Safe Haskell | None |
---|---|

Language | Haskell98 |

Larry Polansky. "Morphological Metrics". Journal of New Music Research, 25(4):289-368, 1996.

- type Interval a n = a -> a -> n
- dif_i :: (Integral a, Num b) => a -> a -> b
- dif_r :: (Real a, Fractional b) => a -> a -> b
- abs_dif :: Num n => Interval a n -> a -> a -> n
- sqr :: Num a => a -> a
- sqr_dif :: Num n => Interval a n -> a -> a -> n
- sqr_abs_dif :: Num n => Interval a n -> a -> a -> n
- sqrt_abs_dif :: Floating c => Interval a c -> a -> a -> c
- city_block_metric :: Num n => Interval a n -> (a, a) -> (a, a) -> n
- euclidean_metric_2 :: Floating n => Interval a n -> (a, a) -> (a, a) -> n
- euclidean_metric_l :: Floating c => Interval b c -> [b] -> [b] -> c
- cbrt :: Floating a => a -> a
- nthrt :: Floating a => a -> a -> a
- minkowski_metric_2 :: Floating a => Interval t a -> a -> (t, t) -> (t, t) -> a
- minkowski_metric_l :: Floating a => Interval t a -> a -> [t] -> [t] -> a
- d_dx :: Interval a n -> [a] -> [n]
- d_dx_abs :: Num n => Interval a n -> [a] -> [n]
- olm_no_delta' :: Fractional a => [a] -> [a] -> a
- olm_general :: Fractional n => Interval a n -> [a] -> [a] -> n
- type Delta n a = [n] -> Int -> a
- ix_dif :: Interval a t -> Delta a t
- abs_ix_dif :: Num n => Interval a n -> Delta a n
- sqr_abs_ix_dif :: Num n => Interval a n -> Delta a n
- type Psi a = a -> a -> a
- olm :: Fractional a => Psi a -> Delta n a -> ([a] -> a) -> [n] -> [n] -> a
- olm_no_delta :: (Real a, Real n, Fractional n) => [a] -> [a] -> n
- olm_no_delta_squared :: Floating a => [a] -> [a] -> a
- second_order :: Num n => ([n] -> [n] -> t) -> [n] -> [n] -> t
- olm_no_delta_second_order :: (Real a, Fractional a) => [a] -> [a] -> a
- olm_no_delta_squared_second_order :: Floating a => [a] -> [a] -> a
- second_order_binonial_coefficient :: Fractional a => a -> a
- direction_interval :: Ord i => [i] -> [Ordering]
- ord_hist :: Integral t => [Ordering] -> (t, t, t)
- direction_vector :: Integral i => Ord a => [a] -> (i, i, i)
- uld :: (Integral n, Ord a) => [a] -> [a] -> Ratio n
- old :: (Ord i, Integral a) => [i] -> [i] -> Ratio a
- ocd :: (Ord a, Integral i) => [a] -> [a] -> Ratio i
- ucd :: (Integral n, Ord a) => [a] -> [a] -> Ratio n
- combinatorial_magnitude_matrix :: Interval a n -> [a] -> [[n]]
- ulm_simplified :: Fractional n => Interval a n -> [a] -> [a] -> n
- ocm_zcm :: Fractional n => Interval a n -> [a] -> [a] -> (n, n, [n])
- ocm :: Fractional n => Interval a n -> [a] -> [a] -> n
- ocm_absolute_scaled :: (Ord n, Fractional n) => Interval a n -> [a] -> [a] -> n

# Documentation

type Interval a n = a -> a -> n Source #

Distance function, ordinarily *n* below is in `Num`

, `Fractional`

or `Real`

.

dif_r :: (Real a, Fractional b) => a -> a -> b Source #

`realToFrac`

`.`

`-`

.

city_block_metric :: Num n => Interval a n -> (a, a) -> (a, a) -> n Source #

City block metric, p.296

city_block_metric (-) (1,2) (3,5) == 2+3

euclidean_metric_2 :: Floating n => Interval a n -> (a, a) -> (a, a) -> n Source #

Two-dimensional euclidean metric, p.297.

euclidean_metric_2 (-) (1,2) (3,5) == sqrt (4+9)

euclidean_metric_l :: Floating c => Interval b c -> [b] -> [b] -> c Source #

*n*-dimensional euclidean metric

euclidean_metric_l (-) [1,2] [3,5] == sqrt (4+9) euclidean_metric_l (-) [1,2,3] [2,4,6] == sqrt (1+4+9)

minkowski_metric_2 :: Floating a => Interval t a -> a -> (t, t) -> (t, t) -> a Source #

Two-dimensional Minkowski metric, p.297

minkowski_metric_2 (-) 1 (1,2) (3,5) == 5 minkowski_metric_2 (-) 2 (1,2) (3,5) == sqrt (4+9) minkowski_metric_2 (-) 3 (1,2) (3,5) == cbrt (8+27)

minkowski_metric_l :: Floating a => Interval t a -> a -> [t] -> [t] -> a Source #

*n*-dimensional Minkowski metric

minkowski_metric_l (-) 2 [1,2,3] [2,4,6] == sqrt (1+4+9) minkowski_metric_l (-) 3 [1,2,3] [2,4,6] == cbrt (1+8+27)

d_dx :: Interval a n -> [a] -> [n] Source #

Integration with *f*.

