Safe Haskell | None |
---|

Marcus Castrén. *RECREL: A Similarity Measure for Set-Classes*. PhD
thesis, Sibelius Academy, Helsinki, 1994.

- t_prime :: [Z12] -> [Z12]
- inv_sym :: [Z12] -> Bool
- sc_t_ti :: [Z12] -> Maybe ([Z12], [Z12])
- t_sc_table :: [(SC_Name, [Z12])]
- t_sc_name :: [Z12] -> SC_Name
- t_sc :: SC_Name -> [Z12]
- t_scs :: [[Z12]]
- t_scs_n :: Integral i => i -> [[Z12]]
- t_subsets :: [Z12] -> [Z12] -> [[Z12]]
- ti_subsets :: [Z12] -> [Z12] -> [[Z12]]
- rle :: (Eq a, Integral i) => [a] -> [(i, a)]
- rle_decode :: Integral i => [(i, a)] -> [a]
- rle_length :: Integral i => [(i, a)] -> i
- t_n_class_vector :: (Num a, Integral i) => i -> [Z12] -> [a]
- ti_n_class_vector :: (Num b, Integral i) => i -> [Z12] -> [b]
- dyad_class_percentage_vector :: Integral i => [Z12] -> [i]
- rel :: Integral i => [Z12] -> [Z12] -> Ratio i

# Documentation

t_prime :: [Z12] -> [Z12]Source

Transpositional equivalence prime form, ie. `t_cmp_prime`

of
`forte_cmp`

.

(forte_prime [0,2,3],t_prime [0,2,3]) == ([0,1,3],[0,2,3])

inv_sym :: [Z12] -> BoolSource

Is *p* symmetrical under inversion.

map inv_sym (scs_n 2) == [True,True,True,True,True,True] map (fromEnum.inv_sym) (scs_n 3) == [1,0,0,0,0,1,0,0,1,1,0,1]

t_sc_table :: [(SC_Name, [Z12])]Source

Transpositional equivalence variant of Forte's `sc_table`

. The
inversionally related classes are distinguished by labels `A`

and
`B`

; the class providing the *best normal order* (Forte 1973) is
always the `A`

class. If neither `A`

nor `B`

appears in the name of
a set-class, it is inversionally symmetrical.

(length sc_table,length t_sc_table) == (224,352) lookup "5-Z18B" t_sc_table == Just [0,2,3,6,7]

t_sc_name :: [Z12] -> SC_NameSource

Lookup a set-class name. The input set is subject to
`t_prime`

before lookup.

t_sc_name [0,2,3,6,7] == "5-Z18B" t_sc_name [0,1,4,6,7,8] == "6-Z17B"

t_sc :: SC_Name -> [Z12]Source

Lookup a set-class given a set-class name.

t_sc "6-Z17A" == [0,1,2,4,7,8]

t_scs_n :: Integral i => i -> [[Z12]]Source

Cardinality *n* subset of `t_scs`

.

map (length . t_scs_n) [2..10] == [6,19,43,66,80,66,43,19,6]

t_subsets :: [Z12] -> [Z12] -> [[Z12]]Source

T-related *q* that are subsets of *p*.

t_subsets [0,1,2,3,4] [0,1] == [[0,1],[1,2],[2,3],[3,4]] t_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4]] t_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6]]

ti_subsets :: [Z12] -> [Z12] -> [[Z12]]Source

T/I-related *q* that are subsets of *p*.

ti_subsets [0,1,2,3,4] [0,1] == [[0,1],[1,2],[2,3],[3,4]] ti_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4],[0,3,4]] ti_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6],[3,6,7]]

rle :: (Eq a, Integral i) => [a] -> [(i, a)]Source

Trivial run length encoder.

rle "abbcccdde" == [(1,'a'),(2,'b'),(3,'c'),(2,'d'),(1,'e')]

rle_decode :: Integral i => [(i, a)] -> [a]Source

Inverse of `rle`

.

rle_decode [(5,'a'),(4,'b')] == "aaaaabbbb"

rle_length :: Integral i => [(i, a)] -> iSource

Length of *rle* encoded sequence.

rle_length [(5,'a'),(4,'b')] == 9

t_n_class_vector :: (Num a, Integral i) => i -> [Z12] -> [a]Source

T-equivalence *n*-class vector (subset-class vector, nCV).

t_n_class_vector 2 [0..4] == [4,3,2,1,0,0] rle (t_n_class_vector 3 [0..4]) == [(1,3),(2,2),(2,1),(4,0),(1,1),(9,0)] rle (t_n_class_vector 4 [0..4]) == [(1,2),(3,1),(39,0)]

ti_n_class_vector :: (Num b, Integral i) => i -> [Z12] -> [b]Source

T/I-equivalence *n*-class vector (subset-class vector, nCV).

ti_n_class_vector 2 [0..4] == [4,3,2,1,0,0] ti_n_class_vector 3 [0,1,2,3,4] == [3,4,2,0,0,1,0,0,0,0,0,0] rle (ti_n_class_vector 4 [0,1,2,3,4]) == [(2,2),(1,1),(26,0)]

dyad_class_percentage_vector :: Integral i => [Z12] -> [i]Source

`icv`

scaled by sum of *icv*.

dyad_class_percentage_vector [0,1,2,3,4] == [40,30,20,10,0,0] dyad_class_percentage_vector [0,1,4,5,7] == [20,10,20,20,20,10]