将数字向量与矩阵按行相乘
multiply a vector of numbers with matrix rowwise
考虑一个数字向量，a <- c(75,26,65,27,97,72)
和一个矩阵10x6矩阵b
1.4168709 0.6253624 2.08645202 2.9475645 1.29317931 0.80175442
0.3669328 0.851852 0.57428245 2.8542504 1.40075478 0.01745655
6.1173956 1.6848444 1.05468424 0.3382552 1.1428774 0.41141215
2.8203602 0.9573334 0.22131122 0.4406137 0.07209113 0.17910147
0.102152 0.1779387 0.94915127 0.3516491 1.48272109 0.06037996
0.3124434 0.4892484 2.04443039 0.1251463 2.41507973 1.25367433
0.2154152 0.3951161 0.60410084 0.7551265 0.55764737 1.17793564
1.5451135 0.7764766 3.11515773 1.3519765 0.08916275 1.39969422
0.4018092 0.2432501 0.06470464 2.6173665 0.24696145 5.27272096
1.1683212 0.1258633 0.19431636 0.4160356 1.61775945 0.78849181
dput
b <- structure(c(1.41687091749774, 0.366932780481875, 6.11739562418232,
2.8203601760972, 0.102152034174651, 0.312443420290947, 0.215415194164962,
1.54511345728281, 0.401809234172106, 1.16832122397808, 0.625362366437912,
0.851851973640633, 1.68484436153414, 0.957333435262454, 0.177938693314666,
0.489248352590948, 0.395116138737649, 0.776476616387118, 0.243250062223524,
0.125863284132781, 2.08645202020619, 0.57428245106712, 1.05468423915856,
0.221311220899224, 0.949151266561806, 2.04443038991633, 0.604100843891501,
3.11515773070936, 0.0647046443940286, 0.194316359037562, 2.94756450172152,
2.85425036383753, 0.338255227074493, 0.440613748457464, 0.351649099495262,
0.125146273523569, 0.755126529331219, 1.35197646259786, 2.61736654663894,
0.416035552509129, 1.29317931454153, 1.40075477585735, 1.14287740174205,
0.072091125883162, 1.48272109049815, 2.41507973323081, 0.557647368015562,
0.0891627511009574, 0.246961451135576, 1.61775945491138, 0.80175441955164,
0.0174565480835137, 0.411412146408111, 0.179101474117488, 0.0603799588836676,
1.25367433010839, 1.17793564121695, 1.39969422101023, 5.27272095591089,
0.788491813423944), .Dim = c(10L, 6L))
我的问题是如何按行将向量 a 与矩阵 b 相乘。我知道 b%*%a 会做什么。
我正在尝试做这样的事情
75*1.4168709 + 26*0.6253624 + 65*2.08645202 + 27*2.9475645 + 97*1.29317931 + 72*0.80175442
75*0.3669328 + 26*0.851852 + 65*0.57428245 + 27*2.8542504 + 97*1.40075478 + 72*0.01745655
等等
非常感谢任何建议。
我们可以在进行乘法之前获得相同的长度，即通过复制 'a' 个元素
a[col(b)] * b
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
# [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
# [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
# [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
# [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
# [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
# [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
# [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
# [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
#[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
或转置'b'，然后乘以'a'并转置输出
t(t(b) * a)
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
# [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
# [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
# [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
# [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
# [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
# [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
# [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
# [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
#[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
或rep更明确地请求rep
rep(a, each = nrow(b)) * b
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
# [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
# [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
# [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
# [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
# [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
# [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
# [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
# [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
#[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
或者我们可以 split 按列将矩阵 'b' 转换为 list，然后将其与 mapply 一起使用。现在，相应的个体单位相乘
mapply(`*`, split(b, col(b)), a)
一次，我们完成了上面的步骤，就做rowSums
out2 <- rowSums(a[col(b)] * b)
out2
#[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
-用OP的方法检查输出
out1 <- (b%*%a)[,1]
out1
#[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
all.equal(out1, out2)
#[1] TRUE
看起来像 sweep 操作。在 R 中，对于应用于边缘的函数，“2”通常表示列操作，根据您的论点和结构，我将如何描述您的预期结果。 n（我知道你会怎么称呼它 "row-wise" 但大多数 R 用户会认为这是按“列方式应用的：.
