文件列表:

LICENSE (1072, 2023-07-19)
Package.swift (635, 2023-07-19)
Plinth.podspec (850, 2023-07-19)
Sources/ (0, 2023-07-19)
Sources/Plinth/ (0, 2023-07-19)
Sources/Plinth/ComplexMatrix.swift (8628, 2023-07-19)
Sources/Plinth/Core/ (0, 2023-07-19)
Sources/Plinth/Core/Arithmetic.swift (34708, 2023-07-19)
Sources/Plinth/Core/Conversions.swift (2213, 2023-07-19)
Sources/Plinth/Core/Functors.swift (4893, 2023-07-19)
Sources/Plinth/Core/Submatrix.swift (13093, 2023-07-19)
Sources/Plinth/Core/Wrappers.swift (17354, 2023-07-19)
Sources/Plinth/Extensions/ (0, 2023-07-19)
Sources/Plinth/Extensions/Comparisons/ (0, 2023-07-19)
Sources/Plinth/Extensions/Comparisons/Comparisons.swift (2830, 2023-07-19)
Sources/Plinth/Extensions/Image Processing/ (0, 2023-07-19)
Sources/Plinth/Extensions/Image Processing/Bitmaps.swift (722, 2023-07-19)
Sources/Plinth/Extensions/Image Processing/Images.swift (2859, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/ (0, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Diagonal.swift (1085, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Division.swift (2144, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Eigendecomposition.swift (9151, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Exponentiation.swift (524, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Identity.swift (557, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Inversion.swift (5320, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Multiplication.swift (5329, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Ones.swift (474, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Products.swift (1072, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Roots.swift (943, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/SquareRoot.swift (595, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Transposition.swift (1180, 2023-07-19)
Sources/Plinth/Extensions/Linear Algebra/Zeros.swift (478, 2023-07-19)
Sources/Plinth/Extensions/Mathematics/ (0, 2023-07-19)
Sources/Plinth/Extensions/Mathematics/Interpolation.swift (1251, 2023-07-19)
Sources/Plinth/Extensions/Mathematics/Powers.swift (5006, 2023-07-19)
Sources/Plinth/Extensions/Signal Processing/ (0, 2023-07-19)
Sources/Plinth/Extensions/Signal Processing/Autocorrelation.swift (1103, 2023-07-19)
Sources/Plinth/Extensions/Signal Processing/FFT.swift (5007, 2023-07-19)
... ...

# Plinth Hardware-accelerated matrix/numeric programming library for Swift. ## Installation ### Swift Package Manager Simply add Plinth to your `Package.swift` file: ```swift let package = Package( name: "Example", dependencies: [ .package(url: "https://github.com/dclelland/Plinth.git", from: "2.0.0"), ], targets: [ .target(name: "Example", dependencies: ["Plinth"]) ] ) ``` Then import Plinth into your Swift files: ```swift import Plinth ``` Or for full [`ComplexMatrix`](https://github.com/dclelland/Plinth/blob/master/#complexmatrix) support you should also import [`swift-numerics`](https://github.com/dclelland/Plinth/blob/master/https://github.com/apple/swift-numerics), as that's where the [`Complex`](https://github.com/dclelland/Plinth/blob/master/https://github.com/apple/swift-numerics/blob/main/Sources/ComplexModule/Complex.swift) type lives. ```swift import Plinth import Numerics ``` ## Links ### Dependencies - [apple/swift-numerics](https://github.com/dclelland/Plinth/blob/master/https://github.com/apple/swift-numerics) ### References/prior art - https://github.com/apple/swift-numerics/issues/6 (discussion on adding a `ShapedArray` type to `swift-numerics`) - [Jounce/Surge](https://github.com/dclelland/Plinth/blob/master/https://github.com/Jounce/Surge) - [hollance/Matrix](https://github.com/dclelland/Plinth/blob/master/https://github.com/hollance/Matrix) - [stsievert/swix](https://github.com/dclelland/Plinth/blob/master/https://github.com/stsievert/swix) - [cgarciae/NDArray](https://github.com/dclelland/Plinth/blob/master/https://github.com/cgarciae/NDArray) ## Todo - [x] Implement Equality/Comparisons extension - [x] Implement both `.zeros` and `.ones` initializers - [x] Implement exception handling for LAPACK calls - [ ] Implement wrappers for `vDSP.fill`, `vDSP.clear`, `vDSP.window`, `vDSP.ramp`, `vDSP.stereoRamp` - [ ] Implement wrapper for `vDSP.convolve` - [x] Revisit `Eigendecomposition.sorted`, is sorting the eigenvalues by real component or the magnitude preferable? - [ ] Write notes on architecture and API design - [ ] Write code examples - [ ] ~~Add Cocoapods support~~ Can't do this, `swift-numerics` only supports SPM. Perhaps I should make my own `Complex` type. # Documentation ## Types ### [Shape](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Shape.swift) Defines the shape of a matrix using `rows` and `columns` properties. ```swift public struct Shape { public let rows: Int public let columns: Int } ``` This includes a number of convenience properties like `count`, `length` and `breadth`; as well as convenience initializers `.row(length:)`, `.column(length:)` and `.square(length:)`. ### [Matrix](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Matrix.swift) Generic matrix struct with `Scalar` type argument and `shape` and `elements` properties. Elements are stored as a single array in row-major format. ```swift public struct Matrix { public let shape: Shape public var elements: [Scalar] } ``` This also includes a large number of convenience initializers and implementations of typical typeclasses such as `Codable` and `ExpressibleByArrayLiteral`. The `elements` property is directly mutable but this is ideally to be avoided; matrix