矩阵/向量的线性组合 [英] Linear combination of a matrix/vector

问题描述

B是[1x8]矩阵，也可以看作是两半，如下所示:

B is a [1x8] matrix which can also be considered as two halves as follows:

B = -1 -1 0 0   0 0 1 1

在上半部可以有一个，两个，三个或四个-1，在下半部应有相等数量的1.应该线性组合完成.

Here there can be either one, two, three or four -1's in the first half, and there should be equal number of 1's in the second half. It should be done in linear combinations.

例如，如果上半部有两个-1，则可以将它们放置为4 choose 2 = 6方式，对于每种方式，将有6种方式将两个1放置在其中下半场.因此，系统共有6 * 6 = 36路.即，如果上半部有两个-1，则B的36个不同值.

For example, if there are two -1's in the first half, they can be placed in 4 choose 2 = 6 ways, and for each of them there will be 6 ways to place the two 1's in the second half. So the system has a total of 6*6 = 36 ways. i.e. 36 different values for B's if there are two -1's in the first half.

我该怎么做?

推荐答案

您可以首先生成所有可能的1和0排列，然后丢弃多余的1.

You can first generate all possible permutations of ones and zeros, and then throw away the superfluous ones.

%# make permutations using dec2bin (start from 17 since it's the first solution)
allB = str2double(num2cell(dec2bin(17:255)));

%# change sign in the first half, then check that the total is ok
allB(:,1:4) = - allB(:,1:4);
allB = allB(sum(allB,2)==0,:);

allB的每一行都是B

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