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.