in the vicinity of switches in direction
!! of monotonicity may be adjusted to produce a more "visually
Expand All @@ -1018,7 +1018,7 @@ subroutine dpchcs (switch, n, h, slope, d, incfd, ierr)
integer,intent(in) :: incfd !! increment between successive values in D.
!! This argument is provided primarily for 2-D applications.
integer,intent(out) :: ierr !! error flag. should be zero.
!! If negative, trouble in [[DPCHSW]]. (should never happen.)
!! If negative, trouble in [[dpchsw]]. (should never happen.)

integer :: i, indx, k, nless1
real(wp) :: del(3), dext, dfloc, dfmx, fact, slmax, wtave(2)
Expand Down Expand Up @@ -1119,13 +1119,13 @@ end subroutine dpchcs

!***************************************************************************
!>
! Computes divided differences for [[DPCHCE]] and [[DPCHSP]]
! Computes divided differences for [[dpchce]] and [[dpchsp]]
!
! Uses a divided difference formulation to compute a K-point
! approximation to the derivative at X(K) based on the data
! in X and S.
!
! Called by [[DPCHCE]] and [[DPCHSP]] to compute 3- and 4-point boundary
! Called by [[dpchce]] and [[dpchsp]] to compute 3- and 4-point boundary
! derivative approximations.
!
!### References
Expand Down Expand Up @@ -1185,24 +1185,24 @@ end function dpchdf
!
! Evaluate a piecewise cubic Hermite function and its first
! derivative at an array of points. May be used by itself
! for Hermite interpolation, or as an evaluator for [[DPCHIM]]
! or [[DPCHIC]].
! for Hermite interpolation, or as an evaluator for [[dpchim]]
! or [[dpchic]].
!
! Evaluates the cubic Hermite function defined by N, X, F, D, to-
! gether with its first derivative, at the points XE(J), J=1(1)NE.
!
! If only function values are required, use [[DPCHFE]], instead.
! If only function values are required, use [[dpchfe]], instead.
!
! To provide compatibility with [[DPCHIM]] and [[DPCHIC]], includes an
! To provide compatibility with [[dpchim]] and [[dpchic]], includes an
! increment between successive values of the F- and D-arrays.
!
!### Programming notes
!
! 1. Most of the coding between the call to [[DCHFDV]] and the end of
! 1. Most of the coding between the call to [[dchfdv]] and the end of
! the IR-loop could be eliminated if it were permissible to
! assume that XE is ordered relative to X.
!
! 2. [[DCHFDV]] does not assume that X1 is less than X2. thus, it would
! 2. [[dchfdv]] does not assume that X1 is less than X2. thus, it would
! be possible to write a version of DPCHFD that assumes a strictly
! decreasing X-array by simply running the IR-loop backwards
! (and reversing the order of appropriate tests).
Expand Down Expand Up @@ -1267,7 +1267,7 @@ subroutine dpchfd (n, x, f, d, incfd, skip, ne, xe, fe, de, ierr)
!! .TRUE. if the user wishes to skip checks for validity of
!! preceding parameters, or to .FALSE. otherwise.
!! This will save time in case these checks have already
!! been performed (say, in [[DPCHIM]] or [[DPCHIC]]).
!! been performed (say, in [[dpchim]] or [[dpchic]]).
!! SKIP will be set to .TRUE. on normal return.

integer :: i, ierc, ir, j, jfirst, next(2), nj
Expand Down Expand Up @@ -1418,22 +1418,22 @@ end subroutine dpchfd
!
! Evaluate a piecewise cubic Hermite function at an array of
! points. May be used by itself for Hermite interpolation,
! or as an evaluator for [[DPCHIM]] or [[DPCHIC]].
! or as an evaluator for [[dpchim]] or [[dpchic]].
!
! Evaluates the cubic Hermite function defined by N, X, F, D at
! the points XE(J), J=1(1)NE.
!
! To provide compatibility with [[DPCHIM]] and [[DPCHIC]], includes an
! To provide compatibility with [[dpchim]] and [[dpchic]], includes an
! increment between successive values of the F- and D-arrays.
!
!### Programming notes
!
! 1. Most of the coding between the call to [[DCHFEV]] and the end of
! 1. Most of the coding between the call to [[dchfev]] and the end of
! the IR-loop could be eliminated if it were permissible to
! assume that XE is ordered relative to X.
!
! 2. [[DCHFEV]] does not assume that X1 is less than X2. thus, it would
! be possible to write a version of [[DPCHFE]] that assumes a
! 2. [[dchfev]] does not assume that X1 is less than X2. thus, it would
! be possible to write a version of [[dpchfe]] that assumes a
! decreasing X-array by simply running the IR-loop backwards
! (and reversing the order of appropriate tests).
!
Expand Down Expand Up @@ -1490,7 +1490,7 @@ subroutine dpchfe (n, x, f, d, incfd, skip, ne, xe, fe, ierr)
!! .TRUE. if the user wishes to skip checks for validity of
!! preceding parameters, or to .FALSE. otherwise.
!! This will save time in case these checks have already
!! been performed (say, in [[DPCHIM]] or [[DPCHIC]]).
!! been performed (say, in [[dpchim]] or [[dpchic]]).
!! SKIP will be set to .TRUE. on normal return.

integer :: i, ierc, ir, j, jfirst, next(2), nj
Expand Down Expand Up @@ -1642,11 +1642,11 @@ end subroutine dpchfe
! 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
! To provide compatibility with [[dpchim]] and [[dpchic]], includes an
! increment between successive values of the F- and D-arrays.
!
!### Programming notes
! 1. The error flag from [[DPCHID]] is tested, because a logic flaw
! 1. The error flag from [[dpchid]] is tested, because a logic flaw
! could conceivably result in IERD=-4, which should be reported.

function dpchia (n, x, f, d, incfd, skip, a, b, ierr) result(value)
Expand Down Expand Up @@ -1693,7 +1693,7 @@ function dpchia (n, x, f, d, incfd, skip, a, b, ierr) result(value)
!! .TRUE. if the user wishes to skip checks for validity of
!! preceding parameters, or to .FALSE. otherwise.
!! This will save time in case these checks have already
!! been performed (say, in [[DPCHIM]] or [[DPCHIC]]).
!! been performed (say, in [[dpchim]] or [[dpchic]]).
!! SKIP will be set to .TRUE. on return with IERR>=0 .
real(wp) :: value !! value of the requested integral.

Expand Down Expand Up @@ -1821,7 +1821,7 @@ end function dpchia
! between successive values of the F- and D-arrays.
!
! The resulting piecewise cubic Hermite function may be evaluated
! by [[DPCHFE]] or [[DPCHFD]].
! by [[dpchfe]] or [[dpchfd]].
!
!### References
! 1. F. N. Fritsch, Piecewise Cubic Hermite Interpolation
Expand All @@ -1845,7 +1845,7 @@ subroutine dpchic (ic, vc, switch, n, x, f, d, incfd, wk, nwk, ierr)
!!
!! Valid values for IBEG:
!!
!! * IBEG = 0 for the default boundary condition (the same as used by [[DPCHIM]]).
!! * IBEG = 0 for the default boundary condition (the same as used by [[dpchim]]).
!! * If IBEG/=0, then its sign indicates whether the boundary
!! derivative is to be adjusted, if necessary, to be
!! compatible with monotonicity:
Expand Down Expand Up @@ -2073,14 +2073,14 @@ end subroutine dpchic
! Evaluates the definite integral of the cubic Hermite function
! defined by N, X, F, D over the interval [X(IA), X(IB)].
!
! To provide compatibility with [[DPCHIM]] and [[DPCHIC]], includes an
! To provide compatibility with [[dpchim]] and [[dpchic]], includes an
! increment between successive values of the F- and D-arrays.
!
!### Programming notes
! 1. This routine uses a special formula that is valid only for
! integrals whose limits coincide with data values. This is
! mathematically equivalent to, but much more efficient than,
! calls to [[DCHFIE]].
! calls to [[dchfie]].

