Signal Processing

Summary: this tutorial demonstrates multiple ways of signal processing with FSharp.Stats.

A common approach for outlier detection is Tukey's fences-method. It determines the interquartile range (IQR) of the data and adds a fraction of it to the third quartile (Q3) or subtracts it from the first quartile (Q1) respectively. An often-used fraction of the IQR is k=1.5 for outliers and k=3 for points 'far out'.

In the generation of box plots the same method determines the whiskers and outliers of a sample.

Reference:

Tukey, JW. Exploratory data analysis. Addison-Wesely, 1977

open FSharp.Stats
open FSharp.Collections

let sampleO1 = [|45.;42.;45.5;43.;47.;51.;34.;45.;44.;46.;48.;37.;46.;|]

let outlierBordersO1 = Signal.Outliers.tukey 1.5 sampleO1

let lowerBorderO1 = Interval.getStart outlierBordersO1
// result: 37.16667

let upperBorderO1 = Interval.getEnd outlierBordersO1
// result: 51.83333

let (inside,outside) =
    sampleO1 
    |> Array.partition (fun x -> outlierBordersO1.liesInInterval x)

let tukeyOutlierChart =
    [
        Chart.Point(inside |> Seq.map (fun x -> 1,x),"sample")
        Chart.Point(outside |> Seq.map (fun x -> 1,x),"outliers")
    ]
    |> Chart.combine
    |> Chart.withShapes(
        [
            Shape.init(ShapeType=StyleParam.ShapeType.Line,X0=0.5,X1=1.5,Y0=lowerBorderO1,Y1=lowerBorderO1,Line=Line.init(Dash=StyleParam.DrawingStyle.Dash,Color=Color.fromString "grey"))
            Shape.init(ShapeType=StyleParam.ShapeType.Line,X0=0.5,X1=1.5,Y0=upperBorderO1,Y1=upperBorderO1,Line=Line.init(Dash=StyleParam.DrawingStyle.Dash,Color=Color.fromString "grey"))
        ]
        )
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withTitle "Tukey's fences outlier borders"

No value returned by any evaluator

Filtering

Savitzgy-Golay description is coming soon.

open FSharp.Stats

// Savitzky-Golay low-pass filtering
let t  = [|-4. ..(8.0/500.).. 4.|]
let dy  = t |> Array.map (fun t -> (-t**2.) + (Distributions.Continuous.Normal.Sample 0. 0.5) )
let dy' = t |> Array.map (fun t -> (-t**2.))

let dysg = Signal.Filtering.savitzkyGolay  31 4 0 1 dy

let savitzgyChart =
    [
        Chart.Point(t, dy, Name="data with noise");
        Chart.Point(t, dy', Name="data without noise");
        Chart.Point(t, dysg, Name="data sg");
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored

No value returned by any evaluator

Padding

If convolution operations should be performed on a signal trace, it often is necessary to extend (pad) the data with artificial data points. There are several padding methods:

Zero: Data points with y-value=zero are introduced. This often is useful when analyzing spectra with sparse data because areas without any data measured are assumed to have zero intensity.
Random: When the baseline of the measured signal is nonzero like in chromatograms, it is necessary to insert data points with random y-values taken from the original data set.
Delete: No datapoints are inserted.
Linear interpolation: When a linear relationship is assumed in the range between two adjacent data points, the padding points should lie on the straight line between those points.

Three regions can be defined where padding points could be introduced:

In the beginning and end of the data set artificial data points have to be added to analyse the start- and end-regions of the data. Therefore, random data points are chosen from the original data set.
If the data is not measured in discrete intervals, the region between two adjacent values have to be padded to ensure sufficient coverage for convolution.
If the gap between two adjacent points is too large, another padding method than in case 2. may be chosen.

open FSharp.Stats.Signal

// get raw data
// data originates from temperature measurements conducted in https://github.com/bvenn/AlgaeWatch
let data = 
    System.IO.File.ReadAllLines(__SOURCE_DIRECTORY__ + "/data/waveletData.txt")
    |> Array.map (fun x -> 
        let tmp = x.Split([|'\t'|])
        float tmp.[0],float tmp.[1])

///interpolate data point y-values when small gaps are present
let innerPadMethod = Padding.InternalPaddingMethod.LinearInterpolation

///take random data point y-values when huge gaps are between data points
let hugeGapPadMethod = Padding.HugeGapPaddingMethod.Random

///padd the start and end of the signal with random data points
let borderPadMethod = Padding.BorderPaddingMethod.Random

///the maximal distance that is allowed between data points is the minimum spacing divided by 2
let minDistance = 
    (Padding.HelperFunctions.getMinimumSpacing data (-)) / 2.

//maximal allowed gap between datapoints where internalPaddingMethod can be applied.
//if internalPaddingMethod = hugeGapPaddingMethod, then it does not matter which value is chosen
let maxSpacing = 10.

//since were dealing with floats the functions are (-) and (+)
let getDiffFu = Padding.HelperFunctions.Float.getDiffFloat      //(-)
let addXValue = Padding.HelperFunctions.Float.addToXValueFloat  //(+)

//number of datapoints the dataset gets expanded to the left and to the rigth
let borderpadding = 1000

//get the paddedDataSet
let paddedData =
    //if a gap is greater than 10. the HugeGapPaddingMethod is applied
    Padding.pad data minDistance maxSpacing getDiffFu addXValue borderpadding borderPadMethod innerPadMethod hugeGapPadMethod

let paddedDataChart=
    [
    Chart.Line (paddedData,Name="paddedData")
    Chart.Area (data,Name = "rawData")
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "Time"
    |> Chart.withYAxisStyle "Temperature"
    |> Chart.withSize(900.,450.)

No value returned by any evaluator

Example for a linear interpolation as huge gap padding method

//get the padded data
let paddedDataLinear =
    //if a gap is greater than 10. the LinearInterpolation padding method is applied
    Padding.pad data minDistance maxSpacing getDiffFu addXValue borderpadding borderPadMethod innerPadMethod Padding.HugeGapPaddingMethod.LinearInterpolation

let paddedDataLinearChart=
    [
    Chart.Line (paddedDataLinear,Name="paddedData")
    Chart.Area (data,Name = "rawData")
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "Time"
    |> Chart.withYAxisStyle "Temperature"
    |> Chart.withSize(900.,450.)

