科学网-王娟的博客-[转载]R语言矩阵运算企业库|免费b2b网站

科学网-王娟的博客-[转载]R语言矩阵运算

鏍忕洰鍒嗙被

鍗氫富濂藉弸

姝ｆ枃

瀛﹁€呯帇濞?鍙戣〃浜?010-5-8 9:50:48
锛? 鈹? 娴忚锛?9

[杞浇]R璇█鐭╅樀杩愮畻

涓昏鍖呮嫭浠ヤ笅鍐呭锛?br />鍒涘缓鐭╅樀鍚戦噺锛涚煩闃靛姞鍑忥紝涔樼Н锛涚煩闃电殑閫嗭紱琛屽垪寮忕殑鍊硷紱鐗瑰緛鍊间笌鐗瑰緛鍚戦噺锛決R鍒嗚В锛涘寮傚€煎垎瑙ｏ紱骞夸箟閫嗭紱backsolve涓巉owardsolve鍑芥暟锛涘彇鐭╅樀鐨勪笂涓嬩笁瑙掑厓绱狅紱鍚戦噺鍖栫畻瀛愮瓑.

1 鍒涘缓涓€涓悜閲?/strong>
鍦≧涓彲浠ョ敤鍑芥暟c()鏉ュ垱寤轰竴涓悜閲忥紝渚嬪锛?br />> x=c(1,2,3,4)
> x
[1] 1 2 3 4
2 鍒涘缓涓€涓煩闃?/strong>
鍦≧涓彲浠ョ敤鍑芥暟matrix()鏉ュ垱寤轰竴涓煩闃碉紝搴旂敤璇ュ嚱鏁版椂闇€瑕佽緭鍏ュ繀瑕佺殑鍙傛暟鍊笺€?br />> args(matrix)
function (data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL)
data椤逛负蹇呰鐨勭煩闃靛厓绱狅紝nrow涓鸿鏁帮紝ncol涓哄垪鏁帮紝娉ㄦ剰nrow涓?font face="Courier New, Courier, Monospace">ncol鐨勪箻绉簲涓虹煩闃靛厓绱犱釜鏁帮紝byrow椤规帶鍒舵帓鍒楀厓绱犳椂鏄惁鎸夎杩涜锛?font face="Courier New, Courier, Monospace">dimnames缁欏畾琛屽拰鍒楃殑鍚嶇О銆備緥濡傦細
> matrix(1:12,nrow=3,ncol=4)
    [,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> matrix(1:12,nrow=4,ncol=3)
    [,1] [,2] [,3]
[1,] 1 5 9
[2,] 2 6 10
[3,] 3 7 11
[4,] 4 8 12
> matrix(1:12,nrow=4,ncol=3,byrow=T)
    [,1] [,2] [,3]
[1,] 1 2 3
[2,] 4 5 6
[3,] 7 8 9
[4,] 10 11 12
> rowname
[1] "r1" "r2" "r3"
> colname=c("c1","c2","c3","c4")
> colname
[1] "c1" "c2" "c3" "c4"
> matrix(1:12,nrow=3,ncol=4,dimnames=list(rowname,colname))
c1 c2 c3 c4
r1 1 4 7 10
r2 2 5 8 11
3 鐭╅樀杞疆
A涓簃×n鐭╅樀锛屾眰A'鍦?font face="Courier New, Courier, Monospace">R涓彲鐢ㄥ嚱鏁?font face="Courier New, Courier, Monospace">t()锛?/font>渚嬪锛?br />> A=matrix(1:12,nrow=3,ncol=4)
> A
   [,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> t(A)
   [,1] [,2] [,3]
[1,] 1 2 3
[2,] 4 5 6
[3,] 7 8 9
[4,] 10 11 12
鑻ュ皢鍑芥暟t()浣滅敤浜庝竴涓悜閲弜锛屽垯R榛樿x涓哄垪鍚戦噺锛岃繑鍥炵粨鏋滀负涓€涓鍚戦噺锛屼緥濡傦細
> x
[1] 1 2 3 4 5 6 7 8 9 10
> t(x)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 1 2 3 4 5 6 7 8 9 10
> class(x)
[1] "integer"
> class(t(x))
[1] "matrix"
鑻ユ兂寰楀埌涓€涓垪鍚戦噺锛屽彲鐢?font face="Courier New, Courier, Monospace">t(t(x))锛?/font>渚嬪锛?br />> x
[1] 1 2 3 4 5 6 7 8 9 10
> t(t(x))
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
[5,] 5
[6,] 6
[7,] 7
[8,] 8
[9,] 9
[10,]  10
> y=t(t(x))
> t(t(y))
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
[5,] 5
[6,] 6
[7,] 7
[8,] 8
[9,] 9
[10,] 10
4 鐭╅樀鐩稿姞鍑?/strong>
鍦≧涓鍚岃鍚屽垪鐭╅樀鐩稿姞鍑忥紝鍙敤绗﹀彿锛?ldquo;锛?rdquo;銆?ldquo;锛?rdquo;锛屼緥濡傦細
> A=B=matrix(1:12,nrow=3,ncol=4)
> A+B
[,1] [,2] [,3] [,4]
[1,] 2 8 14 20
[2,] 4 10 16 22
[3,] 6 12 18 24
> A-B
   [,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 0 0 0 0
5 鏁颁笌鐭╅樀鐩镐箻
A涓簃×n鐭╅樀锛宑>0锛屽湪R涓眰cA鍙敤绗﹀彿锛?ldquo;*”锛屼緥濡傦細
> c=2
> c*A
    [,1] [,2] [,3] [,4]
[1,] 2 8 14 20
[2,] 4 10  16 22
[3,] 6 12  18 24
6 鐭╅樀鐩镐箻
A涓簃×n鐭╅樀锛孊涓簄×k鐭╅樀锛屽湪R涓眰AB鍙敤绗﹀彿锛?ldquo;锛?锛?rdquo;锛屼緥濡傦細
> A=matrix(1:12,nrow=3,ncol=4)
> B=matrix(1:12,nrow=4,ncol=3)
