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Handling missing values

Missing-value support is a first-class feature of Deedle. Every series and frame can contain missing values; the library tracks them explicitly and handles them consistently across all operations.

How missing values are represented

Deedle uses OptionalValue<'T> to represent a value that may or may not be present. You rarely construct OptionalValue directly; instead, certain input values are automatically treated as missing:

Input type

Treated as missing when

float / double

Value is Double.NaN

Reference type (string, obj …)

Value is null

Nullable<T>

.HasValue is false

The following examples show series created from inputs that include missing values:

// float NaN becomes a missing value
Series.ofValues [ 1.0; Double.NaN; 3.0 ]
No value returned by any evaluator
// null in a reference-type series
Series.ofValues [ "a"; null; "c" ]
No value returned by any evaluator
// Nullable<int> without a value
[ Nullable(1); Nullable(); Nullable(3) ] |> Series.ofValues
No value returned by any evaluator

You can also construct a series with an explicit OptionalValue.Missing:

Series.ofOptionalObservations
  [ 1 => OptionalValue(10.0)
    2 => OptionalValue.Missing
    3 => OptionalValue(30.0) ]
No value returned by any evaluator

Counting present and missing values

Stats.count counts the number of present values; Series.countValues is an alias. The total number of keys (including missing) is KeyCount:

let air = Frame.ReadCsv(root + "airquality.csv", separators=";")
let ozone = air?Ozone
// total keys (rows) in the series
ozone.KeyCount
No value returned by any evaluator
// present (non-missing) values
Stats.count ozone
No value returned by any evaluator
// number of missing values
ozone.KeyCount - int (Stats.count ozone)
No value returned by any evaluator

Statistics skip missing values

All functions in the Stats module, as well as common projections such as Series.mapValues and Series.filter, automatically skip missing values. The operation is applied only to present observations:

Stats.mean ozone      // mean of the 116 present values
No value returned by any evaluator
Stats.max ozone       // maximum of the present values
No value returned by any evaluator

Accessing values with TryGet

The safe way to look up a single value by key is TryGet, which returns an OptionalValue<'T>:

let v = ozone.TryGet(1)
match v with
| OptionalValue.Present x -> sprintf "present: %g" x
| OptionalValue.Missing   -> "missing"
No value returned by any evaluator

You can also use Series.observationsAll to iterate over all key-value pairs including missing ones (as OptionalValue), or Series.observations to skip missing values:

ozone
|> Series.observationsAll
|> Seq.truncate 6
|> Seq.map (fun (k, v) ->
    match v with
    | OptionalValue.Present x -> sprintf "%d => %g" k x
    | OptionalValue.Missing   -> sprintf "%d => <missing>" k)
|> Seq.toList
No value returned by any evaluator

Custom handling with Series.mapAll

Series.mapValues skips missing values. When you need to transform the value or the missing-ness of each element, use Series.mapAll, which receives an option<'T> for each key:

ozone
|> Series.mapAll (fun k v ->
    match v with
    | None   -> Some 0.0     // replace missing with zero
    | Some x -> Some (x * 2.0)) // double present values
|> Series.take 5
No value returned by any evaluator

Filling missing values

Fill with a constant

The simplest strategy replaces every missing value with a fixed constant:

ozone |> Series.fillMissingWith 0.0 |> Series.take 6
No value returned by any evaluator

Forward and backward fill

Series.fillMissing propagates the most recent available value in the specified direction:

// Carry the last known value forward
ozone |> Series.fillMissing Direction.Forward |> Series.take 6
No value returned by any evaluator
// Fill from the next available value backward
ozone |> Series.fillMissing Direction.Backward |> Series.take 6
No value returned by any evaluator

Custom fill strategy with fillMissingUsing

For interpolation or other context-sensitive strategies, use Series.fillMissingUsing. The function receives the missing key and should return a replacement value:

ozone
|> Series.fillMissingUsing (fun k ->
    // Linear interpolation from neighbours
    let prev = ozone.TryGet(k, Lookup.ExactOrSmaller)
    let next = ozone.TryGet(k, Lookup.ExactOrGreater)
    match prev, next with
    | OptionalValue.Present p, OptionalValue.Present n -> (p + n) / 2.0
    | OptionalValue.Present v, _
    | _, OptionalValue.Present v -> v
    | _ -> 0.0)
|> Series.take 6
No value returned by any evaluator

Combining fill and drop

Often the cleanest approach is to fill as much as possible in one direction and then discard the remaining missing values:

ozone
|> Series.fillMissing Direction.Forward
|> Series.dropMissing
|> Series.countValues
No value returned by any evaluator

Dropping missing values

Drop from a series

Series.dropMissing removes all missing observations from a series:

ozone |> Series.dropMissing |> Series.countValues
No value returned by any evaluator

Drop sparse rows and columns from a frame

Frame.dropSparseRows removes any row that contains at least one missing value; Frame.dropSparseCols removes columns with any missing value.

After reading the air quality CSV the frame has missing values in several columns:

air.RowCount
No value returned by any evaluator
// Keep only rows that are fully observed
let airComplete = air |> Frame.dropSparseRows
airComplete.RowCount
No value returned by any evaluator

Missing values in frames

The same filling functions are available at the frame level and operate column-by-column:

// Fill every missing cell with 0.0
air
|> Frame.fillMissingWith 0.0
|> Frame.dropSparseRows   // now no rows should be dropped
|> fun f -> f.RowCount
No value returned by any evaluator
// Forward-fill each column independently
air
|> Frame.fillMissing Direction.Forward
|> Frame.dropSparseRows
|> fun f -> f.RowCount
No value returned by any evaluator

Frame.fillMissingUsing accepts a function Series<'R,'T> -> 'R -> 'T so it can base the fill value on the whole column series:

air
|> Frame.fillMissingUsing (fun col key ->
    // Fill with that column's mean
    Stats.mean col)
|> Frame.dropSparseRows
|> fun f -> f.RowCount
No value returned by any evaluator

Missing values in joins

When two frames or series are joined, rows that exist in one source but not the other receive missing values for the absent columns. The join kind controls which rows are retained:

Join kind

Rows kept

Missing values introduced

JoinKind.Inner

Only rows present in both

None

JoinKind.Left

All rows from the left

Right columns for unmatched rows

JoinKind.Right

All rows from the right

Left columns for unmatched rows

JoinKind.Outer

All rows from either

Both sides for unmatched rows

let s1 = series [ 1 => 10.0; 2 => 20.0; 3 => 30.0 ]
let s2 = series [ 2 => 200.0; 3 => 300.0; 4 => 400.0 ]
// Outer join introduces missing values for key 1 (not in s2) and key 4 (not in s1)
Frame.ofColumns ["A" => s1; "B" => s2]
No value returned by any evaluator
// Inner join keeps only keys present in both
let f1 = frame ["A" => s1]
let f2 = frame ["B" => s2]
f1.Join(f2, JoinKind.Inner)
No value returned by any evaluator

After an outer join, Frame.dropSparseRows or Frame.fillMissing can be used to bring the frame back to a fully populated state.