No value returned by any evaluator

Wavelet

Continuous Wavelet

The Continuous Wavelet Transform (CWT) is a multiresolution analysis method to gain insights into frequency components of a signal with simultaneous temporal classification. Wavelet in this context stands for small wave and describes a window function which is convoluted with the original signal at every position in time. Many wavelets exist, every one of them is useful for a certain application, thereby 'searching' for specific patterns in the data. By increasing the dimensions (scale) of the wavelet function, different frequency patterns are studied.

In contrast to the Fourier transform, that gives a perfect frequency resolution but no time resolution, the CWT is capable of mediating between the two opposing properties of time resolution and frequency resolution (Heisenberg's uncertainty principle).

For further information please visit The Wavelet Tutorial or the following publications:

A Practical Guide to Wavelet Analysis, Torrence & Compo, American Meteorological Society, 1998
Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing, Lau & Weng, American Meteorological Society, 1995

open FSharp.Stats
open StyleParam

///Array containing wavelets of all scales that should be investigated. The propagated frequency corresponds to 4 * Ricker.Scale
let rickerArray = 
    [|2. .. 10.|] |> Array.map (fun x -> Wavelet.createRicker (x**1.8))

///the data already was padded with 1000 additional datapoints in the beginning and end of the data set (see above). 
///Not it is transformed with the previous defined wavelets.
let transformedData = 
    rickerArray
    |> Array.map (fun wavelet -> ContinuousWavelet.transform paddedData (-) 1000 wavelet)

///combining the raw and transformed data in one chart
let combinedSignalChart =
    //CWT-chart
    let heatmap =
        let rowNames,colNames = 
            transformedData.[0] |> Array.mapi (fun i (x,_) -> string i, string x) |> Array.unzip
        transformedData
        |> JaggedArray.map snd
        |> fun x -> Chart.Heatmap(x,colNames=colNames,rowNames=rowNames,ShowScale=false)
        |> Chart.withAxisAnchor(X=1)
        |> Chart.withAxisAnchor(Y=1)

    //Rawchart
    let rawChart = 
        Chart.Area (data,LineColor = Color.fromHex "#1f77b4",Name = "rawData")
        |> Chart.withAxisAnchor(X=2)
        |> Chart.withAxisAnchor(Y=2) 

    //combine the charts and add additional styling
    Chart.combine([heatmap;rawChart])
    |> Chart.withXAxisStyle("Time",Side=Side.Bottom,Id=SubPlotId.XAxis 2,ShowGrid=false)
    |> Chart.withXAxisStyle("", Side=Side.Top,ShowGrid=false, Id=SubPlotId.XAxis 1,Overlaying=LinearAxisId.X 2)
    |> Chart.withYAxisStyle("Temperature", MinMax=(-25.,30.), Side=Side.Left,Id=SubPlotId.YAxis 2)
    |> Chart.withYAxisStyle(
        "Correlation", MinMax=(0.,19.),ShowGrid=false, Side=Side.Right,
        Id=SubPlotId.YAxis 1,Overlaying=LinearAxisId.Y 2)
    |> Chart.withLegend true
    //|> Chart.withSize(900.,700.)

No value returned by any evaluator

Because in most cases default parameters are sufficient to transform the data, there are two additional functions to process the raw data with automated padding:

ContinuousWavelet.transformDefault
- padding is chosen in an automated manner based on the used wavelet
- minDistance: median spacing / 2
- maxDistance: median spacing * 10
- internalPadding: LinearInterpolation
- hugeGapPadding: Random
ContinuousWavelet.transformDefaultZero
- padding is chosen in an automated manner based on the used wavelet
- minDistance: smallest occurring spacing
- maxDistance: Infinity
- internalPadding: Zero
- hugeGapPadding: Zero (redundant)

//used wavelets
let rickerArrayDefault = 
    [|2. .. 2. .. 10.|] |> Array.map (fun x -> Wavelet.createRicker (x**1.8))

//transforms the data with default parameters (InternalPadding=LinearInterpol;HugeGapPadd=Random)
let defaultTransform =
    rickerArrayDefault
    |> Array.map (ContinuousWavelet.transformDefault data)

//alternative presentation of the wavelet correlation coefficients as line charts
let defaultChart =
    let rawDataChart =
        [|Chart.Area(data,Name= "rawData")|]
    let cwtCharts =
        let scale i = rickerArrayDefault.[i].Scale
        defaultTransform 
        |> Array.mapi (fun i x -> Chart.Line(x,Name=(sprintf "s: %.1f" (scale i))))

    Array.append rawDataChart cwtCharts
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "Time"
    |> Chart.withYAxisStyle "Temperature and Correlation"
    |> Chart.withTitle "default transform"

No value returned by any evaluator

Because random y-values are introduced, small wavelets are going to receive a high correlation in big gaps!
s = scale
f = frequency [days]

No value returned by any evaluator

//transforms the data with default parameters (InternalPadding=Zero;HugeGapPadd=Zero)
let defaultZeroTransform =
    rickerArrayDefault
    |> Array.map (ContinuousWavelet.transformDefaultZero data)

let defaultZeroChart =
    let rawDataChart =
        [|Chart.Area(data,Name= "rawData")|]
    let cwtCharts =
        let scale i = rickerArrayDefault.[i].Scale
        defaultZeroTransform 
        |> Array.mapi (fun i x -> Chart.Line(x,Name=(sprintf "s: %.1f" (scale i) )))

    Array.append rawDataChart cwtCharts
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "Time"
    |> Chart.withYAxisStyle "Temperature and Correlation"
    |> Chart.withTitle "default Zero transform"

Because zeros are introduced, the adjacent signals are going to receive a high correlation!
In this example the correlation coefficients in general drop to a reduced intensity because a zero values are introduced between every data point (minDistance = minimal spacing / 2.). So here a zero padding makes no sense. The Temperature wont drop to zero between two measurements.
s = scale
f = frequency [days]

