Numeric.EMD

Empirical Mode Decomposition in pure Haskell.

Main interface is emd, with defaultEO. A tracing version that outputs a log to stdout is also available, as emdTrace. This can be used to help track down a specific IMF that might be taking more time than desired.

This package uses "sized vectors" as its main interface, to ensure:

1. The resulting EMD contains IMFs that are all the same length as the input vector
2. We provide a vector of size of at least one.

There are many functions to convert unsized vectors to sized vectors in Data.Vector.Sized and associated modules, including toSized (for when you know the size at compile-time) and withSized (for when you don't).

Empirical Mode Decomposition

emd :: (Vector v a, KnownNat n, Floating a, Ord a) => EMDOpts v (n + 1) a -> Vector v (n + 1) a -> EMD v (n + 1) a

EMD decomposition of a given time series with a given sifting stop condition.

Takes a sized vector to ensure that:

1. The resulting EMD contains IMFs that are all the same length as the input vector
2. We provide a vector of size of at least one.

emdTrace :: (Vector v a, KnownNat n, Floating a, Ord a, MonadIO m) => EMDOpts v (n + 1) a -> Vector v (n + 1) a -> m (EMD v (n + 1) a)

emd, but tracing results to stdout as IMFs are found. Useful for debugging to see how long each step is taking.

emd' :: (Vector v a, KnownNat n, Floating a, Ord a, Applicative m) => (SiftResult v (n + 1) a -> m r) -> EMDOpts v (n + 1) a -> Vector v (n + 1) a -> m (EMD v (n + 1) a)

emd with a callback for each found IMF.

iemd :: (Vector v a, Num a) => EMD v n a -> Vector v n a

Collapse an EMD back into its original time series. Should be a left-inverse to emd: using iemd on the result of emd should give back the original vector.

Since: 0.1.5.0

data EMD v n a

An EMD v n a is an Empirical Mode Decomposition of a time series with n items of type a stored in a vector v.

The component-wise sum of emdIMFs and emdResidual should yield exactly the original series (see iemd).

Constructors

EMD

Fields

• emdIMFs :: ![Vector v n a]
• emdResidual :: !(Vector v n a)

Instances

Eq (v a) => Eq (EMD v n a)

Defined in Numeric.EMD

Methods

(==) :: EMD v n a -> EMD v n a -> Bool

(/=) :: EMD v n a -> EMD v n a -> Bool

Ord (v a) => Ord (EMD v n a)

Defined in Numeric.EMD

Methods

compare :: EMD v n a -> EMD v n a -> Ordering

(<) :: EMD v n a -> EMD v n a -> Bool

(<=) :: EMD v n a -> EMD v n a -> Bool

(>) :: EMD v n a -> EMD v n a -> Bool

(>=) :: EMD v n a -> EMD v n a -> Bool

max :: EMD v n a -> EMD v n a -> EMD v n a

min :: EMD v n a -> EMD v n a -> EMD v n a

Show (v a) => Show (EMD v n a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> EMD v n a -> ShowS

show :: EMD v n a -> String

showList :: [EMD v n a] -> ShowS

Generic (EMD v n a)

Defined in Numeric.EMD

Associated Types

type Rep (EMD v n a) :: Type -> Type

Methods

from :: EMD v n a -> Rep (EMD v n a) x

to :: Rep (EMD v n a) x -> EMD v n a

(Vector v a, KnownNat n, Binary (v a)) => Binary (EMD v n a)

Since: 0.1.3.0

Defined in Numeric.EMD

Methods

put :: EMD v n a -> Put

get :: Get (EMD v n a)

putList :: [EMD v n a] -> Put

NFData (v a) => NFData (EMD v n a)

Since: 0.1.5.0

Defined in Numeric.EMD

Methods

rnf :: EMD v n a -> ()

type Rep (EMD v n a)

Defined in Numeric.EMD

type Rep (EMD v n a) = D1 (MetaData "EMD" "Numeric.EMD" "emd-0.2.0.0-inplace" False) (C1 (MetaCons "EMD" PrefixI True) (S1 (MetaSel (Just "emdIMFs") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 [Vector v n a]) :*: S1 (MetaSel (Just "emdResidual") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Vector v n a))))

Configuration

data EMDOpts v n a

Options for EMD composition.