Summary

Goal

Function

Count present values

Stats.count series

Count keys (incl. missing)

series.KeyCount

Safe lookup

series.TryGet(key)OptionalValue<T>

Iterate with missing

Series.observationsAll

Handle in a transform

Series.mapAll

Fill with constant

Series.fillMissingWith value / Frame.fillMissingWith value

Carry forward/back

Series.fillMissing Direction.* / Frame.fillMissing Direction.*

Custom fill

Series.fillMissingUsing f / Frame.fillMissingUsing f

Remove missing rows

Series.dropMissing / Frame.dropSparseRows

Remove missing cols

Frame.dropSparseCols

See also

namespace System
namespace Deedle
val root: string
Multiple items
module Series from Deedle
<summary> The `Series` module provides an F#-friendly API for working with data and time series. The API follows the usual design for collection-processing in F#, so the functions work well with the pipelining (<c>|&gt;</c>) operator. For example, given a series with ages, we can use `Series.filterValues` to filter outliers and then `Stats.mean` to calculate the mean: ages |&gt; Series.filterValues (fun v -&gt; v &gt; 0.0 &amp;&amp; v &lt; 120.0) |&gt; Stats.mean The module provides comprehensive set of functions for working with series. The same API is also exposed using C#-friendly extension methods. In C#, the above snippet could be written as: [lang=csharp] ages .Where(kvp =&gt; kvp.Value &gt; 0.0 &amp;&amp; kvp.Value &lt; 120.0) .Mean() For more information about similar frame-manipulation functions, see the `Frame` module. For more information about C#-friendly extensions, see `SeriesExtensions`. The functions in the `Series` module are grouped in a number of categories and documented below. Accessing series data and lookup -------------------------------- Functions in this category provide access to the values in the series. - The term _observation_ is used for a key value pair in the series. - When working with a sorted series, it is possible to perform lookup using keys that are not present in the series - you can specify to search for the previous or next available value using _lookup behavior_. - Functions such as `get` and `getAll` have their counterparts `lookup` and `lookupAll` that let you specify lookup behavior. - For most of the functions that may fail, there is a `try[Foo]` variant that returns `None` instead of failing. - Functions with a name ending with `At` perform lookup based on the absolute integer offset (and ignore the keys of the series) Series transformations ---------------------- Functions in this category perform standard transformations on series including projections, filtering, taking some sub-series of the series, aggregating values using scanning and so on. Projection and filtering functions generally skip over missing values, but there are variants `filterAll` and `mapAll` that let you handle missing values explicitly. Keys can be transformed using `mapKeys`. When you do not need to consider the keys, and only care about values, use `filterValues` and `mapValues` (which is also aliased as the `$` operator). Series supports standard set of folding functions including `reduce` and `fold` (to reduce series values into a single value) as well as the `scan[All]` function, which can be used to fold values of a series into a series of intermeidate folding results. The functions `take[Last]` and `skip[Last]` can be used to take a sub-series of the original source series by skipping a specified number of elements. Note that this does not require an ordered series and it ignores the index - for index-based lookup use slicing, such as `series.[lo .. hi]`, instead. Finally the `shift` function can be used to obtain a series with values shifted by the specified offset. This can be used e.g. to get previous value for each key using `Series.shift 1 ts`. The `diff` function calculates difference from previous value using `ts - (Series.shift offs ts)`. Processing series with exceptions --------------------------------- The functions in this group can be used to write computations over series that may fail. They use the type <c>tryval&lt;'T&gt;</c> which is defined as a discriminated union with two cases: Success containing a value, or Error containing an exception. The function `tryMap` lets you create <c>Series&lt;'K, tryval&lt;'T&gt;&gt;</c> by mapping over values of an original series. You can then extract values using `tryValues`, which throws `AggregateException` if there were any errors. Functions `tryErrors` and `trySuccesses` give series containing only errors and successes. You can fill failed values with a constant using `fillErrorsWith`. Hierarchical index operations ----------------------------- When the key of a series is tuple, the elements of the tuple can be treated as multiple levels of a index. For example <c>Series&lt;'K1 * 'K2, 'V&gt;</c> has two levels with keys of types <c>'K1</c> and <c>'K2</c> respectively. The functions in this cateogry provide a way for aggregating values in the series at one of the levels. For example, given a series `input` indexed by two-element tuple, you can calculate mean for different first-level values as follows: input |&gt; applyLevel fst Stats.mean Note that the `Stats` module provides helpers for typical statistical operations, so the above could be written just as `input |&gt; Stats.levelMean fst`. Grouping, windowing and chunking -------------------------------- This category includes functions that group data from a series in some way. Two key concepts here are _window_ and _chunk_. Window refers to (overlapping) sliding windows over the input series while chunk refers to non-overlapping blocks of the series. The boundary behavior can be specified using the `Boundary` flags. The value `Skip` means that boundaries (incomplete windows or chunks) should be skipped. The value `AtBeginning` and `AtEnding` can be used to define at which side should the boundary be returned (or skipped). For chunking, `AtBeginning ||| Skip` makes sense and it means that the incomplete chunk at the beginning should be skipped (aligning the last chunk with the end). The behavior may be specified in a number of ways (which is reflected in the name): - `dist` - using an absolute distance between the keys - `while` - using a condition on the first and last key - `size` - by specifying the absolute size of the window/chunk The functions ending with `Into` take a function to be applied to the window/chunk. The functions `window`, `windowInto` and `chunk`, `chunkInto` are simplified versions that take a size. There is also `pairwise` function for sliding window of size two. Missing values -------------- This group of functions provides a way of working with missing values in a series. The `dropMissing` function drops all keys for which there are no values in the series. The `withMissingFrom` function lets you copy missing values from another series. The remaining functions provide different mechanism for filling the missing values. * `fillMissingWith` fills missing values with a specified constant * `fillMissingUsing` calls a specified function for every missing value * `fillMissing` and variants propagates values from previous/later keys Sorting and index manipulation ------------------------------ A series that is sorted by keys allows a number of additional operations (such as lookup using the `Lookp.ExactOrSmaller` lookup behavior). However, it is also possible to sort series based on the values - although the functions for manipulation with series do not guarantee that the order will be preserved. To sort series by keys, use `sortByKey`. Other sorting functions let you sort the series using a specified comparer function (`sortWith`), using a projection function (`sortBy`) and using the default comparison (`sort`). In addition, you can also replace the keys of a series with other keys using `indexWith` or with integers using `indexOrdinally`. To pick and reorder series values using to match a list of keys use `realign`. Sampling, resampling and advanced lookup ---------------------------------------- Given a (typically) time series sampling or resampling makes it possible to get time series with representative values at lower or uniform frequency. We use the following terminology: - `lookup` and `sample` functions find values at specified key; if a key is not available, they can look for value associated with the nearest smaller or the nearest greater key. - `resample` function aggregate values values into chunks based on a specified collection of keys (e.g. explicitly provided times), or based on some relation between keys (e.g. date times having the same date). - `resampleUniform` is similar to resampling, but we specify keys by providing functions that generate a uniform sequence of keys (e.g. days), the operation also fills value for days that have no corresponding observations in the input sequence. Joining, merging and zipping ---------------------------- Given two series, there are two ways to combine the values. If the keys in the series are not overlapping (or you want to throw away values from one or the other series), then you can use `merge` or `mergeUsing`. To merge more than 2 series efficiently, use the `mergeAll` function, which has been optimized for large number of series. If you want to align two series, you can use the _zipping_ operation. This aligns two series based on their keys and gives you tuples of values. The default behavior (`zip`) uses outer join and exact matching. For ordered series, you can specify other forms of key lookups (e.g. find the greatest smaller key) using `zipAlign`. functions ending with `Into` are generally easier to use as they call a specified function to turn the tuple (of possibly missing values) into a new value. For more complicated behaviors, it is often convenient to use joins on frames instead of working with series. Create two frames with single columns and then use the join operation. The result will be a frame with two columns (which is easier to use than series of tuples). </summary>
<category>Frame and series operations</category>


