NAME

       CSA1XS - 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.

SEE ALSO

       csagrid, csa1s, csa1ls, csa1lxs

       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.

UNIX                                              January 1999                                    CSA1XS(3NCARG)