> A%*%B
    [,1] [,2] [,3]
[1,] 70  158 246
[2,] 80 184 288
[3,] 90 210 330
鑻涓簄×m鐭╅樀锛岃寰楀埌A'B锛屽彲鐢ㄥ嚱鏁?font face="Courier New, Courier, Monospace">crossprod()锛?/font>璇ュ嚱鏁拌绠楃粨鏋滀笌t(A)%*%B鐩稿悓锛屼絾鏄晥鐜囨洿楂樸€備緥濡傦細
> A=matrix(1:12,nrow=4,ncol=3)
> B=matrix(1:12,nrow=4,ncol=3)
> t(A)%*%B
    [,1] [,2] [,3]
[1,] 30   70 110
[2,] 70 174 278
[3,] 110 278 446
> crossprod(A,B)
    [,1] [,2] [,3]
[1,]  30 70 110
[2,]  70 174 278
[3,] 110 278 446
鐭╅樀Hadamard绉細鑻={aij}m×n, B={bij}m×n, 鍒欑煩闃电殑Hadamard绉畾涔変负锛?br />A鈯橞={aij bij }m×n,R涓璈adamard绉彲浠ョ洿鎺ヨ繍鐢ㄨ繍绠楃“*”渚嬪锛?br />> A=matrix(1:16,4,4)
> A
    [,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
> B=A
> A*B
    [,1] [,2] [,3] [,4]
[1,] 1 25 81 169
[2,] 4 36 100 196
[3,] 9 49 121 225
[4,] 16 64 144 256
R涓繖涓や釜杩愮畻绗︾殑鍖哄埆鍖哄姞浠ユ敞鎰忋€?/font>
7 鐭╅樀瀵硅鍏冪礌鐩稿叧杩愮畻
渚嬪瑕佸彇涓€涓柟闃电殑瀵硅鍏冪礌锛?br />> A=matrix(1:16,nrow=4,ncol=4)
> A
    [,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
> diag(A)
[1] 1 6 11 16
瀵逛竴涓悜閲忓簲鐢?font face="Courier New, Courier, Monospace">diag()鍑芥暟灏嗕骇鐢熶互杩欎釜鍚戦噺涓哄瑙掑厓绱犵殑瀵硅鐭╅樀锛屼緥濡傦細
> diag(diag(A))
    [,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 0 6 0 0
[3,] 0 0 11 0
[4,] 0 0 0 16
瀵逛竴涓鏁存暟z搴旂敤diag()鍑芥暟灏嗕骇鐢熶互z缁村崟浣嶇煩闃碉紝渚嬪锛?br />> diag(3)
    [,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 1 0
[3,] 0 0 1
8 鐭╅樀姹傞€?/strong>
鐭╅樀姹傞€嗗彲鐢ㄥ嚱鏁?font face="Courier New, Courier, Monospace">solve()锛?/font>搴旂敤solve(a, b)杩愮畻缁撴灉鏄В绾挎€ф柟绋嬬粍ax = b锛岃嫢b缂虹渷锛屽垯绯荤粺榛樿涓哄崟浣嶇煩闃碉紝鍥犳鍙敤鍏惰繘琛岀煩闃垫眰閫嗭紝渚嬪锛?br />> a=matrix(rnorm(16),4,4)
> a
[,1] [,2] [,3] [,4]
[1,] 1.6986019 0.5239738 0.2332094 0.3174184
[2,] -0.2010667 1.0913013 -1.2093734 0.8096514
[3,] -0.1797628 -0.7573283 0.2864535 1.3679963
[4,] -0.2217916 -0.3754700 0.1696771 -1.2424030
> solve(a)
[,1] [,2] [,3] [,4]
[1,] 0.9096360 0.54057479 0.7234861 1.3813059
[2,] -0.6464172 -0.91849017 -1.7546836 -2.6957775
[3,] -0.7841661 -1.78780083 -1.5795262 -3.1046207
[4,] -0.0741260 -0.06308603 0.1854137 -0.6607851
> solve (a) %*%a
[,1] [,2] [,3] [,4]
[1,] 1.000000e+00 2.748453e-17 -2.787755e-17 -8.023096e-17
[2,] 1.626303e-19 1.000000e+00 -4.960225e-18 6.977925e-16
[3,] 2.135878e-17 -4.629543e-17 1.000000e+00 6.201636e-17
[4,] 1.866183e-17 1.563962e-17 1.183813e-17 1.000000e+00
9 鐭╅樀鐨勭壒寰佸€间笌鐗瑰緛鍚戦噺
鐭╅樀A鐨勮氨鍒嗚В涓篈=UΛU',鍏朵腑Λ鏄敱A鐨勭壒寰佸€肩粍鎴愮殑瀵硅鐭╅樀锛孶鐨勫垪涓篈鐨勭壒寰佸€煎搴旂殑鐗瑰緛鍚戦噺锛屽湪R涓彲浠ョ敤鍑芥暟eigen()鍑芥暟寰楀埌U鍜?Lambda;锛?br />> args(eigen)
function (x, symmetric, only.values = FALSE, EISPACK = FALSE)
鍏朵腑锛歺涓虹煩闃碉紝symmetric椤规寚瀹氱煩闃祒鏄惁涓哄绉扮煩闃碉紝鑻ヤ笉鎸囧畾锛岀郴缁熷皢鑷姩妫€娴媥鏄惁涓哄绉扮煩闃点€備緥濡傦細
> A=diag(4)+1
> A
[,1] [,2] [,3] [,4]
[1,] 2 1 1 1
[2,] 1 2 1 1
[3,] 1 1 2 1
[4,] 1 1 1 2
> A.eigen=eigen(A,symmetric=T)
> A.eigen
$values
[1] 5 1 1 1