No value returned by any evaluator

Continuous Wavelet 3D

When dealing with three dimensional data a three dimensional wavelet has to be used for signal convolution. Here the Marr wavelet (3D mexican hat wavelet) is used for analysis. Common cases are:

(microscopic) images
micro arrays

open FSharp.Stats.Signal

let data2D =
    let rnd = System.Random()
    Array2D.init 50 50 (fun i j -> 
        if (i,j) = (15,15) then 5.
        elif (i,j) = (35,35) then -5.
        else rnd.NextDouble())

let data2DChart = 
    data2D
    |> JaggedArray.ofArray2D
    |> fun data -> Chart.Heatmap(data,ShowScale=false)
    |> Chart.withXAxisStyle "raw data"

//has to be greater than the padding area of the used wavelet
let padding = 11

let paddedData2D =
    //padding the data points with 11 artificial random points on each side
    Padding.Discrete.ThreeDimensional.pad data2D padding Padding.Discrete.ThreeDimensional.Random

let marrWavelet = 
    Wavelet.createMarr 3.

let transformedData2D =
    ContinuousWavelet.Discrete.ThreeDimensional.transform paddedData2D padding marrWavelet

let chartHeatmap =
    transformedData2D
    |> JaggedArray.ofArray2D
    |> fun data -> Chart.Heatmap(data,ShowScale=false)
    |> Chart.withXAxisStyle "wavelet transformed"

let combined2DChart =
    [data2DChart;chartHeatmap]
    |> Chart.Grid(1,2)

No value returned by any evaluator

Fast Fourier transform

The FFT analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa.

open FSharp.Stats 
open System.Numerics

// Fast fourier transform

// Sampling frequency   
let fs = 1000  
// Sampling period      
let tp = 1. / float fs
// Length of signal
let l = 1500;            

// Time vector
let time = Array.init (l-1) (fun x -> float x * tp)       

let pi = System.Math.PI

let signal t = 0.7 * sin (2.*pi*50.*t) + sin (2.*pi*120.*t)
let timeSignal = time |> Array.map signal

let fft = 
    Signal.FFT.inverseInPlace (
        timeSignal 
        |> Array.map (fun v ->  Complex(v, 0.) )) 
    |> Array.map (fun c -> c.Real)

let fftChart = 
    [
        Chart.Line(time,timeSignal) |> Chart.withTraceInfo "signal"
        Chart.Line(time,fft) |> Chart.withTraceInfo "fft"
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored

No value returned by any evaluator

namespace FsMath

namespace Plotly

namespace Plotly.NET

module Defaults from Plotly.NET
<summary> Contains mutable global default values. Changing these values will apply the default values to all consecutive Chart generations. </summary>

val mutable DefaultDisplayOptions: Plotly.NET.DisplayOptions

Multiple items
type DisplayOptions = inherit DynamicObj new: unit -> DisplayOptions static member addAdditionalHeadTags: additionalHeadTags: XmlNode list -> (DisplayOptions -> DisplayOptions) static member addDescription: description: XmlNode list -> (DisplayOptions -> DisplayOptions) static member combine: first: DisplayOptions -> second: DisplayOptions -> DisplayOptions static member getAdditionalHeadTags: displayOpts: DisplayOptions -> XmlNode list static member getDescription: displayOpts: DisplayOptions -> XmlNode list static member getPlotlyReference: displayOpts: DisplayOptions -> PlotlyJSReference static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?AdditionalHeadTags: XmlNode list * [<Optional; DefaultParameterValue ((null :> obj))>] ?Description: XmlNode list * [<Optional; DefaultParameterValue ((null :> obj))>] ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions static member initCDNOnly: unit -> DisplayOptions ...

--------------------
new: unit -> Plotly.NET.DisplayOptions

static member Plotly.NET.DisplayOptions.init: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AdditionalHeadTags: Giraffe.ViewEngine.HtmlElements.XmlNode list * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Description: Giraffe.ViewEngine.HtmlElements.XmlNode list * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?PlotlyJSReference: Plotly.NET.PlotlyJSReference -> Plotly.NET.DisplayOptions

type PlotlyJSReference = | CDN of string | Full | Require of string | NoReference
<summary> Sets how plotly is referenced in the head of html docs. </summary>

union case Plotly.NET.PlotlyJSReference.NoReference: Plotly.NET.PlotlyJSReference

module StyleParam from Plotly.NET

namespace Plotly.NET.LayoutObjects

Multiple items
namespace FSharp

--------------------
namespace Microsoft.FSharp

namespace FSharp.Stats

namespace Microsoft.FSharp.Collections

val sampleO1: float array

val outlierBordersO1: Interval<float>

namespace FSharp.Stats.Signal

module Outliers from FSharp.Stats.Signal

val tukey: k: float -> d: float array -> Interval<float>
<summary>Tukey's fences based on interquartile range. c defines the magnitude of interquartile range that is added/subtracted to Q3 and Q1 respectively.<br />Commonly c is 1.5 for outliers and 3 for points 'far out' (Tukey 1977).</summary>
<remarks></remarks>
<param name="k"></param>
<param name="d"></param>
<returns></returns>
<example><code></code></example>

val lowerBorderO1: float

Multiple items
module Interval from FSharp.Stats

--------------------
type Interval<'a (requires comparison)> = | Closed of intervalStart: 'a * intervalEnd: 'a | LeftOpen of intervalStart: 'a * intervalEnd: 'a | RightOpen of intervalStart: 'a * intervalEnd: 'a | Open of intervalStart: 'a * intervalEnd: 'a | Empty member Equals: Interval<'a> * IEqualityComparer -> bool member GetEnd: unit -> 'a member GetStart: unit -> 'a override ToString: unit -> string member ToTuple: unit -> 'a * 'a member liesInInterval: value: 'a -> bool static member CreateClosed<'a (requires comparison)> : min: 'a0 * max: 'a0 -> Interval<'a0> (requires comparison) static member CreateLeftOpen<'a (requires comparison)> : min: 'a0 * max: 'a0 -> Interval<'a0> (requires comparison) static member CreateOpen<'a (requires comparison)> : min: 'a0 * max: 'a0 -> Interval<'a0> (requires comparison) static member CreateRightOpen<'a (requires comparison)> : min: 'a0 * max: 'a0 -> Interval<'a0> (requires comparison) ...
<summary>Represents an interval between two values of type 'a, which can be either inclusive or exclusive.</summary>
<typeparam name="'a">The type of the interval values, must support comparison.</typeparam>

