tests/applied.Tests.ps1
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& (Join-Path $PSScriptRoot '_setup.ps1') 'applied' Describe 'ConvertTo-Degree' -Tag 'Local', 'Remote' { It 'can convert radian values to degrees' { $PI = [Math]::Pi 0 | ConvertTo-Degree | Should -Be 0 ($PI / 2) | ConvertTo-Degree | Should -Be 90 $PI | ConvertTo-Degree | Should -Be 180 0, (2 * $PI), (4 * $PI) | ConvertTo-Degree | Should -Be 0, 0, 0 } } Describe 'ConvertTo-Radian' -Tag 'Local', 'Remote' { It 'can convert degree values to radians' { $PI = [Math]::Pi 0 | ConvertTo-Radian | Should -Be 0 90 | ConvertTo-Radian | Should -Be ($PI / 2) 180 | ConvertTo-Radian | Should -Be $PI 360 | ConvertTo-Radian | Should -Be 0 0, 360, 720 | ConvertTo-Radian | Should -Be 0, 0, 0 } } Describe 'Get-EarthRadius' -Tag 'Local', 'Remote' { It 'can return earth radius for a given latitude' { $SemiMajorAxis = [Datum]::SemiMajorAxis $SemiMinorAxis = [Datum]::SemiMinorAxis -90 | Get-EarthRadius | Should -Be $SemiMinorAxis -Because 'the radius is equal to semi-minor axis at the poles' Get-EarthRadius | Should -Be $SemiMajorAxis 0 | Get-EarthRadius | Should -Be $SemiMajorAxis -Because 'the radius is equal to semi-major axis at the equator' [Math]::Round((23.437055555555556 | Get-EarthRadius), 4) | Should -Be 6374777.8209 -Because 'it is the Northern Tropic latitude' [Math]::Round((45 | Get-EarthRadius), 4) | Should -Be 6367489.5439 90 | Get-EarthRadius | Should -Be $SemiMinorAxis -Because 'the radius is equal to semi-minor axis at the poles' } } Describe 'Get-Extremum' -Tag 'Local', 'Remote' { It 'can return maximum value from array of numbers' { $Max = 5 $Values = 1, 2, 2, 1, $Max, 2, 3 $Values | Get-Extremum -Max | Should -Be $Max Get-Extremum -Max $Values | Should -Be $Max 0, -1, 4, 2, 7, 2, 0 | Get-Extremum -Max | Should -Be 7 } It 'can return minimum value from array of numbers' { $Min = 0 $Values = 1, 2, 2, 1, $Min, 2, 3 $Values | Get-Extremum -Min | Should -Be $Min Get-Extremum -Min $Values | Should -Be $Min 0, -1, 4, 2, 7, 2, 0 | Get-Extremum -Min | Should -Be -1 } It 'Get-Maximum' { $Max = 5 $Values = 1, 2, 2, 1, $Max, 2, 3 $Values | Get-Maximum | Should -Be $Max Get-Maximum $Values | Should -Be $Max 0, -1, 4, 2, 7, 2, 0 | Get-Maximum | Should -Be 7 } It 'Get-Minimum' { $Min = 0 $Values = 1, 2, 2, 1, $Min, 2, 3 $Values | Get-Minimum | Should -Be $Min Get-Minimum $Values | Should -Be $Min 0, -1, 4, 2, 7, 2, 0 | Get-Minimum | Should -Be -1 } } Describe 'Get-Factorial' -Tag 'Local', 'Remote' { It 'can calculate n!' { 0 | Get-Factorial | Should -Be 1 1 | Get-Factorial | Should -Be 1 2 | Get-Factorial | Should -Be 2 10 | Get-Factorial | Should -Be 3628800 20 | Get-Factorial | Should -Be 2432902008176640000 1..5 | Get-Factorial | Should -Be 1, 2, 6, 24, 120 Get-Factorial 2 | Should -Be 2 Get-Factorial 10 | Should -Be 3628800 } It 'can calculate n! for large n values (n = 200)' { $Value = [BigInt]::Parse('788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000') $Result = 200 | Get-Factorial $Result | Should -Be $Value $Result.GetType().Name | Should -Be 'BigInteger' } } Describe 'Get-Haversine/ArcHaversine' -Tag 'Local', 'Remote' { It 'should return a value in the range [0..1]' { 42, 50, 77 | Get-Haversine | ForEach-Object { [Math]::Round($_, 5) } | Should -Be 0.12843, 0.17861, 0.38752 0.12843, 0.17861, 0.38752 | Get-ArcHaversine | ForEach-Object { [Math]::Round($_) } | Should -Be 42, 50, 77 42, 50, 77 | Get-Haversine | Get-ArcHaversine | Should -Be 42, 50, 77 } } Describe 'Get-HaversineDistance' -Tag 'Local', 'Remote' { It 'can calculate the distance between two points on the earth' { Get-HaversineDistance -From @{} -To @{} | Should -Be 0 $Omaha = @{ Latitude = 41.25; Longitude = -96 } $SanDiego = @{ Latitude = 32.7157; Longitude = -117.1611 } [Math]::Round((Get-HaversineDistance -From $Omaha -To $SanDiego), 4) | Should -Be 2097705.7401 [Math]::Round(($Omaha | Get-HaversineDistance -To $SanDiego), 4) | Should -Be 2097705.7401 } } Describe 'Get-LogisticSigmoid' -Tag 'Local', 'Remote' { It 'can return values along the logistic sigmoid curve' { 0 | Get-LogisticSigmoid | Should -Be 0.5 [Double]::NegativeInfinity | Get-LogisticSigmoid | Should -Be 0 [Double]::PositiveInfinity | Get-LogisticSigmoid | Should -Be 1 [Double]::PositiveInfinity | Get-LogisticSigmoid -MaximumValue 3 | Should -Be 3 0 | Get-LogisticSigmoid -Derivative | Should -Be 0.25 $Left = [Math]::Round((Get-LogisticSigmoid -5), 10) $Right = [Math]::Round(1 - (Get-LogisticSigmoid 5), 10) $Left | Should -Be $Right -Because 'it is a symmetry property of the logistic function' } } Describe 'Get-Mean/Median' -Tag 'Local', 'Remote' { It 'can calculate mean (average) for discrete uniform random variable' { 1..10 | Get-Mean | Should -Be 5.5 Get-Mean -Data (1..10) | Should -Be 5.5 1, 3, 4, 5, 6, 9, 14, 30 | Get-Mean | Should -Be 9 30, 4, 3, 1, 6, 9, 14, 5 | Get-Mean | Should -Be 9 $Population = 4779736, 710231, 6392017, 2915918, 37253956, 5029196, 3574097, 897934 $Population | Get-Mean | Should -Be 7694135.625 } It 'can calculate "trimmed" mean' { 1..10 | Get-Mean -Trim 0.1 | Should -Be 5.5 -Because '1..10 and 2..9 have the same mean' Get-Mean -Data (1..10) -Trim 0.1 | Should -Be 5.5 (1..10 | Get-Mean -Trim 1), (1..10 | Get-Mean -Trim 1) | Test-Equal | Should -BeTrue -Because '10% of 10 is 1' 1, 3, 4, 5, 6, 9, 14, 30 | Get-Mean -Trim 2 | Should -Be 6 30, 4, 3, 1, 6, 9, 14, 5 | Get-Mean -Trim 2 | Should -Be 6 (30, 4, 3, 1, 6, 9, 14, 5 | Get-Mean -Trim 2), (30, 4, 3, 1, 6, 9, 14, 5 | Get-Mean -Trim 0.25) | Test-Equal | Should -BeTrue '25% of 8 is 2' } It 'can calculate median for discrete uniform random variable' { 1..5 | Get-Median | Should -Be 3 2, 1, 4, 5, 3 | Get-Median | Should -Be 3 1..10 | Get-Median | Should -Be 5.5 19, 3, 6, 7, 1, 9, 2, 5, 4, 8 | Get-Median | Should -Be 5.5 Get-Median -Data (1..5) | Should -Be 3 Get-Median -Data (1..10) | Should -Be 5.5 } } Describe 'Get-Permutation' -Tag 'Local', 'Remote' { It 'can return permutations for a given group of items' { Get-Permutation 'ab' | Should -Be @('a', 'b'), @('b', 'a') Get-Permutation 'abc' | Should -Be @('a', 'b', 'c'), @('a', 'c', 'b'), @('c', 'a', 'b'), @('c', 'b', 'a'), @('b', 'c', 'a'), @('b', 'a', 'c') Get-Permutation 2 | Should -Be @(0, 1), @(1, 0) Get-Permutation 2 1 | Should -Be @(1, 2), @(2, 1) Get-Permutation 3 | Should -Be @(0, 1, 2), @(0, 2, 1), @(1, 0, 2), @(1, 2, 0), @(2, 0, 1), @(2, 1, 0) Get-Permutation 3 1 | Should -Be @(1, 2, 3), @(1, 3, 2), @(2, 1, 3), @(2, 3, 1), @(3, 1, 2), @(3, 2, 1) Get-Permutation 1, 2, 3 | Should -Be @(1, 2, 3), @(1, 3, 2), @(3, 1, 2), @(3, 2, 1), @(2, 3, 1), @(2, 1, 3) Get-Permutation 4 | Select-Object -First 10 | Should -Be @(0, 1, 2, 3), @(0, 1, 3, 2), @(0, 2, 1, 3), @(0, 2, 3, 1), @(0, 3, 1, 2), @(0, 3, 2, 1), @(1, 0, 2, 3), @(1, 0, 3, 2), @(1, 2, 0, 3), @(1, 2, 3, 0) } It 'can return permutations for a given group of items via pipeline' { 'ab' | Get-Permutation | Should -Be @('a', 'b'), @('b', 'a') 'abc' | Get-Permutation | Should -Be @('a', 'b', 'c'), @('a', 'c', 'b'), @('c', 'a', 'b'), @('c', 'b', 'a'), @('b', 'c', 'a'), @('b', 'a', 'c') 'foo', 'bar' | Get-Permutation | Should -Be @('foo', 'bar'), @('bar', 'foo') 2 | Get-Permutation | Should -Be @(0, 1), @(1, 0) 2 | Get-Permutation -Offset 1 | Should -Be @(1, 2), @(2, 1) 3 | Get-Permutation | Should -Be @(0, 1, 2), @(0, 2, 1), @(1, 0, 2), @(1, 2, 0), @(2, 0, 1), @(2, 1, 0) 1, 2, 3 | Get-Permutation | Should -Be @(1, 2, 3), @(1, 3, 2), @(3, 1, 2), @(3, 2, 1), @(2, 3, 1), @(2, 1, 3) } It 'can can string concatenate output' { 'cat' | Get-Permutation -Words | Should -Be 'cat', 'cta', 'tca', 'tac', 'atc', 'act' 'foo', 'bar' | Get-Permutation -Words | Should -Be @('foobar'), @('barfoo') 1..3 | Get-Permutation -Words | Should -Be '123', '132', '312', '321', '231', '213' } It 'can handle null values' { $Permutations = $Null, 1, 3 | Get-Permutation $Permutations | ForEach-Object Count | Get-Maximum | Should -Be 3 $Permutations | Should -HaveCount 6 $Permutations = 1, $Null, 3 | Get-Permutation $Permutations | ForEach-Object Count | Get-Maximum | Should -Be 3 $Permutations | Should -HaveCount 6 } It 'can return k-permutations' { 1..3 | Get-Permutation -Choose 1 | Should -Be @(1), @(3), @(2) 1..3 | Get-Permutation -Choose 2 | Should -Be @(1, 2), @(1, 3), @(3, 1), @(3, 2), @(2, 3), @(2, 1) 1..3 | Get-Permutation | Should -Be @(1, 2, 3), @(1, 3, 2), @(3, 1, 2), @(3, 2, 1), @(2, 3, 1), @(2, 1, 3) 3 | Get-Permutation -Choose 1 | Should -Be @(0), @(1), @(2) 3 | Get-Permutation | Should -Be @(0, 1, 2), @(0, 2, 1), @(1, 0, 2), @(1, 2, 0), @(2, 0, 1), @(2, 1, 0) 'cat' | Get-Permutation -Choose 2 -Words | Should -Be 'ca', 'ct', 'tc', 'ta', 'at', 'ac' } It 'can return k-permutations with unique elements (combinations)' { $Results = 1..3 | Get-Permutation -Unique $Results -join '' | Should -Be '123' -Because 'combinations count by membership, not order' 1..3 | Get-Permutation -Choose 2 -Unique | Should -Be @(1, 2), @(1, 3), @(2, 3) -Because 'combinations count by membership, not order' 3 | Get-Permutation -Choose 2 -Unique | Should -Be @(0, 1), @(0, 2), @(1, 2) -Because 'combinations count by membership, not order' # 6 | Get-Permutation -Choose 4 -Unique | Should -HaveCount 15 -Because 'the number of items returned obeys a simple formula' 'cat' | Get-Permutation -Choose 2 -Unique -Words | Should -Be 'ca', 'ct', 'at' 'hello' | Get-Permutation -Choose 2 -Unique -Words | Should -Be 'he', 'hl', 'hl', 'ho', 'el', 'el', 'eo', 'll', 'lo', 'lo' 'hello' | Get-Permutation -Choose 3 -Unique -Words | Should -Be 'hel', 'hel', 'heo', 'hll', 'hlo', 'hlo', 'ell', 'elo', 'elo', 'llo' } } Describe 'Get-Sum' -Tag 'Local', 'Remote' { It 'can return the sum of a list of numbers' { 1..5 | Get-Sum | Should -Be 15 1, 1, 1, 1, 1 | Get-Sum | Should -Be 5 1..100 | Get-Sum | Should -Be 5050 Get-Sum -Values (1..100) | Should -Be 5050 } It 'can return the weighted sum of a list of numbers' { 1, 1, 1, 1, 1 | Get-Sum -Weight 1, 2, 3, 4, 5 | Should -Be 15 Get-Sum -Values 1, 1, 1, 1, 1 -Weight 1, 2, 3, 4, 5 | Should -Be 15 } } Describe 'Get-Variance / Get-Covariance' -Tag 'Local', 'Remote' { It 'can return variance for discrete uniform random variable' { $X = 1..10 $Biased = $X | Get-Variance $Unbiased = [Math]::Round(($X | Get-Variance -Sample), 2) $Biased | Should -Be 8.25 $Unbiased | Should -Be 9.17 [Math]::Round((($Unbiased * ($X.Count - 1)) / $X.Count), 2) | Should -Be $Biased Get-Variance $X | Should -Be 8.25 [Math]::Round((Get-Variance $X -Sample), 2) | Should -Be 9.17 } It 'can return coovariance of two discrete uniform random variables' { $X = 1..5 $X, $X | Get-Covariance | Should -Be (Get-Variance $X) -Because 'Cov(x,x) = Var(x)' Get-Covariance $X, $X | Should -Be (Get-Variance $X) -Because 'Cov(x,x) = Var(x)' $X = 1692, 1978, 1884, 2151, 2519 $Y = 68, 102, 110, 112, 154 $X, $Y | Get-Covariance -Sample | Should -Be 9107.30 $X, $Y | Get-Covariance | Should -Be (Get-Covariance $Y, $X) } } |