cubic_spline_derivatives_from_second_derivs(n, x, y, d2, dy)
First derivatives at knots for an existing cubic spline second-derivative table.
integer intent(in) :: n
real(sp_acc) intent(in) :: x(n)
real(sp_acc) intent(in) :: y(n)
real(sp_acc) intent(in) :: d2(n)
real(sp_acc) intent(out) :: dy(n)
cubic_spline_horner_coefficients(n, x, y, d2, horner)
Interval polynomial coefficients for cubic spline evaluation in normalized Horner form.
integer intent(in) :: n
real(sp_acc) intent(in) :: x(n)
real(sp_acc) intent(in) :: y(n)
real(sp_acc) intent(in) :: d2(n)
real(sp_acc) intent(out) :: horner(:, :)
cubic_spline_integral_array(n, x, y, d2, yint)
Cumulative integral of a cubic spline at the input knots.
integer intent(in) :: n
real(sp_acc) intent(in) :: x(n)
real(sp_acc) intent(in) :: y(n)
real(sp_acc) intent(in) :: d2(n)
real(sp_acc) intent(out) :: yint(n)
cubic_spline_regular_horner_coefficients(n, delta, y, d2, horner)
Interval polynomial coefficients for a regular-grid cubic spline in normalized Horner form.
integer intent(in) :: n
real(sp_acc) intent(in) :: delta
real(sp_acc) intent(in) :: y(n)
real(sp_acc) intent(in) :: d2(n)
real(sp_acc) intent(out) :: horner(:, :)
cubic_spline_regular_second_derivs(n, delta, y, d2, End1, End2)
Second derivatives for a regular-grid cubic spline; delta is x(i+1)-x(i).
integer intent(in) :: n
real(sp_acc) intent(in) :: delta
real(sp_acc) intent(in) :: y(n)
real(sp_acc) intent(out) :: d2(n)
real(sp_acc) intent(in), optional :: End1
real(sp_acc) intent(in), optional :: End2
cubic_spline_second_derivs(n, x, y, d2, End1, End2)
Second derivatives for a cubic spline; omitted endpoints use natural boundary conditions.
integer intent(in) :: n
real(sp_acc) intent(in) :: x(n)
real(sp_acc) intent(in) :: y(n)
real(sp_acc) intent(out) :: d2(n)
real(sp_acc) intent(in), optional :: End1
real(sp_acc) intent(in), optional :: End2
rgbi3p(md, nxd, nyd, xd, yd, zd, nip, xi, yi, zi, ier, wk)
Code converted using TO_F90 by Alan Miller
Date: 2003-06-11 Time: 10:11:03
Rectangular-grid bivariate interpolation
(a master subroutine of the RGBI3P/RGSF3P subroutine package)
Hiroshi Akima
U.S. Department of Commerce, NTIA/ITS
Version of 1995/08
This subroutine performs interpolation of a bivariate function, z(x,y), on a
rectangular grid in the x-y plane. It is based on the revised Akima method.
In this subroutine, the interpolating function is a piecewise function
composed of a set of bicubic (bivariate third-degree) polynomials, each
applicable to a rectangle of the input grid in the x-y plane.
Each polynomial is determined locally.
This subroutine has the accuracy of a bicubic polynomial, i.e., it
interpolates accurately when all data points lie on a surface of a
bicubic polynomial.
The grid lines can be unevenly spaced.
The input arguments are
MD = mode of computation
= 1 for new XD, YD, or ZD data (default)
= 2 for old XD, YD, and ZD data,
NXD = number of the input-grid data points in the x coordinate
(must be 2 or greater),
NYD = number of the input-grid data points in the y coordinate
(must be 2 or greater),
XD = array of dimension NXD containing the x coordinates of the
input-grid data points (must be in a monotonic increasing order),
YD = array of dimension NYD containing the y coordinates of the
input-grid data points (must be in a monotonic increasing order),
ZD = two-dimensional array of dimension NXD*NYD
containing the z(x,y) values at the input-grid data points,
NIP = number of the output points at which interpolation
of the z value is desired (must be 1 or greater),
XI = array of dimension NIP containing the x coordinates
of the output points,
YI = array of dimension NIP containing the y coordinates
of the output points.
The output arguments are
ZI = array of dimension NIP where the interpolated z
values at the output points are to be stored,
IER = error flag
= 0 for no errors
= 1 for NXD = 1 or less
= 2 for NYD = 1 or less
= 3 for identical XD values or XD values out of sequence
= 4 for identical YD values or YD values out of sequence
= 5 for NIP = 0 or less.
N.B. The workspace has been removed from the argument list.
WK = three dimensional array of dimension 3*NXD*NYD used internally
as a work area.
The very fisrt call to this subroutine and the call with a new XD, YD, and
ZD array must be made with MD=1. The call with MD=2 must be preceded by
another call with the same XD, YD, and ZD arrays. Between the call with
MD = 2 and its preceding call, the WK array must not be disturbed.