val getStart: interval: Interval<'a> -> 'a (requires comparison)
<summary>Returns the start value of the interval</summary>
<param name="interval">The input interval</param>
<returns>The start value of the interval</returns>
<example><code> // Create a closed interval [2.0, 7.0] let interval = Interval.CreateClosed(2.0, 7.0) // Get the start value of the interval (2.0) Interval.getStart interval </code></example>

val upperBorderO1: float

val getEnd: interval: Interval<'a> -> 'a (requires comparison)
<summary>Returns the end value of the interval</summary>
<param name="interval">The input interval</param>
<returns>The end value of the interval</returns>
<example><code> // Create a closed interval [2.0, 7.0] let interval = Interval.CreateClosed(2.0, 7.0) // Get the end value of the interval (7.0) Interval.getEnd interval </code></example>

val inside: float array

val outside: float array

Multiple items
module Array from Microsoft.FSharp.Collections

--------------------
module Array from FSharp.Stats
<summary> Module to compute common statistical measure on array </summary>

--------------------
type Array = new: unit -> Array static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array

--------------------
new: unit -> Array

val partition: predicate: ('T -> bool) -> array: 'T array -> 'T array * 'T array

val x: float

member Interval.liesInInterval: value: 'a -> bool

val tukeyOutlierChart: GenericChart.GenericChart

type Chart = static member AnnotatedHeatmap: zData: #('a1 seq) seq * annotationText: #(string seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a4 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible and 'a5 :> IConvertible) + 1 overload static member Area: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillPattern: Pattern * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Bar: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiKeys: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member BoxPlot: [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a0 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a0 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxPoints: BoxPoints * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxMean: BoxMean * [<Optional; DefaultParameterValue ((null :> obj))>] ?Jitter: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?PointPos: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Outline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Notched: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?NotchWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?QuartileMethod: QuartileMethod * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a0 :> IConvertible and 'a1 :> IConvertible and 'a2 :> IConvertible) + 2 overloads static member Bubble: x: #IConvertible seq * y: #IConvertible seq * sizes: int seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Candlestick: ``open`` : #IConvertible seq * high: #IConvertible seq * low: #IConvertible seq * close: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a4 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?IncreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Increasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?DecreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Decreasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((true :> obj))>] ?ShowXAxisRangeSlider: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a4 :> IConvertible and 'a5 :> IConvertible) + 2 overloads static member Column: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiKeys: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member Contour: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a2 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineSmoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursColoring: ContourColoring * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursOperation: ConstraintOperation * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursType: ContourType * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowContourLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLabelFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?Contours: Contours * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?NContours: int * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) static member Funnel: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Offset: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextInfo: TextInfo * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineStyle: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorFillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Connector: FunnelConnector * [<Optional; DefaultParameterValue ((null :> obj))>] ?InsideTextFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutsideTextFont: Font * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) static member Heatmap: zData: #('b seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'c seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'c seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'd seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'd seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'e * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'e seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'b :> IConvertible and 'c :> IConvertible and 'd :> IConvertible and 'e :> IConvertible) + 1 overload ...

static member Chart.Point: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Point: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)

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module Seq from Microsoft.FSharp.Collections

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module Seq from FSharp.Stats
<summary> Module to compute common statistical measures. </summary>

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type Seq = new: unit -> Seq static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float seq static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float seq

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new: unit -> Seq

val map: mapping: ('T -> 'U) -> source: 'T seq -> 'U seq

static member Chart.combine: gCharts: GenericChart.GenericChart seq -> GenericChart.GenericChart

static member Chart.withShapes: shapes: Shape seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?Append: bool -> (GenericChart.GenericChart -> GenericChart.GenericChart)

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type Shape = inherit DynamicObj new: unit -> Shape static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?Editable: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillRule: FillRule * [<Optional; DefaultParameterValue ((null :> obj))>] ?Layer: Layer * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Path: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TemplateItemName: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShapeType: ShapeType * [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?X0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?X1: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?XAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Xref: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?XSizeMode: ShapeSizeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y1: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?YAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Yref: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?YSizeMode: ShapeSizeMode -> Shape static member style: [<Optional; DefaultParameterValue ((null :> obj))>] ?Editable: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillRule: FillRule * [<Optional; DefaultParameterValue ((null :> obj))>] ?Layer: Layer * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Path: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TemplateItemName: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShapeType: ShapeType * [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?X0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?X1: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?XAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Xref: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?XSizeMode: ShapeSizeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y1: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?YAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Yref: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?YSizeMode: ShapeSizeMode -> (Shape -> Shape)
<summary> Shapes are layers that can be drawn onto a chart layout. </summary>

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new: unit -> Shape

static member Shape.init: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Editable: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillRule: FillRule * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Layer: Layer * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Path: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TemplateItemName: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShapeType: ShapeType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?X0: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?X1: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XAnchor: LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Xref: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XSizeMode: ShapeSizeMode * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Y0: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Y1: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YAnchor: LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Yref: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YSizeMode: ShapeSizeMode -> Shape

type ShapeType = | Circle | Rectangle | SvgPath | Line member Convert: unit -> obj override ToString: unit -> string static member convert: (ShapeType -> obj) static member toString: (ShapeType -> string)
<summary> Specifies the shape type to be drawn. If "line", a line is drawn from (`x0`,`y0`) to (`x1`,`y1`) If "circle", a circle is drawn from ((`x0`+`x1`)/2, (`y0`+`y1`)/2)) with radius (|(`x0`+`x1`)/2 - `x0`|, |(`y0`+`y1`)/2 -`y0`)|) If "rect", a rectangle is drawn linking (`x0`,`y0`), (`x1`,`y0`), (`x1`,`y1`), (`x0`,`y1`), (`x0`,`y0`) If "path", draw a custom SVG path using `path`. </summary>

union case ShapeType.Line: ShapeType

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type Line = inherit DynamicObj new: unit -> Line static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?BackOff: BackOff * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoColorScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?CAuto: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?CMax: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CMid: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CMin: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorAxis: SubPlotId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Colorscale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?Dash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Shape: Shape * [<Optional; DefaultParameterValue ((null :> obj))>] ?Simplify: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Smoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlierColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlierWidth: float -> Line static member style: [<Optional; DefaultParameterValue ((null :> obj))>] ?BackOff: BackOff * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoColorScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?CAuto: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?CMax: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CMid: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CMin: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorAxis: SubPlotId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Colorscale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?Dash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Shape: Shape * [<Optional; DefaultParameterValue ((null :> obj))>] ?Simplify: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Smoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlierColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlierWidth: float -> (Line -> Line)
<summary> The line object determines the style of the line in various aspect of plots such as a line connecting datums, outline of layout objects, etc.. </summary>

