# 2D Histograms

Summary: This example shows how to create a bi-dimensional histogram of two data samples in F#.

let's first create some data for the purpose of creating example charts:

open Plotly.NET

//---------------------- generate random normally distributed data ----------------------
let normal (rnd:System.Random) mu tau =
let mutable v1 = 2.0 * rnd.NextDouble() - 1.0
let mutable v2 = 2.0 * rnd.NextDouble() - 1.0
let mutable r = v1 * v1 + v2 * v2
while (r >= 1.0 || r = 0.0) do
v1 <- 2.0 * rnd.NextDouble() - 1.0
v2 <- 2.0 * rnd.NextDouble() - 1.0
r <- v1 * v1 + v2 * v2
let fac = sqrt(-2.0*(log r)/r)
(tau * v1 * fac + mu)

let rnd = System.Random()
let n = 2000
let a = -1.
let b = 1.2
let step i = a +  ((b - a) / float (n - 1)) * float i

//---------------------- generate data distributed in x and y direction ----------------------
let x = Array.init n (fun i -> ((step i)**3.) + (0.3 * (normal (rnd) 0. 2.) ))
let y = Array.init n (fun i -> ((step i)**6.) + (0.3 * (normal (rnd) 0. 2.) ))


A Histogram2d chart can be created using the Chart.Histogram2d or Chart.Histogram2dContour functions.

let histogramContour =
[
Chart.Histogram2dContour (x,y,Line=Line.init(Width=0.))
Chart.Point(x,y,Opacity=0.3)
]
|> Chart.combine

let histogram2d =
Chart.Histogram2d (x,y)

namespace Plotly
namespace Plotly.NET
val normal : rnd:System.Random -> mu:float -> tau:float -> float
val rnd : System.Random
namespace System
Multiple items
type Random = new : unit -> unit + 1 overload member Next : unit -> int + 2 overloads member NextBytes : buffer: byte [] -> unit + 1 overload member NextDouble : unit -> float member Sample : unit -> float
<summary>Represents a pseudo-random number generator, which is an algorithm that produces a sequence of numbers that meet certain statistical requirements for randomness.</summary>

--------------------
System.Random() : System.Random
System.Random(Seed: int) : System.Random
val mu : float
val tau : float
val mutable v1 : float
System.Random.NextDouble() : float
val mutable v2 : float
val mutable r : float
val fac : float
val sqrt : value:'T -> 'U (requires member Sqrt)
<summary>Square root of the given number</summary>
<param name="value">The input value.</param>
<returns>The square root of the input.</returns>
val log : value:'T -> 'T (requires member Log)
<summary>Natural logarithm of the given number</summary>
<param name="value">The input value.</param>
<returns>The natural logarithm of the input.</returns>
val n : int
val a : float
val b : float
val step : i:int -> float
val i : int
Multiple items
val float : value:'T -> float (requires member op_Explicit)
<summary>Converts the argument to 64-bit float. This is a direct conversion for all primitive numeric types. For strings, the input is converted using <c>Double.Parse()</c> with InvariantCulture settings. Otherwise the operation requires an appropriate static conversion method on the input type.</summary>
<param name="value">The input value.</param>
<returns>The converted float</returns>

--------------------
[<Struct>] type float = System.Double
<summary>An abbreviation for the CLI type <see cref="T:System.Double" />.</summary>
<category>Basic Types</category>

