Cross validation

Summary: this tutorial demonstrates how to perform several types of cross validation with FSharp.Stats.

Leave-one-out cross validation (LOOCV)

When fitting a data set it often comes down to the selection of the optimal fitting parameter(s). A method to determine these is given by the leave-one-out cross validation (LOOCV). Thereby, the data set is fitted with a given parameter range (smoothing strength, polynomial order etc.) in order to select the best.

Procedure

In each iteration, one data point is excluded from the fitting procedure. The coefficients are determined based on the remaining (n-1) data points. The difference of the excluded point with its corresponding fitted point is measured. In a two-dimensional problem it is the y-intercept of f(xi) and the y_orig at xi.

After every data point was excluded once, the average (squared) distance is calculated and assigned to the corresponding fitting parameter (polynomial order or smoothing strength). The parameter of the model that shows the minimal average error is the best under the given assumptions. It shows the best compromise between over- and underfitting respectively.

Polynomial loocv

let's first create some polynomial fits to cross validate:

open Plotly.NET
open FSharp.Stats
open FSharp.Stats.Fitting
open LinearRegression.OLS

let xV = vector [1. .. 10.]                            
let yV = vector [1.;20.;51.;40.;37.;6.;-10.;-5.;0.;10.]

// the fitting function fits a polynomial of order 'order' to the training data set (xTrain and yTrain) and applies it to xTest
let getFitFuncPolynomial (xTrain:Matrix<float>) yTrain (xTest:Vector<float>) order = 
    let xDat             = xTrain.Data // |> Matrix.toVector
    let coeffs           = Polynomial.fit order xDat yTrain
    let predictFunction  = Polynomial.predict  coeffs (xTest.[0])
    predictFunction

open Plotly.NET

let rawchart() = 
    Chart.Point (xV,yV) 
    |> Chart.withTraceInfo "raw data"

let chartOrderOpt = 
    [1 .. 2 .. 10]
    |> List.map (fun order -> 
        let coeffs = Polynomial.fit order xV yV
        let predictFunction = Polynomial.predict coeffs
        [1. .. 0.2 .. 10.]
        |> List.map (fun x -> x,predictFunction x)
        |> Chart.Line
        |> Chart.withTraceInfo (sprintf "order=%i" order)
        )
    |> fun x -> Chart.combine (rawchart()::x)
    |> Chart.withTitle "polynomial fits"
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "x"
    |> Chart.withYAxisStyle "y"

And then crossvalidate across the polynomial orders:

// the error is calculated as the squared difference of fitted and original y value
let error (f1:float) f2 = pown (f1 - f2) 2

/// Leave-one-out cross validation. Returns the mean squared error of each leave-out at the 
/// specific polynomial order. Minimize for model selection.
let loocvPolynomial (xData:Vector<float>) (yData:Vector<float>) order =
    let xDataMat = Matrix.ofCols [|xData|]
    let getFitFuncPol xTrain yTrain (xTest:Vector<float>) = 
        getFitFuncPolynomial xTrain yTrain xTest order
    let meanSquaredError = CrossValidation.loocv xDataMat yData getFitFuncPol error
    
    meanSquaredError

// polynomial orders that should be checked
let ordersToCheck = [|1 .. 10|]

let errorPol = 
    ordersToCheck 
    |> Array.map (fun order -> 
        let error = loocvPolynomial xV yV order
        order,error)

let chartPol = 
    errorPol 
    |> Chart.Line 
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "polynomial order"
    |> Chart.withYAxisStyle "mean error"
    |> Chart.withTitle "leave one out cross validation (polynomial)"
    
let result = sprintf "The minimal error is obtained by order=%i" (errorPol |> Seq.minBy snd |> fst)

"The minimal error is obtained by order=3"

Smoothing spline loocv

A smoothing spline is a non-parametric fitting procedure, fitting cubic polynomials in each interval given by the basis points.

let's first create some smoothing splines to cross validate:

// the fitting function fits a smoothing spline with smoothing factor lambda to the training data set (xTrain and yTrain) and applies it to xTest
let getFitFuncSpline (xDat:Matrix<float>) (yDat:Vector<float>) (xDatTrain: Vector<float>) lambda =
    let xDatVec = xDat.Data // |> Matrix.toVector
    let zippedData = Seq.zip xDatVec yDat |> Array.ofSeq
    let xValTest = xDatTrain.[0]
    Spline.smoothingSpline zippedData (xDat.Data) lambda xValTest

    /// in loocv the border points are chosen so that the support range of the training data set does not cover the test point.
    /// if splines are used, that are not defined outside the border points use the following:
    //let xDatSupport = Intervals.create (xDatVec |> Seq.min) (xDatVec |> Seq.max)
    //if Intervals.liesInInterval xValTest xDatSupport then 
    //Spline.smoothingSpline zippedData (xDat |> Array.ofSeq) lambda xValTest
    //else nan

let chartSpline = 
    [0.0002;0.002;0.0216;0.2;2.;20.]
    |> List.map (fun lambda -> 
        let fit = Spline.smoothingSpline (Seq.zip xV yV |> Array.ofSeq) (Array.ofSeq xV) lambda
        [1. .. 0.2 .. 10.]
        |> List.map (fun x -> x,fit x)
        |> Chart.Line
        |> Chart.withTraceInfo (sprintf "l=%.4f" lambda)
        )
    |> fun x -> 
        Chart.combine (rawchart()::x)
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "x"
    |> Chart.withYAxisStyle "y"
    |> Chart.withTitle "smoothing splines"

