Documentation Source Text

}

chng {2019-04-00 (3.28.0)} {
<li> Enhanced [window functions]:
<ol type="a">
<li> Add support the [EXCLUDE clause].
<li> Add support for [window chaining].
<li> Add support for GROUPS [frames].
<li> Add support for "&lt;expr&gt; PRECEDING" and

     "&lt;expr&gt; FOLLOWING" in RANGE [frames].
</ol>
<li> Added the new [sqlite3_stmt_isexplain(S)] interface for determining
     whether or not a [prepared statement] is an [EXPLAIN].
<li> Enhanced [VACUUM INTO] so that it works for read-only databases.
<li> New query optimizations:
<ol type="a">
<li> Enable the [LIKE optimization] for cases when the ESCAPE keyword

}

chng {2019-04-00 (3.28.0)} {
<li> Enhanced [window functions]:
<ol type="a">
<li> Add support the [EXCLUDE clause].
<li> Add support for [window chaining].
<li> Add support for [GROUPS frames].
<li> Add support for "[RANGE n PRECEDING|&lt;expr&gt; PRECEDING]" and
     "[RANGE n FOLLOWING|&lt;expr&gt; FOLLOWING]" boundaries
     in RANGE [frames].
</ol>
<li> Added the new [sqlite3_stmt_isexplain(S)] interface for determining
     whether or not a [prepared statement] is an [EXPLAIN].
<li> Enhanced [VACUUM INTO] so that it works for read-only databases.
<li> New query optimizations:
<ol type="a">
<li> Enable the [LIKE optimization] for cases when the ESCAPE keyword

<tcl>hd_keywords {window functions} {window function}</tcl>

<title>Window Functions</title>
<table_of_contents>

<h1>Introduction to Window Functions</h1>

<p>A window function is a special SQL function where the input
values are taken from
a "window" of one or more rows in the results set of a SELECT statement.










<tcl>
RecursiveBubbleDiagram window-function-invocation window-defn frame-spec filter
</tcl>

<p>Window functions are distinguished from ordinary SQL functions by the
presence of an OVER clause. If a function invocation has an OVER clause,
then it is a window function. If it lacks an OVER clause, then it is an
ordinary aggregate or scalar function. Window functions may have a FILTER
clause in between the function and the OVER clause.

<p>Unlike ordinary functions, window functions
cannot use the DISTINCT keyword.
Also, Window functions may only appear in the result set and in the
ORDER BY clause of a SELECT statement.

<p>The following simple table is used to demonstrate how window









functions work:

<codeblock>
  CREATE TABLE t0(x INTEGER PRIMARY KEY, y TEXT);
  INSERT INTO t0 VALUES (1, 'aaa'), (2, 'ccc'), (3, 'bbb');
</codeblock>

<p>An example of using window functions:

<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   x | y | row_number</i>
  -----------------------
  <i>--   1 | aaa | 1         </i>
  <i>--   2 | ccc | 3         </i>
  <i>--   3 | bbb | 2         </i>
  <i>-- </i>
  SELECT x, y, row_number() OVER (ORDER BY y) AS row_number FROM t0 ORDER BY x;
</codeblock>

<p>The example uses the built-in window function row_number().
The row_number() window function
assigns a monotonically increasing integer to each
row in order of the "ORDER BY" clause within the
<yynonterm>window-defn</yynonterm> (in this case "ORDER BY y"). Note that 
this does not affect the order in which results are returned from
the overall query.  The order of the final output is
still governed by the ORDER BY clause attached to the SELECT
statement (in this case "ORDER BY x").

................................................................................
         <b>win2</b> AS (PARTITION BY y ORDER BY x)
  ORDER BY x;
</codeblock>

<p>The WINDOW clause, when one is present, comes after any HAVING clause and
before any ORDER BY.


<h1 tags="aggregate window functions">Aggregate Window Functions</h1>

<p> The examples in this section all assume that the database is populated as
follows:

<codeblock>
  CREATE TABLE t1(a INTEGER PRIMARY KEY, b, c);
  INSERT INTO t1 VALUES   (1, 'A', 'one'  ),
................................................................................
                          (3, 'C', 'three'),
                          (4, 'D', 'one'  ),
                          (5, 'E', 'two'  ),
                          (6, 'F', 'three'),
                          (7, 'G', 'one'  );
</codeblock>

<p> An aggregate window function is similar to an aggregate function, except

adding it to a query does not change the number of rows returned. Instead,
for each row the result of the aggregate window function is as if the
corresponding aggregate were run over all rows in the "window frame".