$vectors
[,1] [,2] [,3] [,4]
[1,] 0.5 0.8660254 0.000000e+00 0.0000000
[2,] 0.5 -0.2886751 -6.408849e-17 0.8164966
[3,] 0.5 -0.2886751 -7.071068e-01 -0.4082483
[4,] 0.5 -0.2886751 7.071068e-01 -0.4082483

> A.eigen$vectors%*%diag(A.eigen$values)%*%t(A.eigen$vectors)
[,1] [,2] [,3] [,4]
[1,] 2 1 1 1
[2,] 1 2 1 1
[3,] 1 1 2 1
[4,] 1 1 1 2
> t(A.eigen$vectors)%*%A.eigen$vectors
[,1] [,2] [,3] [,4]
[1,] 1.000000e+00 4.377466e-17 1.626303e-17 -5.095750e-18
[2,] 4.377466e-17 1.000000e+00 -1.694066e-18 6.349359e-18
[3,] 1.626303e-17 -1.694066e-18 1.000000e+00 -1.088268e-16
[4,] -5.095750e-18 6.349359e-18 -1.088268e-16 1.000000e+00
10 鐭╅樀鐨凜holeskey鍒嗚В
瀵逛簬姝ｅ畾鐭╅樀A锛屽彲瀵瑰叾杩涜Choleskey鍒嗚В锛屽嵆锛欰=P'P锛屽叾涓璓涓轰笂涓夎鐭╅樀锛屽湪R涓彲浠ョ敤鍑芥暟chol()杩涜Choleskey鍒嗚В锛屼緥濡傦細
> A
[,1] [,2] [,3] [,4]
[1,] 2 1 1 1
[2,] 1 2 1 1
[3,] 1 1 2 1
[4,] 1 1 1 2
> chol(A)
[,1] [,2] [,3] [,4]
[1,] 1.414214 0.7071068 0.7071068 0.7071068
[2,] 0.000000 1.2247449 0.4082483 0.4082483
[3,] 0.000000 0.0000000 1.1547005 0.2886751
[4,] 0.000000 0.0000000 0.0000000 1.1180340
> t(chol(A))%*%chol(A)
[,1] [,2] [,3] [,4]
[1,] 2 1 1 1
[2,] 1 2 1 1
[3,] 1 1 2 1
[4,] 1 1 1 2
> crossprod(chol(A),chol(A))
[,1] [,2] [,3] [,4]
[1,] 2 1 1 1
[2,] 1 2 1 1
[3,] 1 1 2 1
[4,] 1 1 1 2
鑻ョ煩闃典负瀵圭О姝ｅ畾鐭╅樀锛屽彲浠ュ埄鐢–holeskey鍒嗚В姹傝鍒楀紡鐨勫€硷紝濡傦細
> prod(diag(chol(A))^2)
[1] 5
> det(A)
[1] 5
鑻ョ煩闃典负瀵圭О姝ｅ畾鐭╅樀锛屽彲浠ュ埄鐢–holeskey鍒嗚В姹傜煩闃电殑閫嗭紝杩欐椂鐢ㄥ嚱鏁?font face="Courier New, Courier, Monospace">chol2inv()锛?/font>杩欑鐢ㄦ硶鏇存湁鏁堛€傚锛?br />> chol2inv(chol(A))
[,1] [,2] [,3] [,4]
[1,] 0.8 -0.2 -0.2 -0.2
[2,] -0.2 0.8 -0.2 -0.2
[3,] -0.2 -0.2 0.8 -0.2
[4,] -0.2 -0.2 -0.2 0.8
> solve(A)
[,1] [,2] [,3] [,4]
[1,] 0.8 -0.2 -0.2 -0.2
[2,] -0.2 0.8 -0.2 -0.2
[3,] -0.2 -0.2 0.8 -0.2
[4,] -0.2 -0.2 -0.2 0.8
11 鐭╅樀濂囧紓鍊煎垎瑙?/strong>
A涓簃×n鐭╅樀锛?font face="Courier New, Courier, Monospace">rank(A)= r, 鍙互鍒嗚В涓猴細A=UDV',鍏朵腑U'U=V'V=I銆傚湪R涓彲浠ョ敤鍑芥暟scd()杩涜濂囧紓鍊煎垎瑙ｏ紝渚嬪锛?br />> A=matrix(1:18,3,6)
> A
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 4 7 10 13 16
[2,] 2 5 8 11 14 17
[3,] 3 6 9 12 15 18
> svd(A)
$d
[1] 4.589453e+01 1.640705e+00 3.627301e-16
$u
[,1] [,2] [,3]
[1,] -0.5290354 0.74394551 0.4082483
[2,] -0.5760715 0.03840487 -0.8164966
[3,] -0.6231077 -0.66713577 0.4082483
$v
[,1] [,2] [,3]
[1,] -0.07736219 -0.7196003 -0.18918124
[2,] -0.19033085 -0.5089325 0.42405898
[3,] -0.30329950 -0.2982646 -0.45330031
[4,] -0.41626816 -0.0875968 -0.01637004
[5,] -0.52923682 0.1230711 0.64231130
[6,] -0.64220548 0.3337389 -0.40751869
> A.svd=svd(A)
> A.svd$u%*%diag(A.svd$d)%*%t(A.svd$v)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 4 7 10 13 16
[2,] 2 5 8 11 14 17
[3,] 3 6 9 12 15 18
> t(A.svd$u)%*%A.svd$u
[,1] [,2] [,3]
[1,] 1.000000e+00 -1.169312e-16 -3.016793e-17
[2,] -1.169312e-16 1.000000e+00 -3.678156e-17
[3,] -3.016793e-17 -3.678156e-17 1.000000e+00
> t(A.svd$v)%*%A.svd$v
[,1] [,2] [,3]
[1,] 1.000000e+00 8.248068e-17 -3.903128e-18
[2,] 8.248068e-17 1.000000e+00 -2.103352e-17
[3,] -3.903128e-18 -2.103352e-17 1.000000e+00
12 鐭╅樀QR鍒嗚В
A涓簃×n鐭╅樀鍙互杩涜QR鍒嗚В锛孉=QR锛屽叾涓細Q'Q锛滻锛屽湪R涓彲浠ョ敤鍑芥暟qr()杩涜QR鍒嗚В锛屼緥濡傦細
> A=matrix(1:16,4,4)
> qr(A)
$qr
[,1] [,2] [,3] [,4]
[1,] -5.4772256 -12.7801930 -2.008316e+01 -2.738613e+01
[2,] 0.3651484 -3.2659863 -6.531973e+00 -9.797959e+00
[3,] 0.5477226 -0.3781696 2.641083e-15 2.056562e-15
[4,] 0.7302967 -0.9124744 8.583032e-01 -2.111449e-16

