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9.8 0.0 vector-heterogenous VS vectorAn efficient implementation of Int-indexed arrays (both mutable and immutable), with a powerful loop optimisation framework .
A type for points, as distinct from vectors.
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This is a package for type safe heterogenous vectors, or
HVectors. This library was developed to allow the HLearn library to handle multivariate distributions---each data point is an HVector, and the trained multivariate distribution will also be an HVector. This might be of more general interest, however, and so has been separated into its own library. It is called vector-heterogenous on hackage.
The simplest way to construct an
HVector is from an
HList with the
vec function. For example, we can run:
ghci> import Data.Vector.Heterogenous ghci> let hvec = vec ShowBox $ "test":::Nothing:::([4,5,6],()):::HNil
This declaration contains two parts. To the right of the
$ we have the
HList of our data. Notice that any type is allowed. The first argument of
vec is the constructor for an "existential box" that we want to put these elements in. We will call this constructor on each element in the
HList in order to make them all of one type. We then store these homogenous types into a standard vector from
Since we used
ShowBox in our
hvec variable, we can print
hvec to the screen:
ghci> hvec vec ShowBox $ "test":::Nothing:::([4,5,6],()):::HNil
The type of our
HVector has two components as well. First is the type of box we use, and second is the list of which type corresponds to which value in the vector.
ghci> :t hvec (Num b) => HVector ShowBox '[String,Maybe a,([b],())]
Advantages over HLists
The advantage of an
HVector over an
HList is that we get O(1) indexing anywhere in the list. (Technically the type checker still takes time O(n), but run time takes only O(1).) We use the
view function to do this:
ghci> hvec `view` (undefined :: Sing 0) "test" ghci> hvec `view` (undefined :: Sing 1) Nothing ghci> hvec `view` (undefined :: Sing 2) ([4,5,6],())
Unfortunately, this is slightly awkward because we must make our accessor function polymorphic on the index. Maybe someone with a better knowledge of a lens library's internals could come up with a prettier interface.
Advantages over straight ExistentialQuantification
There are two advantages. First, as we have seen, we can recover the original type for each index with our
view function. This would not be possible if we used a type of
HVector also has a
Monoid instance. That means we can do:
ghci> hvec<>hvec vec ShowBox $ "testtest":::Nothing:::([4,5,6,4,5,6],())::HNil
With straight existential quantification, it would not be possible to merge the corresponding positions in each vector because they are not guaranteed to be the same type.
Use of the
view function above is not ideal for performance critical applications because it prevents fusion. The easiest way to work around this is to directly access the underlying vector of existential boxes. We do this with the
ghci> :t getvec getvec :: HVector box xs -> Vector box ghci> getvec hvec fromList [([4,5,6],()),Nothing,"test"]
Notice that elements will now be accessed in reverse order.
Now the compiler can use fusion and everything runs quite zippy. The trick to making this work well is creating a good existential box for your specific application. In the HLearn library, for example, we would use a DatapointBox and a DistributionBox to represent our data points and multivariate distributions.
Based on my tests, a variable of type
HVector ShowBox '[Int,Int,Int,Int,Int,...] performs the same as the standard
Data.Vector.Vector Int. The
HVector has an extra layer of boxing to deal with, but using BangPatterns and
-funbox-strict-fields the compiler can remove this from the generated code.