And then crossvalidate across different lambda values:

// the error is calculated as the squared difference of fitted and original y value
let errorSpl (f1:float) f2 = 
    // if xValue is outside of support area of the fitted model (some smoothing spline algorithms), the error should report 0.
    //if nan.Equals f1 then 0.
    //else pown (f1 - f2) 2
    pown (f1 - f2) 2

/// Leave-one-out cross validation. Returns the mean squared error of each leave-out at the 
/// specific regularization parameter (lambda). Minimize the (MSE) for model selection.
let loocvSmoothingSpline (xData:Vector<float>) (yData:Vector<float>) lambda =
    let xDataMat = Matrix.ofCols [|xData|]
    let getFitFuncSpl xDat yDat (xDatTrain: Vector<float>) =
        getFitFuncSpline xDat yDat xDatTrain lambda
    
    CrossValidation.loocv xDataMat yData getFitFuncSpl errorSpl

// smoothing parameter = lambda = regularization parameter
let lambdasToCheck = [|1. .. 15.|] |> Array.map (fun i -> 0.0001 * i**3.)

let errorSpline = 
    lambdasToCheck 
    |> Array.map (fun lambda -> 
        //basisPoints define, where the knots of the spline are located
        let error = loocvSmoothingSpline xV yV lambda
        lambda,error)

let chartSplineError = 
    errorSpline 
    |> Chart.Line 
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "lambda"
    |> Chart.withYAxisStyle "mean error"
    |> Chart.withTitle "leave one out cross validation (smoothing spline)"
    
let resultSpline = sprintf "The minimal error is obtained by lambda=%f" (errorSpline |> Seq.minBy snd |> fst)

"The minimal error is obtained by lambda=0.021600"

k fold cross validation

The k fold cross validation (kfcv) is a generalized form of the loocv. Rather than excluding every data point separately, kfcv allows the exclusion of data chunks with a defined fraction of the data points. When using k=10, the data is split up into 10 chunks of sub data sets each containing 10% of the data set.

In each loop one chunk is excluded (test data), while the other 9 chunks serve as training data. After 10 (k) loops every single point was evaluated as test data set once and k-1 times as training data. The selection of the subset chunks is random and can be repeated in several iterations. The output contains the average error together with the standardDeviation computed by the given function.

//repeated k fold cross validation for polynomials
let repeatedKFoldPolynomial k (xData: Vector<float>) (yData: Vector<float>) order =
    let xDataMat = [|xData|] |> Matrix.ofCols
    
    let getFitFuncPol xTrain yTrain (xTest:Vector<float>) = 
        getFitFuncPolynomial xTrain yTrain xTest order
        
    CrossValidation.repeatedKFold k 10 xDataMat yData getFitFuncPol error Seq.stDev

//creates an output for 10 iterations where defined 20 % of the data set are taken as testing data set
let kfPolynomial order = repeatedKFoldPolynomial 5 xV yV order

//repeated k fold cross validation for smoothing splines
let repeatedKFoldSpline k (xData: Vector<float>) (yData: Vector<float>) lambda =
    let xDataMat = [|xData|] |> Matrix.ofCols
    
    let getFitFuncSpl xDat yDat (xDatTrain: Vector<float>) =
        getFitFuncSpline xDat yDat xDatTrain lambda

    CrossValidation.repeatedKFold k 10 xDataMat yData getFitFuncSpl errorSpl Seq.stDev

//creates an output for 10 iterations where defined 20 % of the data set are taken as testing data set
let kfSpline lambda = repeatedKFoldSpline 5 xV yV lambda

The given data set is small and therefore the mean errors show a high variability

let kfp = 
    let errorSplinekf = 
        ordersToCheck 
        |> Array.map (fun order -> 
            //basisPoints define, where the knots of the spline are located
            let error = kfPolynomial order
            (order,error.Error),error.ErrorStDev)
        |> Array.unzip

    fst errorSplinekf 
    |> Chart.Line 
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "order"
    |> Chart.withYAxisStyle "mean error"
    |> Chart.withYAxis(LayoutObjects.LinearAxis.init(AxisType=StyleParam.AxisType.Log))
    |> Chart.withYErrorStyle (Array= snd errorSplinekf)
    |> Chart.withTitle "kfoldPolynomial error"

let kfs = 
    let errorSplinekf = 
        lambdasToCheck 
        |> Array.map (fun lambda -> 
            //basisPoints define, where the knots of the spline are located
            let error = kfSpline lambda
            (lambda,error.Error),error.ErrorStDev)
        |> Array.unzip

    fst errorSplinekf 
    |> Chart.Line 
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "lambda"
    |> Chart.withYAxisStyle "mean error"
    |> Chart.withYErrorStyle (Array= snd errorSplinekf)
    |> Chart.withTitle "kfoldSpline error"

Shuffle and split cross validation

The shuffle and split cross validation (sap) is a modified kfcv version. As in kfcv, sap allows the exclusion of data chunks with a defined fraction of the data points. When using p=0.3, 30% of the data are taken as testing data set while 70% serve as training data set. In sap by default only one testing set is evaluated (unlike to kfcv where every data point is once part of a training data set and k-1 times part of testing data set).