<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   a | b | group_concat</i>
  -------------------------
................................................................................
For example, the frame for the row with (a=3) consists of rows (2, 'B', 'two'),
(3, 'C', 'three') and (4, 'D', 'one'). The result of group_concat(b, '.') 
for that row is therefore 'B.C.D'.

<p> All of SQLite's [Aggregate Functions|aggregate functions] may
be used as aggregate window functions. It is also possible to 
[user-defined window functions|create user-defined aggregate window functions].

































































<tcl>hd_fragment framespec {frame specification} {frames}</tcl>
<h2>Frame Specifications</h2>

<tcl>
RecursiveBubbleDiagram frame-spec
</tcl>

<p> The <yynonterm>frame-spec</yynonterm> determines which output rows are
read by an aggregate window function.  The
<yynonterm>frame-spec</yynonterm> consists of three parts:

<ul>
  <li> A frame type - either ROWS, RANGE or GROUPS,
  <li> A starting frame boundary,
  <li> An ending frame boundary,
  <li> An EXCLUDE clause.
</ul>








<p>The ending frame boundary can be omitted, in which case it defaults


to CURRENT ROW.

<p> If the frame type is RANGE or GROUPS, then rows with the same values for
all ORDER BY expressions are considered "peers". Or, if there are no ORDER BY
terms, all rows are peers. Rows that are peers always have the same window
frames.

<p>The default <yynonterm>frame-spec</yynonterm> is:

<codeblock>
    RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE NO OTHERS
</codeblock>

................................................................................
  <i>--   7 | G | one   | A.D.G       </i>
  <i>-- </i>
  SELECT a, b, c, 
         group_concat(b, '.') OVER (ORDER BY c) AS group_concat 
  FROM t1 ORDER BY a;
</codeblock>




<p> There are five options for frame boundaries:





<table striped=1>
<tr><th>Frame Boundary <th>Description
<tr><td>UNBOUNDED&nbsp;PRECEDING <td> The start of the frame is the first
        row in the set.
<tr><td>&lt;expr&gt; PRECEDING <td> &lt;expr&gt; is a constant expression
        that evaluates to a non-negative numeric value. If the frame type
        is ROWS or GROUPS, the expression must evaluate to an integer
        value.<br><br>
        For a ROWS frame, the start or end of the frame is &lt;expr&gt; rows
        before the current row.<br><br>
        For a GROUPS frame, the frame begins or ends with the peers

        &lt;expr&gt; groups of peers before or after the current row's group.
        For both ROWS and GROUPS frames, "0 PRECEDING" is the same as "CURRENT
        ROW".
        <br><br> A RANGE frame that uses "&lt;expr&gt; PRECEDING" must be
        paired with an ORDER BY clause that contains a single expression. If
        the ORDER BY expression for the current row is not a numeric value, 
        then "&lt;expr&gt; PRECEDING" is equivalent to "CURRENT ROW".
        Otherwise, if the ORDER BY value is numeric for the current row, then
        the value of "&lt;expr&gt;" is used as a logical range for determining

        which groups are part of the current frame.
        <br><br>
        For example, if the ORDER BY clause is ASC (not DESC) and the
        "&lt;expr&gt; PRECEDING" is used as the start of the frame, then
        the first group in the frame is that with the smallest value for
        the ORDER BY expression that is greater than (current-row -
        &lt;expr&gt;). If the ORDER BY clause is DESC, then the first group
        is that with an ORDER BY expresion greater than (current-row +
        &lt;expr&gt;).
        <br><br>
        Or, if it is used as the end of the frame and the ORDER BY is ASC, then
        the last group in the grame is that with the largest value for the

        ORDER BY expression that is less than (current-row - &lt;expr&gt;).
        For DESC the last group is that with the smallest ORDER BY value
        that is greater than (current-row + &lt;expr&gt;).







































































<tr><td>CURRENT ROW <td> The current row. For RANGE and GROUPS frame types, all
        peers of the current row are also included in the window frame,

        regardless of whether CURRENT ROW is used as the starting or ending
        frame boundary.

<tr><td>&lt;expr&gt; FOLLOWING <td> &lt;expr&gt; is a constant expression
        that must evaluate to a non-negative numeric value. It is handled
        similarly to "&lt;expr&gt; PRECEDING".
<tr><td>UNBOUNDED&nbsp;FOLLOWING <td> The end of the frame is the last





        row in the set.
</table>



<p> The ending frame boundary must not take a form that appears higher in
the above list than the starting frame boundary.