$rank
[1] 2

$qraux
[1] 1.182574e+00 1.156135e+00 1.513143e+00 2.111449e-16

$pivot
[1] 1 2 3 4

attr(,"class")
[1] "qr"
rank椤硅繑鍥炵煩闃电殑绉╋紝qr椤瑰寘鍚簡鐭╅樀Q鍜孯鐨勪俊鎭紝瑕佸緱鍒扮煩闃礠鍜孯锛屽彲浠ョ敤鍑芥暟qr.Q()鍜?font face="Courier New, Courier, Monospace">qr.R()浣滅敤qr()鐨勮繑鍥炵粨鏋滐紝渚嬪锛?br />> qr.R(qr(A))
[,1] [,2] [,3] [,4]
[1,] -5.477226 -12.780193 -2.008316e+01 -2.738613e+01
[2,] 0.000000 -3.265986 -6.531973e+00 -9.797959e+00
[3,] 0.000000 0.000000 2.641083e-15 2.056562e-15
[4,] 0.000000 0.000000 0.000000e+00 -2.111449e-16
> qr.Q(qr(A))
[,1] [,2] [,3] [,4]
[1,] -0.1825742 -8.164966e-01 -0.4000874 -0.37407225
[2,] -0.3651484 -4.082483e-01 0.2546329 0.79697056
[3,] -0.5477226 -8.131516e-19 0.6909965 -0.47172438
[4,] -0.7302967 4.082483e-01 -0.5455419 0.04882607
> qr.Q(qr(A))%*%qr.R(qr(A))
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
> t(qr.Q(qr(A)))%*%qr.Q(qr(A))
[,1] [,2] [,3] [,4]
[1,] 1.000000e+00 -1.457168e-16 -6.760001e-17 -7.659550e-17
[2,] -1.457168e-16 1.000000e+00 -4.269046e-17 7.011739e-17
[3,] -6.760001e-17 -4.269046e-17 1.000000e+00 -1.596437e-16
[4,] -7.659550e-17 7.011739e-17 -1.596437e-16 1.000000e+00
> qr.X(qr(A))
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
13 鐭╅樀骞夸箟閫?Moore-Penrose)
n×m鐭╅樀A+绉颁负m×n鐭╅樀A鐨凪oore-Penrose閫嗭紝濡傛灉瀹冩弧瓒充笅鍒楁潯浠讹細
鈶? A A+A=A锛涒憽A+A A+= A+锛涒憿(A A+)H=A A+锛涒懀(A+A)H= A+A
鍦≧鐨凪ASS鍖呬腑鐨勫嚱鏁?font face="Courier New, Courier, Monospace">ginv()鍙绠楃煩闃礎鐨凪oore-Penrose閫嗭紝渚嬪锛?br />library(“MASS”)
> A
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
> ginv(A)
[,1] [,2] [,3] [,4]
[1,] -0.285 -0.1075 0.07 0.2475
[2,] -0.145 -0.0525 0.04 0.1325
[3,] -0.005 0.0025 0.01 0.0175
[4,] 0.135 0.0575 -0.02 -0.0975
楠岃瘉鎬ц川1锛?br />> A%*%ginv(A)%*%A
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
楠岃瘉鎬ц川2锛?br />> ginv(A)%*%A%*%ginv(A)
[,1] [,2] [,3] [,4]
[1,] -0.285 -0.1075 0.07 0.2475
[2,] -0.145 -0.0525 0.04 0.1325
[3,] -0.005 0.0025 0.01 0.0175
[4,] 0.135 0.0575 -0.02 -0.0975
楠岃瘉鎬ц川3:
> t(A%*%ginv(A))
[,1] [,2] [,3] [,4]
[1,] 0.7 0.4 0.1 -0.2
[2,] 0.4 0.3 0.2 0.1
[3,] 0.1 0.2 0.3 0.4
[4,] -0.2 0.1 0.4 0.7
> A%*%ginv(A)
[,1] [,2] [,3] [,4]
[1,] 0.7 0.4 0.1 -0.2
[2,] 0.4 0.3 0.2 0.1
[3,] 0.1 0.2 0.3 0.4
[4,] -0.2 0.1 0.4 0.7
楠岃瘉鎬ц川4:
> t(ginv(A)%*%A)
[,1] [,2] [,3] [,4]
[1,] 0.7 0.4 0.1 -0.2
[2,] 0.4 0.3 0.2 0.1
[3,] 0.1 0.2 0.3 0.4
[4,] -0.2 0.1 0.4 0.7
> ginv(A)%*%A
[,1] [,2] [,3] [,4]
[1,] 0.7 0.4 0.1 -0.2
[2,] 0.4 0.3 0.2 0.1
[3,] 0.1 0.2 0.3 0.4
[4,] -0.2 0.1 0.4 0.7
14 鐭╅樀Kronecker绉?/strong>
