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# igradsF

Computes a scalar array from its gradient components on a fixed grid using spherical harmonics.

## Prototype

```	function igradsF (
gzx  : numeric,
gzy  : numeric
)

return_val [dimsizes(gzx)] :  float or double
```

## Arguments

gzx
gzy

gradient arrays (input, two or more dimensions, last two dimensions must be nlat x nlon)

• input values must be in ascending latitude order
• input arrays must be on a global grid

## Return value

Returns an array of size dimsizes (gzx). The return type will be double if gzx or gzy is double, and float otherwise.

## Description

igradsF computes a scalar array given gradient gzx and gzy, and returns it as an array with the same dimensions as gzy, gzy. igradsF operates on a fixed grid.

This function does not handle missing values (defined by the _FillValue attribute). If any missing values are encountered in a particular 2D input grid, then all of the values in the corresponding output grid will be set to the default missing value appropriate to the type of the output.

This function computes a scalar function whose gradient is the irrotational component of the input vector. The gradient is equal to the input vector only if its rotational component is zero.

Note: For the arrays whose last two dimensions are nlat x nlon, the rest of the dimensions (if any) are collectively referred to as N. If the input/output arrays are just two dimensions, then N can either be considered equal to 1 or nothing at all.

Arrays which have dimensions N x nlat x nlon should not include the cyclic (wraparound) points when invoking the procedures and functions which use spherical harmonics (Spherepack).

For example, if an array x has dimensions nlat = 64 and nlon = 129, where the "129" represents the cyclic points, then the user should pass the data to the procedure/function via:

```    z = sample ( x([...],:,0:nlon-2) )  ; does not include cyclic points
```
If the input arrays gzx and gzy are on a gaussian grid, igradsG should be used. Also, note that igradsF is the function version of igradsf.

## Examples

Example 1

Given arrays T_grad_lat(time,lev,lat,lon) and T_grad_lon(time,lev,lat,lon) containing the gradient (latitudinal and longitudinal derivatives), compute the scalar array. The gradient arrays are on a fixed grid.

```  T = igradsF (T_grad_lon, T_grad_lat)
```
Example 2

Given a scalar array T, compute the latitudinal and longitudinal derivatives, and then recompute T. T is on a fixed grid.

```  T_grad_lon = T                ; create arrays to hold output, same size and type as input
T_grad_lat = T
; this procedure will overwrite
; values in T_grad_lon and T_grad_lat

gradsf (T, T_grad_lon, T_grad_lat)
T_grad_lon@long_name = "longitudinal gradient (derivative)"
T_grad_lat@long_name = "latitudinal gradient (derivative)"
T = igradsF (T_grad_lon, T_grad_lat)
```

## Errors

If jer or ker is equal to:

1 : error in the specification of nlat
2 : error in the specification of nlon
4 : error in the specification of N (jer only)