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dim_variance_n

Computes the unbiased estimates of the variance of a variable's given dimension(s) at all other dimensions.

Available in version 5.1.1 and later.

Prototype

	function dim_variance_n (
		x        : numeric,  
		dims [*] : integer   
	)

	return_val  :  float or double

Arguments

x

A variable of numeric type and any dimensionality.

dims

The dimension(s) of x on which to calculate the variance. 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 the 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_variance_n function computes the unbiased estimate of the variance of all elements of the dimensions indicated by dims for each index of the remaining dimensions. Missing values are ignored.

Technically, this function calculates an estimate of the sample variance. This means that it divides by [1/(N-1)] where N is the total number of non-missing values.

Use dim_variance_n_Wrap if retention of metadata is desired.

See Also

dim_variance_n_Wrap, dim_variance_Wrap, variance, dim_avg, dim_median, dim_num, dim_product, dim_rmsd, dim_rmvmean, dim_rmvmed, dim_standardize, dim_stat4, dim_sum, dim_variance

Examples

Example 1

The following calculates the population and sample variance of 5 values. For illustration, a step-by-step calculation of the variance is done. The variances returned by NCL's three built-in variance functions are included.

  f      = (/ 7, 9, -2, -8, 2/)

  favg   = avg(f)             ; average
  fdev   = f-favg             ; deviations
  fdev2  = fdev^2             ; deviations squared
  nf     = dimsizes(f)        ; N

  pvar   = sum(fdev2)/nf      ; population variance 

  svar   = sum(fdev2)/(nf-1)  ; sample variance 
  var1   = variance(f)
  var2   = dim_variance(f)
  var3   = dim_variance_n(f,0)

  print("pvar="+pvar+"  svar="+svar+"  var1="+var1+"  var2="+var2+"  var3="+var3)

===
output:   pvar=37.84  svar=47.3  var1=47.3  var2=47.3  var3=47.3

Example 2

Create a variable q of size (3,5,10) array. Then calculate the sample variance of the rightmost dimension. 

    q   = random_uniform(-20,100,(/3,5,10/))
    qVar= dim_variance_n(q,2)   ;==>  qVar(3,5)
Example 3

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

    xVarLon= dim_variance_n(x,2)    ; ==> xVarLon(ntim,nlat)
Generally, users prefer that the returned variable have metadata associated with it. This can be accomplished via the dim_variance_n_Wrap function: 

    xVarLon = dim_variance_n_Wrap(x,2)    ; ==> xVarLon(time,lat)
Example 4

Let x be defined as in Example 3: x(time,lat,lon). Compute the temporal sample variance at each latitude/longitude grid point. 

    xVarTime = dim_variance_n(x,0)    ; ==> xVarTime(nlat,nlon)
If metadata is desired use 

    xVarTime = dim_variance_n_Wrap(x,0)    ; ==> xVarTime(lat,lon)
Example 5

Let x be defined as x(time,lev,lat,lon). Compute the sample variance at each latitude/longitude grid point. 

    xVar = dim_variance_n(x,(/0,1/))    ; ==> xVar(nlat,nlon)
To compute the variance at each time/lev grid point: 

    xVar = dim_variance_n(x,(/2,3/))    ; ==> xVar(ntim,nlev)