Constructors

EO

Fields

• eoSifter :: Sifter v n a

  stop condition for sifting

• eoSplineEnd :: SplineEnd a

  end conditions for envelope splines

• eoBoundaryHandler :: Maybe BoundaryHandler

  process for handling boundary

Instances

Generic (EMDOpts v n a)

Defined in Numeric.EMD.Internal

Associated Types

type Rep (EMDOpts v n a) :: Type -> Type

Methods

from :: EMDOpts v n a -> Rep (EMDOpts v n a) x

to :: Rep (EMDOpts v n a) x -> EMDOpts v n a

(Vector v a, Fractional a, Ord a) => Default (EMDOpts v n a)

Since: 0.1.3.0

Defined in Numeric.EMD

Methods

def :: EMDOpts v n a

type Rep (EMDOpts v n a)

Defined in Numeric.EMD.Internal

type Rep (EMDOpts v n a) = D1 (MetaData "EMDOpts" "Numeric.EMD.Internal" "emd-0.2.0.0-inplace" False) (C1 (MetaCons "EO" PrefixI True) (S1 (MetaSel (Just "eoSifter") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Sifter v n a)) :*: (S1 (MetaSel (Just "eoSplineEnd") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SplineEnd a)) :*: S1 (MetaSel (Just "eoBoundaryHandler") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe BoundaryHandler)))))

defaultEO :: (Vector v a, Fractional a, Ord a) => EMDOpts v n a

Default EMDOpts

Note: If you immediately use this and set eoSifter, then v will be ambiguous. Explicitly set v with type applications to appease GHC

defaultEO @(Data.Vector.Vector)
   { eoSifter = scTimes 100
   }

data BoundaryHandler

Boundary conditions for splines.

Constructors

BHClamp

Clamp envelope at end points (Matlab implementation)

BHSymmetric

Extend boundaries symmetrically

Instances

Eq BoundaryHandler

Defined in Numeric.EMD.Internal

Methods

(==) :: BoundaryHandler -> BoundaryHandler -> Bool

(/=) :: BoundaryHandler -> BoundaryHandler -> Bool

Ord BoundaryHandler

Defined in Numeric.EMD.Internal

Methods

compare :: BoundaryHandler -> BoundaryHandler -> Ordering

(<) :: BoundaryHandler -> BoundaryHandler -> Bool

(<=) :: BoundaryHandler -> BoundaryHandler -> Bool

(>) :: BoundaryHandler -> BoundaryHandler -> Bool

(>=) :: BoundaryHandler -> BoundaryHandler -> Bool

max :: BoundaryHandler -> BoundaryHandler -> BoundaryHandler

min :: BoundaryHandler -> BoundaryHandler -> BoundaryHandler

Show BoundaryHandler

Defined in Numeric.EMD.Internal

Methods

showsPrec :: Int -> BoundaryHandler -> ShowS

show :: BoundaryHandler -> String

showList :: [BoundaryHandler] -> ShowS

Generic BoundaryHandler

Defined in Numeric.EMD.Internal

Associated Types

type Rep BoundaryHandler :: Type -> Type

Methods

from :: BoundaryHandler -> Rep BoundaryHandler x

to :: Rep BoundaryHandler x -> BoundaryHandler

Binary BoundaryHandler

Since: 0.1.3.0

Defined in Numeric.EMD.Internal

Methods

put :: BoundaryHandler -> Put

get :: Get BoundaryHandler

putList :: [BoundaryHandler] -> Put

type Rep BoundaryHandler

Defined in Numeric.EMD.Internal

type Rep BoundaryHandler = D1 (MetaData "BoundaryHandler" "Numeric.EMD.Internal" "emd-0.2.0.0-inplace" False) (C1 (MetaCons "BHClamp" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "BHSymmetric" PrefixI False) (U1 :: Type -> Type))

data Sifter v n a

A sift stopping condition.

