-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Cluster algorithms, PCA, and chemical conformere analysis
--   
--   Please see the README on GitLab at
--   <a>https://gitlab.com/theoretical-chemistry-jena/quantum-chemistry/ConfoCluster</a>
@package ConClusion
@version 0.0.2


module ConClusion.Numeric.Data

-- | Exception regarding indexing in some kind of aaray.
newtype IndexException
IndexException :: String -> IndexException

-- | Converts a vector from the HMatrix package to the Massiv
--   representation.
vecH2M :: (Element e, Mutable r Ix1 e) => Vector e -> Vector r e

-- | Converts a vector from the Massiv representation to the HMatrix
--   representation.
vecM2H :: (Manifest r Ix1 e, Element e) => Vector r e -> Vector e

-- | Converts a matrix from the HMatrix representation to the Massiv
--   representation.
matH2M :: (Mutable r Ix1 e, Element e) => Matrix e -> Matrix r e

-- | Converts a matrix from Massiv to HMatrix representation.
matM2H :: (Manifest r Ix1 e, Element e, Resize r Ix2, Load r Ix2 e) => Matrix r e -> Matrix e

-- | Magnitude of a vector (length).
magnitude :: (Numeric r e, Source r Ix1 e, Floating e) => Vector r e -> e

-- | Normalise a vector.
normalise :: (Numeric r e, Source r Ix1 e, Floating e) => Vector r e -> Vector r e

-- | Angle between two vectors.
angle :: (Numeric r e, Source r Ix1 e, Floating e) => Vector r e -> Vector r e -> e

-- | Find the minimal distance in a distance matrix, which is not the main
--   diagonal.
minDistAt :: (Manifest r Ix2 e, MonadThrow m, Ord e) => Matrix r e -> m (e, Ix2)

-- | Find the minimal element of a vector, which is at a larger than the
--   supplied index.
minDistAtVec :: (Manifest r Ix1 e, MonadThrow m, Ord e) => Ix1 -> Vector r e -> m (e, Ix1)

-- | Like <a>minimumM</a> but also returns the index of the minimal
--   element.
iMinimumM :: (Manifest r ix a, MonadThrow m, Ord a) => Array r ix a -> m (a, ix)

-- | Quickly print a matrix with numerical values
printMat :: (Source r Ix2 e, Real e) => Matrix r e -> Matrix D Text

-- | A binary tree.
data BinTree e
Leaf :: e -> BinTree e
Node :: e -> BinTree e -> BinTree e -> BinTree e

-- | Look at the root of a binary tree.
root :: BinTree e -> e

-- | Steps down each branch of a tree until some criterion is satisfied or
--   the end of the branch is reached. Each end of the branch is added to a
--   result.
takeBranchesWhile :: (a -> Bool) -> BinTree a -> Vector DL a

-- | Takes the first value in each branch, that does not fullfill the
--   criterion anymore and adds it to the result. Terminal leafes of the
--   branches are always taken.
takeLeafyBranchesWhile :: (a -> Bool) -> BinTree a -> Vector DL a
instance GHC.Show.Show ConClusion.Numeric.Data.IndexException
instance GHC.Generics.Generic (ConClusion.Numeric.Data.BinTree e)
instance GHC.Show.Show e => GHC.Show.Show (ConClusion.Numeric.Data.BinTree e)
instance GHC.Classes.Eq e => GHC.Classes.Eq (ConClusion.Numeric.Data.BinTree e)
instance Data.Aeson.Types.FromJSON.FromJSON e => Data.Aeson.Types.FromJSON.FromJSON (ConClusion.Numeric.Data.BinTree e)
instance Data.Aeson.Types.ToJSON.ToJSON e => Data.Aeson.Types.ToJSON.ToJSON (ConClusion.Numeric.Data.BinTree e)
instance GHC.Base.Functor ConClusion.Numeric.Data.BinTree
instance GHC.Exception.Type.Exception ConClusion.Numeric.Data.IndexException


-- | This module implements routines to work with simple molden style XYZ
--   trajectories. This includes parsers as well as functions to obtain
--   structural features in internal coordinates.
--   
--   For an introduction into PCA see
--   <a>https://www.cs.cmu.edu/~elaw/papers/pca.pdf</a>.
--   
--   Diherdrals require a special metric, see
--   <a>https://onlinelibrary.wiley.com/doi/full/10.1002/prot.20310)</a>.
module ConClusion.Chemistry.Topology

