0001    // Hyperbolic.swift
0002    //
0003    // Copyright (c) 2014–2015 Mattt Thompson (http://mattt.me)
0004    //
0005    // Permission is hereby granted, free of charge, to any person obtaining a copy
0006    // of this software and associated documentation files (the "Software"), to deal
0007    // in the Software without restriction, including without limitation the rights
0008    // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
0009    // copies of the Software, and to permit persons to whom the Software is
0010    // furnished to do so, subject to the following conditions:
0011    //
0012    // The above copyright notice and this permission notice shall be included in
0013    // all copies or substantial portions of the Software.
0014    //
0015    // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
0016    // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
0017    // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
0018    // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
0019    // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
0020    // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
0021    // THE SOFTWARE.
0022    
0023    import Accelerate
0024    
0025    public struct Matrix
Matrix.swift:70
extension Matrix: CustomStringConvertible {
Matrix.swift:97
extension Matrix: SequenceType {
Matrix.swift:117
public func add(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:117
public func add(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:117
public func add(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:126
public func add(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:126
public func add(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:126
public func add(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:135
public func mul(alpha: Float, x: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:135
public func mul(alpha: Float, x: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:142
public func mul(alpha: Double, x: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:142
public func mul(alpha: Double, x: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:149
public func mul(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:149
public func mul(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:149
public func mul(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:152
    var results = Matrix<Float>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
Matrix.swift:158
public func mul(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:158
public func mul(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:158
public func mul(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:161
    var results = Matrix<Double>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
Matrix.swift:167
public func div(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:167
public func div(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:167
public func div(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:173
public func div(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:173
public func div(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:173
public func div(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:179
public func inv(x : Matrix<Float>) -> Matrix<Float> {
Matrix.swift:179
public func inv(x : Matrix<Float>) -> Matrix<Float> {
Matrix.swift:198
public func inv(x : Matrix<Double>) -> Matrix<Double> {
Matrix.swift:198
public func inv(x : Matrix<Double>) -> Matrix<Double> {
Matrix.swift:217
public func transpose(x: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:217
public func transpose(x: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:218
    var results = Matrix<Float>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
Matrix.swift:224
public func transpose(x: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:224
public func transpose(x: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:225
    var results = Matrix<Double>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
Matrix.swift:233
public func + (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:233
public func + (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:233
public func + (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:237
public func + (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:237
public func + (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:237
public func + (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:241
public func * (lhs: Float, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:241
