从给定长度不同的字符串单元格数组创建矩阵 [英] Create matrices from a given cell-array of strings with different lengths

问题描述

我在一个细胞阵列中有3个序列:

I have 3 sequences in a cell-array:

Input_cell= {'ABCD','ACD', 'ABD'}

 S1= 'ABCD' % which means A<B<C<D
 S2= 'ACD'  % which means A<C<D  % missing B in the full string of 'ABCD'
 S3= 'ABD'  % which means A<B<D  % missing C in the full string of 'ABCD'

我想将Input_cell中的每个字符串转换为必须满足以下条件的矩阵M(i -by- j):

I want to convert each of the strings in the Input_cell into a matrix M (i-by-j) which has to satisfy these conditions:

• M(i,j)和M(j,i)是随机的
• M(i,i) = 0.5
• M(i,j) + M(j,i) = 1
• M(i,j) < M(j,i)例如，如果A<B然后M(A,B) < M(B,A)

• M(i,j) and M(j,i) are random
• M(i,i) = 0.5
• M(i,j) + M(j,i) = 1
• M(i,j) < M(j,i) For example if A<B then M(A,B) < M(B,A)

例如，如果我们有S1 = 'ABCD'(表示A<B<C<D)，则将按以下方式预期M1矩阵:

For example if we have S1 = 'ABCD' (which means A<B<C<D), the M1 matrix will be expected as follows:

     A      B     C     D
 A  0.5    0.3   0.2   0.1 
 B  0.7    0.5    0    0.4
 C  0.8     1    0.5   0.1
 D  0.9    0.6   0.9   0.5

如果我们有S2 = 'ACD'(表示A<C<D)，而在'ABCD'的完整字符串中缺少B，我们会将值0.5放在矩阵中B的每个位置， M2矩阵应如下所示:

If we have S2 = 'ACD' (which means A<C<D), missing B in the full string of 'ABCD', we will put the value 0.5 in every position of B in the matrix, the M2 matrix will be expected as follows:

     A      B     C     D
 A  0.5    0.5   0.2   0.1 
 B  0.5    0.5   0.5   0.5
 C  0.8    0.5   0.5   0.1
 D  0.9    0.5   0.9   0.5  

如果我们有S3 = 'ABD'(表示A<B<D)，而在'ABCD'的完整字符串中缺少C，我们会将值0.5放在矩阵中C的每个位置， M3矩阵预计如下:

If we have S3 = 'ABD' (which means A<B<D), missing C in the full string of 'ABCD', we will put the value 0.5 in every position of C in the matrix, the M3 matrix will be expected as follows:

     A      B     C     D
 A  0.5    0.4   0.5   0.1 
 B  0.6    0.5   0.5   0.3
 C  0.5    0.5   0.5   0.5
 D  0.9    0.7   0.5   0.5  

如何从给定的序列单元格数组中创建上述矩阵?

How to create that kind of above matrices from a given cell-array of sequences?

推荐答案

首先，您需要找出如何仅针对单个序列执行此操作:

Firstly you need to work out how to do this just for a single sequence:

1. 创建一个在0.5和1之间的随机数矩阵:

1. Create a matrix of random numbers between 0.5 and 1:

M = 0.5*rand(4) + 0.5;

将主对角线设置为等于0.5

M(logical(eye(4))) = 0.5;

设置M的上三角等于1-下三角:

Set the upper triangle of M equal to 1 - the lower triangle:

M(triu(true(4))) = 1 - M(tril(true(4)));   %// Note the main diagonal doesn't matter...

找出缺少的字母，并相应地将行和列设置为等于0.5:

fullSeq = 'abcd';
idx = find(fullSeq == setdiff(fullSeq, 'abd'));
%// at this point you'll need to check if idx is empty first...
M(:,idx) = 0.5;
M(idx,:) = 0.5;

现在您可以针对一个矩阵执行此操作，只需遍历单元格数组或将其封装到函数中并使用cellfun.

And now that you can do it for one matrix, just loop over your cell array or else encapsulate this into a function and use cellfun.

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