Numeric.DataFrame.Contraction

This modules provides generalization of a matrix product: tensor-like contraction. For matrices and vectors this is a normal matrix*matrix or vector*matrix or matrix*vector product, for larger dimensions it calculates the scalar product of "adjacent" dimesnions of a tensor.

Documentation

class ConcatList as bs asbs => Contraction (t :: Type) (as :: [Nat]) (bs :: [Nat]) (asbs :: [Nat]) | asbs as -> bs, asbs bs -> as, as bs -> asbs where

Minimal complete definition

contract

Methods

contract :: (KnownDim m, PrimArray t (DataFrame t (as +: m)), PrimArray t (DataFrame t (m :+ bs)), PrimArray t (DataFrame t asbs)) => DataFrame t (as +: m) -> DataFrame t (m :+ bs) -> DataFrame t asbs

Generalization of a matrix product: take scalar product over one dimension and, thus, concatenate other dimesnions

Instances

(ConcatList Nat as bs asbs, Dimensions Nat as, Dimensions Nat bs, Num t) => Contraction t as bs asbs

Methods

contract :: (KnownDim Nat m, PrimArray t (DataFrame Type Nat t ((Nat +: as) m)), PrimArray t (DataFrame Type Nat t ((Nat :+ m) bs)), PrimArray t (DataFrame Type Nat t asbs)) => DataFrame Type Nat t ((Nat +: as) m) -> DataFrame Type Nat t ((Nat :+ m) bs) -> DataFrame Type Nat t asbs

(%*) :: (ConcatList as bs (as ++ bs), Contraction t as bs asbs, KnownDim m, PrimArray t (DataFrame t (as +: m)), PrimArray t (DataFrame t (m :+ bs)), PrimArray t (DataFrame t (as ++ bs))) => DataFrame t (as +: m) -> DataFrame t (m :+ bs) -> DataFrame t (as ++ bs) infixl 7

Tensor contraction. In particular: 1. matrix-matrix product 2. matrix-vector or vector-matrix product 3. dot product of two vectors.