<p> In the following example, the window frame for each row consists of all
rows from the current row to the end of the set, where rows are sorted
according to "ORDER BY a".

<codeblock>
................................................................................
  <i>-- </i>
  SELECT c, a, b, group_concat(b, '.') OVER (
    ORDER BY c, a ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
  ) AS group_concat
  FROM t1 ORDER BY c, a;
</codeblock>

<p> Even though they are technically part of the frame-specification, 
[exclude clause|the EXCLUDE clause] and [window chaining] are described
separately below.

<h2>The PARTITION BY Clause</h2>



<p> A <yynonterm>window-defn</yynonterm> may include a PARTITION BY clause.
If so, the rows returned by the SELECT statement are divided into groups -
partitions - with the same values for each PARTITION BY expression, and then
window-function processing is performed separately for each

partition. This is similar to the way the rows are grouped by the
GROUP BY clause of an aggregate query.


<p> For example:













<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   c     | a | b | group_concat</i>
  ---------------------------------

  <i>--   one   | 1 | A | A.D.G       </i>
  <i>--   one   | 4 | D | D.G         </i>
  <i>--   one   | 7 | G | G           </i>
  <i>--   three | 3 | C | C.F         </i>
  <i>--   three | 6 | F | F           </i>
  <i>--   two   | 2 | B | B.E         </i>
  <i>--   two   | 5 | E | E           </i>






  <i>-- </i>

  SELECT c, a, b, group_concat(b, '.') OVER (
    PARTITION BY c ORDER BY a RANGE BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING


  ) AS group_concat








  FROM t1 ORDER BY c, a;
</codeblock>

<h2>The FILTER Clause</h2>

<tcl>
RecursiveBubbleDiagram filter
................................................................................
  <i>-- </i>
  SELECT c, a, b, group_concat(b, '.') FILTER (WHERE c!='two') OVER (
    ORDER BY a
  ) AS group_concat
  FROM t1 ORDER BY a;
</codeblock>

<tcl>hd_fragment wexcls {exclude clause} {EXCLUDE clause}</tcl> 
<h2>The EXCLUDE Clause</h2>

<p> The optional EXCLUDE clause may take any of the following four forms:

<ul>
  <li> <p><b> EXCLUDE NO OTHERS</b>: This is the default. In this case no
  rows are excluded from the window frame as defined by its starting and ending
  frame boundaries.

  <li> <p><b> EXCLUDE CURRENT ROW</b>: In this case the current row is 
  excluded from the window frame.

  <li> <p><b> EXCLUDE GROUP</b>: In this case the current row and all other
  rows that are peers of the current row are excluded from the group. When
  processing an EXCLUDE clause, all rows with the same ORDER BY values, or all
  rows in the partition if there is no ORDER BY clause, are considered peers,
  even if the frame type is ROWS.

  <li> <p><b> EXCLUDE TIES</b>: In this case the current row is part of the
  frame, but all other peers are excluded.
</ul>

<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   c    | a | b | no_others     | current_row | grp       | ties</i>
  <i>--  one   | 1 | A | A.D.G         | D.G         |           | A</i>
  <i>--  one   | 4 | D | A.D.G         | A.G         |           | D</i>
  <i>--  one   | 7 | G | A.D.G         | A.D         |           | G</i>
  <i>--  three | 3 | C | A.D.G.C.F     | A.D.G.F     | A.D.G     | A.D.G.C</i>
  <i>--  three | 6 | F | A.D.G.C.F     | A.D.G.C     | A.D.G     | A.D.G.F</i>
  <i>--  two   | 2 | B | A.D.G.C.F.B.E | A.D.G.C.F.E | A.D.G.C.F | A.D.G.C.F.B</i>
  <i>--  two   | 5 | E | A.D.G.C.F.B.E | A.D.G.C.F.B | A.D.G.C.F | A.D.G.C.F.E</i>
  <i>-- </i>
  SELECT c, a, b,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE NO OTHERS
    ) AS no_others,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE CURRENT ROW
    ) AS current_row,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE GROUP
    ) AS grp,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE TIES
    ) AS ties
  FROM t1 ORDER BY c, a;
</codeblock>

<tcl>hd_fragment wchaining {window chaining}</tcl>
<h2>Window Chaining</h2>

<p>
Window chaining is a shorthand that allows one window to be defined in terms 
of another. Specifically, the shorthand allows the new window to implicitly
................................................................................
<p>
the window used by the group_concat() is equivalent to "PARTITION BY a ORDER 
BY c ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW". In order to use window
chaining, all of the following must be true:

<ul>
  <li><p>The new window definition must not include a PARTITION BY clause. The
       PARTITION BY clause, or lack thereof, is always copied from the base
       window.

