# F# Data Frame design notes

This is the first version of F# Data Frame library and so we are still actively looking at how to improve the design. The best place for discussions is either the issue list on GitHub or the mailing list of the F# for Data and Machine Learning group (for more broader topics).

The current version of the library implements most of the basic functionality, but it hopefully provides the right "core" internals that should make it easier to add all the additional (useful) features.

When developing the library, we follow the principle that there should be a small number of primitive or fundamental functions (these are typically provided as members on the basic objects) that can be used to provide a wide range of useful functions (typically available as extension members and in F# modules). We are generally quite happy to include more extension members and functions for commonly used operations, so feel free to contribute!

## Library principles

• F# and C# friendly - We want to make sure that the library works from both F# and C#. For this reason, most functionality is exposed as extension members (using the C# Extension attribute - so they are only visible in C# and F# 3.1) and as functions in modules (Frame and Series). These are generally very similar. One difference is that functions use tuples and F# option<T> and more abbreviations, while extensions use KeyValuePair<K, V>, OptionalValue<T> (a C#-friendly struct defined in the library).

• Symmetry between rows and columns - The data in data frame is stored as a list of columns and it is good idea to use the data frame in a column-wise way (and there are more functions for working with column-based frames).

However, the data type Frame<'TRowKey, 'TColKey> is symmetric in that it uses custom index for access by both columns (series) and rows. You can also access columns/rows as a series of (nested) series via df.Columns and df.Rows. Although the column key is typically going to be a string (series name), this is not required and you can e.g. transpose frame using the df.Transpose() method.

• Missing and NaN values we assume that data frames can always contain missing values and so there is no type distinction between frame/series that may have missing values and one that may not have missing values. Operations available on the frame and series are designed to handle missing values well - they generally skip over missing values unless you explicitly try to read a value by a key.

The current version treats certain values as "missing" values, including Double.NaN (for numeric values) and null (for Nullable<'T> types and reference types). This means that when you create a series from Double.NaN, this is turned into a missing value and the value is skipped when doing aggregation such as Series.sum. (An alternative would be to support both NaN and missing, but there is no clear conclusion about what is the most useful option.)

• Immutability - A series is fully immutable data type, but a data frame supports limited mutation - you can add new series, drop a series & replace a series (but you cannot mutate the series). The row index of a data frame is mostly immutable - the only case when it changes is when you create an empty data frame and than add the first series.

This seems to be useful because it works nicely with the ?<- operator and you do not have to re-bind when you're writing some research script.

## Library internals

The Deedle implementation uses two layers. In the public API, you work with series and frames. Under the cover, all of the operations are provided by indices (providng lookup and alignment) and vectors (providing data storage). These are implemented in multiple different ways - most notably, Deedle supports in-memory version and BigDeedle provides virtualised implementation that can be used for big time series without fully loading it into memory.

### Vectors and indices

The following types are (mostly) not directly visible to the user, but they represent the "minimal" core that changes infrequently. You could use them when extending the library:

• IVector<'TValue> represents a vector (essentially an abstract data storage) that contains values 'TValue that can be accessed via an address Address. A simple concrete implementation is an array with int addresses, but we aim to make this abstract - one could use an array of arrays with int64 index for large data sets, lazy vector that loads data from a stream or even a virtual vector with e.g. Cassandra data source).

An important thing about vectors is that they handle missing values, so vector of integers is actually more like array<option<int>> (but we have a custom value type so that this is continuous block of memory). We decided that handling missing values is something that is so important for data frame, that it should be directly supported rather than done by e.g. storing optional or nullable values. Our implementation actually does a simple optimization - if there are no missing values, it just stores array<int>.

• VectorConstruction is a discriminated union (DSL) that describes construction of vector. For every vector type, there is an IVectorBuilder that knows how to construct vectors using the construction instructions (these include things like re-shuffling of elements, appending vectors, getting a sub-range etc.)

• IIndex<'TKey> represents an index - that is, a mapping from keys of a series or data frame to addresses in a vector. In the simple case, this is just a hash table that returns the int offset in an array when given a key (e.g. string or DateTime). A super-simple index would just map int offsets to int addresses via an identity function (not implemented yet!) - if you have series or data frame that is simply a list of recrods.

### Series and frames

The following types are the public API, wrapping the vectors and indices:

• Series<'TKey, 'TValue> represents a series of values 'TValue indexed by an index 'TKey. A series uses an abstract vector, index and vector builder, so it should work with any data representation. A series provides some standard slicing operators, projection, filtering etc. There are also some binary operators (multiply by a scalar, add series, etc.) and addtional operations in the Series module.

• Frame<'TRowKey, 'TColumnKey> represents a data frame with rows indexed using TRowKey (this could be DateTime or just ordinal numbers like int) and columns indexed by TColumnKey (typically a string). The data in the frame can be hetrogeneous (e.g. different types of values in different columns) and so accessing data is dynamic - but you can e.g. get a typed series.

The operations available on the data frame include adding & removing series (which aligns the new series according to the row index), joins (again - aligns the series) etc. You can also get all rows as a series of (column) series and all columns as a series of (row) series - they are available as extension methods and in the Frame module.

