# ncl_c_csa3lxs - Man Page

cubic spline approximation, expanded entry for three-dimensional input, list output

## Function Prototype

```float *c_csa3lxs(int, float [], float [], float [], float [],
float [], int [], float, int [],
int, float [], float [], float [], int *);```

## Synopsis

```float *c_csa3lxs(int n, float xi[], float yi[], float zi[], float ui[],
float wts[], int knots, float smth, int nderiv,
int no, float xo[], float yo[], float zo[], int *ier);```

## Description

n

(integer,input) The number of input data points. It must be  that n is greater than 3 and, depending  on the size of knots below, n may have to be larger.

xi

(real, input) An array dimensioned for n containing the X coordinate  values for the input function.

yi

(real, input) An array dimensioned for n containing the Y coordinate  values for the input function.

zi

(real, input) An array dimensioned for n containing the Z coordinate  values for the input function.

ui

(real, input) An array containing the functional values of the input  function -- ui[k] is the functional value at (xi[k], yi[k], zi[k])  for k=0,n-1.

wts

(real, input) An array containing weights for the ui values  at the input values, that is, wts[l] is a weight for the value of ui[l] for l=0,n-1. If  you do not desire to weight the input ui values, then set wts to -1. The weights in  the wts array are relative and may be set to any non-negative value. When c_csa3lxs 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, knots, and 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

(real, input) For each of the two coordinate direction, specifies whether you  want functional values (nderiv=0), first derivative values (nderiv=1),  or second derivative values (nderiv=2). For example, if  nderiv=1, nderiv=1 and nderiv=0, then  the second order mixed partial with respect to X and Y would be computed.

no

(integer, input) The number of X - Y - Z coordinate values  to be calculated for the output array.

xo

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

yo

(real, output) An array dimensioned for no containing the Y coordinates of the output list.

zo

(real, output) An array dimensioned for no containing the Z coordinates of the output list.

ier

(pointer to 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 error list in the  error table for details.

## Usage

c_csa3lxs is called to find values of an approximating cubic spline at specified three-dimensional coordinates.   c_csa3lxs 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 c_csa3ls.

c_csa3lxs returns a pointer to a linear array of data that contains the approximated values calculated at the input list of coordinate values. That is, if out is declared as

`  float *out;`

and we set:

```  out = c_csa3lxs(n, x, y, z, u, wts, knots, smth, nderiv,
no, xo, yo, zo, &ier);```

then out[i] is the approximated function value at coordinate point  (xo[i], yo[i], zo[i]) for 0 <= i < no. The space for out is allocated internal  to c_csa3lxs and is no floats in size.

## Access

To use c_csa3lxs, load the NCAR Graphics library ngmath.