  <li><p>If the base window has an ORDER BY clause, it is copied into the new
       window. In this case the new window must not specify an ORDER BY clause.
       If the base window has no ORDER BY clause, one may be specified as part
       of the new window definition.
  
  <li><p>The base window may not specify a frame specification.

</ul>

<p>The two fragments of SQL below are similar, but not entirely equivalent, as
the latter will fail if the definition of window "win" contains a frame
specification.

<codeblock>
  SELECT group_concat(b, '.') OVER win ...
  SELECT group_concat(b, '.') OVER (win) ...
</codeblock>


<h1>Built-in Window Functions</h1>

<p> As well as aggregate window functions, SQLite features a set of built-in
window functions based on 
<a href=https://www.postgresql.org/docs/10/static/functions-window.html>
those supported by PostgreSQL</a>.

................................................................................
<p> Built-in window functions honor any PARTITION BY clause in the same way
as aggregate window functions - each selected row is assigned to a partition 
and each partition is processed separately. The ways in which any ORDER BY
clause affects each built-in window function is described below. Some of
the window functions (rank(), dense_rank(), percent_rank() and ntile()) use
the concept of "peer groups" (rows within the same partition that have the
same values for all ORDER BY expressions). In these cases, it does not matter
whether the <yynonterm>frame-spec</yynonterm> specifies ROWS or RANGE - for
the purposes of built-in window function processing, rows with the same values
for all ORDER BY expressions are considered peers regardless of the frame type.

<p> Most built-in window functions ignore the
<yynonterm>frame-spec</yynonterm>, the exceptions being first_value(),
last_value() and nth_value(). It is a syntax error to specify a FILTER 
clause as part of a built-in window function invocation.

................................................................................
  <li> <b>xInverse(3)</b> - remove value "3" from the window. The window now
       contains values 8 and 1 only.
  <li> <b>xValue()</b> - invoked to obtain the value for row (x='d'). 9.
</ol>

<h1>History</h1>

<p>Window function support was added to SQLite with release
[version 3.25.0] ([dateof:3.25.0]). The SQLite developers used
the <a href=http://www.postgresql.org>PostgreSQL</a> window function
documentation as their primary reference for how window functions
ought to behave.  Many test cases have been run against PostgreSQL
to ensure that window functions operate the same way in both
SQLite and PostgreSQL.

<tcl>hd_keywords {window functions} {window function}</tcl>

<title>Window Functions</title>
<table_of_contents>

<h1>Introduction to Window Functions</h1>

<p>A window function is an SQL function where the input
values are taken from
a "window" of one or more rows in the results set of a SELECT statement.

<p>Window functions are distinguished from other SQL functions by the
presence of an OVER clause. If a function has an OVER clause,
then it is a window function. If it lacks an OVER clause, then it is an
ordinary aggregate or scalar function. Window functions might also
have a FILTER clause in between the function and the OVER clause.

<p>The syntax for a window function is like this:


<tcl>
RecursiveBubbleDiagram window-function-invocation window-defn frame-spec filter
</tcl>







<p>Unlike ordinary functions, window functions
cannot use the DISTINCT keyword.
Also, Window functions may only appear in the result set and in the
ORDER BY clause of a SELECT statement.

<p>Window functions come in two varieties: 
[aggregate window functions] and
[built-in window functions].  Any
[aggfunc|aggregate function], including application-defined aggregate
functions, can often be used as an aggregate window function, simply
by adding an appropriate OVER clause.  The built-in window functions,
however, special-case handling in the query planner and hence cannot
be extended by the application.

<p>Here is an example using the built-in row_number()
window function:

<codeblock>
  CREATE TABLE t0(x INTEGER PRIMARY KEY, y TEXT);
  INSERT INTO t0 VALUES (1, 'aaa'), (2, 'ccc'), (3, 'bbb');





  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   x | y | row_number</i>
  -----------------------
  <i>--   1 | aaa | 1         </i>
  <i>--   2 | ccc | 3         </i>
  <i>--   3 | bbb | 2         </i>
  <i>-- </i>
  SELECT x, y, row_number() OVER (ORDER BY y) AS row_number FROM t0 ORDER BY x;
</codeblock>

<p>
The row_number() window function
assigns consecutive integers to each
row in order of the "ORDER BY" clause within the
<yynonterm>window-defn</yynonterm> (in this case "ORDER BY y"). Note that 
this does not affect the order in which results are returned from
the overall query.  The order of the final output is
still governed by the ORDER BY clause attached to the SELECT
statement (in this case "ORDER BY x").

