使用gsl，Blas和Lapack计算{Aᵀ×A）*（Bᵀ×B）矩阵

Question

让我有2个对称矩阵：

A = {{1,2}, {2,3}}
B = {{2,3},{3,4}}

我可以使用gsl，Blas和Lapack计算矩阵（A ^T ×A）*（B ^T ×B）吗？

我正在使用

gsl_blas_dsyrk(CblasUpper, CblasTrans, 1.0, A, 0.0, ATA);
gsl_blas_dsyrk(CblasUpper, CblasTrans, 1.0, B, 0.0, BTB);
gsl_blas_dsymm(CblasLeft, CblasUpper, 1.0, ATA, BTB, 0.0, ATABTB); // It doesn't work

它返回：

(Aᵀ·A) = ATA = {{5, 8}, {0, 13}} -- ok, gsl_blas_dsyrk returns symmetric matrix as upper triangular matrix.
(Bᵀ·B) = BTB = {{13, 8}, {0, 25}} -- ok.
(Aᵀ·A)·(Bᵀ·B) = ATABTB = {{65, 290}, {104, 469}} -- it's wrong.