@BeginModule
@NewPage
@Name      = Runstat
@Title     = Running statistical values
@Section   = Statistical values
@Class     = Statistic
@Arguments = infile outfile
@Operators = runmin runmax runrange runsum runmean runavg runstd runstd1 runvar runvar1

@BeginDescription
This module computes running statistical values over a selected number of timesteps. Depending on 
the chosen operator the minimum, maximum, range, sum, average, variance or standard deviation of a selected 
number of consecutive timesteps read from @file{infile} is written to @file{outfile}. 
The time of @file{outfile} is determined by the time in the middle of all contributing timesteps of @file{infile}.
@EndDescription
@EndModule


@BeginOperator_runmin
@Title     = Running minimum
@Parameter = nts

@BeginDescription
@IfMan
o(t+(nts-1)/2,x) = min{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{min}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runmax
@Title     = Running maximum
@Parameter = nts

@BeginDescription
@IfMan
o(t+(nts-1)/2,x) = max{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{max}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runrange
@Title     = Running range
@Parameter = nts

@BeginDescription
@IfMan
o(t+(nts-1)/2,x) = range{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{range}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runsum
@Title     = Running sum
@Parameter = nts

@BeginDescription
@IfMan
o(t+(nts-1)/2,x) = sum{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{sum}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runmean
@Title     = Running mean
@Parameter = nts

@BeginDescription
@IfMan
o(t+(nts-1)/2,x) = mean{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{mean}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runavg
@Title     = Running average
@Parameter = nts

@BeginDescription
@IfMan
o(t+(nts-1)/2,x) = avg{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{avg}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runvar
@Title     = Running variance
@Parameter = nts

@BeginDescription
Normalize by n. 

@IfMan
o(t+(nts-1)/2,x) = var{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{var}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runvar1
@Title     = Running variance (n-1)
@Parameter = nts

@BeginDescription
Normalize by (n-1). 

@IfMan
o(t+(nts-1)/2,x) = var1{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{var1}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runstd
@Title     = Running standard deviation
@Parameter = nts

@BeginDescription
Normalize by n. 

@IfMan
o(t+(nts-1)/2,x) = std{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{std}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_runstd1
@Title     = Running standard deviation (n-1)
@Parameter = nts

@BeginDescription
Normalize by (n-1). 

@IfMan
o(t+(nts-1)/2,x) = std1{i(t,x), i(t+1,x), ..., i(t+nts-1,x)}
@EndifMan
@IfDoc
@BeginMath
o(t+(nts-1)/2,x) = \mbox{\textbf{std1}}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x)\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginParameter
@Item = nts
INTEGER  Number of timesteps
@EndParameter


@BeginEnvironment
@Item = CDO_TIMESTAT_DATE
Sets the time stamp in outfile to the "first", "middle" or "last" contributing timestep of infile.
@EndEnvironment


@BeginExample
To compute the running mean over 9 timesteps use:
@BeginVerbatim
   cdo runmean,9 infile outfile
@EndVerbatim
@EndExample