Julia - 行外积的线性组合

Question

我有一个 (n, m) 维度的矩阵 A 和 (n, p) 维度的矩阵 B 。对于 n 行中的每一行，我想计算 A 行和 B 行之间的外积，它们是 (m, p) 矩阵。然后我有一个大小为 n 的向量 x 我想将这些矩阵中的每一个乘以 x 的相应条目并将所有内容相加.我该怎么做？

# Parameters
n, m, p = 100, 10, 3
# Matrices & Vectors
A, B, x = randn(n, m), randn(n, p), randn(n)
# Slow method
result = zeros(m, p)
for i in 1:n
    result += x[i] * (A[i, :] * B[i, :]')
end

Answer 1

这是另一个版本

# Parameters
n, m, p = 100, 10, 3

# Matrices & Vectors
A, B, x = randn(n, m), randn(n, p), randn(n)

function old_way(A, B, x)
    # Slow method
    result = zeros(m, p)
    for i in 1:n
        result += x[i] * (A[i, :] * B[i, :]')
    end
end

function another_way(A, B, x)
    sum(xi * (Arow * Brow') for (xi, Arow, Brow) in zip(x, eachrow(A), eachrow(B)))
end

和基准测试:

julia> using BenchmarkTools

julia> @benchmark old_way(A, B, x)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):   83.495 μs …   2.653 ms  ┊ GC (min … max): 0.00% … 95.79%
 Time  (median):      87.500 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   101.496 μs ± 115.196 μs  ┊ GC (mean ± σ):  6.46% ±  5.53%

  ▃█▇▆▂    ▁ ▁        ▁                                         ▁
  ███████████████▇█▇██████▆▇▇▇▆▇▇▇▇▇▇▇▇▆▇▆▆▇▆▇▅▆▆▆▄▅▅▅▅▆▅▆▅▅▅▄▅ █
  83.5 μs       Histogram: log(frequency) by time        200 μs <

 Memory estimate: 153.48 KiB, allocs estimate: 1802.


julia> @benchmark another_way(A, B, x)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  25.850 μs … 923.032 μs  ┊ GC (min … max): 0.00% … 95.94%
 Time  (median):     27.477 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   31.851 μs ±  35.440 μs  ┊ GC (mean ± σ):  5.03% ±  4.49%

  ▇█▇▅▃▁           ▁▁▁                                         ▁
  ███████▇▇▆▇████████████▇█▇▇▇▆▇▆▅▆▆▆▅▆▆▅▆▆▇▆▅▅▅▆▅▆▅▅▅▄▃▅▅▅▄▄▄ █
  25.8 μs       Histogram: log(frequency) by time      77.4 μs <

 Memory estimate: 98.31 KiB, allocs estimate: 304.

所以它更快一点，并且使用更少的内存。

这是否回答了您的问题？