tests/Matrix.Tests.ps1
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& (Join-Path $PSScriptRoot '_setup.ps1') 'matrix' Describe 'Matrix class static methods' { It 'can create an NxN multi-dimensional array' { $N = 5 $Matrix = [MatrixTest]::New($N) $Matrix.Rows.Count | Should -Be $N $Matrix.Rows[0].Count | Should -Be $N } It 'can create an MxN multi-dimensional array' { $M = 8 $N = 6 $Matrix = [MatrixTest]::New($M,$N) $Matrix.Rows.Count | Should -Be $M $Matrix.Rows[0].Count | Should -Be $N } It 'can create unit matrices' { $Unit = [MatrixTest]::Unit(1) $Unit.Size | Should -Be 1,1 $Unit.Rows[0] | Should -Be 1 $Unit = [MatrixTest]::Unit(2) $Unit.Size | Should -Be 2,2 $Unit.Rows[0] | Should -Be 1,1 $Unit.Rows[1] | Should -Be 1,1 $Unit = [MatrixTest]::Unit(3) $Unit.Size | Should -Be 3,3 $Unit.Rows[0] | Should -Be 1,1,1 $Unit.Rows[1] | Should -Be 1,1,1 $Unit.Rows[2] | Should -Be 1,1,1 } It 'can create identity matrices' { $Identity = [MatrixTest]::Identity(2) $Identity.Size | Should -Be 2,2 $Identity.Rows[0] | Should -Be 1,0 $Identity.Rows[1] | Should -Be 0,1 $Identity = [MatrixTest]::Identity(4) $Identity.Size | Should -Be 4,4 $Identity.Rows[0] | Should -Be 1,0,0,0 $Identity.Rows[1] | Should -Be 0,1,0,0 $Identity.Rows[2] | Should -Be 0,0,1,0 $Identity.Rows[3] | Should -Be 0,0,0,1 } It 'can transpose matrices' { $A = [MatrixTest]::New(3) $A.Rows = (1..9) $Transposed = [MatrixTest]::Transpose($A) $Transposed.Rows[0] | Should -Be 1,4,7 $Transposed.Rows[1] | Should -Be 2,5,8 $Transposed.Rows[2] | Should -Be 3,6,9 $Original = [MatrixTest]::Transpose($Transposed) $A | Test-Equal $Original | Should -BeTrue $A = [MatrixTest]::New(3,2) $A.Rows = (1..6) $T = [MatrixTest]::Transpose($A) $T.Rows[0] | Should -Be 1,3,5 $T.Rows[1] | Should -Be 2,4,6 } It 'can add two or more Matrices' { $A = [MatrixTest]::Identity(2) $Sum = [MatrixTest]::Add($A,$A) $Sum.Rows[0] | Should -Be 2,0 $Sum.Rows[1] | Should -Be 0,2 $Sum = [MatrixTest]::Add($A,$A,$A) $Sum.Rows[0] | Should -Be 3,0 $Sum.Rows[1] | Should -Be 0,3 } It 'can calculate the determinant for 2x2 matrices' { [MatrixTest]::Det([MatrixTest]::Unit(2)) | Should -Be 0 [MatrixTest]::Det([MatrixTest]::Identity(2)) | Should -Be 1 $A = [MatrixTest]::New(2) $A.Rows = (1..4) [MatrixTest]::Det($A) | Should -Be -2 } It 'can calculate the determinant for 3x3 matrices' { [MatrixTest]::Det([MatrixTest]::Unit(3)) | Should -Be 0 [MatrixTest]::Det([MatrixTest]::Identity(3)) | Should -Be 1 $A = [MatrixTest]::New(3) $A.Rows[0] = 2,3,-4 $A.Rows[1] = 0,-4,2 $A.Rows[2] = 1,-1,5 [MatrixTest]::Det($A) | Should -Be -46 $A = [MatrixTest]::New(3) $A.Rows[0] = 1,2,3 $A.Rows[1] = 4,-2,3 $A.Rows[2] = 2,5,-1 [MatrixTest]::Det($A) | Should -Be 79 } It 'can calculate the determinant for 4x4 matrices' { [MatrixTest]::Det([MatrixTest]::Unit(4)) | Should -Be 0 [MatrixTest]::Det([MatrixTest]::Identity(4)) | Should -Be 1 $A = [MatrixTest]::New(4) $A.Rows[0] = 3,-2,-5,4 $A.Rows[1] = -5,2,8,-5 $A.Rows[2] = -2,4,7,-3 $A.Rows[3] = 2,-3,-5,8 [MatrixTest]::Det($A) | Should -Be -54 $A = [MatrixTest]::New(4) $A.Rows[0] = 5,4,2,1 $A.Rows[1] = 2,3,1,-2 $A.Rows[2] = -5,-7,-3,9 $A.Rows[3] = 1,-2,-1,4 [MatrixTest]::Det($A) | Should -Be 38 } It 'can calculate the determinant for matrices larger than 4x4' { [MatrixTest]::Det([MatrixTest]::Unit(10)) | Should -Be 0 [MatrixTest]::Det([MatrixTest]::Identity(10)) | Should -Be 1 $A = [MatrixTest]::New(6) $A.Rows[0] = 12,22,14,17,20,10 $A.Rows[1] = 16,-4,7,1,-2,15 $A.Rows[2] = 10,-3,-2,3,-2,8 $A.Rows[3] = 7,12,8,9,11,6 $A.Rows[4] = 11,2,4,-8,1,9 $A.Rows[5] = 24,6,6,3,4,22 [MatrixTest]::Det($A) | Should -Be 12228 } It 'can produce the dot product of two matrices' { $Identity = [MatrixTest]::Identity(2) $A = $Identity.Clone() $A.Rows[1][1] = 0 $B = $Identity.Clone() $B.Rows[0][0] = 0 $Product = [MatrixTest]::Dot($A,$B) $Product.Size | Should -Be 2,2 $Product.Rows[0] | Should -Be 0,0 -Because 'the dot product of orthogonal matrices should be zero' $Product.Rows[1] | Should -Be 0,0 -Because 'the dot product of orthogonal matrices should be zero' $A.Rows[0] = 1,2 $A.Rows[1] = 3,4 $B.Rows[0] = 1,1 $B.Rows[1] = 0,2 $Product = [MatrixTest]::Dot($A,$B) $Product.Rows[0] | Should -Be 1,5 $Product.Rows[1] | Should -Be 3,11 $Product = [MatrixTest]::Dot($B,$A) $Product.Rows[0] | Should -Be 4,6 -Because 'the dot product is not commutative' $Product.Rows[1] | Should -Be 6,8 -Because 'the dot product is not commutative' $A = [MatrixTest]::New(1,2) $A.Rows[0] = 2,1 $B = [MatrixTest]::New(2,3) $B.Rows[0] = 1,-2,0 $B.Rows[1] = 4,5,-3 $Product = [MatrixTest]::Dot($A,$B) $Product.Size | Should -Be 1,3 -Because 'dot product supports matrices of different sizes' $Product.Rows[0] | Should -Be 6,1,-3 $A = [MatrixTest]::New(2) $A.Rows[0] = 2,5 $A.Rows[1] = 1,3 $B = [MatrixTest]::New(2) $B.Rows[0] = 3,-5 $B.Rows[1] = -1,2 [MatrixTest]::Dot($A,$B) | Test-Equal $Identity | Should -BeTrue -Because '$A and $B are invertible' } It 'can multiply matrices by a scalar constant' { $A = [MatrixTest]::Identity(2) [MatrixTest]::Add($A,$A,$A) | Test-Equal ([MatrixTest]::Multiply($A,3)) | Should -BeTrue $Product = [MatrixTest]::Multiply($A,7) $Product.Rows[0] | Should -Be 7,0 $Product.Rows[1] | Should -Be 0,7 } It 'can calulate the inverse of a given matrix' { $A = [MatrixTest]::New(3); $A.Rows[0] = 1,2,3 $A.Rows[1] = 2,3,4 $A.Rows[2] = 1,5,7 $Inverse = [MatrixTest]::Invert($A) $Inverse.Rows[0] | Should -Be 0.5,0.5,-0.5 $Inverse.Rows[1] | Should -Be -5,2,1 $Inverse.Rows[2] | Should -Be 3.5,-1.5,-0.5 [MatrixTest]::Dot($A,$Inverse) | Test-Equal ([MatrixTest]::Identity(3)) | Should -BeTrue -Because 'the dot