Sap can be performed multiple times. Each time the training data fraction is taken randomly from the original data set. Unlike in kfcv overlaps may occur. The output contains the average error together with the standardDeviation computed by the given function.

let shuffleAndSplitPolynomial p iterations (xData: Vector<float>) (yData: Vector<float>) order =
   let xDataMat = [|xData|] |> Matrix.ofCols
   
   let getFitFuncPol xTrain yTrain (xTest:Vector<float>) = 
       getFitFuncPolynomial xTrain yTrain xTest order
   
   CrossValidation.shuffleAndSplit p iterations xDataMat yData getFitFuncPol error Seq.stDev

//creates an output for 5 iterations where random 20 % of the data set are taken as testing data set
let sasPolynomial order = shuffleAndSplitPolynomial 0.2 5 xV yV order

let shuffleAndSplitSpline p iterations (xData: Vector<float>) (yData: Vector<float>) lambda =
    let xDataMat = [|xData|] |> Matrix.ofCols
   
    let getFitFuncSpl xDat yDat (xDatTrain: Vector<float>) =
        getFitFuncSpline xDat yDat xDatTrain lambda
   
    CrossValidation.shuffleAndSplit p iterations xDataMat yData getFitFuncSpl errorSpl Seq.stDev

//creates an output for 5 iterations where random 20 % of the data set are taken as testing data set
let sasSpline lambda = shuffleAndSplitSpline 0.2 5 xV yV lambda

The given data set is small and therefore the mean errors show a high variability.

let sasp = 
    let errorSplinekf = 
        ordersToCheck 
        |> Array.map (fun order -> 
            //basisPoints define, where the knots of the spline are located
            let error = sasPolynomial order
            (order,error.Error),error.ErrorStDev)
        |> Array.unzip

    fst errorSplinekf 
    |> Chart.Line 
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "order"
    |> Chart.withYAxisStyle "mean error"
    |> Chart.withYAxis(LayoutObjects.LinearAxis.init(AxisType=StyleParam.AxisType.Log))
    |> Chart.withYErrorStyle (Array= snd errorSplinekf)
    |> Chart.withTitle "shuffle_and_split polynomial error"

let sass = 
    let errorSplinekf = 
        lambdasToCheck 
        |> Array.map (fun lambda -> 
            //basisPoints define, where the knots of the spline are located
            let error = sasSpline lambda
            (lambda,error.Error),error.ErrorStDev)
        |> Array.unzip

    fst errorSplinekf 
    |> Chart.Line 
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withXAxisStyle "lambda"
    |> Chart.withYAxisStyle "mean error"
    |> Chart.withYErrorStyle (Array= snd errorSplinekf)
    |> Chart.withTitle "shuffle_and_split spline error"

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

Multiple items
namespace FSharp

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

namespace FSharp.Stats

namespace FSharp.Stats.Fitting

Multiple items
module LinearRegression from FSharp.Stats.Fitting
<summary> Linear regression is used to estimate the relationship of one variable (y) with another (x) by expressing y in terms of a linear function of x. </summary>

--------------------
type LinearRegression = new: unit -> LinearRegression static member fit: xData: Vector<float> * yData: Vector<float> * ?FittingMethod: Method * ?Constraint: Constraint<float * float> * ?Weighting: Vector<float> -> Coefficients + 1 overload static member predict: coeff: Coefficients -> xValue: float -> float static member predictMultivariate: coeff: Coefficients -> xVector: Vector<float> -> float
<summary> This LinearRegression type summarized the most common fitting procedures. </summary>
<returns>Either linear regression coefficients or a prediction function to map x values/vectors to its corresponding y value.</returns>
<example><code> // e.g. days since experiment start let xData = vector [|1. .. 100.|] // e.g. plant size in cm let yData = vector [|4.;7.;8.;9.;7.;11.; ...|] // Estimate the intercept and slope of a line, that fits the data. let coefficientsSimpleLinear = LinearRegression.fit(xData,yData,FittingMethod=Fitting.Method.SimpleLinear,Constraint=Fitting.Constraint.RegressionThroughOrigin) // Predict the size on day 10.5 LinearRegression.predict(coefficientsSimpleLinear) 10.5 </code></example>

