 NCL Home > Documentation > Functions > Spherical harmonic routines

# ilapvf

Inverts the vector Laplacian (on a fixed grid) using spherical harmonics.

## Prototype

```	procedure ilapvf (
ulap  : numeric,
vlap  : numeric,
u     : float,    ; or double
v     : float     ; or double
)
```

## Arguments

ulap
vlap

the vector Laplacian arrays to invert (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

u
v

vector arrays (output, same dimensions as ulap, vlap)

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

## Description

ilapvf inverts the Laplacian vector ulap, vlap and returns the results in the arrays u and v. ilapvf operates on a fixed grid. If the input arrays ulap and vlap are on a gaussian grid, ilapvg should be used.

This procedure does not handle missing values. If any missing values are encountered in a particular 2D input grid, then all of the values in the corresponding output grids will be set to the missing value defined by the output grids' _FillValue attribute.

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
```

## Examples

Example 1

Read u and v (on a fixed grid) from a netCDF file and compute the inverse vector Laplacian:

```load "\$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_code.ncl"
begin
v200 = a->V(0,{189.},:,:)			; v200 is dimensioned nlat x nlon
u200 = a->U(0,{189.},:,:)			; u200 is dimensioned nlat x nlon
printVarSummary(v200)
ilapl_u = u200			; preallocate space for return array
ilapl_v = v200			; preallocate space for return array
ilapvf(u200,v200,ilapl_u,ilapl_v)
end
```

## 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)