product of a matrix and its inverse is the identity matrix' } It 'can return the trace of a matrix' { $A = [MatrixTest]::New(3); $A.Rows = 1..9 [MatrixTest]::Trace($A) | Should -Be 15 } } Describe 'Matrix class instance' { It 'does not allow for setting matrix Size' { $A = [MatrixTest]::Identity(3) $A.Size | Should -Be 3,3 { $A.Size = 2,2,2 } | Should -Throw } It 'will ensure row and column data adheres to restrictions of matrix size' { $A = [MatrixTest]::New(3) $A.Rows = (1..9) $A.Rows[0] | Should -Be 1,2,3 $A.Rows[1] | Should -Be 4,5,6 $A.Rows[2] | Should -Be 7,8,9 $A = [MatrixTest]::New(2) $A.Rows = (1..9) $A.Rows[0] | Should -Be 1,2 $A.Rows[1] | Should -Be 3,4 -Because 'row length will be maintained by truncating input' $A = [MatrixTest]::New(2) $A.Rows = 1,2,3 $A.Rows[0] | Should -Be 1,2 $A.Rows[1] | Should -Be 3,0 $A = [MatrixTest]::New(2, 3) $A.Rows = (1..6) $A.Rows[0] | Should -Be 1,2,3 $A.Rows[1] | Should -Be 4,5,6 -Because 'non-square sizes should be supported' } It 'provides iterator of index element index pairs' { $A = [MatrixTest]::New(3) $A.Indexes() | Should -HaveCount 9 } It 'can create clones' { $A = [MatrixTest]::New(2) $A.Rows = (1..4) $Clone = $A.Clone() $Clone.Rows[0] | Should -Be 1,2 $Clone.Rows[1] | Should -Be 3,4 } It 'can remove rows' { $A = [MatrixTest]::New(3) $A.Rows = (1..9) $Edited = $A.RemoveRow(0) $Edited.Size | Should -Be 2,3 $Edited.Rows[0] | Should -Be 4,5,6 $Edited.Rows[1] | Should -Be 7,8,9 $Edited = $A.RemoveRow(1) $Edited.Size | Should -Be 2,3 $Edited.Rows[0] | Should -Be 1,2,3 $Edited.Rows[1] | Should -Be 7,8,9 $Edited = $A.RemoveRow(2) $Edited.Size | Should -Be 2,3 $Edited.Rows[0] | Should -Be 1,2,3 $Edited.Rows[1] | Should -Be 4,5,6 $Edited = $A.RemoveRow(2).RemoveColumn(0) } It 'can remove columns' { $A = [MatrixTest]::New(3) $A.Rows = (1..9) $Edited = $A.RemoveColumn(0) $Edited.Size | Should -Be 3,2 $Edited.Rows[0] | Should -Be 2,3 $Edited.Rows[1] | Should -Be 5,6 $Edited.Rows[2] | Should -Be 8,9 $Edited = $A.RemoveColumn(1) $Edited.Size | Should -Be 3,2 $Edited.Rows[0] | Should -Be 1,3 $Edited.Rows[1] | Should -Be 4,6 $Edited.Rows[2] | Should -Be 7,9 $Edited = $A.RemoveColumn(2) $Edited.Size | Should -Be 3,2 $Edited.Rows[0] | Should -Be 1,2 $Edited.Rows[1] | Should -Be 4,5 $Edited.Rows[2] | Should -Be 7,8 $Edited = $A.RemoveColumn(0).RemoveRow(0) $Edited.Size | Should -Be 2,2 $Edited.Rows[0] | Should -Be 5,6 $Edited.Rows[1] | Should -Be 8,9 } It 'can be converted to string output' { $A = [MatrixTest]::New(2) $A.Rows = (1..4) $A.ToString() | ConvertTo-Json | Should -Be '"1,2\r\n3,4"' [MatrixTest]::Unit(3).ToString() | ConvertTo-Json | Should -Be '"1,1,1\r\n1,1,1\r\n1,1,1"' } } Describe 'Matrix helper functions' { It 'can provide wrapper for matrix creation' { $A = 1..9 | New-Matrix 3,3 $A.Size | Should -Be 