--------------------
new: unit -> Line

static member Line.init: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackOff: BackOff * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoColorScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CAuto: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CMax: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CMid: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CMin: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ColorAxis: SubPlotId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Colorscale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Dash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Shape: Shape * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Simplify: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Smoothing: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiWidth: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OutlierColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OutlierWidth: float -> Line

type DrawingStyle = | Solid | Dash | Dot | DashDot | LongDash | LongDashDot | User of int seq member Convert: unit -> obj override ToString: unit -> string static member convert: (DrawingStyle -> obj) static member toString: (DrawingStyle -> string)
<summary> Dash: Sets the drawing style of the lines segments in this trace. Sets the style of the lines. Set to a dash string type or a dash length in px. </summary>

union case DrawingStyle.Dash: DrawingStyle

type Color = override Equals: other: obj -> bool override GetHashCode: unit -> int static member fromARGB: a: int -> r: int -> g: int -> b: int -> Color static member fromColorScaleValues: c: #IConvertible seq -> Color static member fromColors: c: Color seq -> Color static member fromHex: s: string -> Color static member fromKeyword: c: ColorKeyword -> Color static member fromRGB: r: int -> g: int -> b: int -> Color static member fromString: c: string -> Color member Value: obj
<summary> Plotly color can be a single color, a sequence of colors, or a sequence of numeric values referencing the color of the colorscale obj </summary>

static member Color.fromString: c: string -> Color

static member Chart.withTemplate: template: Template -> (GenericChart.GenericChart -> GenericChart.GenericChart)

module ChartTemplates from Plotly.NET

val lightMirrored: Template

static member Chart.withTitle: title: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle: title: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font -> (GenericChart.GenericChart -> GenericChart.GenericChart)

module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>

val toChartHTML: gChart: GenericChart.GenericChart -> string

val t: float array

val dy: float array

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module Array from FSharp.Stats
<summary> Module to compute common statistical measure on array </summary>

--------------------
module Array from Microsoft.FSharp.Collections

--------------------
type Array = new: unit -> Array static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array

--------------------
new: unit -> Array

val map: mapping: ('T -> 'U) -> array: 'T array -> 'U array

val t: float

namespace FSharp.Stats.Distributions

namespace FSharp.Stats.Distributions.Continuous

type Normal = static member CDF: mu: float -> sigma: float -> x: float -> float static member CheckParam: mu: float -> sigma: float -> unit static member Estimate: samples: float seq -> ContinuousDistribution<float,float> static member Init: mu: float -> sigma: float -> ContinuousDistribution<float,float> static member InvCDF: mu: float -> sigma: float -> p: float -> float static member Mean: mu: float -> sigma: float -> float static member Mode: mu: float -> sigma: float -> float static member PDF: mu: float -> sigma: float -> x: float -> float static member Sample: mu: float -> sigma: float -> float static member SampleUnchecked: mu: float -> sigma: float -> float ...
<summary> Normal distribution. </summary>

static member Distributions.Continuous.Normal.Sample: mu: float -> sigma: float -> float

val dy': float array

val dysg: float array

module Filtering from FSharp.Stats.Signal

val savitzkyGolay: windowSize: int -> order: int -> deriv: int -> rate: float -> data: Vector<float> -> float array
<summary> Smooth (or differentiate) data with a Savitzky–Golay filter of given <paramref name="windowSize" /> and polynomial <paramref name="order" />. The <paramref name="deriv" /> parameter specifies the derivative order to compute (0 = smoothing only). The <paramref name="rate" /> helps scale the derivative if deriv > 0. </summary>
<param name="windowSize">Must be odd and at least (order+2) if deriving.</param>
<param name="order">Polynomial order (must be >= deriv). A higher order can better fit curvature.</param>
<param name="deriv">Order of derivative to compute (0 => smoothing).</param>
<param name="rate">Scaling factor for derivative, typically sampling rate = 1.0 if no special scale needed.</param>
<param name="data">The data vector to filter (length N).</param>
<returns> A float[] array with the filtered (or derived) signal, of length = data.Length. </returns>

val savitzgyChart: GenericChart.GenericChart

union case HoverInfo.Name: HoverInfo

val data: (float * float) array

namespace System

namespace System.IO

type File = static member AppendAllLines: path: string * contents: IEnumerable<string> -> unit + 1 overload static member AppendAllLinesAsync: path: string * contents: IEnumerable<string> * encoding: Encoding * ?cancellationToken: CancellationToken -> Task + 1 overload static member AppendAllText: path: string * contents: string -> unit + 1 overload static member AppendAllTextAsync: path: string * contents: string * encoding: Encoding * ?cancellationToken: CancellationToken -> Task + 1 overload static member AppendText: path: string -> StreamWriter static member Copy: sourceFileName: string * destFileName: string -> unit + 1 overload static member Create: path: string -> FileStream + 2 overloads static member CreateSymbolicLink: path: string * pathToTarget: string -> FileSystemInfo static member CreateText: path: string -> StreamWriter static member Decrypt: path: string -> unit ...
<summary>Provides static methods for the creation, copying, deletion, moving, and opening of a single file, and aids in the creation of <see cref="T:System.IO.FileStream" /> objects.</summary>

System.IO.File.ReadAllLines(path: string) : string array
System.IO.File.ReadAllLines(path: string, encoding: System.Text.Encoding) : string array

val x: string

val tmp: string array

System.String.Split([<System.ParamArray>] separator: char array) : string array
System.String.Split(separator: string array, options: System.StringSplitOptions) : string array
System.String.Split(separator: string, ?options: System.StringSplitOptions) : string array
System.String.Split(separator: char array, options: System.StringSplitOptions) : string array
System.String.Split(separator: char array, count: int) : string array
System.String.Split(separator: char, ?options: System.StringSplitOptions) : string array
System.String.Split(separator: string array, count: int, options: System.StringSplitOptions) : string array
System.String.Split(separator: string, count: int, ?options: System.StringSplitOptions) : string array
System.String.Split(separator: char array, count: int, options: System.StringSplitOptions) : string array
System.String.Split(separator: char, count: int, ?options: System.StringSplitOptions) : string array

Multiple items
val float: value: 'T -> float (requires member op_Explicit)

--------------------
type float = System.Double

--------------------
type float<'Measure> = float

val innerPadMethod: Padding.InternalPaddingMethod
interpolate data point y-values when small gaps are present

Multiple items
module Padding from FSharp.Stats.Signal
<summary> padds data points to the beginning, the end and on internal intervals of the data </summary>

--------------------
type Padding = inherit DynamicObj new: unit -> Padding static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?B: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?L: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?R: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?T: int -> Padding static member style: [<Optional; DefaultParameterValue ((null :> obj))>] ?B: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?L: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?R: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?T: int -> (Padding -> Padding)

--------------------
new: unit -> Padding

union case Padding.InternalPaddingMethod.LinearInterpolation: Padding.InternalPaddingMethod
<summary> inserts points lying on the linear interpolation of the two adjacent knots </summary>

val hugeGapPadMethod: Padding.HugeGapPaddingMethod
take random data point y-values when huge gaps are between data points

union case Padding.HugeGapPaddingMethod.Random: Padding.HugeGapPaddingMethod
<summary> inserts random data points taken from the original data set in a huge data gap </summary>

val borderPadMethod: Padding.BorderPaddingMethod
padd the start and end of the signal with random data points

type BorderPaddingMethod = | Random | Zero member Equals: BorderPaddingMethod * IEqualityComparer -> bool
<summary> padds data point at signals start and end </summary>

union case Padding.BorderPaddingMethod.Random: Padding.BorderPaddingMethod
<summary> inserts random data points taken from the original data set </summary>

val minDistance: float
the maximal distance that is allowed between data points is the minimum spacing divided by 2

module HelperFunctions from FSharp.Stats.Signal.Padding

val getMinimumSpacing: data: ('a * float) array -> getDiff: ('a -> 'a -> float) -> float
<summary>minimum spacing of the data points</summary>
<remarks></remarks>
<param name="data"></param>
<param name="getDiff"></param>
<returns></returns>
<example><code></code></example>

val maxSpacing: float

val getDiffFu: (float -> float -> float)

module Float from FSharp.Stats.Signal.Padding.HelperFunctions

val getDiffFloat: a: float -> b: float -> float
<summary>getDiff: calculates the difference of the two events (-)</summary>
<remarks></remarks>
<param name="a"></param>
<param name="b"></param>
<returns></returns>
<example><code></code></example>

val addXValue: (float -> float -> float)

val addToXValueFloat: a: float -> toAdd: float -> float
<summary>addToXValue: adds toAdd to a (+)</summary>
<remarks></remarks>
<param name="a"></param>
<param name="toAdd"></param>
<returns></returns>
<example><code></code></example>

val borderpadding: int

val paddedData: (float * float) array

val pad: data: ('a * float) array -> minDistance: float -> maxDistance: float -> getDiff: ('a -> 'a -> float) -> addToXValue: ('a -> float -> 'a) -> borderpadding: int -> borderPaddingMethod: Padding.BorderPaddingMethod -> internalPaddingMethod: Padding.InternalPaddingMethod -> hugeGapPaddingMethod: Padding.HugeGapPaddingMethod -> ('a * float) array
<summary>Adds additional data points to the beginning and end of data set (number: borderpadding; x_Value distance: minDistance; y_Value: random).<br />Between every pair of data point where the difference in x_Values is greater than minDistance, additional datapoints are generated as defined in internalPaddingMethod.<br />If huge data chunks are missing (missing gap < maxDistance), data points are added as defined in hugeGapPaddingMethod.</summary>
<remarks>default: internalPaddingMethod=LinearInterpolation; hugeGapPaddingMethod=Random (like in border cases)</remarks>
<param name="data"></param>
<param name="minDistance"></param>
<param name="maxDistance"></param>
<param name="getDiff">get the difference in x_Values as float representation (if 'a is float then (-))</param>
<param name="addToXValue">function that adds a float to the x_Value (if 'a is float then (+))</param>
<param name="borderpadding"></param>
<param name="borderPaddingMethod"></param>
<param name="internalPaddingMethod"></param>
<param name="hugeGapPaddingMethod"></param>
<returns></returns>
<example><code></code></example>

val paddedDataChart: GenericChart.GenericChart

static member Chart.Line: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: Fill * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Line: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: Fill * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)

static member Chart.Area: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPatternShape: PatternShape * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Area: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPatternShape: PatternShape * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)

static member Chart.withXAxisStyle: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleText: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleStandoff: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: AxisType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinMax: (#System.IConvertible * #System.IConvertible) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: Mirror * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridDash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: (float * float) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: CategoryOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryArray: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: RangeSelector * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.withYAxisStyle: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleText: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleStandoff: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: AxisType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinMax: (#System.IConvertible * #System.IConvertible) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: Mirror * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridDash: DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Shift: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: (float * float) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: CategoryOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryArray: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: RangeSelector * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.withSize: width: float * height: float -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withSize: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Height: int -> (GenericChart.GenericChart -> GenericChart.GenericChart)

val paddedDataLinear: (float * float) array

union case Padding.HugeGapPaddingMethod.LinearInterpolation: Padding.HugeGapPaddingMethod
<summary> inserts points lying on the linear interpolation of the two adjacent knots </summary>

val paddedDataLinearChart: GenericChart.GenericChart

val rickerArray: Wavelet.Ricker array
Array containing wavelets of all scales that should be investigated. The propagated frequency corresponds to 4 * Ricker.Scale

module Wavelet from FSharp.Stats.Signal

val createRicker: scale: float -> Wavelet.Ricker
<summary>creation function for Ricker</summary>
<remarks></remarks>
<param name="scale"></param>
<returns></returns>
<example><code></code></example>

val transformedData: (float * float) array array
the data already was padded with 1000 additional datapoints in the beginning and end of the data set (see above).
Not it is transformed with the previous defined wavelets.

