Trouble with the Accelerate framework in Swift

Question

I am using the dgeev algorithm from LAPACK in the Accelerate framework to calculate eigenvalues and eigenvectors of a matrix. Here's my code:

    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)")

This prints only arrays containing zeroes which means they aren't being modified by the function. What am I doing wrong?

UPDATE 1

I now have this:

    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)")

Still it prints zeroes.

Answer 1

The problem’s with your lwork variable. This is supposed to be the size of the workspace you supply, with -1 meaning you’re performing a “workspace query”:

 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.

So you probably want something like this:

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)")