The constant in the PARAMETER statement below is
NIPIMX = maximum number of output points to be processed at a time.
The constant value has been selected empirically.
This subroutine calls the RGPD3P, RGLCTN, and RGPLNL subroutines.
Specification statements
.. Parameters ..
integer intent(in) :: md
integer intent(in) :: nxd
integer intent(in) :: nyd
real(GI) intent(in) :: xd(nxd)
real(GI) intent(in) :: yd(nyd)
real(GI) intent(in) :: zd(nxd, nyd)
integer intent(in) :: nip
real(GI) intent(in) :: xi(nip)
real(GI) intent(in) :: yi(nip)
real(GI) intent(out) :: zi(nip)
integer intent(out) :: ier
real(GI) intent(inout) :: wk(3, nxd, nyd)
rglctn(nxd, nyd, xd, yd, nip, xi, yi, inxi, inyi)
Location of the desired points in a rectangular grid
(a supporting subroutine of the RGBI3P/RGSF3P subroutine package)
Hiroshi Akima
U.S. Department of Commerce, NTIA/ITS
Version of 1995/08
This subroutine locates the desired points in a rectangular grid
in the x-y plane.
The grid lines can be unevenly spaced.
The input arguments are
NXD = number of the input-grid data points in the x
coordinate (must be 2 or greater),
NYD = number of the input-grid data points in the y
coordinate (must be 2 or greater),
XD = array of dimension NXD containing the x coordinates of the
input-grid data points (must be in a monotonic increasing order),
YD = array of dimension NYD containing the y coordinates of the
input-grid data points (must be in a monotonic increasing order),
NIP = number of the output points to be located (must be 1 or greater),
XI = array of dimension NIP containing the x coordinates
of the output points to be located,
YI = array of dimension NIP containing the y coordinates
of the output points to be located.
The output arguments are
INXI = integer array of dimension NIP where the interval
numbers of the XI array elements are to be stored,
INYI = integer array of dimension NIP where the interval
numbers of the YI array elements are to be stored.
The interval numbers are between 0 and NXD and between 0 and NYD,
respectively.
Specification statements
.. Scalar Arguments ..
integer intent(in) :: nxd
integer intent(in) :: nyd
real(GI) intent(in) :: xd(nxd)
real(GI) intent(in) :: yd(nyd)
integer intent(in) :: nip
real(GI) intent(in) :: xi(nip)
real(GI) intent(in) :: yi(nip)
integer intent(out) :: inxi(nip)
integer intent(out) :: inyi(nip)
rgpd3p(nxd, nyd, xd, yd, zd, pdd)
Partial derivatives of a bivariate function on a rectangular grid
(a supporting subroutine of the RGBI3P/RGSF3P subroutine package)
Hiroshi Akima
U.S. Department of Commerce, NTIA/ITS
Version of 1995/08
This subroutine estimates three partial derivatives, zx, zy, and
zxy, of a bivariate function, z(x,y), on a rectangular grid in
the x-y plane. It is based on the revised Akima method that has
the accuracy of a bicubic polynomial.
The input arguments are
NXD = number of the input-grid data points in the x
coordinate (must be 2 or greater),
NYD = number of the input-grid data points in the y
coordinate (must be 2 or greater),
XD = array of dimension NXD containing the x coordinates of the
input-grid data points (must be in a monotonic increasing order),
YD = array of dimension NYD containing the y coordinates of the
input-grid data points (must be in a monotonic increasing order),
ZD = two-dimensional array of dimension NXD*NYD
containing the z(x,y) values at the input-grid data points.
The output argument is
PDD = three-dimensional array of dimension 3*NXD*NYD,
where the estimated zx, zy, and zxy values at the
input-grid data points are to be stored.
Specification statements
.. Scalar Arguments ..
integer intent(in) :: nxd
integer intent(in) :: nyd
real(GI) intent(in) :: xd(nxd)
real(GI) intent(in) :: yd(nyd)
real(GI) intent(in) :: zd(nxd, nyd)
real(GI) intent(out) :: pdd(3, nxd, nyd)
rgplnl(nxd, nyd, xd, yd, zd, pdd, nip, xi, yi, inxi, inyi, zi)
Polynomials for rectangular-grid bivariate interpolation and surface fitting
(a supporting subroutine of the RGBI3P/RGSF3P subroutine package)
Hiroshi Akima
U.S. Department of Commerce, NTIA/ITS
Version of 1995/08
This subroutine determines a polynomial in x and y for a rectangle of the
input grid in the x-y plane and calculates the z value for the desired
points by evaluating the polynomial for rectangular-grid bivariate
interpolation and surface fitting.