n×m鐭╅樀A涓巋×k鐭╅樀B鐨刱ronecker绉负涓€涓猲h×mk缁寸煩闃碉紝
鍦≧涓璳ronecker绉彲浠ョ敤鍑芥暟kronecker()鏉ヨ绠楋紝渚嬪锛?br />> A=matrix(1:4,2,2)
> B=matrix(rep(1,4),2,2)
> A
[,1] [,2]
[1,] 1 3
[2,] 2 4
> B
[,1] [,2]
[1,] 1 1
[2,] 1 1
> kronecker(A,B)
[,1] [,2] [,3] [,4]
[1,] 1 1 3 3
[2,] 1 1 3 3
[3,] 2 2 4 4
[4,] 2 2 4 4
15 鐭╅樀鐨勭淮鏁?/strong>
鍦≧涓緢瀹规槗寰楀埌涓€涓煩闃电殑缁存暟锛屽嚱鏁?font face="Courier New, Courier, Monospace">dim()灏嗚繑鍥炰竴涓煩闃电殑缁存暟锛?font face="Courier New, Courier, Monospace">nrow()杩斿洖琛屾暟锛?font face="Courier New, Courier, Monospace">ncol()杩斿洖鍒楁暟锛屼緥濡傦細
> A=matrix(1:12,3,4)
> A
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> nrow(A)
[1] 3
> ncol(A)
[1] 4
16 鐭╅樀鐨勮鍜屻€佸垪鍜屻€佽骞冲潎涓庡垪骞冲潎
鍦≧涓緢瀹规槗姹傚緱涓€涓煩闃电殑鍚勮鐨勫拰銆佸钩鍧囨暟涓庡垪鐨勫拰銆佸钩鍧囨暟锛屼緥濡傦細
> A
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> rowSums(A)
[1] 22 26 30
> rowMeans(A)
[1] 5.5 6.5 7.5
> colSums(A)
[1] 6 15 24 33
> colMeans(A)
[1] 2 5 8 11
涓婅堪鍏充簬鐭╅樀琛屽拰鍒楃殑鎿嶄綔锛岃繕鍙互浣跨敤apply()鍑芥暟瀹炵幇銆?br />> args(apply)
function (X, MARGIN, FUN, ...)
鍏朵腑锛歺涓虹煩闃碉紝MARGIN鐢ㄦ潵鎸囧畾鏄琛岃繍绠楄繕鏄鍒楄繍绠楋紝MARGIN锛?琛ㄧず瀵硅杩愮畻锛?font face="Courier New, Courier, Monospace">MARGIN锛?琛ㄧず瀵瑰垪杩愮畻锛?font face="Courier New, Courier, Monospace">FUN鐢ㄦ潵鎸囧畾杩愮畻鍑芥暟, ...鐢ㄦ潵缁欏畾FUN涓渶瑕佺殑鍏跺畠鐨勫弬鏁帮紝渚嬪锛?br />> apply(A,1,sum)
[1] 22 26 30
> apply(A,1,mean)
[1] 5.5 6.5 7.5
> apply(A,2,sum)
[1] 6 15 24 33
> apply(A,2,mean)
[1] 2 5 8 11
apply()鍑芥暟鍔熻兘寮哄ぇ锛屾垜浠彲浠ュ鐭╅樀鐨勮鎴栬€呭垪杩涜鍏跺畠杩愮畻锛屼緥濡傦細
璁＄畻姣忎竴鍒楃殑鏂瑰樊
> A=matrix(rnorm(100),20,5)
> apply(A,2,var)
[1] 0.4641787 1.4331070 0.3186012 1.3042711 0.5238485
> apply(A,2,function(x,a)x*a,a=2)
[,1] [,2] [,3] [,4]
[1,] 2 8 14 20
[2,] 4 10 16 22
[3,] 6 12 18 24
娉ㄦ剰锛?font face="Courier New, Courier, Monospace">apply(A,2,function(x,a)x*a,a=2)涓?font face="Courier New, Courier, Monospace">A*2鏁堟灉鐩稿悓锛屾澶勬棬鍦ㄨ鏄庡浣曞簲鐢?font face="Courier New, Courier, Monospace">alpply鍑芥暟銆?/font>
17 鐭╅樀X'X鐨勯€?/strong>
鍦ㄧ粺璁¤绠椾腑锛屾垜浠父甯搁渶瑕佽绠楄繖鏍风煩闃电殑閫嗭紝濡侽LS浼拌涓眰绯绘暟鐭╅樀銆俁涓殑鍖?ldquo;strucchange”鎻愪緵浜嗘湁鏁堢殑璁＄畻鏂规硶銆?br /> > args(solveCrossprod)
function (X, method = c("qr", "chol", "solve"))
鍏朵腑锛?font face="Courier New, Courier, Monospace">method鎸囧畾姹傞€嗘柟娉曪紝閫夌敤“qr”鏁堢巼鏈€楂橈紝閫夌敤“chol”绮惧害鏈€楂橈紝閫夌敤“slove”涓巗love(crossprod(x,x))鏁堟灉鐩稿悓锛屼緥濡傦細
> A=matrix(rnorm(16),4,4)
> solveCrossprod(A,method="qr")
[,1] [,2] [,3] [,4]
[1,] 0.6132102 -0.1543924 -0.2900796 0.2054730
[2,] -0.1543924 0.4779277 0.1859490 -0.2097302
[3,] -0.2900796 0.1859490 0.6931232 -0.3162961
[4,] 0.2054730 -0.2097302 -0.3162961 0.3447627
> solveCrossprod(A,method="chol")
[,1] [,2] [,3] [,4]
[1,] 0.6132102 -0.1543924 -0.2900796 0.2054730
