R语言：基于矩阵对应关系计算指定矩阵索引的均值

Got it, let's work through this problem step by step. First, let's fix a small issue in your sample code—you mentioned m1 is a 100×100 matrix, but the original code generates only 1000 elements (which makes a 10×100 matrix). Here's the corrected code to create the 100×100 m1 you described:

# Corrected sample data generation
m1 <- matrix(rexp(100*100, rate = .1), ncol = 100)  # 100 rows × 100 columns of decimals
m2 <- matrix(sample(c(rep(0, 1000), rep(1, 10), rep(2, 1)), 300 * 100, replace = T), 300, 100)  # 300 rows × 100 columns of sparse integers

To recap your goal clearly:

• Each row in m1 corresponds to the same-indexed column in m2
• The value at m2[i,j] represents how many times the j-th row of m1 appears in the i-th observation
• We need to calculate a 100-dimensional mean vector for each observation (each row in m2), where each dimension's mean is the weighted average of the corresponding values from m1, weighted by their occurrence counts in m2.

Step-by-Step Implementation #

1. Calculate Weighted Sums
   Transpose m1 and multiply it with m2—this gives us a 300×100 matrix where each entry [i,k] is the total weighted sum of the k-th dimension across all m1 rows included in the i-th observation. Matrix multiplication is far more efficient than looping here, especially for large matrices.

   weighted_sums <- m2 %*% t(m1)
   

2. Get Total Counts per Observation
   Use rowSums() to compute the total number of occurrences for each observation (row in m2):

   total_counts <- rowSums(m2)
   

3. Compute Weighted Means
   Divide each row of the weighted sums matrix by the corresponding total count. We also handle cases where an observation has 0 total counts (to avoid division by zero errors):

   # Use R's broadcasting to divide each row by its total count
   mean_matrix <- weighted_sums / total_counts
   # Replace infinite values (from 0/0) with NA (adjust this to 0 or another value if needed)
   mean_matrix[is.infinite(mean_matrix)] <- NA
   

What You Get #

The resulting mean_matrix is a 300×100 matrix where each row is the mean vector for the corresponding observation in m2. Each entry [i,k] is the average value of the k-th dimension across all m1 rows that appeared in the i-th observation, weighted by how many times each row showed up.

内容的提问来源于stack exchange，提问作者Christopher Costello