> sweep(b,2,a,"*")
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
[2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
[3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
[4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
[5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
[6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
[7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
[8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
[9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
然后 rowSums:
> rowSums( sweep(b,2,a,"*") )
[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
或者，矩阵运算：
a %*% t(b)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
以及速度稍快的单功能版本：
tcrossprod(a,b)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
考虑一个数字向量，a <- c(75,26,65,27,97,72)
和一个矩阵10x6矩阵b
1.4168709 0.6253624 2.08645202 2.9475645 1.29317931 0.80175442
0.3669328 0.851852 0.57428245 2.8542504 1.40075478 0.01745655
6.1173956 1.6848444 1.05468424 0.3382552 1.1428774 0.41141215
2.8203602 0.9573334 0.22131122 0.4406137 0.07209113 0.17910147
0.102152 0.1779387 0.94915127 0.3516491 1.48272109 0.06037996
0.3124434 0.4892484 2.04443039 0.1251463 2.41507973 1.25367433
0.2154152 0.3951161 0.60410084 0.7551265 0.55764737 1.17793564
1.5451135 0.7764766 3.11515773 1.3519765 0.08916275 1.39969422
0.4018092 0.2432501 0.06470464 2.6173665 0.24696145 5.27272096
1.1683212 0.1258633 0.19431636 0.4160356 1.61775945 0.78849181
dput
b <- structure(c(1.41687091749774, 0.366932780481875, 6.11739562418232,
2.8203601760972, 0.102152034174651, 0.312443420290947, 0.215415194164962,
1.54511345728281, 0.401809234172106, 1.16832122397808, 0.625362366437912,
0.851851973640633, 1.68484436153414, 0.957333435262454, 0.177938693314666,
0.489248352590948, 0.395116138737649, 0.776476616387118, 0.243250062223524,
0.125863284132781, 2.08645202020619, 0.57428245106712, 1.05468423915856,
0.221311220899224, 0.949151266561806, 2.04443038991633, 0.604100843891501,
3.11515773070936, 0.0647046443940286, 0.194316359037562, 2.94756450172152,
2.85425036383753, 0.338255227074493, 0.440613748457464, 0.351649099495262,
0.125146273523569, 0.755126529331219, 1.35197646259786, 2.61736654663894,
0.416035552509129, 1.29317931454153, 1.40075477585735, 1.14287740174205,
0.072091125883162, 1.48272109049815, 2.41507973323081, 0.557647368015562,
0.0891627511009574, 0.246961451135576, 1.61775945491138, 0.80175441955164,
0.0174565480835137, 0.411412146408111, 0.179101474117488, 0.0603799588836676,
1.25367433010839, 1.17793564121695, 1.39969422101023, 5.27272095591089,
0.788491813423944), .Dim = c(10L, 6L))
我的问题是如何按行将向量 a 与矩阵 b 相乘。我知道 b%*%a 会做什么。
我正在尝试做这样的事情
75*1.4168709 + 26*0.6253624 + 65*2.08645202 + 27*2.9475645 + 97*1.29317931 + 72*0.80175442
75*0.3669328 + 26*0.851852 + 65*0.57428245 + 27*2.8542504 + 97*1.40075478 + 72*0.01745655
等等
非常感谢任何建议。
我们可以在进行乘法之前获得相同的长度，即通过复制 'a' 个元素
a[col(b)] * b
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
# [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
# [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
# [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
# [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
# [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
# [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
# [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
# [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
#[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
或转置'b'，然后乘以'a'并转置输出
t(t(b) * a)
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
# [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
# [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
# [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
# [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
# [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
# [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
# [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
# [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
#[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
或rep更明确地请求rep
rep(a, each = nrow(b)) * b
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
# [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
# [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
# [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
# [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
# [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
# [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
# [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
# [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
#[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
或者我们可以 split 按列将矩阵 'b' 转换为 list，然后将其与 mapply 一起使用。现在，相应的个体单位相乘
mapply(`*`, split(b, col(b)), a)
一次，我们完成了上面的步骤，就做rowSums
out2 <- rowSums(a[col(b)] * b)
out2
#[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
-用OP的方法检查输出
out1 <- (b%*%a)[,1]
out1
#[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
all.equal(out1, out2)
#[1] TRUE
看起来像 sweep 操作。在 R 中，对于应用于边缘的函数，“2”通常表示列操作，根据您的论点和结构，我将如何描述您的预期结果。 n（我知道你会怎么称呼它 "row-wise" 但大多数 R 用户会认为这是按“列方式应用的：.
> sweep(b,2,a,"*")
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318
[2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871
[3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675
[4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306
[5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357
[6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552
[7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366
[8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984
[9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909
[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411
然后 rowSums:
> rowSums( sweep(b,2,a,"*") )
[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
或者，矩阵运算：
a %*% t(b)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
以及速度稍快的单功能版本：
tcrossprod(a,b)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541