................................................................................
         <b>win2</b> AS (PARTITION BY y ORDER BY x)
  ORDER BY x;
</codeblock>

<p>The WINDOW clause, when one is present, comes after any HAVING clause and
before any ORDER BY.

<tcl>hd_fragment aggwinfunc {aggregate window functions}</tcl>
<h1>Aggregate Window Functions</h1>

<p> The examples in this section all assume that the database is populated as
follows:

<codeblock>
  CREATE TABLE t1(a INTEGER PRIMARY KEY, b, c);
  INSERT INTO t1 VALUES   (1, 'A', 'one'  ),
................................................................................
                          (3, 'C', 'three'),
                          (4, 'D', 'one'  ),
                          (5, 'E', 'two'  ),
                          (6, 'F', 'three'),
                          (7, 'G', 'one'  );
</codeblock>

<p> An aggregate window function is similar to an 
[aggfunc|ordinary aggregate function], except
adding it to a query does not change the number of rows returned. Instead,
for each row the result of the aggregate window function is as if the
corresponding aggregate were run over all rows in the "window frame"
specified by the OVER clause.


<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   a | b | group_concat</i>
  -------------------------
................................................................................
For example, the frame for the row with (a=3) consists of rows (2, 'B', 'two'),
(3, 'C', 'three') and (4, 'D', 'one'). The result of group_concat(b, '.') 
for that row is therefore 'B.C.D'.

<p> All of SQLite's [Aggregate Functions|aggregate functions] may
be used as aggregate window functions. It is also possible to 
[user-defined window functions|create user-defined aggregate window functions].


<tcl>hd_fragment ptxn {partition}</tcl>
<h2>The PARTITION BY Clause</h2>

<p> For the purpose of computing window functions, the entire result set
of a query is divided into one or more "partitions".  A partition consists
of all rows that have the same value for all terms of the PARTITION BY clause
in the <yynonterm>window-defn</yynonterm>.  If there is no PARTITION BY clause,
then the entire result set of the query is a single partition.
Window-function processing is performed separately for each partition.

<p> For example:

<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   c     | a | b | group_concat</i>
  ---------------------------------
  <i>--   one   | 1 | A | A.D.G       </i>
  <i>--   one   | 4 | D | D.G         </i>
  <i>--   one   | 7 | G | G           </i>
  <i>--   three | 3 | C | C.F         </i>
  <i>--   three | 6 | F | F           </i>
  <i>--   two   | 2 | B | B.E         </i>
  <i>--   two   | 5 | E | E           </i>
  <i>-- </i>
  SELECT c, a, b, group_concat(b, '.') OVER (
    PARTITION BY c ORDER BY a RANGE BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
  ) AS group_concat
  FROM t1 ORDER BY c, a;
</codeblock>

<p> In the query above, the "PARTITION BY c" clause breaks the
result set up into three partitions. The first partition has
three rows with c=='one'.  The second partition has two rows with
c=='three' and the third partition has two rows with c=='two'.

<p> In the example above, all the rows for each partition are
grouped together in the final output.  This is because the PARTITION BY
clause is a prefix of the ORDER BY clause on the overall query.  
But that does not have
to be the case.  A partition can be composed of rows scattered
about haphazardly within the result set.  For example:

<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>
  <i>--   c     | a | b | group_concat</i>
  ---------------------------------
  <i>--   one   | 1 | A | A.D.G       </i>
  <i>--   two   | 2 | B | B.E         </i>
  <i>--   three | 3 | C | C.F         </i>
  <i>--   one   | 4 | D | D.G         </i>
  <i>--   two   | 5 | E | E           </i>
  <i>--   three | 6 | F | F           </i>
  <i>--   one   | 7 | G | G           </i>
  <i>-- </i>
  SELECT c, a, b, group_concat(b, '.') OVER (
    PARTITION BY c ORDER BY a RANGE BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
  ) AS group_concat
  FROM t1 ORDER BY a;
</codeblock>


<tcl>hd_fragment framespec {frame specification} {frames}</tcl>
<h2>Frame Specifications</h2>