--------------------
type float<'Measure> = float
<summary>The type of double-precision floating point numbers, annotated with a unit of measure. The unit of measure is erased in compiled code and when values of this type are analyzed using reflection. The type is representationally equivalent to <see cref="T:System.Double" />.</summary>
<category index="6">Basic Types with Units of Measure</category>
val x : float []
module Array from Microsoft.FSharp.Collections
<summary>Contains operations for working with arrays.</summary>
val init : count:int -> initializer:(int -> 'T) -> 'T []
<summary>Creates an array given the dimension and a generator function to compute the elements.</summary>
<param name="count">The number of elements to initialize.</param>
<param name="initializer">The function to generate the initial values for each index.</param>
<returns>The created array.</returns>
<exception cref="T:System.ArgumentException">Thrown when count is negative.</exception>
val y : float []
val histogramContour : GenericChart.GenericChart
type Chart = static member Area : x:seq<#IConvertible> * y:seq<#IConvertible> * ?Name:string * ?ShowMarkers:bool * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?Dash:DrawingStyle * ?Width:float -> GenericChart + 1 overload static member Bar : keys:seq<#IConvertible> * values:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?Marker:Marker -> GenericChart + 1 overload static member BarPolar : r:seq<#IConvertible> * theta:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?Dash:DrawingStyle * ?LineWidth:float -> GenericChart static member BoxPlot : ?x:'a0 * ?y:'a1 * ?Name:string * ?Showlegend:bool * ?Color:string * ?Fillcolor:'a2 * ?Opacity:float * ?Whiskerwidth:'a3 * ?Boxpoints:Boxpoints * ?Boxmean:BoxMean * ?Jitter:'a4 * ?Pointpos:'a5 * ?Orientation:Orientation * ?Marker:Marker * ?Line:Line * ?Alignmentgroup:'a6 * ?Offsetgroup:'a7 * ?Notched:bool * ?NotchWidth:float * ?QuartileMethod:QuartileMethod -> GenericChart + 1 overload static member Bubble : x:seq<#IConvertible> * y:seq<#IConvertible> * sizes:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:Orientation * ?GroupNorm:GroupNorm * ?UseWebGL:bool -> GenericChart + 1 overload static member Bubble3d : x:seq<#IConvertible> * y:seq<#IConvertible> * z:seq<#IConvertible> * sizes:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font -> GenericChart + 1 overload static member BubblePolar : r:seq<#IConvertible> * theta:seq<#IConvertible> * sizes:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?UseWebGL:bool -> GenericChart + 1 overload static member Candlestick : open:seq<#IConvertible> * high:seq<#IConvertible> * low:seq<#IConvertible> * close:seq<#IConvertible> * x:seq<#IConvertible> * ?Increasing:Line * ?Decreasing:Line * ?WhiskerWidth:float * ?Line:Line * ?XCalendar:Calendar -> GenericChart + 1 overload static member ChoroplethMap : locations:seq<string> * z:seq<#IConvertible> * ?Text:seq<#IConvertible> * ?Locationmode:LocationFormat * ?Autocolorscale:bool * ?Colorscale:Colorscale * ?ColorBar:ColorBar * ?Marker:Marker * ?GeoJson:'a2 * ?FeatureIdKey:string * ?Zmin:float * ?Zmax:float -> GenericChart static member ChoroplethMapbox : locations:seq<#IConvertible> * z:seq<#IConvertible> * geoJson:'a2 * ?FeatureIdKey:string * ?Text:seq<#IConvertible> * ?Below:string * ?Colorscale:Colorscale * ?ColorBar:ColorBar * ?ZAuto:bool * ?ZMin:float * ?ZMid:float * ?ZMax:float -> GenericChart ...
<summary> Provides a set of static methods for creating charts. </summary>
static member Chart.Histogram2dContour : x:seq<#System.IConvertible> * y:seq<#System.IConvertible> * ?Z:seq<#seq<'d>> * ?Name:'e * ?Colorscale:StyleParam.Colorscale * ?Showscale:'f * ?Line:Line * ?zSmooth:StyleParam.SmoothAlg * ?ColorBar:'g * ?zAuto:'h * ?zMin:'i * ?zMax:'j * ?nBinsx:int * ?nBinsy:int * ?xBins:Bins * ?yBins:Bins * ?HistNorm:StyleParam.HistNorm * ?HistFunc:StyleParam.HistNorm -> GenericChart.GenericChart (requires 'd :> System.IConvertible)
Multiple items
type Line = inherit DynamicObj new : unit -> Line static member init : ?Width:float * ?Color:string * ?Shape:Shape * ?Dash:DrawingStyle * ?Smoothing:float * ?Colorscale:Colorscale * ?OutlierColor:string * ?OutlierWidth:float -> Line static member style : ?Width:float * ?Color:string * ?Shape:Shape * ?Dash:DrawingStyle * ?Smoothing:float * ?Colorscale:Colorscale * ?OutlierColor:string * ?OutlierWidth:float -> (Line -> Line)
<summary> Line type inherits from dynamic object </summary>

--------------------
new : unit -> Line
static member Line.init : ?Width:float * ?Color:string * ?Shape:StyleParam.Shape * ?Dash:StyleParam.DrawingStyle * ?Smoothing:float * ?Colorscale:StyleParam.Colorscale * ?OutlierColor:string * ?OutlierWidth:float -> Line
static member Chart.Point : xy:seq<#System.IConvertible * #System.IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:StyleParam.Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#System.IConvertible> * ?TextPosition:StyleParam.TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:StyleParam.Orientation * ?GroupNorm:StyleParam.GroupNorm * ?UseWebGL:bool -> GenericChart.GenericChart
static member Chart.Point : x:seq<#System.IConvertible> * y:seq<#System.IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:StyleParam.Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#System.IConvertible> * ?TextPosition:StyleParam.TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:StyleParam.Orientation * ?GroupNorm:StyleParam.GroupNorm * ?UseWebGL:bool -> GenericChart.GenericChart
static member Chart.combine : gCharts:seq<GenericChart.GenericChart> -> GenericChart.GenericChart
module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>
val toChartHTML : gChart:GenericChart.GenericChart -> string
<summary> Converts a GenericChart to it HTML representation. The div layer has a default size of 600 if not specified otherwise. </summary>
val histogram2d : GenericChart.GenericChart
static member Chart.Histogram2d : x:seq<#System.IConvertible> * y:seq<#System.IConvertible> * ?Z:seq<#seq<'d>> * ?Name:string * ?Showlegend:bool * ?Opacity:float * ?Colorscale:StyleParam.Colorscale * ?Showscale:'e * ?zSmooth:StyleParam.SmoothAlg * ?ColorBar:'f * ?zAuto:'g * ?zMin:'h * ?zMax:'i * ?nBinsx:int * ?nBinsy:int * ?xBins:Bins * ?yBins:Bins * ?HistNorm:StyleParam.HistNorm * ?HistFunc:StyleParam.HistNorm -> GenericChart.GenericChart (requires 'd :> System.IConvertible)