I'm optimizing a function and I want to get rid of slow for loops. I'm looking for a faster way to multiply each row of a matrix by a vector.
我在优化一个函数,我想摆脱循环的缓慢。我在寻找一种更快的方法将矩阵的每一行乘以一个向量。
Any ideas?
什么好主意吗?
EDIT:
编辑:
I'm not looking for a 'classical' multiplication.
我不是在寻找“经典”乘法。
Eg. I have matrix that has 23 columns and 25 rows and a vector that has length of 23. In a result I want to have matrix 25x23 that has each row multiplied by vector.
如。我有一个有23列25行的矩阵和一个长度为23的向量。结果,我想要一个矩阵25x23每一行乘以一个向量。
62
I think you're looking for sweep()
.
我想你是在找横扫()。
> (mat <- matrix(rep(1:3,each=5),nrow=3,ncol=5,byrow=TRUE))
[,1] [,2] [,3] [,4] [,5]
[1,] 1 1 1 1 1
[2,] 2 2 2 2 2
[3,] 3 3 3 3 3
> vec <- 1:5
> sweep(mat,MARGIN=2,vec,`*`)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 2 3 4 5
[2,] 2 4 6 8 10
[3,] 3 6 9 12 15
It's been one of R's core functions, though improvements have been made on it over the years.
这是R的核心功能之一,尽管多年来已经有了改进。
33
> MyMatrix <- matrix(c(1,2,3, 11,12,13), nrow = 2, ncol=3, byrow=TRUE)
> MyMatrix
[,1] [,2] [,3]
[1,] 1 2 3
[2,] 11 12 13
> MyVector <- c(1:3)
> MyVector
[1] 1 2 3
You could use either:
您可以使用:
> t(t(MyMatrix) * MyVector)
[,1] [,2] [,3]
[1,] 1 4 9
[2,] 11 24 39
or:
或者:
> MyMatrix %*% diag(MyVector)
[,1] [,2] [,3]
[1,] 1 4 9
[2,] 11 24 39
22
Actually, sweep
is not the fastest option on my computer:
事实上,扫地不是我电脑上最快的选择:
MyMatrix <- matrix(c(1:1e6), ncol=1e4, byrow=TRUE)
MyVector <- c(1:1e4)
Rprof(tmp <- tempfile(),interval = 0.001)
t(t(MyMatrix) * MyVector) # first option
Rprof()
MyTimerTranspose=summaryRprof(tmp)$sampling.time
unlink(tmp)
Rprof(tmp <- tempfile(),interval = 0.001)
MyMatrix %*% diag(MyVector) # second option
Rprof()
MyTimerDiag=summaryRprof(tmp)$sampling.time
unlink(tmp)
Rprof(tmp <- tempfile(),interval = 0.001)
sweep(MyMatrix ,MARGIN=2,MyVector,`*`) # third option
Rprof()
MyTimerSweep=summaryRprof(tmp)$sampling.time
unlink(tmp)
Rprof(tmp <- tempfile(),interval = 0.001)
t(t(MyMatrix) * MyVector) # first option again, to check order
Rprof()
MyTimerTransposeAgain=summaryRprof(tmp)$sampling.time
unlink(tmp)
MyTimerTranspose
MyTimerDiag
MyTimerSweep
MyTimerTransposeAgain
This yields:
这个收益率:
> MyTimerTranspose
[1] 0.04
> MyTimerDiag
[1] 40.722
> MyTimerSweep
[1] 33.774
> MyTimerTransposeAgain
[1] 0.043
On top of being the slowest option, the second option reaches the memory limit (2046 MB). However, considering the remaining options, the double transposition seems a lot better than sweep
in my opinion.
除了是最慢的选项之外,第二个选项达到内存限制(2046 MB)。然而,在我看来,考虑到其他的选择,双置换比清除要好得多。
Edit
编辑
Just trying smaller data a repeated number of times:
只是反复尝试更小的数据:
MyMatrix <- matrix(c(1:1e3), ncol=1e1, byrow=TRUE)
MyVector <- c(1:1e1)
n=100000
[...]
for(i in 1:n){
# your option
}
[...]
> MyTimerTranspose
[1] 5.383
> MyTimerDiag
[1] 6.404
> MyTimerSweep
[1] 12.843
> MyTimerTransposeAgain
[1] 5.428
-2
Google "R matrix multiplcation" yields Matrix Multiplication, which describes the %*% operator and says "Multiplies two matrices, if they are conformable. If one argument is a vector, it will be promoted to either a row or column matrix to make the two arguments conformable. If both are vectors it will return the inner product (as a matrix)."
谷歌“R矩阵多重化”产生矩阵乘法,矩阵乘法描述了%*%的运算符,并说“如果两个矩阵是可整合的,则相乘”。如果一个参数是一个向量,它将被提升到一个行或列矩阵,使两个参数一致。如果两个都是向量,它会返回内积(作为一个矩阵)
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