# Smith charts

Summary: This example shows how to create smith charts in F#.

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

open Plotly.NET

// real coordinates
let real = [ 0.5; 1.; 2.; 3. ]

// imaginary coordinates
let imaginary = [ 0.5; 1.; 2.; 3. ]


The Smith chart, invented by Phillip H. Smith (1905-1987) and independently by Mizuhashi Tosaku, is a graphical calculator or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits

The Smith chart is a mathematical transformation of the two-dimensional Cartesian complex plane. Complex numbers with positive real parts map inside the circle. Those with negative real parts map outside the circle. If we are dealing only with impedances with non-negative resistive components, our interest is focused on the area inside the circle.

(Wikipedia).

Still, you can plot any kind of imaginary numbers on this plane.

## point smith charts

Use Chart.PointSmith to create a chart that displays points on a smith subplot:

let pointSmith = Chart.PointSmith(real, imaginary)


## line smith charts

Use Chart.LineSmith to create a plot that displays a line connecting the data on a smith subplot.

This example also changes the styles of the line.

let lineSmith =
Chart.LineSmith(
real = real,
imag = imaginary,
LineDash = StyleParam.DrawingStyle.DashDot,
LineColor = Color.fromKeyword Purple
)


## bubble smith charts

Use Chart.BubbleSmith to create a plot that displays datums on a smith subplot, with an additional 3rd dimension set as the marker size.

As for all other plots above, you can, for example, add labels to each datum:

let bubbleSmith =
Chart.BubbleSmith(
real = real,
imag = imaginary,
sizes = [ 10; 20; 30; 40 ],
MultiText = [ "one"; "two"; "three"; "four"; "five"; "six"; "seven" ],
TextPosition = StyleParam.TextPosition.TopCenter
)

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: 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: ?AdditionalHeadTags: XmlNode list * ?Description: XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions static member initCDNOnly: unit -> DisplayOptions ...

