Question

我想使用相应的scipy格式之一构造一个块矩阵。最终，矩阵必须转换为CSC。

我实际上获得的块是（密集的）numpy数组（具有ndim == 2）或偶尔是稀疏的标识。对于行的每个子集（从上到下），我从左到右添加相应的块。目前，我正在创建矩阵，然后根据索引切片分配块。

我的问题（关于表现）如下：

建议使用切片还是应该使用scipy.sparse.bmat？
如果我使用切片，应该使用哪种矩阵类型插入块（我以M[a:b,:]和M[:,a:b]的形式分配切片）？

Answer 1

我不知道scipy方法的效率如何，但是使用coo格式，手工构建块矩阵相对简单。所有需要做的就是收集块的row，col和data属性，将块偏移量添加到坐标（即row和col ），然后串联：

import numpy as np
from scipy import sparse
from collections import namedtuple
from operator import attrgetter

submat = namedtuple('submat', 'row_offset col_offset block')

def join_blocks(blocks):
    roff, coff, mat = zip(*blocks)
    row, col, data = zip(*map(attrgetter('row', 'col', 'data'), mat))
    row = [o + r for o, r in zip(roff, row)]
    col = [o + c for o, c in zip(coff, col)]
    row, col, data = map(np.concatenate, (row, col, data))
    return sparse.coo_matrix((data, (row, col))).tocsr()

example = [*map(submat, range(0, 10, 2), range(8, -2, -2), map(sparse.coo_matrix, np.multiply.outer([6, 2, 1, 3, 4], [[1, 0], [-1, 1]])))]

print('Example:')
for sm in example:
    print(sm)

print('\nCombined')
print(join_blocks(example).A)

打印：

Example:
submat(row_offset=0, col_offset=8, block=<2x2 sparse matrix of type '<class 'numpy.int64'>'
        with 3 stored elements in COOrdinate format>)
submat(row_offset=2, col_offset=6, block=<2x2 sparse matrix of type '<class 'numpy.int64'>'
        with 3 stored elements in COOrdinate format>)
submat(row_offset=4, col_offset=4, block=<2x2 sparse matrix of type '<class 'numpy.int64'>'
        with 3 stored elements in COOrdinate format>)
submat(row_offset=6, col_offset=2, block=<2x2 sparse matrix of type '<class 'numpy.int64'>'
        with 3 stored elements in COOrdinate format>)
submat(row_offset=8, col_offset=0, block=<2x2 sparse matrix of type '<class 'numpy.int64'>'
        with 3 stored elements in COOrdinate format>)

Combined
[[ 0  0  0  0  0  0  0  0  6  0]
 [ 0  0  0  0  0  0  0  0 -6  6]
 [ 0  0  0  0  0  0  2  0  0  0]
 [ 0  0  0  0  0  0 -2  2  0  0]
 [ 0  0  0  0  1  0  0  0  0  0]
 [ 0  0  0  0 -1  1  0  0  0  0]
 [ 0  0  3  0  0  0  0  0  0  0]
 [ 0  0 -3  3  0  0  0  0  0  0]
 [ 4  0  0  0  0  0  0  0  0  0]
 [-4  4  0  0  0  0  0  0  0  0]]

哪种稀疏矩阵格式更适合构建块矩阵

1 个答案: