column

the sparseMatrix function with comments: extension Array where Element == [Double] { // A sparse matrix is a mattrix where all zero's are ommitted. // Normal matrix: Sparse matrix: // 0 1 0 1 // 1 3 0 1 3 // 4 0 2 4 2 // Find the sparse matrix of this matrix. Returns an array of doubles containing the values of the sparse matrix (omitting all zero's) and a SparseMatrixStructure containing information about where the columns start and where the rows start. The values array of the sparse matrix above would be [1, 4, 1, 3, 2]. func sparseMatrix() -> (structure: SparseMatrixStructure, values: [Double]) { let columns = self.transpose() // Get the row indices of the matrix. The row indices of the sparse matrix above would be // [1, 2 column 0 // 0, 1, column 1 // 2] column 2 var rowIndices: [Int32] = columns.map { column in column.indices.compactMap { indexInColumn in if column[indexInColumn] != 0 { return Int32(indexInColumn) } return nil } }.reduce

The SavitzkyGolay class with comments: class SavitzkyGolay { static func coefficients(windowLength: Int, polynomialOrder: Int, derivativeOrder: Int = 0, delta: Int = 1) -> [Double] { // windowLength is the number of coefficients returned by this function. guard windowLength > 0 else { fatalError(windowLength must be positive) } // polynomialOrder is the order of the polynomial used to smooth the noisy data (the coefficients are calculated independently from the noisy data) guard polynomialOrder < windowLength else { fatalError(polynomialOrder must be less than windowLength) } // The derivativeOrder is the order of the derivative to compute. If it is set to zero, the noisy data is smoothed without differentiating. guard derivativeOrder <= polynomialOrder else { return [Double](repeating: 0, count: windowLength) } let (halfWindow, remainder) = windowLength.quotientAndRemainder(dividingBy: 2) var pos = Double(halfWindow) // pos should not be a round number (because otherwise this function won't work

I would also like to mention that running the code below gives me almost identical elapsed times for the matrix array and matrix buffer solutions. So, at least for this case, I'm not seeing any performance differences between the two approaches. func runBenchmark1() { print(Benchmark matrix multiplication) for _ in 1...3 { let tic = Date.now let n = 8_000 let a = Matrix(rows: n, columns: n, fill: 1.5) let b = Matrix(rows: n, columns: n, fill: 2.8) let c = a * b let toc = tic.timeIntervalSinceNow.magnitude let elapsed = String(format: %.4f, toc) print(Elapsed time is (elapsed) sec, first element is (c[0, 0])) } }

Hi @kittens , You're seeing this behavior because the NavigationSplitView is collapsing down to a stack and showing content based on the content of the split view's columns. Here, it's showing the sidebar, and then navigating to the detail view, so the back button is taking you back to the sidebar no matter what. To change this to the behavior you are looking for, you can put a NavigationStack in the detail view. For example: NavigationSplitView { Text(Here is the FirstView) NavigationLink(Go to SecondView) { SecondView() } } detail: { NavigationStack { Text(nothing selected yet) } } Hope this helps, Sydney

Xcode creates one .lproj folder for each localization when compiling your String Catalog, so you can still check the existence of en.lproj by looking into your app bundle. Note that Xcode creates the .lproj folder only when the localization contains at least one localized string. As an example, if you select your String Catalog in Xcode, and see that the strings under the Enlgish (en) column are all gray, Xcode won't create en.lproj for you. So be sure that you add at least one localized string (which will then be shown in black) for your English localization. Best, —— Ziqiao Chen  Worldwide Developer Relation.