Grouping.xtl

1⍝# Grouping: grouping by key -- the groups, and counts, sums, means,
2⍝# least and greatest per key, or any function per key.
3⍝# Import it with an alias of your choice: "gr:" u_se< "Grouping".
4⍝# Put libs/Grouping/src on XETAL_PATH ("just path"); the reference is libs/Grouping/docs.
5⍝# Names with l: are exported; those under h: are private to this file.
6⍝#
7⍝# Keys and values are lists of one length: item i of the values
8⍝# belongs to key i. Keys may be numbers, characters or texts (boxes).
9⍝# Every result has one item per distinct key, in the order of
10⍝# u_nique keys (first seen first), as APL's key operator gives them.
11
12⍝## Grouping
13
14⍝# keys g_roups values: the values of each key, a list per key.
15ˡg̲roups ← { k v → '{ u → (k = u) r̲eplicate v } m̲ap u̲nique k }
16
17⍝# keys 'f b_y values: f applied to each key's values (f gives one
18⍝# number per group): keys '{ '+ r_/ _r } gr:b_y values.
19ˡb̲y ← { f̲ k v → '{ u → f̲ (k = u) r̲eplicate v } e̲ach u̲nique k }
20
21⍝## Per-key summaries
22
23⍝# gr:c_ount keys: how many items each key has.
24ˡc̲ount ← { k → '{ u → t̲ally w̲here k = u } e̲ach u̲nique k }
25
26⍝# keys s_um values, keys m_ean values: per key.
27ˡs̲um ← { k v → k '{ '+ r̲/ ⍵ } ˡb̲y v }
28ˡm̲ean ← { k v → (f̲loat k ˡs̲um v) ÷ f̲loat ˡc̲ount k }
29
30⍝# keys l_east values, keys g_reatest values: per key.
31ˡl̲east ← { k v → k '{ 'm̲in r̲/ ⍵ } ˡb̲y v }
32ˡg̲reatest ← { k v → k '{ 'm̲ax r̲/ ⍵ } ˡb̲y v }