3,3 $A.Rows[0] | Should -Be 1,2,3 $A.Rows[1] | Should -Be 4,5,6 $A.Rows[2] | Should -Be 7,8,9 $A = New-Matrix -Size 3,3 -Values (1..9) $A.Size | Should -Be 3,3 $A.Rows[0] | Should -Be 1,2,3 $A.Rows[1] | Should -Be 4,5,6 $A.Rows[2] | Should -Be 7,8,9 $A = New-Matrix $A.Size | Should -Be 2,2 -Because '2x2 is the default matrix size' $A.Rows[0] | Should -Be 0,0 -Because 'an empty matrix should be created by default' $A.Rows[1] | Should -Be 0,0 -Because 'an empty matrix should be created by default' $A = @(1,2,3,@(4,5,6)) | New-Matrix 2,3 $A = 1..6 | New-Matrix 2,3 $A.Rows[0] | Should -Be 1,2,3 -Because 'function accepts non-square sizes' $A.Rows[1] | Should -Be 4,5,6 -Because 'values array should be flattened' } It 'can create diagonal matrices' { $A = 1..3 | New-Matrix 3,3 -Diagonal $A.Size | Should -Be 3,3 $A.Rows[0] | Should -Be 1,0,0 $A.Rows[1] | Should -Be 0,2,0 $A.Rows[2] | Should -Be 0,0,3 $A = New-Matrix -Values (1..3) -Size 3,3 -Diagonal $A.Size | Should -Be 3,3 $A.Rows[0] | Should -Be 1,0,0 $A.Rows[1] | Should -Be 0,2,0 $A.Rows[2] | Should -Be 0,0,3 } It 'can test if a matrix is diagonal' { 1,0,0, 0,2,0, 0,0,3 | New-matrix 3,3 | Test-DiagonalMatrix | Should -BeTrue 1,0,0, 2,2,0, 3,0,3 | New-Matrix 3,3 | Test-DiagonalMatrix | Should -BeFalse -Because 'second and third rows have non-zero elements off the main diagonal' 1,0,0, 0,2,1, 0,0,3 | New-Matrix 3,3 | Test-DiagonalMatrix | Should -BeFalse -Because 'second row has a non-zero element off the main diagonal' 1,0, 0,1 | New-Matrix | Test-DiagonalMatrix | Should -BeTrue 1,0,0, 0,2,0 | New-matrix 2,3 | Test-DiagonalMatrix | Should -BeFalse -Because 'only square matrices can be diagonal' 1,0,2, 0,2,2 | New-matrix 2,3 | Test-DiagonalMatrix | Should -BeFalse -Because 'only square matrices can be diagonal' } It 'can test if a matrix is square' { (1..4) | New-Matrix | Test-SquareMatrix | Should -BeTrue (1..9) | New-Matrix 3,3 | Test-SquareMatrix | Should -BeTrue (1..6) | New-Matrix 3,2 | Test-SquareMatrix | Should -BeFalse -Because 'the # of rows and # of columns are different' } It 'can test if a matrix is symmetric' { 1,2,3, 2,1,4, 3,4,1 | New-Matrix 3,3 | Test-SymmetricMatrix | Should -BeTrue (1..9) | New-Matrix 3,3 | Test-SymmetricMatrix | Should -BeFalse -Because 'elements off main diagonal are not equal' 1,1,1,1 | New-Matrix | Test-SymmetricMatrix | Should -BeTrue 1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1 | New-Matrix 4,4 | Test-SymmetricMatrix | Should -BeTrue -Because 'diagonal matrices are symmetric' 1,0,0, 2,2,0, 3,0,3 | New-Matrix 3,3 | Test-SymmetricMatrix | Should -BeFalse 1,0,0, 0,2,1, 0,0,3 | New-Matrix 2,3 | Test-SymmetricMatrix | Should -BeFalse 1,0,0, 0,0,3 | New-Matrix 2,3 | Test-SymmetricMatrix | Should -BeFalse -Because 'only square matrices can be symmetric' } } |