--------------------
new: unit -> LinearRegression

module OLS from FSharp.Stats.Fitting.LinearRegressionModule
<summary> Ordinary Least Squares (OLS) regression aims to minimise the sum of squared y intercepts between the original and predicted points at each x value. </summary>

val xV: Vector<float>

val vector: l: 'a seq -> Vector<'a> (requires 'a :> System.Numerics.INumber<'a>)

val yV: Vector<float>

val getFitFuncPolynomial: xTrain: Matrix<float> -> yTrain: Vector<float> -> xTest: Vector<float> -> order: int -> float

val xTrain: Matrix<float>

Multiple items
module Matrix from FsMath

--------------------
type Matrix<'T (requires 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType)> = interface IEquatable<Matrix<'T>> new: rows: int * cols: int * data: Vector<'T> -> Matrix<'T> override Equals: obj: obj -> bool override GetHashCode: unit -> int member GetSlice: rowStart: int option * rowEnd: int option * colStart: int option * colEnd: int option -> Matrix<'T> + 1 overload member SetCol: j: int * colData: 'T array -> unit member SetRow: i: int * rowData: 'T array -> unit override ToString: unit -> string member Transpose: unit -> Matrix<'T> member toArray2D: unit -> 'T array2d ...
<summary> Matrix type to hold values of a matrix in a 1D Arrays (Flattened Representation) </summary>

--------------------
new: rows: int * cols: int * data: Vector<'T> -> Matrix<'T>

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

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

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

val yTrain: Vector<float>

val xTest: Vector<float>

Multiple items
module Vector from FSharp.Stats

--------------------
module Vector from FsMath

--------------------
type Vector = static member add: v1: Vector<'T> -> v2: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member addScalar: scalar: 'T -> v: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member divide: v1: Vector<'T> -> v2: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member divideScalar: scalar: 'T -> v: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member dot: v1: Vector<'T> -> v2: Vector<'T> -> 'T (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member max: v: Vector<'T> -> 'T (requires 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType) static member mean: v: Vector<'T> -> 'T (requires 'T :> INumber<'T> and member DivideByInt and default constructor and value type and 'T :> ValueType) static member min: v: Vector<'T> -> 'T (requires 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType) static member multiply: v1: Vector<'T> -> v2: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member multiplyScalar: scalar: 'T -> v: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) ...

--------------------
type Vector<'T (requires 'T :> INumber<'T>)> = 'T array
<summary> Vector as a Array type alias </summary>

val order: int

val xDat: Vector<float>

property Matrix.Data: Vector<float> with get
<summary> Exposes the raw underlying data array (row-major flattened). </summary>

val coeffs: LinearRegression.Coefficients

Multiple items
union case Method.Polynomial: int -> Method
<summary>Fits a polynomial of the specified order (degree) to twodimensional data (OLS).</summary>

--------------------
module Polynomial from FSharp.Stats.Fitting.LinearRegressionModule.OLS
<summary> Linear regression using polynomials as regression function: f(x) = a + bx + cx^2 + .... </summary>

val fit: order: int -> xData: Vector<float> -> yData: Vector<float> -> LinearRegression.Coefficients
<summary> Calculates the polynomial coefficients for polynomial regression. </summary>
<param name="order">order of the polynomial (1 = linear, 2 = quadratic, ... )</param>
<param name="xData">vector of x values</param>
<param name="yData">vector of y values</param>
<returns>vector of polynomial coefficients sorted as [intercept;constant;quadratic;...]</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. temperature measured at noon of the days specified in xData let yData = vector [|4.;7.;9.;8.;7.;9.;|] // Estimate the three coefficients of a quadratic polynomial. let coefficients = LinearRegression.OLS.Polynomial.fit 2 xData yData </code></example>

val predictFunction: float

val predict: coef: LinearRegression.Coefficients -> x: float -> float
<summary> Takes polynomial coefficients and x value to predict the corresponding y value. </summary>
<param name="coef">vector of polynomial coefficients (e.g. determined by Polynomial.coefficients), sorted as [intercept;constant;quadratic;...]</param>
<param name="x">x value of which the corresponding y value should be predicted</param>
<returns>predicted y value with given polynomial coefficients at X=x</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. temperature measured at noon of the days specified in xData let yData = vector [|4.;7.;9.;8.;7.;9.;|] // Define the polynomial coefficients. let coefficients = LinearRegression.OLS.Polynomial.fit xData yData // Predict the temperature value at midnight between day 1 and 2. LinearRegression.OLS.Polynomial.predict coefficients 1.5 </code></example>
<remarks>If all coefficients are nonzero, the order is equal to the length of the coefficient vector!</remarks>

val rawchart: unit -> 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: #('a1 seq) seq * [<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))>] ?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: '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))>] ?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 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> 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: '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: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.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: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.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: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.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 'a2 :> 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: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.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: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.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: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.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.withTraceInfo: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: StyleParam.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)

val chartOrderOpt: GenericChart.GenericChart

Multiple items
module List from FSharp.Stats
<summary> Module to compute common statistical measure on list </summary>

--------------------
module List from Microsoft.FSharp.Collections

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

--------------------
type List<'T> = | op_Nil | op_ColonColon of Head: 'T * Tail: 'T list interface IReadOnlyList<'T> interface IReadOnlyCollection<'T> interface IEnumerable interface IEnumerable<'T> member GetReverseIndex: rank: int * offset: int -> int member GetSlice: startIndex: int option * endIndex: int option -> 'T list static member Cons: head: 'T * tail: 'T list -> 'T list member Head: 'T member IsEmpty: bool member Item: index: int -> 'T with get ...