-- | A Molecule in cartesian coordinates.
data Molecule
type Trajectory = Seq Molecule

-- | Parser for molecules in Molden XYZ format.
xyz :: Parser Molecule

-- | Parser for trajectories in XYZ format as produced by CREST.
trajectory :: Parser Trajectory

-- | Selection of a bond between two atoms.
data B
B :: Int -> Int -> B

-- | Selection of an angle between three atoms.
data A
A :: Int -> Int -> Int -> A

-- | Selection of a dihedral angle between four atoms. Rotation around the
--   central two.
data D
D :: Int -> Int -> Int -> Int -> D

-- | Selections
data Feature
Energy :: Feature
Bond :: B -> Feature
Angle :: A -> Feature
Dihedral :: D -> Feature

-- | Obtains the feature matrix &lt;math&gt; for a principal component
--   analysis. Given &lt;math&gt; features to analyse in &lt;math&gt;
--   measurements, &lt;math&gt; will be a &lt;math&gt; matrix.
getFeatures :: (MonadThrow m, Traversable f) => f Feature -> Trajectory -> m (Matrix DL Double)


module ConClusion.Numeric.Statistics
data PCA
PCA :: Matrix U Double -> Matrix U Double -> Matrix U Double -> Matrix U Double -> Double -> Double -> Vector U Double -> Vector U Double -> Matrix U Double -> Matrix U Double -> PCA

-- | Original feature matrix.
[$sel:x:PCA] :: PCA -> Matrix U Double

-- | Feature matrix in mean deviation form.
[$sel:x':PCA] :: PCA -> Matrix U Double

-- | Transformed data.
[$sel:y:PCA] :: PCA -> Matrix U Double

-- | Transformation matrix to transform feature matrix into PCA result
--   matrix.
[$sel:a:PCA] :: PCA -> Matrix U Double

-- | Mean squared error introduced by PCA.
[$sel:mse:PCA] :: PCA -> Double

-- | Percentage of the behaviour captured in the remaining dimensions.
[$sel:remaining:PCA] :: PCA -> Double

-- | All eigenvalues from the diagonalisation of the covariance matrix.
[$sel:allEigenValues:PCA] :: PCA -> Vector U Double

-- | Eigenvalues that were kept for PCA.
[$sel:pcaEigenValues:PCA] :: PCA -> Vector U Double

-- | All eigenvectors from the diagonalisation of the covariance matrix.
[$sel:allEigenVecs:PCA] :: PCA -> Matrix U Double

-- | Eigenvectors that were kept for PCA.
[$sel:pcaEigenVecs:PCA] :: PCA -> Matrix U Double

-- | Performs a PCA on the feature matrix &lt;math&gt; by solving the
--   eigenproblem of the covariance matrix. The function takes the feature
--   matrix directly and perfoms the conversion to mean deviation form, the
--   calculation of the covariance matrix and the eigenvalue problem
--   automatically.
pca :: (Numeric r Double, Mutable r Ix2 Double, Manifest r Ix1 Double, Source (R r) Ix2 Double, Extract r Ix2 Double, MonadThrow m) => Int -> Matrix r Double -> m PCA

-- | Normalise each value so that the maximum absolute value in each row
--   becomes one.
normalise :: (Ord e, Unbox e, Numeric r e, Fractional e, Source r Ix2 e, Mutable r Ix2 e) => Array r Ix2 e -> Array r Ix2 e

-- | Subtract the mean value of all columns from the feature matrix. Brings
--   the feature matrix to mean deviation form.
meanDeviation :: (Source r Ix2 e, Fractional e, Unbox e, Numeric r e, Mutable r Ix2 e) => Matrix r e -> Matrix r e

-- | Obtains the covariance matrix &lt;math&gt; from the feature matrix
--   &lt;math&gt;. &lt;math&gt; where &lt;math&gt; is the number of columns
--   in the matrix.
--   
--   The feature matrix should be in mean deviation form, see
--   <a>meanDeviation</a>.
covariance :: (Numeric r e, Mutable r Ix2 e, Fractional e) => Matrix r e -> Matrix r e

-- | Distance matrix generator functions.
type DistFn r e = Matrix r e -> Matrix r e

-- | The &lt;math&gt; norm between two vectors. Generalisation of Manhattan
--   and Euclidean distances. &lt;math&gt;
lpNorm :: (Mutable r Ix2 e, Floating e) => Int -> DistFn r e

