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# dim_avg_wgt

Computes the weighted average of a variable's rightmost dimension at all other dimensions.

## Prototype

```	function dim_avg_wgt (
x       : numeric,
w   [*] : numeric,
opt  : integer
)

return_val  :  float or double
```

## Arguments

x

A variable of numeric type and any dimensionality. Missing values are indicated by the _FillValue attribute.

w

A one dimensional array of weights. The length must the same as the right dimension of x

opt

A scalar: (a) opt=0 means compute the weighted average only if all values are not missing; (b) opt=1 means compute the weighted mean of all non-missing values; (c) opt>1 means to return the mean only if the number of non-missing values is greater-then or equal to opt.

## Return value

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

The output dimensionality is the same as the first n-2 dimensions of the input variable. That is, the dimension rank of the input variable will be reduced by one.

## Description

The dim_avg_wgt function computes the weighted average of all elements of the n-1th (rightmost) dimension for each index of the dimensions 0...n-2.

Basically, the following is done for the rightmost dimension.

```
xAvg = SUM [x*w]/SUM[w]
```
The weighting is strictly positional. EG: If x@_FillValue=1e20, and the rightmost dimension is of size 5 and the values are (/3.7, 1e20, 14.3, 1e20, 7.1 /) with weights (/1,3,5,3,1/) then the result will be
```      (3.7*1 + 14.3*5 + 7.1*1)/(1+5+1) = 11.757
```

Use dim_avg_wgt_n if you want to specify which dimension to do the weighted average across.

Use the dim_avg_wgt_Wrap function if metadata retention is desired. The interface is identical.

## Examples

Example 1

Let z(12,nlat,mlon) contain monthly means and with named dimensions "time", "lat" and "lon", respectively. Compute the weighted annual mean at each lat/lon point. Use dimension reordering to make time the rightmost dimension.

Note: Use dim_avg_wgt_n to avoid having to reorder your data.

```    wgt = (/0.08493151, 0.076712325, 0.08493151, 0.08219178 \  ; same size as dimension "time"
,0.08493151, 0.08219178 , 0.08493151, 0.08493151 \
,0.08219178, 0.08493151 , 0.08219178, 0.08493151 /)
zAnn = dim_avg_wgt( z(lat|:,lon|:,time|:), wgt, 0 )    ; ==> zAnn(nlat,mlon)

; Use dim_avg_wgt_Wrap if metadata retention is desired
; zAnn = dim_avg_wgt_Wrap( z(lat|:,lon|:,time|:), wgt, 0 )    ; ==> zAnn(nlat,mlon)

zAnn = dim_avg_wgt_n( z, wgt, 0, 0)                    ; no reordering needed

; Use dim_avg_wgt_n_Wrap if metadata retention is desired
; zAnn = dim_avg_wgt_n_Wrap( z, wgt, 0, 0)                    ; no reordering needed
```

Example 2

Let T(time,lev,lat,lon). Compute the weighted vertical average total at each time/lat/lon point. Use dimension reordering to make level the rightmost dimension.

Note: Use dim_avg_wgt_n to avoid having to reorder your data.

```    wgt  = (/50,50,100,100,100,50,25,10/)  ; same size as dimension "lev"

Tavg = dim_avg_wgt( T(time|:,lat|:,lon|:,lev|:), wgt, 0 )   ; ==> Tavg(time,lat,lon)

; Use dim_avg_wgt_Wrap if metadata retention is desired
; Tavg = dim_avg_wgt_Wrap( T(time|:,lat|:,lon|:,lev|:), wgt, 0 )   ; ==> Tavg(time,lat,lon)

Tavg = dim_avg_wgt_n( T, wgt, 0, 1 )   ; no reordering needed

; Use dim_avg_wgt_n_Wrap if metadata retention is desired
; Tavg = dim_avg_wgt_n_Wrap( T, wgt, 0, 1 )   ; no reordering needed
```