--------------------
type Series = static member ofNullables: values: Nullable<'a> seq -> Series<int,'a> (requires default constructor and value type and 'a :> ValueType) static member ofObservations: observations: ('a * 'b) seq -> Series<'a,'b> (requires equality) static member ofOptionalObservations: observations: ('K * 'a option) seq -> Series<'K,'a> (requires equality) static member ofValues: values: 'a seq -> Series<int,'a>

--------------------
type Series<'K,'V (requires equality)> = interface ISeriesFormattable interface IFsiFormattable interface ISeries<'K> new: index: IIndex<'K> * vector: IVector<'V> * vectorBuilder: IVectorBuilder * indexBuilder: IIndexBuilder -> Series<'K,'V> + 3 overloads member After: lowerExclusive: 'K -> Series<'K,'V> member Aggregate: aggregation: Aggregation<'K> * keySelector: Func<DataSegment<Series<'K,'V>>,'TNewKey> * valueSelector: Func<DataSegment<Series<'K,'V>>,OptionalValue<'R>> -> Series<'TNewKey,'R> (requires equality) + 1 overload member AsyncMaterialize: unit -> Async<Series<'K,'V>> member Before: upperExclusive: 'K -> Series<'K,'V> member Between: lowerInclusive: 'K * upperInclusive: 'K -> Series<'K,'V> member Compare: another: Series<'K,'V> -> Series<'K,Diff<'V>> ...
<summary> The type <c>Series&lt;K, V&gt;</c> represents a data series consisting of values `V` indexed by keys `K`. The keys of a series may or may not be ordered </summary>
<category>Core frame and series types</category>


--------------------
new: pairs: Collections.Generic.KeyValuePair<'K,'V> seq -> Series<'K,'V>
new: keys: 'K seq * values: 'V seq -> Series<'K,'V>
new: keys: 'K array * values: 'V array -> Series<'K,'V>
new: index: Indices.IIndex<'K> * vector: IVector<'V> * vectorBuilder: Vectors.IVectorBuilder * indexBuilder: Indices.IIndexBuilder -> Series<'K,'V>
static member Series.ofValues: values: 'a seq -> Series<int,'a>
[<Struct>] type Double = member CompareTo: value: float -> int + 1 overload member Equals: obj: float -> bool + 1 overload member GetHashCode: unit -> int member GetTypeCode: unit -> TypeCode member ToString: unit -> string + 3 overloads member TryFormat: utf8Destination: Span<byte> * bytesWritten: byref<int> * ?format: ReadOnlySpan<char> * ?provider: IFormatProvider -> bool + 1 overload static member (<) : left: float * right: float -> bool static member (<=) : left: float * right: float -> bool static member (<>) : left: float * right: float -> bool static member (=) : left: float * right: float -> bool ...
<summary>Represents a double-precision floating-point number.</summary>
field Double.NaN: float = NaN
Multiple items
type Nullable = static member Compare<'T (requires default constructor and value type and 'T :> ValueType)> : n1: Nullable<'T> * n2: Nullable<'T> -> int static member Equals<'T (requires default constructor and value type and 'T :> ValueType)> : n1: Nullable<'T> * n2: Nullable<'T> -> bool static member GetUnderlyingType: nullableType: Type -> Type static member GetValueRefOrDefaultRef<'T (requires default constructor and value type and 'T :> ValueType)> : nullable: inref<Nullable<'T>> -> inref<'T>
<summary>Supports a value type that can be assigned <see langword="null" />. This class cannot be inherited.</summary>

--------------------
[<Struct>] type Nullable<'T (requires default constructor and value type and 'T :> ValueType)> = new: value: 'T -> unit member Equals: other: obj -> bool member GetHashCode: unit -> int member GetValueOrDefault: unit -> 'T + 1 overload member ToString: unit -> string static member op_Explicit: value: Nullable<'T> -> 'T static member op_Implicit: value: 'T -> Nullable<'T> member HasValue: bool member Value: 'T
<summary>Represents a value type that can be assigned <see langword="null" />.</summary>
<typeparam name="T">The underlying value type of the <see cref="T:System.Nullable`1" /> generic type.</typeparam>