### Vector builders and index builders

The indices and vectors are constructed using IIndexBuilder and IVectorBuilder. Typically, index builder creates a new index and returns a VectorConstruction that can then be passed to IVectorBuilder.Build to perform the corresponding transformation on all vectors (for example, transform all vectors of a data frame according to an operation applied to the index).

Indices and vectors are connected via an address. Addresses are represented by the Address type and they are used to map keys (of the index) to values (in the vector). Here is a brief summary of what we assume (and don't assume) about addresses:

• Address is int64 (although we might need to generalize this in the future)
• Different data sources can use different addressing schemes (as long as both index and vector use the same scheme)
• Addresses don't have to be continuous (e.g. if the source is partitioned, it can use 32bit partition index + 32bit offset in the partition)
• In the in-memory representation, address is just index into an array
• In the BigDeedle representation, address is abstracted and comes with AddressOperations that specifies how to use it (tests use linear offset and partitioned representation)

To capture the different options, Deedle has an interface called IAddressingScheme. This represents the addressing mode used (it has no methods - it is just an object that can be compared). Vectors and indices both expose AddressingScheme property that can be used to check that their addressing schemes match.

Whenever we have index and vector, we need to make sure that they share the same addressing scheme. There is a number of things that ensure this:

• Series and frames keep an IIndexBuilder and a IVectorBuilder to be used for performing operations with the internal structures. These should always match, i.e. they should produce indices/vectors with the same addressing scheme.

• IIndexBuilder may not be able to perform all operations without fully materializing the index (e.g. BigDeedle can only do some operations). In that case, it returns an index with different addressing scheme. When calling IVectorBuilder.Build, this takes VectorConstruction together with IAddressingScheme and so it can ensure that the created vector has the correct addressing scheme (i.e. if the required addressing scheme is linear, partitioned virtual index can materialize the vector before returning it).

• IVector can also materialize vectors (when using Select or Convert methods). When those are called, the caller should apply IIndexBuilder.Project on the index, which performs the corresponding materialization on the index.

• When the calling code creates a new index or vector directly (typically in-memory index/vector calculated from keys or values), it needs to make sure that the other structure matches too. When a new vector is created using IVectorBuilder.Create, the index needs to be transformed using IIndexBuilder.Recreate.

## BigDeedle and virtual series and frames

The "BigDeedle" project implements virtualized data sources that can perform many operations of Deedle without actually evaluating the data. This consists of VirtualVector<'T> and VirtualOrderedIndex<'T> and VirtualOrdinalIndex<'T> (there are two indices - one for ordinal keys and one for user-specified keys) together with their builders.

BigDeedle is extensible and you only need to provide fairly small number of operations to use it. The interfaces to look at are:

• IVirtualVectorSource<'T> where 'T is the type of values of the source. This interface is used as a source for both virtual vectors (data access) and virtual indices (keys). Once you have a value of this, you can use Virtual.CreateSeries and similar methods to build a series or a frame.

The most tricky thing of the implementation is often IAddressOperations:

• If you already have some underlying infrastructure that handles merging and slicing of virtual sources, then you can implement the interface directly on top of this (and use the infrastructure in merging and slicing operations of IVirtualVectorSource).

• More frequently, you'll want to use the Ranges<'K> type provided by Deedle. This represents a mapping from some keys 'K to offsets and it supports merging and slicing (so you do not have to write your own code to merge slices of virtual soruces). To use this, you can use RangesAddressOperations(...) which gives you an implementation of IAddressOperations. For a reasonably simple example, see the code in tests using partitioned addressing scheme.

## Discussion and open questions

We're hoping that the design of the internals is now reasonable, but the end user API may still be missing some useful functionality (let us know if you need some!) Here are a few things that we discussed earlier and that we may still look into at some point:

• Time series vs. pivot table - there is some mismatch between two possible interpretations and uses of the library. One is for time-series data (e.g. in finance) where one typically works with dates as row indices. More generally, you can see this as continous index. It makes sense to do interpolation, sort the observations, align them, re-scale them etc. (Note that continuous is stronger than ordered - aside from time, the only continuous measure we can think of is distance-dependent series.)

The other case is when we have some discrete observations (perhaps a list of records with customer data, a list of prices of different stock prices etc.) In this case, we need more "pivot table" functions etc.

Although these two uses are quite different, we feel that it might make sense to use the same type for both (just with a different index). The problem is that this might make the API more complex. Although, if we can keep the distincion in the type, we can use F# 3.1 extension methods that extend just "discrete data frame" or "continous data frame". However, for now all functions are available in Frame/Series module and as extension methods that extend any type.

• Type provider - we are thinking about using type providers to give some additional safety (like checking column names and types in a data frame). This is currently on the TODO list - we think we can do something useful here, although it will certainly be limited.

The current idea is that you migth want to do some research/prototyping using a dynamic data frame, but once you're done and have some more stable data, you should be able to write, say DataFrame<"Open:float,Close:float">(dynamicDf) and get a new typed data frame.

If you have any comments regarding the topics above, please submit an issue on GitHub or, if you are interested in more actively contributing, join the F# for Data and Machine Learning working group.