解決Swift中的Accelerate框架問題

Question

我在Accelerate框架中使用來自LAPACK的dgeev算法來計算矩陣的特征值和特征向量。 這是我的代碼：

    var matrix:[__CLPK_doublereal] = [1,2,3,4,5,6,7,8,9]

    var N = __CLPK_integer(sqrt(Double(matrix.count)))
    var pivots = [__CLPK_integer](count: Int(N), repeatedValue: 0)
    var workspace = [Double](count: Int(N), repeatedValue: 0.0)
    var error : __CLPK_integer = 0
    var lwork = __CLPK_integer(-1)
    // Real parts of eigenvalues
    var wr = [Double](count: Int(N), repeatedValue: 0)
    // Imaginary parts of eigenvalues
    var wi = [Double](count: Int(N), repeatedValue: 0)
    // Left eigenvectors
    var vl = [__CLPK_doublereal](count: Int(N*N), repeatedValue: 0)
    // Right eigenvectors
    var vr = [__CLPK_doublereal](count: Int(N*N), repeatedValue: 0)

    dgeev_(UnsafeMutablePointer(("V" as NSString).UTF8String), UnsafeMutablePointer(("V" as NSString).UTF8String), &N, &matrix, &N, &wr, &wi, &vl, &N, &vr, &N, &workspace, &lwork, &error)

    println("\(wr), \(vl), \(vr)")

這僅打印包含零的數組，這意味着它們不會被函數修改。 我究竟做錯了什么？

更新1

我現在有這個：

    var matrix:[__CLPK_doublereal] = [1,2,3,4,5,6,7,8,9]

    var N = __CLPK_integer(sqrt(Double(matrix.count)))
    var pivots = [__CLPK_integer](count: Int(N), repeatedValue: 0)
    var workspaceQuery = [Double](count: 1, repeatedValue: 0.0)
    var error : __CLPK_integer = 0
    var lwork = __CLPK_integer(-1)
    // Real parts of eigenvalues
    var wr = [Double](count: Int(N), repeatedValue: 0)
    // Imaginary parts of eigenvalues
    var wi = [Double](count: Int(N), repeatedValue: 0)
    // Left eigenvectors
    var vl = [__CLPK_doublereal](count: Int(N*N), repeatedValue: 0)
    // Right eigenvectors
    var vr = [__CLPK_doublereal](count: Int(N*N), repeatedValue: 0)

    dgeev_(UnsafeMutablePointer(("V" as NSString).UTF8String), UnsafeMutablePointer(("V" as NSString).UTF8String), &N, &matrix, &N, &wr, &wi, &vl, &N, &vr, &N, &workspaceQuery, &lwork, &error)
    var workspace = [Double](count: Int(workspaceQuery[0]), repeatedValue: 0.0)

    dgeev_(UnsafeMutablePointer(("V" as NSString).UTF8String), UnsafeMutablePointer(("V" as NSString).UTF8String), &N, &matrix, &N, &wr, &wi, &vl, &N, &vr, &N, &workspace, &lwork, &error)

    println("\(wr), \(vl), \(vr)")

它仍打印零。

Answer 1

你的lwork變量存在問題。 這應該是您提供的工作空間的大小， -1表示您正在執行“工作空間查詢”：

 LWORK   (input) INTEGER   
        The dimension of the array WORK.  LWORK >= max(1,3*N), and   
        if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N.  For good   
        performance, LWORK must generally be larger.   

        If LWORK = -1, then a workspace query is assumed; the routine   
        only calculates the optimal size of the WORK array, returns   
        this value as the first entry of the WORK array, and no error   
        message related to LWORK is issued by XERBLA.

所以你可能想要這樣的東西：

var workspaceQuery: Double = 0.0
dgeev_(UnsafeMutablePointer(("V" as NSString).UTF8String), UnsafeMutablePointer(("V" as NSString).UTF8String), &N, &matrix, &N, &wr, &wi, &vl, &N, &vr, &N, &workspaceQuery, &lwork, &error)

// prints "102.0"
println("\(workspaceQuery)")

// size workspace per the results of the query:
var workspace = [Double](count: Int(workspaceQuery), repeatedValue: 0.0)
lwork = __CLPK_integer(workspaceQuery)

dgeev_(UnsafeMutablePointer(("V" as NSString).UTF8String), UnsafeMutablePointer(("V" as NSString).UTF8String), &N, &matrix, &N, &wr, &wi, &vl, &N, &vr, &N, &workspace, &lwork, &error)

// this now prints non-zero values
println("\(wr), \(vl), \(vr)")