tests/applied.Tests.ps1
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& (Join-Path $PSScriptRoot '_setup.ps1') 'applied' Describe 'Constant Class' { It 'provides immutable values' { [Math]::Round([ConstantTest]::Phi, 3) | Should -Be 1.618 { [ConstantTest]::Phi = 5 } | Should -Throw -Because 'constants are immutable' } } Describe 'Coordinate Class' { It 'can dynamically assign cardinal directions at constuction' { $A = [CoordinateTest]::New(37, -111) $A.Hemisphere | Should -Be 'N','W' $A = [CoordinateTest]::New(-41.25, 96.4) $A.Hemisphere | Should -Be 'S','E' $A = [CoordinateTest]@{ Latitude = 37; Longitude = -111 } $A.Hemisphere | Should -Be 'N','W' $A = [CoordinateTest]@{ Latitude = -41; Longitude = 96.4 } $A.Hemisphere | Should -Be 'S','E' } It 'can convert geodetic values to cartesian' { [CoordinateTest]::ToCartesian(41.25, 96.0) | ForEach-Object { [Math]::Round($_, 5) } | Should -Be -501980.22547,4776022.81393,4183337.2134 [CoordinateTest]::ToCartesian(41.25, 96.0, 1000) | ForEach-Object { [Math]::Round($_, 5) } | Should -Be -502058.81413,4776770.53508,4183996.55921 [CoordinateTest]::ToCartesian(41.25, 96.0, 10000) | ForEach-Object { [Math]::Round($_, 5) } | Should -Be -502766.11207,4783500.02543,4189930.67155 [CoordinateTest]::ToCartesian(41.25, 96.0, 100000) | ForEach-Object { [Math]::Round($_, 5) } | Should -Be -509839.09144,4850794.92896,4249271.79491 } It 'can convert cartesian to geodetic' { $X = -501980.22547 $Y = 4776022.81393 $Z = 4183337.2134 [CoordinateTest]::ToGeodetic($X, $Y, $Z) | ForEach-Object { [Math]::Round($_, 2) } | Should -Be 41.25,96,0 $X = -502058.81413 $Y = 4776770.53508 $Z = 4183996.55921 [CoordinateTest]::ToGeodetic($X, $Y, $Z) | ForEach-Object { [Math]::Round($_, 2) } | Should -Be 41.25,96,1000 $X = -502766.11207 $Y = 4783500.02543 $Z = 4189930.67155 [CoordinateTest]::ToGeodetic($X, $Y, $Z) | ForEach-Object { [Math]::Round($_, 2) } | Should -Be 41.25,96,10000 $X = -509839.09144 $Y = 4850794.92896 $Z = 4249271.79491 [CoordinateTest]::ToGeodetic($X, $Y, $Z) | ForEach-Object { [Math]::Round($_, 2) } | Should -Be 41.25,96,100000 $X = -501980.22547 $Y = 4776022.81393 $Z = 4183337.2134 $Geodetic = [CoordinateTest]::FromCartesian($X, $Y, $Z) [Math]::Round($Geodetic.Latitude, 2) | Should -Be 41.25 [Math]::Round($Geodetic.Longitude, 2) | Should -Be 96 [Math]::Round($Geodetic.Height, 2) | Should -Be 0 } It 'can convert decimal to sexagesimal' { [CoordinateTest]::ToSexagesimal(32.7157) | Should -Be 32,42,56.52 [CoordinateTest]::ToSexagesimal(96) | Should -Be 96,0,0 [CoordinateTest]::ToSexagesimal(116.7762) | Should -Be 116,46,34.32 [CoordinateTest]::ToSexagesimal(-116.7762) | Should -Be -116,46,34.32 } } Describe 'ConvertTo-Degree' { 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' { 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' { It 'can return earth radius for a given latitude' { $SemiMajorAxis = [CoordinateTest]::SemiMajorAxis $SemiMinorAxis = [CoordinateTest]::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' { 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' { 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 $Result.GetType().Name | Should -Be 'BigInteger' } } Describe 'Get-Haversine/ArcHaversine' { It 'should return a value in the range [0..1]' { 42,50,77 | Get-Haversine | ForEach-Object { [Math]::Round($_, 5) } | Should -Be 0.12843,0.17861,0.38752 0.12843,0.17861,0.38752 | Get-ArcHaversine | ForEach-Object { [Math]::Round($_) } | Should -Be 42,50,77 42,50,77 | Get-Haversine | Get-ArcHaversine | Should -Be 42,50,77 } It -Skip 'should be provided via static method of Prelude class' { [PreludeTest]::Hav(42), [PreludeTest]::Hav(50), [PreludeTest]::Hav(77) | ForEach-Object { [Math]::Round($_, 5) } | Should -Be 0.12843,0.17861,0.38752 } } Describe 'Get-HaversineDistance' { 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' { 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' { 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' { 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' { 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' { 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) } } |