public func * (lhs: Float, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:245
public func * (lhs: Double, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:245
public func * (lhs: Double, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:249
public func * (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:249
public func * (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:249
public func * (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:253
public func * (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:253
public func * (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:253
public func * (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:257
public func / (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:257
public func / (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:257
public func / (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:261
public func / (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:261
public func / (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:261
public func / (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:266
public postfix func ′ (value: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:266
public postfix func ′ (value: Matrix<Float>) -> Matrix<Float> {
Matrix.swift:270
public postfix func ′ (value: Matrix<Double>) -> Matrix<Double> {
Matrix.swift:270
public postfix func ′ (value: Matrix<Double>) -> Matrix<Double> {
<T
Matrix.swift:26
    public typealias Element = T
 where T: FloatingPointType, T: FloatLiteralConvertible> {
0026        public typealias Element
Matrix.swift:30
    var grid: [Element]
Matrix.swift:32
    public init(rows: Int, columns: Int, repeatedValue: Element) {
Matrix.swift:36
        self.grid = [Element](count: rows * columns, repeatedValue: repeatedValue)
Matrix.swift:39
    public init(_ contents: [[Element]]) {
Matrix.swift:42
        let repeatedValue: Element = 0.0
Matrix.swift:98
    public func generate() -> AnyGenerator<ArraySlice<Element>> {
 = T
0027    
0028        let rows
Matrix.swift:33
        self.rows = rows
Matrix.swift:64
        return row >= 0 && row < rows && column >= 0 && column < columns
Matrix.swift:74
        for i in 0..<rows {
Matrix.swift:77
            switch (i, rows) {
Matrix.swift:82
            case (rows - 1, _):
Matrix.swift:99
        let endIndex = rows * columns
Matrix.swift:118
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:118
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:127
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:127
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:150
    precondition(x.columns == y.rows, "Matrix dimensions not compatible with multiplication")
Matrix.swift:152
    var results = Matrix<Float>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:159
    precondition(x.columns == y.rows, "Matrix dimensions not compatible with multiplication")
Matrix.swift:161
    var results = Matrix<Double>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:169
    precondition(x.columns == yInv.rows, "Matrix dimensions not compatible")
Matrix.swift:175
    precondition(x.columns == yInv.rows, "Matrix dimensions not compatible")
Matrix.swift:180
    precondition(x.rows == x.columns, "Matrix must be square")
Matrix.swift:184
    var ipiv = [__CLPK_integer](count: x.rows * x.rows, repeatedValue: 0)
Matrix.swift:184
    var ipiv = [__CLPK_integer](count: x.rows * x.rows, repeatedValue: 0)
Matrix.swift:199
    precondition(x.rows == x.columns, "Matrix must be square")
Matrix.swift:203
    var ipiv = [__CLPK_integer](count: x.rows * x.rows, repeatedValue: 0)
Matrix.swift:203
    var ipiv = [__CLPK_integer](count: x.rows * x.rows, repeatedValue: 0)
Matrix.swift:218
    var results = Matrix<Float>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
Matrix.swift:219
    vDSP_mtrans(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
Matrix.swift:225
    var results = Matrix<Double>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
Matrix.swift:226
    vDSP_mtransD(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
: Int
0029        let columns
Matrix.swift:34
        self.columns = columns
Matrix.swift:54
            return grid[(row * columns) + column]
Matrix.swift:59
            grid[(row * columns) + column] = newValue
Matrix.swift:64
        return row >= 0 && row < rows && column >= 0 && column < columns
Matrix.swift:75
            let contents = (0..<columns).map{"\(self[i, $0])"}.joinWithSeparator("\t")
Matrix.swift:99
        let endIndex = rows * columns
Matrix.swift:108
            nextRowStartIndex += self.columns
Matrix.swift:118
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:118