[2,] -0.1543924 0.4779277 0.1859490 -0.2097302
[3,] -0.2900796 0.1859490 0.6931232 -0.3162961
[4,] 0.2054730 -0.2097302 -0.3162961 0.3447627
> solveCrossprod(A,method="solve")
[,1] [,2] [,3] [,4]
[1,] 0.6132102 -0.1543924 -0.2900796 0.2054730
[2,] -0.1543924 0.4779277 0.1859490 -0.2097302
[3,] -0.2900796 0.1859490 0.6931232 -0.3162961
[4,] 0.2054730 -0.2097302 -0.3162961 0.3447627
> solve(crossprod(A,A))
[,1] [,2] [,3] [,4]
[1,] 0.6132102 -0.1543924 -0.2900796 0.2054730
[2,] -0.1543924 0.4779277 0.1859490 -0.2097302
[3,] -0.2900796 0.1859490 0.6931232 -0.3162961
[4,] 0.2054730 -0.2097302 -0.3162961 0.3447627
18 鍙栫煩闃电殑涓娿€佷笅涓夎閮ㄥ垎
鍦≧涓紝鎴戜滑鍙互寰堟柟渚跨殑鍙栧埌涓€涓煩闃电殑涓娿€佷笅涓夎閮ㄥ垎鐨勫厓绱狅紝鍑芥暟lower.tri()鍜屽嚱鏁?font face="Courier New, Courier, Monospace">upper.tri()鎻愪緵浜嗘湁鏁堢殑鏂规硶銆?br /> > args(lower.tri)
function (x, diag = FALSE)
鍑芥暟灏嗚繑鍥炰竴涓€昏緫鍊肩煩闃碉紝鍏朵腑涓嬩笁瑙掗儴鍒嗕负鐪燂紝涓婁笁瑙掗儴鍒嗕负鍋囷紝閫夐」diag涓虹湡鏃跺寘鍚瑙掑厓绱狅紝涓哄亣鏃朵笉鍖呭惈瀵硅鍏冪礌銆?font face="Courier New, Courier, Monospace">upper.tri()鐨勬晥鏋滀笌涔嬪瓚鐒剁浉鍙嶃€備緥濡傦細
> A
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
> lower.tri(A)
[,1] [,2] [,3] [,4]
[1,] FALSE FALSE FALSE FALSE
[2,] TRUE FALSE FALSE FALSE
[3,] TRUE TRUE FALSE FALSE
[4,] TRUE TRUE TRUE FALSE
> lower.tri(A,diag=T)
[,1] [,2] [,3] [,4]
[1,] TRUE FALSE FALSE FALSE
[2,] TRUE TRUE FALSE FALSE
[3,] TRUE TRUE TRUE FALSE
[4,] TRUE TRUE TRUE TRUE
> upper.tri(A)
[,1] [,2] [,3] [,4]
[1,] FALSE TRUE TRUE TRUE
[2,] FALSE FALSE TRUE TRUE
[3,] FALSE FALSE FALSE TRUE
[4,] FALSE FALSE FALSE FALSE
> upper.tri(A,diag=T)
[,1] [,2] [,3] [,4]
[1,] TRUE TRUE TRUE TRUE
[2,] FALSE TRUE TRUE TRUE
[3,] FALSE FALSE TRUE TRUE
[4,] FALSE FALSE FALSE TRUE
> A[lower.tri(A)]=0
> A
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 0 6 10 14
[3,] 0 0 11 15
[4,] 0 0 0 16
> A[upper.tri(A)]=0
> A
[,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 2 6 0 0
[3,] 3 7 11 0
[4,] 4 8 12 16
19 backsolve&fowardsolve鍑芥暟
杩欎袱涓嚱鏁扮敤浜庤В鐗规畩绾挎€ф柟绋嬬粍锛屽叾鐗规畩涔嬪鍦ㄤ簬绯绘暟鐭╅樀涓轰笂鎴栦笅涓夎銆?br />> args(backsolve)
function (r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE)
> args(forwardsolve)
function (l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE)
鍏朵腑锛歳鎴栬€卨涓簄×n缁翠笁瑙掔煩闃碉紝x涓簄×1缁村悜閲忥紝瀵圭粰瀹氫笉鍚岀殑upper.tri鍜?font face="Courier New, Courier, Monospace">transpose鐨勫€硷紝鏂圭▼鐨勫舰寮忎笉鍚?br />瀵逛簬鍑芥暟backsolve()鑰岃█锛?br />渚嬪锛?br /> > A=matrix(1:9,3,3)
> A
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
> x=c(1,2,3)
> x
[1] 1 2 3
> B=A
> B[upper.tri(B)]=0
> B
