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# dim_sum_wgt

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

## Prototype

```	function dim_sum_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 be the same as the right dimension of x.

opt

A scalar: (a) opt=0 means compute the weighted sum only if all values are not missing; (b) opt=1 means compute the weighted sum of all non-missing values; (c) opt>1 means to return the sum only if the number of non-missing values is greater-than 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_sum_wgt function computes the weighted sum 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) = 82.3
```

Use dim_sum_wgt_n if you want to specify which dimension to do the weighted sum across.

Use the dim_sum_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 sum (total) at each lat/lon point. Use dimension reordering to make time the rightmost dimension.

```    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 /)
pTot = dim_sum_wgt(precip(lat|:,lon|:,time|:), wgt, 0 )    ; ==> pTot(nlat,mlon)

; Use dim_sum_wgt_Wrap if metadata retention is desired
; pTot = dim_sum_wgt_Wrap(precip( \
;                                      lat|:,lon|:,time|:), wgt, 0 )    ; ==> pTot(nlat,mlon)

pTot = dim_sum_wgt_n(precip, wgt, 0, 0)                    ; no reordering needed

; Use dim_sum_wgt_n_Wrap if metadata retention is desired
; pTot = dim_sum_wgt_n_Wrap(precip, wgt, 0, 0) ; no reordering needed
```

Example 2

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

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

Tsum = dim_sum_wgt( T(time|:,lat|:,lon|:,lev|:), wgt, 0 )   ; ==> Tsum(time,lat,lon)

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

Tsum = dim_sum_wgt_n( T, wgt, 0, 1 )                        ; no reordering needed

; Use dim_sum_wgt_n_Wrap if metadata retention is desired
; Tsum = dim_sum_wgt_n( T, wgt, 0, 1 )                        ; no reordering needed
```