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:127
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:127
    precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
Matrix.swift:150
    precondition(x.columns == y.rows, "Matrix dimensions not compatible with multiplication")
Matrix.swift:152
    var results = Matrix<Float>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:159
    precondition(x.columns == y.rows, "Matrix dimensions not compatible with multiplication")
Matrix.swift:161
    var results = Matrix<Double>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:169
    precondition(x.columns == yInv.rows, "Matrix dimensions not compatible")
Matrix.swift:175
    precondition(x.columns == yInv.rows, "Matrix dimensions not compatible")
Matrix.swift:180
    precondition(x.rows == x.columns, "Matrix must be square")
Matrix.swift:185
    var lwork = __CLPK_integer(x.columns * x.columns)
Matrix.swift:185
    var lwork = __CLPK_integer(x.columns * x.columns)
Matrix.swift:188
    var nc = __CLPK_integer(x.columns)
Matrix.swift:199
    precondition(x.rows == x.columns, "Matrix must be square")
Matrix.swift:204
    var lwork = __CLPK_integer(x.columns * x.columns)
Matrix.swift:204
    var lwork = __CLPK_integer(x.columns * x.columns)
Matrix.swift:207
    var nc = __CLPK_integer(x.columns)
Matrix.swift:218
    var results = Matrix<Float>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
Matrix.swift:219
    vDSP_mtrans(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
Matrix.swift:225
    var results = Matrix<Double>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
Matrix.swift:226
    vDSP_mtransD(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
: Int
0030        var grid
Matrix.swift:36
        self.grid = [Element](count: rows * columns, repeatedValue: repeatedValue)
Matrix.swift:47
            grid.replaceRange(i*n..<i*n+min(m, row.count), with: row)
Matrix.swift:54
            return grid[(row * columns) + column]
Matrix.swift:59
            grid[(row * columns) + column] = newValue
Matrix.swift:110
            return self.grid[currentRowStartIndex..<nextRowStartIndex]
Matrix.swift:121
    cblas_saxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
Matrix.swift:121
    cblas_saxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
Matrix.swift:121
    cblas_saxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
Matrix.swift:130
    cblas_daxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
Matrix.swift:130
    cblas_daxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
Matrix.swift:130
    cblas_daxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
Matrix.swift:137
    cblas_sscal(Int32(x.grid.count), alpha, &(results.grid), 1)
Matrix.swift:137
    cblas_sscal(Int32(x.grid.count), alpha, &(results.grid), 1)
Matrix.swift:144
    cblas_dscal(Int32(x.grid.count), alpha, &(results.grid), 1)
Matrix.swift:144
    cblas_dscal(Int32(x.grid.count), alpha, &(results.grid), 1)
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:153
    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:162
    cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
Matrix.swift:190
    sgetrf_(&nc, &nc, &(results.grid), &nc, &ipiv, &error)
Matrix.swift:191
    sgetri_(&nc, &(results.grid), &nc, &ipiv, &work, &lwork, &error)
Matrix.swift:209
    dgetrf_(&nc, &nc, &(results.grid), &nc, &ipiv, &error)
Matrix.swift:210
    dgetri_(&nc, &(results.grid), &nc, &ipiv, &work, &lwork, &error)
Matrix.swift:219
    vDSP_mtrans(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
Matrix.swift:219
    vDSP_mtrans(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
Matrix.swift:226
    vDSP_mtransD(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
Matrix.swift:226
    vDSP_mtransD(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
: [Element]
0031    
0032        public init
Matrix.swift:44
        self.init(rows: m, columns: n, repeatedValue: repeatedValue)
(rows: Int, columns: Int, repeatedValue: Element) {
0033            self.rows = rows
0034            self.columns = columns
0035    
0036            self.grid = [Element](count: rows * columns, repeatedValue: repeatedValue)
0037        }
0038    
0039        public init(_ contents: [[Element]]) {
0040            let m: Int = contents.count
0041            let n: Int = contents[0].count
0042            let repeatedValue: Element = 0.0
0043    
0044            self.init(rows: m, columns: n, repeatedValue: repeatedValue)
0045    
0046            for (i, row) in contents.enumerate() {
0047                grid.replaceRange(i*n..<i*n+min(m, row.count), with: row)