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 2 5 0
[3,] 3 6 9
> C=A
> C[lower.tri(C)]=0
> C
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 0 5 8
[3,] 0 0 9
> backsolve(A,x,upper.tri=T,transpose=T)
[1] 1.00000000 -0.40000000 -0.08888889
> solve(t(C),x)
[1] 1.00000000 -0.40000000 -0.08888889
> backsolve(A,x,upper.tri=T,transpose=F)
[1] -0.8000000 -0.1333333 0.3333333
> solve(C,x)
[1] -0.8000000 -0.1333333 0.3333333
> backsolve(A,x,upper.tri=F,transpose=T)
[1] 1.111307e-17 2.220446e-17 3.333333e-01
> solve(t(B),x)
[1] 1.110223e-17 2.220446e-17 3.333333e-01
> backsolve(A,x,upper.tri=F,transpose=F)
[1] 1 0 0
> solve(B,x)
[1] 1.000000e+00 -1.540744e-33 -1.850372e-17
瀵逛簬鍑芥暟forwardsolve()鑰岃█锛?br />渚嬪锛?br /> > A
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
> B
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 2 5 0
[3,] 3 6 9
> C
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 0 5 8
[3,] 0 0 9
> x
[1] 1 2 3
> forwardsolve(A,x,upper.tri=T,transpose=T)
[1] 1.00000000 -0.40000000 -0.08888889
> solve(t(C),x)
[1] 1.00000000 -0.40000000 -0.08888889
> forwardsolve(A,x,upper.tri=T,transpose=F)
[1] -0.8000000 -0.1333333 0.3333333
> solve(C,x)
[1] -0.8000000 -0.1333333 0.3333333
> forwardsolve(A,x,upper.tri=F,transpose=T)
[1] 1.111307e-17 2.220446e-17 3.333333e-01
> solve(t(B),x)
[1] 1.110223e-17 2.220446e-17 3.333333e-01
> forwardsolve(A,x,upper.tri=F,transpose=F)
[1] 1 0 0
> solve(B,x)
[1] 1.000000e+00 -1.540744e-33 -1.850372e-17
20 row()涓巆ol()鍑芥暟
鍦≧涓畾涔変簡鐨勮繖涓や釜鍑芥暟鐢ㄤ簬鍙栫煩闃靛厓绱犵殑琛屾垨鍒椾笅鏍囩煩闃碉紝渚嬪鐭╅樀A={aij}m×n锛?br />row()鍑芥暟灏嗚繑鍥炰竴涓笌鐭╅樀A鏈夌浉鍚岀淮鏁扮殑鐭╅樀锛岃鐭╅樀鐨勭i琛岀j鍒楀厓绱犱负i锛屽嚱鏁癱ol()绫讳技銆備緥濡傦細
> x=matrix(1:12,3,4)
> row(x)
[,1] [,2] [,3] [,4]
[1,] 1 1 1 1
[2,] 2 2 2 2
[3,] 3 3 3 3
> col(x)
[,1] [,2] [,3] [,4]
[1,] 1 2 3 4
[2,] 1 2 3 4
[3,] 1 2 3 4
杩欎袱涓嚱鏁板悓鏍峰彲浠ョ敤浜庡彇涓€涓煩闃电殑涓婁笅涓夎鐭╅樀锛屼緥濡傦細
> x
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> x[row(x)<col(x)]=0
> x
[,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 2 5 0 0
[3,] 3 6 9 0
> x=matrix(1:12,3,4)
> x[row(x)>col(x)]=0
> x
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 0 5 8 11
[3,] 0 0 9 12
21 琛屽垪寮忕殑鍊?/strong>
鍦≧涓紝鍑芥暟det(x)灏嗚绠楁柟闃祒鐨勮鍒楀紡鐨勫€硷紝渚嬪锛?br />> x=matrix(rnorm(16),4,4)
> x
[,1] [,2] [,3] [,4]
[1,] -1.0736375 0.2809563 -1.5796854 0.51810378
[2,] -1.6229898 -0.4175977 1.2038194 -0.06394986
[3,] -0.3989073 -0.8368334 -0.6374909 -0.23657088
[4,] 1.9413061 0.8338065 -1.5877162 -1.30568465
> det(x)
[1] 5.717667
22鍚戦噺鍖栫畻瀛?/strong>
鍦≧涓彲浠ュ緢瀹规槗鐨勫疄鐜板悜閲忓寲绠楀瓙锛屼緥濡傦細

vec<-function (x){
t(t(as.vector(x)))
}
vech<-function (x){
t(x[lower.tri(x,diag=T)])
}
> x=matrix(1:12,3,4)
> x
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> vec(x)
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
[5,] 5
[6,] 6
[7,] 7
[8,] 8
[9,] 9
[10,] 10
[11,] 11
[12,] 12
> vech(x)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 2 3 5 6 9
23 鏃堕棿搴忓垪鐨勬粸鍚庡€?/strong>
鍦ㄦ椂闂村簭鍒楀垎鏋愪腑锛屾垜浠父甯歌鐢ㄥ埌涓€涓簭鍒楃殑婊炲悗搴忓垪锛孯涓殑鍖?ldquo;fMultivar”涓殑鍑芥暟tslag()鎻愪緵浜嗚繖涓姛鑳姐€?br /> > args(tslag)
function (x, k = 1, trim = FALSE)
鍏朵腑锛歺涓轰竴涓悜閲忥紝k鎸囧畾婊炲悗闃舵暟锛屽彲浠ユ槸涓€涓嚜鐒舵暟鍒楋紝鑻rim涓哄亣锛屽垯杩斿洖搴忓垪涓庡師搴忓垪闀垮害鐩稿悓锛屼絾鍚湁NA鍊硷紱鑻rim椤逛负鐪燂紝鍒欒繑鍥炲簭鍒椾腑涓嶅惈鏈塏A鍊硷紝渚嬪锛?br />> x=1:20
> tslag(x,1:4,trim=F)
[,1] [,2] [,3] [,4]
[1,] NA NA NA NA
[2,] 1 NA NA NA
[3,] 2 1 NA NA
[4,] 3 2 1 NA
[5,] 4 3 2 1
[6,] 5 4 3 2
[7,] 6 5 4 3
[8,] 7 6 5 4
[9,] 8 7 6 5
[10,] 9 8 7 6
[11,] 10 9 8 7
[12,] 11 10 9 8
[13,] 12 11 10 9
[14,] 13 12 11 10
[15,] 14 13 12 11
[16,] 15 14 13 12
[17,] 16 15 14 13
[18,] 17 16 15 14
[19,] 18 17 16 15
[20,] 19 18 17 16
> tslag(x,1:4,trim=T)
[,1] [,2] [,3] [,4]
[1,] 4 3 2 1
[2,] 5 4 3 2
[3,] 6 5 4 3
[4,] 7 6 5 4
[5,] 8 7 6 5
[6,] 9 8 7 6
[7,] 10 9 8 7
[8,] 11 10 9 8
[9,] 12 11 10 9
[10,] 13 12 11 10
[11,] 14 13 12 11
[12,] 15 14 13 12
[13,] 16 15 14 13
[14,] 17 16 15 14
[15,] 18 17 16 15
[16,] 19 18 17 16

鏈枃寮曠敤鍦板潃锛?

褰撳墠鎺ㄨ崘鏁帮細0

鍙戣〃璇勮锛?/td>

鐢ㄦ埛鍚嶏細

蹇呭～

鐢靛瓙閭锛?/td>

楠岃瘉鐮?/span>锛?input name="Right_content1$txtvalidate" type="text" id="Right_content1_txtvalidate" onfocus="javascript:document.getElementById('Image1').src='blogCode1.aspx?f=13&'+Math.random();document.getElementById('Image1').style.display=''" />

郑重声明：资讯【科学网-王娟的博客-[转载]R语言矩阵运算】由发布，版权归原作者及其所在单位，其原创性以及文中陈述文字和内容未经(企业库qiyeku.com)证实，请读者仅作参考，并请自行核实相关内容。若本文有侵犯到您的版权，请你提供相关证明及申请并与我们联系（qiyeku # qq.com）或【在线投诉】，我们审核后将会尽快处理。

—— 相关资讯 ——