function dpchid (n, x, f, d, incfd, skip, ia, ib, ierr) result(value)

Expand Down Expand Up @@ -2118,7 +2118,7 @@ function dpchid (n, x, f, d, incfd, skip, ia, ib, ierr) result(value)
!! .TRUE. if the user wishes to skip checks for validity of
!! preceding parameters, or to .FALSE. otherwise.
!! This will save time in case these checks have already
!! been performed (say, in [[DPCHIM]] or [[DPCHIC]]).
!! been performed (say, in [[dpchim]] or [[dpchic]]).
!! SKIP will be set to .TRUE. on return with IERR = 0 or -4.
real(wp) :: value !! value of the requested integral.

Expand Down Expand Up @@ -2186,18 +2186,18 @@ end function dpchid
! Hermite interpolant to the data given in X and F.
!
! Default boundary conditions are provided which are compatible
! with monotonicity. (See [[DPCHIC]] if user control of boundary conditions
! with monotonicity. (See [[dpchic]] if user control of boundary conditions
! is desired.)
!
! If the data are only piecewise monotonic, the interpolant will
! have an extremum at each point where monotonicity switches direction.
! (See [[DPCHIC]] if user control is desired in such cases.)
! (See [[dpchic]] if user control is desired in such cases.)
!
! To facilitate two-dimensional applications, includes an increment
! between successive values of the F- and D-arrays.
!
! The resulting piecewise cubic Hermite function may be evaluated
! by [[DPCHFE]] or [[DPCHFD]].
! by [[dpchfe]] or [[dpchfd]].
!
!### References
! 1. F. N. Fritsch and J. Butland, A method for constructing
Expand All @@ -2209,7 +2209,7 @@ end function dpchid
! 2 (April 1980), pp. 238-246.
!
!### Programming notes
! 1. The function [[DPCHST]](ARG1,ARG2) is assumed to return zero if
! 1. The function [[dpchst]](ARG1,ARG2) is assumed to return zero if
! either argument is zero, +1 if they are of the same sign, and
! -1 if they are of opposite sign.

Expand Down Expand Up @@ -2245,7 +2245,7 @@ subroutine dpchim (n, x, f, d, incfd, ierr)
!! X(I). DPCHIM is designed for monotonic data, but it will
!! work for any F-array. It will force extrema at points where
!! monotonicity switches direction. If some other treatment of
!! switch points is desired, [[DPCHIC]] should be used instead.
!! switch points is desired, [[dpchic]] should be used instead.
real(wp),intent(out) :: d(incfd,*) !! array of derivative values at the data
!! points. If the data are monotonic, these values will
!! determine a monotone cubic Hermite function.
Expand Down Expand Up @@ -2382,7 +2382,7 @@ end subroutine dpchim
! 3. 0<=KNOTYP<=2 . (Acts like KNOTYP=0 for any other value.)
!
!### Internal Notes
! Since this is subsidiary to [[DPCHBS]], which validates its input before
! Since this is subsidiary to [[dpchbs]], which validates its input before
! calling, it is unnecessary for such validation to be done here.

subroutine dpchkt (n, x, knotyp, t)
Expand Down Expand Up @@ -2445,7 +2445,7 @@ end subroutine dpchkt
! between successive values of the F- and D-arrays.
!
! The resulting piecewise cubic Hermite function may be evaluated
! by [[DPCHFE]] or [[DPCHFD]].
! by [[dpchfe]] or [[dpchfd]].
!
!### References
! * Carl de Boor, A Practical Guide to Splines, Springer-Verlag,
Expand Down Expand Up @@ -2818,7 +2818,7 @@ end function dpchst
!>
! Switch Excursion Limiter.
!
! Called by [[DPCHCS]] to adjust D1 and D2 if necessary to insure that
! Called by [[dpchcs]] to adjust D1 and D2 if necessary to insure that
! the extremum on this interval is not further than DFMAX from the
! extreme data value.
!
Expand Down

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