0048            }
0049        }
0050    
0051        public subscript
Matrix.swift:75
            let contents = (0..<columns).map{"\(self[i, $0])"}.joinWithSeparator("\t")
(row: Int, column: Int) -> Element {
0052            get {
0053                assert(indexIsValidForRow(row, column: column))
0054                return grid[(row * columns) + column]
0055            }
0056    
0057            set {
0058                assert(indexIsValidForRow(row, column: column))
0059                grid[(row * columns) + column] = newValue
0060            }
0061        }
0062    
0063        private func indexIsValidForRow
Matrix.swift:53
            assert(indexIsValidForRow(row, column: column))
Matrix.swift:58
            assert(indexIsValidForRow(row, column: column))
(row: Int, column: Int) -> Bool {
0064            return row >= 0 && row < rows && column >= 0 && column < columns
0065        }
0066    }
0067    
0068    // MARK: - Printable
0069    
0070    extension Matrix: CustomStringConvertible {
0071        public var description: String {
0072            var description = ""
0073    
0074            for i in 0..<rows {
0075                let contents = (0..<columns).map{"\(self[i, $0])"}.joinWithSeparator("\t")
0076    
0077                switch (i, rows) {
0078                case (0, 1):
0079                    description += "(\t\(contents)\t)"
0080                case (0, _):
0081                    description += "⎛\t\(contents)\t⎞"
0082                case (rows - 1, _):
0083                    description += "⎝\t\(contents)\t⎠"
0084                default:
0085                    description += "⎜\t\(contents)\t⎥"
0086                }
0087    
0088                description += "\n"
0089            }
0090    
0091            return description
0092        }
0093    }
0094    
0095    // MARK: - SequenceType
0096    
0097    extension Matrix: SequenceType {
0098        public func generate() -> AnyGenerator<ArraySlice<Element>> {
0099            let endIndex = rows * columns
0100            var nextRowStartIndex = 0
0101    
0102            return anyGenerator {
0103                if nextRowStartIndex == endIndex {
0104                    return nil
0105                }
0106    
0107                let currentRowStartIndex = nextRowStartIndex
0108                nextRowStartIndex += self.columns
0109    
0110                return self.grid[currentRowStartIndex..<nextRowStartIndex]
0111            }
0112        }
0113    }
0114    
0115    // MARK: -
0116    
0117    public func add
Matrix.swift:234
    return add(lhs, y: rhs)
(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
0118        precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
0119    
0120        var results = y
0121        cblas_saxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
0122    
0123        return results
0124    }
0125    
0126    public func add
Matrix.swift:238
    return add(lhs, y: rhs)
(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
0127        precondition(x.rows == y.rows && x.columns == y.columns, "Matrix dimensions not compatible with addition")
0128    
0129        var results = y
0130        cblas_daxpy(Int32(x.grid.count), 1.0, x.grid, 1, &(results.grid), 1)
0131    
0132        return results
0133    }
0134    
0135    public func mul
Matrix.swift:242
    return mul(lhs, x: rhs)
(alpha: Float, x: Matrix<Float>) -> Matrix<Float> {
0136        var results = x
0137        cblas_sscal(Int32(x.grid.count), alpha, &(results.grid), 1)
0138    
0139        return results
0140    }
0141    
0142    public func mul
Matrix.swift:246
    return mul(lhs, x: rhs)
(alpha: Double, x: Matrix<Double>) -> Matrix<Double> {
0143        var results = x
0144        cblas_dscal(Int32(x.grid.count), alpha, &(results.grid), 1)
0145    
0146        return results
0147    }
0148    
0149    public func mul
Matrix.swift:176
    return mul(x, y: yInv)
Matrix.swift:250
    return mul(lhs, y: rhs)
(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
0150        precondition(x.columns == y.rows, "Matrix dimensions not compatible with multiplication")
0151    
0152        var results = Matrix<Float>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
0153        cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
0154    
0155        return results
0156    }
0157    
0158    public func mul
Matrix.swift:170
    return mul(x, y: yInv)
Matrix.swift:254
    return mul(lhs, y: rhs)
(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
0159        precondition(x.columns == y.rows, "Matrix dimensions not compatible with multiplication")
0160    