<p> The <yynonterm>frame-spec</yynonterm> determines which output rows are
read by an aggregate window function.  The
<yynonterm>frame-spec</yynonterm> consists of four parts:

<ul>
  <li> A frame type - either ROWS, RANGE or GROUPS,
  <li> A starting frame boundary,
  <li> An ending frame boundary,
  <li> An EXCLUDE clause.
</ul>

<p> Here are the syntax details:

<tcl>
RecursiveBubbleDiagram frame-spec
</tcl>


<p>The ending frame boundary can be omitted (if the
BETWEEN and AND keywords that surround the starting frame boundary
are also omitted),
in which case the ending frame boundary defaults to CURRENT ROW.

<p> If the frame type is RANGE or GROUPS, then rows with the same values for
all ORDER BY expressions are considered "peers". Or, if there are no ORDER BY
terms, all rows are peers. Peers are always within the same frame.


<p>The default <yynonterm>frame-spec</yynonterm> is:

<codeblock>
    RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE NO OTHERS
</codeblock>

................................................................................
  <i>--   7 | G | one   | A.D.G       </i>
  <i>-- </i>
  SELECT a, b, c, 
         group_concat(b, '.') OVER (ORDER BY c) AS group_concat 
  FROM t1 ORDER BY a;
</codeblock>

<tcl>hd_fragment frametype {frame type}</tcl>
<h3>Frame Type</h3>


<p>
There are three frame types:  ROWS, GROUPS, and RANGE.
The frame type determines how the starting and ending boundaries
of the frame are measured.






<ul>
<li><p><b>ROWS</b>: 
The ROWS frame type means that the starting and ending boundaries
for the frame are determined by counting individual rows relative
to the current row.


<tcl>hd_fragment grouptype {GROUPS frames}</tcl>
<li><p><b>GROUPS</b>:
The GROUPS frame type means that the starting and ending boundaries
are determine by counting "groups" relative to the current group.
A "group" is a set of rows that all have equivalent values for all
all terms of the window ORDER BY clause.  ("Equivalent" means that
the [IS operator] is true when comparing the two values.)
In other words, a group consists of all peers of a row.


<tcl>hd_fragment rangetype {RANGE frames}</tcl>
<li><p><b>RANGE</b>:
The RANGE frame type requires that the ORDER BY clause of the
window have exactly one term.  Call that term "X".  With the
RANGE frame type, the elements of the frame are determined by
computing the value of expression X for all rows in the partition
and framing those rows for which the value of X is within a certain
range of the value of X for the current row.  See the description
in the "[RANGE n PRECEDING|&lt;expr&gt; PRECEDING]" boundary
specification below for details.
</ul>


<p>The ROWS and GROUPS frame types are similar in that they
both determine the extent of a frame by counting relative to
the current row.  The difference is that ROWS counts individual
rows and GROUPS counts peer groups.
The RANGE frame type is different.
The RANGE frame type determines the extent of a frame by
looking for expression values that are within some band of
values relative to the current row.

<tcl>hd_fragment frameboundary {frame boundary}</tcl>
<h3>Frame Boundaries</h3>

<p> There are five ways to describe starting and ending frame boundaries:

<ol>
<li><p> <b>UNBOUNDED PRECEDING</b><br>
     The frame boundary is the first
     row in the [partition].