--------------------
Nullable ()
Nullable(value: 'T) : Nullable<'T>
static member Series.ofOptionalObservations: observations: ('K * 'a option) seq -> Series<'K,'a> (requires equality)
Multiple items
module OptionalValue from Deedle
<summary> Provides various helper functions for using the <c>OptionalValue&lt;T&gt;</c> type from F# (The functions are similar to those in the standard <c>Option</c> module). </summary>
<category>Primitive types and values</category>


--------------------
type OptionalValue = class end
<summary> Non-generic type that makes it easier to create <c>OptionalValue&lt;T&gt;</c> values from C# by benefiting the type inference for generic method invocations. </summary>
<category>Primitive types and values</category>


--------------------
[<Struct>] type OptionalValue<'T> = new: value: 'T -> OptionalValue<'T> override Equals: y: obj -> bool override GetHashCode: unit -> int override ToString: unit -> string member HasValue: bool with get member Value: 'T with get member ValueOrDefault: 'T with get static member Missing: OptionalValue<'T> with get
<summary> Value type that represents a potentially missing value. This is similar to <c>System.Nullable&lt;T&gt;</c>, but does not restrict the contained value to be a value type, so it can be used for storing values of any types. When obtained from <c>DataFrame&lt;R, C&gt;</c> or <c>Series&lt;K, T&gt;</c>, the <c>Value</c> will never be <c>Double.NaN</c> or <c>null</c> (but this is not, in general, checked when constructing the value). The type is only used in C#-friendly API. F# operations generally use expose standard F# <c>option&lt;T&gt;</c> type instead. However, there the <c>OptionalValue</c> module contains helper functions for using this type from F# as well as <c>Missing</c> and <c>Present</c> active patterns. </summary>
<category>Primitive types and values</category>


--------------------
OptionalValue ()
new: value: 'T -> OptionalValue<'T>
Multiple items
active recognizer Missing: 'T opt -> Choice<unit,'T>
<summary> Complete active pattern that can be used to pattern match on `OptionalValue&lt;T&gt;`. For example: let optVal = OptionalValue(42) match optVal with | OptionalValue.Missing -&gt; printfn "Empty" | OptionalValue.Present(v) -&gt; printfn "Contains %d" v </summary>

