src/applied.ps1
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function ConvertTo-Degree { <# .SYNOPSIS Convert radians to degrees #> [CmdletBinding()] [Alias('toDegree')] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Double] $Radians ) Process { ($Radians * (180 / [Math]::Pi)) % 360 } } function ConvertTo-Radian { <# .SYNOPSIS Convert degrees to radians #> [CmdletBinding()] [Alias('toRadian')] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Double] $Degrees ) Process { ($Degrees % 360) * ([Math]::Pi / 180) } } function Get-Haversine { <# .SYNOPSIS Return haversine of an angle .DESCRIPTION The Haversine is most frequently used within the Haversine formula when calculating great-circle distance between two points on a sphere. Note: Available as static method of Prelude class - [Prelude]::Hav #> [CmdletBinding()] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Double] $Degrees ) Process { 0.5 * (1 - [Math]::Cos((ConvertTo-Radian $Degrees))) } } function Get-ArcHaversine { <# .SYNOPSIS Return archaversine (ahav) of a value, in degrees. This is the inverse function of Get-Haversine. Note: Available as static method of Prelude class - [Prelude]::Ahav #> [CmdletBinding()] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Double] $Value ) Process { ConvertTo-Degree ([Math]::Acos(1 - (2 * $Value))) } } function Get-EarthRadius { <# .SYNOPSIS Get earth's radius at a given geographic latitude .PARAMETER Latitude Latitude value in decimal format #> [CmdletBinding()] [OutputType([Double])] Param( [Parameter(Position=0, ValueFromPipeline=$true)] [Double] $Latitude ) Process { $GeocentricLatitude = [Math]::Pow((1 - [Constant]::EarthFlattening), 2) * [Math]::Tan((ConvertTo-Radian $Latitude)) [Constant]::EarthSemiMajorAxis * (1 - ([Constant]::EarthFlattening * [Math]::Pow([Math]::Sin($GeocentricLatitude), 2))) } } function Get-LogisticSigmoid { <# .SYNOPSIS For a given value, x, returns value of logistic sigmoid function at x Note: Available as static method of Prelude class - [Prelude]::Sigmoid .DESCRIPTION The logistic sigmoid function is commonly used as an activation function within neural networks and to model population growth. .PARAMETER Midpoint Abscissa axis coordinate of logistic sigmoid function reflection point .PARAMETER MaximumValue Logistic sigmoid function maximum value .PARAMETER Derivative Switch parameter to determine which function to use, f(x) or f'(x) = f(x) * f(-x) #> [Diagnostics.CodeAnalysis.SuppressMessageAttribute('PSReviewUnusedParameter', '', Scope='Function')] [CmdletBinding()] [Alias('sigmoid')] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Alias('x')] [Double] $Value, [Alias('k')] [Double] $GrowthRate = 1, [Alias('x0')] [Double] $Midpoint = 0, [Alias('L')] [Double] $MaximumValue = 1, [Switch] $Derivative ) Process { $Sigmoid = { Param($x) $MaximumValue / (1 + [Math]::Pow([Constant]::Euler, -$GrowthRate * ($x - $Midpoint))) } if ($Derivative) { (& $Sigmoid $Value) * (& $Sigmoid -$Value) } else { & $Sigmoid $Value } } } |