np.dot 在乘法矩阵中的结果问题答案

【问题标题】：problems with the result of np.dot in multiplying matricesnp.dot 在乘法矩阵中的结果问题
【发布时间】：2018-07-13 14:17:30
【问题描述】：

我对@987654321@ 的矩阵乘法有些问题。

我将两个矩阵相乘，定义如下：

A = np.diagflat(diag)

其中 diag 是一个随机数数组，B 是一个简单的对称矩阵。 A 和 B 都是 100 x 100。

当我尝试做A.dot(B) 时，我得到以下结果：

array([[<100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    ...,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>],
   [<100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    ...,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>],
   [<100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    ...,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>],
   ...,
   [<100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    ...,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>],
   [<100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    ...,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>],
   [<100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    ...,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>,
    <100x100 sparse matrix of type '<class 'numpy.float64'>'
with 460 stored elements in Compressed Sparse Row format>]], dtype=object)

我不明白这个结果，它似乎是一个稀疏矩阵的数组，但这是为什么呢？我哪里错了？

谢谢！

【问题讨论】：

正确的用法是np.dot(A, B)
这无关紧要，A.dot(B) = np.dot(A, B)
我使用 dot 得到相同的结果 :(
您应该考虑重构问题以包含B 的性质，包括考虑编辑标题，以便将来人们可能会发现这个问题。
问题是np.dot 使用错误的方式将B 转换为密集数组。 np.array(B) 产生 about 结果； B,toarray() 是正确的。

标签： python numpy matrix sparse-matrix algebra

【解决方案1】：

你说过A是一个随机向量的对角矩阵：

A = np.diagflat(np.random.randint(10, size=100))

而B 是关联到图的矩阵的拉普拉斯算子：

R = nx.grid_graph(dim=[10,10])
B = nx.laplacian_matrix(R)

矩阵B 是一个sparse matrix，如果您希望查看它，则需要将其转换为numpy 数组，例如用于调试，但如果您的代码需要扩展你应该保持稀疏。

那么np.dot产品是：

product = A.dot(B.toarray())

您也可以使用 B.A 表示法，尽管在这种情况下会造成混淆：

product = A.dot(B.A)

product 是：

array([[16, -8,  0, ...,  0,  0,  0],
   [-3,  9, -3, ...,  0,  0,  0],
   [ 0, -1,  3, ...,  0,  0,  0],
   ...,
   [ 0,  0,  0, ..., 27, -9,  0],
   [ 0,  0,  0, ...,  0,  0,  0],
   [ 0,  0,  0, ...,  0, -4,  8]], dtype=int64)

【讨论】：

很抱歉我没有具体说明我是如何创建 B 的：我正在研究一个图形，所以我使用 networkx 库作为 R = nx.grid_graph(dim=[10,10] ) 然后我得到矩阵 B，因为它是拉普拉斯矩阵： B = nx.laplacian_matrix(R) 其中拉普拉斯矩阵是半定正对称矩阵
哦哦！谢谢！完美，现在我明白了！