The CharacterFrequencies(s) command returns an expression sequence of equations of the form character = frequency, where character is a single character string, and frequency is the number of times the corresponding character occurs in the string s.

The expression CharacterFrequencies( s ) is equivalent to seq( ch = CountCharacterOccurrences( s, ch ), ch = Support( s ) ), but computes the latter result more efficiently.

The frequencies appear in ASCII order; that is, in order of the numeric byte value of the character on the left-hand side of each equation. For an example illustrating how to sort by frequency, see the examples below.

To specify that the frequencies of only certain characters be returned, use an optional character class filter parameter. The parameter can be a string of characters to return, for example, "abcd" or one of the following character class names.

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathrm{with}\left(\mathrm{StringTools}\right)\:$

$\mathrm{CharacterFrequencies}\left(''''\right)$

$\mathrm{CharacterFrequencies}\left(''aaaa''\right)$

$''a''=4$

$\mathrm{CharacterFrequencies}\left(''abcadaeb''\right)$

$''a''=3,''b''=2,''c''=1,''d''=1,''e''=1$

$\mathrm{CharacterFrequencies}\left(''abracadabra''\right)$

$''a''=5,''b''=2,''c''=1,''d''=1,''r''=2$

$\mathrm{CharacterFrequencies}\left(\mathrm{Random}\left(1000000\,'\mathrm{lower}'\right)\right)$

$''a''=38715,''b''=38351,''c''=38615,''d''=38449,''e''=38194,''f''=38657,''g''=38420,''h''=38624,''i''=37981,''j''=38519,''k''=38495,''l''=38382,''m''=38407,''n''=38522,''o''=38175,''p''=38798,''q''=38050,''r''=38676,''s''=38658,''t''=38402,''u''=38559,''v''=38293,''w''=38421,''x''=38494,''y''=38644,''z''=38499$

$\mathrm{CharacterFrequencies}\left(\mathrm{Random}\left(1000000\,'\mathrm{dna}'\right)\right)$

$''A''=251057,''C''=249668,''G''=249658,''T''=249617$

$\mathrm{CharacterFrequencies}\left(\mathrm{Random}\left(1000000\,'\mathrm{binary}'\right)\right)$

$''0''=499805,''1''=500195$

$\mathrm{Shakespeare}≔''When\; in\; disgrace\; with\; Fortune\; and\; men\text{'}s\; eyes,\backslash nI\; all\; alone\; beweep\; my\; outcast\; state,\backslash nAnd\; trouble\; deaf\; heaven\; with\; my\; bootless\; cries,\backslash nAnd\; look\; upon\; my\; self\; and\; curse\; my\; fate,\backslash nWishing\; me\; like\; to\; one\; more\; rich\; in\; hope,\backslash nFeatured\; like\; him,\; like\; him\; with\; friends\; possessed,\backslash nDesiring\; this\; man\text{'}s\; art,\; and\; that\; man\text{'}s\; scope,\backslash nWith\; what\; I\; most\; enjoy\; contented\; least,\backslash nYet\; in\; these\; thoughts\; my\; self\; almost\; despising,\backslash nHaply\; I\; think\; on\; thee,\; and\; then\; my\; state,\backslash n(Like\; to\; the\; lark\; at\; break\; of\; day\; arising\backslash nFrom\; sullen\; earth)\; sings\; hymns\; at\; heaven\text{'}s\; gate,\backslash n\; For\; thy\; sweet\; love\; remembered\; such\; wealth\; brings,\backslash n\; That\; then\; I\; scorn\; to\; change\; my\; state\; with\; kings.''\:$

$\mathrm{cf}≔\mathrm{CharacterFrequencies}\left(\mathrm{Shakespeare}\right)$

$\mathrm{cf}≔''''=13,''''=106,''\text{'}''=4,''(''=1,'')''=1,'',''=15,''.''=1,''A''=2,''D''=1,''F''=4,''H''=1,''I''=4,''L''=1,''T''=1,''W''=3,''Y''=1,''a''=35,''b''=6,''c''=10,''d''=15,''e''=66,''f''=6,''g''=11,''h''=31,''i''=31,''j''=1,''k''=9,''l''=19,''m''=20,''n''=38,''o''=28,''p''=7,''r''=21,''s''=42,''t''=48,''u''=9,''v''=3,''w''=8,''y''=13$

$\mathrm{sort}\left(\left[\mathrm{cf}\right]\,\mathrm{key}=\mathrm{rhs}\right)$

$\left[''(''=1\,'')''=1\,''.''=1\,''D''=1\,''H''=1\,''L''=1\,''T''=1\,''Y''=1\,''j''=1\,''A''=2\,''W''=3\,''v''=3\,''\text{'}''=4\,''F''=4\,''I''=4\,''b''=6\,''f''=6\,''p''=7\,''w''=8\,''k''=9\,''u''=9\,''c''=10\,''g''=11\,''''=13\,''y''=13\,'',''=15\,''d''=15\,''l''=19\,''m''=20\,''r''=21\,''o''=28\,''h''=31\,''i''=31\,''a''=35\,''n''=38\,''s''=42\,''t''=48\,''e''=66\,''''=106\right]$

$\mathrm{CharacterFrequencies}\left(\mathrm{Shakespeare}\,''ABCYZ''\right)$

$''A''=2,''Y''=1$

$\mathrm{CharacterFrequencies}\left(\mathrm{Shakespeare}\,'\mathrm{upper}'\right)$

$''A''=2,''D''=1,''F''=4,''H''=1,''I''=4,''L''=1,''T''=1,''W''=3,''Y''=1$

$\mathrm{CharacterFrequencies}\left(\mathrm{Random}\left(1000000\right)\,'\mathrm{lower}'\right)$

$''a''=3972,''b''=3990,''c''=3839,''d''=3885,''e''=3851,''f''=3949,''g''=3921,''h''=4017,''i''=3926,''j''=4025,''k''=4089,''l''=3815,''m''=3881,''n''=3962,''o''=3950,''p''=3801,''q''=3910,''r''=3877,''s''=3789,''t''=3820,''u''=3918,''v''=4004,''w''=3948,''x''=3851,''y''=3855,''z''=3809$