swift之Swift 中的 Accelerate 框架出现问题

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)") 

这只打印包含零的数组，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。

请您参考如下方法:

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)")