regularity is not enforced, except during encoding to or decoding from a serialization format. There is a computed property `state` which can be used to check if the matrix is considered to be malformed: ```swift let malformed = Matrix( shape: .init(rows: 2, columns: 2), elements: [1.0, 2.0, 3.0, 4.0, 5.0] ) print(malformed.state) ``` ``` > Malformed: Mismatched shape and elements; 2×2 != 5 ``` ### [ComplexMatrix](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/ComplexMatrix.swift) Generic complex matrix struct encapsulating two separate matrices for the `real` and `imaginary` parts. ```swift public struct ComplexMatrix where Scalar: Real { public var real: Matrix public var imaginary: Matrix } ``` This also includes a large number of convenience initializers and implementations of typical typeclasses such as `Codable` and `ExpressibleByArrayLiteral`. The `real` and `imaginary` properties are also directly mutable; `ComplexMatrix` has its own `state` property which can be used to check if the parts are mismatched or malformed. ## Core ### [Arithmetic](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Core/Arithmetic.swift) `+` and `-` prefix operators and `+`, `-`, `*`, `/` infix operators. Implements fast pointwise arithmetic for combinations of `Scalar`, `Complex`, `Matrix` and `ComplexMatrix`, where `Scalar` is `Float` or `Double`. ### [Conversions](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Core/Conversions.swift) Fast type conversions between the integer types `UInt8`, `UInt16`, `UInt32`, `Int8`, `Int16`, `Int32` and the floating point types `Float` and `Double`. ### [Functors](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Core/Functors.swift) Higher-order functions for shape-preserving operations on a matrix's elements. Includes support for complex matrix operations on [`DSPSplitComplex`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/dspsplitcomplex)/[`DSPDoubleSplitComplex`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/dspdoublesplitcomplex). > Disclaimer: These are not true functors, Swift lacks higher-kinded types... ### [Submatrix](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Core/Submatrix.swift) Fast submatrix read/write access using a Swift subscript interface. > Uses Accelerate's [`vDSP_mmov`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1449950-vdsp_mmov)/[`vDSP_mmovD`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1449956-vdsp_mmovd). ### [Wrappers](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Core/Wrappers.swift) Wrappers over most of the basic `vDSP` and `vForce` functions in Accelerate. ## Transformations ### [Center](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Transformations/Center.swift) Find the center point of a matrix, given a rounding rule. ### [Crop](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Transformations/Crop.swift) Crop a matrix towards the center, given a rounding rule. ### [Pad](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Transformations/Pad.swift) Zero-pad a matrix away from the center, given a rounding rule. ### [Reshape](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Transformations/Reshape.swift) Apply a new shape to a matrix, or reshape it as a single row or column. This also supports both `.rowMajor` and `.columnMajor` orderings. ### [Shift](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Transformations/Shift.swift) Apply a circular shift to a matrix. ### [Concatenate](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Transformations/Concatenate.swift) Concatentate multiple matrices together, row-wise or column-wise. ## Comparisons ### [Comparisons](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Comparisons/Comparisons.swift) `<`, `<=`, `>`, `>=`, `==`, `!==` infix operators. Pointwise comparison or equality checks, returning `0.0` for `false` and `1.0` for `true`. ## Mathematics ### [Powers](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Mathematics/Powers.swift) `**` infix operator. Implements fast pointwise power operations for `Scalar` and `Matrix`. Includes special functions for taking integer powers of matrices, for use when recursive application of `vDSP.multiply` will be faster than `vForce.pow` (which is quite an expensive operation). This also supports negative integers by applying `vForce.reciprocal` to the result. ### [Interpolation](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Statistics/Interpolation.swift) Linear interpolate values from a given range to/from `0.0...1.0`. > This is similar to C++'s [`std::lerp`](https://github.com/dclelland/Plinth/blob/master/https://en.cppreference.com/w/cpp/numeric/lerp). ## Statistics ### [Random](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Statistics/Random.swift) Generate matrices populated with random noise. ### [Gaussian](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Statistics/Gaussian.swift) Generate matrices populated with Gaussian noise. > This is derived from an answer on the [comp.lang.c FAQ](https://github.com/dclelland/Plinth/blob/master/http://c-faq.com/lib/gaussian.html). ### [Moments](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Statistics/Moments.swift) Calculate central and standardized moments; convenience methods for `variance`, `standardDeviation`, `skewness`, and `kurtosis`. ### [Normalization](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Statistics/Normalization.swift) Normalize a matrix to `0.0...1.0` using its `minimum()` and `maximum()` values; or shift it so that its `mean()` is centered on zero. ## Linear Algebra ### [Zeros](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Zeros.swift) Generate matrices populated by zeros. ### [Ones](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Ones.swift) Generate matrices populated by ones. ### [Identity](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Identity.swift) Generate identity matrices. ### [Diagonal](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Diagonal.swift) Generate diagonal matrices. ### [Transposition](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Transposition.swift) Transpose a matrix. > Uses Accelerate's [`vDSP_mtrans`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1449988-vdsp_mtrans)/[`vDSP_mtransD`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1450422-vdsp_mtransd). ### [Inversion](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Inversion.swift) Calculate the inverse of a matrix. > Uses LAPACK's [`sgetri_`](https://github.com/dclelland/Plinth/blob/master/http://www.netlib.org/lapack/explore-html/d8/ddc/group__real_g_ecomputational_ga1af62182327d0be67b1717db399d7d83.html)/[`dgetri_`](https://github.com/dclelland/Plinth/blob/master/http://www.netlib.org/lapack/explore-html/dd/d9a/group__double_g_ecomputational_ga56d9c860ce4ce42ded7f914fdb0683ff.html) for real matrices and [`cgetri_`](https://github.com/dclelland/Plinth/blob/master/http://www.netlib.org/lapack/explore-html/d4/d7e/group__complex_g_ecomputational_gae22ce12a3734b080ad8369ebf7e9c3a7.html)/[`zgetri_`](https://github.com/dclelland/Plinth/blob/master/http://www.netlib.org/lapack/explore-html/d3/d01/group__complex16_g_ecomputational_gab490cfc4b92edec5345479f19a9a72ca.html) for complex matrices. ### [Multiplication](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Multiplication.swift) `<*>` infix operator. Implements matrix multiplication. > Uses Accelerate's [`vDSP_mmul`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1449984-vdsp_mmul)/[`vDSP_mmulD`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1450386-vdsp_mmuld) for real matrices and [`vDSP_zmmul`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1449712-vdsp_zmmul)/[`vDSP_zmmulD`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1450796-vdsp_zmmuld) for complex matrices. ### [Division](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Division.swift) `/>` and ` Formula taken from MATLAB's [`sqrt`](https://github.com/dclelland/Plinth/blob/master/https://www.mathworks.com/help/matlab/ref/sqrt.html) function. ### [Exponentiation](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Mathematics/Exponentiation.swift) Complex exponentials. > Formula taken from MATLAB's [`exp`](https://github.com/dclelland/Plinth/blob/master/https://www.mathworks.com/help/matlab/ref/exp.html) function. ### [Products](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Products.swift) Inner and outer products. ### [Eigendecomposition](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Eigendecomposition.swift) Calculate the eigendecomposition of a matrix. Includes support for only calculating the necessary components. Also includes support for sorting the eigenvectors by properties of the eigenvalues. > Uses LAPACK's [`sgeev_`](https://github.com/dclelland/Plinth/blob/master/http://www.netlib.org/lapack/explore-html/d3/dfb/group__real_g_eeigen_ga104525b749278774f7b7f57195aa6798.html)/[`dgeev_`](https://github.com/dclelland/Plinth/blob/master/http://www.netlib.org/lapack/explore-html/d9/d8e/group__double_g_eeigen_ga66e19253344358f5dee1e60502b9e96f.html). > Swift implementation cribbed from [Surge](https://github.com/dclelland/Plinth/blob/master/https://github.com/Jounce/Surge/blob/master/Sources/Surge/Linear%20Algebra/Matrix.swift#L944). ### [Roots](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Linear%20Algebra/Roots.swift) Calculate the roots of a polynomial by taking the eigenvalues of a companion matrix. ## Image Processing ### [Bitmaps](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Image%20Processing/Bitmaps.swift) Conversion to and from floating point formats in the range `0.0...1.0` to 8-bit bitmaps in the range `0...255`. ### [Images](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Image%20Processing/Images.swift) Conversion to and from 8-bit bitmaps and `CGImage`, `CIImage`, `NSImage`, and `UIImage`. ## Signal Processing ### [FFT](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Signal%20Processing/FFT.swift) Forward and inverse two-dimensional fourier transforms. Includes support for creating, reusing, and destroying your own [`FFTSetup`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/fftsetup)/[`FFTSetupD`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/fftsetupd) structure. Some of the inverse fourier transform methods implement energy conservation by dividing by the size of the matrix. > Uses Accelerate's [`vDSP_fft2d_zip`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1450430-vdsp_fft2d_zip)/[`vDSP_fft2d_zipD`](https://github.com/dclelland/Plinth/blob/master/https://developer.apple.com/documentation/accelerate/1450508-vdsp_fft2d_zipd). ### [FFTShift](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Signal%20Processing/FFTShift.swift) Apply a circular rotation to a frequency-domain matrix so that the DC/DC signal is at the top left of the lower right quadrant. ### [Autocorrelation](https://github.com/dclelland/Plinth/blob/master/Sources/Plinth/Extensions/Signal%20Processing/Autocorrelation.swift) Calculate the autocorrelation of a matrix by taking the square magnitudes in the frequency domain.

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