Swift 中 Accelerate 框架的问题

Question

我在 Accelerate 框架中使用来自 LAPACK 的 dgeev 算法来计算矩阵的特征值和特征向量。这是我的代码：

    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)")

这仅打印包含零的数组，这意味着它们没有被函数修改。我做错了什么？

更新 1

我现在有了这个：

    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)")

它仍然打印零。

Answer 1

问题出在您的 lwork 变量上。这应该是您提供的工作空间的大小，-1 表示您正在执行“工作空间查询”：

 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.

所以你可能想要这样的东西：

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)")