@BeginModule
@NewPage
@Name      = Daystat
@Title     = Daily statistical values
@Section   = Statistical values
@Class     = Statistic
@Arguments = ifile ofile
@Operators = daymin daymax daysum daymean dayavg daystd daystd1 dayvar dayvar1

@BeginDescription
This module computes statistical values over timesteps of the same day.
Depending on the chosen operator the minimum, maximum, sum, average, variance
or standard deviation of timesteps of the same day is written to @file{ofile}.
The time stamp in @file{ofile} is from the middle contributing timestep of @file{ifile}.
@EndDescription
@EndModule


@BeginOperator_daymin
@Title     = Daily minimum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = min{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf min}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_daymax
@Title     = Daily maximum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = max{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf max}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_daysum
@Title     = Daily sum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = sum{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf sum}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_daymean
@Title     = Daily mean

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = mean{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf mean}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_dayavg
@Title     = Daily average

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = avg{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf avg}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_dayvar
@Title     = Daily variance

@BeginDescription
@IfMan
Divisor is n. For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = var{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
Divisor is n. For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf var}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_dayvar1
@Title     = Daily variance (n-1)

@BeginDescription
@IfMan
Divisor is (n-1). For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = var1{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
Divisor is (n-1). For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf var1}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_daystd
@Title     = Daily standard deviation

@BeginDescription
@IfMan
Divisor is n. For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = std{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
Divisor is n. For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf std}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_daystd1
@Title     = Daily standard deviation (n-1)

@BeginDescription
@IfMan
Divisor is (n-1). For every adjacent sequence t_1, ...,t_n of timesteps of the same day it is

o(t,x) = std1{i(t',x), t_1<t'<=t_n}
@EndifMan
@IfDoc
Divisor is (n-1). For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same day it is: \\
@BeginMath
o(t,x) = \mbox{\bf std1}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginExample
To compute the daily mean of a time series use:
@BeginVerbatim
   cdo daymean ifile ofile
@EndVerbatim
@EndExample
