# ncl_csa2xs - Man Page

cubic spline approximation, expanded entry for two-dimensional input, gridded output

## Synopsis

CALL CSA2XS (NI, XI, UI, WTS, KNOTS, SMTH, DERIV, NXO, NYO, XO, YO, 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 coordinates of the input data points. XI is dimensioned for 2 x NI. XI(1,L) is the X coordinate and XI(2,L) is the Y 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 the coordinate (XI(1,L),XI(2,L)) for L=1,NI.

- 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 CSA2XS 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 2 and provides the number of knots to be used in the X and the Y directions. Both KNOTS(1) and KNOTS(2) must be at least 4. 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 2 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.

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

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

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

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

CSA2XS is called to find an approximating cubic spline for two-dimensional input data. CSA2XS 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 CSA2S.

## Access

To use CSA2XS, load the NCAR Graphics library ngmath.

## See Also

csagrid, csa2s, csa2ls, csa2lxs

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.