MidDate

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`MidDate`

New in 14.2

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MidDate[datespec]

gives the midpoint instant of a date or list of dates datespec.

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MidDate[datespec,gran]

gives the midpoint date object with granularity gran.

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MidDate[datespec,gran,x]

gives the date that is the fraction x between the beginning and end of datespec.

Details and Options

MidDate gives the date that is midway through a given date or list of dates.
Possible forms of datespec in MidDate[datespec,…] include:

	DateObject[…]	mid date of a date object of any granularity
	TimeObject[…]	mid time of a time object of any granularity
	DateInterval[…]	mid date of a date interval
	{d₁,d₂,…}	mid date of a list of dates, times and intervals
	TimeSeries[…]	mid date of the times of a time series
	EventSeries[…]	mid date of the times of an event series
	TemporalData[…]	mid date of the times of temporal data

MidDate[(d₁,d₂,…}] gives the midpoint instant based on the sum of probability density functions for a uniform distribution of the d_i dates.
MidDate takes the following options:

CalendarType	Automatic	calendar for generated date
DateFormat	Automatic	format used to display date
DateGranularity	Automatic	calendar granularity for generated date
Method	Automatic	midpoint detection method
TimeSystem	Automatic	time system being used
TimeZone	Automatic	time zone being used

With MidDate[{d₁,d₂,…},Methodmethod], the Method option value method determines how midpoint dates are calculated for the d_i dates. Possible Method values include:

	"GranularMean"	mean weighted by granularity length (default)
	"GranularMedian"	median weighted by granularity length
	"WeightedMean"	mean weighted by full duration of each date
	"UnionedMean"	mean of the unioned region of all dates
	"MidpointMean"	mean of midpoints
	"MidpointMedian"	median of midpoints
	"BoundsMean"	mean of the date bounds

Examples

open allclose all

Basic Examples (4)Summary of the most common use cases

Get the midpoint instant for a month-granular date:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-ppn0uf

Out[1]=1

Find the day that falls in the middle of a year:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-2hziip

Out[1]=1

Find the hour that is 2/3 of the way through a given week:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-s9e0xz

Out[1]=1

Find the mid date of three instants in the year 2024:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-03yf3o

Out[1]=1

Scope (7)Survey of the scope of standard use cases

For list inputs, the midpoint is taken based on the implicit interval for each date in the list:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-pwon6h

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-odwg27

Out[2]=2

The full time interval for each date is taken into account:

In[3]:=3

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https://wolfram.com/xid/0enxc2jv4-b94rbu

Out[3]=3

For mid dates with coarse granularity, the date given corresponds to the instance that encompasses the midpoint, even if it begins before the first date:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-qmdmic

Out[1]=1

Get the mid date for an EventSeries:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-hwc1fs

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-lsix7z

Out[2]=2

Get the mid date from a Databin:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-01s3kr

Out[1]=1

Find the mid date for an Association:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-j73bb9

Out[1]=1

Find the mid time of five times today:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-vhym9o

Out[1]=1

Find the midpoint instant of three date intervals:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-sq4sl1

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-zor1ck

Out[2]=2

Options (9)Common values & functionality for each option

CalendarType (1)

Return the midpoint date in the Japanese calendar:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-z3uidz

Out[1]=1

DateFormat (1)

Return the midpoint date in an "ISODateTime" format:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-m9xm76

Out[1]=1

Method (5)

The default midpoint detection method ("GranularMean") takes into account granularity length when selecting a midpoint:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-8mg5gk

Out[1]=1

This means a one-week period is weighted equally whether it appears as a single "Week" date or as a sequence of seven "Day" dates:

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-2f3e9

Out[2]=2

The method "WeightedMean" takes into account the full length of each date, not just its granularity:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-58y2rg

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-whziig

Out[2]=2

The method "MidpointMedian" gives equal weight to all dates, regardless of granularity:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-5bkfq

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-xfdp9

Out[2]=2

The method "BoundsMean" considers only the outer date bounds of the dates:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-pwc7jf

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-pm4tga

Out[2]=2

Some midpoint detection methods weight for granularity, while others treat all dates as equally weighted:

In[1]:=1

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https://wolfram.com/xid/0enxc2jv4-8dlpvg

In[2]:=2

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https://wolfram.com/xid/0enxc2jv4-wxbgh4

In[3]:=3

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https://wolfram.com/xid/0enxc2jv4-lcyyeo

In[4]:=4

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https://wolfram.com/xid/0enxc2jv4-1cddjx

With only two dates given, "Weighted" methods will account for granularity and be pulled toward coarser granularity dates:

In[5]:=5

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https://wolfram.com/xid/0enxc2jv4-wzx9ih

Out[5]=5

With the coarser granularity broken up into individual dates, the "Weighted" methods remain consistent:

In[6]:=6

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https://wolfram.com/xid/0enxc2jv4-7oj7zj

Out[6]=6

Midpoint methods weight all dates equally and thus do not account for difference in granularity:

In[7]:=7

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https://wolfram.com/xid/0enxc2jv4-8b1dd6

Out[7]=7

If broken into individual days, these midpoint methods will be pulled to the right:

In[8]:=8

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https://wolfram.com/xid/0enxc2jv4-lv44q3

Out[8]=8

"WeightedMean" and "UnionedMean" both account for the full duration of dates, but "WeightedMean" will account for overlapping intervals, while "UnionedMean" will flatten all intervals:

In[9]:=9