-- | The Manhattan distance between two vectors. Specialisation of the
--   &lt;math&gt; norm for &lt;math&gt;. &lt;math&gt;
manhattan :: (Mutable r Ix2 e, Floating e) => DistFn r e

-- | The Euclidean distance between two vectors. Specialisation of the
--   &lt;math&gt; norm for &lt;math&gt;. &lt;math&gt;
euclidean :: (Mutable r Ix2 e, Floating e) => DistFn r e

-- | Mahalanobis distance between points. Suitable for non correlated axes.
--   &lt;math&gt; where &lt;math&gt; is the covariance matrix.
mahalanobis :: (Unbox e, Numeric r e, Mutable r Ix2 e, Mutable r Ix1 e, Field e) => DistFn r e

-- | Representation of clusters.
type Clusters = Vector B IntSet

-- | Exception for invalid search distances.
newtype DistanceInvalidException e
DistanceInvalidException :: e -> DistanceInvalidException e

-- | DBScan algorithm.
dbscan :: (MonadThrow m, Ord e, Num e, Typeable e, Show e, Source r Ix2 e) => DistFn r e -> Int -> e -> Matrix r e -> m Clusters

-- | A dendrogram as a binary tree.
data Dendrogram e

-- | A strategy/distance measure for clusters.
data JoinStrat e
SingleLinkage :: JoinStrat e
CompleteLinkage :: JoinStrat e
Median :: JoinStrat e
UPGMA :: JoinStrat e
WPGMA :: JoinStrat e
Centroid :: JoinStrat e
Ward :: JoinStrat e
LWFB :: e -> JoinStrat e
LW :: e -> e -> e -> e -> JoinStrat e

-- | Performance improved hierarchical clustering algorithm.
--   <tt>GENERIC_LINKAGE</tt> from figure 3,
--   <a>https://arxiv.org/pdf/1109.2378.pdf</a>.
hca :: (MonadThrow m, Mutable r Ix1 e, Mutable r Ix2 e, Mutable r Ix1 (e, Ix1), Manifest (R r) Ix1 e, OuterSlice r Ix2 e, Ord e, Unbox e, Fractional e) => DistFn r e -> JoinStrat e -> Matrix r e -> m (Dendrogram e)

-- | Cut a <a>Dendrogram</a> at a given distance and obtain all clusters
--   from it.
cutDendroAt :: Ord e => Dendrogram e -> e -> Clusters
instance GHC.Classes.Eq e => GHC.Classes.Eq (ConClusion.Numeric.Statistics.DistanceInvalidException e)
instance GHC.Show.Show e => GHC.Show.Show (ConClusion.Numeric.Statistics.DistanceInvalidException e)
instance GHC.Generics.Generic (ConClusion.Numeric.Statistics.DendroNode e)
instance GHC.Show.Show e => GHC.Show.Show (ConClusion.Numeric.Statistics.DendroNode e)
instance GHC.Classes.Eq e => GHC.Classes.Eq (ConClusion.Numeric.Statistics.DendroNode e)
instance GHC.Generics.Generic (ConClusion.Numeric.Statistics.Dendrogram e)
instance GHC.Classes.Eq e => GHC.Classes.Eq (ConClusion.Numeric.Statistics.Dendrogram e)
instance GHC.Show.Show e => GHC.Show.Show (ConClusion.Numeric.Statistics.Dendrogram e)
instance GHC.Show.Show e => GHC.Show.Show (ConClusion.Numeric.Statistics.JoinStrat e)
instance GHC.Classes.Eq e => GHC.Classes.Eq (ConClusion.Numeric.Statistics.JoinStrat e)
instance Data.Aeson.Types.ToJSON.ToJSON e => Data.Aeson.Types.ToJSON.ToJSON (ConClusion.Numeric.Statistics.Dendrogram e)
instance Data.Aeson.Types.FromJSON.FromJSON e => Data.Aeson.Types.FromJSON.FromJSON (ConClusion.Numeric.Statistics.Dendrogram e)
instance Data.Aeson.Types.FromJSON.FromJSON e => Data.Aeson.Types.FromJSON.FromJSON (ConClusion.Numeric.Statistics.DendroNode e)
instance Data.Aeson.Types.ToJSON.ToJSON e => Data.Aeson.Types.ToJSON.ToJSON (ConClusion.Numeric.Statistics.DendroNode e)
instance (Data.Typeable.Internal.Typeable e, GHC.Show.Show e) => GHC.Exception.Type.Exception (ConClusion.Numeric.Statistics.DistanceInvalidException e)