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-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 * $Value))) } } function Get-EarthRadius { <# .SYNOPSIS Get earth's radius at a given geodetic latitude .PARAMETER Latitude Latitude value in decimal degree format #> [CmdletBinding()] [OutputType([Double])] Param( [Parameter(Position=0, ValueFromPipeline=$true)] [ValidateRange(-90, 90)] [Double] $Latitude ) Process { $a = [Coordinate]::SemiMajorAxis $b = [Coordinate]::SemiMinorAxis $Beta = ConvertTo-Radian $Latitude [Math]::Sqrt( ([Math]::Pow(([Math]::Pow($a, 2) * [Math]::Cos($Beta)), 2) + [Math]::Pow(([Math]::Pow($b, 2) * [Math]::Sin($Beta)), 2)) / ([Math]::Pow(($a * [Math]::Cos($Beta)), 2) + [Math]::Pow(($b * [Math]::Sin($Beta)), 2)) ) } } function Get-Extremum { <# .SYNOPSIS Function to return extremum (maximum or minimum) of an array of numbers .EXAMPLE $Maximum = 1,2,3,4,5 | Get-Extremum -Max # 5 .EXAMPLE $Minimum = 1,2,3,4,5 | Get-Extremum -Min # 1 #> [Diagnostics.CodeAnalysis.SuppressMessageAttribute('PSReviewUnusedParameter', 'Maximum')] [Diagnostics.CodeAnalysis.SuppressMessageAttribute('PSReviewUnusedParameter', 'Minimum')] [CmdletBinding()] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Array] $InputObject, [Alias('Max')] [Switch] $Maximum, [Alias('Min')] [Switch] $Minimum ) Begin { function Invoke-GetExtremum { param ( [Parameter(Position=0)] [Array] $Values ) if ($Values.Count -gt 0) { $Type = Find-FirstTrueVariable 'Maximum','Minimum' $Values | Measure-Object -Maximum:$Maximum -Minimum:$Minimum | ForEach-Object { $_.$Type } } } Invoke-GetExtremum $InputObject } End { Invoke-GetExtremum $Input } } function Get-Factorial { <# .SYNOPSIS Return factorial of Value, Value!. .EXAMPLE Get-Factorial 10 # 3628800 #> [CmdletBinding()] [OutputType([Int32])] Param( [Parameter(Position=0, ValueFromPipeline=$true)] [Int] $Value ) Process { if ($Value -eq 0) { 1 } else { 1..$Value | Invoke-Reduce { Param($Acc,$Item) $Acc * $Item } -InitialValue 1 } } } function Get-Haversine { <# .SYNOPSIS Return haversine of an angle .DESCRIPTION The Haversine is most frequently used within the Haversine formula when calculating great-circle distance between two points on a sphere. Note: Available as static method of Prelude class - [Prelude]::Hav #> [CmdletBinding()] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Double] $Degrees ) Process { 0.5 * (1 - [Math]::Cos((ConvertTo-Radian $Degrees))) } } function Get-HaversineDistance { <# .SYNOPSIS Calculate the distance (in meters) between two geodetic coordinates on the earth using the "Haversine formula" #> [CmdletBinding()] [OutputType([Double])] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Coordinate] $From, [Parameter(Mandatory=$true, Position=1)] [Coordinate] $To ) $Radius = ((Get-EarthRadius $From.Latitude) + (Get-EarthRadius $To.Latitude)) / 2 $Radicand = (Get-Haversine ($To.Latitude - $From.Latitude)) + (([Math]::Cos((ConvertTo-Radian $From.Latitude))) * ([Math]::Cos((ConvertTo-Radian $To.Latitude))) * (Get-Haversine ($To.Longitude - $From.Longitude))) (2 * $Radius * [Math]::Asin([Math]::Sqrt($Radicand))) } 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 $Value } } } function Get-Maximum { <# .SYNOPSIS Wrapper for Get-Extremum with the -Maximum switch #> [CmdletBinding()] [Alias('max')] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Array] $Values ) Begin { if ($Values.Count -gt 0) { Get-Extremum -Maximum $Values } } End { if ($Input.Count -gt 0) { $Input | Get-Extremum -Maximum } } } function Get-Mean { <# .SYNOPSIS Calculate mean (average) for list of numerical values .DESCRIPTION Specifically, this function returns the "expected value" (mean) for a discrete uniform random variable. .PARAMETER Trim Return "trimmed" mean where a certain number of items from the beginning and end of the sorted data are excluded from the mean. Note: If this parameter value is in the range (0,1), it will be treated as a percentage. .EXAMPLE 1..10 | mean .EXAMPLE 1..10 | mean -Trim 1 #> [CmdletBinding()] [Alias('mean')] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Array] $Data, [ValidateRange(0, [Double]::PositiveInfinity)] [Double] $Trim = 0 ) End { if ($Input.Count -gt 0) { $Data = $Input } if ($Trim -gt 0 -and $Trim -lt 1) { $Trim = [Math]::Floor($Trim * $Data.Count) } $Data = $Data | Sort-Object $Data = $Data[$Trim..($Data.Count - 1 - $Trim)] ($Data | Measure-Object -Sum).Sum / $Data.Count } } function Get-Median { <# .SYNOPSIS Calculate median for list of numerical values .DESCRIPTION Specifically, this function returns the median for a discrete uniform random variable. .EXAMPLE 1..10 | median #> [CmdletBinding()] [Alias('median')] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Array] $Data ) End { if ($Input.Count -gt 0) { $Data = $Input } $Sorted = $Data | Sort-Object $Index = $Sorted.Count / 2 if ($Sorted.Count % 2 -eq 0) { $Left = $Sorted[$Index - 1] $Right = $Sorted[$Index] } else { $Left = [Math]::Floor($Sorted[$Index]) $Right = $Left } ($Left + $Right) / 2 } } function Get-Minimum { <# .SYNOPSIS Wrapper for Get-Extremum with the -Minimum switch #> [CmdletBinding()] [Alias('min')] Param( [Parameter(Mandatory=$true, Position=0, ValueFromPipeline=$true)] [Array] $Values ) Begin { if ($Values.Count -gt 0) { Get-Extremum -Minimum $Values } } End { if ($Input.Count -gt 0) { $Input | Get-Extremum -Minimum } } } |