--------------------
new: unit -> List

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

val predictFunction: (float -> float)

val x: float

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: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.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: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.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: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.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: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.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: '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: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.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: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.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: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.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: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.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 'a2 :> System.IConvertible)

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

val x: GenericChart.GenericChart list

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

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)

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

module ChartTemplates from Plotly.NET

val lightMirrored: Template

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: StyleParam.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: StyleParam.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: StyleParam.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: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.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: StyleParam.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: LayoutObjects.RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.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: StyleParam.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: StyleParam.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: StyleParam.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: StyleParam.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: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.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: StyleParam.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: LayoutObjects.RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.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: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

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

val toChartHTML: gChart: GenericChart.GenericChart -> string

val error: f1: float -> f2: float -> float

val f1: float

val f2: float

val pown: x: 'T -> n: int -> 'T (requires member One and member ( * ) and member (/))

val loocvPolynomial: xData: Vector<float> -> yData: Vector<float> -> order: int -> float
Leave-one-out cross validation. Returns the mean squared error of each leave-out at the
specific polynomial order. Minimize for model selection.

val xData: Vector<float>

val yData: Vector<float>

val xDataMat: Matrix<float>

val ofCols: cols: 'T array array -> Matrix<'T> (requires 'T :> System.Numerics.INumber<'T> and default constructor and value type and comparison and 'T :> System.ValueType)

val getFitFuncPol: xTrain: Matrix<float> -> yTrain: Vector<float> -> xTest: Vector<float> -> float

val meanSquaredError: float

module CrossValidation from FSharp.Stats.Fitting

val loocv: xData: Matrix<'T> -> yData: Vector<'T> -> fitFunc: (Matrix<'T> -> Vector<'T> -> Vector<'T> -> 'T) -> error: ('T -> 'T -> 'T) -> 'T (requires 'T :> System.Numerics.INumber<'T> and default constructor and value type and comparison and 'T :> System.ValueType and member DivideByInt)
<summary>Computes a leave one out cross-validation xData: rowwise x-coordinate matrix, yData: yData vector fit: x and y data lead to function that maps an xData row vector to a y-coordinate, error: defines the error of the fitted y-coordinate and the actual y-coordinate</summary>
<remarks></remarks>
<param name="xData"></param>
<param name="yData"></param>
<param name="fitFunc"></param>
<param name="error"></param>
<returns></returns>
<example><code></code></example>

val ordersToCheck: int array

val errorPol: (int * float) array

Multiple items
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 error: float

val chartPol: GenericChart.GenericChart

val result: string

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

--------------------
module Seq from Microsoft.FSharp.Collections

--------------------
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

--------------------
new: unit -> Seq

val minBy: projection: ('T -> 'U) -> source: 'T seq -> 'T (requires comparison)

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

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

val getFitFuncSpline: xDat: Matrix<float> -> yDat: Vector<float> -> xDatTrain: Vector<float> -> lambda: float -> float

val xDat: Matrix<float>

val yDat: Vector<float>

val xDatTrain: Vector<float>

val lambda: float

val xDatVec: Vector<float>

val zippedData: (float * float) array

val zip: source1: 'T1 seq -> source2: 'T2 seq -> ('T1 * 'T2) seq

val ofSeq: source: 'T seq -> 'T array

val xValTest: float

module Spline from FSharp.Stats.Fitting

val smoothingSpline: data: (float * float) array -> basispts: float array -> (float -> float -> float)
<summary>Creates a smoothing spline through some data. Takes as spline points the x-values given by basispts. The resulting function takes lambda (regularization parameter) and a x_Value as input. </summary>
<remarks></remarks>
<param name="data"></param>
<param name="basispts"></param>
<returns></returns>
<example><code></code></example>

val chartSpline: GenericChart.GenericChart
in loocv the border points are chosen so that the support range of the training data set does not cover the test point.
if splines are used, that are not defined outside the border points use the following:

val fit: (float -> float)

val errorSpl: f1: float -> f2: float -> float

val loocvSmoothingSpline: xData: Vector<float> -> yData: Vector<float> -> lambda: float -> float
Leave-one-out cross validation. Returns the mean squared error of each leave-out at the
specific regularization parameter (lambda). Minimize the (MSE) for model selection.

val getFitFuncSpl: xDat: Matrix<float> -> yDat: Vector<float> -> xDatTrain: Vector<float> -> float

val lambdasToCheck: float array

val i: float

val errorSpline: (float * float) array

val chartSplineError: GenericChart.GenericChart

val resultSpline: string

val repeatedKFoldPolynomial: k: int -> xData: Vector<float> -> yData: Vector<float> -> order: int -> CrossValidation.CrossValidationResult<float>

val k: int

val repeatedKFold: k: 'a -> iterations: int -> xData: Matrix<'T> -> yData: Vector<'T> -> fit: (Matrix<'T> -> Vector<'T> -> Vector<'T> -> 'T) -> error: ('T -> 'T -> 'T) -> getStDev: ('T seq -> 'T) -> CrossValidation.CrossValidationResult<'T> (requires member op_Explicit and 'T :> System.Numerics.INumber<'T> and default constructor and value type and comparison and 'T :> System.ValueType and member DivideByInt)
<summary>Computes a repeated k fold cross-validation, k: training set size (and number of iterations), iterations: number of random subset creation, xData: rowwise x-coordinate matrix, yData: yData vector fit: x and y data lead to function that maps a xData row vector to a y-coordinate, error: defines the error of the fitted y-coordinate and the actual y-coordinate, getStDev: function that calculates the standard deviation from a seq<^T>. (Seq.stDev)</summary>
<remarks></remarks>
<param name="k"></param>
<param name="iterations"></param>
<param name="xData"></param>
<param name="yData"></param>
<param name="fit"></param>
<param name="error"></param>
<param name="getStDev"></param>
<returns></returns>
<example><code></code></example>

val stDev: items: 'T seq -> 'U (requires member (-) and member Zero and member DivideByInt and member (+) and member ( * ) and member (+) and member (/) and member Sqrt)
<summary> Computes the sample standard deviation. </summary>
<param name="items">The input sequence.</param>
<remarks>Returns NaN if data is empty or if any entry is NaN.</remarks>
<returns>The sample standard deviation (Bessel's correction by N-1) of the input sequence.</returns>
<example><code> let values = [1.0; 2.0; 3.0; 4.0; 5.0] let sd = Seq.stDev values // returns approximately 1.58114 </code></example>

val kfPolynomial: order: int -> CrossValidation.CrossValidationResult<float>

val repeatedKFoldSpline: k: int -> xData: Vector<float> -> yData: Vector<float> -> lambda: float -> CrossValidation.CrossValidationResult<float>

val kfSpline: lambda: float -> CrossValidation.CrossValidationResult<float>

val kfp: GenericChart.GenericChart

val errorSplinekf: (int * float) array * float array

val error: CrossValidation.CrossValidationResult<float>

CrossValidation.CrossValidationResult.Error: float

CrossValidation.CrossValidationResult.ErrorStDev: float

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

static member Chart.withYAxis: yAxis: LayoutObjects.LinearAxis * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

namespace Plotly.NET.LayoutObjects

Multiple items
type LinearAxis = inherit DynamicObj new: unit -> LinearAxis static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Title: Title * [<Optional; DefaultParameterValue ((null :> obj))>] ?AxisType: AxisType * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoTypeNumbers: AutoTypeNumbers * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoRange: AutoRange * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeMode: RangeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?Range: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?FixedRange: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ScaleAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?ScaleRatio: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Constrain: AxisConstraint * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConstrainToward: AxisConstraintDirection * [<Optional; DefaultParameterValue ((null :> obj))>] ?Matches: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Rangebreaks: Rangebreak seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickMode: TickMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?NTicks: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Tick0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?DTick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickVals: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickText: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Ticks: TickOptions * [<Optional; DefaultParameterValue ((null :> obj))>] ?TicksOn: CategoryTickAnchor * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelMode: TickLabelMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelPosition: TickLabelPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelStep: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelOverflow: TickLabelOverflow * [<Optional; DefaultParameterValue ((null :> obj))>] ?Mirror: Mirror * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLen: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoMargin: TickAutoMargin * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeMode: SpikeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeSnap: SpikeSnap * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickAngle: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickPrefix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickSuffix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowExponent: ShowExponent * [<Optional; DefaultParameterValue ((null :> obj))>] ?ExponentFormat: ExponentFormat * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinExponent: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Minor: Minor * [<Optional; DefaultParameterValue ((null :> obj))>] ?SeparateThousands: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormatStops: TickFormatStop seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Shift: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowDividers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?DividerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?DividerWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Anchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Side: Side * [<Optional; DefaultParameterValue ((null :> obj))>] ?Overlaying: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Layer: Layer * [<Optional; DefaultParameterValue ((null :> obj))>] ?Domain: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?Position: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryOrder: CategoryOrder * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryArray: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?UIRevision: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeSlider: RangeSlider * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeSelector: RangeSelector * [<Optional; DefaultParameterValue ((null :> obj))>] ?Calendar: Calendar * [<Optional; DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool -> LinearAxis static member initCarpet: [<Optional; DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Title: Title * [<Optional; DefaultParameterValue ((null :> obj))>] ?AxisType: AxisType * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoTypeNumbers: AutoTypeNumbers * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoRange: AutoRange * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeMode: RangeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?Range: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?FixedRange: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickMode: TickMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?NTicks: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Tick0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?DTick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickVals: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickText: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Ticks: TickOptions * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickAngle: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickPrefix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickSuffix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowExponent: ShowExponent * [<Optional; DefaultParameterValue ((null :> obj))>] ?ExponentFormat: ExponentFormat * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinExponent: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?SeparateThousands: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormatStops: TickFormatStop seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryOrder: CategoryOrder * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryArray: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrayDTick: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrayTick0: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?CheaterType: CheaterType * [<Optional; DefaultParameterValue ((null :> obj))>] ?EndLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?EndLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?EndLineWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?LabelPadding: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?LabelPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?LabelSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridCount: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Smoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartLineWidth: int -> LinearAxis static member initCategorical: categoryOrder: CategoryOrder * [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Title: Title * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoTypeNumbers: AutoTypeNumbers * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoRange: AutoRange * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeMode: RangeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?Range: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?FixedRange: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ScaleAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?ScaleRatio: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Constrain: AxisConstraint * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConstrainToward: AxisConstraintDirection * [<Optional; DefaultParameterValue ((null :> obj))>] ?Matches: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Rangebreaks: Rangebreak seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickMode: TickMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?NTicks: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Tick0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?DTick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickVals: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickText: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Ticks: TickOptions * [<Optional; DefaultParameterValue ((null :> obj))>] ?TicksOn: CategoryTickAnchor * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelMode: TickLabelMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelPosition: TickLabelPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelOverflow: TickLabelOverflow * [<Optional; DefaultParameterValue ((null :> obj))>] ?Mirror: Mirror * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLen: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoMargin: TickAutoMargin * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeMode: SpikeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeSnap: SpikeSnap * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickAngle: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickPrefix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickSuffix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowExponent: ShowExponent * [<Optional; DefaultParameterValue ((null :> obj))>] ?ExponentFormat: ExponentFormat * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinExponent: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Minor: Minor * [<Optional; DefaultParameterValue ((null :> obj))>] ?SeparateThousands: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormatStops: TickFormatStop seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Shift: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowDividers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?DividerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?DividerWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Anchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Side: Side * [<Optional; DefaultParameterValue ((null :> obj))>] ?Overlaying: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Layer: Layer * [<Optional; DefaultParameterValue ((null :> obj))>] ?Domain: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?Position: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryArray: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?UIRevision: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeSlider: RangeSlider * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeSelector: RangeSelector * [<Optional; DefaultParameterValue ((null :> obj))>] ?Calendar: Calendar -> LinearAxis static member initIndicatorGauge: [<Optional; DefaultParameterValue ((null :> obj))>] ?DTick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?ExponentFormat: ExponentFormat * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinExponent: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?NTicks: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Range: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?SeparateThousands: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowExponent: ShowExponent * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickPrefix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickSuffix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?Tick0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickAngle: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormatStops: TickFormatStop seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLen: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickMode: TickMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Ticks: TickOptions * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickText: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickVals: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool -> LinearAxis static member style: [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Title: Title * [<Optional; DefaultParameterValue ((null :> obj))>] ?AxisType: AxisType * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoTypeNumbers: AutoTypeNumbers * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoRange: AutoRange * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeMode: RangeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?Range: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?FixedRange: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ScaleAnchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?ScaleRatio: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Constrain: AxisConstraint * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConstrainToward: AxisConstraintDirection * [<Optional; DefaultParameterValue ((null :> obj))>] ?Matches: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Rangebreaks: Rangebreak seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickMode: TickMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?NTicks: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Tick0: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?DTick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickVals: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickText: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Ticks: TickOptions * [<Optional; DefaultParameterValue ((null :> obj))>] ?TicksOn: CategoryTickAnchor * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelMode: TickLabelMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelPosition: TickLabelPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelStep: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLabelOverflow: TickLabelOverflow * [<Optional; DefaultParameterValue ((null :> obj))>] ?Mirror: Mirror * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickLen: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?AutoMargin: TickAutoMargin * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeMode: SpikeMode * [<Optional; DefaultParameterValue ((null :> obj))>] ?SpikeSnap: SpikeSnap * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickAngle: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickPrefix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowTickSuffix: ShowTickOption * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowExponent: ShowExponent * [<Optional; DefaultParameterValue ((null :> obj))>] ?ExponentFormat: ExponentFormat * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinExponent: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Minor: Minor * [<Optional; DefaultParameterValue ((null :> obj))>] ?SeparateThousands: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TickFormatStops: TickFormatStop seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverFormat: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?GridWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZeroLineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Shift: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowDividers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?DividerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?DividerWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Anchor: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Side: Side * [<Optional; DefaultParameterValue ((null :> obj))>] ?Overlaying: LinearAxisId * [<Optional; DefaultParameterValue ((null :> obj))>] ?Layer: Layer * [<Optional; DefaultParameterValue ((null :> obj))>] ?Domain: Range * [<Optional; DefaultParameterValue ((null :> obj))>] ?Position: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryOrder: CategoryOrder * [<Optional; DefaultParameterValue ((null :> obj))>] ?CategoryArray: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?UIRevision: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeSlider: RangeSlider * [<Optional; DefaultParameterValue ((null :> obj))>] ?RangeSelector: RangeSelector * [<Optional; DefaultParameterValue ((null :> obj))>] ?Calendar: Calendar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrayDTick: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrayTick0: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?CheaterType: CheaterType * [<Optional; DefaultParameterValue ((null :> obj))>] ?EndLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?EndLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?EndLineWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?LabelPadding: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?LabelPrefix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?LabelSuffix: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridCount: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?MinorGridWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Smoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartLine: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartLineWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool -> (LinearAxis -> LinearAxis)
<summary>Linear axes can be used as x and y scales on 2D plots, and as x,y, and z scales on 3D plots.</summary>

--------------------
new: unit -> LayoutObjects.LinearAxis

static member LayoutObjects.LinearAxis.init: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: StyleParam.AxisType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoTypeNumbers: StyleParam.AutoTypeNumbers * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoRange: StyleParam.AutoRange * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeMode: StyleParam.RangeMode * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Range: StyleParam.Range * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FixedRange: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ScaleAnchor: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ScaleRatio: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Constrain: StyleParam.AxisConstraint * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ConstrainToward: StyleParam.AxisConstraintDirection * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Matches: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Rangebreaks: LayoutObjects.Rangebreak seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickMode: StyleParam.TickMode * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?NTicks: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Tick0: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?DTick: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickVals: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickText: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Ticks: StyleParam.TickOptions * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TicksOn: StyleParam.CategoryTickAnchor * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickLabelMode: StyleParam.TickLabelMode * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickLabelPosition: StyleParam.TickLabelPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickLabelStep: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickLabelOverflow: StyleParam.TickLabelOverflow * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: StyleParam.Mirror * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickLen: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickWidth: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowTickLabels: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoMargin: StyleParam.TickAutoMargin * [<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))>] ?SpikeDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeMode: StyleParam.SpikeMode * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeSnap: StyleParam.SpikeSnap * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickFont: Font * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickAngle: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowTickPrefix: StyleParam.ShowTickOption * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickPrefix: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowTickSuffix: StyleParam.ShowTickOption * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickSuffix: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowExponent: StyleParam.ShowExponent * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ExponentFormat: StyleParam.ExponentFormat * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinExponent: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Minor: LayoutObjects.Minor * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SeparateThousands: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickFormat: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TickFormatStops: TickFormatStop seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?HoverFormat: string * [<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))>] ?LineWidth: float * [<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: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridWidth: float * [<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))>] ?ZeroLineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Shift: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowDividers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?DividerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?DividerWidth: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Layer: StyleParam.Layer * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: StyleParam.Range * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: StyleParam.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))>] ?UIRevision: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: LayoutObjects.RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.RangeSelector * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Calendar: StyleParam.Calendar * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool -> LayoutObjects.LinearAxis

module StyleParam from Plotly.NET

type AxisType = | Auto | Linear | Log | Date | Category | MultiCategory member Convert: unit -> obj override ToString: unit -> string static member convert: (AxisType -> obj) static member toString: (AxisType -> string)
<summary> Sets the axis type. By default (Auto), plotly attempts to determined the axis type by looking into the data of the traces that referenced the axis in question. </summary>

union case StyleParam.AxisType.Log: StyleParam.AxisType

static member Chart.withYErrorStyle: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Type: StyleParam.ErrorType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Symmetric: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Array: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Arrayminus: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Value: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Valueminus: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Traceref: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Tracerefminus: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Copy_ystyle: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Thickness: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: float -> (GenericChart.GenericChart -> GenericChart.GenericChart)

val kfs: GenericChart.GenericChart

val errorSplinekf: (float * float) array * float array

val shuffleAndSplitPolynomial: p: float -> iterations: int -> xData: Vector<float> -> yData: Vector<float> -> order: int -> CrossValidation.CrossValidationResult<float>

val p: float

val iterations: int

val shuffleAndSplit: p: float -> iterations: int -> xData: Matrix<'T> -> yData: Vector<'T> -> fit: (Matrix<'T> -> Vector<'T> -> Vector<'T> -> 'T) -> error: ('T -> 'T -> 'T) -> getStDev: ('T seq -> 'T) -> CrossValidation.CrossValidationResult<'T> (requires 'T :> System.Numerics.INumber<'T> and default constructor and value type and comparison and 'T :> System.ValueType and member DivideByInt)
<summary>Computes a repeated shuffel-and-split cross validation p: percentage of training set size from original size, iterations: number of random subset creation, xData: rowwise x-coordinate matrix, yData: yData vector fit: x and y data lead to function that maps a xData row vector to a y-coordinate, error: defines the error of the fitted y-coordinate and the actual y-coordinate, getStDev: function that calculates the standard deviation from a seq<^T>. (Seq.stDev)</summary>
<remarks></remarks>
<param name="p"></param>
<param name="iterations"></param>
<param name="xData"></param>
<param name="yData"></param>
<param name="fit"></param>
<param name="error"></param>
<param name="getStDev"></param>
<returns></returns>
<example><code></code></example>

val sasPolynomial: order: int -> CrossValidation.CrossValidationResult<float>

val shuffleAndSplitSpline: p: float -> iterations: int -> xData: Vector<float> -> yData: Vector<float> -> lambda: float -> CrossValidation.CrossValidationResult<float>

val sasSpline: lambda: float -> CrossValidation.CrossValidationResult<float>

val sasp: GenericChart.GenericChart

val sass: GenericChart.GenericChart