如何在Matlab中通过索引矩阵实现指定位置的赋值操作？

Hey there! Let's break down your problem and work through solutions for both examples.

Second Example: Clear Row Mapping Rule #

Looking at your second example, the pattern is straightforward and generalizable:

• For each column j (from 1 to 4), the value index(j) maps directly to which row gets a 1:
  • Values 1 or 2 → set row 1 of column j to 1
  • Values 3 or 4 → set row 2 of column j to 1

You can simplify this mapping using ceil(index/2) to group index values into row numbers (1 or 2). Here's the clean MATLAB code to achieve your desired output:

% Initialize 2x4 zero matrix
A = zeros(2, 4);
% Define your index vector
index = [1 3 2 4];

% Identify which columns belong to each row
row1_cols = ceil(index ./ 2) == 1;
row2_cols = ceil(index ./ 2) == 2;

% Assign 1s to the correct positions
A(1, row1_cols) = 1;
A(2, row2_cols) = 1;

Running this code will produce exactly the matrix you want:

A =
     1     0     1     0
     0     1     0     1

First Example: Deriving the Underlying Rule #

For your first example, let's map the desired A matrix back to the index vector to unpack the pattern:
Desired A:

A =
     1     1     0     0
     0     1     1     0

The 1s are at positions (1,1), (1,2), (2,2), (2,3). Looking at index = [1 2 2 3], the initial pattern seems a bit inconsistent at first glance:

• index(j)=1: Only row 1 of column j gets a 1
• index(j)=2: Both rows of column j get a 1 (column 2) OR only row 2 gets a 1 (column 3)
• index(j)=3: No rows get a 1

A more consistent interpretation that aligns with most of your desired output is treating index(j) as a range indicator:

• index(j)=1: Set row 1 only
• index(j)=2: Set rows 1 and 2
• index(j)=3: Set row 2 only (but since your desired column 4 is all zeros, maybe index(j)=3 means no assignment here?)

But this would set column 3's row 1 to 1, which doesn't match your desired result. To get exactly your first example's output, we'd need a minor adjustment for column 3—maybe a case-specific rule where index(j)=2 sets only row 2 when j>2. Here's code that does that:

A = zeros(2, 4);
index = [1 2 2 3];

for j = 1:length(index)
    k = index(j);
    switch k
        case 1
            A(1, j) = 1;
        case 2
            if j == 2
                A(:, j) = 1;
            else
                A(2, j) = 1;
            end
        case 3
            % Do nothing for column 4
    end
end

If there's a general rule you're following that I missed (e.g., index(j) indicates a sliding window of rows), feel free to clarify and we can refine the solution to be fully generalizable!

内容的提问来源于stack exchange，提问作者Duan Yu