scala - 使用 LAPACK-BLAS DGEMM 的矩阵点积

Question

使用lapack-blas dgemm 函数，我们试图得到这些矩阵的点积

    A = Array(Array(0.7266678772119796, 0.37866742996700287, 0.011693659632231124),
Array(0.09987886438245919, 0.3676551935579567, 0.6323601372667774))

    B = Array(Array(0.1539391703466485, 0.8259866297685163, 0.14377752901280771, 0.7412313835216213), 
Array(0.1415314251516353, 0.6226998769259113, 0.22445999933643912, 0.2190218035735153), 
Array(0.8696518309547832, 0.6548401943199273, 0.7637877932908158, 0.14197100882023972))

我们使用了以下参数:

    val A_ = A.flatten
    val B_ = B.flatten
    val m = A.size
    val k1 = A(0).size
    val k2 = B.size
    val n = B(0).size
    require(k1 == k2, "number of columns in A must match number of rows in B")
    var C = Array.fill[Double](m*n)(0.0)
    blas.dgemm("N", "N", m, n, k2, 1.0, A_ , m, B_ , k2, 1.0, C, m)

这给了我们一个错误的结果。我们预计点积为:

    Array(Array(0.17562540366704119, 0.8436715912415502, 0.19840567736364106, 0.6232256201072643), 
Array(0.6173431842237301, 0.7255322855240385, 0.5798731746316419, 0.2443346590424818))

但它给了我们以下值:

 Array(Array(0.34876402380669536, 1.5384458001585097, 0.9708020997951017, 1.0739583742659222), 
     Array(0.4634190691304188, 1.3771735213529386, 1.3136089825838326, 0.8280594349415209))

知道为什么这些值是错误的吗？

Answer 1

1) flatten 似乎按行遍历元素，但 Fortran 需要按列遍历元素，所以这个矩阵确实相乘:

    A2 = Array(Array(0.7266678772119796, 0.011693659632231124, 0.3676551935579567),
Array(0.37866742996700287, 0.09987886438245919, 0.6323601372667774))

    B2 = Array(Array(0.1539391703466485, 0.7412313835216213, 0.22445999933643912, 0.6548401943199273), 
Array(0.8259866297685163, 0.14377752901280771, 0.2190218035735153, 0.7637877932908158), 
Array(0.1415314251516353, 0.6226998769259113, 0.8696518309547832, 0.14197100882023972))

2) 这给出了错误的结果:

    Array(Array(0.1743820119033477, 0.7692229000792548, 0.4854010498975508, 0.5369791871329611),
Array(0.2317095345652094, 0.6885867606764693, 0.6568044912919163, 0.4140297174707604))

3) 并且这个错误的结果以某种方式加倍(m 值泄漏到 alpha 值？)，产生您正在观察的结果。