--------------------
new: unit -> DisplayOptions
static member DisplayOptions.init: ?AdditionalHeadTags: Giraffe.ViewEngine.HtmlElements.XmlNode list * ?Description: Giraffe.ViewEngine.HtmlElements.XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> 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 PlotlyJSReference.NoReference: PlotlyJSReference
val real: float list
val imaginary: float list
val pointSmith: GenericChart.GenericChart
type Chart = static member AnnotatedHeatmap: zData: seq<#seq<'a1>> * annotationText: seq<#seq<string>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?X: seq<'a3> * ?MultiX: seq<seq<'a3>> * ?XGap: int * ?Y: seq<'a4> * ?MultiY: seq<seq<'a4>> * ?YGap: int * ?Text: 'a5 * ?MultiText: seq<'a5> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?ZSmooth: SmoothAlg * ?Transpose: bool * ?UseWebGL: bool * ?ReverseYAxis: bool * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible and 'a5 :> IConvertible) + 1 overload static member Area: x: seq<#IConvertible> * y: seq<#IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: MarkerSymbol * ?MultiMarkerSymbol: seq<MarkerSymbol> * ?Marker: Marker * ?LineColor: Color * ?LineColorScale: Colorscale * ?LineWidth: float * ?LineDash: DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: Orientation * ?GroupNorm: GroupNorm * ?FillColor: Color * ?FillPatternShape: PatternShape * ?FillPattern: Pattern * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Bar: values: seq<#IConvertible> * ?Keys: seq<'a1> * ?MultiKeys: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerPatternShape: PatternShape * ?MultiMarkerPatternShape: seq<PatternShape> * ?MarkerPattern: Pattern * ?Marker: Marker * ?Base: #IConvertible * ?Width: 'a4 * ?MultiWidth: seq<'a4> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member BoxPlot: ?X: seq<'a0> * ?MultiX: seq<seq<'a0>> * ?Y: seq<'a1> * ?MultiY: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Text: 'a2 * ?MultiText: seq<'a2> * ?FillColor: Color * ?MarkerColor: Color * ?Marker: Marker * ?Opacity: float * ?WhiskerWidth: float * ?BoxPoints: BoxPoints * ?BoxMean: BoxMean * ?Jitter: float * ?PointPos: float * ?Orientation: Orientation * ?OutlineColor: Color * ?OutlineWidth: float * ?Outline: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?Notched: bool * ?NotchWidth: float * ?QuartileMethod: QuartileMethod * ?UseDefaults: bool -> GenericChart (requires 'a0 :> IConvertible and 'a1 :> IConvertible and 'a2 :> IConvertible) + 2 overloads static member Bubble: x: seq<#IConvertible> * y: seq<#IConvertible> * sizes: seq<int> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: MarkerSymbol * ?MultiMarkerSymbol: seq<MarkerSymbol> * ?Marker: Marker * ?LineColor: Color * ?LineColorScale: Colorscale * ?LineWidth: float * ?LineDash: DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: Orientation * ?GroupNorm: GroupNorm * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Candlestick: open : seq<#IConvertible> * high: seq<#IConvertible> * low: seq<#IConvertible> * close: seq<#IConvertible> * ?X: seq<'a4> * ?MultiX: seq<seq<'a4>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Text: 'a5 * ?MultiText: seq<'a5> * ?Line: Line * ?IncreasingColor: Color * ?Increasing: FinanceMarker * ?DecreasingColor: Color * ?Decreasing: FinanceMarker * ?WhiskerWidth: float * ?ShowXAxisRangeSlider: bool * ?UseDefaults: bool -> GenericChart (requires 'a4 :> IConvertible and 'a5 :> IConvertible) + 2 overloads static member Column: values: seq<#IConvertible> * ?Keys: seq<'a1> * ?MultiKeys: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerPatternShape: PatternShape * ?MultiMarkerPatternShape: seq<PatternShape> * ?MarkerPattern: Pattern * ?Marker: Marker * ?Base: #IConvertible * ?Width: 'a4 * ?MultiWidth: seq<'a4> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member Contour: zData: seq<#seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?X: seq<'a2> * ?MultiX: seq<seq<'a2>> * ?Y: seq<'a3> * ?MultiY: seq<seq<'a3>> * ?Text: 'a4 * ?MultiText: seq<'a4> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?Transpose: bool * ?ContourLineColor: Color * ?ContourLineDash: DrawingStyle * ?ContourLineSmoothing: float * ?ContourLine: Line * ?ContoursColoring: ContourColoring * ?ContoursOperation: ConstraintOperation * ?ContoursType: ContourType * ?ShowContourLabels: bool * ?ContourLabelFont: Font * ?Contours: Contours * ?FillColor: Color * ?NContours: int * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) static member Funnel: x: seq<#IConvertible> * y: seq<#IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Width: float * ?Offset: float * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?Orientation: Orientation * ?AlignmentGroup: string * ?OffsetGroup: string * ?MarkerColor: Color * ?MarkerOutline: Line * ?Marker: Marker * ?TextInfo: TextInfo * ?ConnectorLineColor: Color * ?ConnectorLineStyle: DrawingStyle * ?ConnectorFillColor: Color * ?ConnectorLine: Line * ?Connector: FunnelConnector * ?InsideTextFont: Font * ?OutsideTextFont: Font * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) static member Heatmap: zData: seq<#seq<'a1>> * ?X: seq<'a2> * ?MultiX: seq<seq<'a2>> * ?Y: seq<'a3> * ?MultiY: seq<seq<'a3>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?XGap: int * ?YGap: int * ?Text: 'a4 * ?MultiText: seq<'a4> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?ZSmooth: SmoothAlg * ?Transpose: bool * ?UseWebGL: bool * ?ReverseYAxis: bool * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) + 1 overload ...
static member Chart.PointSmith: realImag: seq<#System.IConvertible * #System.IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.PointSmith: real: seq<#System.IConvertible> * imag: seq<#System.IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'c * ?MultiText: seq<'c> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>
val toChartHTML: gChart: GenericChart.GenericChart -> string
val lineSmith: GenericChart.GenericChart
static member Chart.LineSmith: realImag: seq<#System.IConvertible * #System.IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?Fill: StyleParam.Fill * ?FillColor: Color * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.LineSmith: real: seq<#System.IConvertible> * imag: seq<#System.IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'c * ?MultiText: seq<'c> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?Fill: StyleParam.Fill * ?FillColor: Color * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
module StyleParam from Plotly.NET
type DrawingStyle = | Solid | Dash | Dot | DashDot | LongDash | LongDashDot | User of seq<int> member Convert: unit -> obj override ToString: unit -> string static member convert: (DrawingStyle -> obj) static member toString: (DrawingStyle -> string)
<summary> Dash: Sets the drawing style of the lines segments in this trace. Sets the style of the lines. Set to a dash string type or a dash length in px. </summary>
union case StyleParam.DrawingStyle.DashDot: StyleParam.DrawingStyle
type Color = override Equals: other: obj -> bool override GetHashCode: unit -> int static member fromARGB: a: int -> r: int -> g: int -> b: int -> Color static member fromColorScaleValues: c: seq<#IConvertible> -> Color static member fromColors: c: seq<Color> -> Color static member fromHex: s: string -> Color static member fromKeyword: c: ColorKeyword -> Color static member fromRGB: r: int -> g: int -> b: int -> Color static member fromString: c: string -> Color member Value: obj
<summary> Plotly color can be a single color, a sequence of colors, or a sequence of numeric values referencing the color of the colorscale obj </summary>
static member Color.fromKeyword: c: ColorKeyword -> Color
union case ColorKeyword.Purple: ColorKeyword
val bubbleSmith: GenericChart.GenericChart
static member Chart.BubbleSmith: realImagSizes: seq<#System.IConvertible * #System.IConvertible * int> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.BubbleSmith: real: seq<#System.IConvertible> * imag: seq<#System.IConvertible> * sizes: seq<int> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'c * ?MultiText: seq<'c> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
type TextPosition = | TopLeft | TopCenter | TopRight | MiddleLeft | MiddleCenter | MiddleRight | BottomLeft | BottomCenter | BottomRight | Auto ... member Convert: unit -> obj override ToString: unit -> string static member convert: (TextPosition -> obj) static member toString: (TextPosition -> string)
<summary> Sets the positions of the text elements. Note that not all options work for every type of trace, e.g. Pie Charts only support "inside" | "outside" | "auto" | "none" - Cartesian plots: Sets the positions of the text elements with respects to the (x,y) coordinates. - Pie Charts and derivatives: Specifies the location of the text with respects to the sector. </summary>
union case StyleParam.TextPosition.TopCenter: StyleParam.TextPosition