--------------------
property OptionalValue.Missing: OptionalValue<'T> with get
<summary> Returns a new instance of `OptionalValue&lt;T&gt;` that does not contain a value. </summary>
val air: Frame<int,string>
Multiple items
module Frame from Deedle
<summary> The `Frame` module provides an F#-friendly API for working with data frames. The module follows the usual desing for collection-processing in F#, so the functions work well with the pipelining operator (`|&gt;`). For example, given a frame with two columns representing prices, we can use `Frame.pctChange` to calculate daily returns like this: let df = frame [ "MSFT" =&gt; prices1; "AAPL" =&gt; prices2 ] let rets = df |&gt; Frame.pctChange 1 rets |&gt; Stats.mean Note that the `Stats.mean` operation is overloaded and works both on series (returning a number) and on frames (returning a series). You can also use `Frame.diff` if you need absolute differences rather than relative changes. The functions in this module are designed to be used from F#. For a C#-friendly API, see the `FrameExtensions` type. For working with individual series, see the `Series` module. The functions in the `Frame` module are grouped in a number of categories and documented below. Accessing frame data and lookup ------------------------------- Functions in this category provide access to the values in the fame. You can also add and remove columns from a frame (which both return a new value). - `addCol`, `replaceCol` and `dropCol` can be used to create a new data frame with a new column, by replacing an existing column with a new one, or by dropping an existing column - `cols` and `rows` return the columns or rows of a frame as a series containing objects; `getCols` and `getRows` return a generic series and cast the values to the type inferred from the context (columns or rows of incompatible types are skipped); `getNumericCols` returns columns of a type convertible to `float` for convenience. - You can get a specific row or column using `get[Col|Row]` or `lookup[Col|Row]` functions. The `lookup` variant lets you specify lookup behavior for key matching (e.g. find the nearest smaller key than the specified value). There are also `[try]get` and `[try]Lookup` functions that return optional values and functions returning entire observations (key together with the series). - `sliceCols` and `sliceRows` return a sub-frame containing only the specified columns or rows. Finally, `toArray2D` returns the frame data as a 2D array. Grouping, windowing and chunking -------------------------------- The basic grouping functions in this category can be used to group the rows of a data frame by a specified projection or column to create a frame with hierarchical index such as <c>Frame&lt;'K1 * 'K2, 'C&gt;</c>. The functions always aggregate rows, so if you want to group columns, you need to use `Frame.transpose` first. The function `groupRowsBy` groups rows by the value of a specified column. Use `groupRowsBy[Int|Float|String...]` if you want to specify the type of the column in an easier way than using type inference; `groupRowsUsing` groups rows using the specified _projection function_ and `groupRowsByIndex` projects the grouping key just from the row index. More advanced functions include: `aggregateRowsBy` which groups the rows by a specified sequence of columns and aggregates each group into a single value; `pivotTable` implements the pivoting operation [as documented in the tutorials](../frame.html#pivot). The `melt` and `unmelt` functions turn the data frame into a single data frame containing columns `Row`, `Column` and `Value` containing the data of the original frame; `unmelt` can be used to turn this representation back into an original frame. The `stack` and `unstack` functions implement pandas-style reshape operations. `stack` converts `Frame&lt;'R,'C&gt;` to a long-format `Frame&lt;'R*'C, string&gt;` where each cell becomes a row keyed by `(rowKey, colKey)` with a single `"Value"` column. `unstack` promotes the inner row-key level to column keys, producing `Frame&lt;'R1, 'C*'R2&gt;` from `Frame&lt;'R1*'R2,'C&gt;`. A simple windowing functions that are exposed for an entire frame operations are `window` and `windowInto`. For more complex windowing operations, you currently have to use `mapRows` or `mapCols` and apply windowing on individual series. Sorting and index manipulation ------------------------------ A frame is indexed by row keys and column keys. Both of these indices can be sorted (by the keys). A frame that is sorted allows a number of additional operations (such as lookup using the `Lookp.ExactOrSmaller` lookup behavior). The functions in this category provide ways for manipulating the indices. It is expected that most operations are done on rows and so more functions are available in a row-wise way. A frame can alwyas be transposed using `Frame.transpose`. Index operations: The existing row/column keys can be replaced by a sequence of new keys using the `indexColsWith` and `indexRowsWith` functions. Row keys can also be replaced by ordinal numbers using `indexRowsOrdinally`. The function `indexRows` uses the specified column of the original frame as the index. It removes the column from the resulting frame (to avoid this, use overloaded `IndexRows` method). This function infers the type of row keys from the context, so it is usually more convenient to use `indexRows[Date|String|Int|...]` functions. Finally, if you want to calculate the index value based on multiple columns of the row, you can use `indexRowsUsing`. Sorting frame rows: Frame rows can be sorted according to the value of a specified column using the `sortRows` function; `sortRowsBy` takes a projection function which lets you transform the value of a column (e.g. to project a part of the value). The functions `sortRowsByKey` and `sortColsByKey` sort the rows or columns using the default ordering on the key values. The result is a frame with ordered index. Expanding columns: When the frame contains a series with complex .NET objects such as F# records or C# classes, it can be useful to "expand" the column. This operation looks at the type of the objects, gets all properties of the objects (recursively) and generates multiple series representing the properties as columns. The function `expandCols` expands the specified columns while `expandAllCols` applies the expansion to all columns of the data frame. Frame transformations --------------------- Functions in this category perform standard transformations on data frames including projections, filtering, taking some sub-frame of the frame, aggregating values using scanning and so on. Projection and filtering functions such as `[map|filter][Cols|Rows]` call the specified function with the column or row key and an <c>ObjectSeries&lt;'K&gt;</c> representing the column or row. You can use functions ending with `Values` (such as `mapRowValues`) when you do not require the row key, but only the row series; `mapRowKeys` and `mapColKeys` can be used to transform the keys. You can use `reduceValues` to apply a custom reduction to values of columns. Other aggregations are available in the `Stats` module. You can also get a row with the greaterst or smallest value of a given column using `[min|max]RowBy`. The functions `take[Last]` and `skip[Last]` can be used to take a sub-frame of the original source frame by skipping a specified number of rows. Note that this does not require an ordered frame and it ignores the index - for index-based lookup use slicing, such as `df.Rows.[lo .. hi]`, instead. Finally the `shift` function can be used to obtain a frame with values shifted by the specified offset. This can be used e.g. to get previous value for each key using `Frame.shift 1 df`. The `diff` function calculates difference from previous value using `df - (Frame.shift offs df)`. Processing frames with exceptions --------------------------------- The functions in this group can be used to write computations over frames that may fail. They use the type <c>tryval&lt;'T&gt;</c> which is defined as a discriminated union with two cases: Success containing a value, or Error containing an exception. Using <c>tryval&lt;'T&gt;</c> as a value in a data frame is not generally recommended, because the type of values cannot be tracked in the type. For this reason, it is better to use <c>tryval&lt;'T&gt;</c> with individual series. However, `tryValues` and `fillErrorsWith` functions can be used to get values, or fill failed values inside an entire data frame. The `tryMapRows` function is more useful. It can be used to write a transformation that applies a computation (which may fail) to each row of a data frame. The resulting series is of type <c>Series&lt;'R, tryval&lt;'T&gt;&gt;</c> and can be processed using the <c>Series</c> module functions. Missing values -------------- This group of functions provides a way of working with missing values in a data frame. The category provides the following functions that can be used to fill missing values: * `fillMissingWith` fills missing values with a specified constant * `fillMissingUsing` calls a specified function for every missing value * `fillMissing` and variants propagates values from previous/later keys We use the terms _sparse_ and _dense_ to denote series that contain some missing values or do not contain any missing values, respectively. The functions `denseCols` and `denseRows` return a series that contains only dense columns or rows and all sparse rows or columns are replaced with a missing value. The `dropSparseCols` and `dropSparseRows` functions drop these missing values and return a frame with no missing values. Joining, merging and zipping ---------------------------- The simplest way to join two frames is to use the `join` operation which can be used to perform left, right, outer or inner join of two frames. When the row keys of the frames do not match exactly, you can use `joinAlign` which takes an additional parameter that specifies how to find matching key in left/right join (e.g. by taking the nearest smaller available key). Frames that do not contian overlapping values can be combined using `merge` (when combining just two frames) or using `mergeAll` (for larger number of frames). Tha latter is optimized to work well for a large number of data frames. Finally, frames with overlapping values can be combined using `zip`. It takes a function that is used to combine the overlapping values. A `zipAlign` function provides a variant with more flexible row key matching (as in `joinAlign`) Hierarchical index operations ----------------------------- A data frame has a hierarchical row index if the row index is formed by a tuple, such as <c>Frame&lt;'R1 * 'R2, 'C&gt;</c>. Frames of this kind are returned, for example, by the grouping functions such as <c>Frame.groupRowsBy</c>. The functions in this category provide ways for working with data frames that have hierarchical row keys. The functions <c>applyLevel</c> and <c>reduceLevel</c> can be used to reduce values according to one of the levels. The <c>applyLevel</c> function takes a reduction of type <c>Series&lt;'K, 'T&gt; -&gt; 'T</c> while <c>reduceLevel</c> reduces individual values using a function of type <c>'T -&gt; 'T -&gt; 'T</c>. The functions <c>nest</c> and <c>unnest</c> can be used to convert between frames with hierarchical indices (<c>Frame&lt;'K1 * 'K2, 'C&gt;</c>) and series of frames that represent individual groups (<c>Series&lt;'K1, Frame&lt;'K2, 'C&gt;&gt;</c>). The <c>nestBy</c> function can be used to perform group by operation and return the result as a series of frems. </summary>
<category>Frame and series operations</category>


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type Frame = static member ReadCsv: location: string * [<Optional>] hasHeaders: Nullable<bool> * [<Optional>] inferTypes: Nullable<bool> * [<Optional>] inferRows: Nullable<int> * [<Optional>] schema: string * [<Optional>] separators: string * [<Optional>] culture: string * [<Optional>] maxRows: Nullable<int> * [<Optional>] missingValues: string array * [<Optional>] preferOptions: bool * [<Optional>] encoding: Encoding -> Frame<int,string> + 1 overload static member ReadReader: reader: IDataReader -> Frame<int,string> static member CustomExpanders: Dictionary<Type,Func<obj,(string * Type * obj) seq>> with get static member NonExpandableInterfaces: ResizeArray<Type> with get static member NonExpandableTypes: HashSet<Type> with get
<summary> Provides static methods for creating frames, reading frame data from CSV files and database (via IDataReader). The type also provides global configuration for reflection-based expansion. </summary>
<category>Frame and series operations</category>


