构造限制矩阵使得奇数行为零

Question

我有两个数组：A 的形状为 (m,n)，B 的形状为 (2*m,n)。此外，B的偶数行是A的行。让a = numpy.reshape(A,(A.size,1))和b = numpy.reshape(B,(B.size,1))。我的目标是构造一个对角矩阵 R 使得 R*b = a。数组如下所示：

[[13865.995  14020.785  14020.788 ]
 [ 6885.634   6784.8813  6837.428 ]
 [14510.425  14712.554  14657.217 ]
 [ 7688.0923  7817.8457  7792.413 ]
 [10473.903  10417.55   10469.508 ]
 [10485.661  10348.152  10632.414 ]]
[[14662.705  14869.951  15166.294 ]
 [13865.995  14020.785  14020.788 ]
 [ 9780.559  10038.395  10202.31  ]
 [ 6885.634   6784.8813  6837.428 ]
 [ 7167.9575  7357.9062  7287.3003]
 [14510.425  14712.554  14657.217 ]
 [12825.017  12680.751  12823.563 ]
 [ 7688.0923  7817.8457  7792.413 ]
 [ 6861.9443  6826.6245  6758.8965]
 [10473.903  10417.55   10469.508 ]
 [ 8498.976   8637.245   8718.052 ]
 [10485.661  10348.152  10632.414 ]]

我确定我可以在正确的索引处构造一个数组 x，其值为 0 和 1，然后设置 R = np.diag(x)，但我不确定我怎样才能使这项工作，如果这是最好的解决方案。感谢任何帮助

Answer 1

这需要一些创造性的数组索引，但希望这就是您所追求的。注意：在这种情况下，R 实际上不是对角矩阵。

import numpy

A = numpy.array([[13865.995,  14020.785,  14020.788 ],
    [ 6885.634,   6784.8813,  6837.428 ],
    [14510.425,  14712.554,  14657.217 ],
    [ 7688.0923,  7817.8457,  7792.413 ],
    [10473.903,  10417.55,   10469.508 ],
    [10485.661,  10348.152,  10632.414 ]])
B = numpy.array([[14662.705,  14869.951,  15166.294 ],
    [13865.995,  14020.785,  14020.788 ],
    [ 9780.559,  10038.395,  10202.31  ],
    [ 6885.634,   6784.8813,  6837.428 ],
    [ 7167.9575,  7357.9062,  7287.3003],
    [14510.425,  14712.554,  14657.217 ],
    [12825.017,  12680.751,  12823.563 ],
    [ 7688.0923,  7817.8457,  7792.413 ],
    [ 6861.9443,  6826.6245,  6758.8965],
    [10473.903,  10417.55,   10469.508 ],
    [ 8498.976,   8637.245,   8718.052 ],
    [10485.661,  10348.152,  10632.414 ]])
a = numpy.reshape(A,(A.size,1))
b = numpy.reshape(B,(B.size,1))
R = numpy.zeros((A.size,B.size))
R[[a for a in range(A.size)],[a for a in range(B.size) if (a // 3) % 2]] = 1
print( numpy.all(numpy.dot(R, b) == a) )
# True

构造限制矩阵使得奇数行为零

Construct restriction matrix such that the odd rows are zero

python

arrays

indexing

numpy

diagonal