LAPack dpbsv 为正定矩阵返回 3

Question

I am trying to use the LAPACK banded symmetric matrix solver dpbsv. I am testing the matrix:

4,  2,  0,   0, 0
2   4,  3,   0, 0
0,  3, 11,  7,  0
0,  0,  7, 11,  5
0,  0,  0,  5, 13

Mathematica tells me that this matrix is positive definite, with a determinate of 3684

I am using swift and have constructed the array

var a: [Double] = [ 0, 2,  3,  7,  5,
                    4, 4, 11, 11, 13]
var b: [Double] = [1, 2, 3, 4, 5]

And I am calling dpbsv as

    var uplo = Int8("U".utf8.first!) // set to 'U'

    var n = __CLPK_integer(5)
    var kd = __CLPK_integer(1)
    var ldab = kd + 1
    var nrhs = __CLPK_integer(1)
    var ldb = __CLPK_integer(5)
    var info: __CLPK_integer = 0

    dpbsv_(&uplo,
           &n,
           &kd,
           &nrhs,
           &a,
           &ldab,
           &b,
           &ldb,
           &info)

    if info != 0 {
        // here info is 3, indicating non-positive definite.
        NSLog("error \(info)")
    }

Any idea what the issue is here? Am I interpreting the parameters to dpbsv_ correctly? I've tried other matrices that Mathematica claims are pos-def with the same result.