It is a Pipe consumer that takes single sift step results upstream and terminates with '()' as soon as it is satisfied with the latest sift step.

Use combinators like siftOr and siftAnd to combine sifters, and the various sifters in Numeric.EMD.Sift to create sifters from commonly established ones or new ones from scratch.

Since: 0.2.0.0

Instances

(Vector v a, Fractional a, Ord a) => Default (Sifter v n a)

Since: 0.1.3.0

Defined in Numeric.EMD.Sift

Methods

def :: Sifter v n a

defaultSifter :: (Vector v a, Fractional a, Ord a) => Sifter v n a

Default Sifter

defaultSifter = siftStdDev 0.3 siftOr siftTimes 50

R package uses siftTimes 20, Matlab uses no limit

data SplineEnd a

End condition for spline

Constructors

SENotAKnot

"Not-a-knot" condition: third derivatives are continuous at endpoints. Default for matlab spline.

SENatural

"Natural" condition: curve becomes a straight line at endpoints.

SEClamped a a

"Clamped" condition: Slope of curves at endpoints are explicitly given.

Since: 0.1.2.0

Instances

Eq a => Eq (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

(==) :: SplineEnd a -> SplineEnd a -> Bool

(/=) :: SplineEnd a -> SplineEnd a -> Bool

Ord a => Ord (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

compare :: SplineEnd a -> SplineEnd a -> Ordering

(<) :: SplineEnd a -> SplineEnd a -> Bool

(<=) :: SplineEnd a -> SplineEnd a -> Bool

(>) :: SplineEnd a -> SplineEnd a -> Bool

(>=) :: SplineEnd a -> SplineEnd a -> Bool

max :: SplineEnd a -> SplineEnd a -> SplineEnd a

min :: SplineEnd a -> SplineEnd a -> SplineEnd a

Show a => Show (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

showsPrec :: Int -> SplineEnd a -> ShowS

show :: SplineEnd a -> String

showList :: [SplineEnd a] -> ShowS

Generic (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Associated Types

type Rep (SplineEnd a) :: Type -> Type

Methods

from :: SplineEnd a -> Rep (SplineEnd a) x

to :: Rep (SplineEnd a) x -> SplineEnd a

Binary a => Binary (SplineEnd a)

Since: 0.1.3.0

Defined in Numeric.EMD.Internal.Spline

Methods

put :: SplineEnd a -> Put

get :: Get (SplineEnd a)

putList :: [SplineEnd a] -> Put

type Rep (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

type Rep (SplineEnd a) = D1 (MetaData "SplineEnd" "Numeric.EMD.Internal.Spline" "emd-0.2.0.0-inplace" False) (C1 (MetaCons "SENotAKnot" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "SENatural" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "SEClamped" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))

Internal

sift :: forall v n a. (Vector v a, KnownNat n, Floating a, Ord a) => EMDOpts v (n + 1) a -> Vector v (n + 1) a -> SiftResult v (n + 1) a

Iterated sifting process, used to produce either an IMF or a residual.

data SiftResult v n a

The result of a sifting operation. Each sift either yields a residual, or a new IMF.

Constructors

SRResidual !(Vector v n a)

SRIMF !(Vector v n a) !Int

number of sifting iterations

envelopes :: (Vector v a, KnownNat n, Fractional a, Ord a) => SplineEnd a -> Maybe BoundaryHandler -> Vector v (n + 1) a -> Maybe (Vector v (n + 1) a, Vector v (n + 1) a)

Returns cubic splines of local minimums and maximums. Returns Nothing if there are not enough local minimum or maximums to create the splines.

Orphan instances

(Vector v a, Fractional a, Ord a) => Default (EMDOpts v n a)

Since: 0.1.3.0

Methods

def :: EMDOpts v n a