0161        var results = Matrix<Double>(rows: x.rows, columns: y.columns, repeatedValue: 0.0)
0162        cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, Int32(x.rows), Int32(y.columns), Int32(x.columns), 1.0, x.grid, Int32(x.columns), y.grid, Int32(y.columns), 0.0, &(results.grid), Int32(results.columns))
0163    
0164        return results
0165    }
0166    
0167    public func div
Matrix.swift:258
    return div(lhs, y: rhs)
(x: Matrix<Double>, y: Matrix<Double>) -> Matrix<Double> {
0168        let yInv = inv(y)
0169        precondition(x.columns == yInv.rows, "Matrix dimensions not compatible")
0170        return mul(x, y: yInv)
0171    }
0172    
0173    public func div
Matrix.swift:262
    return div(lhs, y: rhs)
(x: Matrix<Float>, y: Matrix<Float>) -> Matrix<Float> {
0174        let yInv = inv(y)
0175        precondition(x.columns == yInv.rows, "Matrix dimensions not compatible")
0176        return mul(x, y: yInv)
0177    }
0178    
0179    public func inv
Matrix.swift:174
    let yInv = inv(y)
(x : Matrix<Float>) -> Matrix<Float> {
0180        precondition(x.rows == x.columns, "Matrix must be square")
0181    
0182        var results = x
0183    
0184        var ipiv = [__CLPK_integer](count: x.rows * x.rows, repeatedValue: 0)
0185        var lwork = __CLPK_integer(x.columns * x.columns)
0186        var work = [CFloat](count: Int(lwork), repeatedValue: 0.0)
0187        var error: __CLPK_integer = 0
0188        var nc = __CLPK_integer(x.columns)
0189    
0190        sgetrf_(&nc, &nc, &(results.grid), &nc, &ipiv, &error)
0191        sgetri_(&nc, &(results.grid), &nc, &ipiv, &work, &lwork, &error)
0192    
0193        assert(error == 0, "Matrix not invertible")
0194    
0195        return results
0196    }
0197    
0198    public func inv
Matrix.swift:168
    let yInv = inv(y)
(x : Matrix<Double>) -> Matrix<Double> {
0199        precondition(x.rows == x.columns, "Matrix must be square")
0200    
0201        var results = x
0202    
0203        var ipiv = [__CLPK_integer](count: x.rows * x.rows, repeatedValue: 0)
0204        var lwork = __CLPK_integer(x.columns * x.columns)
0205        var work = [CDouble](count: Int(lwork), repeatedValue: 0.0)
0206        var error: __CLPK_integer = 0
0207        var nc = __CLPK_integer(x.columns)
0208    
0209        dgetrf_(&nc, &nc, &(results.grid), &nc, &ipiv, &error)
0210        dgetri_(&nc, &(results.grid), &nc, &ipiv, &work, &lwork, &error)
0211    
0212        assert(error == 0, "Matrix not invertible")
0213    
0214        return results
0215    }
0216    
0217    public func transpose
Matrix.swift:267
    return transpose(value)
(x: Matrix<Float>) -> Matrix<Float> {
0218        var results = Matrix<Float>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
0219        vDSP_mtrans(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
0220    
0221        return results
0222    }
0223    
0224    public func transpose
Matrix.swift:271
    return transpose(value)
(x: Matrix<Double>) -> Matrix<Double> {
0225        var results = Matrix<Double>(rows: x.columns, columns: x.rows, repeatedValue: 0.0)
0226        vDSP_mtransD(x.grid, 1, &(results.grid), 1, vDSP_Length(results.rows), vDSP_Length(results.columns))
0227    
0228        return results
0229    }
0230    
0231    // MARK: - Operators
0232    
0233    public func + (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
0234        return add(lhs, y: rhs)
0235    }
0236    
0237    public func + (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
0238        return add(lhs, y: rhs)
0239    }
0240    
0241    public func * (lhs: Float, rhs: Matrix<Float>) -> Matrix<Float> {
0242        return mul(lhs, x: rhs)
0243    }
0244    
0245    public func * (lhs: Double, rhs: Matrix<Double>) -> Matrix<Double> {
0246        return mul(lhs, x: rhs)
0247    }
0248    
0249    public func * (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
0250        return mul(lhs, y: rhs)
0251    }
0252    
0253    public func * (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
0254        return mul(lhs, y: rhs)
0255    }
0256    
0257    public func / (lhs: Matrix<Double>, rhs: Matrix<Double>) -> Matrix<Double> {
0258        return div(lhs, y: rhs)
0259    }
0260    
0261    public func / (lhs: Matrix<Float>, rhs: Matrix<Float>) -> Matrix<Float> {
0262        return div(lhs, y: rhs)
0263    }
0264    
0265    postfix operator ′ {}
0266    public postfix func ′ (value: Matrix<Float>) -> Matrix<Float> {
0267        return transpose(value)
0268    }
0269    
0270    public postfix func ′ (value: Matrix<Double>) -> Matrix<Double> {
0271        return transpose(value)
0272    }
0273