val wavelet: Wavelet.Ricker

module ContinuousWavelet from FSharp.Stats.Signal
<summary> Continuous wavelet transform on non discrete data </summary>

val transform: paddedData: ('a * float) array -> getDiff: ('a -> 'a -> float) -> borderpadding: int -> wavelet: Wavelet.Ricker -> ('a * float) array
<summary>calculates the continuous wavelet transform</summary>
<remarks></remarks>
<param name="paddedData">data to transform (x_Value,y_Value) []</param>
<param name="getDiff">get the difference in x_Values as float representation (if 'a is float then (-))</param>
<param name="borderpadding">define the number of points padded to the beginning and end of the data (has to be the same as used in padding)</param>
<param name="wavelet">used wavelet</param>
<returns></returns>
<example><code></code></example>

val combinedSignalChart: GenericChart.GenericChart
combining the raw and transformed data in one chart

val heatmap: GenericChart.GenericChart

val rowNames: string array

val colNames: string array

val mapi: mapping: (int -> 'T -> 'U) -> array: 'T array -> 'U array

val i: int

Multiple items
val string: value: 'T -> string

--------------------
type string = System.String

val unzip: array: ('T1 * 'T2) array -> 'T1 array * 'T2 array

module JaggedArray from FSharp.Stats

val map: mapping: ('T -> 'U) -> jArray: 'T array array -> 'U array array
<summary>Builds a new jagged array whose inner arrays are the results of applying the given function to each of their elements.</summary>
<remarks></remarks>
<param name="mapping"></param>
<param name="jArray"></param>
<returns></returns>
<example><code></code></example>

val snd: tuple: ('T1 * 'T2) -> 'T2

val x: float array array

static member Chart.Heatmap: zData: #('b seq) seq * colNames: string seq * rowNames: string seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XGap: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YGap: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'b :> System.IConvertible and 'c :> System.IConvertible)
static member Chart.Heatmap: zData: #('b seq) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?X: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiX: 'c seq seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Y: 'd seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiY: 'd seq seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XGap: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YGap: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'e * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'e seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'b :> System.IConvertible and 'c :> System.IConvertible and 'd :> System.IConvertible and 'e :> System.IConvertible)

static member Chart.withAxisAnchor: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?X: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Y: int -> (GenericChart.GenericChart -> GenericChart.GenericChart)

argument X: int option
<summary> Sets the axis anchor ids for the chart's cartesian and/or carpet trace(s). If the traces are not of these types, nothing will be set and a warning message will be displayed. </summary>
<param name="X">The new x axis anchor id for the chart's cartesian and/or carpet trace(s)</param>
<param name="Y">The new x axis anchor id for the chart's cartesian and/or carpet trace(s)</param>

argument Y: int option
<summary> Sets the axis anchor ids for the chart's cartesian and/or carpet trace(s). If the traces are not of these types, nothing will be set and a warning message will be displayed. </summary>
<param name="X">The new x axis anchor id for the chart's cartesian and/or carpet trace(s)</param>
<param name="Y">The new x axis anchor id for the chart's cartesian and/or carpet trace(s)</param>

val rawChart: GenericChart.GenericChart

static member Color.fromHex: s: string -> Color

union case Side.Bottom: Side

union case SubPlotId.XAxis: int -> SubPlotId

union case Side.Top: Side

type LinearAxisId = | Free | X of int | Y of int member Convert: unit -> obj override ToString: unit -> string static member convert: (LinearAxisId -> obj) static member toString: (LinearAxisId -> string)

union case LinearAxisId.X: int -> LinearAxisId

union case Side.Left: Side

union case SubPlotId.YAxis: int -> SubPlotId

union case Side.Right: Side

union case LinearAxisId.Y: int -> LinearAxisId

static member Chart.withLegend: showlegend: bool -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withLegend: legend: Legend -> (GenericChart.GenericChart -> GenericChart.GenericChart)

val rickerArrayDefault: Wavelet.Ricker array

val defaultTransform: (float * float) array array

val transformDefault: rawData: (float * float) array -> wavelet: Wavelet.Ricker -> (float * float) array
<summary>minDistance is half the median spacing; maxDistance is 10 times the median spacing; internal padding=linear interpolation; hugeGap padding=random</summary>
<remarks></remarks>
<param name="rawData"></param>
<param name="wavelet"></param>
<returns></returns>
<example><code></code></example>

val defaultChart: GenericChart.GenericChart

val rawDataChart: GenericChart.GenericChart array

val cwtCharts: GenericChart.GenericChart array

val scale: i: int -> float

val x: (float * float) array

val sprintf: format: Printf.StringFormat<'T> -> 'T

val append: array1: 'T array -> array2: 'T array -> 'T array

val defaultZeroTransform: (float * float) array array

val transformDefaultZero: rawData: (float * float) array -> wavelet: Wavelet.Ricker -> (float * float) array
<summary>minDistance is half the overall minimum spacing; maxDistance is infinity; internal padding=zero; hugeGap padding=zero (but redundant)</summary>
<remarks></remarks>
<param name="rawData"></param>
<param name="wavelet"></param>
<returns></returns>
<example><code></code></example>

val defaultZeroChart: GenericChart.GenericChart

val data2D: float array2d

val rnd: System.Random

Multiple items
type Random = new: unit -> unit + 1 overload member GetItems<'T> : choices: ReadOnlySpan<'T> * length: int -> 'T array + 2 overloads member Next: unit -> int + 2 overloads member NextBytes: buffer: byte array -> unit + 1 overload member NextDouble: unit -> float member NextInt64: unit -> int64 + 2 overloads member NextSingle: unit -> float32 member Shuffle<'T> : values: Span<'T> -> unit + 1 overload static member Shared: Random
<summary>Represents a pseudo-random number generator, which is an algorithm that produces a sequence of numbers that meet certain statistical requirements for randomness.</summary>