<li><p> <b>&lt;expr&gt; PRECEDING</b><br>
        &lt;expr&gt; must be a non-negative constant numeric expression.
        The boundary is a row that is &lt;expr&gt; "units" prior to
        the current row.  The meaning of "units" here depends on the
        frame type:
        <ul>
        <li><p> <b>ROWS &rarr;</b>
        The frame boundary is the row that is &lt;expr&gt;
        rows before the current row, or the first row of the
        partition if there are fewer than &lt;expr&gt; rows
        before the current row.  &lt;expr&gt; must be an integer.
        <li><p> <b>GROUPS &rarr;</b>
        A "group" is a set of peer rows - rows that all have
        the same values for every term in the ORDER BY clause.
        The frame boundary is the group that is &lt;expr&gt;
        groups before the group containing the current row, or the
        first group of the partition if there are fewer
        than &lt;expr&gt; groups before the current row.
        For the starting boundary of a frame, the first
        row of the group is used and for the ending boundary
        of a frame, the last row of the group is used.
        &lt;expr&gt; must be an integer.
        <tcl>hd_fragment exprrange {RANGE n PRECEDING} {RANGE n FOLLOWING}</tcl>
        <li><p> <b>RANGE &rarr;</b>
        For this form, the ORDER BY clause of the
        <yynonterm>window-defn</yynonterm> must have a single
        term.  Call that ORDER BY term "X".  Let
        X<sub><small>i</small></sub> be the value of the X
        expression for the i-th row in the partition and let
        X<sub><small>c</small></sub> be the value of X for the
        current row.  Informally, a RANGE bound is the first row
        for which X<sub><small>i</small></sub> is within
        the &lt;expr&gt; of X<sub><small>c</small></sub>.
        More precisely:
        <ol type="a">
        <li> If either X<sub><small>i</small></sub> or
             X<sub><small>c</small></sub> are non-numeric, then
             the boundary is the first row for which the expression
             "X<sub><small>i</small></sub> IS X<sub><small>c</small></sub>"
             is true.
        <li> Else if the ORDER BY is ASC then the boundary
             is the first row for which
             X<sub><small>i</small></sub>&gt;=X<sub><small>c</small></sub>-&lt;expr&gt;.
        <li> Else if the ORDER BY is DESC then the boundary
        is the first row for which
        X<sub><small>i</small></sub>&lt;=X<sub><small>c</small></sub>-&lt;expr&gt;.
        </ol>
        For this form, the &lt;expr&gt; does not have to be an
        integer. It can evaluate to a real number as long as
        it is constant and non-negative.
        </ul>
    The boundary description "0 PRECEDING" always means the same
    thing as "CURRENT ROW".

<li><p><b>CURRENT ROW</b><br>
        The current row. For RANGE and GROUPS frame types,
        peers of the current row are also included in the frame,
        unless specifically excluded by the EXCLUDE clause.
        This is true regardless of whether CURRENT ROW is used
        as the starting or ending frame boundary.

<li><p><b>&lt;expr&gt; FOLLOWING</b><br>

        This is the same as "&lt;expr&gt; PRECEDING" except that

        the boundary is &lt;expr&gt; units after the current
        rather than before the current row.

<li><p> <b>UNBOUNDED FOLLOWING</b><br>
   The frame boundary is the last
   row in the [partition].


</ol>

<p> The ending frame boundary may not take a form that appears higher in
the above list than the starting frame boundary.

<p> In the following example, the window frame for each row consists of all
rows from the current row to the end of the set, where rows are sorted
according to "ORDER BY a".

<codeblock>
................................................................................
  <i>-- </i>
  SELECT c, a, b, group_concat(b, '.') OVER (
    ORDER BY c, a ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
  ) AS group_concat
  FROM t1 ORDER BY c, a;
</codeblock>

<tcl>hd_fragment wexcls {exclude clause} {EXCLUDE clause}</tcl> 
<h3>The EXCLUDE Clause</h3>



<p> The optional EXCLUDE clause may take any of the following four forms:

<ul>
  <li> <p><b> EXCLUDE NO OTHERS</b>: This is the default. In this case no
  rows are excluded from the window frame as defined by its starting and ending
  frame boundaries.


  <li> <p><b> EXCLUDE CURRENT ROW</b>: In this case the current row is 
  excluded from the window frame.  Peers of the current row remain in
  the frame for the GROUPS and RANGE frame types.


  <li> <p><b> EXCLUDE GROUP</b>: In this case the current row and all other
  rows that are peers of the current row are excluded from the frame. When
  processing an EXCLUDE clause, all rows with the same ORDER BY values, or all
  rows in the partition if there is no ORDER BY clause, are considered peers,
  even if the frame type is ROWS.

  <li> <p><b> EXCLUDE TIES</b>: In this case the current row is part of the
  frame, but peers of the current row are excluded.
</ul>

<p> The following example demonstrates the effect of the various
forms of the EXCLUDE clause:

<codeblock>
  <i>-- The following SELECT statement returns:</i>
  <i>-- </i>


  <i>--   c    | a | b | no_others     | current_row | grp       | ties</i>
  <i>--  one   | 1 | A | A.D.G         | D.G         |           | A</i>