The input arguments are
NXD = number of the input-grid data points in the x
coordinate (must be 2 or greater),
NYD = number of the input-grid data points in the y
coordinate (must be 2 or greater),
XD = array of dimension NXD containing the x coordinates of the
input-grid data points (must be in a monotonic increasing order),
YD = array of dimension NYD containing the y coordinates of the
input-grid data points (must be in a monotonic increasing order),
ZD = two-dimensional array of dimension NXD*NYD
containing the z(x,y) values at the input-grid data points,
PDD = three-dimensional array of dimension 3*NXD*NYD
containing the estimated zx, zy, and zxy values
at the input-grid data points,
NIP = number of the output points at which interpolation
is to be performed,
XI = array of dimension NIP containing the x coordinates
of the output points,
YI = array of dimension NIP containing the y coordinates
of the output points,
INXI = integer array of dimension NIP containing the
interval numbers of the input grid intervals in the
x direction where the x coordinates of the output points lie,
INYI = integer array of dimension NIP containing the
interval numbers of the input grid intervals in the
y direction where the y coordinates of the output points lie.
The output argument is
ZI = array of dimension NIP, where the interpolated z
values at the output points are to be stored.
Specification statements
.. Scalar Arguments ..
integer intent(in) :: nxd
integer intent(in) :: nyd
real(GI) intent(in) :: xd(nxd)
real(GI) intent(in) :: yd(nyd)
real(GI) intent(in) :: zd(nxd, nyd)
real(GI) intent(in) :: pdd(3, nxd, nyd)
integer intent(in) :: nip
real(GI) intent(in) :: xi(nip)
real(GI) intent(in) :: yi(nip)
integer intent(in) :: inxi(nip)
integer intent(in) :: inyi(nip)
real(GI) intent(out) :: zi(nip)
rgsf3p(md, nxd, nyd, xd, yd, zd, nxi, xi, nyi, yi, zi, ier, wk)
Rectangular-grid surface fitting
(a master subroutine of the RGBI3P/RGSF3P subroutine package)
Hiroshi Akima
U.S. Department of Commerce, NTIA/ITS
Version of 1995/08
This subroutine performs surface fitting by interpolating values of a
bivariate function, z(x,y), on a rectangular grid in the x-y plane.
It is based on the revised Akima method.
In this subroutine, the interpolating function is a piecewise function
composed of a set of bicubic (bivariate third-degree) polynomials, each
applicable to a rectangle of the input grid in the x-y plane.
Each polynomial is determined locally.
This subroutine has the accuracy of a bicubic polynomial, i.e., it fits the
surface accurately when all data points lie on a surface of a bicubic
polynomial.
The grid lines of the input and output data can be unevenly spaced.
The input arguments are
MD = mode of computation
= 1 for new XD, YD, or ZD data (default)
= 2 for old XD, YD, and ZD data,
NXD = number of the input-grid data points in the x
coordinate (must be 2 or greater),
NYD = number of the input-grid data points in the y
coordinate (must be 2 or greater),
XD = array of dimension NXD containing the x coordinates
of the input-grid data points (must be in a
monotonic increasing order),
YD = array of dimension NYD containing the y coordinates
of the input-grid data points (must be in a
monotonic increasing order),
ZD = two-dimensional array of dimension NXD*NYD
containing the z(x,y) values at the input-grid data points,
NXI = number of output grid points in the x coordinate
(must be 1 or greater),
XI = array of dimension NXI containing the x coordinates
of the output grid points,
NYI = number of output grid points in the y coordinate
(must be 1 or greater),
YI = array of dimension NYI containing the y coordinates
of the output grid points.
The output arguments are
ZI = two-dimensional array of dimension NXI*NYI, where the interpolated
z values at the output grid points are to be stored,
IER = error flag
= 0 for no error
= 1 for NXD = 1 or less
= 2 for NYD = 1 or less
= 3 for identical XD values or XD values out of sequence
= 4 for identical YD values or YD values out of sequence
= 5 for NXI = 0 or less
= 6 for NYI = 0 or less.
N.B. The workspace has been removed from the argument list.
WK = three-dimensional array of dimension 3*NXD*NYD used internally
as a work area.
The very first call to this subroutine and the call with a new XD, YD, or
ZD array must be made with MD=1. The call with MD=2 must be preceded by
another call with the same XD, YD, and ZD arrays. Between the call with
MD = 2 and its preceding call, the WK array must not be disturbed.
The constant in the PARAMETER statement below is
NIPIMX = maximum number of output points to be processed at a time.
The constant value has been selected empirically.
This subroutine calls the RGPD3P, RGLCTN, and RGPLNL subroutines.
Specification statements
.. Parameters ..
integer intent(in) :: md
integer intent(in) :: nxd
integer intent(in) :: nyd
real(GI) intent(in) :: xd(nxd)
real(GI) intent(in) :: yd(nyd)
real(GI) intent(in) :: zd(nxd, nyd)
integer intent(in) :: nxi
real(GI) intent(in) :: xi(nxi)
integer intent(in) :: nyi
real(GI) intent(in) :: yi(nyi)
real(GI) intent(out) :: zi(nxi, nyi)
integer intent(out) :: ier
real(GI) intent(inout) :: wk(3, nxd, nyd)