# ncl_csa1xs - Man Page

cubic spline approximation, expanded entry for one-dimensional input

## Synopsis

CALL CSA1XS (NI, XI, YI, WTS, KNOTS, SMTH, DERIV, NO, XO, YO, NWRK, WORK, IER)

## Description

NI

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

XI

(real, input) An array dimensioned for NI containing the X  coordinates of the input data points.

YI

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

WTS

(real, input) An array dimensioned for NI containing weights for the YI  values at the input XI values, that is, WTS(L) is a weight for the  value of YI(L) for L=1,NI.  If you do not desire to weight the input  YI 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 CSA1XS 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 must be at least 4.  The larger the value 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) Specifies whether you want functional values (NDERIV=0), first derivative values (NDERIV=1), or second derivative values (NDERIV=2).

NO

(integer, input) The number of values to be calculated for the output curve.

XO

(real, input) An array dimensioned for NO  containing the X coordinates of the output curve.

YO

(real, output) An array dimensioned for NO containing the calculated function values for the output curve.

NWRK

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

CSA1XS is called to find an approximating cubic spline for one-dimensional input data.  CSA1XS 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 CSA1S.

## Access

To use CSA1XS, load the NCAR Graphics library ngmath.