--------------------
System.Random() : System.Random
System.Random(Seed: int) : System.Random

module Array2D from Microsoft.FSharp.Collections

val init: length1: int -> length2: int -> initializer: (int -> int -> 'T) -> 'T array2d

val j: int

System.Random.NextDouble() : float

val data2DChart: GenericChart.GenericChart

val ofArray2D: arr: 'T array2d -> 'T array array
<summary>Converts a jagged array into an Array2D</summary>
<remarks></remarks>
<param name="arr"></param>
<returns></returns>
<example><code></code></example>

val data: float array array

val padding: int

val paddedData2D: float array2d

module Discrete from FSharp.Stats.Signal.Padding

module ThreeDimensional from FSharp.Stats.Signal.Padding.Discrete

val pad: data: 'a array2d -> borderpadding: int -> paddingMethod: Padding.Discrete.ThreeDimensional.Padding3DMethod -> float array2d (requires member op_Explicit)
<summary> Pads artificial data points to the borders of the given two dimensional array. </summary>
<param name="data">A two dimensional array</param>
<param name="borderpadding">The number of points to add to each side</param>
<param name="paddingMethod">The padding method to use</param>
<returns>A two dimensional array, containing the data of the original array padded with artificial data points on each side.</returns>
<example><code> let data2D = let rnd = System.Random() Array2D.init 50 50 (fun i j -> if (i,j) = (15,15) then 5. elif (i,j) = (35,35) then -5. else rnd.NextDouble()) let padding = 11 // padding the data points with 11 artificial random points on each side let paddedData2D = Padding.Discrete.ThreeDimensional.pad data2D padding Padding.Discrete.ThreeDimensional.Random </code></example>

union case Padding.Discrete.ThreeDimensional.Padding3DMethod.Random: Padding.Discrete.ThreeDimensional.Padding3DMethod
<summary> Adds random data points taken from the original data to the Array2D borders </summary>

val marrWavelet: Wavelet.Marr

val createMarr: radius: float -> Wavelet.Marr
<summary>creation function for Marr</summary>
<remarks></remarks>
<param name="radius"></param>
<returns></returns>
<example><code></code></example>

val transformedData2D: float array2d

module Discrete from FSharp.Stats.Signal.ContinuousWavelet

module ThreeDimensional from FSharp.Stats.Signal.ContinuousWavelet.Discrete

val transform: paddedData: 'a array2d -> borderpadding: int -> wavelet: Wavelet.Marr -> float array2d (requires member op_Explicit)
<summary>performs a continuous wavelet transform on discrete data. (paddingNumber = borderpadding)</summary>
<remarks></remarks>
<param name="paddedData"></param>
<param name="borderpadding"></param>
<param name="wavelet"></param>
<returns></returns>
<example><code></code></example>

val chartHeatmap: GenericChart.GenericChart

val combined2DChart: GenericChart.GenericChart

static member Chart.Grid: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SubPlots: (LinearAxisId * LinearAxisId) array array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XAxes: LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YAxes: LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RowOrder: LayoutGridRowOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Pattern: LayoutGridPattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: Domain * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XSide: LayoutGridXSide * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YSide: LayoutGridYSide -> (#('a1 seq) -> GenericChart.GenericChart) (requires 'a1 :> GenericChart.GenericChart seq)
static member Chart.Grid: nRows: int * nCols: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SubPlots: (LinearAxisId * LinearAxisId) array array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XAxes: LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YAxes: LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RowOrder: LayoutGridRowOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Pattern: LayoutGridPattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: Domain * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XSide: LayoutGridXSide * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YSide: LayoutGridYSide -> (#(GenericChart.GenericChart seq) -> GenericChart.GenericChart)

namespace System.Numerics

val fs: int

val tp: float

val l: int

val time: float array

val init: count: int -> initializer: (int -> 'T) -> 'T array

val x: int

val pi: float

type Math = static member Abs: value: decimal -> decimal + 7 overloads static member Acos: d: float -> float static member Acosh: d: float -> float static member Asin: d: float -> float static member Asinh: d: float -> float static member Atan: d: float -> float static member Atan2: y: float * x: float -> float static member Atanh: d: float -> float static member BigMul: a: int * b: int -> int64 + 2 overloads static member BitDecrement: x: float -> float ...
<summary>Provides constants and static methods for trigonometric, logarithmic, and other common mathematical functions.</summary>

field System.Math.PI: float = 3.14159265359

val signal: t: float -> float

val sin: value: 'T -> 'T (requires member Sin)

val timeSignal: float array

val fft: float array

module FFT from FSharp.Stats.Signal
<summary> FFT analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. </summary>

val inverseInPlace: a: Complex array -> Complex array

val v: float

Multiple items
[<Struct>] type Complex = new: real: float * imaginary: float -> unit member Equals: value: Complex -> bool + 1 overload member GetHashCode: unit -> int member ToString: unit -> string + 3 overloads member TryFormat: destination: Span<char> * charsWritten: byref<int> * ?format: ReadOnlySpan<char> * ?provider: IFormatProvider -> bool + 1 overload static member ( * ) : left: float * right: Complex -> Complex + 2 overloads static member (+) : left: float * right: Complex -> Complex + 2 overloads static member (-) : left: float * right: Complex -> Complex + 2 overloads static member (/) : left: float * right: Complex -> Complex + 2 overloads static member (<>) : left: Complex * right: Complex -> bool ...
<summary>Represents a complex number.</summary>

--------------------
Complex ()
Complex(real: float, imaginary: float) : Complex

val c: Complex

property Complex.Real: float with get
<summary>Gets the real component of the current <see cref="T:System.Numerics.Complex" /> object.</summary>
<returns>The real component of a complex number.</returns>

val fftChart: GenericChart.GenericChart

static member Chart.withTraceInfo: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: Visible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendRank: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroupTitle: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)