--------------------
type Frame<'TRowKey,'TColumnKey (requires equality and equality)> = interface IDynamicMetaObjectProvider interface INotifyCollectionChanged interface IFrameFormattable interface IFsiFormattable interface IFrame new: rowIndex: IIndex<'TRowKey> * columnIndex: IIndex<'TColumnKey> * data: IVector<IVector> * indexBuilder: IIndexBuilder * vectorBuilder: IVectorBuilder -> Frame<'TRowKey,'TColumnKey> + 1 overload member AddColumn: column: 'TColumnKey * series: 'V seq -> unit + 3 overloads member AggregateRowsBy: groupBy: 'TColumnKey seq * aggBy: 'TColumnKey seq * aggFunc: Func<Series<'TRowKey,'a>,'b> -> Frame<int,'TColumnKey> member Clone: unit -> Frame<'TRowKey,'TColumnKey> member ColumnApply: f: Func<Series<'TRowKey,'T>,ISeries<'TRowKey>> -> Frame<'TRowKey,'TColumnKey> + 1 overload ...
<summary> A frame is the key Deedle data structure (together with series). It represents a data table (think spreadsheet or CSV file) with multiple rows and columns. The frame consists of row index, column index and data. The indices are used for efficient lookup when accessing data by the row key `'TRowKey` or by the column key `'TColumnKey`. Deedle frames are optimized for the scenario when all values in a given column are of the same type (but types of different columns can differ). </summary>
<remarks><para>Joining, zipping and appending:</para><para> More info </para></remarks>
<category>Core frame and series types</category>


--------------------
new: names: 'TColumnKey seq * columns: ISeries<'TRowKey> seq -> Frame<'TRowKey,'TColumnKey>
new: rowIndex: Indices.IIndex<'TRowKey> * columnIndex: Indices.IIndex<'TColumnKey> * data: IVector<IVector> * indexBuilder: Indices.IIndexBuilder * vectorBuilder: Vectors.IVectorBuilder -> Frame<'TRowKey,'TColumnKey>
static member Frame.ReadCsv: reader: IO.TextReader * ?hasHeaders: bool * ?inferTypes: bool * ?inferRows: int * ?schema: string * ?separators: string * ?culture: string * ?maxRows: int * ?missingValues: string array * ?preferOptions: bool * ?typeResolver: (string -> string option) -> Frame<int,string>
static member Frame.ReadCsv: stream: IO.Stream * [<Runtime.InteropServices.Optional>] hasHeaders: Nullable<bool> * [<Runtime.InteropServices.Optional>] inferTypes: Nullable<bool> * [<Runtime.InteropServices.Optional>] inferRows: Nullable<int> * [<Runtime.InteropServices.Optional>] schema: string * [<Runtime.InteropServices.Optional>] separators: string * [<Runtime.InteropServices.Optional>] culture: string * [<Runtime.InteropServices.Optional>] maxRows: Nullable<int> * [<Runtime.InteropServices.Optional>] missingValues: string array * [<Runtime.InteropServices.Optional>] preferOptions: Nullable<bool> * [<Runtime.InteropServices.Optional>] encoding: Text.Encoding -> Frame<int,string>
static member Frame.ReadCsv: location: string * [<Runtime.InteropServices.Optional>] hasHeaders: Nullable<bool> * [<Runtime.InteropServices.Optional>] inferTypes: Nullable<bool> * [<Runtime.InteropServices.Optional>] inferRows: Nullable<int> * [<Runtime.InteropServices.Optional>] schema: string * [<Runtime.InteropServices.Optional>] separators: string * [<Runtime.InteropServices.Optional>] culture: string * [<Runtime.InteropServices.Optional>] maxRows: Nullable<int> * [<Runtime.InteropServices.Optional>] missingValues: string array * [<Runtime.InteropServices.Optional>] preferOptions: bool * [<Runtime.InteropServices.Optional>] encoding: Text.Encoding -> Frame<int,string>
static member Frame.ReadCsv: path: string * ?hasHeaders: bool * ?inferTypes: bool * ?inferRows: int * ?schema: string * ?separators: string * ?culture: string * ?maxRows: int * ?missingValues: string array * ?preferOptions: bool * ?typeResolver: (string -> string option) * ?encoding: Text.Encoding -> Frame<int,string>
static member Frame.ReadCsv: stream: IO.Stream * ?hasHeaders: bool * ?inferTypes: bool * ?inferRows: int * ?schema: string * ?separators: string * ?culture: string * ?maxRows: int * ?missingValues: string array * ?preferOptions: bool * ?typeResolver: (string -> string option) * ?encoding: Text.Encoding -> Frame<int,string>
static member Frame.ReadCsv: path: string * indexCol: string * ?hasHeaders: bool * ?inferTypes: bool * ?inferRows: int * ?schema: string * ?separators: string * ?culture: string * ?maxRows: int * ?missingValues: string array * ?preferOptions: bool * ?typeResolver: (string -> string option) * ?encoding: Text.Encoding -> Frame<'R,string> (requires equality)
val ozone: Series<int,float>
property Series.KeyCount: int with get
<summary> Returns the total number of keys in the specified series. This returns the total length of the series, including keys for which there is no value available. </summary>
<category>Series data</category>
type Stats = static member corr: series1: Series<'K,'V1> -> series2: Series<'K,'V2> -> float (requires equality) static member corrFrame: frame: Frame<'R,'C> -> Frame<'C,'C> (requires equality and equality) static member count: series: Series<'K,'V> -> int (requires equality) + 1 overload static member cov: series1: Series<'K,'V1> -> series2: Series<'K,'V2> -> float (requires equality) static member covFrame: frame: Frame<'R,'C> -> Frame<'C,'C> (requires equality and equality) static member describe: series: Series<'K,'V> -> Series<string,float> (requires equality and equality) + 1 overload static member expandingCount: series: Series<'K,'V> -> Series<'K,float> (requires equality) static member expandingKurt: series: Series<'K,'V> -> Series<'K,float> (requires equality) static member expandingMax: series: Series<'K,'V> -> Series<'K,float> (requires equality) static member expandingMean: series: Series<'K,'V> -> Series<'K,float> (requires equality) ...
static member Stats.count: frame: Frame<'R,'C> -> Series<'C,int> (requires equality and equality)
static member Stats.count: series: Series<'K,'V> -> int (requires equality)
Multiple items
val int: value: 'T -> int (requires member op_Explicit)