  <i>--  one   | 4 | D | A.D.G         | A.G         |           | D</i>
  <i>--  one   | 7 | G | A.D.G         | A.D         |           | G</i>
  <i>--  three | 3 | C | A.D.G.C.F     | A.D.G.F     | A.D.G     | A.D.G.C</i>
  <i>--  three | 6 | F | A.D.G.C.F     | A.D.G.C     | A.D.G     | A.D.G.F</i>
  <i>--  two   | 2 | B | A.D.G.C.F.B.E | A.D.G.C.F.E | A.D.G.C.F | A.D.G.C.F.B</i>
  <i>--  two   | 5 | E | A.D.G.C.F.B.E | A.D.G.C.F.B | A.D.G.C.F | A.D.G.C.F.E</i>
  <i>-- </i>
  SELECT c, a, b,
    group_concat(b, '.') OVER (

      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE NO OTHERS
    ) AS no_others,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE CURRENT ROW
    ) AS current_row,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE GROUP
    ) AS grp,
    group_concat(b, '.') OVER (
      ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE TIES
    ) AS ties
  FROM t1 ORDER BY c, a;
</codeblock>

<h2>The FILTER Clause</h2>

<tcl>
RecursiveBubbleDiagram filter
................................................................................
  <i>-- </i>
  SELECT c, a, b, group_concat(b, '.') FILTER (WHERE c!='two') OVER (
    ORDER BY a
  ) AS group_concat
  FROM t1 ORDER BY a;
</codeblock>




















































<tcl>hd_fragment wchaining {window chaining}</tcl>
<h2>Window Chaining</h2>

<p>
Window chaining is a shorthand that allows one window to be defined in terms 
of another. Specifically, the shorthand allows the new window to implicitly
................................................................................
<p>
the window used by the group_concat() is equivalent to "PARTITION BY a ORDER 
BY c ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW". In order to use window
chaining, all of the following must be true:

<ul>
  <li><p>The new window definition must not include a PARTITION BY clause. The
       PARTITION BY clause, if there is one, must be supplied by the base
       window specification.

  <li><p>If the base window has an ORDER BY clause, it is copied into the new
       window. In this case the new window must not specify an ORDER BY clause.
       If the base window has no ORDER BY clause, one may be specified as part
       of the new window definition.
  
  <li><p>The base window may not specify a frame specification.  The frame
      specification can only be given in the new window specification.
</ul>

<p>The two fragments of SQL below are similar, but not entirely equivalent, as
the latter will fail if the definition of window "win" contains a frame
specification.

<codeblock>
  SELECT group_concat(b, '.') OVER win ...
  SELECT group_concat(b, '.') OVER (win) ...
</codeblock>

<tcl>hd_fragment builtins {built-in window functions} {built-ins}</tcl>
<h1>Built-in Window Functions</h1>

<p> As well as aggregate window functions, SQLite features a set of built-in
window functions based on 
<a href=https://www.postgresql.org/docs/10/static/functions-window.html>
those supported by PostgreSQL</a>.

................................................................................
<p> Built-in window functions honor any PARTITION BY clause in the same way
as aggregate window functions - each selected row is assigned to a partition 
and each partition is processed separately. The ways in which any ORDER BY
clause affects each built-in window function is described below. Some of
the window functions (rank(), dense_rank(), percent_rank() and ntile()) use
the concept of "peer groups" (rows within the same partition that have the
same values for all ORDER BY expressions). In these cases, it does not matter
whether the <yynonterm>frame-spec</yynonterm> specifies ROWS, GROUPS, or RANGE.
For the purposes of built-in window function processing, rows with the same values
for all ORDER BY expressions are considered peers regardless of the frame type.

<p> Most built-in window functions ignore the
<yynonterm>frame-spec</yynonterm>, the exceptions being first_value(),
last_value() and nth_value(). It is a syntax error to specify a FILTER 
clause as part of a built-in window function invocation.

................................................................................
  <li> <b>xInverse(3)</b> - remove value "3" from the window. The window now
       contains values 8 and 1 only.
  <li> <b>xValue()</b> - invoked to obtain the value for row (x='d'). 9.
</ol>

<h1>History</h1>

<p>Window function support was first added to SQLite with release
[version 3.25.0] ([dateof:3.25.0]). The SQLite developers used
the <a href=http://www.postgresql.org>PostgreSQL</a> window function
documentation as their primary reference for how window functions
ought to behave.  Many test cases have been run against PostgreSQL
to ensure that window functions operate the same way in both
SQLite and PostgreSQL.

<p>In SQLite [version 3.28.0] ([dateof:3.28.0]),
windows function support was extended to include the EXCLUDE clause,
GROUPS frame types, window chaining, and support for
"&lt;expr&gt; PRECEDING" and "&lt;expr&gt; FOLLOWING" boundaries
in RANGE frames.