# ncl_csa3xs - Man Page

cubic spline approximation, expanded entry for three-dimensional input

## Synopsis

CALL CSA3XS (NI, XI, UI, WTS, KNOTS, SMTH, NDERIV,

NXO, ,NYO, NZO, XO, YO, ZO, UO, NWRK,

WORK, IER)

## Description

- NI
(integer,input) The number of input data points. It must be that NI .gt. 3 and, depending on the size of KNOTS below, NI may have to be larger.

- XI
(real, input) An array containing the X - Y - Z coordinates of the input data points. XI is dimensioned for 3 x NI. XI(1,L) is the X coordinate, XI(2,L) is the Y coordinate, and XI(2,L) is the Z coordinate for the input domain for L=1,NI.

- UI
(real, input) An array dimensioned for NI containing function values at the input XI values, that is, UI(L) is the value of the input function at XI(L) for L=1,NI. through the input function values.

- WTS
(real, input) An array dimensioned for NI containing weights for the UI values at the input XI values, that is, WTS(L) is a weight for the value of UI(L) for L=1,NI. If you do not desire to weight the input UI values, then set WTS(1) to -1. The weights in the WTS array are relative and may be set to any non-negative value. When CSA3XS is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.

- KNOTS
(integer, input) The number of knots to be used in constructing the approximation spline. KNOTS is dimensioned for 3 and provides the number of knots to be used in the X, Y, and Z directions. Both KNOTS(I) must be at least 4 for I=1,3. The larger the values for KNOTS, the closer the approximated curve will come to passing through the input function values.

- SMTH
(real, input) A parameter that controls extrapolation into data sparse regions. If SMTH is zero, then nothing special is done in data sparse regions. A good first choice for SMTH is 1.

- NDERIV
(integer, input) An array dimensioned for 3 that specifies, for each coordinate, whether you want functional values (=0), first derivative values (=1), or second derivative values (=2).

- NXO
(integer, input) The number of X coordinate values in the output grid.

- NYO
(integer, input) The number of Y coordinate values in the output grid.

- NZO
(integer, input) The number of Z coordinate values in the output grid.

- XO
(real, input) An array dimensioned for NXO containing the X coordinates of the output spline.

- YO
(real, input) An array dimensioned for NYO containing the Y coordinates of the output spline.

- ZO
(real, input) An array dimensioned for NZO containing the Z coordinates of the output spline.

- UO
(real, output) An array dimensioned for NXO x NYO x NZO containing the calculated function values for the output function. UO(I,J,K) is the calculated functional value at (XO(I), YO(J), ZO(K)) for I=1,NXO and J=1,NYO and K=1,NZO.

- NWRK
(integer, input) The size of the WORK array. NWRK must be at least NK * (NK+3) where NK = KNOTS(1) * KNOTS(2) * KNOTS(3).

- WORK
(real, input) A work array dimensioned for NWRK.

- IER
(integer, output) An error return value. If IER is returned as 0, then no errors were detected. If IER is non-zero, then refer to the man page for csagrid_errors for details.

## Usage

CSA3XS is called to find an approximating cubic spline for three-dimensional input data. CSA3XS is called if you want to weight the input data values, calculate derivatives, or handle data sparse areas specially. If you do not want to do any of these three things, then use CSA3S.

## Access

To use CSA3XS, load the NCAR Graphics library ngmath.

## See Also

csagrid, csa3s, csa3ls, csa3lxs

Complete documentation for Csagrid is available at URL

http://ngwww.ucar.edu/ngdoc/ng/ngmath/csagrid/csahome.html

## Copyright

Copyright (C) 2000

University Corporation for Atmospheric Research

The use of this Software is governed by a License Agreement.