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# dim_rmsd

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

## Prototype

```	function dim_rmsd (
x  : numeric,
y  : numeric
)

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.

## Return value

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

The output dimensionality is the same as the first n-1 dimensions of the input variable. That is, the dimension rank of the input variable will be reduced by one.

## Description

The dim_rmsd function computes the root-mean-square-difference of all elements of the n-1 dimension for each index of the dimensions 0...n-2. Missing values are ignored.

Use dim_rmsd_n if you want to specify which dimension(s) to do the calculation on.

Use the dim_rmsd_Wrap function 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(q,r)   ;==>  rmsd(3,5)

; Use dim_rmsd_Wrap if metadata retention is desired
; rmsd= dim_rmsd_Wrap(q,r)   ;==>  rmsd(3,5)
```
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( x,y )    ; ==> rmsdLon(ntim,nlat)

; Use dim_rmsd_Wrap if metadata retention is desired
; rmsdLon= dim_rmsd_Wrap( x,y )    ; ==> 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. Use named subscripting to reorder the input array such that "time" is the rightmost dimension.

```    rmsdTime = dim_rmsd( x(lat|:,lon|:,time|:), \
y(lat|:,lon|:,time|:) )
; ==> rmsdTime(nlat,nlon)

; Use dim_rmsd_Wrap if metadata retention is desired
; rmsdTime = dim_rmsd_Wrap( x(lat|:,lon|:,time|:), \
; y(lat|:,lon|:,time|:) )
; ==> rmsdTime(nlat,nlon)

```

Important note: reordering arrays can be an expensive operation, especially if your variable is large or you are repeatedly reordering arrays in your script. Use the dim_rmsd_n or dim_rmsd_n_Wrap functions to avoid reordering:

```    rmsdTime = dim_rmsd_n( x, y, 0 )
; ==> no reordering needed

; Use dim_rmsd_n_Wrap if metadata retention is desired
; rmsdTime = dim_rmsd_n_Wrap( x, y, 0 )
```