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# dim_rmsd_n

Computes the root-mean-square-difference between two variables' given dimensions at all other dimensions.

## Prototype

```	function dim_rmsd_n (
x        : numeric,
y        : numeric,
dims [*] : integer
)

return_val  :  float or double
```

## Arguments

x

A variable of numeric type and any dimensionality.

y

A variable of numeric type and same dimensionality as x.

dims

The dimension(s) of x on which to to do the root-mean-square-difference on. Must be consecutive and monotonically increasing.

## Return value

The output will be double if x is double, and float otherwise.

The output dimensionality will be the same as all but dims's dimensions of the input variable. The dimension rank of the input variable will be reduced by the rank of dims.

## Description

The dim_rmsd_n function computes the root-mean-square-difference of all elements of the dimensions indicated by dims for each index of the remaining dimensions. Missing values are ignored.

Use the dim_rmsd_n_Wrap if metadata retention is desired. The interface is identical.

## Examples

Example 1

Create two variables q nd r of size (3,5,10) array. Then calculate the root-mean-square-difference of the rightmost dimension.

```    q   = random_uniform(-20,100,(/3,5,10/))
r   = random_uniform(-50, 99,(/3,5,10/))
rmsd= dim_rmsd_n(q,r,2)   ;==>  rmsd(3,5)

; Use dim_rmsd_n_Wrap if metadata retention is desired
; rmsd= dim_rmsd_n_Wrap(q,r,2)   ;==>  rmsd(3,5)
```
Note: when operating across the rightmost dimension, it is simpler to use dim_rmsd.

Example 2

Let x and y be of size (ntim,nlat,mlon) and with named dimensions "time", "lat" and "lon", respectively. Then, for each time and latitude, the root-mean-square-difference is:

```    rmsdLon= dim_rmsd_n( x,y,2 )    ; ==> rmsdLon(ntim,nlat)

; Use dim_rmsd_n_Wrap if metadata retention is desired
; rmsdLon= dim_rmsd_n_Wrap( x,y,2 )    ; ==> rmsdLon(ntim,nlat)
```
Example 3

Let x be defined as in Example 2: x(time,lat,lon). Compute the temporal root-mean-square-difference at each latitude/longitude grid point.

```    rmsdTime = dim_rmsd_n(x, y, 0)    ; ==> rmsdTime(nlat,nlon)

; Use dim_rmsd_n_Wrap if metadata retention is desired
; rmsdTime = dim_rmsd_n_Wrap(x, y, 0)    ; ==> rmsdTime(nlat,nlon)
```
Example 4

Let x be defined as x(time,lev,lat,lon). Compute the temporal root-mean-square-difference at each latitude/longitude grid point.

```    rmsd = dim_rmsd_n(x,y,(/0,1/)) ; ==> rmsd(nlat,nlon)

; Use dim_rmsd_n_Wrap if metadata retention is desired
; rmsd = dim_rmsd_n_Wrap(x,y,(/0,1/)) ; ==> rmsd(nlat,nlon)
```