如何在Matlab中实现泊松分布的矩阵式计算？

Hey there! Let's break down how to fix those dimension mismatches and generate the exact 20×20 matrices you need for each pair of A/B values, then compute the region sums you're after. I'll walk through this step by step with code examples that match your Excel workflow.

First, Align with Your Excel Logic #

In Excel, you’re calculating POISSON(x, μ, FALSE) where x starts at 0 (like cell AD313 uses x=0 for both A and B). So in MATLAB, we need to use z = 0:19 (20 values total, from 0 to 19) instead of 1:20—that’s one key fix for your earlier dimension error.

Step 1: Import Your Data #

First, load your CSV data properly (assuming A is column 1, B is column 2):

% Load the CSV file
data = readmatrix('your_data.csv');
A = data(:, 1);  % 110×1 vector of A values
B = data(:, 2);  % 110×1 vector of B values

Step 2: Generate the Grid for Matrix Indices #

We need a 20×20 grid where each row corresponds to x = row-1 (for A) and each column corresponds to y = column-1 (for B). Use meshgrid to create this:

z_values = 0:19;  % Matches your Excel x=0 to x=19 (20 values total)
[Z_row, Z_col] = meshgrid(z_values, z_values);
% Z_row: 20×20 matrix where each row is [0,1,...,19]
% Z_col: 20×20 matrix where each column is [0,1,...,19]

Step 3: Batch Generate All 110 Matrices #

To avoid slow loops, we’ll use MATLAB’s broadcasting feature by reshaping A and B into 3D arrays. This lets us compute all 110 matrices at once:

% Reshape A and B to 1×1×110 to enable broadcasting with the 20×20 grids
A_3d = reshape(A, 1, 1, []);
B_3d = reshape(B, 1, 1, []);

% Calculate the Poisson product for every cell in every matrix
poisson_matrices = poisspdf(Z_row, A_3d) .* poisspdf(Z_col, B_3d);
% Result: 20×20×110 array, where poisspdf(:,:,i) is the matrix for A(i) and B(i)

Step 4: Sum Specific Regions of Each Matrix #

Now compute the sum for your target region. Let’s use an example—adjust the mask to match your actual region:

% Define your region mask (customize this to your exact needs!)
% Example: Sum all cells where x + y ≤ 5 (x = row-1, y = column-1)
region_mask = (Z_row + Z_col) <= 5;

% Sum the masked region for each matrix
region_sums = squeeze(sum(sum(poisson_matrices .* region_mask, 1), 2));
% squeeze converts the 1×1×110 result to a clean 110×1 vector

If your target region is based on row/column ranges (e.g., rows 1-10 and columns 5-15), adjust the mask like this:

% Rows 1-10 → x = 0-9; Columns 5-15 → y = 4-14
region_mask = (Z_row >= 0 & Z_row <=9) & (Z_col >=4 & Z_col <=14);

Step 5: Add Sum Results as a New Column #

Finally, append the sums to your original data and save it back to CSV:

% Combine original data with the new sum column
data_with_sums = [data, region_sums];

% Save to a new CSV file
writematrix(data_with_sums, 'your_results_with_sums.csv');

Why Your Earlier Code Had Issues #

• You used z=1:20 instead of 0:19, which didn’t align with Excel’s starting x=0.
• When you tried Poisspdf(z,A), MATLAB couldn’t broadcast a 1×20 vector with a 110×1 vector. Reshaping A/B to 3D arrays lets MATLAB automatically apply each A/B pair to the entire 20×20 grid.

内容的提问来源于stack exchange，提问作者blowbuh