--------------------
type int = int32

--------------------
type int<'Measure> = int
static member Stats.mean: frame: Frame<'R,'C> -> Series<'C,float> (requires equality and equality)
static member Stats.mean: series: Series<'K,'V> -> float (requires equality)
static member Stats.max: frame: Frame<'R,'C> -> Series<'C,float> (requires equality and equality)
static member Stats.max: series: Series<'K,'V> -> float (requires equality)
val v: OptionalValue<float>
member Series.TryGet: key: 'K -> OptionalValue<'V>
member Series.TryGet: key: 'K * lookup: Lookup -> OptionalValue<'V>
active recognizer Present: 'T opt -> Choice<unit,'T>
<summary> Complete active pattern that can be used to pattern match on `OptionalValue&lt;T&gt;`. For example: let optVal = OptionalValue(42) match optVal with | OptionalValue.Missing -&gt; printfn "Empty" | OptionalValue.Present(v) -&gt; printfn "Contains %d" v </summary>
val x: float
val sprintf: format: Printf.StringFormat<'T> -> 'T
val observationsAll: series: Series<'K,'T> -> ('K * 'T option) seq (requires equality)
<summary> Returns all keys from the sequence, together with the associated (optional) values. </summary>
<category>Accessing series data and lookup</category>
module Seq from Microsoft.FSharp.Collections
val truncate: count: int -> source: 'T seq -> 'T seq
val map: mapping: ('T -> 'U) -> source: 'T seq -> 'U seq
val k: int
val v: float option
val toList: source: 'T seq -> 'T list
val mapAll: f: ('K -> 'T option -> 'R option) -> series: Series<'K,'T> -> Series<'K,'R> (requires equality)
<summary> Returns a new series whose values are the results of applying the given function to values of the original series. This specified function is called even when the value is missing. It returns <c>option&lt;'T&gt;</c> so that it can create/eliminate missing values in the result. </summary>
<category>Series transformations</category>
union case Option.None: Option<'T>
union case Option.Some: Value: 'T -> Option<'T>
val take: count: int -> series: Series<'K,'T> -> Series<'K,'T> (requires equality)
<summary> Returns a series that contains the specified number of keys from the original series. </summary>
<param name="count">Number of keys to take; must be smaller or equal to the original number of keys</param>
<param name="series">Input series from which the keys are taken</param>
<category>Series transformations</category>
val fillMissingWith: value: 'a -> series: Series<'K,'T> -> Series<'K,'T> (requires equality)
<summary> Fill missing values in the series with a constant value. </summary>
<param name="series">An input series that is to be filled</param>
<param name="value">A constant value that is used to fill all missing values</param>
<category>Missing values</category>
val fillMissing: direction: Direction -> series: Series<'K,'T> -> Series<'K,'T> (requires equality)
<summary> Fill missing values in the series with the nearest available value (using the specified direction). Note that the series may still contain missing values after call to this function. This operation can only be used on ordered series. </summary>
<param name="series">An input series that is to be filled</param>
<param name="direction">Specifies the direction used when searching for the nearest available value. `Backward` means that we want to look for the first value with a smaller key while `Forward` searches for the nearest greater key.</param>
<example><code> let sample = Series.ofValues [ Double.NaN; 1.0; Double.NaN; 3.0 ] // Returns a series consisting of [1; 1; 3; 3] sample |&gt; Series.fillMissing Direction.Backward // Returns a series consisting of [&lt;missing&gt;; 1; 1; 3] sample |&gt; Series.fillMissing Direction.Forward </code></example>
<category>Missing values</category>
[<Struct>] type Direction = | Backward = 0 | Forward = 1
<summary> Specifies in which direction should we look when performing operations such as `Series.Pairwise`. </summary>
<example><code> let abc = [ 1 =&gt; "a"; 2 =&gt; "b"; 3 =&gt; "c" ] |&gt; Series.ofObservations // Using 'Forward' the key of the first element is used abc.Pairwise(direction=Direction.Forward) // [ 1 =&gt; ("a", "b"); 2 =&gt; ("b", "c") ] // Using 'Backward' the key of the second element is used abc.Pairwise(direction=Direction.Backward) // [ 2 =&gt; ("a", "b"); 3 =&gt; ("b", "c") ] </code></example>
<category>Parameters and results of various operations</category>
Direction.Forward: Direction = 1
Direction.Backward: Direction = 0
val fillMissingUsing: f: ('K -> 'T) -> series: Series<'K,'T> -> Series<'K,'T> (requires equality)
<summary> Fill missing values in the series using the specified function. The specified function is called with all keys for which the series does not contain value and the result of the call is used in place of the missing value. </summary>
<param name="series">An input series that is to be filled</param>
<param name="f">A function that takes key `K` and generates a value to be used in a place where the original series contains a missing value.</param>
<remarks> This function can be used to implement more complex interpolation. For example see [handling missing values in the tutorial](../frame.html#missing) </remarks>
<category>Missing values</category>
val prev: OptionalValue<float>
[<Struct>] type Lookup = | Exact = 1 | ExactOrGreater = 3 | ExactOrSmaller = 5 | Greater = 2 | Smaller = 4
<summary> Represents different behaviors of key lookup in series. For unordered series, the only available option is `Lookup.Exact` which finds the exact key - methods fail or return missing value if the key is not available in the index. For ordered series `Lookup.Greater` finds the first greater key (e.g. later date) with a value. `Lookup.Smaller` searches for the first smaller key. The options `Lookup.ExactOrGreater` and `Lookup.ExactOrSmaller` finds the exact key (if it is present) and otherwise search for the nearest larger or smaller key, respectively. </summary>
<category>Parameters and results of various operations</category>
Lookup.ExactOrSmaller: Lookup = 5
<summary> Lookup a value associated with the specified key or with the nearest smaller key that has a value available. Fails (or returns missing value) only when the specified key is smaller than all available keys. </summary>
val next: OptionalValue<float>
Lookup.ExactOrGreater: Lookup = 3
<summary> Lookup a value associated with the specified key or with the nearest greater key that has a value available. Fails (or returns missing value) only when the specified key is greater than all available keys. </summary>
val p: float
val n: float
val v: float
val dropMissing: series: Series<'K,'T> -> Series<'K,'T> (requires equality)
<summary> Drop missing values from the specified series. The returned series contains only those keys for which there is a value available in the original one. </summary>
<param name="series">An input series to be filtered</param>
<example><code> let s = series [ 1 =&gt; 1.0; 2 =&gt; Double.NaN ] s |&gt; Series.dropMissing // val it : Series&lt;int,float&gt; = series [ 1 =&gt; 1] </code></example>
<category>Missing values</category>
val countValues: series: Series<'K,'T> -> int (requires equality)
<summary> Returns the total number of values in the specified series. This excludes missing values or not available values (such as values created from `null`, `Double.NaN`, or those that are missing due to outer join etc.). </summary>
<category>Accessing series data and lookup</category>
property Frame.RowCount: int with get
val airComplete: Frame<int,string>
val dropSparseRows: frame: Frame<'R,'C> -> Frame<'R,'C> (requires equality and equality)
<summary> Creates a new data frame that contains only those rows of the original data frame that are _dense_, meaning that they have a value for each column. The resulting data frame has the same number of columns, but may have fewer rows (or no rows at all). </summary>
<category>Missing values</category>
val fillMissingWith: value: 'T -> frame: Frame<'R,'C> -> Frame<'R,'C> (requires equality and equality)
<summary> Fill missing values of a given type in the frame with a constant value. The fill value is applied to columns whose element type matches the fill value type (using safe numeric widening). This includes both cases where the column type can be widened to the fill value type (e.g. decimal columns filled with a float value) and cases where the fill value can be widened to the column type (e.g. an integer fill value filling float columns). Columns whose element type is incompatible with the fill value type are left unchanged. </summary>
<param name="frame">An input data frame that is to be filled</param>
<param name="value">A constant value that is used to fill all missing values</param>
<category>Missing values</category>
val f: Frame<int,string>
val fillMissing: direction: Direction -> frame: Frame<'R,'C> -> Frame<'R,'C> (requires equality and equality)
<summary> Fill missing values in the data frame with the nearest available value (using the specified direction). Note that the frame may still contain missing values after call to this function (e.g. if the first value is not available and we attempt to fill series with previous values). This operation can only be used on ordered frames. </summary>
<param name="frame">An input data frame that is to be filled</param>
<param name="direction">Specifies the direction used when searching for the nearest available value. `Backward` means that we want to look for the first value with a smaller key while `Forward` searches for the nearest greater key.</param>
<category>Missing values</category>
val fillMissingUsing: f: (Series<'R,'T> -> 'R -> 'T) -> frame: Frame<'R,'C> -> Frame<'R,'C> (requires equality and equality)
<summary> Fill missing values in the frame using the specified function. The specified function is called with all series and keys for which the frame does not contain value and the result of the call is used in place of the missing value. The operation is only applied to columns (series) that contain values of the same type as the return type of the provided filling function. The operation does not attempt to convert between numeric values (so a series containing `float` will not be converted to a series of `int`). </summary>
<param name="frame">An input data frame that is to be filled</param>
<param name="f">A function that takes a series <c>Series&lt;R, T&gt;</c> together with a key `K` in the series and generates a value to be used in a place where the original series contains a missing value.</param>
<category>Missing values</category>
val col: Series<int,float>
val key: int
val s1: Series<int,float>
val series: observations: ('a * 'b) seq -> Series<'a,'b> (requires equality)
<summary> Create a series from a sequence of key-value pairs that represent the observations of the series. This function can be used together with the `=&gt;` operator to create key-value pairs. </summary>
<example> // Creates a series with squares of numbers let sqs = series [ 1 =&gt; 1.0; 2 =&gt; 4.0; 3 =&gt; 9.0 ] </example>
val s2: Series<int,float>
static member Frame.ofColumns: cols: Series<'C,#ISeries<'R>> -> Frame<'R,'C> (requires equality and equality)
static member Frame.ofColumns: cols: ('C * #ISeries<'R>) seq -> Frame<'R,'C> (requires equality and equality)
val f1: Frame<int,string>
val frame: columns: ('a * #ISeries<'c>) seq -> Frame<'c,'a> (requires equality and equality)
<summary> A function for constructing data frame from a sequence of name - column pairs. This provides a nicer syntactic sugar for `Frame.ofColumns`. </summary>
<example> To create a simple frame with two columns, you can write: <code> frame [ "A" =&gt; series [ 1 =&gt; 30.0; 2 =&gt; 35.0 ] "B" =&gt; series [ 1 =&gt; 30.0; 3 =&gt; 40.0 ] ] </code></example>
<category>Frame construction</category>
val f2: Frame<int,string>
member Frame.Join: otherFrame: Frame<'TRowKey,'TColumnKey> -> Frame<'TRowKey,'TColumnKey>
member Frame.Join: colKey: 'TColumnKey * series: Series<'TRowKey,'V> -> Frame<'TRowKey,'TColumnKey>
member Frame.Join: otherFrame: Frame<'TRowKey,'TColumnKey> * kind: JoinKind -> Frame<'TRowKey,'TColumnKey>
member Frame.Join: colKey: 'TColumnKey * series: Series<'TRowKey,'V> * kind: JoinKind -> Frame<'TRowKey,'TColumnKey>
member Frame.Join: otherFrame: Frame<'TRowKey,'TColumnKey> * kind: JoinKind * lookup: Lookup -> Frame<'TRowKey,'TColumnKey>
member Frame.Join: colKey: 'TColumnKey * series: Series<'TRowKey,'V> * kind: JoinKind * lookup: Lookup -> Frame<'TRowKey,'TColumnKey>
[<Struct>] type JoinKind = | Outer = 0 | Inner = 1 | Left = 2 | Right = 3
<summary> This enumeration specifies joining behavior for `Join` method provided by `Series` and `Frame`. Outer join unions the keys (and may introduce missing values), inner join takes the intersection of keys; left and right joins take the keys of the first or the second series/frame. </summary>
<category>Parameters and results of various operations</category>
JoinKind.Inner: JoinKind = 1
<summary> Take the intersection of the keys available in both structures and align the values of the two structures. The resulting structure cannot contain missing values. </summary>

Type something to start searching.