d_dx (-) [0,2,4,1,0] == [2,2,-3,-1] d_dx (-) [2,3,0,4,1] == [1,-3,4,-3]

olm_no_delta' :: Fractional a => [a] -> [a] -> a Source #

Ordered linear magnitude (no delta), p.300

olm_no_delta' [0,2,4,1,0] [2,3,0,4,1] == 1.25

olm_general :: Fractional n => Interval a n -> [a] -> [a] -> n Source #

Ordered linear magintude (general form) p.302

olm_general (abs_dif (-)) [0,2,4,1,0] [2,3,0,4,1] == 1.25 olm_general (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 4.6

type Delta n a = [n] -> Int -> a Source #

`Delta`

(Δ) determines an interval given a sequence and an index.

ix_dif :: Interval a t -> Delta a t Source #

*f* at indices *i* and *i+1* of *x*.

map (ix_dif (-) [0,1,3,6,10]) [0..3] == [-1,-2,-3,-4]

sqr_abs_ix_dif :: Num n => Interval a n -> Delta a n Source #

map (sqr_abs_ix_dif (-) [0,2,4,1,0]) [0..3] == [4,4,9,1] map (sqr_abs_ix_dif (-) [2,3,0,4,1]) [0..3] == [1,9,16,9]

olm :: Fractional a => Psi a -> Delta n a -> ([a] -> a) -> [n] -> [n] -> a Source #

Ordered linear magintude (generalised-interval form) p.305

olm (abs_dif dif_r) (abs_ix_dif dif_r) (const 1) [1,5,12,2,9,6] [7,6,4,9,8,1] == 4.6 olm (abs_dif dif_r) (abs_ix_dif dif_r) maximum [1,5,12,2,9,6] [7,6,4,9,8,1] == 0.46

olm_no_delta :: (Real a, Real n, Fractional n) => [a] -> [a] -> n Source #

olm_no_delta_squared :: Floating a => [a] -> [a] -> a Source #

second_order :: Num n => ([n] -> [n] -> t) -> [n] -> [n] -> t Source #

olm_no_delta_second_order :: (Real a, Fractional a) => [a] -> [a] -> a Source #

olm_no_delta_squared_second_order :: Floating a => [a] -> [a] -> a Source #

second_order_binonial_coefficient :: Fractional a => a -> a Source #

Second order binomial coefficient, p.307

map second_order_binonial_coefficient [2..10] == [1,3,6,10,15,21,28,36,45]

direction_interval :: Ord i => [i] -> [Ordering] Source #

ord_hist :: Integral t => [Ordering] -> (t, t, t) Source #

Histogram of list of `Ordering`

s.

ord_hist [LT,GT,GT] == (1,0,2)

direction_vector :: Integral i => Ord a => [a] -> (i, i, i) Source #

Histogram of *directions* of adjacent elements, p.312.

direction_vector [5,9,3,2] == (1,0,2) direction_vector [2,5,6,6] == (2,1,0)

uld :: (Integral n, Ord a) => [a] -> [a] -> Ratio n Source #

Unordered linear direction, p.311 (Fig. 5)

uld [5,9,3,2] [2,5,6,6] == 2/3 uld [5,3,6,1,4] [3,6,1,4,2] == 0

old :: (Ord i, Integral a) => [i] -> [i] -> Ratio a Source #

Ordered linear direction, p.312

direction_interval [5,3,6,1,4] == [GT,LT,GT,LT] direction_interval [3,6,1,4,2] == [LT,GT,LT,GT] old [5,3,6,1,4] [3,6,1,4,2] == 1

ocd :: (Ord a, Integral i) => [a] -> [a] -> Ratio i Source #

Ordered combinatorial direction, p.314

ocd [5,9,3,2] [2,5,6,6] == 5/6 ocd [5,3,6,1,4] [3,6,1,4,2] == 4/5

ucd :: (Integral n, Ord a) => [a] -> [a] -> Ratio n Source #

Unordered combinatorial direction, p.314

ucd [5,9,3,2] [2,5,6,6] == 5/6 ucd [5,3,6,1,4] [3,6,1,4,2] == 0 ucd [5,3,7,6] [2,1,2,1] == 1/2 ucd [2,1,2,1] [8,3,5,4] == 1/3 ucd [5,3,7,6] [8,3,5,4] == 1/3

combinatorial_magnitude_matrix :: Interval a n -> [a] -> [[n]] Source #

`half_matrix_f`

, Fig.9, p.318

let r = [[2,3,1,4] ,[1,3,6] ,[4,7] ,[3]] in combinatorial_magnitude_matrix (abs_dif (-)) [5,3,2,6,9] == r

ulm_simplified :: Fractional n => Interval a n -> [a] -> [a] -> n Source #

Unordered linear magnitude (simplified), p.320-321

let r = abs (sum [5,4,3,6] - sum [12,2,11,7]) / 4 in ulm_simplified (abs_dif (-)) [1,6,2,5,11] [3,15,13,2,9] == r

ulm_simplified (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 3

ocm_zcm :: Fractional n => Interval a n -> [a] -> [a] -> (n, n, [n]) Source #

ocm :: Fractional n => Interval a n -> [a] -> [a] -> n Source #

Ordered combinatorial magnitude (OCM), p.323

ocm (abs_dif (-)) [1,6,2,5,11] [3,15,13,2,9] == 5.2 ocm (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 3.6

ocm_absolute_scaled :: (Ord n, Fractional n) => Interval a n -> [a] -> [a] -> n Source #

Ordered combinatorial magnitude (OCM), p.323

ocm_absolute_scaled (abs_dif (-)) [1,6,2,5,11] [3,15,13,2,9] == 0.4 ocm_absolute_scaled (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 54/(15*11)