src/matrix.ps1
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if (-not ('Prelude.Matrix' -as [Type])) { Add-Type -Path (Join-Path $PSScriptRoot 'cs/Matrix/Matrix.dll') $Accelerators = [PowerShell].Assembly.GetType('System.Management.Automation.TypeAccelerators') $Accelerators::Add('Matrix', 'Prelude.Matrix') } function New-Matrix { <# .SYNOPSIS Utility wrapper function for creating matrices .DESCRIPTION New-Matrix is a wrapper function for the [Matrix] class and is intended to reduce the effort required to create [Matrix] objects. Use "New-Matrix | Get-Member" to see available methods: Adj: Return matrix adjugate ("classical adjoint") > Note: Available as a class method - [Matrix]::Adj Det: Return matrix determinant (even matrices larger than 3x3 > Note: Available as a class method - [Matrix]::Det Dot: Return dot product between matrix and one other matrix (with compatible size) > Note: Available as a class method - [Matrix]::Dot Clone: Return new matrix with identical values as original matrix Cofactor: Return cofactor for given row and column index pair > Example: $Matrix.Cofactor(0, 1) Indexes: Return list of "ij" pairs (useful for iterating through matrix values) > Example: (New-Matrix).Indexes() | ForEach-Object { "(i,j) = ($($_[0]),$($_[1]))" } Inverse: Return matrix inverse (Note: Det() must return non-zero value) > Note: Available as a class method - [Matrix]::Invert Multiply: Return result of multiplying matrix by scalar value (ex: 42) > Note: Available as a class method - [Matrix]::Multiply RemoveColumn: Return matrix with selected column removed RemoveRow: Return matrix with selected column removed Transpose: Return matrix transpose > Note: Available as a class method - [Matrix]::Transpose Trace: Return matrix trace (sum of diagonal elements) > Note: Available as a class method - [Matrix]::Trace *** All methods that return a [Matrix] object provide a "fluent" interface and can be chained *** *** All methods are "non destructive" and will return a clone of the original matrix (when applicable) *** .PARAMETER Size Size = @(number of rows, number of columns) .EXAMPLE $Matrix = 1..9 | matrix 3,3 #> [CmdletBinding()] [Alias('matrix')] [OutputType([Matrix])] Param( [Parameter(ValueFromPipeline=$True)] [Array] $Values, [Parameter(Position=0)] [Array] $Size = @(2,2), [Switch] $Diagonal ) Begin { $Matrix = [Matrix]::New($Size[0], $Size[1]) if ($Values.Count -gt 0) { $Values = $Values | Invoke-Flatten if ($Diagonal) { $Index = 0 foreach ($Pair in $Matrix.Indexes()) { $Row,$Column = $Pair if ($Row -eq $Column) { $Matrix.Rows[$Row][$Column] = $Values[$Index] $Index++ } } } else { $Matrix.Rows = $Values } } } End { if ($Input.Count -gt 0) { $Values = $Input | Invoke-Flatten if ($Diagonal) { $Index = 0 foreach ($Pair in $Matrix.Indexes()) { $Row,$Column = $Pair if ($Row -eq $Column) { $Matrix.Rows[$Row][$Column] = $Values[$Index] $Index++ } } } else { $Matrix.Rows = $Values } } $Matrix } } function Test-DiagonalMatrix { <# .SYNOPSIS Return true if passed value is a "diagonal" matrix .DESCRIPTION A diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. Example: 1 0 0 1 The primary purpose of this function is to be used as a Matrix object type extension. #> [CmdletBinding()] [OutputType([Bool])] Param( [Parameter(Position=0, ValueFromPipeline=$True)] [Matrix] $Value ) Process { (Test-SquareMatrix $Value) -and ($Value.Indexes() | ForEach-Object { $Row, $Col = $_ ($Row -eq $Col) -or ($Value.Rows[$Row][$Col] -eq 0) } | Invoke-Reduce -Every) } } function Test-SquareMatrix { <# .SYNOPSIS Return true if passed value is a "square" matrix .DESCRIPTION A square matrix is a matrix that has the same number of rows as columns. Example: 1 1 1 1 The primary purpose of this function is to be used as a Matrix object type extension. #> [CmdletBinding()] [OutputType([Bool])] Param( [Parameter(Position=0, ValueFromPipeline=$True)] [Matrix] $Value ) Process { $Rows, $Columns = $Value.Size $Rows -eq $Columns } } function Test-SymmetricMatrix { <# .SYNOPSIS Return true if passed value is a "symmetric" matrix .DESCRIPTION A symmetric matrix is a matrix for which every element of the matrix (a_ij -eq a_ji) is true Example: 1 2 3 2 1 4 3 4 1 The primary purpose of this function is to be used as a Matrix object type extension. #> [Diagnostics.CodeAnalysis.SuppressMessageAttribute('PSUseDeclaredVarsMoreThanAssignments', 'Result')] [CmdletBinding()] [OutputType([Bool])] Param( [Parameter(Position=0, ValueFromPipeline=$True)] [Matrix] $Value ) Process { (Test-SquareMatrix $Value) -and (0..($Value.Size[0] - 1) | ForEach-Object { $Row = $_ 0..$Row | ForEach-Object { $Value.Rows[$Row][$_] -eq $Value.Rows[$_][$Row] } } | Invoke-Reduce -Every) } } |